EPRI Transmission Line
Reference Book—Wind-Induced
Conductor Motion
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Foreword
One of the major challenges faced by electric utilities
and transmission companies today is identifying and
preventing damage to overhead lines caused by windinduced conductor motion. Probably no other large
structure has as much of its mass in highly flexible form
and so continuously exposed to the forces of the wind,
as does the modern transmission line. This makes the
line susceptible to the occurrence of sustained cyclic
conductor motions, which can take the form of vibration, galloping, or other types of movement. Because
conductors are supported and supplemented by thousands of pieces of hardware, numerous opportunities
for damage arise during these motions.
The damage is insidious, however, because it is typically
very difficult to perceive at any given moment and can
often only be truly identified when the conductor is
taken out of service and broken strands are discovered
under the clamp. Given the budget and manpower limits in today’s utilities, there is a growing tendency for
vibration-caused problems to go undiagnosed, even
when they result in outages. Crews are dispatched to
the outage to repair or replace the failed line component on a “like-for-like” basis, and the cause of the line
break may not be investigated.
It is important, however, to understand the causes and
possible solutions to problems arising from vibration
and other conductor motions because they can sometimes represent a broader, more systemic issue than initially indicated by a small number of outages. In the
late 1970s, EPRI sponsored development of a state-ofthe-art reference guide to conductor motion. The book,
written by experts in the field, covered three primary
types of motion: aeolian vibration, conductor galloping, and wake-induced oscillation. For each motion,
the book contained detailed information on causes,
mechanisms, incidence, factors influencing motion,
resulting damage, and protection methods available at
that time. The resulting book was entitled Transmission
Line Reference Book: Wind-Induced Conductor Motion,
and was one of a series of EPRI overhead reference
vii
books. Published in 1979 with a bright orange cover, it
quickly became known in the industry as the “Orange
Book.”
The book enabled several generations of overhead line
designers to anticipate the circumstances in which
cyclic conductor motion might be expected, become
familiar with protection methods, and refine their inhouse design practices. More than twenty-five years
since its publication, the Orange Book is still the industry standard, and is still commonly used by electric utilities to diagnose and solve conductor motion issues.
However, over the years, considerable further progress
has been made to understand the mechanisms of
motion, design new mitigation methods, and analyze
the behavior of new conductor technology, including
bundled conductors and fiber optic cables.
As a result, EPRI sponsored an updating of the Orange
Book to include the new information. The objective of
updating the book is to provide transmission and distribution line designers with the best practical tool to
design overhead lines effectively in order to minimize
damages to the lines from wind-induced conductor
motion and, to analyze existing lines for improvements
of their performance related to such motion.
The tasks of the revision involved:
• Update existing information in the Orange Book to
reflect the state-of-the art knowledge in the field of
wind-induced conductor motion.
• Add new information to the book to cover new topics, interests, and technology that have been developed since the book was last published.
• Acquire global utility experience in conductor
motion and share it with the readers.
• Provide examples to facilitate the understanding of
wind-induced conductor motion and the application
of the knowledge to practical uses.
Foreword
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
• Provide an index, applets, and other suitable electronic media to facilitate the use of the book.
• The project of revising the Orange Book was started
in 2003. I was assigned the overall responsibility for
the project. To undertake such a monumental task, I
immediately formed an Editorial Committee to
assist me in guiding the revision and ensuring the
high quality of the final product. Consequently, I
enlisted technical assistance from Dr. Dave Havard
of Toronto, Canada who has extensive experience
with conductor motion and, editorial assistance
from Mr. Jonas Weisel of California, who was
involved in the publication of the third edition of the
EPRI Transmission Line Reference Book—200 kV
and Above (the so-called Red Book). In the following
year, we were very fortunate to have Mr. Chuck
Rawlins of New York joining our Editorial Committee. Chuck was one of the key authors of the original
Orange Book and is well respected in the field of
conductor motion.
The Editorial Committee first developed a strategy for
the revision of the book including an approach and
implementation plan that involved peer and user
reviews. The Committee then developed an initial revision plan for each chapter of the new edition. These
plans were captured in “skeleton outlines.” The outlines indicated the scope of information to be included
in each chapter, material from the previous edition that
was to be reduced or moved, new areas of information
to be added, possible examples and applets, and references. These outlines were intended to be initial positions, for the authors’ use and reference.
The Editorial Committee selected a suitable expert for
each of the chapters as the lead author, who would
receive assistance from co-authors. Assignments were
subsequently made as follows:
Chapter
Lead Author
Chapter 1, Introduction
Editorial
Committee
Giorgio Diana,
Italy
Louis Cloutier,
Canada
Jean-Louis Lilien,
Belgium
Claude Hardy,
Canada
Jeff Wang,
United States
Anand Goel,
Canada
Chapter 2, Aeolian Vibration
Chapter 3, Fatigue of
Overhead Conductors
Chapter 4, Galloping
Conductors
Chapter 5, Bundle Conductor
Oscillations
Chapter 6, Overhead Fiber
Optic Cables
Chapter 7, Other Motions
viii
Information on the lead author and co-authors for
each chapter is included at the front of that chapter.
Chapters 6 and 7 are new additions to the Orange
Book.
Chapter 6, Overhead Fiber Optic Cables, reflects the
growth of the use of fiber optic cables on overhead
transmission lines. It is intended to provide a reference
on the types of cable construction in use, and the hardware used to attach overhead fiber optic wires.
The chapter describes the aerodynamic problems that
can occur with these wires and the vibration control
devices available. Test procedures in use to qualify the
cables mechanically and optically and the hardware
used are presented. Field experience with the cables is
also described.
Chapter 7, Other Motions, covers transient dynamic
motions of overhead lines, which can be damaging to
overhead conductors, hardware, and structures. Some
of the topics were mentioned briefly in the original volume, but additional experience with several of these
phenomena provides new insights. A number of procedures to ameliorate the effects and defer extensive damage have been developed and are described in this
chapter. Analysis of some of the instabilities can be
used to improve design of lines to reduce the levels of
damage that can occur.
Work on the first draft of chapters was initiated in May
2005. The new volume was compiled in less than two
years. An electronic version of the revised edition is
first being published at the end of 2006. The intention
of the soft copy is to allow changes and improvements
to be made easily. Applets have not been developed.
They can be added to the soft copy whenever they are
available. A hard copy will be published in the future
when there is such a demand.
The new revision presents a state-of-art study of conductor fatigue, aeolian vibration, conductor galloping,
wake-induced oscillation, and other motions as well as
fiber optic cables. Overhead line designers will find this
state-of-the-art book a useful reference in the control
of conductor motions and will be able to understand
and recognize the pitfalls, shortcoming, and uncertainty of various control methods and devices as well as
knowledge gaps that require future research. A new
“Highlights” section is added to the end of each chapter. The Highlights capture the key points for that
chapter that an overhead line designer can put to practical use.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Foreword
It was a great pleasure and rewarding experience for me
to work with all the authors and the Editorial Committee members. I personally would like to thank them all,
especially the Editorial Committee members with
whom I worked closely together for the last three years.
They have shown enormous patience and tremendous
effort in guiding and editing the revision of the Orange
Book. Without their valuable contributions and dedication, the revision could not have been accomplished.
Editorial Committee
John K. Chan
John K. Chan
David Havard
Charles B. Rawlins
Jonas Weisel
Electric Power Research Institute
Palo Alto, California
USA
ix
Contents
x
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Contents
SYMBOLS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-1
Chapter 1
2.5
Introduction
1.1
OVERVIEW OF THE CONDUCTOR
MOTION PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1
1.2
THE BOOK: WIND-INDUCED CONDUCTOR MOTION. 1-2
2.6
Purpose and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
Organization and Use of the Book . . . . . . . . . . . . . . . . . 1-4
1.3
2.7
ASSESSMENT OF CONDUCTOR
VIBRATION SEVERITY . . . . . . . . . . . . . . . . . . . . . . . 2-113
General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-113
Analytical Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . 2-113
Outdoor Test Spans . . . . . . . . . . . . . . . . . . . . . . . . . . 2-113
Indoor Test Spans . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-114
Actual Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-115
Aeolian Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-116
Vibration Assessments . . . . . . . . . . . . . . . . . . . . . . . . 2-116
Vibration Measurements on Actual Lines . . . . . . . . . . 2-118
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8
Chapter 2
IMPACT OF VIBRATION UPON LINE DESIGN . . . . 2-103
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-103
Historical Background. . . . . . . . . . . . . . . . . . . . . . . . . 2-103
Single Unprotected Conductors . . . . . . . . . . . . . . . . . 2-106
Damped Single Conductors . . . . . . . . . . . . . . . . . . . . 2-109
Bundled Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . 2-111
Effect of Tension on Line Costs . . . . . . . . . . . . . . . . . 2-111
INTRODUCTION TO TYPES OF
CONDUCTOR MOTION . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
Aeolian Vibration and Fatigue . . . . . . . . . . . . . . . . . . . . . 1-5
Conductor Galloping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Wake-Induced Oscillation . . . . . . . . . . . . . . . . . . . . . . . . 1-6
Overhead Fiber Optic Cables . . . . . . . . . . . . . . . . . . . . . 1-7
Other Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7
Summary of Types of Conductor Motion . . . . . . . . . . . . . 1-8
SYSTEM RESPONSE . . . . . . . . . . . . . . . . . . . . . . . . . 2-65
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-65
Mechanical Behavior of Single Conductors . . . . . . . . . 2-68
Mechanical Behavior of Single Conductors
Plus Dampers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-78
Mechanical Behavior of Bundle Conductors
Equipped with Spacers and Dampers . . . . . . . . . 2-86
Aeolian Vibration
2.1
INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-3
2.2
EXCITATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-5
2.8
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-5
Vortex Shedding in the Case of a
Stationary Conductor . . . . . . . . . . . . . . . . . . . . . . .2-5
The Wind Power Input. . . . . . . . . . . . . . . . . . . . . . . . . .2-13
Conductors and Wind Exposure . . . . . . . . . . . . . . . . . .2-15
Appendix 2.1
Numerical Values of
Figure 2.2-15 . . . . . . . . . . . . . . . . . . . . . . . . 2-132
Appendix 2.2
Calculation of the Bending
Stiffness for a 795 kcmil Drake
ACSR Conductor . . . . . . . . . . . . . . . . . . . . . 2-133
Appendix 2.3
Conductor Self-Damping Data . . . . . . . . . . . 2-134
Appendix 2.4
Deam Method . . . . . . . . . . . . . . . . . . . . . . . . 2-144
Appendix 2.5
Characterization of the Elastic
and Damping Properties
of Spacer-Dampers . . . . . . . . . . . . . . . . . . . 2-145
Appendix 2.6
Natural Frequencies and
Modes of Vibration of the Cable Plus
Damper System . . . . . . . . . . . . . . . . . . . . . . 2.147
Appendix 2.7
Recommended Conductor Safe Design
Tension with Respect to Aeolian Vibration . . 2-149
2.3
CONDUCTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-17
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-17
Types and Basic Properties of Conductors . . . . . . . . . .2-17
Inner Conductor Mechanics . . . . . . . . . . . . . . . . . . . . 2- 21
Stress Distribution in the Conductor Wires . . . . . . . . . 2-26
Temperature and Creep Effects . . . . . . . . . . . . . . . . . .2-27
Conductor Self-Damping. . . . . . . . . . . . . . . . . . . . . . . .2-28
The Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2-34
2.4
DAMPING DEVICES. . . . . . . . . . . . . . . . . . . . . . . . . . .2-38
Stockbridge-type Dampers . . . . . . . . . . . . . . . . . . . . . .2-39
Other Damper Types . . . . . . . . . . . . . . . . . . . . . . . . . . .2-45
Testing of Vibration Dampers . . . . . . . . . . . . . . . . . . . .2-48
The Application of Dampers . . . . . . . . . . . . . . . . . . . . .2-55
Other Protection Methods . . . . . . . . . . . . . . . . . . . . . . .2-58
Spacers and Spacer-dampers. . . . . . . . . . . . . . . . . . . .2-60
xi
HIGHLIGHTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-130
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-150
Contents
Chapter 3
3.1
3.2
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Fatigue of Overhead Conductors
Interphase Spacers . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-80
Aerodynamic Control Devices . . . . . . . . . . . . . . . . . . . 4-85
Torsional Control Devices . . . . . . . . . . . . . . . . . . . . . . . 4-88
Bundle Modification . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-96
Summary of Galloping Control Devices . . . . . . . . . . . . 4-98
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-3
FATIGUE ENDURANCE OF CONDUCTORS . . . . . . . .3-6
Conductor Fatigue Mechanisms . . . . . . . . . . . . . . . . . . .3-7
Calculation of Idealized Stress . . . . . . . . . . . . . . . . . . . .3-9
Comparison of Calculated with Measured Stress . . . . .3-12
Use of Conductor Fatigue Test Data . . . . . . . . . . . . . . .3-13
Fatigue Performance Relative to fymax. . . . . . . . . . . . . .3-14
Fatigue Performance Relative to Bending Amplitude . .3-23
Effects of Armor Rods . . . . . . . . . . . . . . . . . . . . . . . . . .3-29
Other Supporting Devices . . . . . . . . . . . . . . . . . . . . . . .3-33
4.6
HIGHLIGHTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-100
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-119
Appendix 4.1
Coordinate System Aerodynamic
Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . 4-102
Appendix 4.2
The Equations of Galloping . . . . . . . . . . . . . 4-102
3.3
HIGH-AMPLITUDE FATIGUE TESTS. . . . . . . . . . . . . .3-33
Appendix 4.3
Estimation of Unstable Conditions . . . . . . . . 4-105
3.4
SPACER AND SPACER-DAMPER CLAMPS. . . . . . . .3-37
Appendix 4.4
Tension Variations . . . . . . . . . . . . . . . . . . . . 4-109
3.5
SPECTRUM LOADING AND CUMULATIVE
DAMAGE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-40
Appendix 4.5
Galloping Amplitude Evaluation . . . . . . . . . . 4-112
Appendix 4.6
The Parameters of Galloping . . . . . . . . . . . . 4-115
3.6
TESTS AND INSPECTIONS . . . . . . . . . . . . . . . . . . . . .3-41
Appendix 4.7
Example of Vertical and Torsional Frequencies for
Single and Bundle Conductors in Single or MultiSpan Section . . . . . . . . . . . . . . . . . . . . . . . . 4-117
Appendix 4.8
CATV Cable Galloping . . . . . . . . . . . . . . . . . 4-118
Bundle Conductor Oscillations
Early Warnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-41
Measurement of Vibration Intensity. . . . . . . . . . . . . . . .3-41
Visual Inspections . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-42
Radiographic Inspections . . . . . . . . . . . . . . . . . . . . . . .3-43
Electro-magneto-acoustic Transducers (EMAT) . . . . . .3-44
Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-44
3.7
REMEDIAL MEASURES. . . . . . . . . . . . . . . . . . . . . . . .3-45
Chapter 5
3.8
HIGHLIGHTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3-45
5.1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3
5.2
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4
Appendix 3.1
Appendix 3.2
Laboratory Determination of Fatigue
Endurance Capability . . . . . . . . . . . . . . . . . . .3-46
Types of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4
Factors Influencing Oscillation . . . . . . . . . . . . . . . . . . . . 5-6
Damage Caused by Wake-Induced Oscillations. . . . . . 5-15
Protection Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-16
A Statistical Analysis of Fatigue Data . . . . . . .3-39
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3--51
5.3
Chapter 4
INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-3
4.2
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-4
Principal Characteristics of Galloping . . . . . . . . . . . . . . .4-4
Damage and Other Penalties . . . . . . . . . . . . . . . . . . . . .4-8
Causes of Galloping: The Forces in Action . . . . . . . . . .4-10
Causes of Galloping: How the Wind May Transfer its
Energy to Vertical Movement? . . . . . . . . . . . . . . .4-12
Causes of Galloping: Factors Influencing Galloping . . .4-15
Protection Methods: Overview . . . . . . . . . . . . . . . . . . .4-20
4.3
TESTING IN NATURAL WIND . . . . . . . . . . . . . . . . . . .4-48
Tests Using Artificial Ice . . . . . . . . . . . . . . . . . . . . . . . .4-49
Tests with Natural Ice . . . . . . . . . . . . . . . . . . . . . . . . . .4-54
Observer Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-58
4.5
GALLOPING PROTECTION METHODS . . . . . . . . . . .4-61
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-61
Ice Prevention, Melting, or Removal . . . . . . . . . . . . . . .4-64
Alternative Conductor Designs . . . . . . . . . . . . . . . . . . .4-71
Increased Clearances . . . . . . . . . . . . . . . . . . . . . . . . . .4-72
xii
5.4
TESTING IN NATURAL WINDS . . . . . . . . . . . . . . . . . . 5-36
Visual Inspections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-37
Deformation Gages . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-39
Vibration Recorders . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-40
Deflection Counters . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-40
Automatic Camera Systems . . . . . . . . . . . . . . . . . . . . 5-41
Dedicated Test Lines . . . . . . . . . . . . . . . . . . . . . . . . . . 5-42
5.5
PROTECTION METHODS . . . . . . . . . . . . . . . . . . . . . . 5-44
Bundle Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-44
Tilting of Bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-45
Reduction of Proportion of Conductors in Wakes . . . . . 5-47
Short Subspan Lengths . . . . . . . . . . . . . . . . . . . . . . . . 5-48
Staggered Subspan Systems . . . . . . . . . . . . . . . . . . . . 5-49
MECHANISMS OF GALLOPING . . . . . . . . . . . . . . . . .4-21
Basic Mechanisms of Galloping . . . . . . . . . . . . . . . . . .4-21
Influence of Structural Factors . . . . . . . . . . . . . . . . . . .4-27
Estimation of Galloping Amplitudes . . . . . . . . . . . . . . .4-39
Tension Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4-44
How Many Loops Will Occur? . . . . . . . . . . . . . . . . . . . .4-47
4.4
Mechanisms of Wake-Induced Oscillation . . . . . . . . . . 5-17
Survey of Analytical Methods . . . . . . . . . . . . . . . . . . . . 5-33
Wind Tunnel Testing for Subconductor Oscillation . . . . 5-35
Galloping Conductors
4.1
ANALYSIS OF WAKE-INDUCED OSCILLATIONS . . . 5-17
5.6
SPACER AND SPACER-DAMPER SYSTEMS . . . . . . 5-52
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-52
Types of Spacers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-53
Material Used in Spacers . . . . . . . . . . . . . . . . . . . . . . . 5-56
Design Criteria for Spacers . . . . . . . . . . . . . . . . . . . . . 5-57
Clamping Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-61
Spacer Articulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-65
Spacer-Damper Main Framev67
Standard and Recommendation for Spacers . . . . . . . . 5-68
Criteria for Spacer Distribution along the Spans . . . . . 5-69
Damping Systems for Expanded Bundles . . . . . . . . . . 5-72
Spacers for Jumper Loops . . . . . . . . . . . . . . . . . . . . . . 5-73
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Spacer-Damper Installation. . . . . . . . . . . . . . . . . . . . . .5-73
Current Practice and Field Experience . . . . . . . . . . . . . 5-74
5.7
HIGHLIGHTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-75
Chapter 7
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4
7.2
SHORT-CIRCUIT FORCES IN POWER LINES AND
SUBSTATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5
Fault Currents and Interphase Forces . . . . . . . . . . . . . . 7-7
Behavior of Bundle Conductors under Short Circuits . . . 7-9
Interphase Effects under Short Circuits . . . . . . . . . . . . 7-12
Estimation of Design Loads . . . . . . . . . . . . . . . . . . . . . 7-13
Interphase Spacers as a Mean to Limit Clearances Problem
Linked with Short Circuit. . . . . . . . . . . . . . . . . . . . 7-16
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5-76
6.1
Overhead Fiber Optic Cables
PURPOSE AND OBJECTIVE. . . . . . . . . . . . . . . . . . . . .6-3
Purpose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-3
Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-3
6.2
7.3
REQUIREMENTS FOR OVERHEAD FIBER OPTIC
CABLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-8
Electrical Requirements . . . . . . . . . . . . . . . . . . . . . . . . .6-9
Mechanical Requirements. . . . . . . . . . . . . . . . . . . . . . .6-10
Optical Requirements . . . . . . . . . . . . . . . . . . . . . . . . . .6-10
Environmental Requirements . . . . . . . . . . . . . . . . . . . .6-10
Installation Requirements . . . . . . . . . . . . . . . . . . . . . . . 6-11
Hardware and Accessory Requirements . . . . . . . . . . . 6-11
6.4
7.4
7.5
Cable Characteristics Tests . . . . . . . . . . . . . . . . . . . . .6-17
Installation Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-18
In-Service Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-21
6.6
7.6
FIBER OPTIC CABLE VIBRATION AND CONTROL . .6-26
EXPERIENCE AND OPERATIONAL
CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . .6-30
Warning Sphere Vibration Problems on OPGW Lines .6-30
Electric Field Effect for ADSS . . . . . . . . . . . . . . . . . . . .6-30
Clearance Requirements . . . . . . . . . . . . . . . . . . . . . . .6-30
Long Spans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-30
6.8
6.9
7.7
HIGHLIGHTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-38
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-39
NOISE FROM OVERHEAD LINES . . . . . . . . . . . . . . . 7-39
Sources of Noise from Overhead Lines . . . . . . . . . . . . 7-39
Radio and Audible Noise . . . . . . . . . . . . . . . . . . . . . . . 7-39
Noise Levels and Abatement Methods . . . . . . . . . . . . . 7-39
Utility Case: Vibration and Noise Emanating from Steel
Pole Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-39
CASE STUDIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-31
OPGW Selection for a 345 kV Double-Circuit Transmission
Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-31
ADSS Selection for Retrofitting on a 161 kV Transmission
Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-33
Lashed Cable Solution for a 24 kV Double-Circuit
Distribution Line . . . . . . . . . . . . . . . . . . . . . . . . . .6-34
Parts of the Lashed System . . . . . . . . . . . . . . . . . . . . .6-35
VIBRATION OF TOWER MEMBERS . . . . . . . . . . . . . 7-32
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-32
Some Cases of Structure Member Damage. . . . . . . . . 7-32
Natural Frequencies of Vibration for Towers and Tower
Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-35
Vibration of Tower Members Induced by
Conductor Motion . . . . . . . . . . . . . . . . . . . . . . . . . 7-36
Direct Wind-Induced Vibrations of Tower Members . . . 7-37
Mitigation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 7-38
Fiber Optic Cable Vibration . . . . . . . . . . . . . . . . . . . . . .6-26
Vibration Control of Fiber Optic Cable. . . . . . . . . . . . . .6-28
6.7
GUST RESPONSE . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-25
Gust Wind Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-25
Width of Right-of-Way. . . . . . . . . . . . . . . . . . . . . . . . . . 7-26
Effect of Wind Direction on Exposure . . . . . . . . . . . . . . 7-26
Effect of Elevation on Wind Exposure. . . . . . . . . . . . . . 7-26
Mean Blowout of Different Conductor Configurations . 7-27
Effect of Gustiness on Blowout. . . . . . . . . . . . . . . . . . . 7-28
Effect of Lateral Scale on Blowout . . . . . . . . . . . . . . . . 7-29
Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 7-31
HARDWARE AND ACCESSORIES FOR OVERHEAD
FIBER OPTIC CABLES . . . . . . . . . . . . . . . . . . . . . . . .6-12
ACCEPTANCE TESTS FOR OVERHEAD FIBER OPTIC
CABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-16
ICE AND SNOW SHEDDING. . . . . . . . . . . . . . . . . . . . 7-19
Types of Atmospheric Ice Accretion . . . . . . . . . . . . . . . 7-20
Process of Ice and Snow Shedding . . . . . . . . . . . . . . . 7-20
Consequences of Ice and Snow Shedding. . . . . . . . . . 7-21
Model Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-23
Line Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-25
Suspension Hardware. . . . . . . . . . . . . . . . . . . . . . . . . .6-12
Deadend Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-14
Optical Tension Device (OTD). . . . . . . . . . . . . . . . . . . .6-16
Other Accessories. . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-16
6.5
BUNDLE CONDUCTOR ROLLING . . . . . . . . . . . . . . . 7-16
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-16
Bundle Rolling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-17
Field Tests and Analysis . . . . . . . . . . . . . . . . . . . . . . . . 7-17
Conductor Torsional Stiffness . . . . . . . . . . . . . . . . . . . . 7-18
Bundle Torsional Stiffness and Bundle Collapse . . . . . 7-18
General Theory for Torsional Stiffness of
Multispan Bundle Lines . . . . . . . . . . . . . . . . . . . . 7-19
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-19
TYPES AND DESCRIPTIONS OF OVERHEAD FIBER
OPTIC CABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-3
Optical Ground Wire . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-3
All-Dielectric Self-Supporting Cable . . . . . . . . . . . . . . . .6-6
Wrapped and Lashed Fiber Optic Cable . . . . . . . . . . . . .6-7
Optical Phase Conductors or Optical Conductors. . . . . .6-8
Optical Attached Cable . . . . . . . . . . . . . . . . . . . . . . . . . .6-8
6.3
Other Motions
7.1
Appendix 5.1 Instability Index . . . . . . . . . . . . . . . . . . . . . . . . . .5-76
Chapter 6
Contents
7.8
EARTHQUAKE EFFECTS ON OVERHEAD
CONDUCTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-40
Experience from Past Earthquakes . . . . . . . . . . . . . . . 7-40
Current Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-41
Earthquake Ground Motion . . . . . . . . . . . . . . . . . . . . . 7-41
Behavior of Transmission Lines during Earthquakes . . 7-44
Evaluation of Conductor Motion during Earthquakes . . 7-45
Emergency Preparedness and Training . . . . . . . . . . . . 7-45
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-45
xiii
Contents
7.9
7.10
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Conductor Tables
CORONA VIBRATION . . . . . . . . . . . . . . . . . . . . . . . . . 7-45
Appendix 1
Corona-induced Vibration Phenomenon . . . . . . . . . . . . 7-45
Major Parameters Affecting CIV . . . . . . . . . . . . . . . . . . 7-46
Corona-induced Force. . . . . . . . . . . . . . . . . . . . . . . . . . 7-47
Composition of Corona-induced Forces . . . . . . . . . . . . 7-48
Audible Noise from CIV . . . . . . . . . . . . . . . . . . . . . . . . . 7-49
Remedies to CIV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-49
A1.1
SCOPE OF CONDUCTOR TABLES . . . . . . . . . . . . . . A1-1
A1.2
SOURCES OF DATA . . . . . . . . . . . . . . . . . . . . . . . . . . A1-1
A1.3
UNITS USED IN TABLES. . . . . . . . . . . . . . . . . . . . . . . A1-2
A1.4
VALUES OF EI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A1-2
STATION BUS VIBRATIONS . . . . . . . . . . . . . . . . . . . . 7-50
A1.5
“K” FACTORS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A1-2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-50
Operating Experience and Field Observations . . . . . . . 7-50
Aerodynamic Driving Force . . . . . . . . . . . . . . . . . . . . . . 7-50
Natural Frequency of Bus Spans . . . . . . . . . . . . . . . . . 7-51
Resonant Wind Speed . . . . . . . . . . . . . . . . . . . . . . . . . 7-51
Resonant Vibration Amplitudes . . . . . . . . . . . . . . . . . . 7-51
Resonant Vibration Bending Stresses . . . . . . . . . . . . . 7-52
Damping Requirements. . . . . . . . . . . . . . . . . . . . . . . . . 7-53
Energy Balance Method . . . . . . . . . . . . . . . . . . . . . . . . 7-53
Vibration Behavior of a Rigid Bus Span System . . . . . . 7-54
Vibration Control Measures. . . . . . . . . . . . . . . . . . . . . . 7-54
Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-55
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A1-4
Appendix 2
Units and Conversion
Factors . . . . . . . . . . . . . . . . . . . . . . . . . A2-1
Appendix 3
Catenary Effects
A3.1
EQUATION FOR THE PARABOLIC FORM . . . . . . . . .A3-2
A3.2
EQUATIONS FOR THE CATENARY FORM . . . . . . . .A3-2
HIGHLIGHTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-56
A3.3
HYBERBOLIC FUNCTIONS . . . . . . . . . . . . . . . . . . . .A3-2
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-58
A3.4
INCLINED SPANS . . . . . . . . . . . . . . . . . . . . . . . . . . . .A3-2
7.11
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-1
xiv
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
CHAPTER 1
INTRODUCTION
1.1
OVERVIEW OF THE CONDUCTOR MOTION PROBLEM
During the last decade, changing pressures imposed by population growth, changing
sources of energy supply, emphasis on short-term economic returns, increased environmental assessment requirements, and changing regulatory environment have strongly
affected the demands on and consequently the design of overhead transmission lines.
Restricted energy sources, environmental considerations, and the high cost of transporting fuel have sharply limited the number and location of available power plant sites.
Many of the available sites are quite remote from the load centers, which must be supplied. Steadily increasing population growth has made necessary the generation and
transmission of very large blocks of power. Inflation and environmental concerns have
made line rights-of-way far more expensive and difficult to obtain than in prior years.
Changes in power flows due the new open market have led to increased loads on some
lines. Critical lines have suffered failures during peak loads, leading to major power outages and emphasizing the need for increased reliability of overhead lines.
The pressures resulting from these conditions have tended to require the construction of
long, high-capacity, high-voltage transmission lines. The line voltages and the requirements for increased capacity per circuit have prompted line designers to use bundles of
large conductors. Increased dependency on communication systems has led to the introduction of a wide range of designs of fiber optic cables on overhead power lines. Meanwhile, the costs of material and construction continue to spiral upward. As a result,
conductors installed on a major transmission line can involve a very large investment.
In addition, these conductors can impose a high degree of structural continuity upon an
entire line. Dynamic forces and motions applied to conductors locally can be transmitted
through an indefinite number of structures and spans.
Probably no other large structure has as much of its mass in highly flexible form, and so
continuously exposed to the forces of wind, as does the modern transmission line. This
makes the line susceptible to the development of sustained, cyclic conductor motions.
These motions may take the form of aeolian vibration, conductor galloping, wakeinduced oscillations or one of several other dynamic effects. In all of them, incremental
amounts of mechanical power are repeatedly absorbed from the wind into the conductor.
When this happens to a very large elastic mechanical system (i.e., the continuous conductor), which is supported and supplemented by thousands of elastic or semi-elastic
mechanical subsystems (i.e., clamps, hardware, insulators, dampers, spacers, and structures), the possibility of eventual damage or failure becomes appreciable.
An additional complication is one that is peculiar to overhead electrical lines. Due to the
voltages involved, the type of close-range, bare-handed inspection desired for the early
1-1
Chapter 1: Introduction
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
detection of damage to the conductor, or to energized
conductor hardware, is generally possible only when the
line is taken out of service. (Recently a device called the
Electro-Magnetic-Acoustic-Transducer, or EMAT,
developed by the Electric Power Research Institute
[EPRI] has shown promise of allowing linemen to identify broken conductor strands under a clamp while the
line is energized.) The degree of difficulty and cost of
loss of transmission capacity to the utility, encountered
in arranging for scheduled outages increases as the
importance of a line increases. Therefore, problems
caused by conductor motion either must be anticipated
and prevented during the design and construction
stages, or must be resolved at high cost after visible
damage or motion has occurred. The difficulty of
obtaining outages for climbing inspections has led to
increased use of helicopter based fly-by and live line
inspections. This has made early detection of minor
damage, indicating a progressing failure mode, more difficult and costly.
In summary, the conductors and their auxiliaries comprise a vital line component, which is very expensive,
which may be subjected to frequent and possibly damaging cyclic motion, and which is very difficult to
inspect or repair.
Under these conditions, any improvement in the understanding of cyclic conductor motion that may lead to
reduction or resolution of the problem is desirable.
Developments achieved during the past 25 years have
augmented the status of the technology at the time of
the writing the first edition of this book. These are summarized in the current volume, by a team of experts
involved in the development and application of these
technologies.
1.2
THE BOOK: WIND-INDUCED CONDUCTOR
MOTION
1.2.1
Purpose and Scope
This book presents a state-of-the-art study of aeolian
vibration, conductor fatigue, conductor galloping,
wake-induced oscillation, fiber optic cables and their
associated aerodynamic problems, and other motions.
Each conductor behavior is explored in depth in separate chapters that examine the causes, mechanisms, incidence, types of motion, factors influencing motion,
resulting damage, and protection methods associated
with its particular topic.
One or more detailed theoretical analyses are presented
for each type of conductor behavior. Whenever possible,
supporting (or conflicting) data from laboratory tests
1-2
and field tests are presented. The strengths and limitations of the theories and of the various types of testing
methods are discussed. Extensive references to the work
of other researchers are also included.
Need for a Revised Edition
Development of a new edition has been undertaken for
several reasons. First, although the book is still a wellused reference for conductor vibrations, it is now almost
a quarter of a century old. Since its publication, there
have been considerable developments in both approach
and technology in this field. Second, there has also been
a concern that the original book was too academic and
could not easily be put to practical uses.
To address these concerns, this revision of the book
updates existing information in the first edition to
reflect the state-of-the art knowledge in the field of
wind-induced conductor motion. The revision process
has also added new information to the book to cover
topics, interests, and technology that have been developed since the book was last published. In addition, the
revision broadens the scope of the book to acquire global utility experience in conductor motion.
Developments that have taken place since publication of
the first edition include the following. In the area of aeolian vibration, progress has been made in analysis of
wind excitation data, behavior of new conductor
designs, improved laboratory measurements using laser
technology, interpretation of vibration records, and
modeling of vibration behavior. Regarding conductor
fatigue, there have been considerable developments on
inspection tools and fatigue endurance of conductors
and clamps. With galloping, field studies have led to
improved knowledge of galloping amplitudes, with and
without control devices, for single and bundle conductor
lines and refinement of application techniques, as well
as some new galloping control devices. In the area of
bundle conductor oscillation, new information is available on spacer and spacer-damper systems. Experience
has shown that the clamping systems require careful
selection to avoid loosening wear and ultimately strand
and conductor failures.
Since publication of the first edition, the use of fiber
optic cables has grown, and some information is available on the aerodynamic problems that can occur.
Research results are also available for a number of
motions not previously covered in the earlier edition,
including short-circuit forces, bundle rolling, ice drop,
gust response, structural member vibration, acoustic
effects, earthquake damage, corona-induced vibration,
and station bus vibration.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 1: Introduction
The materials, design, and manufacture of conductors
have also advanced in the past 25 years. Driven by the
increased demand placed on overhead lines from regulation of the power industry, advanced conductors were
developed in recent years. These conductors can be
used to raise the power capacity of an overhead line
quickly by replacing the existing conductor with minimal changes to the structures. This type of advanced
conductors possesses the “High-Temperature Low-Sag”
characteristics. Aluminum zirconium is used instead of
aluminum for the outer strands to attain higher annealing temperatures. As a result, the operating conductor
can go beyond 2000C instead of 900C, thus increasing
the power transfer capability of the line. The steel used
for the center core of the conductor is either replaced
with composite materials or steel alloy. Composite
materials can either be metallic matrix or carbon fiber.
One of the common steel alloys used for the conductor
core is Invar, an alloy of steel and nickel. These materials do not expand as much as steel with increasing temperatures and thus produce smaller conductor sag.
decisions are guided by data from field tests and field
experience.
Users of this Guidebook
The audience for this book consists primarily of transmission and distribution line designers and staff responsible for maintenance of overhead lines, interpretation
of line failures, and correction of poor designs. In the
past two decades, changes in the power industry have
presented challenges to these utility employees. At many
companies, tight budgets have caused fewer resources to
be devoted to issues of conductor motion. In addition,
retirements and staff attrition have led to a loss of experience and expertise. As a result, users today, who may
not have the means to conduct their own tests, need
ready access to the results of the latest research and
information on control devices. New, less experienced
engineers need fundamental information on the mechanisms of conductor motion.
The objective of this revised edition is to provide users
with the best practical tool to design overhead lines
effectively in order to minimize damages to the lines
from wind-induced conductor motion, and to analyze
existing lines for improvements of their performance
related to such motion. The new edition includes
worked examples to facilitate the understanding of
wind-induced conductor motion and the application of
the knowledge to practical uses.
In the case of the areas covered in Chapter 7, “Other
Motions,” usefulness of existing theories in actual
design varies with the area in question. Unpredictability
of the phenomenon, without support of an adequate
statistical data base, limits application of theory in connection with ice and snow shedding, earthquakes and,
to a lesser extent, gust response. Vibration of tower
members covers several different mechanisms of excitation, and it is probably fair to say that the technology is
still under development in each of them. On the other
hand, the theory covering bundle rolling, and effects of
short circuits on bundled conductors, distribution lines,
and substation flexible and rigid bus is in reasonable
agreement with actual test and can be applied at the
design stage. The problems of noise from overhead lines
and corona vibration do not reach the level where they
affect line design. However, when they arise during
operation, they must be recognized and dealt with.
Although the book must be described as a state-of-theart reference rather than as a design manual, the overhead line designer should find it helpful in:
• Recognizing and properly identifying cyclic conductor motion when it occurs
• Anticipating the circumstances in which it may be
When the first edition of this book was originally
planned, it was hoped that it would be possible to
present a design manual that would provide specific
instructions, formulae, and reference data for the solution of all types of conductor motion problems. However, it soon became apparent that this would be
impossible. Theories have been developed to explain virtually all types of conductor motion. However, the volume of laboratory and field testing necessary for the
confirmation of these theories has been limited. This
has been particularly true for galloping and wakeinduced oscillation. In the case of aeolian vibration,
efforts to confirm the technology have met with only
limited success. This has required the use of significant
safety factors when attempting to apply the technology
to design problems. In all three of these areas, design
expected
• Becoming familiar with protection methods currently
in use
• Understanding the theoretical principles (where
known) upon which currently used protection methods operate
• Evaluating the cost-effectiveness of current or proposed protection methods
• Soliciting proposals or bids relative to protection of
new or existing lines
• Critically evaluating such proposals and the claims
made for them
• Formulating tests or test programs for evaluating
proposed protection systems
1-3
Chapter 1: Introduction
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Meeting the Needs of Different Users
One of the challenges in preparing this book is spanning
a wide range of technical sophistication in a single volume. To meet this challenge, the authors have organized
the chapters to make the information as readily accessible as possible. Each chapter’s opening Introduction
provides a broad overview on the subject, with information on developments in the field and areas of primary
interest. Also included in this section is a “roadmap” to
the chapter, which outlines the sequence of the chapter’s
presentation.
Section titles and subheadings are used to describe, as
clearly as possible, the areas covered and the subordination of information. An index has also been added to
this edition to make it easier for users to locate specific
topics.
In some cases, more technical information is included.
This technical information includes background material, discussions of alternate methods, and detailed
development of formulae used in the text. However, as
much as possible, this information is generally included
at the end of chapters in appendices or at the end of the
whole book in appendices.
1.2.2
Organization and Use of the Book
Chapter Organization
This book is divided into seven chapters. Chapter 1
includes an introduction and overview of the conductor
motion problem and brief descriptions of each type of
motion.
Chapters 2 through 7, respectively, provide detailed
studies of aeolian vibration, fatigue of overhead conductors, conductor galloping, wake-induced oscillation,
fiber optic cables, and other motions. As described
below, appendices at the back of the book provide a
number of reference tools. Equations, tables, and figures are numbered in each section of each chapter. Citations are made within the text with author’s name and
date, and full references are listed at the back of each
chapter.
Highlights: Practical Information for Users
A new feature of this edition, the final section in each
chapter includes a brief list of “Highlights.” This section
offers a listing of the main points of the chapter for
practical application by users.
Symbols
A listing of symbols used in the book is provided immediately following the Table of Contents. This section lists
the symbols for, and definitions of, those mechanical
and aerodynamic terms that are used repeatedly
1-4
throughout the text. Other terms, which may have limited or special application, are defined locally.
Appendices
Three appendices provide reference material at the back
of the book.
Appendix 1. Conductor Tables. Tables of conductor physical characteristics are provided in Appendix 1. These
tables cover most of the available American, Canadian,
English, and Australian sizes of ACSR, ACAR, AAAC
(6201-T81 Alloy), AAC, Self-Damping ACSR, Alumoweld, and galvanized steel strand.
Other conductor types, including some that are limited
to short-span applications, and some that appear to be
superseded by stronger alloys, have been omitted from
the tables. These include “Compacted,” SSAC, and
some AAAC (5005-H19 Alloy).
All tables are based upon AWG or CM sizes. All conductor dimensions and physical characteristics are
described in parallel columns of English and SI units.
Appendix 2. Units and Conversion Factors. Appendix 2
provides definitions of the basic units and tables of factors for converting both from English to SI and from SI
to English. In most cases throughout this book numerical quantities are shown in both English and SI (metric)
units. Many of the equations are presented in both
English and SI form, with coefficients adjusted accordingly, and with the units locally described and defined.
However, certain equations used in the development of
mathematical concepts do not have assigned units.
Appendix 3. Catenary Effects. Appendix 3 provides a discussion and an example of the application of catenary
formulae for solving span end tension and span arc
length.
1.3
INTRODUCTION TO TYPES OF
CONDUCTOR MOTION
For the purposes of this book, wind-induced conductor
motion is considered to include those types of repetitive
or cyclic motion that derive their energy from wind
forces applied to conductors.
Energy absorbed by the conductor may be dissipated by
internal friction at the molecular level; by inter-strand
friction within the conductor; by transference to clamps,
dampers, spacers. spacer-dampers, and suspension
assemblies; by transference to adjoining subconductors
(in the case of bundled conductors); or by return of
energy to the wind.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
The relative magnitudes of these dissipations, and their
phase positions within each motion cycle, determine
whether the conductor motion will be suppressed, sustained, or accelerated.
Three different categories of cyclic conductor motion
are recognized. These are aeolian vibration, conductor
galloping, and wake-induced oscillation. They are distinguished from each other by different mechanisms of
energy transfer, by different motion patterns, by vastly
different frequencies and amplitudes of vibration, and
by different effects upon conductors, clamps, and other
equipment.
Other forms of dynamic motion that affect overhead
power lines, and also substations, are included in this
book. While many of these, (structural member vibration, noise, station bus vibration, gust response) derive the
energy from the wind, not all do so (electromagnetic collapse in bundles, bundle rolling, ice jump, acoustic effects,
earthquake damage, and corona-induced vibration).
1.3.1
Aeolian Vibration and Fatigue
Although the ancient Greeks had no concern for maintenance of overhead transmission lines, they were evidently aware that movement of air past a tensioned
string would cause it to vibrate. Long before the days of
radio and TV, they mounted strings on a sounding box.
The assembly produced musical tones when placed in a
natural air path such as an open window. Aeolus, the
god of wind, lent his name to the device, known as the
aeolian harp. The tradition is preserved in speaking of
aeolian vibration.
Obstructions in water streams can produce well-defined
trails of eddies, which were at times accurately depicted
by observant artists such as Leonardo da Vinci. A problem with vibration of a submarine periscope is noted by
von Karman (von Karman 1954).
The appearance of nonductile fractures in the strands of
transmission conductors in the early 1900s was at first
viewed with an air of mystery, but was ultimately recognized as having the properties of fatigue breaks. A few
early reports referred to this type of fracture as crystallization, a misnomer that occasionally persists in presentday literature. The implication of this term is that the
material has undergone an internal molecular rearrangement causing a loss of ductility. The term stems
from the granular appearance of the fractures.
Observations in the early 1920s showed that the breaks
were properly attributed to metal fatigue resulting from
the fact that the lines, under certain wind conditions,
Chapter 1: Introduction
were vibrating. The instruments and equipment available to early investigators were extremely crude by
today’s standards. In spite of this, the quality of the
investigation carried out in the period between
1920 and the mid-1930s was very high. Many of the
investigators displayed an amazing insight into the phenomenon, demonstrating an understanding and appreciation of details at times rediscovered by others 30 or
40 years later.
Varney (Varney 1926), for example, recorded the action
of a vibrating line “by attaching one end of a string to a
transmission wire and the other end to a light wooden
block arranged to slide in a slot in a vertical board
which was fastened to a board resting on the ground.
The lower end of this block had attached to it a light
spring which served to keep the string taut and yet permitted the block, with the pencil attached, to move up
and down in response to the vibrations of the transmission line wire. The string was attached as nearly as possible to the middle point of the first node from the
insulator clamp. A wooden slide with a strip of paper
attached to it was then moved in a direction of right
angles to the movement of the pencil and was timed
with a stop-watch.” From the records that Varney produced in this manner, it is possible to check the traveling
wave return time within 0.1 seconds, since he recognized
the importance of traveling wave velocity and included a
calculated value together with span length and tension.
Early observations also indicated that vibration
occurred with relatively low velocity winds, and recognized the fact that air turbulence decreased the severity
of the vibration. It was also known that the basic cause
of the vibration was the regular shedding of vortices
from the conductor whenever the wind blew with a significant component at right angles to the line.
Early efforts at protecting overhead lines against the
harmful effects of vibration were directed toward reinforcing the conductor at the point of support by means
of rods or wire tapes. Concurrent with these efforts was
the development of early damping devices which
reduced the intensity by dissipating some of the
mechanical energy present. The development of some of
these devices appears to have been largely intuitive, and
detailed investigations years later led to refinement and
improvement.
The vibration itself is not very evident and may be
missed except by those who watch for it. It is most
noticeable during early morning or late evening hours
when smooth, low-velocity winds are present. Under
these conditions the peak-to-peak amplitude rarely
exceeds one conductor diameter. For higher velocity
1-5
Chapter 1: Introduction
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
winds, the amplitude generally decreases. In steel structures, vibration can often be felt by placing a hand on
the tower leg. At times it may be detected through the
rattling of loose parts such as cotter pins in the hardware or components within the structure. Parts within
the suspension system that show signs of chafing or
rotation may provide evidence that vibration has
occurred. Most finely divided metallic powders (aluminum included) are black in color. The appearance of
black powder between conductor strands near the suspension indicates that inter-strand motion is taking
place. The appearance of broken strands is a definite
sign of trouble. Strand fracture may be difficult to
detect, often occurring within the clamp on the lower
side of the conductor. With conductors that have more
than one aluminum layer, first fractures may be within
an inner layer. Strand fracture is practically always associated with either the suspension or points of line hardware attachment. Where poor design practice has been
followed, fatigue breaks may occur within the first year
of construction. Ideally, the first strand fracture would
occur on the day after the line has been taken out of service at the end of its amortized life. The survival of a line
without fatigue fracture indicates either good design or
a design that has been overly cautious.
With the increased use of bundled conductor systems,
problems in aeolian vibration have decreased somewhat.
Other forms of line action associated with bundle systems have occurred, and are covered elsewhere in this
book. For single conductors, observations of terrain
factors, judgment concerning conductor tension and
span length, and the use of vibration dampers where
necessary will normally permit design of an adequate
and economical line.
1.3.2
Conductor Galloping
Conductor galloping is a very low-frequency, highamplitude, primarily vertical conductor motion. It is
nearly always caused by moderately strong, steady
crosswinds acting upon an asymmetrically iced conductor surface.
The ice is normally deposited on the windward surface
of the conductor. If an ice deposit has the proper shape,
the rotation of the conductor with respect to the wind
can lead to a variation in the lift on the conductor, and
this can lead to oscillation of the conductor in the vertical direction. Apparent rotation with respect to the wind
can result from the conductor’s own motion. After vertical oscillation starts, the vector sum of the true wind
velocity and the conductor velocity produces an apparent wind velocity that will be alternately angled above or
below the horizontal (see Figure 4.2-14). This has the
effect of alternately changing the position of the ice
1-6
deposit relative to the wind that the conductor actually
feels.
If the upward conductor velocity coincides with a negative aerodynamic lift force, and if the downward velocity
coincides with a positive lift, the motion will be suppressed, and the conductor will not gallop. However, if
the upward velocity is coincident with a positive aerodynamic lift force, and the downward velocity is coincident
with a negative lift force, accelerating galloping can
result.
Under these conditions the power transmitted from the
wind to the conductor is much greater than the power
associated with aeolian vibration. The amplitude of the
galloping can approach, or even exceed, the sag of the
conductor for the span involved.
Very thin ice (1 to 2 mm thick) has been known to cause
galloping.
Protection methods include electrical ice melting, the
use of increased conductor spacing, rugged construction, and the use of mechanical devices, such as aerodynamic “drag” and torsional dampers.
The occurrence of conductor galloping may be limited
to six or eight spans in a 100-mile transmission line.
However, at the present state-of-the–art, it is very difficult, if not impossible, to predict which spans will gallop
and which will not.
Such protection methods as increased conductor spacing, increased structural safety factors, and ice melting
use a “broadside” approach to the problem. They are
based upon the assumption that galloping can occur
any place along a line. If and when the theoretical and
practical problems of galloping prediction can be
resolved, it should become possible to achieve substantial savings in line cost.
It is fortunate that sustained high-amplitude conductor
galloping is a rare occurrence because no other type of
cyclic conductor motion can cause so much damage in
such a short time. Galloping can not only break conductor strands, but can damage dampers, tie-wires, insulator
pins, suspension hardware, crossarm hardware, poles
and towers. In several instances the losses of revenue due
to galloping-induced outages have exceeded $1 million.
1.3.3
Wake-Induced Oscillation
Wake-induced oscillation is peculiar to bundled conductors exposed to moderate-to-strong crosswinds, and
arises from the shielding effect by windward subconductors on leeward ones. The wake proceeding downwind
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
from a stationary windward subconductor can subject
the leeward subconductor to a complex and variable set
of forces (see Figures 5.3-4 through 5.3-7).
Depending upon the relative magnitudes and phase
relationships of the forces involved, they may suppress
motion of the leeward subconductor, or may cause it to
move in an elliptical or irregular orbit.
If the leeward subconductor moves, some forces are
transmitted to the windward subconductor through
spacers or other hardware. When this occurs, the windward subconductor may move in a pattern which frequently differs in phase and amplitude from that of the
leeward subconductor. This further complicates both
the aerodynamic and mechanical forces acting upon the
leeward subconductor.
Wake-induced oscillation can take several forms. The
subspan mode (Figure 5.2-1a) involves motion of the
subconductors within subspans. The rigid-body modes
(Figures –5.2-1b, c, and d) involve vertical or horizontal
motion or twisting of the entire bundle throughout the
length of the span.
Several methods have been used for preventing or reducing wake-induced oscillation.
Subspan staggering, with or without damping spacers,
has been used effectively to prevent subconductor oscillation. Successful prevention of the rigidbody modes of
oscillation appears to require reduction of the exposure
of leeward subconductors to the wakes of the windward
subconductors. This has been accomplished by tilting
the bundles to angles greater than 20° from the horizontal, and by increasing the ratio of subconductor spacing
to conductor diameter (a/d).
The theoretical analysis of wake-induced oscillation has
attracted the attention of a rather large number of competent investigators. However, no proven, workable
rules are yet available to the line designer. The principal
reasons for this include the great complexity of the phenomenon and the large number of important variables
that are involved.
Wake-induced oscillation has not been a widespread
problem. Significant damage has been restricted to
localized sections of a relatively few major lines. At its
worst, it may cause suspension hardware failure or
crushing of conductor strands due to clashing. In most
cases, damage has been limited to rapid wear in suspension hardware, or to fatigue of spacers or other accessories. There is evidence that four-conductor bundles in a
Chapter 1: Introduction
square configuration are more susceptible to wakeinduced oscillation than are two- or three-conductor
bundles. In one case, the use of a four-conductor diamond configuration has been specified in an attempt to
alleviate this problem.
1.3.4
Overhead Fiber Optic Cables
The use of fiber optic cables on overhead transmission
lines has grown since the publication of the first edition
of this book. Installations especially proliferated since
the mid-1990s, driven by the advent of the Internet and
the need of utilities and telecommunication companies
for high-speed telecommunication between system control centers.
There are five basic types of overhead fiber optic cables,
meeting different operational, technical and economic
requirements. These types are: Optical Ground Wire
(OPGW), All-Dielectric Self-supporting Fiber Optic
Cable (ADSS), Lashed Fiber Optic Cable, Wrapped
Fiber Optic Cable, and Optical Phase Wire (OPPW).
The most common type is OPGW, which is a composite
cable serving the double function of a ground wire (also
know as shield wire, sky wire, earth wire, or static wire)
and a communication link.
Overhead fiber optic cables are susceptible to windinduced motions and damage much like conductors are,
and appropriate measures must be taken. Motions
affecting fiber optic cables include aeolian vibration,
galloping, buffeting, and short-circuit forces. Failure of
fiber optic cables is more often determined by loss of
optical continuity than by mechanical damage to the
outer layers.
Unfortunately there are few published laboratory or
field studies on overhead fiber optic cables, because they
are relatively new to the industry and have been treated
mainly from a telecommunications perspective. In addition, because fiber optic cables are often custom-engineered for specific applications, the proprietary nature
of their designs precludes public disclosure of laboratory tests or problems arising in the field.
1.3.5
Other Motions
A number of other motions of overhead lines and structures can occur and be damaging to overhead conductors, hardware, and structures. Some of these topics
were mentioned in the first edition, but in the intervening years, additional experience with several of these
phenomena has been gained, and procedures have been
developed to ameliorate the effects and defer extensive
damage.
1-7
Chapter 1: Introduction
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
These phenomena include overhead conductor motions
precipitated by causes other than wind; some of these
motions are transient, while others are cyclic. One
example of these other motions are short-circuit oscillations, which occur when short-circuit currents generate
electromagnetic forces within the conductors. Short-circuit forces may be important for high-voltage bundle
conductor lines due to the small distance between subconductors, and in distribution lines due to the change
in phase-spacing during short-circuit occurrences as
well as in substations where conductors are spaced
closely together.
the various legs of a supporting structure or between
different supporting structures.
Mechanical vibrations of transmission line conductors
may be initiated by corona discharges under rain conditions or under wet snow and intense fog.
Other components susceptible to wind-induced
motions are hollow tubular aluminum conductors (also
called rigid bus), which are used in some transmission
substations.
1.3.6
Another conductor motion, not covered in preceding
chapters, is bundle rolling, which occurs under heavy ice
loads due to nonuniform loading on subconductors of
bundle conductors. Rolling can leave the bundle in the
collapsed state from which it is very difficult to restore
normal alignment.
Sudden ice or snow shedding from transmission lines
may result in high-amplitude vibrations and the application of transient dynamic forces to the supporting structures, which in turn can lead to severe structural damage
or to flashover between conductors.
The increase of wind velocity over short time periods
during gusts also has the potential to cause conductor
damage and flashovers between adjacent phases. Experimental and field work has been conducted to assess
gust response and variation of the wind speed with
height above ground level.
Also worthy of note is the motion of other parts of the
overhead line system such as tower members. The supporting structures of transmission lines are very often
impacted by the wind-induced conductor motions. In
addition, members in lattice towers are subjected to
wind-induced motions and can fail under cyclic loadings if not designed properly.
Another phenomenon related to overhead line vibration
is the noise produced from power lines through vibrating conductors or hardware or other causes.
Earthquakes can cause damage to transmission lines
due to foundation settlement or movement at supporting structures or due to differential settlement between
1-8
Summary of Types of Conductor Motion
Table 1.3-1 provides a cursory comparison of the characteristics of aeolian vibration, conductor galloping,
and wake-induced oscillation.
Care should be exercised in interpreting this table. The
numerical ranges shown for frequency, amplitude, wind
velocity, and time required to cause damage are
intended to provide a comparison among the three types
of motion as they affect all types of overhead lines.
These values should not be considered as representing
either extreme limits or normal operating conditions for
any one particular span or line.
Similarly, the verbal descriptions are presented only for
qualitative comparison. The relative importance of individual factors may vary widely from line to line.
The “other” motions can occasionally cause similar
forms of damage to these three main wind-induced
motions. The conditions required and the effects produced are presented in Chapter 7.
REFERENCES
Varney, T. 1926. “Notes on the Vibration of Transmission Line Conductors.” AIEE Transactions. p. 79 1.
Von Karman, T. 1954. Aerodynamics, Cornell University Press.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 1: Introduction
Table 1.3-1 Comparison of Types of Cyclic Conductor Motion
Aeolian Vibration
Conductor Galloping
Wake-induced Oscillation
Limited to lines with bundled
conductors
Types of Overhead Lines Affected
All
All
Approx. Frequency Range (Hz)
3 to 150
0.08 to 3
0.15 to 10
5 to 300
Rigid-Body Mode:
0.5 to 80
Subspan Mode:
0.5 to 20
Approx. Range of Vibration Amplitudes
(Peak-to-Peak) (Expressed in conductor
diameters)
0.01 to 1
Weather Conditions Favoring Conductor
Motion
Wind Character
Steady
Steady
Steady
Wind Velocity
1 to 7 m/s
(2 to 15 mph)
7 to 18 m/s
(15 to 40 mph)
4 to 18 m/s
(10 to 40 mph)
Conductor Surface
Bare or uniformly iced (i.e.
hoarfrost)
Asymmetrical ice deposit on
conductor
Bare, dry
Design Conditions Affecting Conductor
Motion
Ratio of vertical natural freSubconductor separation, tilt of
Line tension, conductor
quency to torsional natural
bundle, subconductor arrangeself-damping, use of dampfrequency; sag ratio and supment, subspan staggering
ers, armor rods
port conditions
Damage
Approx, time required for severe damage
to develop
3 mos to 20 + years
1 to 48 hours
1 mo to 8 + years
Direct causes of damage
Metal fatigue due to cyclic
bending
High dynamic loads
Conductor clashing, accelerated wear in hardware
Line components most affected
by damage
Conductor and shield wire
strands
Conductor, all hardware,
insulators, structures
Suspension hardware, spacers,
dampers, conductor strands
1-9
Chapter 1: Introduction
1-10
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
CHAPTER 2
Aeolian Vibration
Giorgio Diana
Umberto Cosmai
André Laneville
Alessandra Manenti
David Hearnshaw
Konstantin O. Papailiou
This chapter describes aeolian vibration of overhead conductors. It includes the
physics of the phenomenon, issues related to the properties and mechanics of the
conductor itself, damping devices, simulation of the response of the conductor plus
damping devices to aeolian vibration, impact of aeolian vibration on line design, and
methods of assessing the severity of aeolian vibration.
Giorgio Diana obtained his Mechanical Engineering degree in 1961 and
became Professor of Applied Mechanics at the Politecnico di Milano in
1971. He is currently a full Professor of ‘Mechanical Systems Modelling
and Simulation’, a member of the Senato Accademico and Administration Board, Director of the Mechanical Department, Coordinator of the
Department Directors’ Council and Director of CIRIVE (Inter-Department Centre for Wind Engineering) of the Politecnico di Milano. He has
carried out extensive research work in the fields of fluid-elasticity, aeroelasticity (vibrations of bridges and structures), rotor-dynamics, vibration problems in
mechanical engineering, railway vehicles dynamics and interaction between pantograph
and catenary. He has authored more than 200 papers presented at national and international conferences or published in specialised reviews. He is a consultant in several countries for the wind induced vibration of overhead transmission line conductors and, in
general, problems of fluid-structure interaction, such as the Messina Straits Bridge and
Millenium Wheel in London. He is a member of IEEE and CIGRE SCB2 WG11 and
Chairman of TF1 of that working group.
Umberto Cosmai is an international independent consultant based in
Italy with more than 45 years of experience in overhead transmission
lines. He worked for ENEL as a laboratory engineer and researcher for
23 years. In that capacity, he was involved with conductor self-damping
measurements and tests on spacer dampers, vibration dampers and
other line fittings. Moreover, he designed and operated outdoor test stations for studies on wind-induced conductor motions. In 1982,
Umberto Cosmai became technical director of a conductor fitting manufacturer, for which he designed and tested vibration-damping systems for overhead
transmission lines up to 1000 kV, including special projects for long crossing spans. He
has taught for 12 years and authored several papers and two books. He has conducted
seminars on overhead conductor vibrations and performed field vibration measurements
in 25 countries worldwide. He is a member of IEC TC7 and TC11 and CIGRE SC B2
WG11.
2-1
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
André Laneville is a professor in the
Department of Mechanical Engineering at the Université de Sherbrooke,
Québec, Canada. For over 30 years,
his research projects have included
fundamental studies of flow-induced
oscillation and instability of structures. In 1977, he designed and built a
wind tunnel to pursue his basic and applied research
projects. In addition to teaching aerodynamic and
thermo-fluid courses, he supervised 28 highly trained
personnel (9 Ph.D. and 19 M.A.Sc.). He has given general lectures in the field of flow-induced vibrations in
international meetings in Japan, France, Greece, and
Canada. As a consultant for IREQ, the Research Institute of Hydro-Québec, he worked on the measurement
of the power imparted by wind to conductors in single
and tandem configurations, as well as on the problem of
galloping. He is also a member of CIGRE SCB2 WG11.
Alessandra Manenti obtained her
Mechanical Engineering degree in
1982 and her Ph.D. in Mechanical
Engineering in 1987 at the Politecnico
di Milano. She became a researcher in
Mechanical Measurements in 1986
and since 1998 she has been Associate
Professor of Mechanical Measurements. Since 2002 she has been with the Department of
Mechanics of the Politecnico di Milano. She is a member
of the Department of Mechanics Quality committee.
Her research work is in the fields of experimental and
analytical behavior of overhead transmission line conductors, rotordynamics and statistical data analysis. She
has authored more than 40 papers, which have been presented at national and international conferences or published in specialised reviews. She is a hardware and
fittings consultant and she collaborates with the Department of Mechanics research group for analytical and
experimental studies of wind-induced vibration. She is a
member of CIGRE SCB2 WG11, “Mechanical Behaviour of Conductors and Fittings” and was Secretary of
this working group from 1998 to 2004.
2-2
David Hearnshaw obtained a degree
in mechanical engineering in 1967 and
is a professional engineer. He has been
a company director with over 32 years
experience in the overhead transmission line industry, including 24 years
experience of managing medium-sized
manufacturing exporting companies,
most recently as Managing Director of Preformed Line
Products (GB) Ltd. He is now a consultant and has
extensive experience in engineering research and the
design and development of overhead transmission line
accessories, together with wide experience of associated
engineering practices in the United Kingdom, Western
and Eastern Europe, the United States, Australasia, the
Middle East, and Africa. He has been closely involved
with major International Technical Committees,
CIGRE, and IEEE, and is Convenor of CIGRE SCB2
WG11, having previously been Secretary for 6 years. He
has authored a number of technical papers and has contributed to Guides and Standards for the industry.
Konstantin O. Papailiou was born in
Athens, Greece. He received his electrical engineering degree from the
Technical University of Braunschweig,
his civil engineering degree from the
University of Stuttgart and his Ph.D.
from the Swiss Federal Institute of
Technology (ETH) Zürich. He became
involved with transmission line work and high-voltage
engineering in 1975 as director of research and development in the Overseas Department of GEA in Fellbach,
Germany. Presently he is the Chief Executive Officer of
Pfisterer Holding in Winterbach, Germany. He is a
member of various working groups of CIGRE, IEC,
CENELEC, and SEV and has published several papers
in this field. He is also chairman of SEV TK 36 (insulators), a senior member of IEEE, and national member
for Greece of CIGRE SCB2 (overhead lines). He was
Convenor of the CIGRE SCB2 WG11 from 1998 to
2004, and is a recipient of the CIGRE Technical Committee 2004 Award.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
2.1
INTRODUCTION
Aeolian vibration is one of the most important problems in transmission lines because it represents the
major cause of fatigue failure of conductor strands or of
items associated with the support, use, and protection of
the conductor.
Aeolian vibrations can occur on almost any transmission line and at any time, in low to moderate winds.
Measurements and analyses have revealed the following
facts:
• Aeolian vibrations are characterized by vibration frequencies in the approximate range of 3–200 Hz. The
frequency range depends on the size and tensile load
of the conductor: lower frequencies are typical of
large conductors in low winds, while upper frequencies are typical of small ground wires in moderate
winds.
• Vibration frequency f in Hz is approximately given by
the Strouhal formula: f = S V/D, where S is the Strouhal number (S = 0.18 - 0.22), V is the wind velocity in
m/s, and D is the conductor diameter in m.
• Vibration amplitudes can be, at maximum, about one
conductor diameter.
• Records of vibration at a point on a conductor usually show a beat pattern (Figure 2.1-1).
• Conductor vibration causes localized bending which,
depending on its level, may cause, sometimes in a
short period of time, fatigue failures of the conductor
strands at the suspension clamps or at the clamps of
spacers, spacer dampers, dampers, and other devices
installed on the conductor, as shown in Figure 2.1-2.
The conductor vibration may also cause fatigue damage of items associated with the support and protection of the conductor itself—i.e., tower arms, spacers,
dampers, and warning spheres, etc.
Chapter 2: Aeolian Vibration
• This type of vibration is most serious when the conductor tensions are high, the terrain is smooth, with
frequent, low-to-moderate, steady winds, and the
spans are long.
• Aeolian vibrations can be successfully controlled in
most cases using dampers and/or spacer-dampers.
Reliable transmission-line design requires that aeolian
vibration of the conductors is controlled below critical
levels to avoid fatigue damage.
Approaches available to guide an assessment of the
severity of aeolian vibration can be pragmatic, through
design rules based on past experience. Also conditions
can be assessed through measurements on existing lines,
using special-purpose measuring instruments.
Another way is to use an analytical approach to simulate the aeolian vibration behavior of conductor(s) plus
damping devices. This approach can be usefully used to
investigate alternatives in the design or redesign process
and, being aware of its limits, also in the direct design of
the damping system for a new line. The most used analytical models are based on the Energy Balance Principle (EBP), and they give an estimate of an upper bound
to the expected vibratory motions.
The aim of this chapter is to deal with the aeolian vibration phenomenon in such a way to:
• give methods of assessment of the vibration severity
• assess the influence of the line and environmental
parameters on the vibration severity
• give methods of assessment of the need for control
devices
• give methods of assessment of the effectiveness of
vibration control devices.
Whichever approach is used to assess aeolian vibration
severity, it is necessary to have a clear picture of the characteristics of all the elements interacting in the aeolian
vibration phenomenon: wind, vortex-shedding mecha-
Figure 2.1-1 Record of vibration at a point on a
conductor.
Figure 2.1-2 Fatigue failure of conductor strands at
the suspension clamp.
2-3
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
nism, conductors, and their mechanical properties, and
damping devices. The knowledge of these properties
allows an understanding of the phenomenon and the
interaction among the system elements and, finally,
allows for successful control of the vibration level.
As already observed, aeolian vibrations are due to the
wind—in particular, forces induced by vortex shedding
are the cause of this type of vibration. From an aerodynamic and aeroelastic point of view, vortex shedding is a
very complex phenomenon. In addition, some differences arise in the mechanics of the phenomenon depending on whether single or bundled conductors are being
considered. These aspects are covered in Section 2.2.
The conductor types and properties—together with
their mechanical models, self-damping, and bending
stiffness—are discussed in Section 2.3. Damping devices
used to control aeolian vibration are described in Section 2.4.
Once the excitation mechanism and the mechanical system (conductor(s) and damping devices) are characterized, as already observed, the aeolian vibration
phenomenon, from an engineering point of view, may be
simplified through an approach known as the Energy
Balance Principle (EBP). The principle holds that the
steady-state amplitude of vibration of the conductor or
bundle due to aeolian vibration is that for which the
energy dissipated by the conductor and other devices
used for its support and protection equals the energy
input from the wind.
This approach, even if it does not reproduce all the phenomenon’s features, can be used to develop mathematical
models. These models are only an approximation of reality. Thus their results are also an approximation of the
real system response. However, they can be usefully
adopted to estimate an upper bound to the expected
vibratory motions and also to perform parametric analyses with the aim of better understanding the sensitivity of
the phenomenon to the line and the environmental characteristics and to compare the effectiveness of different
damping solutions. Such analyses and comparisons
would be very expensive and time consuming if based
only on measurements on outdoor test spans and/or laboratory spans or on field measurements. As noted above,
however, they are significantly less realistic.
The EBP approach requires that the energy dissipated
by the conductor and other devices used for its support
and protection and the energy input from the wind are
known as a function of the vibration frequency and
amplitude.
2-4
A good approximation of the energy introduced by the
wind to single and bundle conductors can be achieved
through wind-tunnel measurements. Section 2.2 provides
information on such aspects as vortex-shedding frequency, lock-in, synchronization range, modes of vortex
shedding, variables controlling the phenomenon, and
energy input for both single and bundle conductors.
The energy dissipated by the conductor and damping
devices can be determined through laboratory measurements, which are described in Sections 2.3 and 2.4.
From the comparison between introduced and dissipated energies, the steady-state amplitude of vibration
of the conductor can be evaluated together with strains
and stresses in the most significant/critical locations—
i.e., at the suspension clamps or at the clamps of the
other devices installed on the conductor such as spacers,
spacer-dampers, dampers, and other devices.
The main features and controlling variables of the computation programs based on the EBP principle are
described and discussed in Section 2.5.
The effects on line design of the aeolian vibration phenomenon are discussed in Section 2.6. Section 2.7
describes the methods and associated instrumentation
to perform aeolian vibration measurements in the field.
It is important to underline that, currently, several computation methods have been developed on the basis of
the EBP; their performances have been compared by
reference to benchmarks and to experimental data by
CIGRE SCB2 WG11 TF1 (CIGRE 1998, 2005a). The
work of CIGRE SCB2 WG11 TF1 is described in Section 2.5, together with a reliability assessment of the
method.
Analytical methods are used mainly by damping device
manufacturers for the design of damping systems for
new transmission lines and in tenders for damping system adjudication. This was not true up to 20 years ago,
when computation programs were only at a research
stage. However, many damping applications continue to
be based on utilities’ in-house guidelines and suppliers’
experience, in the form of damper application guides—
tables and nomograms.
Efforts continue to improve realism in the analytical
approach. The results of the computations are often
compared to field measurements to test their accuracy
and to guide research to achieve improvements.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
2.2
EXCITATION
2.2.1
Introduction
This section deals with the physics of the aeolian vibration, which is an instability generated by the wind blowing on conductors; it is concerned with the details of the
flow, which interacts with the motion of the conductor.
Aeolian vibration is closely related on the wind side, to
the vortex-shedding phenomenon and its energy input
to the structure and, on the conductor side, to its damping ability. The complexity of this wind-conductor interaction is described by referring to state-of-the-art
research findings. With different sets of experimental
data, a “maximum” level of the wind energy input to a
conductor undergoing aeolian vibration can be defined.
Aeolian vibration can be characterized by its amplitude
(on the order of the conductor’s diameter) and frequency range (3–200 Hz). If insufficiently damped, the
conductor experiences fatigue problems that can result
in failure.
Subsection 2.2.2 describes the vortex-shedding phenomenon resulting from the wind flowing around a stationary cylindrical structure. Historical contributions are
included, as well as a dimensional analysis for a generalization of the available data. In the particular case of a
stationary conductor, the vortex-shedding process is
observed to generate vortices of the Von Karman type
in the wake of the structure. The dimensional analysis of
the primary variables identifies two relevant similitude
criteria—the Reynolds and Strouhal Numbers. The
effect of the Reynolds Number on the configuration of
the vortices in the wake is shown using flow visualizations. These criteria, obtained in the case of a stationary
structure differing from that an oscillating one, remain
relevant since they identify the onset of aeolian vibrations. The criteria are applied to a given span of the
Drake conductor to predict the vortex-shedding frequency.
Subsection 2.2.3 examines the vortex-shedding process in
the case of a vibrating conductor. The onset of this instability occurs at a wind speed for which the vortex-shedding frequency (determined using the Strouhal Number)
approaches a natural frequency of the conductor: the
conductor is then in resonance and stays in resonance for
wind speeds as large as 130% of the onset velocity. The
configuration of the vortices is then shown to be modified
according to the amplitude of the conductor’s motion.
Two new configurations of vortices are reported—the 2S
and 2P types. The previous dimensional analysis is
extended to take into account the dynamics of the structure: it allows the definition of the additional similitude
Chapter 2: Aeolian Vibration
criteria linking the wind power input or the amplitude of
the motion to the conductor properties and the wind
characteristics. As can be expected, the level of both the
wind power input and the amplitude of motion depend
upon the type of vortices acting on the conductor. The
“maximum” of these two possible wind power inputs is
selected for design purposes.
Subsection 2.2.4 presents the available data of the wind
power input in the case of single and mechanically coupled conductors. Subsection 2.2.5 underlines the influence of the topography of the terrain, as well as the
variability of the direction and the intensity of the wind
upon the span of conductors.
2.2.2
Vortex Shedding in the Case of a
Stationary Conductor
This section deals with the flow in the wake of a stationary conductor: the variables of this interaction between
the conductor and the vortices shed in its wake are
defined and regrouped under their dimensionless form.
Flow visualizations obtained at different velocities show
the evolution of the vortex-shedding process. In addition, pressure distributions measured over the cylinder’s
surface are used to demonstrate the effect of this process: the pressure fluctuation due to vortex shedding is
responsible for a fluctuating lift force with a prevailing
frequency equal to the Strouhal frequency fST.
First Observations and Variables Controlling the
Phenomenon
The flow of a fluid interacting with a cylindrical shape
has been observed to generate vortices that are shed in a
downstream wake.
Leonardo da Vinci sketched such vortices downstream
from a stationary pile (Figure 2.2-1). Ancient civilizations also knew that aeolian sound was caused by wind
blowing over a string. Cenek Vincent Strouhal (1878)
formed a dimensionless parameter from his measurements of fST, the frequency of audible tone generated by
wires and rods (diameter d) whirled through the air at
velocity V; this dimensionless parameter, fSTd/V, was to
be defined as the Strouhal Number following a suggestion by Henri Bénard (1926). Adapting Strouhal (1878)
data, Zdravkovich (1985) produced a dimensionless
graph of the variation of the Strouhal Number in terms
of the Reynolds Number, Vd/υ; υ is the kinematic viscosity of the fluid (1.51 × 10-5 m2/s for air at 20°C). In
the range of Reynolds’ number at which aeolian vibrations occur, the value of the Strouhal number is 0.18; as
a consequence, the vortex-shedding frequency f ST is
given by fST = 0.18 V/d.
2-5
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
parameters, S and R, respectively the Strouhal and Reynolds Numbers. One must note that additional variables
may influence the value of the Strouhal Number and the
different coefficients. These are, to name a few, and in
accordance with the factors influencing the boundary
layer: the turbulence content of the oncoming flow, and
the proximity of boundaries such as external walls modifying the flow acceleration around the conductor and
Table 2.2-1 Independent and Dependent Variables
Primary Independent Variables
Description
Symbol
units
Flow velocity
V
m/sec
Fluid density
ρ
kg/m3
Fluid dynamic viscosity
µ
kg/(m-sec)
Cylinder diameter
d
m
m
Cylinder length
k
Roughness surface of the cylinder
m
Primary dependent variables
Figure 2.2-1 Studies of water flow interacting with an
obstacle. Circa 1513 by Leonardo da Vinci from
Pedretti in Galluzzi (1987).
A list of the usual independent and dependent variables
in the case of a long stationary cylinder is given in Table
2.2-1 and that of the dimensionless parameters in Table
2.2-2.
Strouhal or vortex shedding frequency
fST
Hz
Local surface pressure
p
Pa or N/ m2
Lift force (normal to the flow direction)
L
N
Drag force (parallel to the flow direction)
D
N
Table 2.2-2 Dimensionless Variables
Dimensionless Variables
Description
This dimensional analysis shows that the loading coefficients and the vortex-shedding process represented by
the Strouhal number may be functions of three criteria:
the Reynolds Number, the relative surface roughness,
and the aspect ratio.
In the case of conductors, the span is many orders of
magnitude longer than its diameter: for a uniform spanwise wind, the effect of the aspect ratio relative to the
vortex-shedding process is expected to be small, and
two-dimensional conditions are generally assumed.
Secondly, with respect to the relative roughness, experimental data show its effect as small, especially in the
range of the Reynolds Numbers of the conductors in
usual wind exposure (350 < R < 35000). As indicated in
Figure 2.2-2, the effect of the relative roughness is to
induce an earlier critical regime on the drag force coefficient but mostly in a Reynolds Number range past that
of conductors. Compact conductors have relatively
smooth surfaces.
Vortex shedding in the case of a stationary cylinder is
then a phenomenon controlled by two dimensionless
2-6
Symbol
Definition
Reynolds Number
R
ρVd/ µ
Strouhal Number
S
fSTd/V
Pressure coefficient
Cp
(p-pref)/(V2/2)*
Lift coefficient
CL
L/( dV2/2)
Drag coefficient
CD
D/( dV2/2)
k/d
Relative surface roughness
Aspect ratio
/d
c* pref is the static pressure of the oncoming flow velocity,
usually the atmospheric pressure.
Figure 2.2-2 Variation of drag force coefficient for a
circular cylinder, with rough surface, in smooth flow (after
Zdravkovich 1997) with k = surface roughness height.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
the form of the wake (blockage effects in wind-tunnel
tests).
The wake downstream from a stationary has been the
subject of numerous studies and, with the aid of fast
image capture systems, recent flow visualizations have
allowed detailed observations of the vortex-shedding
process. The wake certainly changes with the Reynolds
N u m b e r, a s p r e v i o u s ly r e c o g n i z e d b y s e v e r a l
researchers. Table 2.2-3 shows the evolution of the
vortex-shedding process as the Reynolds Number is
varied.
The fluid flows from left to right in all the visualizations.
From a Reynolds Number of 1 to 41, the symmetry
between the upstream and downstream flow regions is
gradually lost, and standing eddies are formed in the
wake and become increasingly elongated as the Reynolds Number is increased. The vortex pair appears at
R∼6. The standing eddies form a near wake region completed by a steady laminar trail. In the cases of R >35,
the trail begins to oscillate in a periodic fashion, and the
length of the closed near wake gradually reduces as the
Reynolds Number is increased; the wavelength of the
trail gradually decreases with rising Reynolds Number,
and staggered eddies are formed at the end of the closed
near wake (see photo (2,2) of the table). The roll-up of
eddies takes place gradually along the wake until the
pattern becomes “frozen” and carried downstream
Table 2.2-3 Vortex Shedding with Respect to Reynolds
Number Variation
Identification according to (row, column):
(1,1) R=1.1 (Taneda), (1,2) R=9.6 (Taneda), (2,1) R=26
(Taneda), (2,2) R=140 (Taneda), (3,1) R=2000 (Werlé &
Gallon), (3,2) R=10000 (Corke & Nagib); sources: Van
Dyke (1982) and Nakayama et al. (1988).
Chapter 2: Aeolian Vibration
motionless (if a tracer is injected in the “frozen” wake, it
will describe a straight line in the flow direction). Two
rows of staggered eddies are generated to form a
Kármán-Bénard eddy street. The wake remains laminar
until R∼170. As the Reynolds Number is further
increased, eddies or vortices will be shed regularly, but
their states will be modified because of the occurrence of
transition: transition from the laminar to the turbulent
states will progressively move upstream—that is, from
the wake to the shear layer and then to boundary layer.
The photos of the third row of Table 2.2-3 show the typical flow to be expected around a conductor. At R =
2000, the boundary layer is laminar over the front, and
then separates to form a shear layer that breaks up into
a turbulent wake. At R = 10000, the flow pattern
remains almost identical, and one can infer that the
dimensionless variables such as the Strouhal Number
and the force coefficients will vary slightly in this range.
In the particular cases of stationary cylindrical conductors (5 mm < d < 50 mm and 1 m/s < V < 10 m/s), the
Reynolds Number may range from a value of 350 to
35000 and, once it has been determined, the Strouhal
number can be evaluated using Figure 2.2-3.
Consider a 28.143 mm diameter Drake conductor in a
5 m/s wind (10°C): the Reynolds Number is then 9900,
and the Strouhal Number is 0.185 according to Figure
2.2-3. The vortices would be shed at the frequency or
the Strouhal frequency:
fST (Hz) = S∗V(m/s)/d(m) = 0,185∗ 5/0.028 = 33.1Hz
2.2-1
If mixed English units (V in mph, d in inches and f in
Hz) are adopted, the value of the Strouhal number
remains the same but the formula for the determination
of the frequency of the vortex shedding must be modified according to:
fST (Hz) = S ∗V(m/s)/d(m) = S∗ V(mph) ∗17.6/d (in.)
2.2-2
Figure 2.2-3 Relationship between Reynolds Number
and Strouhal Number (Chen 1972).
2-7
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
For a 0.75 inch diameter conductor (IBIS/SD) in an 11
mph wind, the value of the Reynolds number is 6700,
and that of the Strouhal Number remains close to 0.185
according to Figure 2.2-3; in this case, the Strouhal frequency—that is, the frequency at which vortices are
shed downstream from this particular stationary conductor—is 47.8 Hz.
The Wake of Vortices and the Aerodynamic Force
Transfer
The alternate shedding of vortices at the Strouhal frequency in the wake of the stationary conductor induces
an unsteady pressure distribution on its surface. Figure
2.2-4 shows the measured unsteady pressure distributions on such a stationary cylinder at nine instants of
the period of the vortex-shedding process. The pressure
is given in terms of Cp, the pressure coefficient (see
Table 2.2-1), and its scale is defined on the upper left
part of the figure; its value is positive when the arrow
points inside the cylinder, and its intensity is proportional to its length. Superimposed on each distribution
is the instantaneous force coefficient (vector sum of CD
and CL, the drag and lift coefficients) obtained from the
integration of the pressure distribution.
Since the cylinder remains fixed, the incoming relative
flow velocity does not change during the entire vortexshedding process. Almost three-quarters of the cylinder
surface is exposed to negative pressure, the peak suction
shifting from one side to the other as the vortex is
formed. This alternating pressure unbalance is translated in mean and fluctuating loads: the mean and fluctuating drag and lift forces, respectively, in the streamwise and cross-flow directions. As can be observed in
Figure 2.2-4, the process is not fully periodic, but is of
random nature; moreover, it does not occur simultaneously along the cylinder axis, as can be clearly seen in
Figure 2.2-5—i.e., there is a phase lag among the vortices shed along the cylinder axis. The random nature of
the process and a lack of correlation along the cylinder
make the value of the lift force due to vortex shedding
small, if compared to the case of a vibrating cylinder—
as will be better explained in Section 2.2.3.
Theodore von Kármán and Henri Bénard for their pioneering work in this field.
Figure 2.2-7 shows a flow visualization of the near wake
downstream from a stationary circular cylinder using a
fog generator, a laser sheet, and a digital high-speed
camera; half of the cylinder shows lightly on the left of
the figure.
The photo, obtained at a Reynolds number matching
that of a typical conductor, shows the turbulent nature
of vortex shedding in the case of a conductor; it differs
significantly from visualizations obtained at much lower
Reynolds numbers (Koopmann 1967; Figure 2.2-6),
because of the mixing process generated by transition to
Figure 2.2-5 Top view of the inclined filaments of a
vortex wake shedding from a stationary cylinder (R =
200, Frequency = 28 Hz) (courtesy Journal of Fluid
Mechanics and G. H. Koopmann).
Vortices shed downstream from a stationary cylindrical
conductor are named Kármán-Bénard vortices after
Figure 2.2-4 Measured unsteady pressure and force
coefficients at nine instants of a period of vortex shedding
(case of the stationary cylinder) (Zasso et al. 2005).
2-8
Figure 2.2-6 Cross-sectional view of vortex wake
shedding from a vibrating cylinder
(R = 200, cylinder frequency = 28 Hz) (courtesy Journal
of Fluid Mechanics and G. H. Koopmann).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
turbulence in the shear layer downstream separation.
The length of formation of the vortices can be observed
to be on the order of three diameters. In the next section, the vortex street will be shown organized differently in the wake of the conductor as its motion onsets
and increases.
2.2.3 Vortex Shedding in the Case of a Vibrating
Conductor: Aeolian Vibration
This section deals with the effect of the cross-flow
motion of the conductor on the process of vortex shedding and the fluid-structure interaction. Measured pressure distributions and forces indicate different
characteristics due to two additional modes of vortex
shedding, the 2S and 2P modes, as a function of the
vibration amplitude. The onset of aeolian vibration is
defined by a matching between the Strouhal frequency
and one of the natural frequencies of the conductor. A
dimensional analysis, taking into account the dynamic
of the conductor and the flow, leads to the dimensionless amplitude of motion and to a coefficient of power
input by the flow regions. The 2S and 2P modes of vortex shedding are discussed within the general map of the
modes of vortex shedding.
Physics of the Flow and the Modifications Resulting
from the Motion
In the particular range of Reynolds Numbers typical of
aeolian vibrations (4000 to 15,000), the boundary layer
developing from the point of stagnation to the point of
separation remains laminar. Nevertheless, the length for
which the laminar state can be sustained shortens as the
flow speed or Reynolds Number increases. Ballengee
and Chen (1971) have measured the location of the separation point: its angle from the stagnation point varies
almost linearly with Reynolds Number, from 91° at Re
= 104 to 83° at Re = 3.9×104. In the 4000 < R < 15,000
Figure 2.2-7 Kármán-Bénard vortices R = 8800
(Source: photo by P.-O. Dallaire as presented in
Laneville [2005]).
Chapter 2: Aeolian Vibration
range, transition occurs in the shear layer proceeding
from the point of separation; the shear layer then rolls
on itself to form a vortex that is shed downstream in the
wake. The state of the boundary layer upstream of separation is expected to influence the amount of vorticity
contained in the released vortices as well as their configuration—more certainly, if the cylinder is set in motion
and modifies the relative velocity at the edge of the
boundary layer.
Initiation of Aeolian Vibration: Onset and Lock-in
When the velocity of the oncoming flow is such that the
frequency of the vortices shed in the wake of the conductor approaches a modal frequency of the conductor,
the latter, if insufficiently damped, will initiate a
motion—largely in the direction transverse to the
flow—excited by the fluctuations of the lift force due to
vortex shedding. The motion in the in-line direction is
related to the fluctuations of the drag forces that are less
important than the fluctuating lift forces.
This onset velocity, V S, can be calculated using the
Strouhal Number definition (average Strouhal Number
~0.18) and the conductor overhead line’s modal frequency and diameter.
For example, if one assumes a line span with given tension, mass per unit length, and diameter, a modal frequency can be determined, say fn = 26.4 Hz; then, if d =
19 mm (0.75 in.), the value of the onset velocity is:
VS = fST × d/S = fn×d/S
= 26.4×0.75 × 3600/(0.18 × 12 × 5280)
= 6.25 mph
2.2-3
VS = fST×d/S = fn × d/S
= 26.4 ×19/(0.18 ×1000)
= 2.79 m/sec
2.2-4
The experimental evidence shows that aeolian vibrations for a given conductor mode occur rather over a
range of velocities than at a unique velocity and that the
flow velocity at the onset of the conductor motion corresponds approximately to V S. Once the conductor
starts to vibrate, a lock-in effect takes place and the vortex-shedding frequency is controlled by the vibration,
even if the wind velocity changes around the Strouhal
VS velocity. The range of wind velocities around VS for
which the lock-in effect occurs—and vibrations are
excited—is between 90 and 130% of VS. More precisely,
as A, the amplitude (peak-to-peak displacement/2) of
the conductor motion, increases and reaches values on
the order of 0.1d to 0.2d, the vortices in the wake
become driven by the oscillating frequency of the conductor: their shedding frequency is locked-in or synchronized with that of the conductor and a phase
difference can been measured.
2-9
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
To better understand the process of vortex shedding in
the wake of the cylinder at onset, two sets of data are
useful—the first set using the signal of hot wire giving
the instantaneous velocity in the wake, and the second
using the signal of the instantaneous lift force. These
data show the transient regime as the cylinder ceases to
be stationary and its oscillation grows toward a steadystate condition.
Figure 2.2-8 shows the time history of the dimensionless
amplitude A/d, the phase between the hot wire signal
and the cylinder displacement and the rms and dc values of the hot wire signal.
The figure shows clearly that three regimes are present:
the first, at small amplitudes (A/d < 0.1) where there is
no definite phase, and then two more, each showing a
different steady-phase value separated by a sudden
jump. The hot wire signal spectrum shows a peak at the
Strouhal frequency only in the regime with A/d < 0.1;
for the two next regimes, the peak is at the frequency of
motion of cylinder. The three regimes will be each associated with a mode of vortex shedding later: the Von
Kármán mode for which the vortices are shed at the
Strouhal frequency (cylinder almost stationary) and the
2P and 2S modes for which the vortices are shed at the
frequency of the vibrating cylinder either in two pairs or
in two single vortices.
In a map of vortex-shedding modes proposed by Williamson and Roshko (1988), the range 4.4 < V R < 6.7
and dimensionless amplitude A/d, two modes of vortex
shedding are possible, the 2S and the 2P modes. The 2S
mode of vortex shedding is characterized by the shedding of two single vortices per cycle of oscillation, while
the 2P by two pairs of vortices per cycle of oscillation. A
boundary separates these two modes of vortex shedding, the critical curve drawn by interpolations of the
visualization results.
Brika and Laneville (1993), using an aeroelastic model
simulating the half wavelength of vibrating conductors
at their typical Reynolds Numbers (similar to that of
Rawlins [1983]), observed and associated the presence of
bifurcations to the crossing of the critical curve: they
measured the coordinates of the critical curve as the
transient response of the simulated conductors move
from the 2P to the 2S modes of vortex shedding. Their
tests included flow visualizations in support.
The bottom part of Figure 2.2-9 shows a typical bifurcation that they observed in the recordings of the displacement: this displacement can be represented as a
single constant frequency, the amplitude of which varies
with time. Until a given amplitude is reached (A/d <
~0.1), the phase (not shown in the figure) is irregular,
indicating a vortex-shedding frequency changing irregularly from that of the Strouhal frequency to that of the
vibrating cylinder. This chaotic behavior ceases once
A/d is larger than ~0.1, and on both sides of the bifurcation point, a different excitation or mode of vortex shedding is observed. Visualizations of the flow in the wake
region posterior and prior to the bifurcation point are
shown in upper parts of Figure 2.2-9. A sketch is
included for each visualization. The 2S mode can be
observed after the bifurcation point and the 2P mode,
prior to bifurcation.
Figure 2.2-10 reports time histories of the cylinder
dimensionless displacement and of the frequency of the
lift force coefficient at a Reynolds Number of 50,000,
Figure 2.2-8 Transient behavior at R = 8000; from top,
amplitude of the cylinder, phase between the hot wire
signal and the displacement of the cylinder, the rms and
dc values of the hot wire signal (after Laneville and
Dallaire, 2006).
2-10
Figure 2.2-9 Transient response and phase measured at
the antinodes of an aeroelastic model of a conductor (VR
= 5.47, R = 7114) after Brika and Laneville (1993).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
larger than in the previous case. Nevertheless, both sets
of data are in agreement. At the onset of motion, when
the vibration amplitudes are small, the Strouhal frequency is dominant in the lift force spectrum; when the
vibration amplitudes are larger, lock-in occurs, and the
lift force is synchronized to the natural frequency of the
mechanical system.
Both figures clearly explain the lock-in phenomenon:
cylinder motion drives the vortex-shedding frequency.
As can be expected, lock-in occurs at different A/d values for different velocities. Lock-in, or the change from
a Von Kármán to a 2P mode of vortex shedding, will be
identified as a boundary (Laneville and Dallaire 2006).
Figure 2.2-10 shows eight instantaneous surface pressure distributions applied on a conductor within a
period of its motion once the lock-in has happened. In
this particular case, the cylinder dimensionless vibration
amplitude, A/d, is equal to 0.6. This figure is to be compared with Figure 2.2-11 This is the case of the steadystate oscillations. The position of the cylinder on the
sinusoidal curve corresponds to its position in the
motion cycle. The relative velocity consists of the vector
sum of the oncoming horizontal flow velocity and the
sinusoidal transverse velocity of the conductor (shown
as a solid arrow). The figure shows clearly that this relative velocity causes the pressure distribution to shift
position (this is confirmed most of the time by the alignment of the stagnation point with the direction of the
relative velocity), but that the resultant force coefficient,
shown as an open arrow, is much larger that in the case
of the stationary cylinder.
Figure 2.2-10 Frequency of the lift force and
dimensionless vibration amplitude as function of time (VR
= 6.5) (Zasso et al. 2005).
Chapter 2: Aeolian Vibration
The intensity of the local pressure coefficients is also
much larger. The shedding of vortices in these conditions of motion will obviously differ from that of the
stationary cylinder. The frequency of the process of vortex shedding is now influenced by the frequency of
motion and rapidly can lock onto the latter. The configuration of the vortices in the wake will then differ from
the von Kármán mode.
Considering the details of the flow close to the cylinder’s
surface as the structure is set in motion, one deduces that
both the stagnation and separation points are displaced
and that the shear generated in the boundary layer is
modified from that of the stationary structure. This
implies that the vorticity at the separation point, and
consequently the mode of vortex shedding, should be
influenced by both the oncoming flow velocity and that
of the moving surface. More precisely, as the vortex is
formed, it is fed by fluid from the boundary (shear) layer,
the wake, and the external regions. According to the
level of motion, the frequency of the moving cylinder
should perturbate the fluid near the wall; the larger the
velocity of the wall, the more strongly the frequency of
the moving structure will influence and control the vortex shedding. This description contains the ingredients
required for an aeroelastic instability characterized by:
1. An onset caused by a matching between two frequencies, that of the Strouhal frequency and of the structure modal frequency, followed by:
2. A flutter-type response, where the motion of the
structure and its modal frequency control the shedding of vortices. Along this line of reasoning, we
Figure 2.2-11 Surface pressure distribution, resultant
force coefficient, and resultant velocity at eight instants
of a cycle of vibration (A/d = 0.6 and VR = 6.5) (Zasso et
al. 2005).
2-11
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
anticipate some dislocation of the wake in the case of
the X-Y motion of the structure.
damped structures such as overhead transmission lines,
the term 2πζ corresponds to δ, the log-decrement.
Once lock-in is established, the phenomenon has
become nonlinear and hysteretic. The energy from the
oncoming flow has to be shared by both the wake and
the conductor, but more importantly, the dissipation of
energy by the wake vortices can now bivalued and controlled by the motion of the conductor. To better identify these different modes of vortex shedding, additional
variables, describing the interactions between the
oncoming flow, the dynamic of the conductor’s system,
and the wake, need to be defined.
In several references, Sc, the Scruton Number, is
a d o p t e d i n l i e u o f t h e “ Re d u c e d D a m p i n g ” o r
Additional Variables Controlling the Phenomenon
In the case of a stationary conductor, the variables controlling the fluctuating pressures or forces were the Reynolds and Strouhal Numbers, while the dependant
variables were the force and pressure coefficients. In the
lock-in range, the Strouhal Number remains useful to
calculate VS, the velocity at the onset, and the end of the
range of excitation. Within the range, the frequency of
the vortices does not correspond anymore to the Strouhal frequency.
Table 2.2-4 Independent and Dependent Variables
Primary Independent Variables
Description
Symbol
units
Flow velocity
V
m/sec
Fluid density
ρ
kg/m3
Fluid dynamic viscosity
µ
kg/(m-sec)
Cylinder diameter and length
d,
m
Cylinder mass per unit length
mL
kg/m
Cylinder system modal frequency
(in vacuum)
fn
Hz
Cylinder system vibrating frequency
fv
Hz
Cylinder system structural damping
coefficient
C
N-sec/m
Primary Dependent Variables
A
m
Pinput
Watts/m
CC
N-sec/m
Amplitude of the oscillations (at antinode)
Since the conductor, a vibrating mechanical system, is
extracting energy from the flow, additional variables
taking into account this facet of the phenomenon must
be introduced: fv, the vibrating frequency of the conductor; m L , its mass per unit length; , the length of the
conductor; and C, its structural damping. The additional dependent variables are A, the amplitude of
motion of the conductor or P input , the average power
input by the wind to the conductor over a cycle of vibration and per unit length. For rigorousness sake, a distinction will be maintained between fn , the conductor
modal frequency in vacuum, and fv, the vibrating frequency, although these two frequencies are very close to
each other if the conductor is exposed to the wind. Table
2.2-4 gives the dimensional analysis of an increased
number of variables that control vortex-induced vibrations of a cylinder in the lock-in range. The effect of turbulence is not included but will be discussed later.
From the eleven primitive variables, eight dimensionless
variables should be deduced. Table 2.2-5 resumes the
results of the dimensional analysis.
Power per unit length
Definition
Cylinder system critical damping coefficient
Table 2.2-5 Results of the Dimensionless Analysis
Dimensionless Variables
Description
Symbol
Definition
Reynolds Number
R
Mass ratio
m*
ρVd/ µ
mL/(ρd2)
fv/ fn
Frequency ratio
Reduced velocity
VR
V/(fvd)
Structural damping Ratio
ζ
C/ CC
A/d
Pinput
/(ρd4 fv3)
Reduced amplitude
Power input coefficient per unit length
/d
Aspect ratio
In the lock-in range, the Strouhal Number is then
replaced by VR, the reduced velocity, which has the form
of the inverse of the Strouhal Number.
The critical damping for a taut string and a given mode,
C C, is defined as [(2 (m L /2) ωn ) or (4 π (m L /2)f n )],
where (mL /2) is the modal mass of a taut string with
mass per unit length equal to mL. In the case of lightly
2-12
Combined Dimensionless Variables
Logarithmic decrement (lightly damped
case)
Scruton Number
δ
2πζ
Sc
2πζm* or
δm*
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
“Reduced Decrement.” The value of these dimensionless variables are related according to Sc = “Reduced
Damping”/2. Care should be exercised.
As already seen in the previous paragraphs, the vortexshedding phenomenon is very complex, and as a consequence, the power input is a function of the A/d amplitude of vibration as well as of the reduced velocity VR.
For design purposes or the selection of a damping device
to absorb the wind power input to the conductor, it is
useful to determine, for a given amplitude of vibration,
A/d, the maximum power input coefficient per unit
length, Pinput max/(ρd4 fv3), over all the reduced velocities:
Pinput max/(ρd4 fv3) = f [A/d]
2.2-5
2.2.4 The Wind Power Input
This section deals with the different power inputs
absorbed by a conductor undergoing aeolian vibration.
Using dimensionless variables defined in previous sections and considering the different modes of vortex
shedding, the cases of single conductors and conductors
in tandem are discussed. The actual observations and
measured data are presented in order to be applied in
the section dealing with the system response.
Introduction
Once a conductor is in motion, as observed in the preceding sections, there are several modes of vortex shedding, each of them being closely linked to its amplitude,
A/d, and the reduced velocity VR. The fact that different
values of A/d and modes of vortex shedding can be
present at the same reduced velocity also implies different wind power input coefficients. Since conductors are
mounted relatively close to each other in bundles, additional interactions may influence the responses.
Chapter 2: Aeolian Vibration
The Case of Single Conductors
Vortex-induced vibration of cylindrical structures has
been the subject of several studies. In the case of a rigid
cylinder mounted on an elastic system (such as springs),
the steady-state maximum amplitudes of oscillation can
be predicted using several empirical correlations. Figure
2.2-13 shows four of these correlations, and the agreement is fairly good. From Figure 2.2-13, once the modal
damping for a given cylinder has been determined, the
Scruton Number can be easily calculated and the
steady-state maximum amplitude is obtained.
An alternative and more used approach to determine
the amplitude of aeolian vibrations consists in using the
Energy Balance Principle (EBP), already mentioned in
Section 2.1.
This approach allows one to estimate an upper bound to
the expected vibratory motions. The steady-state amplitude of vibration of the conductor or bundle due to aeolian vibration is that for which the energy dissipated by
the conductor and other devices used for its support and
protection equals the energy input from the wind.
Figure 2.2-12 Geometry of conductors in tandem.
In the case of a vibrating conductor, either solitary or
mounted in the upstream position of a tandem, one
expects similar amplitude and wind power input in both
configurations.
The flow picture changes significantly, especially for the
downstream conductor in a tandem configuration since
its oncoming flow can be the wake of the upstream one
(see Figure 2.2-12). The response of the downstream
conductor becomes dependent upon the motion of the
upstream conductor—the mode of vortex shedding contained in the wake as well as upon the distance and the
geometry of the arrangement. To add to this already
complicated interaction, the shielding effect produced
by the upstream conductor modifies the intensity of the
flow velocity “seen” by the downstream conductor.
Figure 2.2-13 Amplitude of the aeolian vibrations in the
case of single conductors as function of the Scruton
Number.
2-13
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
A methodology adopted to compute the wind power
input is based on buildup tests made in still air and in
the airflow at different reduced velocities. The first set of
data allows for the determination of the system damping (once the aerodynamic damping in still air has been
removed), and the second set allows for the calculation
of the net transfer of energy from the wind to the
mechanical system. A typical set of data is shown in
Figure 2.2-14, where the net power input has been calculated at given vibration amplitudes for different
reduced wind velocities.
The maximum energy input curve is finally determined
by the envelope of all the curves, as shown in Figure
2.2-14. Figure 2.2-15 shows the experimental data of the
maximum power coefficient measured by several
researchers. Most of the data were obtained in wind tunnel measurements with low turbulence, smooth flow,
and controlled velocities. Although different methodologies were adopted in these studies, the agreement is
fair. Some of these tests are related to a vibrating rigid
cylinder, while others are related to a flexible cylinder
undergoing a sinusoidal deflection shape.
The numerical data underlying the curves in Figure
2.2-15 are reported in Appendix 2.1, together with a
table giving the coefficients of a polynomial fit of each
set of data.
The ordinate of Figure 2.2-15 is not dimensionless
because of the absence of the air density at the denominator, as defined in the Table 2.2-2. The dimensionless
power input is 20% smaller than the value of the figure,
since most of these data were obtained in the case of
wind conditions in the range of 10°C to 30°C (ρ =
1.2 kg/m3). Under extreme conditions such as -40°C, the
Figure 2.2-14 Wind power input curves measured for
different reduced velocities; the value of the reduced
velocity VR corresponds to the ratio of V/VS divided by
the Strouhal Number (after Belloli et al. 2003).
2-14
density of air rises to 1.52 kg/m3 and should be taken
into account.
The data for the maximum wind power coefficient of the
different tests reported in Figure 2.2-15 can be averaged
at given values of A/d and then fit with the empirical
function:
Pinput max /(ρd4 fv3) = 32(A/d)3/2
in the range 0.01 < A/d < 0.6.
The Case of Conductors Coupled Mechanically
When mechanical coupling is combined with aerodynamic coupling, the response of the cylinders in bundle
becomes even more complicated (Laneville and Brika
1999b), because of the mechanical energy transfer
within the bundle from one conductor to another.
Although much more research needs to be done in this
domain, some observations are deduced from the available data:
• The steady-state amplitude of the cylinders in bundle
has a magnitude similar to that of a single cylinder
but occurring at multiple wind velocities, the peak at
a different wind velocity.
• The phase imposed to the motion of the cylinders
plays an important role in the aerodynamic exposure
of the downstream cylinder.
• The modes of vortex shedding for the individual cylinders resemble that of the conductors coupled aerodynamically but with a different timing.
In a reported case (Figure 2.2-16) of two cables of the
bundle coupled mechanically by a rigid spacer (Belloli et
al. 2003), the specific power input for a single cable and
for one cable of the twin bundle has been observed to be
similar. However, the report CIGRE WG B2.11.04 2005
(CIGRE 2005b) points out that field recordings have
shown that bundled conductors mostly vibrate at ampli-
Figure 2.2-15 Maximum wind power input coefficient
per unit length in the case of a solitary conductor (after
Brika and Laneville 1995).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
tudes smaller than single conductors of the same size as
the subconductors of the bundle.
Further research is certainly required to better understand the physics of the flow and its effect on the
response of the conductors.
2.2.5
Conductors and Wind Exposure
This subsection presents the flow environment to which
a conductor is exposed.
A conductor is exposed to a multifaceted environment
along its route. The wind is an important component of
its environment and causes steady and fluctuating loadings and can trigger instabilities such as aeolian vibration. Figure 2.2-17 shows generic wind profiles used to
describe natural winds to which a conductor is submitted. These natural winds result from the atmospheric
pressure gradients, and meteorological observations
indicate that the mean wind velocity varies with altitude
as in a boundary layer. As can be deduced from the figure, the roughness of the earth surface (shown using
scaled objects) plays an important role in the height of
the boundary layer (the gradient height) as well as in the
mean and fluctuating (gusting) velocities. In Figure
2.2-17, the mean velocity reaches the value of 100% at
the gradient height.
Chapter 2: Aeolian Vibration
others) deal with wind actions on structures; they
already provide guidelines and recommend a methodology to define the velocity profile and the turbulence
characteristics. The design engineer is referred to the
code prevailing in the country of the installation to
identify the properties of the incoming flow.
A power or logarithmic law is usually adopted to
describe the mean wind profile:
V(Z)/Vref =(Z/Zref)α
or V(Z)/Vbasic=KT ln(Z/Z0) range Zmin Z 200m
2.2-6
where α varies according to the topology of the terrain
as does the value of Z0, Zmin, and KT in the case of the
logarithmic profile. The meteorological properties are
measured in practice at the standard height Zref =10 m.
The value of Vbasic and Vref, to be used in order to evaluate the applied static loads on the structure supporting
the conductor, are based on probabilistic meteorological
data such as the period of return of an event.
Instabilities such as aeolian vibration and galloping may
be initiated at much lower flow velocities. Nevertheless,
the concept of the velocity profile is needed to evaluate
the span-wise variation of the flow velocity and turbulence along the conductor. Figure 2.2-18 shows such a
Accordingly, the relevant characteristics of the flow at
the location of the conductor must be determined in
order to evaluate the static and dynamic interactions
between the wind and a conductor. They are the mean
wind speed and the turbulence. These characteristics, as
expected, are functions of the topology of the local terrain and meteorological data. Several national codes
(Eurocode, Canadian NBC, and Australian AS among
Figure 2.2-17 Typical categories of atmospheric wind
profiles according to several national codes for load
calculations (Australian Wind Loading Code).
Figure 2.2-16 Comparison of the specific maximum
power input as function of the dimensionless amplitude
in the cases of a single cable and the same cable in the
twin bundle mechanically coupled by a rigid spacer
(after Belloli et al. 2003); (N.B. u/D = A/d).
Figure 2.2-18 Wind velocity profile incoming on the
conductor.
2-15
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
conceptual representation of the span-wise variation of
the wind incoming on a conductor, where x is a coordinate along the conductor. In the frame of reference of a
stationary conductor, the local wind speed amounts to a
function of time. Meteorological observations show that
fairly stable mean values of the wind are provided if an
averaging period of approximately one hour to ten minutes is chosen. This tendency for the mean to stay relatively steady is of considerable significance since it
allows the concept of “local stationarity” to be applied
and becomes basic to wind-tunnel testing. Laboratories
specialized in wind engineering simulate the local properties of the turbulent wind as shown in Figure 2.2-19.
Table 2.2-6 shows the atmospheric boundary layer characteristics in the case of the four typical categories of
terrain adopted in several national codes.
In the case of a flat terrain, the turbulence intensity (Iu),
according to Eurocode 1, can be evaluated using the following approximation:
Iu = 1/ln(Z/Z0).
2.2-7
Types 2 and 3 exposures will be used to determine the
variation of the flow velocity in the case of a span of
Drake conductor with its ends at the same altitude and
having a 25.7 m sag; both ends will be mounted at 100 m
(typical of a river crossing) in the first example and at
50 m in the second. The Drake conductor (overall diameter = 28.143 mm, mass per unit length = 1.6281 kg/m)
adopts a catenary form under its own weight. The sag
value (25.7 m) has been calculated for the case of a
600 m horizontal span and a 28.024 kN horizontal ten-
Figure 2.2-19 Typical wind velocity time history (Galleria
del Vento, Politecnico di Milano).
Table 2.2-6 Boundary Layer Characteristics for Four
Typical Terrain Categories
Boundary Layer
Definition Properties
Power Law
Properties
α
Type 1 Open terrain
Type 2 Farmlands
At the higher altitude (100 m), the mean flow velocity
over this span of Drake conductor remains fairly uniform (5% variation), while at the lower altitude (50 m),
this variation at least doubles for both types of terrain
and becomes more important as the terrain roughness
increases (15% variation in the case of Type 3).
Since aeolian vibration occurs in narrow ranges of
velocities (the onset velocity plus or minus 20%, as will
be shown in the following sections), the span of the conductor may be partly triggered in resonance because of
its exposure to a nonuniform wind speed.
With respect to the turbulence characteristics, the span
of Drake conductor at 100 m is exposed to lower and
more uniform levels of turbulence than at a 50 m altitude: their average and variations are, respectively, for
Type 2 and 3 terrains, 13.4%±0.3% and 17.6%±0.5% at
1 0 0 m , t o b e c o m p a r e d wi t h 1 5 . 3 % ± 0 . 9 % a n d
21.1%±1.6% at 50 m. The comparison between the flow
characteristics of a first location at 100 m in farmlands
terrain and that of a second one at 50 m in suburban
region shows that the environmental surroundings
expose a given span to widely different fluid-loading
conditions.
These observations of the widely different types of exposure show the relevance of determining the wind conditions at the location of the conductor and the effect that
they may have on the conductor’s response.
The turbulent fluctuations of the natural wind cover a
wide range of frequencies; the ones susceptible to cause
dynamic wind effects on a structure such as a conductor
are within the frequency range of 0.001 Hz and 10 Hz,
the range known as the micrometeorological peak in the
spectrum of the natural turbulent wind. The intensity of
these turbulent fluctuations, as indicated earlier, varies
with terrain.
According to their frequencies, these turbulent fluctuations interact differently with a conductor.
Table 2.2-7 Flow Variations for Types 2 and 3 Terrain
Exposures
Logarithmic Law
Exposure
Type 2 Farmlands
Type 3 Suburban
Terrain
0.17
Altitude z
50 m
100 m
50 m
0.19
V(z-sag)/V(z)
89%
95%
85%
94%
8m
0.22
Iu (z)
14.5%
13.1%
19.5%
17.2%
16m
0.24
Iu (z-sag)
16.2%
13.7%
22.7%
18.1%
Z0
Zmin
Iu
0.12
0.01m
2m
0.16
0.05m
4m
Type 3 Suburban terrain
0.22
0.3m
Type 4 Urban area
0.30
1m
2-16
sion. Section 2.5.2 gives the details of the methodology
to determine the sag. Table 2.2-7 resumes the results.
100 m
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
In the high-frequency range, turbulence, represented as
small-scale eddies, modifies the boundary layer that
develops from the stagnation point on the conductor
and induces an earlier transition in the shear layer by an
increased mixing. Small-scale eddies traveling on the
upstream stagnation line are responsible for the effect.
The eddies located away from the stagnation line deviate
outside the boundary layer (Laneville et al. 1975). From
their data, Modi and El Sherbiny (1975) conclude that
the effect of small-scale turbulence on a stationary cylinder is equivalent to an increase of the Reynolds Number as expected from an increased mixing.
In the case of the low-frequency range (< 0.1 Hz), the
turbulence, represented as large-scale eddies, may be
considered as a slow variation of the mean wind speed.
If this slowly varying wind speed is restricted to fw, a single-turbulence frequency, the periodic wind speed
becomes simply:
Chapter 2: Aeolian Vibration
Noiseux et al. (1988). The fluctuations of turbulence are
represented as a normal distribution around a selected
wind mean speed, and the wind energy input for this
selected turbulent wind is then calculated as the
weighted sum of several energy inputs in nonturbulent
steady wind at the different mean wind speeds within the
normal distribution. The intensity of turbulence in this
simulation corresponds to the standard deviation of the
normal distribution.
An analytical approach has been used by Diana et al.
(1979) to define reduced wind energy input curves in
turbulence conditions (see also Section 2.5.2).
The unsteady nature of the atmospheric wind and its
interaction with a vibrating conductor are still research
subjects to be pursued.
2.3
CONDUCTORS
2.3.1
Introduction
V(t) = Vmean + ΔV sin(2fw × t)
where ΔV and Vmean are, respectively, the intensity of the
wind fluctuation and the mean wind speed. Wind tunnel
tests of aeolian vibration using such a wind speed control (Laguë and Laneville 2002) indicate the following:
• Most of the characteristics of the aeolian vibration
observed in steady wind such as the 2S and 2P modes
of vortex shedding are present but slightly modified.
Bifurcations are observed.
• The steady-state amplitude of vibration is modulated
at a frequency fw.
• If the fluctuation of wind due to turbulence is small
enough to stay in the range of synchronization (or
lock-in range) previously defined (from 90 to 130% of
the Strouhal velocity), it can affect only in a small
amount the maximum amplitude of vibration due to
vortex shedding.
• If the fluctuation of the wind velocity due to turbulence is large enough for the wind speed to exceed the
synchronization range, the maximum amplitude of
vibration detected in a constant wind cannot be
reached in this case, and as a consequence, the maximum power input for a given Vmean is expected to be
lower than that measured at the same constant wind
speed.
Natural wind includes a combination of eddies, from
small to large scales, and one concludes that the effect of
the time and space variations of the natural wind on the
aeolian vibration of a conductor remains a complex
problem.
An attempt to simulate statically the effect of turbulence
is, nevertheless, proposed by Rawlins (1983, 1998) and
The conductor of an overhead power line is considered
to be the most important component of the overhead
line, since its function is to transfer electric power, and
its contribution toward the total cost of the line is significant. Conductor cost (material and installation costs)
associated with the capital investment of a new overhead power line can contribute up to 40% of total capital costs of the line. Consequently, much attention has
to be given to the selection of a conductor configuration
to meet present and predicted future load requirements.
Continuous changes in the cost of suitable conductive
materials for bare conductors, changes in mechanical
requirements, changes in electrical requirements,
improvements in manufacturing technology, and a more
recent focus on line upgrading and the related increase
in mechanical tensions in the conductors have led to
dynamic development, resulting in a variety of possible
options and applications. The move has been from simple copper wire or copper-based bare conductors in the
early days to more cost-effective solutions, such as aluminium and variations of aluminium alloy conductors.
This section covers four broad areas related to conductors: the geometric, mechanical, and electrical properties of conductors; inner conductor mechanics and, in
particular, the bending stiffness of conductors; conductor self-damping; and suspension hardware.
2.3.2
Types and Basic Properties of Conductors
Overhead transmission lines transmit electric power
using stranded cables called conductors. In fact, conductors are the only power-carrying component of a
transmission line and account for a significant propor2-17
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
tion of the overall costs of the line, which can be up to
40%. Conductors have to sustain a range of electrical,
mechanical, and environmental “loads” over the projected life expectancy of a line, which can be well over 50
years of service. As a result, special attention is given to
the selection of their constituent materials and their layout and design. As part of this book’s comprehensive
coverage of the effects of conductor vibration, this section summarizes the common types and basic properties
of conductors employed today in transmission lines in
this chapter (Aluminum Association 1982; Southwire
Company 1994).
The most widely used form of conductors is that of layers of round wires stranded, first, around a so-called
core, which can be of the same material or different, and
then around each other. In order to keep the integrity of
this construction, the stranding takes place in alternating directions from layer to layer. For aluminum conductors, the usual convention is to wrap the outer layer
with a right-hand lay, as opposed to copper conductors,
which have a left-hand lay in their outer layer. For conductors with equal-diameter wires, each lay has six wires
more than the layer beneath it, which provides, in most
of the cases, a good “fit” in every layer (see Figure
2.3-1). However, in order to tailor the conductor for various strength-to-weight ratios, unequal-diameter wires
are often used with success. Details of conductor design
and fabrication are covered extensively in a recent publication (Rawlins 2005a).
Most of the requirements for conductor design come
from mechanical constraints. The electrical aspects of
conductors are usually limited to current density, electrical resistance, and the associated power loss and voltage gradient, which are solved by adding area and
adjusting the outside diameter or using multiconductor
bundles on the line. Some overhead conductors are constructed from commercially pure aluminum, known as
AA1350-H19 and referred to as All Aluminum Conductor (AAC) or Aluminum Stranded Conductor (ASC).
Because of its relative low strength-to-weight ratio
(which is the most important mechanical criterion),
these types of conductors are suitable for short spans in
distribution networks, and for areas where ice and wind
Figure 2.3-1 Structure of a typical conductor.
2-18
loads are limited (Figure 2.3-2), as well as for flexible
bus bars in substations.
For added strength, various aluminum alloys have been
developed, and these conductors are referred to as All
Aluminum Alloy Conductor (AAAC) or Aluminum
Alloy Stranded Conductor (AASC). Early versions of
these alloys used magnesium as the main alloying element, which had strain-hardening properties. This produced mechanical characteristics that vary with wire
diameters, which is not desirable. For this reason, most
alloys used today are of the AA6000 series, which are
heat-treatable and more consistent. It should be noted
that any improvements in strength are usually to the
detriment of conductivity (see Figure 2.3-3).
When a better strength-to-weight ratio is desired, a
strength member has to be added to the conductor. This
can be achieved by adding an aluminum alloy core to
the AAC to create an ACAR (Aluminum Conductor
Alloy Reinforced), but it is usually done with steel wires
(see Figure 2.3-4), which offer much higher strength-toweight ratios than aluminum alloys. Aluminum Conductor Steel Reinforced (ACSR), the most commonly
used conductor type, and Aluminum Alloy Conductor
Steel Reinforced (AACSR) are variations of the above
conductors. In a few special cases—for instance, under
Figure 2.3-2 Bare conductors—typical use.
Figure 2.3-3 Properties of aluminum and some alloys.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 2: Aeolian Vibration
extreme corrosive (marine) environments—the use of
ACAR eliminates the galvanic reaction that is possible
between the steel and the aluminum. Copper conductors may be used because of their superior electrical
characteristics, but offer very poor mechanical properties and, therefore, are seldom selected.
Figure 2.3-4 Properties of steel.
Apart from the “standard” conductor designs, there are
also a number of special designs, such as conductors
with high steel content for very long spans (river crossings), smooth-body conductors, expanded conductors,
etc. (see Figure 2.3-5). One way to improve and tailor
conductors to special situations is to shape the aluminum wires. Over the past 30 years, the development of
trapezoidal, and more recently Z-shaped, wires has contributed to the improvement of conductor design. These
conductors make better use of their space compared to
Figure 2.3-5 Cross sections of special conductors.
2-19
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
round-wire conductors, and are, therefore, called “Compact.” The shape of the wires allows for an infinite number of area and strength-to-weight ratios and also
allows them to be used with some alloys. Noteworthy is
the Self-Damping Conductor (SDC), which allows
much higher conductor tensions without the harmful
effect of aeolian vibrations, and which, since the 1970s,
has seen significant use in North America (McCulloch
et al. 1980).
A number of national and international standards exist
for these conductors—ASTM in the United States, CSA
in Canada, CENELEC, and IEC—all of which regulate
the various constructions and properties of these conductors.
High-Temperature Conductors
The need to transport an ever-increasing amount of
electrical power, coupled with the difficulties in obtaining approval for new transmission corridors, has forced
utilities to find creative ways to increase the capacity of
their lines—through so-called uprating (CIGRE 2004a).
One of the solutions has been to increase the operating
temperature of the conductors. The benefit of hightemperature operation is the added current-carrying
capacity gained by exceeding the traditional thermal
limits of conductors. The two main disadvantages of
high-temperature operation, ignoring the higher electrical losses, are the loss of strength of the aluminum
portion of the conductor (at these temperatures a socalled partial annealing takes place) and the added sag
produced at high temperature. Whereas in some areas of
the world, and in particular in Japan, this difficulty was
avoided by the use of special heat-resistant aluminium
alloys, in North America, the solution was found to be
the use of an ACSS (Asselin 2002).
ACSS (Aluminum Conductor, Steel Supported), formerly known as SSAC (Steel Supported Aluminum
Conductor) and patented in 1974, is a composite concentric lay-stranded conductor consisting of a stranded
steel core with one or more layers of 1350-0 aluminum
wires. This high-temperature conductor constitutes
approximately 15% of all the American line installed
and is gaining some recognition in Europe. At a glance,
there is almost no difference in appearance between an
ACSR and an ACSS. They have the same geometry,
including the possibility of being compacted. There are,
however, important differences in the properties and
performance of the two constructions.
ACSS can carry a significant increase in current compared with ACSR. They can operate continuously at
200°C (392°F), and up to 250°C (482°F). Since the alu-
2-20
minum wires have been annealed in the factory, there is
no concern of the conductor losing strength at high
temperature. The annealing process also increases the
conductivity of the aluminium, from 61% IACS to typically over 63% IACS.
When the ACSS is heated up, the aluminum wires elongate and quickly shift their load onto the steel core. At
this point, the conductor essentially behaves as a steel
conductor—that is, the thermal elongation and the
modulus of elasticity are those of the steel core. When
the temperature is brought back down, the aluminum
wires have been stretched and will not return to their
original length Therefore they will carry a lower load.
The low stress in the aluminum wires decreases the
effects of aeolian vibrations and increases the selfdamping of the conductor, since their relative looseness
can act as an impact damper. This is why it is generally
recommended to prestress this conductor.
In an ACSS, the minimum elongation of the annealed
aluminium wires is approximately 20%. Contrary to an
ACSR, where the steel core is limited to its strength at
1% elongation, this property allows the conductor to
utilize the steel core at its full strength. This fact makes
the use of extra-high-strength steel more attractive. The
conductor may have a rated strength almost as high as
its equivalent ACSR. Moreover, the high elongation of
the aluminum means that the creep properties of the
conductor are ruled by the steel core, which usually
exhibits very low creep. Like most other conductors,
ACSS constructions can be compacted. An ACSS compact can carry approximately 20% more current, due to
its increase in area.
A multitude of conductors developed in Japan use aluminum zirconium alloys. Many variations have been creat e d t o t a i l o r t h e c o n d u c t o r s t o t h e o p e rat i n g
temperature. Some of them incorporate a greased gap
between the core and the aluminum layers to allow the
components to slide better on one another. In addition,
there is a great variety of metallic core materials to further reduce the sag at high temperature (CIGRE 2004a).
A small addition of zirconium in aluminum tends to
increase its recrystallisation temperature, thus retaining
its original strength after an excursion at higher temperature. The maximum attainable temperature depends on
the amount of zirconium alloyed in the aluminum. The
conductivity of these alloys varies from 55 to 60% IACS,
with a strength from 170 up to 250 MPa. Elongation is
similar to 1350-H19 wires. The continuous maximum
temperature can be in excess of 250°C.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
These conductors usually replace the traditional steel
core of the ACSR with a core made of composite material. One of these products consists of alumina fibers in
an aluminium matrix. The strength of this core is comparable to a steel core and has a lot of other useful properties. The alumina fibers have a lower ther mal
expansion than aluminum or steel, the core has great
resistance to corrosion, exhibits no creep, has no undesirable magnetic properties, and can operate at high
temperature. The ampacity gains are estimated at 1.5 to
3.0 times the equivalent ACSR.
2.3.3
Inner Conductor Mechanics
“Inner conductor mechanics” refers to the calculation
of the stresses and strains in the individual conductor
wires because of external loads/deformations of the conductor. Science has not yet created a universally
accepted and applicable mechanical model to perform
this calculation.
Definition of the Problem
It is well known—and extensively treated in the other
parts of this book—that aeolian vibration leads to conductor fatigue. The fatigue mechanism of vibrating conductors is a complicated chemomechanical process
called fretting fatigue (see Chapter 3). Fatigue failures
frequently occur at fret locations in the vicinity of the
last point of contact between overhead electrical conductors and their supporting suspension clamps. Failures occur as minute cracks resulting from fretting, and
cyclic strain variations propagate through individual
conductor strands. This process is a highly localized
phenomenon, involving complex contact stresses
between strands in the vicinity of the clamp. However,
conductor strand crack initiation and growth are sensitive to the macro-strain levels maintained at the clamp,
and hence fatigue failures are sensitive and closely
related to macro-strain levels.
Fretting fatigue depends on many factors. These factors
shown in Figure 2.3-6 are probably the most important
ones, because they greatly influence the stress pattern at
the interstrand contacts, where as explained above,
fatigue is initiated. Because these interstrand stresses
evade measurement, it is useful to assess the factors via
suitable conductor models and to understand their
dependence on the various conductor design parameters, such as number and size of wires, lay angles, etc.—
keeping in mind that models always remain more or less
crude approximations of reality.
A better understanding of inner conductor mechanics
could thus lead to a reasonably accurate prediction of
the parameters (a) to (c) in Figure 2.3-6, which in turn
may enable a quantitative approach to conductor
fatigue. The ultimate vision could be (CEA 1986) to
Chapter 2: Aeolian Vibration
reduce full-size conductor fatigue tests to fatigue tests of
individual conductor wires and thus significantly reduce
the complexity of the problem.
In particular, there is a demand to bridge via adequate
modeling of a vibrating conductor, the difference existing today between the industry standard for vibration
measurements (see Chapter 3), which is based on bending amplitudes Yb—this being defined as the vibration
amplitude peak-to-peak of conductor with respect to
clamp measured at a distance of 3.5 in. (89 mm) from the
last point of contact of the conductor with the clamp—
and the endurance limit of the conductors, which is
based on stresses σb or strains εb (see Figure 2.3-7).
Progress in inner conductor mechanics could also lead
to a better analytical description of conductor selfdamping and of the damping properties and thus the
modeling of the dynamic behavior of Stockbridge
dampers.
a)The macroscopic or bulk stresses (or strains) in the individual wires
of the conductor.
b)The relative movement dx between the wires.
c)The normal forces acting FN between two adjacent wires and the
resulting contact stresses at the crossing “points.”
Figure 2.3-6 Parameters influencing fatigue at the
crossing point of two conductor wires.
Figure 2.3-7 Parameters describing vibration near
the suspension location.
2-21
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Bending Stiffness
The bending stiffness of a section, EI, is quantified by
the product of its moment of inertia relative to a given
axis and by the modulus of elasticity of the material of
the section. Applied to a stranded conductor, the bending stiffness is the sum of its components’ stiffness, as
shown in Equation 2.3-1.
EI C = ∑ ( E i I i )
2.3-1
where EIC is the flexural stiffness of the conductor, and
Ii and Ei are the moment of inertia and Young’s modulus of wire i, respectively.
The moment of inertia Ii relative to the neutral axis of
the conductor, for each wire is given by:
I i = I 0 i + Ai d i
2
2.3-2
Where I0i is the moment of inertia of wire i relative to its
own axis, Ai is the area of the wire, and di is the distance
from the wire's neutral axis to the conductor's neutral
axis. Referring to Figure 2.3-8, di is defined as:
d i = rn sin(α i )
2.3-3
EIc then becomes,
EI C = ∑ Ei ( I 0i + Ai rn2 sin 2 (α i ))
2.3-4
This is the exact method of calculating EIC for a given
rigid section. This method assumes that all the wires act
together as a solid. The value that it yields is the maximum attainable value of stiffness for the conductor, and
for this reason, it is usually referred to as EImax. It can
be shown (Dane and Hard 1977; Appendix II in Papailiou 1995) that the sum of sin 2 (a i) over all k wires of a
layer is numerically equal to ki/2, which makes the calculation of Equation 2.3-4 significantly easier.
ignores the factor rnsin(ai) in Equation 2.3-3. The calculation of EIC is given by:
EI C = ∑ ( E i I 0i )
2.3-5
Equation 2.3-5 yields a much lower value for EIC. This
is the lowest theoretical value that this factor can attain.
For this reason, it is called EImin. “Exact” calculation of
the bending stiffness also sometimes includes a factor to
take into account the lay angle of the conductor. This
results in 5 to 10% lower stiffness values, which is not of
great concern in the context of the other uncertainties in
determining this parameter, as will be explained in the
following. As an example, in Appendix 2.2, both bending stiffness values—i.e., EI min . and EI zp — are calculated for a 795 kcmil Drake ACSR.
Calculation of EI for conductors with Z-shaped or trapezoidal wires becomes quite tedious, since the flexural
rigidity of each wire assumes a different value depending
on its location within the conductor cross section.
Values to be used for modulus of elasticity of commonly
used conductor metals are given in Table 2.3-1.
The Conductor Bending Phenomenon
Qualitatively, when a conductor is bent, the movement
of its wires is suppressed by the friction forces acting
between the wires and mainly between the wires of two
adjacent layers. Mechanically, this situation is described
in a first approximation by the axial force equilibrium of
a differential wire element (see Figure 2.3-9) (Papailiou
1997).
Table 2.3-1 Modulus of Elasticity for Various Wire
Components
Component
ASTM
Designation
IEC
Designation
E
(GPa)
Aluminum
wires
• 1350-H19
• 6201-T81
• A1
• A2, A3
68.9
"
210
"
Steel wires
• Galvanized Steel
• S1, S2
(GA)
• High-Strength
• S3
Galvanized Steel (HS)
Another theoretical value of EIC assumes that all the
wires act independently of one another and therefore
• 20SA Type A
• 20SA type B
• Aluminum-Clad Steel
• 27SA
(AW)
Aluminium• 30SA
clad steel wires
• 40SA
Figure 2.3-8 Conductor cross section with
parameters for bending stiffness calculation.
2-22
Figure 2.3-9 Axial force equilibrium of a differential
(d…) wire element.
162
155
140
132
109
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 2: Aeolian Vibration
Figure 2.3-10 Calculated bending stiffness EI of ACSR Cardinal as a function of the
conductor curvature κ with the tension T as parameter.
This way, the wires develop a bending strain as if the
conductor were behaving as a solid body with the wires
sticking to each other. Above a certain bending conductor curvature (or corresponding conductor deflection),
the interlayer friction forces R caused by the interlayer
compression forces N, which themselves are caused by
the wire tension force Z, are not enough to prevent a relative wire movement dx (see also Figure 2.3-10). In this
case, the wires slip relative to each other, and their bending strain (and related stress) develops as though they
bend around their own neutral axis. Additionally, they
retain the maximum strain (and stress) value just before
slip, which is constantly distributed over the wire cross
section and causes a secondary tensile stress. It can be
shown that slip starts at the neutral axis of the conductor, where the maximum wire displacement also takes
place (see also Section 3.2.1 and in particular Figures
3.2-1, 3.2-2, and 3.2-3). This process leads to a variation
of the conductor bending stiffness during bending. At
small bending amplitudes, the bending stiffness can be
calculated as though the wires are “welded” together,
and is called EImax (Equation 2.3-4). At large bending
amplitudes, the bending stiffness can be calculated as
though the wires are completely loose and do not interact with each other. and is called EImin (Equation 2.3-5).
In between these two extremes, a more or less smooth
transition takes place, as indicated in Figure 2.3-10.
It is worth noting that—since the bending stiffness varies with curvature and so along the bent conductor (Figure 2.3-13)—classical Bernoulli-Euler bending theory,
which postulates that plane sections remain plain during
bending, cannot be applied to the conductor as a whole
(although it is still valid for the bending behavior of the
individual conductor strands). Calculations of the
deflection made by this model compared to experimental measurements showed very good correlation,
although the model exhibits a relatively high sensitivity
to the coefficient of friction chosen. Also the “stiffening” of the conductor—i.e., the dependence of its flexural stiffness on the applied tensile load—and the
hysteresis due to friction losses during a loadingunloading cycle could be demonstrated by this model
(Papailiou 1997) (Figure 2.3-11). Dastous (2005) and
Hong et al. (2005) have recently further developed this
concept. In another recently proposed model (Rawlins
2005), the deflection is treated analytically for a singlelayer cable, showing impressively that the deflection
curve near the clamp (fixed end) is in reality a 3-D curve
with displacements not only in the bending plane but
also—though much smaller—perpendicular to it.
The fact that the conductor bending stiffness varies during bending also becomes evident in the nonlinearity of
the load-deflection curve of a messenger wire (Figure
2.3-12) and is the base for power dissipation in the messenger wire of the Stockbridge dampers (Sturm 1936;
Claren and Diana 1969b; Knapp and Liu 2005).
Figure 2.3-11 Schematic of load-deflection diagram of a
conductor showing hysteresis.
2-23
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
because it changes the vibration loop length (see also
Chapter 1).
Figure 2.3-12 Hysteresis loops obtained at 16 Hz on
19-strand cable with four different values of shaker
vibration amplitude.
The correct values of cable stiffness for the damper messenger wire can be obtained from the hysteresis loops by
tracing a line through the center of the x/y axis at the
angle of the loop to the x axis. The stiffness decreases
with increasing amplitude of rotation (or displacement)
and tends to a constant, as predicted by the model.
In the case of dampers, a useful gain can be made from
messenger cable stiffness nonlinearity. As a result of a
decrease in stiffness with increasing cable deformation
due to increased vibration amplitudes, the resonance
frequencies of the damper move toward lower frequencies. If the conductor excites the damper at a frequency
below its nominal lower resonant frequency, then such a
resonance frequency shift improves the damper
response and partially mitigates the causes of increased
vibration amplitude.
Also, the fact that the conductor bending stiffness
changes along the vibration loop and most significantly
near the suspension clamp (Figure 2.3-13) is to be considered during vibration analysis and assessment
Figure 2.3-13 Variation of the bending stiffness near
the suspension clamp.
2-24
Hardy and Leblond (2003) also described the bending
process from the point of view of contact mechanics.
The contact interface between wires of adjacent layers is
assumed to be an elliptical region (see Figure 2.3-21). At
rest, this area is considered to be “stuck”. As soon as
bending is applied to the conductor, there is tangential
traction created in the contact interfaces between layers,
and a “slip” zone develops on their common periphery.
This is where microslippage occurs. As bending
increases, so does this elliptical ring, to a point where
ultimately there is virtually no “stick” area left. This
mechanism explains, among other things, some of the
variations found in the measurements of the bending
stiffness of a conductor.
This conductor model was tested on a 380-A1-37 (Petunia AAC) with average values of EIC of around 60% of
EI max (for small values of conductor curvature)—i.e.,
the conductor in this model is assumed never to reach
EImax, irrespective of the amount of bending.
There is significant literature on the mechanical modelling of stranded ropes, but only a few papers have been
presented, specifically for the bending of overhead line
conductors. Cardou and Jolicoeur (1997) and more
recently Cardou (2006) have published excellent and
extensive reviews on this subject, and the interested
reader is referred there for more details.
Idealized Dynamic Bending Stresses
Because of the complexity of the bending process of a
conductor under tension, as described above, a simplified model was developed in 1965 (Poffenberger and
Swart 1965), and since then, has been used almost exclusively and extensively in order to calculate “idealized”
conductor stresses. These are used as a surrogate or reference stresses, in order to compare the vibration intensity of different conductors as determined by bending
amplitude measurements in the field. They thus determine the so-called safe stress limits or fatigue endurance
limits (accumulated stress or S/N (Wöhler) curves)
(CIGRE WG 22.04 1979c) (also see Section 2.7 and
Chapter 3).
The Poffenberger-Swart approach assumes that the
vibrating conductor near the clamp (where the bending
amplitudes measurements are also taken (Figure 2.3-2),
acts as a fixed cantilever beam under tension, with an
imposed deflection (half the bending amplitude) at the
free end. The bending stiffness of this beam is taken as
the sum of the bending stiffnesses of the individual
wires, EI min , which are considered to be parallel, and
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
with the assumption that the wires are loose with no
interstrand friction. Using classic bending theory, it is
possible to calculate the deflection curve of the conductor near the fixed end (clamp), its curvature at that location, and the resulting stresses in the wires of the outer
layer. The outer layer wires are assumed to bend around
their own neutral axes, which are coincident with their
centers of gravity. It can be shown that the formula for
the wire stress (or strain) obtained this way is a good
approximation for the stress obtained if the differential
equation of a taut vibrating string with constant bending stiffness is used (see Chapter 3, Appendix 3.1). The
so-called Poffenberger-Swart formula ultimately relates
(measured) bending amplitudes with (calculated) wire
stresses in the outer conductor layer and is derived in
Chapter 3.
The Poffenberger-Swart formula has been an extremely
valuable tool for the assessment of vibration severity of
overhead line conductors for more than 40 years.
Because of its relatively easy and straightforward application, it has been adopted by most researchers in this
field and has become the de facto standard for the calculation of a nominal conductor stress at the outer layer
for a given (measured) bending amplitude. Because of
this quasi-standardization, its main contribution has
been to enable approximate but very important comparative statements to be made on the effects of a certain
vibration level on the (mechanical) safety level (limit
stress) of a conductor.
Since the introduction of this formula, certain reservations have been raised regarding its universal application without considering the approximations underlying
Chapter 2: Aeolian Vibration
its development. Small vibration amplitudes accumulate
the highest number of cycles in the field and thus have a
significant effect on conductor endurance. Poffenberger
and Swart noted that there is significant uncertainty in
this region.
The main reason for this observation is that, intuitively,
the individual strands of the conductor would be
expected to stick together at small bending amplitudes.
Consequently, the conductor would behave as a solid
rod, responding to the bending load with its maximum
bending stiffness. Theoretically, this should lead to significantly higher stresses in the wires for small bending
amplitudes than those predicted by the Poffenberger
Swart formula. With increasing bending amplitudes,
more and more wires slip and the conductor bending
stiffness comes closer to EImin. In this case, the Poffenberger-Swart formula becomes a good approximation for
the wire stresses in the outer layer (see Figure 2.3-14).
Various approaches have been taken to overcome this
problem, such as using empirical factors for the bending
stiffness etc., but none of them achieved wide acceptance. Also, there have been some publications (Claren
and Diana 1969a; Ramey and Townsend 1981; CEA
1986) presenting strain measurement results on conductors that do not agree with the Poffenberger-Swart formula. Finally the application of the Poffenberger-Swart
formula leads to different so-called safe vibration stress
levels (limit stresses) for multilayer and single-layer conductors, respectively, differing by almost a factor of
three (8.5 MPa for multilayer vs. 22.5 MPa for singlelayer conductors, see Chapter 3).
Figure 2.3-14 Bending strain vs. bending amplitude: comparison between strains measured at the clamp
(Est 1, Est 2, and Est15 indicate the location of the strain gauges shown in Figure 2.3-12) and strains
calculated by the Poffenberger-Swart formula (PoffenSw) for a Drake conductor at 20% RTS.
2-25
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Despite being based on rather crude approximations,
there are several reasons why the Poffenberger-Swart
formula gives reasonable results when checked in the
laboratory by simultaneous bending amplitude/stress
measurements (see Figure 2.3-15).
1. The formula was initially, and often subsequently,
verified on conductors in commercial or custommade suspension clamps, which clearly strongly deviate from the fixed end assumed by the analytical
development of the formula. This means that the
measured stress, which is compared with the formula,
depends heavily on where the strain gauge is placed
laterally with respect to the fixed end for the actual
clamp—i.e., the location where the tangent to the
deflection curve is horizontal (the first derivative
being zero there). Even for small distances x away
from that location, the stresses σb decline quasiexponentially with distance, showing values closer to
the Poffenberger-Swart formula.
2. The maximum stress in the wires is not necessarily on
the wire top where the strain gauges are normally
placed. This stress depends not only on the change of
magnitude of the strand curvature vector but also on
its change of direction. Depending on conductor
geometry, this stress is displaced along the conductor
and the wire perimeter—i.e., measured values tend to
be smaller than the actual maximum wire stress val-
ues, thus coming closer to stresses calculated with the
Poffenberger-Swart formula.
3. Laboratory spans are short compared to field spans,
and the tensile stresses before bending in the individual wires tend to differ from each other considerably,
although the sum of these stresses over the conductor
cross section equate to the external tensile load. Since
the bending stresses depend on the tensile stresses, it
is probable that the measured stress show much lower
values in some wires—i.e., closer to the PoffenbergerSwart formula than expected by the stick-slip model.
It is worth noting that the above statements are not to
be understood as a criticism to the Poffenberger-Swart
formula, the value of which cannot be overemphasized,
but as an indication of the complexity of the matter, the
limits of the simple conductor model, and possibly also
areas of future research.
2.3.4
Stress Distribution in the Conductor Wires
The tensile loads and the tensile stresses acting on the
individual wires of a conductor are often important to
know. For monometallic conductors, these stresses are
calculated in a first approximation by dividing the conductor tension T by the total metallic area of the conductor (this being the sum of the areas of the conductor
wires). For bimetallic conductors, they are calculated
under the assumption of constant strain for all conductor wires. Neglecting the influence of the helical shape
of the wire, which has a small effect on the stress distribution, the following formulas apply:
σ Al =
E Al T
E Al AAl + E St ASt
2.3-6
for the aluminum wire stress σAl, and:
σ St =
E St T
E Al AAl + E St ASt
2.3-7
for the steel wire stress σSt, with T the conductor tension, and ΑAl and ΑSt the cross sections of aluminum
and steel, respectively.
Equation 2.3-6 can be simplified, taking advantage of
the fact that in SI units, the modulus of elasticity of steel
E St equals approximately three times the modulus of
elasticity of aluminum EAl, i.e.:
Figure 2.3-15 Sources of possible errors when
checking the Poffenberger-Swart formula.
2-26
σ Al =
T
AAl + 3 ASt
and σ St = 3 σ Al
2.3-8
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Evidently these simple formulae do not cover many
important factors in the stress distribution/redistribution in the wires, such as the different behavior between
the core strands and the enveloping strands in the creep,
thermal expansion, and material nonlinearities, etc.
When these issues have to be considered, the use of dedicated software is recommended.
2.3.5
Temperature and Creep Effects
Conductor length in a given span varies when the temperature or the external loads vary, and this variation in
conductor length also implies a variation in conductor
tension, which has to be taken into account, given the
predominant role that conductor tension plays in vibration issues (see Sections 2.3.6 and 2.6). With the socalled state change equation (for details see Kiessling et
al. 2003), it is possible that, if the conditions are known
(tension of conductor or sag) in one state (defined by a
certain temperature), then the conditions of the conductor at any other state (temperature) can be calculated.
Special attention is drawn here to the situation of a temperature drop (e.g., in a cold winter night) in relative
short spans. In this case, the state change equation leads
to a considerable increase in tension in the conductor,
which can have detrimental effects on its vibration
behavior. This is demonstrated in Figure 2.3-16 for a
Drake conductor with a span length of 200 m. For the
short span, the tension in the conductor increases by
50% (from 31 to 42 kN) by a temperature drop from to
+10 to -20°C.
A further issue is related to temperature variations in
composite (mainly ACSR) conductors. As the thermal
expansion coefficients of steel and aluminum are different (aluminum is twice that of steel), there is a load shift
taking place between aluminum and steel, and this is
Figure 2.3-16 Tension over ambient temperature in a
200 m for 795 kcmil Drake ACSR.
Chapter 2: Aeolian Vibration
dependent on the temperature. For a temperature
increase, the load shifts from aluminum to steel, and the
opposite is true for a temperature decrease. In this case,
the aluminum strands of the conductor have to carry an
extra load (see Figure 2.3-17) (Ziebs 1970). This can be
critical in the winter period, where this unfavorable
characteristic coincides with the highest tension in the
conductor (Figure 2.3-16) and is important for vibration assessment.
Creep
When a material is subjected to a mechanical stress over
an extended period of time, a permanent change occurs
in its internal molecular structure. As a direct consequence of this, conductors experience permanent elongation under tension, even if the tension level does not
exceed “everyday” levels. This permanent elongation
caused by everyday tension levels is called “creep.”
Creep can be determined by long-term laboratory tests,
which are used to generate creep versus time curves
(CIGRE 22.05 1972, 1981; IEC 1995). Creep in aluminum conductors is quite predictable as a function of
time and obeys a simple exponential relationship. Creep
of steel strands is much less significant and is normally
neglected. Due to this fact, creep in the aluminum
strands reduces their tensile load and increases the load
in the steel core strands. This load shift depends also on
the ratio of aluminum to steel (Figure 2.3-18) (Ziebs
1970; CIGRE WG 22.04 1979c).
Although there cannot be any load shift but only creepinduced stress relaxation in monometallic conductors
like AAAC, this phenomenon is of great advantage for
bimetallic conductors in a vibration regime. By reducing
Figure 2.3-17 Significant load increase at low
temperatures in the aluminum wires of ACSR
Drake strung at 20% RTS.
2-27
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 2.3-18 Load shift (given as a difference in stress Δσal due to creep in the aluminum
wires of ACSR conductors with a constant load of 25% RTS at a temperature of 20°C over
time and over aluminium to steel ratio AAl/ASt).
the static loads in the aluminum strands, higher vibratory bending stresses may be sustained. At the same
time, smaller tensile loads in the aluminum strands facilitate strand movement and result in increased selfdamping because of frictional losses. This and other
related issues are covered in Section 2.3.6.
2.3.6
Conductor Self-Damping
Conductor self-damping describes a physical characteristic of the conductor that defines its capacity to dissipate energy internally while vibrating. For conventional
stranded conductors, energy dissipation is due to structural causes—i.e., reciprocating frictional micro-slip
within the multitude of tiny contact patches between
overlapping individual wires, as the conductor flexes
with the vibration wave shape.
This characteristic is important because it governs the
response of the otherwise undamped conductor to vortex-induced excitation (aeolian vibrations) over much of
the frequency range of interest. It, therefore, determines
the range of frequencies where vibration dampers may
be needed. Methods for measuring conductor flexural
self-damping have been specified in an IEEE Standard,
which came into force in 1978: Standard 563-1978
“IEEE Guide on Conductor Self-Damping Measurements” (IEEE 1978) and is practically identical to
CIGRE 1979. To some extent, all conductors are able to
dissipate a portion of the mechanical energy received
from the wind. A single strand of a wire, rod, or tube
possesses a small amount of self-dissipation in the form
of material damping, which exists as frictional dissipation at a molecular level. This type of self-damping is
normally quite low, so vibration problems may be
readily anticipated on single-strand systems.
With stranded conductors, the damping is considerably
greater, since the losses induced by relative motion
between strands are added to the material damping.
2-28
Conductor self-damping is nonlinear, appearing as a
curve if dissipated power or energy is plotted against
resulting conductor strain or amplitude. Plotting of
these relationships on log-log paper usually results in a
fairly straight line for tests run at a given frequency. If
tests are made at various frequencies on a particular
conductor at a fixed tension, a series of parallel straight
lines is normally observed, each line representing a
result from a particular frequency (see Figure 2.3-19).
Effect of Tension
It may be seen from Figure 2.3-20 that when tension is
increased, the self-damping is decreased, and consequently the vibration amplitude is increased, especially
for high frequencies, where the difference in self-damping for different tensions is pronounced.
It is important to note that the vibration levels would be
different were other materials of different strength, such
as aluminum alloys and high-strength steel, substituted
Figure 2.3-19 Power dissipation characteristics
(Power dissipated per unit length) of a Drake
conductor tensioned at 28,500 N (20% RTS) versus
(antinode amplitude/conductor diameter).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
for the aluminum or steel of ACSR 564/72, the conductor that is represented in Figure 2.3-20.
This point is important, because as discussed in Section
2.6, it has sometimes been assumed that conductors
strung at equal percentages of their strength would
experience the same level of vibration and would be
equally susceptible to aeolian vibration damage. The
assumption is reliable for practical purposes within narrow classes of conductor type and size, but certainly not
between classes of conductors as dissimilar as ACSR,
aluminum alloy conductors, or steel ground wires. For
example, serious operational problems have resulted by
assuming that EDS limits established for multilayer
ACSR conductors could be used with aluminum alloy
conductors. The experimental data now available indicate that the self-damping properties are different at the
same tension expressed as a percent of rated strength. In
addition, the resistance to fatigue damage is different for
the two conductor types (see Chapter 3).
Dissipation Mechanism
Energy in a vibrating conductor is dissipated through
friction due to the relative motion of the wires (see Figure 2.3-1). A simple formula to estimate the bending
amplitude for which this so-called macroslip starts is
given in the discussion by Papailiou (2000) relating to
the paper by Diana et al. (2000). It is less evident, however, that energy would still be dissipated at the wirecore interface without any gross slipping over any segment taking place, as described in Section 2.3.3. In practice, examination of conductors from the field and from
laboratory fatigue tests does not show the fretting that
testifies to gross sliding, except near clamps.
Chapter 2: Aeolian Vibration
This phenomenon is explained by considering that the
“points” of contact between two wires are actually elliptically shaped areas (Figure 2.3-21) (Hardy et al. 1999).
The capacity of these mating surfaces to drive the wire
into a uniform displacement across the contact strip
grows from zero on each side of the strip to a maximum
at the strip center-line. This means that some slip, called
microslip, occurs on each side of the contact strip as
soon as some friction forces appear at the contact interface, which causes the energy dissipation leading to selfdamping. As the friction forces grow, the “slip” region
also grows, while the inner”stick” region narrows down.
It is worth noting that almost all self-damping in a
vibrating conductor is associated with the energy dissipation mechanism, as described above, between the
wires of the outer layer and the so-called penultimate
layer just below it.
Measurement of Conductor Self-damping and
Associated Problems
Conductor self-damping is generally measured in a laboratory test span, as sketched in Figure 2.3-22. The experimental methods described below are also used for the
laboratory testing of damping hardware (see Section 2.4).
The test span comprises two massive blocks, 30 to 90 m
(98 to 295 ft) apart, onto which the conductor to be
tested is strung to the required tension and held rigidly.
The conductor is then excited at a sequence of resonance frequencies at controlled antinode amplitude by
means of an electromagnetic shaker (IEEE 1978). More
Figure 2.3-21 Elliptical interface between adjacent
layers.
Figure 2.3-20 Self-damping of ACSR 564/72 over the
frequency for various conductor tensions at a free span
angle (for a definition, see Section 3.2, Equation 3.2-6.)
of 10 min. (Kiessling et al. 2003).
Figure 2.3-22 Test span arrangement for self-damping
measurements.
2-29
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
details on the test arrangement and the measurement
procedure are also given in Section 2.4.
Several problems exist in dealing with a test program
intended to provide data on the self-damping of a particular conductor. Self-damping is influenced by conductor tension, so that tests are necessary at various
conductor tensions. It is necessary to be certain that
losses assigned to the conductor were not due to other
sources. Loss of energy through end fixtures or support
hardware must be either reduced to a minimum or properly accounted for in the measurement system.
In the artificial excitation of the indoor test span by
means of an attached vibration drive system, the vibration exciter becomes a part of the system being measured. If the mass of the moving system within the
shaker is high, conductor distortion is induced in that
portion of the span where the shaker is attached.
Springs or soft couplings are sometimes used to overcome this effect or to allow greater motion at the drive
point than the shaker is capable of generating.
Apart from the main energy loss due to the cable transversal motion, some other phenomena take place in the
experimental span, also giving energy losses; these
extraneous effects must be carefully evaluated and or
eliminated. Energy dissipation is mainly due to:
• Cable clamping system at the span ends
• Local deformation induced by the device used to
force it to vibrate
• Cable motion in the air (aerodynamic drag)
• Torsional and other transversal motion; the mode of
cable vibration should be examined to ensure the
absence of this kind of motion.
In an actual span, the contribution to the overall energy
dissipation given by the span ends is less significant than
in a laboratory testing span due to the reduced length of
an experimental span with respect to actual spans.
Finally, taking account of the aerodynamic dissipation
depends on the methods used to calculate the energy
introduced in the line by the wind.
Also proper conductor conditioning is an important
prerequisite for repeatable test results, itself a formidable task. Any excessive looseness in the aluminum layers
should be eliminated from the conductor by artificial
aging—i.e., by prestressing it at the highest tension at
which the tests are to be made for a minimum of 2 hours
and, preferably, overnight. The terminations should be
pressed onto the conductor from the span end, in order
to prevent looseness from being introduced back into
the test length by this very action.
2-30
The methods to measure the self-damping of cables are
essentially two: the Power method (PM) and the Inverse
Standing Wave Ratio method (ISWR). As these methods are widely described in IEEE (1978) and CIGRE
(1979a), only a brief summary is given here.
Power Method (PM)
The cable is tensioned on the experimental span and is
forced to vibrate at one of its resonant frequencies, with
both amplitude and frequency being controlled by
means of an electrodynamic shaker.
When a stationary condition is reached, the energy
introduced by the shaker to the span is equal to that dissipated by the span over one cycle of vibration. The
energy introduced in the cable—and largely dissipated
by its self-damping mechanism—is calculated by measuring the force F developed between the cable and the
shaker and the displacement of the forcing point μF. The
result is then given by the formula:
Eintroduced = Ediss = π F μ F sin(φ )
2.3-9
where φ is the phase between force F and displacement
μF.
The power dissipated per unit length (Pdiss) by the cable
is then given by: Pdiss = Ediss f /L, where f is the excited
natural frequency and L is the laboratory span length.
The non-dimensional damping coefficient, ζ, which is
another way of expressing conductor self-damping, can
be calculated by dividing the energy dissipated by the
cable Ediss by the maximum kinetic energy of the cable
Ek,max , according to the following relationship (Ginocchio et al, 1998):
ζ =
1 Ediss
4π Ek ,max
2.3-10
being the maximum kinetic energy of the cable given by
the formula (L =span length, ω = circular natural frequency = 2πf, A = antinode vibration amplitude, m L
conductor mass per unit length):
Ek ,max =
1
mL Lω 2 A2
4
2.3-11
While the application of this method is quite simple
since it requires a limited number of measurements, all
the external dissipation is part of the total calculation of
the cable self–damping, and special care must, therefore,
be devoted to reducing all these external loss sources.
For instance, in a laboratory span, it is comparatively
easy to determine the total amount of vibration energy
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
dissipation in the span, because it is equal to the total
amount of energy introduced into the system. This
would be quite sufficient for determining the selfdamping of the conductor if all the loops of the span
had equal energy dissipation. Unfortunately, the loops
at the ends of the span and at both sides of the shaker
behave quite differently from the rest of the span, having
an energy dissipation that can be much higher than that
of all of the rest of the span. As the energy dissipation of
the conductor is, to a first approximation, proportional
to the square of the curvature, it is easy to explain the
large dissipation of energy near the end of the span.
Therefore, in order to provide correct self-damping
data, it is absolutely necessary to separate the endpoint
damping from the free span self-damping. Also, the
largest error in the free span damping occurs at the
lowest measured frequencies, because of the difficulty in
separating the free span damping from the much larger
endpoint losses. The end loop problem can be avoided
by mounting the span termination on a wide, flat bar of
sufficient strength to accommodate the span tension but
also flexible enough in the vertical direction to allow it
to bend readily. This procedure has the undesirable
effect, though, of including the end termination in the
test span.
Inverse Standing Wave Ratio Method (ISWR)
Another measurement method resulting from the work
of Tompkins et al. (1956) is based on the measurement
of nodal and antinodal amplitudes along the test span.
To understand the principle involved, it is necessary to
trace the waves leaving the vibration shaker as they are
reflected at the span ends. The shaker is assumed to be
attached near one of the span terminations. Impulses
induced by the shaker travel to the far end of the span to
return as reflected waves. If no losses are present in the
system, the incident and reflected waves are equal. Perfect nodes are formed where the two waves meet and
pass. That is, zero motion exists at the nodes. The antinodes have an amplitude equal to the sum of the incident
and reflected waves. If losses are present in the system,
however, motion appears at the nodes. The amplitude of
this motion is the difference between the incident and
the reflected waves. The ratio between nodal amplitude
and antinodal amplitude is indicative of the dissipation
within the system. Where low span losses are present,
the very fine measurements necessary for determining
nodal amplitude can pose a problem.
From an electromechanical analogy—but also a
mechanical reformulation of the problem is possible
(Tompkins et al. 1956)—the mechanical power Pi flowing in one section of the cable is given by:
V2
Pi =
S i Tm
2
2.3-12
Chapter 2: Aeolian Vibration
with:
V =ω A
Si =
ai
A
(inverse standing wave ratio - ISWR)
where ai is the amplitude of vibration in a node and A
that of an antinode.
The power dissipated between the node j and the node k
will be:
P = Pk – Pj
2.3-13
And the power dissipated per length unit will be:
Pdiss =
Pk − Pj
nv
2.3-14
λ
2
where nv is the number of nodes between k and j, and λ
is the wave length.
Considering the kinetic energy of the portion of cable
between the two nodes:
Ek ,max =
1 2 2 mL 1
Aω
2
4 f
T
nv
mL
2.3-15
the value of the nondimensional self-damping coefficient ζ is given by:
ζ =
Sk − S j
π nv
2.3-16
The advantage of this method is that the measured dissipation relates to the considered portion of cable only;
therefore, the estimated self-damping value is not
affected by the above-mentioned factors (that is, span
ends and shaker-cable link).
The main problems that the method presents are the
correct estimation of the node positions and the measurement of the node amplitude of vibration, which is a
very small value on the order of a few micrometers,
since as happens with small quantities; an error in the
antinode vibration amplitude significantly changes the
self-damping estimation.
Decay Method
Application of the vibration decay test to transmission
line conductors provides a simple method of evaluating
conductor self-damping in laboratory spans (Hard and
2-31
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Holben 1967). This method, if correctly employed, can
give a first approximation of the value of the self-damping
at all amplitudes in one trial—i.e., it is very quick and
easy, requiring in its simplest form just one vibration
transducer measuring the decay after the exciter (Diana et
al. 1986). The cable is forced to vibrate at one of its natural frequencies, and then the exciter is stopped. The rate
of decay is a function of the system losses.
If a lightly-damped system (ζ<<1) is left free to vibrate
from a forced resonance condition, it undergoes a transient decay of motion that looks like Figure 2.3-23.
In highly damped spans, the decay is reported by some
authors in the form of a step curve (Slethei and Huse
1965). This is probably due, as observed by the authors
themselves, to the transient induced by the exciting force
disconnection. A method to avoid this problem is to
provide an elastic link between the cable and the exciter.
This should be soft enough to dynamically uncouple the
cable from the forcing device.
Considering two successive peaks (Figure 2.3-23) and
the log-decrement δ as:
⎛
⎞
e −ζω0t X cos(ωt + φ )
⎛ Xi ⎞
δ = ln ⎜
⎟
⎟ = ln ⎜⎜ −ζω0t +T
X cos(ω (t + T ) + φ ) ⎟⎠
⎝ X i +1 ⎠
⎝e
2.3-17
simplifying:
δ = ln ( eζ ω T ) = ζω0T
0
2.3-18
if ζ<<1, as in the case of cables, we can consider T as a
function of ω0—i.e.:
T = 2π/ω0 giving: ζ =
δ
2π
The ideal mode of excitation places the shaker within
the end loop of the span. Although the shaker need not
be at an antinode, it will show significant motion, and
the shaker force will be at a relatively low value. The frequency of this type of excitation is slightly lower than
the frequency observed for the nodal-type drive. Release
Figure 2.3-23 A decay trace.
2-32
of the shaker creates little or no disturbance of the decay
pattern. Ideal decay records show an essentially exponential decay, which can be transformed electronically
into straight-line recordings through the use of logarithmic converters. In some cases, a transfer of energy may
occur between the horizontal and vertical response of
the span, although the initial conditions imposed vertical excitation. When this happens, erratic recordings
may be observed. Normally, these occur at certain frequencies that are not prevalent enough to influence the
entire program, and these frequencies can be avoided.
Another possibility is the use of paired vertical and horizontal transducers connected to a vector-resolving circuit. This procedure properly accounts for both vertical
and horizontal span losses, but is not generally necessary in most test programs.
The main concern that this method presents is that,
when the exciter is stopped, it becomes an unwanted
loss source if it is not separated from the cable itself.
With proper precautions, the shaker can be disconnected without inducing an unwanted impulse into the
system. The primary means of avoiding this comes from
the observation that for nearly the same frequency, two
conditions of drive may exist. The one to be avoided is
the nodal drive, in which very small motion exists at the
shaker under conditions of high force input. If the
shaker is located near one of the span terminations, the
short section of conductor between the shaker and the
termination is practically motionless, and the span acts
as if the shaker were a termination. When the shaker is
released, a shift to the true span termination takes place.
This induces a traveling wave, which upsets the decay
measurements, producing a response of the type
reported by some authors (Slethei and Huse 1965).
One method of disconnecting the shaker is shown in
Figure 2.3-24. The shaker is coupled to the span
through a link mechanism that is held shut by a length
Figure 2.3-24 Fuse wire system disconnecting a
shaker from a test span; this double exposure
shows the mechanism both closed and open.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
of fuse wire. Opening of the link is accomplished by
blowing the fuse.
To improve the results, it is possible to calculate the
energy transferred from the cable to the shaker during
the decay with the same setup already described for the
power method. However this shaker loss is usually one
order of magnitude less than that of the cable.
It is, therefore, possible to remove the cable self-damping from the total dissipation, but the end losses are still
included in the measurement.
Measurement Results
Data measured in the laboratory span are generally
expressed empirically through a power law:
Pdiss =
P
Al f m
=k n
L
T
Chapter 2: Aeolian Vibration
above empirical rule, self-damping determined in short
laboratory spans could be extrapolated to actual much
longer spans.
IEEE (1978) and CIGRE (1979a) standards recommend
that the measurement results be presented in diagrams
as illustrated in Figure 2.3-19, showing the power dissipated per unit conductor length, as a function of the
ratio of the antinode displacement amplitude to conductor diameter for each loop length and corresponding
frequency and tensile load T.
Table 2.3-2 from CIGRE 22.11 TF1 (1998) summarizes
the exponents obtained by a number of investigators for
Equation 2.3-19, together with the method of measurement used, the test span length, span end conditions,
and number of conductors and tensions tested.
2.3-19
in which P/L describes the power per unit length dissipated by the conductor, k is a factor of proportionality,
A is the antinode displacement of vibration, f is the frequency of vibration, while l, m, and n are the amplitude,
frequency, and tension exponent, respectively. Using the
The power method for conductor self-damping measurements on laboratory test spans with rigidly fixed
extremities produces empirical rules with an amplitude
exponent close to 2.0 and a frequency exponent close to
4.0—in comparison to about 2.4 to 2.5 and 5.5, respectively, for the ISWR method and PT method with pivoted extremities.
Table 2.3-2 Comparison of Conductor Self-damping Empirical Parameters
Investigations
End
Cond.
Span length
(m)
n° cables
x tensions
ISWR
N.A.
36
1x2
PT
M.B.
46
3x3
ISWR
N.A.
36
1x8
ISWR
N.A.
36
1x1
PT
M.B.
46
1x1
l
m
n
Method
Tompkings et al. (1956)
2.3-2.6
5.0-6.0
1.9 (1)
Claren & Diana (1969b)
2.0
4.0
2.5;3.0;1.5
Seppä (1971), Noiseux (1991)
2.5
5.75
2.8
Rawlings (1983)
2.2
5.4
Lab. A (CIGRE 22.01 1989)
2.0
4.0
Lab. B (CIGRE 22.01 1989)
2.3
5.2
PT
P.E.
30
1x1
Lab. C (CIGRE 22.01 1989)
2.44
5.5
ISWR
N.A.
36
1x1
Kraus & Hagedorn (1991)
2.47
5.38
2.80
PT
P.E.
30
1x?
Noiseux (1991) (2)
2.44
5.63
2.76
ISWR
N.A.
63
7x4
Tavano (1988)
1.9-2.3
3.8-4.2
PT
M.B.
92
4x1
Möcks & Schmidt (1989)
2.45
5.38
2.4
PT
P.E.
30
16 x 3
Mech.Lab Politecnico di Milano
(2000)
2.43
5.5
2
ISWR
P.E.
46
4x2
ISWR: Inverse Standing Wave Method
PT: Power Method
N.A.: Non applicable
M.B.: Massive block
P.E.: Pivoted Extremity
(1): extrapolated
(2): Data corrected for aerodynamic damping
2-33
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Such differences in the above exponent values, together
with those in the k factor of proportionality, may lead to
large differences in the predicted self-damping values.
Figure 2.3-25 shows different types of suspension
clamps. Figure 2.3-26 shows a special clamp for a long
river crossing.
It thus appears that the major disparities among conductor self-damping values reported by different laboratories
are mainly related to end effects. Therefore, the use of the
Power Method for conductor self-damping measurement
on laboratory test spans with rigidly fixed extremities is of
questionable accuracy. The use of pivoted extremities is
suggested whenever this method is used.
Because practically 99% of vibration failures take place
very near to, or at, the clamp location, clamp design is
of great importance for the mechanical integrity of the
conductor and thus for the operational safety of a line.
Nevertheless the conductor-clamp combination is not
susceptible to a quantitative approach, and so there are
more practical engineering design rules, which have
evolved from experience over the years for a good, practical clamp design (CIGRE 22.11 TF3 1989b). These
rules are summarized below, with particular emphasis
on the influence of clamps on the stress and strains of
the conductors. The influence of the clamps on the
fatigue performance of the conductors is discussed in
Chapter 3.
Finally, Appendix 2.3 (Tavano et al. 1994) gives details
of various self-damping measurements of several conductors and OPGWs originating from five different laboratories and carefully collected by the CIGRE 22.11
TF1 in 1994.
Self-damping data have always been regarded as difficult to measure and obtain. So, in case no experimental
data are available, a possible alternative is to use the
approach developed by Noiseux (1992) based on the socalled similarity laws for the internal damping of
stranded cables in transverse vibrations. These laws are
derived from the assumption of an hysteretic loss factor
associated with the flexural rigidity of the conductor
(see also Figure 2.3-32) and the assumption that this
loss factor is the same for all conductors of the same
construction. Noiseux’s findings can be brought in the
form of Equation 2.3-20:
P
= D 4σ Al−2.76 A2.44 f 5.63
L
Body and Keeper Profile
Theoretically, the profile of the body should follow the
natural curvature of the conductor and should not
reduce the breaking strength of the conductor. However,
since there are different load assumptions, it is not possible to satisfy this theoretical requirement under maximum, minimum, and average turning angles.
An optimum profile design of the body and keeper must
be found for the different load assumptions and the con-
2.3-20
with D the overall conductor diameter in mm and sAl. the
stress in the aluminium wires in N/m2 (see Equation 2.38).
2.3.7
The Suspension
Suspension clamps, which are used to suspend the conductors from a suspension tower, have to fulfil a number
of duties:
Figure 2.3-25 Different types of suspension clamps.
• Withstand the mechanical loads imposed by the conductor
• Avoid damage to the conductor in the clamp area
• Prevent/reduce strand failures because of vibration as
much as possible
• Offer high corrosion resistance
• Provide sufficient corona inception voltage as specified for the respective voltage level of the line
• Withstand short circuits, and have low contact resistance and low electrical losses
• Allow simple and safe erection
2-34
Figure 2.3-26 Special river crossing clamp made from
hard-drawn aluminium alloy material; minimum breaking
strength of the clamp: 400 kN.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
tact length of the suspension clamp. The profile of the
body must also cope with asymmetrical adjacent spans—
i.e., with different sag angles on each side of the clamp.
The manufacturer should explain which criteria have been
take into account for the optimization of the shape—for
instance, which tests or what type of calculations.
The main profile of the body must be rounded and
curved into a bell mouth at the ends in order to avoid
damage to the conductor in the case of exceptional overloads (see Figure 2.3-25). This consideration should also
be applied to the keeper design when conductor uplift is
assumed.
Because armor rods increase the stiffness of the conductor, they also decrease its bending in the clamp.
Mobility
A suspension clamp should be able to rotate in a longitudinal vertical plane in order to accommodate asymmetrical loads and different spans on each side of the
clamp. The amount of rotation required at the pivot
point is generally much greater for earth wires than for
phase conductors because of the short link in the support assembly of the former.
It is generally believed that the axis of rotation should
not be more than a few conductor diameters from the
conductor axis. In the case of a slip clamp, the rotational axis of the clamp should correspond as nearly as
possible to the longitudinal axis of the conductor—i.e.,
the moment of inertia related to the rotational axis is
minimized in order to reduce dynamic stresses. Keeping
the clamp mass low is an advantage; however, the contact area and contact pressure between conductor and
clamp must withstand high current flows during flashovers—i.e., in these cases, the suspension clamp has to
act as a current-carrying clamp. This requirement may
contradict the requirements for good vibration behavior
of the clamp, as will be explained later. As is usual in
these cases, the design is ultimately a compromise.
Chapter 2: Aeolian Vibration
rods, strains on the order of 500-1000 microstrain have
been measured on the aluminum strands with application of the clamp. Because of the many variables that
enter into the clamping procedure, the strains from this
source cannot be accurately predicted.
Strains induced in the aluminum stranding through tensile loading of the conductor can be calculated with reasonable accuracy. In actual conductors, some inequality
of strand loading may exist. Long-term static creep
tends, in time, to reduce the inequalities. With a short
laboratory specimen of conductor, uneven strand loading is probably a greater problem than it is in the field.
Laboratory measurements are often made at a suspension, which, of necessity, is close to a conductor termination. Small amounts of bird-caging or uneven strand
gripping by the termination cause measurement problems that are less likely to occur in the field, where the
suspension clamp is normally separated from a splice or
termination by a considerable distance.
Fatigue failures frequently occur at fret locations in the
vicinity of the last point of contact between overhead
electrical conductors and their supporting suspension
clamps. Failures occur as minute cracks resulting from
fretting, and cyclic strain variations propagate through
individual conductor strands. This process is a highly
localized phenomenon, involving complex contact
stresses between strands in the vicinity of the clamp.
However, conductor strand crack initiation and growth
are sensitive to the macro strain levels maintained at the
clamp, and hence fatigue failures are sensitive and
closely related to macro strain levels. Bearing strains are
highly localized strains that help to create an adverse
strain environment for the conductor at the suspension
clamp locations. They are due to the combined effects of
conductor tension/sag angle and clamp keeper pressure
resulting from torque applied to the clamp keeper bolts.
Accumulation of Stresses at the Suspension
The highest static and dynamic loading of a conductor
span is normally near its suspensions, Figure 2.3-27. If
fatigue takes place, it is usually in this locality (Möcks
and Swart 1969; see also Chapter 3.).
Three primary sources account for the static stresses.
These are clamping (σD), stringing (σZ), and bending (σb
and σbw). Few experimental data are available on the
conductor stresses induced by application of the suspension clamp (Mehta 1968). It is known that with a high
torque on the U-bolts, the yield point of the strands can
be exceeded on a bare conductor. Even under armor
Figure 2.3-27 Stress situation in a conductor at
hardware locations. σz tensile stress, σb static bending
stress, σD compressive stress, σbW dynamic bending
stress.
2-35
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Accurate quantitative assessments of strand strains
induced by the bearing forces are not possible; however,
it is apparent from observations of tested conductors
that significant plastic bearing deformations take place
adjacent to the keeper, thus indicating high levels of
bearing strains at that location (Ramey and Townsend
1981). Qualitatively, the bearing strains are reduced as
the conductor support area increases. Also, the closeness
of fit between the conductor and clamp affects the level
of conductor-bearing strains at the clamp supports. A
close fit, or good geometric compatibility, between the
clamp and keeper cross section and the conductor cross
section minimizes conductor-bearing strains and deformations at the clamp and should, therefore, enhance
conductor fatigue performance. The higher interstrand
pressure in the inner strands explains why there are a relatively large number of failures of the conductor inner
strands in comparison to the outer ones.
Experimental Analysis
To better understand the effects of clamp geometry and
line parameters on conductor strain levels and fatigue
performances, an experimental investigation was undertaken (Ramey and Townsend 1981). The tests used a
Drake ACSR conductor, which is a multilayered conductor, consisting of two aluminum layers helically
wrapped around a steel core composed of seven strands
of steel. A brief summary of the results is presented
below, with main emphasis on the clamp influence on
the conductor strains.
monitored to obtain a range and mean of strand strain
levels.
Effect of Clamp Curvature on Strain
Results of the effects of sag angle and line tension on
strain levels in the conductor are graphically illustrated
in Figure 2.3-29.
For each clamp geometry, the general form of the curves
is the same for a given tensile load applied to the conductor. The smaller radius clamp exhibits a strain
response that is directly proportional to increasing sag
angle for a given tension. The larger radius clamps,
however, show a softened strain response as the sag
angle increases. The softened response continued until
the strain values levelled off. This response can be
attributed to the fact that the last point of contact
between the clamp support and the conductor moves
further from the center of the clamp with increasing sag
angle. This implies a larger available support area for
the conductor with the larger radius clamps. It also indicates that the curvature and, therefore, the bending
moment, remains constant at the clamp after a critical
sag angle value is reached.
Effect of Clamp “Fit” on Strain
The effects of clamp groove depth and “fit” on conductor strand strains at different sag angles and tension lev-
A set of generic clamps was developed for the testing,
Figure 2.3-28. The geometric parameters that were varied
in the testing were the longitudinal radius of curvature
and the cross-sectional radius or “fit”. Three variations in
the longitudinal radius of curvature were incorporated
and are referred to as short, medium, and long radius
clamps, corresponding to clamp inserts of 15.2-cm (6-in.),
30.5-cm (12-in.), and 61.0-cm (24-in.) longitudinal radii,
respectively. Two variations in the cross-sectional “fit”
were considered and are classified as either a deepgrooved or shallow-grooved clamp and keeper assembly.
The deep-grooved clamp cross section conformed more
closely to the actual conductor cross section than did the
shallow-grooved clamp cross section.
Although commercially available clamps were not used,
the generic clamps developed for the testing program
had similar geometries to these.
Static Testing
The static test series involved determining conductor
strain levels at the mouth of the various generic clamps.
In each static test, four outer-layer strands were straingauged near the support clamp, and these gauges were
2-36
Figure 2.3-28 Line drawings of suspension clamps
tested. (a) short radius, deep groove; (b) medium
radius, shallow groove; (c) medium radius, deep
groove; (d) long radius, deep groove.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
els are shown in Figure 2.3-30. The data shown is for a
clamp with 30.5-cm (12 in.) longitudinal radius and with
deep and shallow groove depths as described earlier.
From Figure 2.3-30, it is evident that at the higher sag
angles, the strain levels associated with the shallowgrooved clamp are higher than the corresponding strain
levels in the deep-grooved clamp. In general, this would
be expected due to a reduced supporting area being
available in the shallow groove, thus resulting in higher
localized bearing strains. Also, the shallow-grooved
clamp results in greater conductor cross-section
“squashing,” with a resulting increase in strand-bending
strains.
Chapter 2: Aeolian Vibration
dynamic bending-strain amplitude varies inversely with
the clamp radius of curvature.
Fatigue Testing
Each conductor specimen was subject to approximately
8.2 million cycles of vibration at a constant mid-loop
amplitude of 17.8 mm (0.7 in.). At the end of each
fatigue test, the conductor was opened and visually
inspected for strand breaks. Strand break results for
each of the three longitudinal radii of curvature clamps
Dynamic Testing
The dynamic test series involved resonant vibration testing on approximately 10.67-m (35-ft) long conductor
specimens.
Effect of Clamp Curvature on Strain
Dynamic bending strains induced in the top strands of
the Drake ACSR conductor were measured with strain
gauges positioned identically to those in the static tests.
Maximum and average dynamic bending strains are
shown in Figure 2.3-31 for the three clamp radii of curvatures tested. From this figure, it is evident that the
Figure 2.3-30 Strain level versus sag angle at
various tension levels for two different “groovefits” for a 12-in. radius clamp.
Figure 2.3-29 Strain level versus sag angle at
various tension levels for various radius clamps.
Figure 2.3-31 Dynamic strain amplitude
versus clamp radius.
2-37
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
are summarized in Figure 2.3-32. As is evident in the figure, the fatigue damage increased as the radius of curvature decreased.
The effect of clamp groove depth on fatigue performance is summarized in Figure 2.3-33. When looking at
the maximum number of strand failures, it appears that
the deep groove clamp provides a slightly superior
fatigue resistance performance. However, when considering the average number of strand breaks, there is no
difference in fatigue performance of the deep and shallow grooved lamp. This result is consistent with the
measured strain data in that the shallow-grooved clamp
yielded the larger static strains but not the smaller
dynamic strains. It appears that these two opposite
effects may have cancelled each other and resulted in the
same fatigue performance.
The influence of the suspension clamp properties on the
fatigue endurance of the conductor is covered in more
detail in Chapter 3.
Armor Rods
Armor rods were the first effective means for preventing
fatigue failure of conductor strands at points of support. Armor rods were conceived originally with the
idea of reinforcing the conductor at points where it
undergoes the greatest bending—i.e., at the suspension.
By increasing the flexural rigidity of the conductor, it
was thought that bending stresses could be reduced,
even if there was no reduction in vibration amplitude.
This is in fact true, as extensive tests have shown (Aluminum Company of America 1961), where the fatigue
life of a Drake Conductor (795 MCM, ACSR 26/7),
vibrated at various tensions and at the same vibration
amplitude levels (i.e., with and without armor rods),
increased, when armor rods were installed, by factors
ranging between 5 and 30.
Armor rods also contribute significant vibration damping
(see Section 2.5). The principal mechanism by which they
dissipate vibration energy is the same as that by which the
conductor dissipates it (see Section 2.3.6)—that is, there is
slipping between armor rods and conductor.
2.4
Figure 2.3-32 Fatigue failures (number of
strand breaks) versus clamp radius.
Figure 2.3-33 Fatigue failures (number of strand
breaks) versus groove depth for a 12-in. (30.5 cm)
radius clamp.
2-38
DAMPING DEVICES
Since 1923, when conductor strand failures were first
recognized as a problem associated with aeolian
vibration, a number of protection and mitigating
devices have been developed following two main
concepts. The first and most intuitive concept sought to
provide reinforcement against the effect of vibration of
the conductor at the suspension points, where the strand
failures occurred. This approach was achieved with an
additional layer of strands extending for a short
distance at both sides of the suspension clamps
(Aluminum Company of America 1961). This method
led to the design and application of the so-called armor
rods as noted in Section 2.4.5. The second concept took
into consideration the application to the conductor of
energy-dissipating devices, which were able to reduce the
level of conductor aeolian vibration. This approach was
soon recognized as the most practical and effective
method, and a number of vibration dampers have been
developed to date.
Coverage of damper types is not intended to be complete here, but rather is intended to indicate designs that
have had significant use. Existing damping devices,
which perform adequately in practically all problem
spans, can currently be obtained. Among these devices,
the so-called Stockbridge damper (Figure 2.4-1) has
reached a satisfactory level of efficiency at a cost that is
difficult to compete with. Therefore, it seems unlikely
that, in the near future, new concepts may replace some
or all of the models here mentioned.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
The damper market is highly competitive, and although
reliable performance is required in an aggressive environment, economic constraints apply. It is difficult to
judge how great a price increase could be justified by
even an outstanding improvement in performance.
Moreover, the transmission line industry is rather conservative and is reluctant to accept the replacement of
devices that performed well for many years, with more
modern and promising items that still do not have a
convincing service experience.
Regardless of how effective a damper is, it cannot be
expected to reduce the amplitude of vibration to zero. A
small amount of vibration is always necessary to actuate
a damper. If this level is sufficiently low through an
acceptable range of frequencies, the damper performance is adequate.
2.4.1
Stockbridge-type Dampers
The Stockbridge-type damper is one of the earliest commercial damping devices. It dates from about 1924, and
is referred to in the December 26, 1925 issue of Electrical World.
Chapter 2: Aeolian Vibration
mode of the cantilever beam, within the frequency range
of operation of the damper.
Basically, it consists of two shaped masses, rigidly
attached at the extremities of a stranded steel cable,
which in turn is rigidly clamped to the conductor (Figure 2.4-3). Because of the weight of the masses, the steel
supporting cable is not stiff enough to force them to
accurately follow the motion of the cable clamp, and
this results in flexure of the supporting steel cable. The
deflection of the damper cable is amplified by the resonance condition of the damper. The flexure causes slipping between strands of the steel cable and consequent
dissipation of energy by interstrand friction. The length
of stranded cable is called messenger cable, because
Stockbridge’s original model used the type of cable
employed, at that time, in overhead telephone lines.
The mechanical system on each side of the clamp is a
cantilever, with a mass attached at one extremity, presenting to two degrees of freedom (Figure 2.4-4).
After its invention by George. H. Stockbridge, the
damper has undergone a long period of development
and modification, during which it has been the subject
of a number of improvements from its original “oneresonance-frequency” design (Figure 2.4-2a).
Not long after the first appearance of the Stockbridge
damper, Monroe and Templin (1932) enhanced the twodegree of freedom damper (Figure 2.4-2b) in which both
the shape and the moment of inertia of the masses were
designed to take advantage of the second vibration
Figure 2.4-2 Stockbridge damper, and Monroe and
Templin damper.
Figure 2.4-3 Vibration damper of Stockbridge type.
Figure 2.4-1 Vibration dampers of Stockbridge type
(courtesy U. Cosmai).
Figure 2.4-4 Vibration modes of a two-degree-offreedom cantilever with attached mass.
2-39
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
For many years since its invention, the Stockbridge
damper has been manufactured worldwide, with equal
masses supported by two equal lengths of steel stranded
cable (Figure 2.4-5).
Because conductor vibration frequency changes with
the wind velocity, the important characteristic of a
damper is its response in term of damping capacity over
the range of vibration frequencies expected for the cond u c t o r i nvol ve d . Th e d a mpi n g c ap a c it y c an b e
expressed in various ways. One of them is by graphs of
the reaction force versus frequency and phase between
reaction force and displacement versus frequency.
The symmetrical Stockbridge-type damper has two primary modes of response. At the first (lower) natural frequency, the outer ends of the two weights are the points
of maximum motion (Figure 2.4-6). At the second
(upper) natural frequency, the motion of the weights is a
rotation about their own center of gravity. For a given
vibration amplitude of the damper clamp, the greatest
dissipation occurs at these resonant frequencies. However, they may be not the frequencies providing greatest
dissipation when the damper is attached to a span. This
happens when the resonances are characterized by sharp
force peaks (Figure 2.4-6) that make the damper clamp
hard to drive because it presents high mechanical
impedance to the vibrating conductor and tends to force
a point of low amplitude, a node point, to occur at the
damper location. The reduced amplitude at the damper
Figure 2.4-5 Symmetrical vibration dampers of
Stockbridge type with bell-shaped masses.
2-40
clamp when the damper is resonant results in decreased
damper dissipation.
Frequencies of reduced performance occur when the
damper is too easily driven by the conductor, and does
not resist the conductor motion with enough force to
induce sufficient dissipation. These frequencies are
found between the two resonances noted above, and
also below the lower natural frequency and above the
upper one. The choice of the best weight of damper, in
any case, involves a compromise between performance
at those frequencies where it resists conductor motion
too weakly, and those frequencies (at resonance) where
it resists too strongly. Given the basic design, there is an
optimum weight that provides the best overall balance.
The efficiency of the damper, even with the optimum
choice of weight, depends considerably upon the sharpness of its resonances, and also upon how widely they
are separated.
Two general approaches to maintaining high performance are currently used. One is to employ closely
spaced resonances in the damper, so that at least one is
partly excited. This keeps the damper’s resistance to
motion from falling too low between resonances. The
other approach is to use damper cable processed to
achieve a high loss factor, and to thus produce broad,
low resonance peaks in the overall damper response.
4-R Stockbridge-type Dampers
A significant modification to the basic Stockbridge type
was designed by Claren and Diana in 1968. The two
halves were made asymmetrical, providing two different
Figure 2.4-6 Dynamic response of symmetric
Stockbridge-type damper. Test performed at constant
displacement of 2 mm peak-to-peak up to 14 Hz and 1
mm peak-to-peak above 14 Hz (courtesy U. Cosmai).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
masses with different moments of inertia and different
lengths of the messenger cable (Figure 2.4-7).
The modified damper, known by the acronym 4-R, is a
four-resonance system, and the four resonance frequencies are evenly distributed in the frequency range of
interest in order to flatten the damper response curve
(Figure 2.4-8) and broaden the frequency range of conductor vibration that can be covered with a specific
damper size (Claren and Diana 1969a and b).
Haro Dampers
In 1970, Lauri Haro and Tapani Seppa developed a
vibration damper based on the Stockbridge principle,
known as the Haro damper (Figure 2.4-9). It was
equipped with three weights and two clamps for the
Figure 2.4-7 Asymmetrical Stockbridge-type damper
with fork-shaped masses.
Chapter 2: Aeolian Vibration
connection to the conductor: the weights were of varying dimensions and at different moment arms on the
messenger cable. Each of the two external weights had
two degrees of freedom, as in the conventional Stockbridge damper. The central mass had only one degree of
freedom; therefore, the device was provided with five
resonances.
The Haro damper provided satisfactory performance,
despite the extreme care required for its installation in
order to avoid disturbance of its messenger. It was over
a meter in length and was difficult to transport and
install. Many became bent and damaged during transportation.
Torsional Stockbridge-type Dampers
Some elaborations of the Stockbridge-type vibration
damper include a symmetrical damper that, in addition
to the two flexural resonances, develops a torsional resonance. This is achieved by using weights whose center
of gravity is offset with respect to the axis of the messenger cable. Among various solutions, the most popular
are the Australian “Dogbone” damper (Figure 2.4-10)
and the Japanese Asahi torsional damper.
A torsional damper with asymmetrical arms can produce six resonances. However, very few 6-R damper
solutions are currently available on the market.
Design Characteristics
The Stockbridge-type vibration damper has a simple
structure, but it cannot be theoretically designed fully,
because the dynamic response of the messenger cable
cannot be satisfactorily modelled. This is due to the fact
that, first, there is a large scatter in the dynamic characteristics of the same cable type produced by different
manufacturers, second, the system response is not linear, and the cable dynamic stiffness and damping
depend of the amplitude of cable deflection.
Nonlinearity in the behavior of Stockbridge-type dampers has important practical effects. This behavior was
investigated by Sturm 1936, Tompkins et al. 1956, and
others.
Figure 2.4-8 Dynamic response of a 4-R Stockbridgetype damper. Test performed at constant displacement of
1 mm peak-to-peak (courtesy U. Cosmai).
Figure 2.4-9 Haro damper.
Figure 2.4-10 “Dogbone” damper.
2-41
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 2.4-11 shows hysterisis loops obtained by applying a load at the center of gravity of the damper weight
(Sturm 1936). Nonlinearity is reflected in the variation
in the effective stiffness of the damper cable with respect
to amplitude of deflection, corresponding to the average
slope of the hysterisis loop. This variation causes the resonant frequencies of the damper to vary with the amplitude at which the damper is vibrated.
equipped with a messenger cable with insufficient damping capacity. The curve is characterized by sharp resonances with low force and phase values between them,
although the resonance frequencies are suitably spaced.
For the messenger cable, galvanized steel is generally
preferred, although stainless steel is used in very polluted areas. Originally, seven-strand messenger cables
Figure 2.4-12 illustrates this effect upon the impedance
characteristics of a two-resonance Stockbridge-type
damper, where the variation in the two resonant frequencies with damper clamp amplitude can be seen.
This variation affects the behavior of the damper as it
protects a field span. When the excitation frequency
from the wind falls at one of the resonant peaks for
small damper clamp amplitude, where damping may be
poor, the amplitude of the span increases. The damper
clamp amplitude increases with it, shifting the frequency of the resonant peak away from the excitation
frequency. The shift continues until a damper amplitude
is reached where the damping efficiency is high enough
to prevent further increase. This occurs well within the
range of vibration amplitudes that are safe for the conductor. Thus, the effect of nonlinearity is to make the
damper self-tuning.
Calculation methods to be described later in the chapter
show that, when the damper of Figure 2.4-12 is applied
to Drake ACSR at 25%RS tension, the damping efficiency at 30 Hz shows the trend displayed in Figure
2.4-13 for the five damper amplitudes of Figure 2.4-12.
The efficiency more than doubles when the damper
amplitude increases from 0.5 to 2.0 mm peak-to-peak.
The use of a messenger cable with poor energy-absorbing capacity can cause a bad performance and a poor
fatigue endurance of the damper. Figure 2.4-14 shows a
typical response curve of a four-resonance damper
Figure 2.4-11 Load-deflection curves for a
Stockbridge-type damper (Sturm 1936).
2-42
Figure 2.4-12 Mechanical impedance of tworesonance Stockbridge damper.
Figure 2.4-13 Effect of damper amplitude on damping
efficiency.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
were employed, but the superior performance of 19
strand cables, in terms of damping capacity and homogeneity of response, was soon recognized (Figure
2.4-15). Among the mechanical characteristics that a
cable should have, the tensile strength is not as important as the fatigue resistance. The stainless steel messenger cable has shown practically the same damping
capacity as an equivalent galvanized steel cable but a
slightly better performance in term of fatigue endurance.
Clamps must be as light as possible in order to remain
mobile at the higher conductor vibration frequencies.
Great care must be taken in selecting the clamp materials, especially those that are in contact with the conductors, to avoid any corrosion problem.
For the clamps, primary aluminum alloys are used for
aluminum- and steel-based conductors with only a few
cases of steel clamps for steel shield wire. Generally, aluminum clamps are also considered more appropriate for
steel cable because of their light weight. Aluminum
clamps can be either cast directly onto the messenger
cable or cast separately in shell molds and then assembled onto the messenger cable by compression. The sec-
Figure 2.4-14 Dynamic response of a 4-R Stockbridgetype damper incorporating a messenger cable with poor
energy-absorbing capacity. Test performed at constant
displacement of 1 mm peak-to-peak (courtesy U.
Cosmai).
Figure 2.4-15 Stranding of the messenger cables
used for Stockbridge-type vibration dampers.
Chapter 2: Aeolian Vibration
ond procedure is preferred by some users on the
assumption that the casting process reduces the
mechanical strength of the steel messenger cable or, in
case of galvanized steel, removes the zinc deposit
around the clamp. According to the experience of some
manufacturers, the temperature reached by the messenger cable during the casting of the clamp is generally too
low to produce the above-mentioned effects. Therefore,
both the methods of connecting the clamp to the messenger cable are considered valid. Another type of
clamp is manufactured by extrusion and then compressed on the cable.
Clamps are generally of the cantilever type; only a few
opposed-hinge nutcracker-type clamps have been
designed for small conductors (9-10 mm diameter) to
provide an increased grip. The clamp is generally
designed in a hook shape that allows the damper to be
hung on the conductor during the installation (Figure
2.4-16). This automatically places the damper in the
right vertical position and facilitates installation, especially for heavy units. Also, in case of clamp loosening,
the damper may slip toward the center of the span, but
the hook clamp, in most of the cases, prevents the
damper from falling to the ground.
Damper clamps contain a single bolt, generally
equipped with a plain washer and a split washer. The
latter is sometimes replaced with a Belleville washer.
The bolt is normally made of galvanized steel. Aluminum or stainless steel are also used, especially when
breakaway bolts are required. The bolt is either engaged
in a captive nut of the same material or in a threaded
hole of the clamp body. Thread lubrication can be
applied to improve the fastener performance. Boltless
open clamps are also used in combination with a set of
relatively short helical rods. These clamps can be either
of metal-to-metal type or elastomer-lined (or elastomercovered) type.
Figure 2.4-16 Hook-shaped clamp of a Stockbridgetype vibration damper.
2-43
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
The clamp grip must be sufficient to restrain the damper
from slipping and rotating on the conductor during normal operating conditions. The clamp loading must not
cause damaging deformation of either the conductor or
the clamp component, and must be maintained, within
appropriate limits, throughout the service temperature
range. Therefore, the clamp must be designed to avoid
significant losses of clamp pressure, and to prevent loosening under the effect of the clamp embedding on the
conductor, thermal cycles, vibrations, and conductor
diameter reduction due to creep and cold flow. Cold
flow is due to the compressive effect of the clamp on the
interstrand crossover point of the conductor.
Clamping of the vibration dampers is not as critical as
in the case of spacer dampers, because of the lower
torque required, and the effect of clamp loosening is less
dangerous. For these reasons, damper clamps are generally designed with a relatively wide range of clamping
capability. The clamp bore has to be smooth and free of
projections, and it is not advisable to subject the bore
surfaces to treatment such as sand blasting, grooving, or
rifling in order to artificially increase the coefficient of
friction between the clamp and the conductor, because
these can cause damage to the conductor.
The damper masses have been designed and produced in a
large variety of shapes, although within a small group of
materials. The first were bell-shaped masses made of galvanized cast iron, installed on the messenger cable by
means of tapered aluminum sleeves. Later, another assembling technique based on the pouring of a “white metal”
between the messenger cable and the mass hole was used,
the melted material being zinc alloy or aluminum.
In the 1970s, a new technology based on the direct casting of the masses on the messenger cable was developed.
Zinc-aluminum alloys (Zamax), whose density was similar to the density of cast iron, were used for the masses,
and the shape changed into a fork shape, more suitable
for this technology. For many years, the low cost of the
zinc alloys and the cheaper process for mass assembly
made this solution the most used. In recent years, strong
international competition has forced manufacturers to
find new, cheaper solutions, using forged steel masses or
extruded steel rods or tubes bent upwards (Figure
2.4-17) to avoid corona discharges. These masses are
generally compressed onto the messenger cable.
An attempt to use concrete for the masses was quickly
rejected because of the poor mechanical performance of
2-44
this material, and now some utilities’ specifications
expressly forbid its use.
Stockbridge-type dampers are also used on vertical
members such as cable bridge stays, guy ropes, and similar structures in which the aeolian vibration can assume
any transversal orientation in relation to the wind directions. For these applications, vibration dampers with
bell-shaped masses can provide the best performance,
because they can guarantee the same response for all
vibration directions in the plane perpendicular to the
cable on which the damper is installed.
Some concern has been shown in the past regarding the
corrosion of the galvanized steel messenger cable, and
some remedies have been applied with few or no positive
results. One approach was to cover the messenger cable
with a rubber sleeve or with a flexible steel sleeve. The
internal parts were filled with grease to make them
waterproof. The rubber sleeve was also intended to
increase the damping capacity of the damper but with
indifferent results.
Because of its wide popularity and effectiveness, the
Stockbridge-type damper in many respects has become
a standard of comparison for other damping concepts.
Some degree of caution should be exercised, however,
when the claim is made that a particular damper equals
or exceeds the performance of the Stockbridge damper.
In most cases, the particular size, model, or source of
origin of the particular Stockbridge damper used in the
comparison is not given. In some cases, a new device
may be compared with a Stockbridge-type damper of
inadequate size for the particular application, or the
damper may not have been placed at its optimum position for the frequency range being investigated. In addition to this, dampers from various sources, although
similar in appearance, will not necessarily be equivalent
in performance throughout their entire range of frequencies.
Figure 2.4-17 Stockbridge-type vibration damper
equipped with helical rod attachment and masses
obtained using steel round bars (courtesy RIBE).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
2.4.2
Other Damper Types
A number of vibration mitigation devices other than
Stockbridge-type dampers have been used with varying
degrees of success. The most common are the following.
Torsional Dampers
A torsional damper (Figure 2.4-18) was invented by
Tebo of Ontario Hydro and used in large numbers in
Canada and other countries worldwide for many years.
It consists of an arm projecting sideways from the conductor and a dumbbell connected to the arm via an
articulation containing rubber inserts. The arm is bolted
to the conductor so that it protrudes in a horizontal
direction. When vibration occurs, the elastomer is
loaded in shear due to the inertia of the dumbbell mass
and absorbs energy by deformation.
The original concept behind the torsional damper was
that it provided an inertial reference promoting torsional rotation of the conductor, thereby activating the
conductor’s self-damping in the torsion. Later study
showed that the principal source of dissipation is the
elastomeric bushing contained in the joint between the
arm and the inertial mass at its end.
Although these dampers were generally abandoned
because of inefficiency at most frequencies and a tendency to freeze up, they are still in service on some lines
worldwide.
Chapter 2: Aeolian Vibration
fitted to a vertical shaft. Each mass rests on an elastomeric washer. This damper appears to be an interesting
study in extrapolation. Since the elastomer is extremely
hard, there is little compression until the masses are able
to impact. Before a mass can be lifted from its pad, the
acceleration of the damper must exceed 1 g. Tests have
shown that this type of damper performs fairly well for
accelerations of about 2 g. When the damper was first
invented, overhead conductors were somewhat smaller
in diameter and, therefore, vibrated at higher frequencies. As conductor diameter increased, the size of the
damper was adjusted accordingly.
One further problem with the ELGRA damper is that
the masses are momentarily able to free themselves electrically from the conductor. During this short time, the
conductor voltage changes, so that the conductor and
mass acquire different charges, giving rise to radio interference. For this reason, interference skirts were added
to the damper on high-voltage lines.
Bretelle Dampers
The bretelle (Figures 2.4-20 and 2.4-21), a jumper loop
connecting two adjacent spans at the suspension points,
is widely used in France. Its discovery as a damping
device was largely accidental. Originally it was conceived as a safety device, but when the requirement for
its use was relaxed on the French system, vibration
problems became apparent. Normally it is made from
In recent years, Hydro Quebec has designed a new type
of torsional damper based on the same principle and
equipped with either a cantilever clamp or a helical rod
attachment clamp.
Impact Dampers
A Swedish damper called ELGRA (Figure 2.4-19) consists of a vertical stem having three cast masses loosely
Figure 2.4-18 Tebo dumbbell damper.
Figure 2.4-19 ELGRA damper.
2-45
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
The ability of a relatively short length of conductor to
damp an entire span is probably due to its extremely low
tension. On the French system, the bretelle is installed
with a sag of 30 or 40 cm. The distance from the suspension clamp to the end of the bretelle is calculated
according to the following empirical formula (Quey and
Rols 1976):
=
d
2
H
m
2.4-1
Where
= distance (m).
d = conductor diameter (m).
H = conductor tension (N).
m = conductor mass (kg/m).
Figure 2.4-20 Bretelle dampers on a bundled
conductor line in France (courtesy Preformed Line
Products Company).
Figure 2.4-21 Bretelle damper profile.
pieces of scrap conductor that are the same size as the
line on which it is used.
Although the bretelle concept may be economically
attractive, there are numerous factors to be considered
in its use. The configuration does not lend itself to
indoor laboratory investigations, making it difficult to
conduct a definitive investigation of the design variables.
On large conductors, it can become unwieldy and difficult to install. Maintenance of conductor-to-steel clearances can result in higher tower costs. Sometimes, this is
avoided by supporting the center of the hanging loop at
the suspension clamp, but the effect of interrupting the
loop has not been fully evaluated.
Since the bretelle is not a commercial product, the user
becomes the designer, and must carry out development
work without the benefit of a manufacturer’s aid and
expertise.
Because of its close association with the French electrical system, most of the data available on the use of bretelles are associated with aluminum alloy conductors
(Almelec) rather than ACSR, but the basic concept
would still apply.
2-46
An analysis indicated that the true units of ( ) are
meters squared per second.
Generally, these distances appear to be long enough for
a node to form at the end of the bretelle within the ordinary range of vibration-producing wind velocities. For
the French design, the end of the bretelle could be
expected to reach a node at a wind velocity of about
5.4 m/s (12.1 mph).
Hautefeville et al. 1964 investigated bretelles of various
length and mass under field conditions, but their published values are not complete enough to make a comprehensive analysis possible. Their final design was
based on obtaining peak performance for a wind velocity of 2.6 m/s, essentially confirming the previous suppositions.
Bretelle dampers were also used in Russia, and a design
by Savvaitov (1972) would be nodal for a velocity of
4 m/s (8.9 mph).
The French and Russian designs indicate a concern for
low frequencies, with possible loss of performance at the
higher end of the normal significant range. Possibly, the
high frequencies could be improved without seriously
affecting the lower frequencies.
Because the bretelle is simultaneously influenced by the
reaction of two spans, it would seem logical to investigate asymmetry in bretelle design, making the distance
on one side of the suspension longer than the other.
In many reports, the bretelle is listed as being roughly
equivalent to a Stockbridge damper. These comparisons
are questionable when the size and source of the Stockbridge damper are not given.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
A comparative analysis between the efficiency of a bretelle damper and a Stockbridge-type damper suitable
for the same application is reported in Section 2.4.3
under “Inverse Standing Wave Ratio (ISWR) Method.”
Festoon Dampers
Festoon dampers, shown in Figure 2.4-22, have been
used on numerous long spans. Their development
appears to be partly a matter of intuition, and practically no design rules have been published for their use.
Like the bretelle, they consist of scrap conductor and
are relatively inexpensive. The primary problems that
have been reported in the use of festoons have occurred
at their clamps. Some designs have used uniform length
loops that could, conceivably, allow a standing wave to
be established on the conductor in spite of the festoon.
Although this could occur only at one frequency, it
would seem more logical to avoid the possibility.
In Norway and other cold countries, festoon dampers
are preferred to Stockbridge-type dampers on long
fjords because the latter can be damaged by both conductor galloping and aeolian vibration of increased
severity, during periods of icing. Rawlins (1989) investigated the effect of ice coating on overhead ground wires.
Chapter 2: Aeolian Vibration
Spiral Impact Dampers
Several designs that slap, shake, and rattle can be suitably
used on small conductors, such as overhead ground
wires, because of the high frequencies experienced and
the resulting low displacements necessary for exceeding
1 g of acceleration. The “spiral impact damper” is,
among the helical designs, the most commonly used (Figure 2.4-24). It is made from one piece of rigid polyvinyl
chloride (PVC) rod, helically preformed to obtain a short
gripping section with a small helix diameter to grip the
conductor and a larger damping section of internal
diameter larger that the conductor diameter. This
damper, called SVD (spiral vibration damper), is basically an impact damper, and energy is dissipated as the
conductor slaps up and down between opposite sides of
the preformed helix.
It is not necessary to make engineering calculations for
placement of an SVD, and lay direction is not critical.
Some manufacturers suggest that the gripping section
should be placed at approximately one hand’s width
from the span end or ends of armor rods or other hard-
Festoon dampers have been widely used in long spans
usually with satisfactory experience (Ervik et al. 1968)
(See Figure 2.4-23). However, in the long crossing spans
of the Bay of Cadiz and the Messina Channel (Falco et
al, 1973), festoons were installed initially, but after some
strand failure on the conductors, they were replaced by
Stockbridge-type vibration dampers.
Figure 2.4-23 Festoon-type damper on Sognefjord
Crossing in Norway. Design configuration by Norwegian
Research Institute of Electricity Supply (EFI). Note armor
rods on conductor (courtesy Preformed Line Products
Company).
Figure 2.4-22 Festoon dampers. (a) and (b) are festoon
dampers for suspension points; (c) is a festoon damper for
tension points.
Figure 2.4-24 Spiral impact damper.
2-47
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
ware. The surface hardness of the rod is designed so as
not to damage any kind of conductor.
established and can be accomplished by testing a
damper mounted directly on a shaker (Figure 2.4-25).
This damper is suitable for small conductors and guy
ropes with a diameter less than 19 mm and is widely
used for shield wires, including OPGW and for ADSS
cables. For the latter, due to its low weight, the SVD can
be used for larger diameters. Generally, the SVD’s
length varies, in accordance to the conductor diameter,
between 1.2 and 1.7 m. Special heavy-duty designs can
reach 2.5 m. The units can be installed in parallel or in
series. The number of SVDs to be installed in each span
is recommended by the manufacturers on the basis of
the span length and irrespective of the conductor type
and tension. One of the leading manufacturers (Preformed Line Products) recommends:
Nevertheless, there are several arguments favoring span
testing with the damper mounted on a conductor that is
similar to or identical with the size and type that it is
intended to protect during service. These arguments are
based on the concept that both the damper and conductor ultimately act as an integrated system, and because
of loop length changes, the damper may go from its
ideal position at the antinode to its least-effective location at the node at different frequencies. The mass of the
damper on the vibrating loop also exerts an influence on
conductor loop shapes, as it would in service.
Up to 250 m, two dampers per span (one on each
span extremity).
From 251 to 500 m, four dampers per span (two on
each span extremity).
From 501 to 750 m, six dampers per span (three on
each span extremity).
The design and testing of these dampers are difficult
because the behavior of the cable-damper system cannot
easily be modelled, and so it is not possible to optimize
their characteristics in relation to the required application. Their efficiency can only be tested in a laboratory
span (Sunkle 1998) or determined by field testing. Reference can be made also to satisfactory field experience.
Acoustic noise may be generated by these devices in
action, but normally it is barely audible at ground level.
2.4.3
Testing of Vibration Dampers
General Technical Considerations
The basic engineering approach to the control of aeolian vibration of overhead conductors is the balance
between the energy introduced by the wind into the conductor and the energy dissipated by the conductor with
and without additional damping. The wind power input
and the power loss due to self-damping in conventional
conductors can be obtained using the methods
described in Section 2.3. For a given conductor span at
a given frequency and vibration amplitude, the difference between the wind power input and the conductor
self-damping is the amount of power that ideally should
be dissipated by the vibration damper (IEEE 1993).
In one respect, it is desirable to separate the damper and
the conductor during testing, to avoid giving the damper
credit for damping due to conductor properties. This
allows the dynamic characteristics of the damper to be
2-48
It is clear that testing the damper on the shaker is easier
and cheaper than on the span. However, the shaker only
imposes a vertical motion to the damper clamp, while
on the test span and in service the clamp rotates and
translates. The contribution of these motions to the
energy dissipation of the dampers has been analyzed by
Tompkins et al. 1956, Rawlins 1997, and Diana et al.
2003 (Part I and II). The results show that the clamp
rocking provides a contribution to the energy dissipation, which is not negligible, especially when the damper
is close to a node of the cable-deflected shape.
IEEE and CIGRE cooperated in the development of a
guide (IEEE 1993) for the measurement of vibration
damper performance on single conductors. The guide
was first published in 1980 and then reviewed and republished in 1993 with the title IEEE Guide for Laboratory
Measurement of the Power Dissipation Characteristics of
Aeolian Vibration Dampers for Single Conductors. The
purpose of the guide is to describe the current methodologies, including apparatus, procedures, and measurement accuracies, for the testing of vibration dampers. In
addition, some basic guidance is provided to the users
about the strengths and weaknesses of the given methods. The guide provides a valuable reference that clarifies
Figure 2.4-25 Example of shaker setup for the
damper characteristic test.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
the problem of damper testing, establishing limitations
and ranges for approaches that have been in use.
In 1998, the International Electrotechnical Commission IEC) published the IEC 61897 Standard, titled:
“Overhead Lines Requirement and Test for Stockbridge
Type Aeolian Vibration Dampers.” The standard has
been adopted by CENELEC as the European standard
with no changes. This standard is specifically intended
for Stockbridge-type dampers; however, it can also be
used for other damper types. Compared to the IEEE
Std. 664, the test procedure recommended by the IEC
standard has some different parameters and concepts.
The main utility specifications require dynamic testing
on dampers that is generally derived from the IEC
61897 Standard or from the IEEE Std. 664, quite often
with different test parameters and different evaluation
criteria.
IEEE Standard 664
Four basic test procedures are described in this standard
for the measurement of the power dissipated by a vibration damper. Three of them, called “basic methods,” are
performed in the laboratory test span. They are: Inverse
Standing Wave Ratio (ISWR) test, Power test, and
Decay test. The first two generally require that the conductor self-damping properties be established for the
span without the damper. The damper is then tested on
the span. Although in most cases (with efficient dampers), the span self-damping is considerably less than the
damper contribution, decay and power measurements
involve the entire length of the span, including losses at
both terminations. The Inverse Standing Wave Ratio
method, however, is capable of restricting the measured
losses to a shorter segment of the span containing the
damper.
The fourth test procedure, called “direct method,” is the
Forced Response test, which is performed with the
damper mounted directly on the shaker.
It is suggested that the tests on the laboratory span
should be performed at a constant free-loop antinode
velocity of 200 mm/s and the forced response test at
100 mm/s. Since the responses of the systems under test
are not linear, additional tests to cover the free-loop
antinode velocities of 100 mm/s, 200 mm/s and 300
mm/s are also recommended to provide a good spectrum of results for end user's evaluation. Moreover, it is
suggested to investigate the damper performance in a
frequency range corresponding to wind velocities
between 1 and 7 m/s. This range, for a given conductor
size, can be expressed as 185/d to 1300/d, where d is the
conductor diameter in millimeters.
Chapter 2: Aeolian Vibration
Inverse Standing Wave Ratio (ISWR) Method
The Inverse Standing Wave Ratio method is described in
Section 2.3. It can be used to determine the power dissipation characteristics of a damper by measurement of
nodal and antinodal amplitude on the test span at each
tunable harmonic.
One advantage lies in the fact that measurements made
near one span end (which can contain the damper)
include the conductor damping losses only for the section of conductor in which the measurements are made.
As noted by Rawlins (1958) and Tompkins et al. (1956),
the ratio of nodal amplitude to antinodal amplitude is
equal to the ratio existing between the power being dissipated by the damper and line section and the maxim u m p o w e r t h at t h e c o n d u c t o r i s c a p ab l e o f
transmitting at a particular free-loop amplitude and frequency. For this reason, the Inverse Standing Wave
Ratio—i.e., the ratio of nodal amplitude to antinodal
amplitude Ymin/Ymax is called “efficiency” and can be
practically attributed to the sole damper, when the
power losses due to span terminations and conductor
self-damping are minimized.
The maximum power Pmax that can be transmitted by a
conductor vibrating at an amplitude Ymax is:
1
⎛Y ⎞
Pmax = Z 0ω 2 ⎜ max ⎟
2
⎝ 2 ⎠
2
2.4-2
Z0 in this case is the conductor mechanical impedance,
or,
⎛Y ⎞
Tm , and ω ⎜ max ⎟ is the antinode velocity Vu , so
⎝ 2 ⎠
we may write:
Pmax =
1
Tm ⋅ Vu2
2
2.4-3
Where
T = conductor tension (N).
m = conductor mass/unit length (kg/m).
ω = 2πf
f = frequency (Hz).
Y ma x = conductor free-loop amplitude (peak-topeak) (m).
Pmax = max power dissipated (W).
Following the acquisition of the data, the power PD dissipated by the damper can be calculated by the following formula:
PD =
⎛Y ⎞
1
Tm ⋅ Vu2 ⎜⎜ min ⎟⎟
2
⎝ Ymax ⎠
2.4-4
2-49
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Where
Vu = velocity of the antinode (m/s).
Ymin = amplitude at the node (peak-to-peak) (m).
PD = power dissipated by the damper (W).
Ymin/Ymax = damper efficiency.
Equation 2.4-4 can be written
⎛Y ⎞
PD = Pmax ⎜⎜ min ⎟⎟
⎝ Ymax ⎠
Thus
⎛Y ⎞
PD
= ⎜⎜ min ⎟⎟ = damper efficiency
Pmax ⎝ Ymax ⎠
One problem in the system is the determination of true
node location. Where the damping is high, the amount
of motion at nodes is also large, and therefore, nodes are
difficult to find. With low damping, a sensitive measurement system is necessary for accurate determination of
the small motion present at a node. Both of these conditions may be encountered (at different frequencies) during the course of a test series on a given damper. Since
the nodal and antinodal positions change with frequency, a noncontact measurement system, such as a
track-mounted laser displacement transducers, can be
used. Recently, lightweight accelerometers with a fast
installation system have also been used, since they are
less expensive than a laser transducer and so light (3-6
g) that their mass does not alter the shape of the conductor vibration.
A method for measuring the damper effectiveness in
laboratory spans has been developed by Rawlins (1998).
This method, called DEAM (Damping Efficiency
Amplitude Measurement), is similar to the Inverse
Standing Wave Ratio method but with the remarkable
advantage that it does not require the location of nodes
and antinodes along the test span and the relocation of
the transducers at each vibration frequency.
The DEAM method assumes that conductor aeolian
vibration takes the form of two opposed travelling wave
trains carrying vibration energy: one train moves toward
the span end where the damper is installed, and the
other is reflected by the span terminations and moves in
the opposite direction.
The DEAM procedure separately evaluates the amplitudes and powers of these waves. The difference between
the power conveyed by the incident waves and the power
conveyed by the reflected waves yields the power dissi-
2-50
pated by the damper and the span termination. The
wave amplitudes are measured by means of two suitable
transducers (generally noncontacting photo-optical
devices, although Leblond et al. 1997 did use accelerometers in a field setup), located preferably close to the
damping device in order to reduce losses related to conductor self-damping and spaced not too far apart (for
example, 305 mm or 1 ft).
Rawlins’s theoretical approach is described in Appendix
2.4.
A comparative analysis between the efficiency of a bretelle damper and a Stockbridge-type damper suitable
for the same application has been performed by Leblond et al. 1997 on a full-scale test line using the DEAM
procedure. The results shown in Figure 2.4-26 demonstrate the higher efficiency of the Stockbridge type
damper.
Power Method
The power method, described in Section 2.3, can be
used to determine the dissipation characteristics of a
damper, at each tunable harmonic of the test span, by
the measurement of the force and velocity imparted to
the test span at the point of attachment of the shaker
(Figure 2.4-28). The force signal is obtained by coupling
the shaker to the span through a load cell. The velocity
is generally measured by means of an accelerometer, and
its signal is integrated to obtain velocity and, when necessary, double-integrated to obtain displacement.
Damper reaction at certain frequencies may distort the
shape of the force signal. The measurement system is
based on sine wave assumptions, and deviations from
the assumed shape are undesirable. The component of
the signal other than the fundamental are filtered. In
this case, the accelerometer signal is also filtered to
avoid phase shift between the two signals. Alternatively,
an FFT (Fast Fourier Transform) analysis can be
performed.
A Lissajous figure displayed on an oscilloscope is a convenient method of monitoring, since it combines the two
signals, and also provides a phase-angle indication that
can be useful in tuning the shaker to the specific span
resonant mode.
In the system, which uses mechanical force as being
equivalent to voltage (EMF), and velocity as equivalent
to current (an ampere is a coulomb per second),
mechanical power becomes:
P = 0.5 FV cos Φ
Where
2.4-5
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 2: Aeolian Vibration
Figure 2.4-27 Example of laboratory test span equipped
for the power test.
Figure 2.4-28 Laboratory test span. Flexible connection
between the shaker and the conductor. (courtesy Damp).
F = the force (peak value) (N).
V = the drive point velocity (peak value) (m/s).
Φ = the phase angle between force and drive point
velocity (degrees).
If acceleration or displacement is used, Equation 2.4-5
can be converted accordingly.
The power method allows the calculation of the damper
“efficiency” as the power input to the damper P D
divided by the power dissipation of an ideal damper
P max that corresponds to the P max given by Equation
2.4-3.
Efficiency = PD/Pmax:
An example of the test span layout for the power test is
given in Figure 2.4-27.
Figure 2.4-26 Efficiency of a Stockbridge-type
damper (A) and a bretelle damper (B) as a
function of predominant vibration frequency on a
450-m test span.
A laboratory investigation has been conducted by
Sunkle (1998) to determine the energy dissipation of
spiral impact dampers. Tests were performed on a test
span, in accordance with IEEE 664 on six different
cables (Figure 2.4-29), demonstrating that this standard
can be usefully employed not only for Stockbridge-type
dampers but also for other damper types. The results for
a galvanized steel shield wire of 12.7 mm diameter and
for an OPGW of 11 mm diameter are shown in Figure
2.4-30.
2-51
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 2.4-29 Test setup for spiral damper efficiency
tests (the conductor parameters are relevant to the shield
wire of 12.7 mm diameter).
Decay Method
The decay method is described in Section 2.3. It may be
used to determine the power dissipation characteristics
of a damper, at each tunable harmonic of the test span,
by the measurement of the decay rate of the conductor
vibration amplitude, following a period of forced vibration at a natural frequency of the test span and fixed
amplitude. It is the simplest method, since it requires
only one transducer, generally an accelerometer, but
also displacement or velocity transducers can be used.
However, this procedure is not as straightforward as the
IEEE guide suggests. As an example, in highly damped
spans, the decay is reported by some authors in the form
of a step curve (Slethei and Huse 1965). This is probably
due, as observed by the authors themselves, to the transient induced by the exciting force disconnection. A
method to avoid this problem is to provide an elastic
link between the cable and the exciter. This should be
soft enough to dynamically uncouple the cable from the
forcing device.
Decay testing of dampers is subject to a major limitation. Good vibration dampers are capable of performing
satisfactorily on spans of relatively great length, so that a
single damper on a short indoor test span normally provides excessively high damping. As a result, the span
amplitude during decay may drop to a low level in a
small number of cycles, limiting the accuracy of the measurement. This method is more suitable when low damping is present in the system, as is the case with an
undamped conductor strung at a normal service tension.
Forced Response Method
The forced response method determines the dynamic
characteristics of a damper mounted directly on a
shaker (Figure 2.4-25) by the measurement of the reaction force of the damper driven at constant velocity in
the whole range of vibration frequency for which the
damper has been designed. Some utility’s specifications
require shaker testing performed at constant displacement instead of constant velocity.
A typical layout of this type of test makes use of a computer-controlled data acquisition system as indicated in
Figure 2.4-31.
Figure 2.4-30 Power dissipation of spiral vibration
damper(s) vs. 250 m span wind power input. (A) test on
12.27 mm diameter shield wire. (B) test on 11 mm
diameter OPGW.
2-52
The damper is installed on a rigid support fixed to the
shaker table. Ideally, the damper should be positioned
as in service; however, for Stockbridge-type dampers, an
inverted position is generally used to simplify the support, with equivalent results (Figure 2.4-25).
Through this test, the power dissipated by the damper is
evaluated by measuring the damper force and the
damper clamp acceleration. The reaction force of the
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
damper is measured by means of two miniature load
cells. In the standard procedure, the two signals produced by the cells are summed to obtain the total vertical force. By using two separate cells, it can be assured
that the single transducer is not affected by any shear or
moment due to damper asymmetry. The use of a single
cell may introduce large errors in the measured values
because of the transverse sensitivity of the transducers.
The displacement of the clamp is measured by means of
an accelerometer whose signal is integrated to obtain
the corresponding velocity value or when necessary,
double integrated to obtain the corresponding amplitude value. This solution is advantageous in terms of
measurement setup, because it provides an immediate
absolute measurement. Displacement transducers and
some velocity transducers are relative, needing an external fixed point, and therefore requiring a more complex
test arrangement. Adequate sensitivity is required, especially at the lower frequency, where acceleration reaches
its lower values. Following the acquisition of the data,
the power dissipated by the damper can be calculated by
means of Equation 2.4-5.
Evaluating the damper dynamic characteristics through
a continuous frequency sweep, even if in a quasi-static
condition as suggested by the IEEE 664 Std, may not
enable the damper to reach its operating steady-state
conditions. Moreover this introduces errors in the Fourier transform of the signals, when it is used. Therefore,
it seems more accurate (and faster) to operate at discrete
frequency steps generally of 0.5 or 1 Hz.
Calibration of the whole system and determination of
possible phase shifting between the transducers and resonances of the fixture can be made by using a rigid mass
in place of the damper and vibrating it over the frequency range of interest. The rigid mass develops inertia
forces that can be easily calculated and gives a phase
angle of 90 degrees between force and velocity.
Figure 2.4-31 Example of layout for forced response
tests.
Chapter 2: Aeolian Vibration
The inertia force developed by the structure holding the
damper should be evaluated and subtracted from the
force measured to obtain the pure reaction force of the
damper. In particular, the weight of the holding structure above the force cells, plus a portion of the weight of
the cells corresponding to the part of the cell mass that
is sensed by the cell itself, should be considered.
The forced response method does not evaluate the performance of the damper in service. The test is generally
performed to characterize the damper, while its effectiveness on a specific conductor is determined by tests
on laboratory spans because its effectiveness strongly
depends on the damper location.
However, for conductors of standard use, some utilities
have established power limits or force and phase limits
(Figure 2.4-32) that can be used as evaluation criteria of
the damper effectiveness without the need to perform
tests on a laboratory span. These limits are only valid
for the given conductor and for standardized line
parameters, and require the damper positioning and
quantity per span to be specified by the user. In some
cases, the tests are performed at constant displacements
of 0.5, 1, or 2 mm, depending of the damper size and,
generally, the same damper is driven at two displacement levels, with the higher level used at the lower frequencies (Figure 2.4-6).
The results of the forced response test are generally
expressed by graphs showing one or more of the following quantities in the domain of the vibration frequency:
• Reaction force of the damper and phase angle
between force and velocity or displacement (examples of these graphs are shown in Figures 2.4-6, 2.4-8,
2.4-14, and 2.4-32)
• Damper mechanical impedance and phase angle
between force and velocity
Figure 2.4-32 Performance limits established by ENEL,
Italy, for vibration dampers to be installed on OPGW
cable 17.9 mm diameter and response curves of a
suitable vibration damper (courtesy U. Cosmai).
2-53
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
• Damper mechanical reactance and mechanical resistance, as shown in Figure 2.4-12.
• Power dissipated by the damper
IEC 61897 Standard
The IEC 61897 Standard, entitled: “Overhead Lines
Requirement and Test for Stockbridge-type Aeolian
Vibration Dampers,” specifies mechanical and electrical
tests including performance and fatigue tests.
Performance tests
The assumption of the 150 microstrain as reference
value for the test is questionable. In the standard, it is
specified that the value of 150 microstrain is only for test
purposes, and it is not directly related to life expectancy.
However, it seems logical to assume that the value of
150 microstrain is taken as the endurance limit of the
conductor—i.e., the maximum bending strain value that
can be endured indefinitely by the conductor. In fact, if
at this value, the power dissipated by the system exceeds
the assumed wind power input, it means that in service
the value of 150 microstrain will never be achieved.
The performance tests are:
• Damper characteristic test
• Damper effectiveness evaluation
The damper characteristic test is quite similar to the
forced response test of the IEEE Std.664. It is performed at a constant velocity of 100 mm/s but in a frequency range between 180/d and 1400/d, d, being the
conductor diameter in millimeters.
These test results can be used for establishing the effectiveness of the damper for a particular application, when
the user specifies performance limits in terms of force
and phase or power. These tests results also provide a
useful quality control tool and constitute a reference for
sample (acceptance) tests of the production lots.
The damper effectiveness evaluation is similar to the
power test method but with different test parameters and
evaluation criteria. The damper is installed on a test
span having a minimum free length of 30 m (Figure
2.4-33). Conductor bending strain is monitored at one
span extremity and at both sides of the damper(s) by
means of strain gauges. The span is excited by a shaker
to achieve stable conductor motion at the frequencies for
which the resonance occurs. A maximum of 20 tuneable
harmonics should be excited. The vibration amplitude is
adjusted at each tuneable frequency until the highest
bending strain reaches 150 microstrain (single peak). In
this condition, the power required to vibrate the span
must exceed the assumed wind power input in the real
span.
Figure 2.4-33 Laboratory test span equipped for the
damper effectiveness test as required by IEC 61897
Standard.
2-54
It has been established by several test engineers that 150
microstrains may be difficult to achieve when a damper
with high power dissipation is installed on the test span
and may require high vibration amplitude. In this case,
due to the nonlinear response of the damper, its behavior at high amplitude will be different from that at a
lower, more realistic amplitude. It is speculated that the
parameters given in IEEE 664, (constant antinode loop
velocity at 100, 200, or 300 mm/s) are more realistic.
The tolerance allowed for position of the strain gauges
has been criticized because large errors in the measurements could result. Some users have suggested the use of
the bending amplitude measurements in place of the
strain measurements as the most practical method.
Damper Fatigue Tests
The fatigue tests of dampers are performed with a
damper attached directly to a shaker, as shown in Figure
2.4-25. They are required by the IEC61897 Standard
and by most of the utility’s specifications.
Two alternative methods are proposed in the standard.
The first requires sweeping frequency at constant velocity of 100 mm/s and accumulates 100 million cycles,
whereas the second excites vibration with constant
amplitude of 0.5 mm at the higher resonant frequency
of the damper and accumulates 10 million cycles.
The swept frequency method can be performed with a
linear sweep rate of 0.5 Hz/s or with a logarithmic sweep
rate of 0.2 decade/min. Using these test parameters, the
test for a medium-size damper may take 60-70 days.
The resonant frequency fatigue test, performed at the
highest resonance of the damper, can be completed in
few days, even for larger dampers. However, the resonant frequency method appears suitable for symmetrical
dampers having only two resonances, since both sides
are involved, and the messenger cables can be stressed at
the maximum bending stress both at the clamp and
mass attachments. For asymmetric dampers with four
resonances, the test should be performed at the higher
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
resonant frequency of each side. Also, the constant
amplitude of 0.5 mm may be considered suitable for a
phase conductor damper where the highest resonance
frequency is, for example, 30 Hz, but not for an earth
wire damper, where the highest frequency can be, for
example, around 80Hz and the acceleration and force
on the damper increase greatly. This may not represent
the practical situation. Further, it is probable that maintaining such a constant amplitude makes the test much
more severe on a high-performing damper. Thus, it
seems more reasonable and realistic to perform the resonant frequency fatigue test at constant velocity of 100
mm/s as for the sweeping frequency fatigue test.
The main utility specifications generally require the resonant frequency fatigue test, with only few exceptions
imposing the swept frequency method.
Damping Efficiency Evaluation
As previously mentioned, the damping efficiency of a
vibration damper can be defined as the ratio of power
actually dissipated by the damper to that which would
be dissipated by a perfect damper: PD/Pmax.
The basic criteria for the evaluation of the effectiveness of
a vibration damper is to compare the wind power input
with the total power dissipated by the damper and by the
conductor for all the tunable harmonics of the test span.
The power dissipated is measured at a given vibration
velocity (IEEE Std 664) or at a given maximum bending
stress (IEC 61897). For each test frequency, the dissipated power must exceed the assumed wind power input.
The wind power curve is selected from among the various
curves available in the literature.
Bonneville Power Administration (1982) included a different approach in its specifications based on a simple
acceptance curve, shown in Figure 2.4-34, valid for
Drake and Bunting conductors. The Tennessee Valley
Authority has adopted the same curve for acceptance of
dampers fitted to conductors with diameter in the range
of 19.58 to 46.36 mm.
Chapter 2: Aeolian Vibration
interaction results in satisfactory efficiency when there is
a good impedance match between the damper’s impedance and the conductor’s impedance over the range of
frequencies where protection is needed. The acceptance
curve presents a standard for minimum acceptable efficiency. The protective capacity of the damper in the
intended application depends not only on the damping
efficiency achieved, but also on the self-damping characteristics of the conductor and, importantly, the power
supplied by the wind. That power is subject to some
uncertainty. Different experts rely on different sources of
data on it, and they provide for effects of terrain-induced
turbulence in different ways. Thus, the damping efficiency is a matter of measurement, but determination of
protectable span lengths requires judgement. Generally,
it is the responsibility of the damper supplier to provide
that judgment, since liability for unsatisfactory protection rests with the supplier.
The basic idea for the generation of an acceptance curve
has been known since 1956 (Tompkins et al. 1956), and
the curve was illustrated for hypothetical situations by
Rawlins in 1958.
The acceptance curve represents the minimum acceptable values of the damper efficiency determined by
either the ISWR test method or the power test method
for all the tunable resonance frequencies of the test span
corresponding to the wind velocity range of 1 to 7 m/s.
2.4.4
The Application of Dampers
As already mentioned, application criteria for vibration
dampers are the responsibility of the damper manufacturer, who should provide clear installation instructions
and damper distribution tables. The latter contain information about the damper quantity and positioning in
This method has been also adopted by other utilities
worldwide and included in some National Standards
(Australian Standard 1985).
The approach separates the protection question into two
parts: (1) the quality of the damper; and (2) its protective
capacity in terms of the length of span that it can protect. The acceptance curve addresses the first of these. In
particular, it concerns how efficient the damper is when
applied to the conductor in question. That involves both
the quality of the damper’s fundamental design and the
interaction between the damper and the conductor. That
Figure 2.4-34 Damper efficiency acceptance curve.
2-55
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
relation to span lengths and for both suspension and
tension span extremities.
Vibration dampers are normally applied near the span
terminations, falling within the end vibration loops of
the conductor (see Figure 2.4-35). Because of traveling
wave effects, a single damper placed near one end of a
span is able to reduce the amplitude of the entire span,
providing there are no reflection points, such as warning
devices, or other heavy items within the span. For normal suspension spans, or areas of moderate vibration
severity, one damper per span can provide adequate protection.
The location point in the span is an important factor in
the effectiveness of most vibration dampers. Some of the
helical-type dampers, which can be used on small-diameter conductors, such as ground wires, are noncritical in
this respect, since a significant part of their length
always lies in the region of the antinode.
Effective distributed mass dampers for larger conductors have not been developed; hence, damper positioni n g i s a n i m p o r t a n t c o n s i d e r at i o n wi t h p h a s e
conductors. Because vibration loop length is a function
of wind velocity, the relative position of a fixed damper
with respect to the optimum position is rarely ideal. It is
only possible, within the range of vibration-producing
wind velocities, to select a placement that will not be
located at a node, where its effectiveness is minimal.
As noted previously, the normal range of wind velocities
able to generate conductor vibration is about 1-7 m/s,
Figure 2.4-35 Distribution of Stockbridge-type vibration
dampers along the spans.
(A) installation of one damper at one span end, at the
distance P from the suspension clamp.
(B)Installation of two dampers per span, one at each
extremity.
(C)Installation of four damper per span, two at each
extremity spaced by the distance P1.
2-56
extending to 10 m/s under some conditions. The upper
limit is apparently fixed by two factors. Higher velocity
winds tend to become more turbulent, and conductor
self-damping increases at the higher frequencies. It is,
therefore, possible to calculate the significant range of
loop lengths for damper performance from known line
parameters. The relationships that solve for nodal wind
velocity when loop length is known are easily recast to
solve for loop length when wind velocity is known:
=
2.703
H
d
Vw
w
2.4-6
Where
Vw = wind velocity (m/s)
= loop length (m)
d = conductor diameter (m)
H = conductor tension (N)
w = conductor mass per meter (kg/m)
Solving for loop lengths of a Drake conductor tensioned
at 20% of its Rated Strength and for a wind speed of 7
m/s:
l=
28,024
2.703
⋅ 0.02814 ⋅
= 1.43m
1.6281
7
A damper placed at this location would be relatively
ineffective near the frequency range that generates this
loop length (46 Hz).
The avoidance of nodal locations is not the only consideration in damper location, although it does provide one
point in the prediction of performance. Most dampers
are very nonlinear with respect to performance at various frequencies. This information is not normally provided to the user, although any manufacturer should be
expected to have determined the characteristics of their
product. Final location may be selected to enhance a
strength or to protect a weakness in the damper itself.
Manufacturers will usually recommend an installation
distance for any particular damper and situation.
A generic criterion for the damper positioning considers
the installation of the damper at a distance P from the
span end equal to 70-80% of the loop length, corresponding to the maximum wind velocity considered. For
example, considering the installation point at 80% of the
shorter loop, the distance P can be calculated using the
following equations.
P = 0.31 ⋅ d ⋅
H
w for maximum wind speed of 7 m/s
2.4-7
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
and
P = 0.22 ⋅ d ⋅
H
w for maximum wind speed of 10 m/s
2.4-8
In suspension spans, when two dampers per span are
necessary, the application of one damper per span
extremity is preferable to the solution of placing both
dampers at one extremity only. Sometimes, the use of
different spacings is advocated as a method of increasing
the frequency coverage. In long spans, where two dampers per span extremity are necessary, the second damper
positioning, P1, is generally taken at a distance from the
first damper equal to 80-100% of the distance P.
U.S. practice has normally recommended a distance P1
corresponding to about 85% of P, but with newer
damper models an even shorter spacing is being recommended.
If Equation 2.4-7 is applied to Drake conductor,
wherein H = 28024 N, w = 1.628 kg/m, and d = 0.02814
m (28.14 mm), a value of P = 1.14 m (3.49 ft) is
obtained. Considering P1 = 0.8P, the distance of the
second damper from the first one will be 0.91 m
(2.78 ft). If these values of P and P1 are substituted for
loop length ( ) in Equation (2.4-6), the solutions indicate that the dampers would be at nodal position,
respectively, at winds of 8.75 and 4.91 m/s, or 19.6 and
11 mph.
Special considerations apply for the application of
dampers near tension clamps. It is recognized that tension clamps are less critical compared to suspension
clamps. The jumper loop act somehow as a bretelle
damper. Moreover, for low vibration frequencies, a tension clamp articulates, and little or no bending stress is
applied on the conductor. With increasing frequency,
the inertia of the clamp and its attached jumper reduces
gradually its articulation, and it finally becomes a fixed
point. For this reason, the application of two dampers
at the tension clamp is sometimes suggested on the
assumption that one damper will fall near a node for a
given vibration frequency. For example, long deadend
insulator strings may contain a full loop, and the
damper may fall in a node at some frequency.
The same concept has been considered for the application of dampers near fittings such as warning spheres
and other devices that show a degree of mobility at
lower frequencies. For example, on the OPGW of the
Orinoco River crossing of the 400-kV Guayana
Chapter 2: Aeolian Vibration
B-Palital, Venezuela, in subspans between warning
spheres, two dampers near one of the spheres has been
installed rather than one damper near each sphere.
Section 2.5.3 also deals with the problem of the damper
position optimization: in the case of conductor with
only one damper or with more dampers and also in the
case the armor rods are present.
For the installation of asymmetric Stockbridge-type
dampers (4-R) at span extremities, questions have been
often formulated about the most convenient orientation
of the masses. The difference of the damper performance when the big mass is oriented toward the span
center, and when it is oriented toward the span end, is
generally unknown, but it is supposed to be small. However, some damper manufacturers suggest installing the
units with the big mass oriented toward the center of the
span because it, considering the clamp rotation effect
discussed in Section 2.4.3, will slightly improve the control of the lower vibration frequencies.
Multiple and In-Span Damping
The use of a heavy inert mass as a damper can be misleading. Although a heavy mass placed a short distance
from the suspension may reduce the conductor strain at
the suspension, it is essentially serving as a reflection
point, and a high strain level may then exist at the mass.
The same problem can be imposed on a line through the
addition of heavy warning spheres or catenary lights.
Although the span ends may be damped, heavy masses
added to a span can create sections (subspans) between
them that are isolated from the end span damping. The
same effect, sometimes with a more complex distribution of the conductor tension, is determined by the
installation of interphase spacers used for the mitigation
of the conductor galloping. In these cases, a suitable
application of vibration dampers in each subspan
should be considered.
With very long spans, a single damper near each end
may not provide adequate protection. The normal
damping procedures use additional dampers at each
end, spacing them along the conductor in patterns calculated to minimize the number of dampers that could
simultaneously fall near a node. In many cases, this procedure has provided adequate protection, and groups of
dampers up to five to six units have been usefully
applied. However, this procedure is only effective to a
certain limit, since the amount of damping fails to
increase in proportion to the number of dampers. The
dampers applied at the greatest distance from the suspension tend to receive a higher proportion of the vibration load and, in time, may fail through fatigue. The
damper nearest the suspension is protected by the outly-
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
ing dampers, and receives little vibration excitation. The
multiple damping approach includes the possibility of
progressive damper failures, which could, in time,
endanger the span.
in Section 2.5.3, methods of calculation are available in
order to define the type, number and position of the
dampers suitable to control aeolian vibrations for a certain application.
An alternate procedure is the use of in-span damping
(Rawlins 1961; Sellers 1962) that consists of installing
vibration dampers in the central part of the span in addition to the dampers installed at the span extremities.
2.4.5
A single damper placed a significant distance from the
span termination is likely to become a nodal point at
nearly all frequencies. However, if it is given a properly
spaced partner—i.e., a second damper placed not too
far apart—it becomes impossible for both to be simultaneously nodal within the normal range of wind velocities that generate significant vibration. If the Energy
Balance Principle is applied to an in-span damping
problem, a safe assumption would be that only one of
the paired dampers could act at a time. However, when
more damping capacity is deemed necessary, a group of
three or more dampers can be considered instead of the
paired units. Experience with bundled hardware tends to
make complex assemblies within the span more acceptable. However, dampers and their clamps should receive
special attention because of their inaccessibility and the
damping should err on the side of caution to avoid
future maintenance.
A combination of multiple and in-span damping has
been used for the damping system of the Chacao Channel crossing, a 200-kV single-circuit line section with one
alumoweld conductor per phase strung at 34% UTS
(Cosmai 1998). The central span of 2682 m, as well as the
lateral spans of 450 m, have been equipped with groups
of five vibration dampers of Stockbridge type at each
span extremity. Each group, as shown in Figure 2.4-36,
consists of five dampers: three for low- and mediumvibration frequencies (ST4), and two for high frequencies
(ST3). Preliminary calculations demonstrated that inspan damping was also necessary, and due to the presence of warning spheres, two dampers, one ST4 and one
ST3, have been installed on each subspan. As explained
Other Protection Methods
Armor Rods
Armor rods are among the earliest methods used for
protecting overhead lines from the effects of vibration.
When first used, in 1925 (Aluminum Company of
America 1961), the armor rods were made from strands
of the same conductor on which they were applied, thus
providing an additional layer of strand extending a
short distance from both sides of the suspension clamp.
Varney (1928) experimented with their use on a line that
had experienced fatigue breaks within two or three
months after construction. Three years after armor rods
were installed, no further breaks were reported. His
analysis emphasized the reduction in bending at the suspension that could be realized through the use of rods.
To avoid an abrupt change in section at the rod ends, he
advocated tapered rods. The rods were twisted in place
by means of a special tool, and the ends were secured by
a bolted two-piece clamp. The use of armor rods
became common overhead line practice, either with or
without additional damping devices. An additional consideration in the use of armor rods was protection of the
conductor during insulator flashover, especially where
overhead ground wires were not used.
Wrench-Formed Armor Rods
Any device added to an overhead line has its own potential hazards, and rods are no exception. Wrenches used
for installing armor rods mark the conductor, but normally the marks are far enough from the suspension
point to be harmless. However, a report from Sweden
(Bovallius et al. 1960) documents a case in which armor
rods contributed to conductor damage. Tapered rods
had been installed, and the ends secured with a singlepiece annular ferrule, pressed in place. Chafing developed as a result of motion between the rods and the conductor. Ultimately, some rods wore through entirely, the
Figure 2.4-36 Chacao Channel Crossing. Distribution of vibration damper at each extremity of the
central span (2682 m) and of the lateral spans (450 m). In-span damping was also necessary.
2-58
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
end ferrule was lost, and considerable conductor damage
resulted, most of it caused by abrasion against the armor
rods. The area in which this occurred was evidently a
severe vibration zone. It is quite possible that the total
line damage might have been greater if it had been constructed without rods or dampers, but more secure end
clamps would have reduced the damage.
Wrench-formed rods without tapered ends were introduced as a means of obtaining some of the benefits of
armor rods at reduced cost.
Factory-Formed Armor Rods
The development of factory-formed armor rods provided for easier installation and a closer fit than was
possible with wrench-formed rods. End clamps became
unnecessary. Factory-formed rods have not been produced with tapered ends. This has precipitated arguments about the contribution of the tapered section.
Factory-formed rods have given good long-term service,
and the question of taper has not been completely
resolved. The design of armor rods is an engineering
compromise. Large-diameter rods reduce conductor
bending at the suspension, but can become difficult to
apply and may cause high conductor dynamic and static
bending strain at the ends of the rods.
With the advent of bundled conductor systems, armor
rods, where used, have tended to be the factory-formed
type. Presently, tapered armor rods are not commercially available, although many units are still in service
on old lines (Figure 2.4-37).
Factory-formed rods evolved into a family of helical
products, which also include splices, repair sleeves for
damaged conductors, tension clamps, and so-called
hairpin spacers.
Chapter 2: Aeolian Vibration
When used as full tension splices, the rod grip is
enhanced by coating the internal parts in contact with
the conductor with a conductive aluminium oxide grit.
On overhead cables incorporating optical fibers such as
OPGW and ADSS, armor rods are also used as a protection under vibration damper clamps, factory-formed
suspension and tension clamps, and warning spheres.
Factory-formed rods are also applied under the clamps
of interphase spacers and in special cases under the
clamps of bundle spacers.
Materials used in armor rods are aluminum alloy for
aluminum-based conductors and galvanized steel or
alumoweld for steel-based or alumoweld-based shield
wires. Copperweld or phosphor bronze are used for rods
to be fitted on copper and copperweld conductors.
The rods are factory matched and packed in sets or preassembled in subsets for faster and easier installation
(Figure 2.4-38).
Armor rods are intended for a single application, as
during installation they may be permanently deformed,
and the manufacturers recommend the use of new sets
of rods in case of replacement.
The actual damping realized with factory-formed rods
is less than the damping obtained with wrench-formed
rods, because the factory-formed rods grip the conductor tightly. Although the damping due to armor rods is
low in comparison to that of properly applied dampers,
there may be situations in which rods alone will provide
adequate protection. The effects of armor rods installed
at tangent supports of the conductors is discussed in
Chapter 3 in terms of damping and reinforcing of the
conductor against the dynamic bending caused by aeolian vibration.
In order to obtain the maximum efficiency, it is essential
that the lay direction of the armor rod set be identical to
Figure 2.4-37 Tapered armor rods (courtesy ISELFA).
Figure 2.4-38 Factory-formed rods packed in sets or
preassembled in subsets.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
the lay direction of the conductor outer layer strands
(Figure 2.4-39). Armor rods are generally produced
with right-hand lay. Left-hand lay should be specifically
required.
Armor rod manufacturers provide users with suitable
installation instructions, including tables for the correct
choice of the rod sets in terms of number and diameter
of the rods in relation to the overall diameter of the conductor to be protected. As illustrated in Figure 2.4-40,
the correct number of rods should, after application,
provide a slight gap between the rods. The gap should
preferably be distributed as in Example 1; however, a
gap concentrated in one location (Example 2) can be
also accepted. An excessive number of rods installed as
in Example 3 produces bridging conditions and can lead
to rod abrasion, while, if installed as in Example 4 provide little protection and may damage the rods and the
conductor.
To meet the corona and RIV requirements and for safe
handling, the rod extremities are rounded, which is
Figure 2.4-39 Correct lay direction of armor rods in
relation to the lay direction of the conductor outer layer.
Figure 2.4-40 Examples of correct and incorrect
installation of the armor rods.
2-60
known as “ball-ending.” However, for most EHV applications, the rod extremities assume a “parrot bill shape”
instead of the standard “ball-end” shape to enhance the
electrical performance (Figure 2.4-41). In this regard,
the alignment of the rod extremities should be maintained within the tolerances given by the manufacturer.
2.4.6
Spacers and Spacer-dampers
General
The trend toward bundled conductors in transmission
lines (Figure 2.4-42), which began in the early 1950s,
was based primarily on electrical considerations but
introduced mechanical problems not previously encountered on overhead lines. Most of the troubles were associated with line spacers. Early rigid spacers caused
excessive conductor wear and conductor strand failure,
and in some cases the spacers themselves fractured.
Loose-fitting joints in articulated spacers often showed
a high rate of wear. Once the need for some degree of
flexibility or articulation was recognized, there was a
tendency to design for unrealistic limits. Spacer-testing
machines constructed in various countries subjected
new designs to motions that were highly improbable in
final use, but designs were evolved to meet these tests.
Figure 2.4-41 Armor rods with “parrot bill”
terminations, for EHV transmission line
conductors (courtesy Nuova Elettromeccanica
Sud).
Figure 2.4-42 Conventional conductor bundles.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
The accumulation of experience from operating lines
and experimental test spans led to a better understanding of spacer requirements, and spacer designs became
more realistic (Edwards and Boyd 1965). However, there
are still utility specifications requiring performances
that the spacers and spacer-dampers will never confront
in service.
The different types of spacers employed on transmission
lines can be classified as follows (Figure 2.4-43):
1. Rigid spacers
2. Semirigid spacers
3. Articulated spacers
4. Flexible spacers
5. Spacer-dampers
The characteristics and performance of each type of
spacer are fully described in Chapter 5. Here, some
notes are given about their main features and about the
testing performed on spacer and spacer-dampers with
particular regards to the effectiveness of the damping
systems against aeolian vibration.
Rigid, articulated, and flexible spacers do not contribute any damping or control of aeolian vibration, but
provide coupling between the subconductors, which has,
per se, a positive effect in reducing vibration or oscillation levels (Hardy and Van Dyke 1995). However, in
Chapter 2: Aeolian Vibration
most of the cases, this reduction is not enough to maintain the vibration levels within limits that do not produce fatigue accumulation on the subconductor strands.
Control of the aeolian vibration can be achieved either
by combining semirigid, articulated, and flexible spacers
with vibration dampers or installing spacer-dampers
only. The second solution is generally preferred for economical reasons and for the lower number of items to be
installed on the line. However, there are cases in which
spacer-dampers alone may be unable to control, within
safety limits, the levels of aeolian vibrations. For example, on twin bundles of light and strong conductors such
as AAAC, strung with high H/w, and under severe wind
conditions, spacer-dampers may be insufficient to mitigate aeolian vibration. In this case, the most rational
solution is to apply both spacer-dampers or nonrigid
spacers along the span and vibration dampers at span
extremities. The spacers employed should be light to
avoid the subspan effect—i.e., to prevent entrapment of
aeolian vibrations inside the subspans. Thus, the aeolian
vibrations will be able to travel along the span and reach
the vibration damper locations where they can be
damped. For bundles of three or more conductors,
spacer-dampers are generally sufficient to control within
safety limits the conductor vibrations, and vibration
dampers are installed only in special cases involving
long crossing spans.
Spacing and damping systems for bundled conductors
have reached levels of efficiency more than satisfactory
in controlling aeolian vibration and subspan oscillation.
However, the great number of clamps involved represent
a risk for the integrity of the subconductors on which
they are installed. In a transmission line, there are thousands of spacer clamps, and if just one of them gets
loose, the relevant subconductor will be seriously damaged and, if left unattended, it will break down and fall
to the ground.
This happens because the subconductor vibrations and
oscillations cause a sustained hammering between the
loose clamp and the conductor. Spacer clamps are generally made of aluminum silicon alloy, which is harder
than the pure aluminum of the conductor outer layer so
that, as a result of the continuous clashing, the conductor is the most damaged (Figures 2.7-8 and 2.7-9).
Figure 2.4-43 Main types of spacers.
The serious consequences of conductor failures, in term
of outage and repair costs, are well known. Thus, is very
important that the spacer clamps are provided with a
reliable locking system able to maintain a suitable clamp
grip for the whole life of the line.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Nevertheless, a good clamp design is not enough when
clamps are not correctly installed. So, the two main
points to be considered to prevent clamp loosening are:
Proper clamp design
Correct clamp installation
Design characteristics of spacer clamps and the correct
installation of the same are reported in Chapter 5. In
Figure 2.4-44, the main types of spacer clamps are illustrated.
Spacer-dampers
Spacer-dampers are articulated spacers that incorporate
into the articulations an energy-absorbing mechanism
generally consisting of elastomer in shear or compression, but also consisting of cables in bending and, in the
past, sliding surfaces. The damping mechanisms are
activated by the rotation of the spacer-damper arms.
The term “spacer-damper system” identifies the complexity of spacer-damper units, installed on the line
together with the relevant in-span distribution scheme,
which is an important factor especially for the control of
subspan oscillation (Hearnshaw 1974) (see Section
5.6.9).
A spacer-damper (Figure 2.4-45) consists of a central
frame, a number of clamps for attachment to the subconductors, a number of resilient articulations (one or
two per arm) containing the damping elements, and a
number of arms connecting the clamps to the central
frame via the articulations (see also Figure 5.6-9).
It has been illustrated in Section 2.5.4 that, in any bundle, there are resonant vibration modes in which no relative motion between subconductors exists, called rigid
modes and other natural vibration modes in which some
relative movement between the subconductors can cause
an elastic reaction of the spacer articulations with
respect to the spacer frame (Claren et al. 1974).
The ability of a spacer-damper to control aeolian vibrations is strongly related to the capacity of the main
frame to develop inertia forces able to combine rigid
modes, where no damping effect can be produced, with
one or more of the other natural modes, which can
cause spacer arm rotation and consequently dissipation
of energy.
Spacers and Spacer-damper Tests
The laboratory tests usually performed on the components of a spacer system can be classified as follows
(Cosmai 1966):
1. Prototype tests
2. Type tests
3. Routine tests
4. Inspection (sample) test
The prototype tests are part of an iterative cycle that is
usually executed during the spacer-damper design. Test
results are intended to optimize the design parameters
and suggest modifications that can improve the spacerdamper performance.
The type tests are performed to qualify the spacerdamper design. These tests are carried out by the manufacturer and are normally witnessed by the purchaser's
representatives. Independent test laboratories are often
employed to perform some of the tests.
Figure 2.4-44 Main types of spacer clamp.
2-62
Figure 2.4-45 Early design of triple spacer-damper
(courtesy U. Cosmai).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
The routine tests control production and continuously
verify its compliance with the design parameters.When
routine tests are intended to prove conformance of spacers to a specific requirements, they may be performed on
every spacer. Routine tests are generally nondestructive
tests.
The inspection tests are usually performed by the manufacturer in the presence of the purchaser's representative, on production lots, prior to shipment. The purpose
of these tests is to demonstrate that the materials concerned are in compliance with the requirements of the
users’ Technical Specification.
The prototype and type tests also provide the input data
for analytical prediction of the damping system performance. In the calculation, the spacers are defined by the
values of the torsional stiffness and damping of the
articulations, as well as by the axial stiffness and damping of the same. Moreover, the geometrical characteristics, weight, center of gravity, and inertial moments of
each component are considered.
In addition to the above laboratory tests, field tests are
sometimes requested by the users to verify the behavior
of the system including the bundle and the relevant
damping system under aeolian vibration on lines under
Chapter 2: Aeolian Vibration
construction and on lines in operation. Sometimes, subspan oscillation is also considered.
The flowchart of Figure 2.4-46 shows a possible organization of the investigation methods available for the
manufacturer and users of vibration damping units and
systems for transmission lines.
In 1998, IEC published the first international standard
on spacers, the IEC 61854, “Overhead Lines. Requirements and Tests on Spacers.”
The standards have been prepared by IEC TC11 WG09
consisting of utility and manufacturer representatives
from 10 countries worldwide. Different points of view
among the working group members about the performance of the spacer-dampers resulted in the identification of more than one procedure for some tests.
Moreover, test parameters were left to agreement
between purchaser and supplier when agreement on a
specific value was impossible to achieve. Therefore, in
the standard, there are tests in which the parameters are
fully indicated and tests in which the parameters are left
to the agreement between purchaser and supplier.
The application of these standards, during the past 7-8
years, demonstrated that the lack of test parameters and
Figure 2.4-46 Investigation methods available for the manufacturer and
users of vibration damping units and systems for transmission lines.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
the presence of alternative procedures for the same test
could create confusion for the users. However, the positive effect of the standard is that it helps to avoid some
unrealistic and expensive tests, which are sometimes
required by the users.
Spacer-damper Tests
To ensure a proper performance during their lifetime,
spacer-dampers should fulfil the requirements described
below.
Mechanical Characteristics
• Clamping. To prevent the spacer clamp loosening or
slipping, the clamping characteristics should be verified by a clamp slip test (longitudinal and torsional),
breakaway bolt test, and clamp bolt tightening test.
The tests should be performed using the conductors
for which the clamps are designed. At the end of
fatigue tests (see next section: “Dynamic Characteristics”), the residual tightening torque of the clamp
bolts is measured to verify the capacity of the fastening system to resist the loosening effect of conductor
vibration and oscillation. Clamping requirements are
fully described in Section 5.6.5.
• Mechanical Strength. In service, spacers should withstand mechanical loads due to environmental or
short-circuit conditions (Manuzio 1967), as reported
in Section 5.6.4. These loads can be reproduced in the
laboratory by performing compression and tension
tests, as well as simulated short-circuit tests. The
actual short-circuit test, to be performed at high
power test laboratories, is still required by some users,
but has not been included in the IEC Standard
61854.
Dynamic Characteristics
• Flexibility. Longitudinal, vertical, conical, and transversal flexibility tests should be carried out to demonstrate the ability of the spacers to accommodate
any expected relative movement or static displacement of the subconductors under normal service conditions, without damage to the conductors or spacers,
as reported in more detail in Section 5.6.4.
• Fatigue. The fatigue endurance of spacers subjected
to the alternating motions and vibrations occurring
in service should be in excess of the expected life of
the line. A subspan oscillation test and an aeolian
vibration test, as prescribed by the IEC Standard
61854 (IEC TC11 1998), are the most representative
tests. It should be noted that the IEC Standard 61854
does not specify longitudinal and conical fatigue tests
because these movements are considered transient or
negligible in service. Fatigue endurance requirements
of spacers and spacer-dampers are fully discussed in
Section 5.6.6.
2-64
• Elastic and Damping Properties. Tests to determine
the damping properties of spacer-dampers can be
performed in accordance with three methods proposed by the IEC Standard 61854:
—Stiffness-damping method
—Stiffness method
—Damping method
The elastic and damping characteristics determined
by the different methods are not equivalent, and none
of the methods can provide direct information about
the performance of spacer-dampers in service. However, they can be used both to establish acceptance
criteria for sample test and to define the analytical
model of the spacer-damper to be used in computer
programs formulated to predict the behavior of the
damping systems with regard to aeolian vibration
and subspan oscillation.
A description of the three IEC methods is reported in
Appendix 2.5, together with an alternative procedure
for the stiffness-damping method employed in some
computer programs.
Damping and stiffness characteristics should also be
measured before and after the fatigue tests to determine the fatigue endurance of the spacer articulations.
Electrical Characteristics
• Electrical Resistance. The spacer-damper components should be electrically conductive as described
in Section 5.6.4, under the subsection titled “Electrical Characteristics.” Tests are performed to measure
the electrical resistance of the spacer-dampers
between clamps and to verify that the conductivity is
such that potential differences and current flows do
not result in degradation of spacer components or
damage to the subconductors.
• Corona and Radio Interference Voltage. Tests to verify
the electrical behavior of spacers in service conditions
(see the same subsection mentioned above) are performed in high-voltage test laboratories, installing
one spacer on a length of a tube bundle having the
same geometrical characteristics of the real bundle
concerned (Figure 2.4-47).
• Resistance to Environmental Attacks. Spacers are
used worldwide under completely different environmental conditions and levels of pollution. Appropriate climatic and corrosion tests should be carried out
to verify the resistance of the metallic materials and
the elastomers to various aggressive agents such as
ozone, UV, extremes of temperature, and industrial
and marine atmosphere.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
• Galvanized steel is mainly used for the elements of
the clamp-locking system and sometimes for other
components such as hinge pins and bolts, central
frames spring articulations, and steel ropes. The zinc
protection is generally made by hot dip galvanization, in accordance, for example, with ISO1471,
except when spring steel is used (see also Section
5.6.3). In any case, the thickness of the zinc deposit
should guarantee corrosion-resistance for the whole
life of the line. Considering an average consumption
of zinc of 0.8÷1.5 μm per year, typical of rural areas
and coastal areas, a minimum galvanizing thickness
of 40÷50 μm may guarantee the protection for the
expected life of the line.
• Tests on Nonmetallic Components. The chemical composition of the elastomers used in the spacer for the
articulation or for the lining of the clamps is seldom
disclosed by the manufacturers because it represents
the result of long and expensive studies and laboratory tests, and it is kept secret.
The elastomers are generally described using laboratory tests that can be divided in two categories. The
first includes tests to characterize the elastomer
through the measurement of its physical and mechanical characteristics (hardness, density, tensile strength,
Modulus of elasticity, etc.). The second category
includes tests to define the performance of the elastomer with respect to the stresses applied to the spacer
in service (compression set, tear resistance, etc.) and
attacks by environmental agents (aging tests).
Figure 2.4-47 Corona emission of a triple spacerdamper at 360 kV phase to ground. (courtesy Nuova
Elettromeccanica Sud).
2.5
SYSTEM RESPONSE
2.5.1
Introduction
Chapter 2: Aeolian Vibration
This section is aimed at describing the models available
to simulate the response of a system conductor(s) plus
damping devices to aeolian vibrations. The considered
models are based on the Energy Balance Principle
(EBP). Basic assumptions, results, and limits of the
methods are discussed.
As already described in Section 2.2, the onset of aeolian
vibration is defined by matching of the Strouhal frequency with one of the natural frequencies of the conductor—i.e., aeolian vibration occurs when the vortexshedding frequency approaches that of a natural mode
of the system (single conductor, bundle conductor plus
devices etc.) and a resonance condition occurs. When
the vibration amplitude increases, lock-in effects occur,
and a self-excited mechanism is generated.
According to the Energy Balance Principle (EBP)
(CIGRE SC22 WG11 TF1. 1998), already introduced in
Section 2.1, the maximum steady-state amplitudes of
vibration for each of the excited vibration modes (i.e.,
for each of the excited natural frequencies) are the result
of a balance between the wind energy input and the
energy dissipated by the system.
However, as noted in Section 2.2.1, due to the wind variation in time and along the span, more than one vibration mode at a time can be excited, giving rise to a
typical vibration pattern, as shown in Figure 2.5-1,
which refers to a vibration amplitude measured on a single conductor of a real transmission line; the typical
phenomenon of beating is evident. (Beating may be
defined as an alternate increase and decrease in the
amplitude of a wave caused by the addition of another
component of nearly equal frequency.) The beat frequency depends on the difference between the two
excited harmonics. In Figure 2.5-1, the beating period
Tb is 1 second (beating frequency fb = 1/Tb = 1 Hz), 10
vibration cycles occur in 1 second, hence the two beating frequencies are 10 and 11 Hz.
The vibration severity is characterized by the maximum
antinode amplitude found in the time history, which can
be related to the maximum bending strain and to the
bending amplitude registered by commonly used aeolian vibration recorders. This maximum antinode amplitude (or bending strain on the conductor or bending
amplitude) is the value with which theoretical predictions must ultimately be compared.
When more than one frequency is excited, the span
vibration, from one extremity to the other, is no longer
2-65
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 2.5-1 Record of conductor vibration on a 275-m test span equipped with a Drake
conductor (EPRI 1979).
represented by a sinusoidal function, and no vibration
nodes are observed. This condition cannot be reproduced by methods based on the EBP, because the energy
input from the wind should account for the wind variations in space and time, and a more realistic model of
vortex shedding should be defined. Methods accounting
for this aspect of the aeolian vibration phenomenon
have been developed both in the time (Diana et al. 1993)
and the frequency (Noiseux et al. 1988) domain, but
they are still at a research stage.
Some authors derived from these methods a simplified
approach to aeolian vibration in turbulent conditions,
defining a reduced wind energy input to be used in EBP
simulation programs (Noiseux et al. 1988; Diana et al.
1979; Rawlins 1983). However, this aspect of the problem has not yet been fully resolved; research is continuing in this area.
Consolidated models for the simulation of the aeolian
vibration behavior of a system conductor (or bundle)
plus damping devices are based on the EBP, considering
only one mode of vibration at a time. The laboratory
tests allow for a reliable evaluation of the parameters
related to the energy dissipated by the conductor and
the damping devices. The problem related to the evaluation of the wind energy input is much more difficult:
wind tunnel tests to evaluate the maximum energy input
are made on rigid or flexible cylinders, leading to different results, as shown in Fig 2.2-15. The curves representing the flexible cylinder tests are in Rawlins (1983) and
Brika and Laneville (1995), while all the others represent the rigid cylinder tests.
The maximum wind energy input based on a rigid cylinder represents a conservative choice. The maximum
wind energy input based on a flexible cylinder is less so
in the real case, where, due to the beating phenomenon,
no nodes of vibration are present.
In the case of single conductors, the conductor vibration
modes and the energy dissipated by the conductor for
each mode of vibration can be readily identified, as will
be shown in Section 2.5.2.
2-66
For a single conductor plus dampers and other devices,
the task is more difficult, and this will be explained in
Section 2.5.3.
Finally, for the case of bundle conductor plus spacerdampers and other devices, the identification of modes of
vibration must be achieved by suitable numerical computation models, as will be explained in Section 2.5.4.
Once the system vibration modes have been identified,
the conductor vibration amplitudes can be defined
along the span as a function of a reference amplitude,
which then enables the wind energy input to be computed. If the mode of vibration is known, the motion of
the dampers, the spacer dampers, and any other device
present on the conductor can be determined as a function of the reference amplitude. The energy dissipated
may then be computed. The steady-state amplitude for
that mode of vibration is the one balancing the wind
energy input and the dissipated energy.
Most of the empirical functions, derived by wind tunnel
tests, for the wind power imparted to a unit length of
conductor—Pinput—can be expressed in the form:
Pinput = f 3 D 4 fnc( A / D)
2.5-1
where the fnc(A/D) functions are reported in Figure
2.2-15. f is the vibration frequency, and D is the conductor diameter. A/D is the nondimensional antinode
amplitude of vibration.
An analytical expression for the fnc(A/D) function is
given, as an example, in the IEC standard 61897 (IEC
61897 1998):
fnc (A/D) = 10z
where
8
z = ∑ an X n
n=0
X = lg(A/D)
a0 = -0.491949
a2 = -43.5532
2.5-2
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
a3
a4
a1
a5
a6
a7
a8
= -78.5876
= -86.1199
= 11.8029
= -58.1808
= -23.6082
= -5.26705
= -0.495885
Pmax =
The power dissipated by a unit length of conductor
(P/L), as reported in Section 2.3.6, can be measured on
a laboratory span, and the measured data are generally
expressed empirically through a power law:
P
Al f m
=k n
L
T
2.5-3
where T is the conductor tensile load; k is a factor of
proportionality, which depends on the conductor characteristics; and l, m, n are the amplitude exponent, frequency exponent, and tension exponent, respectively.
Values for the exponents are reported in Table 2.3-2,
while an example of the P/L expression including the k
factor is given by expression 2.3-20 (Noiseux 1992) in
Section 2.3.6.
In the case of a single undamped conductor, the steadystate antinode amplitude of vibration A, for each one of
the natural frequencies of the system, will be the one
balancing the expression
Pinput = P/L
2.5-4
For the case of damped conductors and bundles, the
balancing process must also account for the energy dissipated by the damping devices, as will be seen in Sections 2.5.3 and 2.5.4:
Pinput L = P + Pdd
2.5-5
where Pinput multiplied by L, the span length, ƒ is the
power introduced by the wind, P is the power dissipated
by the conductor due to self-damping, and P dd is the
power dissipated by the damping devices.
If the case of a single conductor protected by a damper
is considered, a nondimensional expression of the EBP
can be obtained:
Pw
P
P
=
+ D
Pmax Pmax Pmax
Where:
Pw = Pinput L
Chapter 2: Aeolian Vibration
1
TmL ω 2 A2 (see also Equation 2.4-3
2
in Section 2.4)
PD is the power dissipated by the damper
T is the conductor tensile load.
mL is the conductor mass per unit length.
ω is the vibration circular frequency (ω = 2πf and
f is the vibration frequency).
A is the antinode vibration amplitude.
and the term P D / P max is recognized as damping efficiency (see Section 2.4.3).
Aeolian vibration control is achieved if the system
damping, defined as the energy dissipated by conductors and damping devices for all the system vibration
modes, is high enough to limit vibration amplitudes to
within acceptable levels.
As observed in Section 2.2.4, in other fields of engineering, such as the vortex-induced vibrations of risers and
stay cables of bridges or other structures, the vortexinduced vibration severity is identified through the Scruton number (Sc) value:
2.5-7
Sc = δ mL/(D2 ρ)
Where:
mL is the cable mass per unit length.
D is its diameter.
δ is the damping of the considered mode
expressed as log-decrement.
ρ is the fluid density.
Once the Sc number is defined—i.e., when the system
overall damping (in form of δ) is identified—the amplitude of vibration A/D can be easily identified through
the Sc versus A/D relation reported in Figure 2.2-13.
For the case of a single conductor, this approach can be
readily applied, and A/D is the in-span nondimensional
(or reduced) antinode amplitude.
In case of bundle conductors, reference can be made to
the maximum amplitude along the span.
In Sections 2.5.2, 2.5.3, and 2.5.4 examples are given to
demonstrate the validity of this simple approach.
2.5-6
For clarity’s sake, it is worth recalling that the system
damping and its relation with the power extracted from
the flow may be expressed in different forms, as already
seen in Sections 2.2 and 2.3. In particular, for a certain
natural frequency f, let P be the power dissipated by a
2-67
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
certain length L of a conductor. The energy dissipated E
is simply E = P/f.
The conductor structural nondimensional damping ζ is
defined (Equation 2.3-10) as:
ζ =
1 E
4π Ek ,max
2.5-8
where
Ek,max is the maximum kinetic energy of the length
L of conductor.
For lightly damped systems, the following relation
between the nondimensional damping and the log decrement holds (Table 2.2-5):
δ = 2π ζ
2.5-9
And, finally, the Scruton number Sc, which expresses the
relation between the system structural damping and the
aerodynamic forces, is related to δ through Equation 2.5-7.
In some cases, the “Reduced Damping” or “Reduced
Decrement” (Rawlins 1983; Brika and Laneville 1996) is
used instead of the Scruton number to express the relation between the system damping and the power
extracted from the wind. The following relation (see Section 2.2.3) holds:
Sc = (Reduced Damping)/2
2.5.2
2.5-10
Mechanical Behavior of Single Conductors
Natural Frequencies and Modes of Vibration
T
is the propagation velocity of a flexural
mL
The term
perturbation along the string.
As an example (EPRI 1979), for a 366-m span equipped
with a Drake conductor tensioned at 28,024 N (about
20% of its Ultimate Tensile Strength), the following values are obtained:
T = 28024 N
mL = 1.628 kg/m
L = 366 m
T
= 131.2 m/s
mL
fn =
1
λn
T
n T
=
= 0.179 n Hz
mL 2 L mL
(n = 1, 2, ….)
1
λn
T
n T
=
mL 2 L mL
If wind velocity of 0.75 m/s (V) is considered, which is
usually considered as the lowest wind speed at which aeolian vibration on a conductor occurs, the vortex-shedding
frequency, according to the Strouhal formula is:
f = 0.185 V/d = 0.185 0.75/0.028 ≈ 5 Hz
2.5-11
According to this model, the vibration modes are sinusoidal functions (Figure 2.5-2):
2π
λn
x)
2.5-12
where An is the antinode amplitude of vibration.
Figure 2.5-2 Vibration modes—taut string model.
2-68
2.5-15
which corresponds to the frequency of the 28th mode of
vibration. With a wind speed around 3 m/s, we would
obtain a frequency around 20 Hz.
where L is the span length, λn is the wave length, T is
the tensile load, and m L is the cable mass per unit
length.
yn = An sin(
2.5-14
and then f1 = 0.179 Hz, f2 = 0.358 Hz,... f10 = 1.79 Hz …
f28 = 5.012 Hz … f168 = 30.07 Hz
Usually a single conductor is modelled as a taut string,
and then its natural frequencies, ƒn (where n is the mode
number, n = 1, 2, ….) can be evaluated through the following expression (Sturm 1936; Claren and Diana
1969a):
fn =
2.5-13
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
So it is clear that aeolian vibration excites the higher
modes of vibration of the cable, not the lower ones,
which, on the contrary, can be excited by galloping.
In practice, as has been discussed in Section 2.3, a real
conductor is not like a string because it is characterized
by a certain flexural stiffness (EI). In that case, a more
realistic model of a conductor is a tensioned beam. So
the natural frequencies and vibration modes are represented by the following equations (Morse 1948; Claren
and Diana 1969a):
2
2
⎛ nπ ⎞ T ⎡ ⎛ nπ ⎞ EI ⎤
⎢1 + ⎜
⎥
⎜
⎟
⎟
⎝ L ⎠ mL ⎢⎣ ⎝ L ⎠ T ⎥⎦
1
fn =
2π
2.5-16
y n (x) = A n Sh(z n x) + B n Ch (z n x) + C n sin(a n x) + D n
cos(anx)
where z
n =
an = −
(2π f n ) 2 2.5-17
T
T2
m
+
+
L
EI
EI
(2 EI ) 2
(2π f n ) 2
T
T2
m
+
+ L
EI
EI
(2 EI ) 2
2.5-18
The shape of the vibration mode (A n , B n , C n , D n )
depends on the span end conditions, and this is, in turn,
fundamental to the correct evaluation of the strains and
stresses at the span extremities.
If the end conditions are hinges, the shape of the vibration modes is the same as for the taut string, and the
maximum bending strain on the conductor is found at
the antinode (Claren and Diana 1969b).
Chapter 2: Aeolian Vibration
slippage hypothesis, the maximum bending strain (on
the cable outer layer) is obtained through:
∂ 2 yn ( x ) D
(ε max )n =
∂x 2 2
2.5-19
where
D is the cable diameter.
In practice, however, a slippage mechanism among the
individual wires is present, and as detailed in Section
2.3, the maximum bending strain value is lower than
that defined above, and the cable stiffness is not equal to
the EImax value, and it is not constant along the span.
Usually if (CIGRE WG B2.11.TF1. 2005a) is used, both
for the correct evaluation of the conductor natural frequencies and for the strain computation, the EImax value
is corrected through a reduction coefficient, whose value
is generally around 0.5 (see also Section 2.3.3).
Moreover, the static configuration of a conductor is represented by a catenary, and the tensile load is not constant along the span. This fact makes the frequency and
related shape of the first vibration mode different from
that reported in Figure 2.5-2 (Diana et al. 1999). However, as already observed, aeolian vibration does not
excite the first conductor modes, and therefore, this is
not important.
In both cases, whether the cable flexural stiffness is
accounted for or not, in the free span, the cable mode of
vibration is represented by a sinusoidal function of the
type:
yn = An sin(
2π
λn
x)
2.5-20
If the span extremities are fitted with fixed constraints,
the vibration mode shape is as in Figure 2.5-3, and the
maximum bending strain is found at the span extremities (Claren and Diana 1969b).
The determination of the stresses due to the conductor
bending requires evaluation of the conductor flexural
behavior, which, in turn, depends on its flexural stiffness.
As already discussed in Section 2.3, if no slippage
between the single layers of an ACSR stranded conductor is considered, the equation to get the cable flexural
stiffness EImax is Equation 2.3-4.
The conductor curvature is defined as the second derivative of the conductor displacement, and then in the noFigure 2.5-3 Modes of vibration, beam model, fixed
constraints.
2-69
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
where λn is the wave length. As a consequence, in case of
hinged extremities, the maximum bending strain is at
the antinode (εa) and is given by:
∂ 2 yn ( x) D 4π 2
D
= 2 An
( ε a )n =
2
λn
∂x
2
2
2.5-21
where
An represents the conductor antinode amplitude of
vibration.
In case of clamped extremities (no rotation), the strain
(εc)n at the span extremities is higher than the antinode
strain, and the following relation applies:
⎛ εc ⎞
T
⎜ ⎟ = K λn
EI max
⎝ ε a ⎠n
As the cable stiffness increases, considering the same
vibration frequency, the loop length increases, as shown
in the following example, always related to the case of
the Drake conductor, already used.
Example:
For a Drake conductor: EImax 1600 Nm2
EI = 0.5 1600 ≈ 800 Nm2
Considering a 366-m span (L), the 168th mode has a
wave length of 2L/n = 4.36 m
Without EI: f n =
1
λn
T
= 30.07 Hz
mL
2.5-23
With EI:
2.5-22
T An D
(ε c )n = 4π K
EI max λn 2
1
fn =
2π
2
where the K coefficient depends on the λn
T
EI max
value (Claren and Diana 1969b) according to Figure
2.5-4. Also, in this case, the slippage between the single
wires of a stranded conductor modifies the above relationships through the EI reduction coefficient previously referred to.
A general observation can be made that λn is related to
the mode natural frequency fn through a relation with or
without the flexural stiffness EI.
2
2
⎛ nπ ⎞ T ⎡ ⎛ nπ ⎞ EI ⎤
⎢1 + ⎜
⎥
⎜
⎟
⎟
⎝ L ⎠ mL ⎢⎣ ⎝ L ⎠ T ⎥⎦
2
1 ⎛ 2π ⎞ T ⎡ ⎛ 2π ⎞ EI ⎤
⎢1 + ⎜
⎥
=
⎜
⎟
⎟
2π ⎝ λn ⎠ mL ⎢ ⎝ λn ⎠ T ⎥
⎣
⎦
=
1
λn
2
⎛ 2π ⎞ EI
T
1+ ⎜
⎟
mL
⎝ λn ⎠ T
= 30.95 Hz, with an increment of about 3%.
2.5-24
Considering a higher stiffness, say EI = 1200 Nm2, the
frequency corresponding to a wave length of 4.36 m—
i.e., to the 168 th mode—would be 31.38 Hz, with an
increment of about 3.4%.
As can be seen, the effect of stiffness is not important
for the evaluation of the natural frequencies, while, of
course, it is of primary importance for the evaluation of
the bending strains.
The Energy Balance Principle
Natural frequencies and related vibration modes can be
excited by the wind when the vortex-shedding frequency
approaches one of them. However, as already observed,
the wind velocity variation in space and time (Figure
2.5-5) is such that more vibration modes can be simultaneously excited, and so the vibration amplitude along
the span exhibits the well-known beat pattern.
Figure 2.5-4 Ratio between the strain at the clamp and
the antinode strain as a function of the λn
parameter (Claren and Diana 1969b).
2-70
T
EI max
Once the aeolian vibration phenomenon is initiated, it is
self-sustained due to the lock-in effect.
The presence of more than one vibration mode causes
the disappearance of the vibration nodes, and the phenomenon can become unsteady and very complex; this
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 2: Aeolian Vibration
makes it difficult to use the maximum energy input from
the wind as measured in wind tunnels on rigid cylinders
allowed to move or on flexible cylinders allowed to
vibrate according to an harmonic function (see Section
2.2). As already observed, the first is a conservative
choice, while the second is less so due to the presence of
more modes of vibration (Diana et al. 2005).
The graphical procedure shown in Figures 2.5-6 and
2.5-7, relevant to the Diana and Falco (rigid cylinder)
and to the Rawlins (1958) (rigid cylinder) wind power
input curves of Figure 2.2-15 and to conductor self
damping measured in laboratory, can be substituted by
an automatic evaluation performed by a software based
on the EBP (Equation 2.5-4).
The phenomenon is not easy to reproduce analytically,
and what is generally and cautiously done is to apply an
EBP approach; the EBP works in the frequency domain.
In its simplest form, one mode of vibration at a time is
considered, and the steady-state solutions computed correspond to the maximum vibration amplitude that could
be excited on that conductor at that frequency.
Each rendition of the EBP technology contains an
energy input curve among those in Figure 2.2-15 (or an
The reliability of results of these analytical computations is no better than the background data used in
them, particularly data on the power supplied by wind
during aeolian vibration (see Section 2.2.4) and data of
self-damping in stranded conductors (see Section 2.3.6).
This point has been already discussed in (CIGRE SC22
WG11 TF1 1998) and will be resumed at the end of this
section with some examples.
The balancing (Equation 2.5-4) of conductor self-dissipation (2.5-3) against wind power input (2.5-1) to
obtain predicted amplitudes of natural vibration basically requires determining the intersection of wind input
and conductor dissipation curves. A graphical solution
is shown in Figure 2.5-6.
Figure 2.5-7 presents the same data in an alternate
form.
Figure 2.5-5 Wind speed variation in space and time.
Figure 2.5-6 Prediction of conductor vibration
amplitudes at various frequencies, through cross-points
of wind input and conductor self-dissipation. (Values at
10 Hz are extrapolated) (EPRI 1979).
Figure 2.5-7 Predicted vibration and amplitudes
indicated by Figure 2.5-6 (EPRI 1979).
2-71
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
analytical expression like Equation 2.5-2) and an empirical relation for conductor self-damping (Equation
2.5-3) with parameter values shown in Table 2.3-2. As
an example, the case of the Drake conductor already
worked out in Section 2.5 is solved. The maximum antinode amplitudes of vibration (0-peak values) and relevant bending strains at the clamped extremities are
shown in Figure 2.5-8 as a function of frequency.
As with all analytical tools, the software based on the
EBP can also be used to perform a sensitivity analysis—
i.e., to evaluate the influence of the different line parameters on the aeolian vibration level. The other way to the
sensitivity analysis is to collect data from field measurements and/or experimental spans, with an obvious limitation of the number of conditions that can be
considered.
Test Drake - Orange Book
CONDUCTOR (0 X 0.00 + 0 X 0.00)
DIAMETER 28.110 [MM]
MASS 1.628 [KG/M]
DAMPING CONST.AKAPPA0.324E-04
TENSION 28024.00 [N]
STIFFNESS 800.00 [N*M^2]
TYPE OF WIND: NO TURBULENCE
TYPE OF CONSTRAIN: FIXED CLAMP
Figure 2.5-8 Rendition of the EBP Technology:
Drake conductor response to aeolian vibrations:
maximum antinode amplitudes of vibration (0-peak
values) and bending strains at the clamped
extremities (0-peak values) as a function of
frequency.
2-72
In Figure 2.5-9, which considers a Drake conductor, the
influence of the conductor tension is shown. As can be
seen in the empirical function used to reproduce the dissipated energy (Equation 2.5-3), a change of tension
reflects in a change of dissipated energy and then in a
variation of the vibration amplitude.
Physically, it happens that, at a given frequency and
amplitude of vibration, if the tension increases, the wave
length increases, and then the strain at the antinode,
given by ( ε )
a n =
4π 2
λ
2
n
An
D , decreases and, as a conse2
quence, the slippage between the single wires of the conductor and the dissipated energy decrease. If the
dissipated energy decreases, the vibration amplitude and
related strains increase.
Approximately the same trend of variation of the vibration amplitude with respect to the tensile load variation
could be found experimentally on the Isles de la
Madeleine test line (Hardy and Van Dyke 1995) (see
Figure 2.5-10). The tested conductor is the ACSR Bersfort. Both experimental and analytical results confirm
that the effect of tensile load on the vibration level is
Figure 2.5-9 Conductor tensile load effect.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
very important: an increment of tensile load causes an
enlargement of the frequency spectrum and an increase
of vibration amplitude.
In Figure 2.5-11, which also considers a Drake conductor, the influence of the wind turbulence level is shown.
As observed in Section 2.2.5, the roughness of the earth
surface plays an important role in the height of the
Chapter 2: Aeolian Vibration
boundary layer (the gradient height), as well as on the
mean and fluctuating (gusting) velocities. Accordingly,
the relevant characteristics of the flow at the location of
the conductor must be determined in order to evaluate
the static and dynamic interactions between the wind and
a conductor: they are the mean wind speed and the turbulence. These characteristics, as expected, are functions of
the topology of the local terrain and meteorological data.
In particular, different turbulence levels—qualified by the
turbulence intensity—can be associated with different terrain categories (see Sections 2.2.5 and 2.6).
What happens physically is that important wind velocity
fluctuations cause the loss of synchronization between
conductor vibration and vortex shedding: the wind continuously changes, and the phenomenon is always in
transient conditions. This does not allow the vibration
amplitude to increase up to the maximum values.
Figure 2.5-10 Conductor tension effect, experimental
findings, rms aeolian vibration amplitude versus
frequency (Hardy and Van Dyke 1995).
The phenomenon is reproduced in the EBP-based software by a simplified approach, just reducing the energy
input with respect to that relevant to low turbulence (see
Figure 2.5-12 for reduced wind power curves [Diana et
al. 1979] and also the data in [Rawlins 1998]).
At low frequencies, the cable self-damping is so low
that, even if the energy input is reduced due to turbulence, the vibration amplitude exhibits a small variation
with respect to the low turbulence condition. Moreover,
the estimated normalized wind input curves (Figure
2.5-12) converge at the highest vibration amplitudes.
Also, in the case of the turbulence effect evaluation, a
comparison between experimental and EBP-predicted
Figure 2.5-11 Wind turbulence effect.
Figure 2.5-12 Wind power input curves and low
turbulence curve. (b), (c) are the reduced wind power
input curves, (a) is the low turbulence curve (Diana
Falco 1971;Diana et al. 1979).
2-73
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
findings is possible (Hardy and Van Dyke 1995): Figure
2.5-13 shows the results found on the Isles de la
Madeleine test line on a Bersfort conductor.
For the experimental data, a 10% increase in normal
turbulence corresponds roughly to a decrease in amplitude of 20%; however, bigger reductions are predicted
by the EBP analysis.
However, as observed in Section 2.5.1, this aspect of the
problem has not yet been fully resolved, and research is
continuing in this area.
The last worked example compares the aeolian vibration behavior of the ACSR Drake conductor to that of
an ACS OPGW (around 15 mm diameter) and that of
an ACAR 1300 cable. For the three different conductors, the T/w parameter (ratio between conductor tension and weight per unit length) is kept constant and
equal to 1720 m. The T/w parameter expresses the cable
sensitivity to aeolian vibrations (see Section 2.6).
What can be observed in Figure 2.5-14 (a, b, c) is the
significant enlargement of the aeolian vibration range of
frequencies in the case of the ACS cable.
As introduced in Section 2.2.4, the evaluation of the
aeolian vibration level can also be made by an alternative method to the EBP, adopted in other sectors of
engineering. This approach consists of using the relationship between the Scruton number and the vibration
amplitude due to vortex shedding.
The relationship between the Scruton number and the
aeolian vibration amplitude, in the case of a single
undamped conductor, can be easily obtained, just
applying the EBP—i.e., balancing the equations giving
Figure 2.5-14 (a) Aeolian vibration behavior of an
ACSR Drake conductor, an ACS OPGW (around
15 mm diameter) and an ACAR 1300 cable, with
T/w = 1720 m. Antinode amplitude.
(b) Aeolian vibration behavior of an ACSR Drake
conductor, an ACS OPGW (around 15 mm
diameter) and an ACAR 1300 cable, with T/w =
1720 m. Non-dimensional antinode amplitude.
Figure 2.5-13 Wind turbulence effect, experimental
findings, rms aeolian vibration amplitude versus
frequency (Hardy and Van Dyke 1995).
2-74
(c) Aeolian vibration behavior of an ACSR Drake
conductor, an ACS OPGW (around 15 mm
diameter) and an ACAR 1300 cable, with T/w =
1720 m. Bending strain.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
the wind energy input Einput and the energy dissipated E
by the cable (for a length L of conductor):
Einput = L Pinput /f = fnc(A/D) f2 D4 L
(from Equation 2.5-1)
E = ζ 4π Ek,max (from Equation 2.5-8)
E = 2 (2π ζ) ½ (mL L/2) A2 (2πf)2
(from Equation 2.3-11)
and, being δ = 2πζ (from Equation 2.5-9)
Then, E = Einput becomes:
δ mL f 2 D 2 L 2π 2 ( A / D)2 = fnc(A/D)f 2 D 4 L and
δ mL
fnc(A/D)
= 2
2
2π ( A / D) 2
D
2.5-25
As can be seen the left side of expression 2.5-25 is the
Scruton number Sc multiplied by the air density ρ. So,
whichever the cable, the Scruton number is a function of
the nondimensional amplitude A/D only (remember
that the fnc(A/D) functions account for a “normal” air
density ρ = 1.25 kg/m3):
fnc(A/D)
ρ 2π 2 ( A / D)2
Another Sc(A/D) curve would have been obtained if an
energy input curve pertinent to a certain turbulence
level would have been used.
As an example of the use of this approach for the evaluation of the aeolian vibration level, the usual case of the
Drake conductor can be considered.
E = δ mL (A/D)2 f2 D2 L 2π2
Sc( A / D) =
Chapter 2: Aeolian Vibration
2.5-26
As an example, from the EBP computations, whose
results in terms of amplitudes and strains as a function
of frequency are reported in Figure 2.5-14, a certain
number of decreasing steady-state amplitudes A/D
obtained from the balancing between the wind energy
input and the energy dissipated by the cable have been
sorted. The corresponding system damping, in form of
log-decrement δ (computed by the software from the
dissipation empirical low —see Equations 2.5-3, 2.5-7,
2.5-8, and 2.5-9) has been used to compute the Scruton
number. The values of Scruton number obtained are
reported in Figure 2.5-15, as a function of the nondimensional amplitude A/D. As expected, the points relevant to the three different cables define a single curve; in
other words, whatever the cable and its structural damping, the same Scruton numbers give the same steadystate aeolian vibration amplitudes A/D. Obviously the
same wind power input fnc(A/D) function has been used
for the EBP calculations in the three cases; if another
fnc(A/D) function is used, a different Sc(A/D) curve is
obtained. The dispersion of the different Sc(A/D) curves
to be expected is of the same order as the dispersion of
the different fnc(A/D) functions in Figure 2.2-15.
In Section 2.3.6, Figure 2.3-19 reports the Drake selfdamping for a tension of 28500 N. The same data are
reported in Figure 2.5-16 in the form of nondimensional
damping ζ as a function of A/D. The advantage of this
way of presenting self-damping data is that the dependence of ζ on the vibration amplitude is small and, for
each frequency, a mean value of ζ (and then of δ = 2πζ)
can be easily read.
For instance, at 33 Hz, we can assume ζ = 0.00055 and
then δ = 0.0034.
From Equation 2.5-7, the Scruton number can be computed (air density ρ = 1.25 kg/m3): Sc = 5.65.
From Figure 2.5-15: A/D = 0.15, which is not so far
from what can be read from Figure 2.5-14b, also taking
into account a slight difference in the tensile load value
relevant to the self-damping measurements (28,500 N)
and to the EBP worked example (28,004 N).
The same exercise can be repeated for another frequency: if 47 Hz is considered, we can assume ζ =
0.0008 and then δ = 0.005. The value of Scruton is 8.35,
and from Figure 2.5-15, we read A/D = 0.05. Also, in
this case, this value is close to the one that can be read in
Figure 2.5-14b.
Figure 2.5-15 Relationship between the Scruton
number and the vibration amplitude due to vortex
shedding.
2-75
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 2.5-16 Drake (Tension = 28,500 N) self-damping expressed as
nondimensional damping ζ as a function of A/D.
Some final considerations can be made on the value of
this approach:
1. Due to the fact that the bending strains at the
clamped extremity are proportional to the ratio
between antinode amplitude A and wave length λ—
i.e., to the product between antinode amplitude and
frequency
(ε
c
=k
A
λ
= k1 Af
-
see
Equation
2.5-22)—it comes out that, for each vibration frequency, it is possible to define a limit value of the
Scruton number above which aeolian vibration are
controlled.
2. From the Scruton definition:
Sc =
δρ
δ mL
= (constant) mat it is also possible to
2
D ρ
ρ
understand that heavy conductors will behave better
than light conductors (with the same damping). As a
matter of fact, it is well known that aluminum alloy
cables are more sensitive to aeolian vibrations than
ACSR cables.
3. The usefulness of Figure 2.5-15 is that, once a (safe)
limit value for the aeolian vibration amplitude is
assumed—say, for example, A/D = 0.1—it is easy to
read on the curve in Figure 2.5-15 which is the minimum value of the Scruton number ensuring that
value: Sc 6. From the Scruton definition and the type
of conductor chosen (diameter and mass per unit
length), it is easy to compute the corresponding selfdamping in terms of log-decrement δ or nondimensional damping ζ.
For the case of the Drake conductor at 28,500 N:
δ = Sc D2 ρ / mL = 0.0036
ζ = δ/2π = 5.7 e-4
2-76
From Figure 2.5-16, it is easy to see that, unless for the
highest frequencies, the conductor self-damping cannot
ensure the desired amplitude of vibration (A/D = 0.1),
and then additional damping in terms of dampers will
be required to control the aeolian vibration level within
that level.
What is also interesting, and it will be shown in Sections
2.5.3 and 2.5.4, is that the same curve reported in Figure
2.5-15 also holds for damped single conductors and
bundles.
Reliability of EBP Computations
In this section, the direct comparison between measured
and EBP-computed aeolian vibration level is used to
establish the reliability of this technology.
Three examples are presented: two of them compare
measured and analytical antinode vibration amplitudes,
while the third compares measured and computed bending amplitudes (in this case analytical bending amplitude is computed from the bending strain, through the
Poffenberger-Swart formula—see Section 2.3.3).
In the first two cases, the measured wind turbulence typical of the site is also available.
Computed data come from an EBP application. In any
case, as shown in (CIGRE SC22 WG11 TF1 1998), different EBP-based software give comparable results in
the case of single, undamped conductors.
In all three examples, the curve ‘EXP’ is relevant to the
measured data, while the other curve(s) are relevant to
the predicted values: percentage values refer to the wind
turbulence assumed in the simulations.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
As already found in the CIGRE paper, it can be
observed that the EBP gives a good reproduction of the
frequency range and of the distribution of vibration
amplitudes with frequency. The predicted amplitude
level in some cases is quite close to the measured, but in
some other cases is quite different, due to several reasons, detailed in (CIGRE SC22 WG11 TF1 1998).
Comparing analytical to experimental data, it must be
kept in mind that, in reality, the wind structure cannot be
represented by a stationary random process with constant mean value. If the mean wind speed changes (independently of the turbulence index), a continuous
transient condition is experienced by the cable, and aeolian vibration maximum amplitudes can never be
reached.
Chapter 2: Aeolian Vibration
could also be due, in part, to a lack in experimental
data.
Example 3—Figure 2.5-19
Comments: in this case, the computed vibration level is
close to the measured, except for the higher frequencies,
where a maximum ratio of 1:2 between predicted and
measured values is found. The problem could be due to
the particular three-strand cable considered in this case:
the empirical law for conductor self-damping used in
the software could not perfectly fit the case of this cable
type at the higher frequencies.
Example 1—Figure 2.5-17.
Comments: in this case, the computed vibration level is
close to the measured, and if the variation of the wind
turbulence with the wind speed (the vibration frequency) is accounted for, the agreement is even better.
Example 2—Figure 2.5-18.
Comments: in this case, the computed vibration level is
not close to the measured. If the variation of the wind
turbulence with the wind speed (the vibration frequency) is accounted for, the agreement slightly
improves. The big discrepancies found at low frequency
Figure 2.5-18 Comparison between experimental
aeolian vibration amplitude and EBP technology
rendition at various turbulence levels. 240/40 ACSR
Earth Wire – diameter 21.9 mm – tension 14 kN – span
length 356 m – test line: Near Buren - Germany –
terrain category: hilly, low buildings (Kraus and
Hagedorn 1990). The measured wind turbulence is
reported in the upper part of the figure.
Figure 2.5-17 Comparison between experimental
aeolian vibration amplitude and EBP technology
rendition at various turbulence levels. ACAR 1300
conductor – diameter 33.25 mm – tension 29.1 kN –
span length 366 m – test line: Isles de la Madeleine,
Canada – terrain category: flat, near the sea (Hardy
and Van Dyke 1993). The measured wind turbulence
is reported in the upper part of the figure.
Figure 2.5-19 Comparison between experimental
aeolian vibration amplitude and EBP technology
rendition. 3#6 Alumoweld – diameter 8.86 mm –
tension 11.6 kN – span length 366 m – test line:
Massena, New York, United States – terrain category:
on shallow ridge (Rawlins 1988).
2-77
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Final observations: In designing the damping system for
new lines, it is generally difficult to obtain detailed wind
data (wind statistics and wind turbulence) and the terrain crossed by the line is only roughly described. So, if
the conservative choice of selecting the maximum wind
energy input (low turbulence condition) is made to perform the EBP predictions, it can be expected to always
obtain an estimate of the upper bound of the aeolian
vibration level (care must be taken in the assessment of
the vibratory behavior of particular lines, with conductors whose mechanical properties are poorly defined).
The obtained information, through comparison with
acceptable amplitudes (or bending strains), is quite
valuable, because it allows for assessing the need for
additional damping in terms of damping devices.
2.5.3
Mechanical Behavior of Single Conductors
Plus Dampers
It is well known that if the conductor tensile load (or,
more precisely, the ratio between tension and cable unit
weight H/w) exceeds certain limit values (i.e., 1000 m)
(3280 ft) (CIGRE WG B2.11.04. 2005), aeolian vibration may cause serious damage to both conductor and
fittings. The limit value of H/w is generally exceeded on
transmission lines; therefore, it is common practice to
protect conductors with suitable dampers.
For transmission line design, it is important to know
how much additional damping is needed to control aeolian vibration within safe levels. To this end, various
researchers have developed calculation methods—based
on the energy balance principle (EBP)—to predict the
aeolian vibration level of a cable plus damper and then
to allow for the selection of the suitable damping.
It has be pointed out that, for standard and repetitive
applications, many utilities and damper manufacturers
use simple tables based on conductor size, span length,
and tension to design the number of dampers, and this
can be identified as a rudimentary design method with
generally satisfactory results.
produces a damping effect and also modifies the conductor vibration mode—i.e., it creates a distortion (Figure
2.5-20). Consequently, the vibration modes of a cable
plus damper differ from those of the cable alone.
Figure 2.5-20 shows a vibration mode amplitude (the
frequency is around 35 Hz) for a cable plus damper system; the damper is positioned 0.5 m (1.5 ft) from the
suspension clamp, and only the part of the span close to
the clamp is shown. The antinode vibration amplitude
in the free span is normalized to the value 1. The curve
“damper A” represents the mode obtained using a
d a m p e r s u i t abl e fo r t h e c abl e i n q u e s t i o n ; t h e
curve”damper B” represents the case of too heavy a
damper. Figure 2.5-20 clearly demonstrates that the bigger the damper force, the higher the cable distortion and
the smaller the vibration amplitude at the damper
clamp—and as a consequence, the lower the power dissipated by the damper. In fact, the ratio between antinode and node vibration amplitude is higher for curve
“damper B” than for curve “damper A,” thus indicating
a lower damping efficiency for the system with damper
B than for the system with the “correct” damper A
(Tompkins et al. 1956).
By contrast, if the damper force is too small, the cable
vibration mode is only distorted by a small amount but,
due to the low force value, the dissipated power is low.
It is clear that for a given cable at a particular tensile
load, there will be, as a function of frequency, an optimum damper force—i.e., the force giving the maximum
dissipated power.
Another important fact in determining the damper dissipated power is the position of the damper itself on the
cable. If the damper is situated at a node for a particular
The most commonly used damping devices on single
conductors are the Stockbridge type dampers.
As already described in Section 2.4, this type of damper
is mounted locally on the conductor and is forced to
vibrate due to the conductor motion. When the damper
vibrates at a frequency close to one of its natural frequencies, a resonance condition occurs. The damper masses
vibrate at high amplitude and dissipate power, which corresponds to the transmission of a force component in
phase with the conductor vibration velocity. This force
2-78
Figure 2.5-20 Vibration mode amplitude for a cable plus
damper system.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
vibration frequency, no dissipation takes place and no
distortion occurs.
As will be shown below, these analyses lead to the choice
of the optimum damper for a certain application and to
the optimization of its position.
As already seen, the actual aeolian vibration behavior of
a cable plus damper system depends on the energy introduced by the wind and the energy dissipated by the cable
plus damper system.
With reference to the evaluation of the energy introduced by the wind, all the considerations described in
Sections 2.5.1 and 2.5.2 hold true. However, for the evaluation of the energy dissipated by the cable plus damper
system, different possibilities are available as follows:
1. If a wholly analytical procedure is to be used, a
mechanical model of the damper must be prepared.
Then the modes of vibration of the cable (modelled
as reported in Section 2.5.2) plus damper system
should be calculated.
2. The need for a mechanical model of the damper can
be avoided if the damper response corresponding to a
harmonic excitation imparted to the damper clamp is
directly measured by mounting the damper on a
shaker in a laboratory. The measured response can be
introduced into the cable model as a force transmitted by the damper. This procedure is generally
referred to as the “direct method” (IEEE 1993). The
cable model must be able to correctly reproduce the
cable-damper interactioni.e., the mode of vibration
distortion due to the damper presence.
3. The power dissipated by the damper is directly measured on a laboratory span as a function of the cable
antinode vibration amplitude in the free span at all
the vibration modes of interest for the aeolian vibration phenomenon. The span must be equipped with
the same cable as that to be used for the transmission
line to be studied. This procedure is generally referred
to as the “basic method” (IEEE 1993; Rawlins 1988).
It has the advantage that it avoids the difficulties
associated with the cable-damper interaction simulation. It has the disadvantage of a significantly greater
cost of testing.
The measurement of the power dissipated depends on
the damper position on the cable; a change of position
requires that the measurements to be repeated.
The measurement of the power dissipated by a combination of many dampers, as in a crossing, could become
impractical, because too many tests would be needed in
order to optimize the relative position of the dampers.
Chapter 2: Aeolian Vibration
This situation is summarized in the sketch in Figure
2.5-21 (CIGRE WG B2.11. TF1. 2005), where the various elements present in this technology are represented.
Each step in the analytical chain is affected by errors
caused by assumptions and approximations required by
the analytical procedures and by inaccuracies in input
data. Thus, accuracy deteriorates with progress down
the chain. However, accuracy of the final predictions
can be improved by entering the chain with independent
data at a lower point. For example, vibration amplitudes
are more accurately determined from field recordings
than from power balance analysis based on laboratory
span testing of dampers. Damping efficiency on the conductor is more accurately determined by direct measurement on a laboratory span than by using impedance
matching analysis.
Depending on the situation, it is obvious that it is not
possible to enter the chain at every point. On an existing
transmission line, it is possible to make direct measurements of aeolian vibration amplitudes; if the line and its
damping system have to be designed, the technology
chain must be entered at a preceding level.
It must be noted that field recordings are normally performed only on a “significant” span of the transmission
line and for a certain period of time (generally around
three months). The chosen spans may not necessarily
represent all the possible wind conditions along the
transmission line, and the measurement period may not
necessarily represent the entire year or the entire lifetime
of the line. Therefore, even field measurements should
be treated carefully and critically.
Analytical simulations based on impedance matching
analysis or on laboratory span testing may be considered conservative with respect to the actual situation if
the maximum wind energy input is used and if a suitable
safety factor for the damping system is introduced.
One branch of the technology chain shown in Figure
2.5-21, which started with shaker test data on actual
dampers and ended with the predicted vibration amplitudes, has been assessed in a recent study developed by
CIGRE B2 WG11 TF1 2005 (CIGRE 2005). The reader
can refer to this document in which the technology is
critically analyzed and the software developed by different researchers in the field is compared to one set of
field measurements. The possible causes of the discrepancies in the results obtained by the different researchers and with respect to the experimental data are also
discussed in detail.
2-79
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
The equation of motion of each section admits a steadystate harmonic solution containing four unknown
parameters. End conditions for the first and last section
of the conductor, and equilibrium and congruence
equations for each of the dampers present along the
span, can be written, and an homogenous system in all
the unknown parameters can be obtained. By zeroing
the determinant of this system, the natural frequencies
and modes of vibration are found. More details on this
procedure can be found in Appendix 2.6.
With this approach, the obtained vibration modes
account for the damper presence. Then, in general, with
respect to the vibration mode of an undamped cable, a
distortion, due to the damper interaction with the cable,
can be observed. This aspect is treated below in the section entitled “Effect of the Damper on the Mode of
Vibration.” Reference can be made also to Figure
2.5 23. Far from the dampers, in the free span, the vibration mode continues to be represented by an harmonic
function.
Figure 2.5-21 Chain of data analysis for dissipation of
power by dampers (CIGRE WG11 B2 TF1 2005).
The conclusions are that: “The strains predicted by the
different researchers exhibit considerable variability.
Nevertheless analytical methods based on the EBP and
shaker-based technology can provide a useful tool for
use in design of damping systems for the protection of
single conductors against aeolian vibrations. It should
be used with circumspection and be supplemented by
references to field experience.”
As explained in CIGRE B2 WG11 TF1 2005, the renditions of EBP technology developed by various researchers are based on different models, as reported in Table I
of the CIGRE paper. The main differences in the models are related to: wind power data, wind power data in
turbulence conditions, self-damping data, calculation
method, flexural stiffness, damper rocking, energy balance domain, and mode description. These differences
are responsible for the dispersion of the various predicted results.
The following section describes the model on which the
EPRI software is based.
Natural Frequencies and Modes of Vibration of the
Cable Plus Damper System
The natural frequencies and modes of vibration of the
cable plus dampers system are computed, assuming that
each section of the conductor, as it is divided by the
dampers present on it, behaves as a taut homogeneous
beam (see Appendix 2.6 for more details).
2-80
Another point to be put in evidence is that the homogenous system, from which natural frequencies and modes
of vibration are obtained, contains the force transmitted
by the damper, which is a complex quantity, whose real
and imaginary parts—or its modulus and phase with
respect to the clamp displacement—are measured, as a
function of frequency, through laboratory tests (see Section 2.4.3).
It is well known that Stockbridge dampers have a significant nonlinear behavior as a function of the clamp
amplitude of vibration due to the variation in the relative sliding of the messenger cable wires. This modifies
their flexural stiffness and damping and, therefore, the
damper dynamic behavior. For example, in Figure
2.5-22, a two-resonance damper response, in terms of
dynamic stiffness—amplitude and phase—is reported
for different constant velocities of the damper clamp.
In order to take these nonlinear effects into account, the
damper impedance can be defined at a number of clamp
vibration velocities, or clamp vibration amplitudes, and
the intermediate velocity, or displacement, values are
obtained through interpolation.
Energy Balance Principle
Once the conductor plus damper (and/or other devices)
system natural frequencies and associated vibration
modes have been defined, it is possible to compute the
steady-state amplitudes of vibration using the EBP,
according to the formulation of Equations 2.5-5 and/or
2.5-6.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
For each natural frequency, the conductor vibration
amplitudes can be defined along the span as a function
of a reference amplitude, which then enables the wind
energy input and the energy dissipated by the conductor
to be calculated. With the mode of vibration known, the
motion of the dampers is determined as a function of
the reference amplitude, and the energy dissipated can
then be calculated.
According to the EBP, the steady-state amplitudes of
vibration for each of the excited vibration modes (i.e.,
for each of the excited natural frequencies) are obtained
through a balance between the wind energy input and
the energy dissipated by the system.
Considerations of the wind energy input and the energy
dissipated by the conductor already described in Sections 2.5.1 and 2.5.2 also hold true in this case.
Regarding the energy dissipated by the damper system,
the following relationship is used for each one of the
Chapter 2: Aeolian Vibration
dampers present on the cable, and for each natural frequency (Claren and Diana 1969a),
2
Edamper = π Fu
i i sin ϕi
2.5-27
Where:
Fi is the damper force per unit displacement of the
damper clamp, as measured through a shaker
test at different vibration velocities.
ui is the conductor vibration amplitude at the
clamp of damper i.
ϕ2 is the phase between force and displacement, as
measured through a shaker test.
Optimum Damper
Changing the damper force, the maximum damping that
can be introduced in the system can be evaluated and,
from this, the formulation of the “optimum damper” is
derived (Tompkins et al. 1956; Rawlins 1958; Claren
and Diana 1969a).
Fopt = ω Tm
ϕopt = π 2 rad
Fopt
ω = 2π f
T
m
ϕopt
2.5-28
2.5-29
is the optimum force per unit displacement of the damper clamp and is a linear
function of the vibration frequency f.
is the circular frequency [rad/s].
is the conductor tensile load.
is the conductor mass per unit length.
is the optimum phase between force and
displacement.
Effect of the Damper on the Mode of Vibration
The approach described here to simulate the dynamic
behavior of a conductor plus damper can be extended to
simulate conductors fitted with many other types of discontinuities, such as armor rods (in this case, a part of
cable with a modified stiffness, EI, must be considered),
more dampers distributed close to the span extremities,
or even in-span, warning spheres.
Figure 2.5-22 Nonlinearity of the damper response
(CIGRE WG11 B2 TF1 2005).
As an example, in Figure 2.5-23, a comparison between
the measured and calculated mode of vibration ampli-
Figure 2.5-23 Modes of vibration at 40 and 60 Hz. Case (a): OPGW with armor rods without
damper. Case (b): OPGW with armor rods and damper (Consonni et al. 1998).
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
tude at two natural frequencies for the system in Figure
2.5-24 is shown.
The system consists of an OPGW installed on a laboratory span and forced to vibrate by an electrodynamic
shaker. A number of small accelerometers are positioned on the armor rods and on the OPGW to measure
the cable deflection shape close to the span extremity fitted with the damper. Two sets of measurement are performed—one relevant to the case without damper (‘a’ in
Figure 2.5-23), and the second with the damper
installed on the OPGW as shown in Figure 2.5-24 (‘b’ in
Figure 2.5-23). The antinode vibration amplitude being
imposed by the shaker is kept more or less the same for
the two conditions under consideration.
The effect of the damper on the vibration mode is
clearly evidenced, and the agreement between measured
and simulated amplitudes is fairly good.
Examples
To illustrate the importance of the type of damper and
its mounting position for aeolian vibration control, several examples are presented here, including a Drake
conductor and a Ground Steel Wire (GSW) equipped
with one damper.
• In all the applications, the damper dynamic stiffness
is not supposed to depend on the vibration amplitude
(linear approach).
The first simulation refers to a 366-m span equipped
with a Drake conductor. The conductor tensile load is
28,024 N.
The dynamic stiffness of the damper chosen to damp
aeolian vibrations of this cable is reported in Figure
2.5-25, together the optimum damper for this application, evaluated through the relation in Equations 2.5-28
and 2.5-29.
Two dampers have been installed on the conductor, one
at each side of the span, at the optimum damper position for this application, which has been evaluated as
1.2 m from the suspension clamp. The results of this
simulation are reported in Figure 2.5-26 in terms of
amplitudes of vibration and bending strains. As can be
observed, a suitable damper placed in an optimized
The reported results have been obtained by analytical
simulations and then must be analyzed from a qualitative, more than a quantitative, point of view.
Data common to all the simulations are:
• A low turbulence wind is always considered.
• The results are given in terms of vibration amplitude
and bending strains as a function of frequency. The
free-span antinode vibration amplitude is reported
together with the vibration amplitude at the damper
clamp (mm 0-peak). Strains at the suspension clamp
and at the damper clamp are reported (microstrains
0-peak).
Figure 2.5-25 Dynamic stiffness of the damper chosen
for the Drake conductor simulations.
• In all the figures, a reference curve relevant to the
undamped conductor is also reported.
Figure 2.5-24 Physical and mathematical model relevant
to the modes in Figure 2.5-23 (Consonni et al. 1998).
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Figure 2.5-26 (a) Drake at 28,024 N – 366m span – one
damper both sides of the span at 1.2m: Aeolian vibration
amplitudes of the damped and undamped cable.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
position practically suppresses the conductor aeolian
vibrations.
The influence of the damper position on the damper
efficiency is shown in Figures 2.5-27 and 2.5-28.
Chapter 2: Aeolian Vibration
Figure 2.5-27 reports the results of a simulation run
with the same input data as the first simulation, except
for the damper position, which has been now set to 0.6
m from the suspension clamp. The results reported in
Figure 2.5-28 are relevant to a simulation with the
damper position set to 3 m from the suspension clamp.
In the first case (Figure 2.5-27), the damper is too close
to the suspension clamp, and it is not in condition to
dissipate energy for all the low-frequency modes (the
damper amplitude of vibration—compared to the antinode amplitude—is too small at these frequencies). In the
second case, the damper is too far from the suspension
clamp, and its position is no longer within the first
vibration loop of the highest frequency mode to be
damped. In this condition, there may be some vibration
mode for which the damper is in a node and then cannot
dissipate energy.
Figure 2.5-26 (b) Drake at 28,024 N – 366m span – one
damper both sides of the span at 1.2m: Bending strains
of the damped and undamped cable.
Figure 2.5-27 Drake at 28,024 N – 366m span – one
damper both sides of the span at 0.6 m from the
suspension clamp.
Both the situations are clearly reproduced by the simulation results, which show high conductor vibration
Figure 2.5-28 Drake at 28,024 N – 366m span – one
damper both sides of the span at 3.0 m from the
suspension clamp.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
amplitudes at low frequencies in the first case and
around 25 and 50 Hz in the second case.
Finally the influence of the damper type on the aeolian
vibration response of a single conductor is evaluated,
with particular reference to the choice of the damper
frequency range with respect to the conductor aeolian
vibration frequency range.
The case of the GSW already worked out in Section
2.5.2 is considered here. The aeolian frequency range of
the ground wire, tensioned at 28,026 N, has been found
to be between 12 and 160 Hz (see Figure 2.5-14).
The dynamic stiffness of the damper chosen for this simulation is reported in Figure 2.5-29, together with the
optimum damper for this application.
As can be observed, the damper frequency range is
approximately 6-100 Hz, which is not adequate to provide protection in the whole GSW aeolian frequency
range.
A 366-m span has been considered, and two dampers,
one on each side of the span have been installed on the
GSW, at 0.9 m from the suspension clamp. The results
of the simulation are reported in Figure 2.5-30.
Relation Between the Scruton Number and the Aeolian
Vibration Amplitude A/D
As already reported for the case of the single conductor
(Section 2.5.2), an alternative method to the EBP used
in other sectors of engineering is to use the relationship
between the Scruton number and the vibration amplitude due to vortex shedding.
For the case of the single conductor, the points computed through the EBP software for the ACS cable, the
ACSR Drake, and the ACAR conductor have been
reported on a Scruton–A/d plane. (A/d is the antinode
vibration amplitude normalized to the conductor diameter.) It has been observed that all the points define a
single curve (see Figure 2.5-15). The results of the simulations performed in Section 2.5.3 for the single conductor plus damper (Drake plus damper and GSW plus
damper) have also been processed to be reported on the
same graph, and Figure 2.5-31 reports the obtained
result. As can be observed, the new points also stay on
the same curve previously defined. Hence, as in the case
of a damped conductor, once the fnc(A/D) function has
been chosen, the existence of a one-to-one relation
(Equation 2.5-26) between the Scruton number and the
The simulation results clearly show that the damper is
not in condition to protect the ground wire at frequencies higher than 80-90 Hz, where the damper force (see
Figure 2.5-29) is much smaller than the optimum force,
and the phase rapidly decreases to zero degrees—i.e., no
power can be dissipated according to the relation shown
in Equation 2.5-27. The only solution, in this case, is to
change the damper type, choosing a higher frequency
damper.
Figure 2.5-29 Dynamic stiffness of the damper used for
the GSW simulation.
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Figure 2.5-30 GSW with damper.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
vortex-shedding amplitude of vibration, expressed in
normalized form, is confirmed.
In this case the nondimensional damping δ in the Scruton relation (Sc = δ mL/(D2 ρ)) refers to the cable plus
damper system, and the considered amplitude of vibration is the antinode amplitude in the free span.
The use of curve in Figure 2.5-31 is exactly the same as
described for the case of the single undamped conductor. In this case, the cable plus damper power dissipation
or the nondimensional damping can be measured on a
laboratory span (see Section 2.4.3) and then converted
into the Scruton number.
Referring to the same case treated for the undamped
cable (Drake at 28 500 N), it was found that, if a limit
aeolian vibration amplitude A/D equal to, for instance,
0.1 has to be ensured, the minimum Scruton results
Sc≈6, and then a minimum nondimensional damping ζ
of the order of 5.7 e-4 is needed.
The difference between the required damping ζ and the
cable self-damping ζ c gives the damping ζd that has to
be provided by the damper. From this point of view, it is
useful to recollect the expression of the energy dissipated by a damper (Equation 2.5-27):
2
Edamper = π Fu
i i sin ϕi .
The damper contribution ζ d to the nondimensional
damping, can be evaluated as:
1 Edamper
ζd =
4π Ek ,max
Chapter 2: Aeolian Vibration
Continuing the development of the same test case,
assuming A/D = 0.1 and using Equation 2.3-11 for the
kinetic energy computation (a 400-m span is considered), we get
Edamper = ζd 4π Ek,max = ζd 0.63 f2
2.5-31
where f is the vibration frequency.
Considering a frequency of 20 Hz, the cable self-damping contributes to the system nondimensional damping
ζ with ζc = 2.5 e-4 (see Figure 2.5-16).
So the damper must contribute for ζd = ζ - ζc = 5.7 e-42.5 e-4 = 3.2 e-4, or, in other terms, the energy dissipated
by the damper must be at least equal to:
Edamper = ζd 0.63 f2 = 0.08 J
2.5-32
To have a qualitative evaluation of this amount of energy,
it is possible to compute the energy that would be dissipated by an optimum damper for this application. If one
introduces the damper optimum force (Equations 2.5-28
and 2.5-29) in the equation giving the energy dissipated
by the damper (Equation 2.5-27) and considers a displacement of the damper clamp equal to one half of the
antinode amplitude in the free span, the following equation results (the damper introduces a distortion in the
mode of vibration (see Figures 2.5-20 and 2.5-23) and, in
a first approximation, for the qualitative evaluation of the
energy dissipated by an optimum damper, the damper
clamp amplitude of vibration can be assumed to be half
of the free span antinode amplitude.):
Ed ,optimum damper = π Fi ,opt ui2 sin ϕi ,opt = 0.167 J, which is
2.5-30
more than the required energy (0.08 J), given in Equation 2.5-32).
where Ek,max is the cable maximum kinetic energy.
This means that one suitable damper should be sufficient to maintain the aeolian vibration level within A/D
= 0.1 (A≈2.8mm), at 20 Hz, for the considered case.
However, if, instead of a 400-m span, a 1200-m span is
considered, the energy dissipated by the damper—to
maintain the antinode amplitude A/D lower than 0.1—
must be at least equal to (from Equation 2.5-30):
Edamper = ζd 4π Ek,max = ζd 1.89 f2 = 0.24 J
2.5-33
which is more than the energy that can be dissipated by
the optimum damper (0.167 J).
Figure 2.5-31 Relationship between the Scruton number
and the vibration amplitude due to vortex shedding.
In this case, even if an optimum damper would be available, only one damper would not be enough to limit the
aeolian vibration level of the considered span within the
desired level (A/D < 0.1).
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Chapter 2: Aeolian Vibration
2.5.4
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Mechanical Behavior of Bundle
Conductors Equipped with Spacers and
Dampers
As already described in Section 2.5.1, the onset of aeolian vibration on bundle conductors is defined by matching of the Strouhal frequency with one of the natural
frequencies of the system, which consists of conductors,
spacers, and eventually, other devices. Therefore, it
remains of paramount importance to identify the bundle
natural frequencies and modes of vibration.
To this end, it may be observed that the spacer creates a
discontinuity on the conductor, as does a damper.
Between one spacer and the next, the conductor vibration is represented by a sinusoidal function with
unequal amplitudes in the different sub-spans; in the
zones close to a spacer, the deflection shape is controlled
by the conductor flexural stiffness.
As in the case of a single conductor plus dampers, the
bundle system natural frequencies and modes of vibration must be evaluated; therefore, it is important to
identify the spacer mechanical impedance.
Spacer Dynamic Behavior – Bundle Natural
Frequencies and Modes of Vibration
For simplicity’s sake, reference is made to a twin and a
quadruple bundle spacer.
The variables defining the horizontal and vertical displacements of the spacer clamp centers are identified by
xi, where i = 1, 2, … 8, as shown in Figure 2.5-32.
The vector containing all the xi variables is then defined
as:
⎧ x1 ⎫
⎪ ⎪
x=⎨ ⎬
⎪x ⎪
⎩ 2n ⎭
2.5-34
By analogy, a force vector can be defined, containing
the 2 x n components of the forces transmitted by the
clamps:
⎧ F1 ⎫
⎪ ⎪
F =⎨ ⎬
⎪F ⎪
⎩ 2n ⎭
2.5-35
Using the hypothesis of spacer linear behavior, the following equation of motion can be written:
Mx + Rx + Kx = F
2.5-36
where M is the 2n x 2n spacer mass matrix dependent on
the spacer inertial characteristics, K is the spacer elastic
matrix, and R is the damping matrix.
This equation allows the relation between the displacements imposed on the spacer clamps and the forces
applied to the clamps to be defined.
In case of harmonic motion: x = XeiΩt ,
⎡⎣ −Ω 2 M + iΩR + K ⎤⎦ X = F
F = FeiΩt :
2.5-37
where X represents the complex vector of the displacement amplitudes, and F represents the force amplitudes
vector.
The equation can be also expressed as:
F = [ H (iΩ) ] X
2.5-38
where H(iΩ ) is the harmonic transfer matrix between
the input displacements (at the spacer clamps) and the
output forces (spacer dynamic stiffness matrix).
If H(iΩ) is known, the dynamic behavior of the bundle
can be evaluated, independently on the adopted methodology.
where n is the number of conductors of the bundle.
Different methodologies are available; the finite elements technique (in which the conductors are modelled
through tensioned beam elements [Curami et al. 1977]),
the matrix transfer technique [Claren et al. 1971; Claren
et al. 1974], and the constants transfer technique [Diana
and Massa 1969]].
In order to better understand the problem, it is appropriate to analyze the various difficulties as they are
encountered.
Figure 2.5-32 Variables defining the horizontal and
vertical displacements of the spacer clamp centers.
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Returning to Equation 2.5-36, the bundle natural frequencies and vibration modes can be evaluated neglecting damping. In this case Equation 2.5-36 becomes:
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Mx + Kx = F
To better understand the problem, let us neglect the
mass matrix—i.e., the spacer inertia effect. Equation
2.5-36 then simply becomes:
Kx = F
2.5-39
where K is the spacer elastic matrix, which can be easily
defined as a function of the spacer elastic characteristic,
as explained in the following (see Figure 2.5-33).
Of course, the spacer inertia may only be neglected if the
frequencies are very low—around a few Hz—but this
simplification is only used here to better understand the
nature of the problem.
The K matrix for a quad spacer is an 8 x 8 matrix, for a
twin spacer, a 4 x 4 matrix, and so forth. Eigenvalues
and eigenvectors of the K matrix can be evaluated and
are known as spacer eigenvalues and eigenvectors.
As the spacer is free to move in the spacer plane,
3 eigenvalues will be null. The corresponding eigenvectors identify rigid modes of vibration—i.e., modes with
no relative displacement between the spacer clamps (see
Figure 2.5-34 for a twin bundle). For these modes, in the
hypothesis of neglecting the spacer mass, no force is
transmitted to the spacer clamps. This means that, for
these modes, the bundle always behaves as if the spacers
are not present.
Chapter 2: Aeolian Vibration
At low frequencies, if all the bundle conductors vibrate
with purely horizontal, vertical, or torsional modes, the
spacer does not apply any force, and then the bundle
vibration modes would be the same as for a single conductor—i.e., with the same amplitude all along the span.
An example is given in Figure 2.5-35, where two of the
possible modes of vibration associated with a spacer null
eigenvalue are represented for a twin bundle with two
equally spaced spacers. The spacer position is marked by
the two vertical lines in each figure. The deflection shape
along the span is the same for the two conductors (only
one line is present). The vibration amplitude is constant
along the span. Transverse to the bundle axis, the vibration plane will be defined by the associated eigenvector.
These types of bundle modes are called rigid modes or
typical modes of the conductor, because they are not
affected by the spacer characteristics.
Considering the other (2n-3) eigenvectors—for instance,
in the case of a twin bundle—only one eigenvector can
be defined besides the three rigid ones. Let the associated eigenvalue be known as λ1. λ1 represents an equivalent stiffness between the two subconductors for the
type of movement, as defined in Figure 2.5-36:
or, with vector notation:
X1
1
X
0
X (1) = 2 =
X 3 −1
X4
0
2.5-40
in which the normalization chosen imposes unit amplitude at the coordinate x1.
Figure 2.5-33 Forces and displacements at the spacer
clamps.
Figure 2.5-35 Rigid modes of vibration for a twin bundle
(spacer inertia neglected).
Figure 2.5-34 Eigenvectors corresponding to the rigid
modes of vibration for a twin bundle (spacer inertia
neglected).
Figure 2.5-36 Eigenvector associated to the λ1
eigenvalue (twin bundle).
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 2.5-37 Model for the definition of the twin bundle natural frequency and mode of vibration associated to the λ1
eigenvalue (spacer mass matrix ignored).
At low frequency, in order to define the twin bundle natural frequencies and modes of vibration associated to
this eigenvalue/eigenvector, the simple model shown in
Figure 2.5-37 can be adopted. According to this model,
each conductor of the bundle can be represented as a
single conductor free to move only in the plane defined
by the eigenvector and connected to the ground through
springs whose stiffness equals λ1 —i.e., the considered
eigenvalue (see Figure 2.5-37).
The conductor can be modelled as seen in the previous
sections—i.e., with mass and a tensile load or with mass,
tensile load, and flexural stiffness.
The two conductors of the twin bundle vibrate with
exactly the same deflection shape, but with opposite
sign, as shown in the two lines appearing in Figure
2.5-38. An example is given in Figure 2.5-38, where two
of the possible modes of vibration associated to the
spacer first eigenvector are represented for a twin bundle
with two equally spaced spacers. Transverse to the bundle axis, the vibration planes are defined by the associated eigenvector. It is important to observe that the
vibration amplitude is not constant along the span but
differs from one sub-span to another.
The procedure can be generalized for any type of bundle, for the calculation of the 2n - 3 = m eigenvalues and
relevant eigenvectors.
These modes of vibration depend on the spacer characteristics (elastic parameters and geometry of the spacer)
and are called nonrigid modes or modes typical of the
bundle.
All the above procedure holds true if the spacer mass
can be neglected. If a harmonic motion is taken into
account:
⎡⎣ −Ω 2 M + K ⎤⎦ X = F
2.5-41
The term –Ω2M can be neglected if compared to K only
for very low frequencies, in the range of a few Hz.
The spacer eigenvalues and eigenvectors are given in
Figure 2.5-39 for a twin bundle, in Figure 2.5-40 for a
three bundle, and in Figure 2.5-41 for a quad bundle—
all for a typical, widely used spacer of the type shown in
Figure 2.5-42.
At low frequencies, the bundle natural frequencies and
modes of vibration associated with each non-null eigenvector can be calculated using the procedure explained
above for the twin bundle.
With increasing the frequency, the spacer inertia must
be taken into account; the motion of the masses induces
For each of the λi (i = 1, … m) non-null eigenvalues, a
model similar to that in Figure 2.5-37 can be adopted;
the spring stiffness equals λi, and the bundle natural frequencies and modes of vibration can be readily evaluated. The other conductors of the bundle vibrate with
amplitudes defined by the corresponding eigenvector.
Figure 2.5-38 Two of the possible modes of vibration
associated to the spacer first eigenvector are
represented for a twin bundle with two equally spaced
spacers.
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Figure 2.5-39 Eigenvalues and eigenvectors for a twin
bundle.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 2: Aeolian Vibration
inertia forces that modify the spacer behavior with
respect to that described above.
The distinction between modes typical of the conductor
and modes typical of the bundle no longer holds true.
An example relevant to a twin bundle is considered here.
As previously observed, it is possible to have vibration
modes typical of the conductor at low frequencies (0–
5 Hz); this means that the bundle can vibrate—for
instance, in the vertical direction—without transmission
of forces to the spacer clamps.
Figure 2.5-40 Eigenvalues and eigenvectors for a triple
bundle.
With increasing frequency—considering, for example,
an harmonic, vertical, equal amplitude, movement of
the spacer clamps (see Figure 2.5-43), an inertia force
associated to the spacer body mass arises, and as a consequence, forces are developed at the spacer clamps with
a relative motion between spacer arms and spacer body.
In this situation, the spacer inertia elastic and damping
characteristics influence the bundle behavior and define
a new vibration mode, given by the spacer equation:
⎡⎣ −Ω 2 M + iΩR + K ⎤⎦ X = F
2.5-42
and by the conductor characteristics.
When vibration frequencies are higher than about 5 Hz,
the system inertia modifies the vibration modes with
respect to the low-frequency analysis.
Figure 2.5-42 Type of spacer to which the modes shown
in Figures 2.5-39, 2.5-40 and 2.5.41 are relevant.
Figure 2.5-41 Eigenvalues and eigenvectors for a
quadruple bundle.
Figure 2.5-43 Twin bundle: central body inertia force
due to the vertical movement of the spacer clamps.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
As previously observed, the definition of the bundle natural frequencies and modes of vibration in the field of
aeolian vibration (i.e., over 5 Hz) requires calculation
methods based on FEM or on the transfer matrix or
transfer constants techniques.
In any event, if, as generally applies, the spacers along a
span are equal and equally oriented (all the spacers lie in
parallel planes and there is no torsion in the bundle), the
bundle conductor vibration planes remain the same all
along the span for each one of the bundle natural frequencies. Changing the frequency changes the directions of the conductors’ vibration planes.
An appropriate way to interpret the component of
motion in a plane normal to the bundle axis for these
new modes of vibration is to treat them as linear combinations of the spacer eigenvectors previously defined.
If rigid modes prevail in the combination, the energy
dissipation associated with the spacer is small because
no, or small, relative displacements between the spacer
parts occur. On the contrary, for modes typical of the
bundle, relative movements between the spacer elements
take place, with associated stiffness and damping related
to the considered spacer dynamic stiffness matrix eigenvalue, and then energy can be dissipated. The elastic and
damping properties of the spacer hinges can be optimized to enhance energy dissipation related to this type
of modes.
The fact that inertia forces modify and couple the bundle vibration modes is very important and helps in the
use of spacers to also damp the bundle vertical and torsional rigid modes. In fact, the spacer central body
vibrates with respect to the spacer arms and behaves as
a damper. For standard values of the central body inertia characteristics, this happens for frequencies higher
than about 15 Hz. As the spacer central body mass and
moment of inertia increase, the frequency for which this
effect becomes important decreases, thus covering the
frequency range of aeolian vibration.
effectively but has a worse performance at high frequency, and vice versa for high stiffness.
This is due to the fact that the central body mass is a
vibrating system elastically suspended by the spacer
arms through the elastic hinges. The central body, as
previously noted, plays the role of a dynamic absorber—
i.e., if its resonance is close enough to the excitation frequency, the damping efficiency is high. The central body
resonance can be changed by varying the hinge stiffness
or the central body mass and moment of inertia.
Another fact that has to be noted is that the aeolian
vibration behavior of a bundle exhibits vibration amplitudes that remain constant between one spacer and the
next, but change from one subspan to the next (see Figure 2.5-44). This happens for the modes typical of the
bundle in which the spacer elastic, inertial, and geometrical characteristics play an important role.
The behavior of flexible spacers is different from the
behavior of rigid spacers; the rigid spacer does not allow
for the transmission of vibration from one subspan to
the other for modes typical of the bundle. This fact, for
some mode of vibration, causes the end subspans to
have low amplitudes of vibration. This fact compromises the possibility of controlling the bundle aeolian
vibration level through dampers installed close to the
span extremities. If the damper amplitude of vibration is
low, the dissipated energy is small; on the contrary, if the
conductors have high amplitudes of vibration in the
central subspans, the energy input from the wind is
high, and the phenomenon cannot be controlled.
Some examples are provided below to better show the
influence of all of these parameters.
Identification of the Spacer Dynamic Stiffness
Matrix
One way to experimentally identify the spacer stiffness
matrix is to fix the center of all the spacer clamps, except
one at which horizontal or vertical displacements are
On the contrary, spacer arms’ mass and moment of
inertia should be kept as low as possible, because the
arms are directly and rigidly connected to the conductors, and their inertia is directly transmitted to the conductors without coupling with the modes typical of the
bundle.
Another important parameter is the stiffness of the
spacer hinges, reference always being made to a type of
spacer similar to the one shown in Figure 2.5-42, which
is widely used for transmission line bundles. If the stiffness is small, the spacer damps the low frequencies more
2-90
Figure 2.5-44 For the modes typical of the bundle, the
aeolian vibration behavior of a bundle exhibits vibration
amplitudes that remain constant between one spacer
and the next, but change from one subspan to the next.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
applied. The arms of the spacer are allowed to rotate
around the center of the clamps.
If the imposed displacement is static or, at least, a lowfrequency harmonic displacement, below 2 Hz, the
effect due to the spacer elements’ mass can be neglected,
and the method allows for identifying the spacer elastic
matrix. The direct term of the matrix is given by the
ratio between the force applied to the moving clamp and
the related displacement (if the x 1 displacement is
imposed to clamp 1, the direct term is F1/x1 = k11 - see
Figure 2.5-45).
The ratios between the forces at the other (fixed) spacer
clamps and the imposed displacement represent a column of the spacer elastic matrix.
If the x1 displacement is imposed on clamp 1, the measurement of F1 at clamp 1, F2 at clamp 1, F3 at clamp 2
and so on, up to F 8 , allows for the calculation of the
ratios Fi/x1, with i = 1,.. 8, and thus the identification of
the first column of the spacer elastic matrix.
The construction of the matrix can exploit the fact that
the matrix is naturally symmetrical.
If the harmonic displacement applied has a higher frequency, this method allows for the identification of the
spacer dynamic stiffness matrix H(iΩ), where Ω is the
circular frequency of the applied displacement.
The stiffness matrix can also be evaluated via an analytical procedure. Of course, the geometry of the spacer,
the mass and moment of inertia of its elements (arms
and central body), and the elastic and damping properties of the hinges connecting arms to the central body
must be known. The hinges’ elastic and damping properties can be evaluated according to the laboratory procedure presented in Section 2.4.6.
Referring, for simplicity sake, to a twin bundle, the procedure consists of defining the potential elastic energy V
of the spacer.
Figure 2.5-45 Forces and displacements at the
spacer clamps.
Chapter 2: Aeolian Vibration
The system in Figure 2.5-46 has five degrees of freedom,
and the free coordinates can be assumed as: x1, x2, x3,
x4, xc1. The potential elastic energy can be written as:
2
1
V = ∑ ki (φi − φc ) 2
1 2
2.5-43
Where:
φi is the arm rotation.
φc is the central body rotation.
ki is the torsional stiffness of hinge i.
φi and φc can be expressed as a function of x1, x2, x3, x4,
xc1, solving the system kinematics.
Now it is possible to write the following equation system:
⎧ ∂V
⎪ ∂x = F1
⎪ 1
⎪ ∂V
⎪ ∂x = F2
⎪ 2
⎪ ∂V
= F3
⎨
⎪ ∂x3
⎪ ∂V
= F4
⎪
⎪ ∂x4
⎪ ∂V
=0
⎪
∂
x
⎩ c1
(1)
(2)
(3)
2.5-44
(4)
(5)
In Equation 2.5-44, part 5 allows xc1 to be expressed as a
function of x1, x2, x3, x4. Substituting xc1 = f(x1, x2, x3,
x4) in V, parts 1 to 4 allow for the determination of the
spacer elastic matrix: k11 = F1/x1, k12 = F1/x2 and so on).
If the kinetic energy for the system in Figure 2.5-46 is
defined, the spacer mass matrix M can be determined.
The same holds true for the determination of the spacer
dissipation matrix from the dissipated energy.
However, the spacer dissipation matrix, H, is generally
considered proportional to the spacer elastic matrix, K,
through the hinge damping parameter β = h/k evaluated
Figure 2.5-46 Model for the identification of the spacer
dynamic stiffness and mass matrices.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
through the laboratory test described in Section 2.4.6,
and then [H]=β [Κ].
dles (see Figure 2.5-47), the energy input in one conductor is slightly lower than that relevant to a single one.
Energy Balance Principle (EBP)
Once the bundle natural frequencies and associated vibration modes have been defined, it is possible to calculate
the steady-state amplitudes of vibration using the EBP.
Regarding the energy dissipated by the bundle system,
the methods to calculate the energy dissipated by conductors and dampers have been already presented in
Sections 2.5.1 and 2.5.2.
The vibration amplitudes of the conductors can be
defined along the span as a function of a reference
amplitude, which then enables the wind energy input
associated with the vertical component to be calculated.
The energy dissipated by the conductors is directly
related to their movement, independently on the direction. The motion of the dampers, the spacer dampers,
and any other device present on the conductor can be
determined as a function of the reference amplitude,
and the energy dissipated may then be calculated.
According to the EBP, the steady-state amplitudes of
vibration for each of the excited vibration modes—i.e.,
for each of the excited natural frequencies—are
obtained through a balance between the wind energy
input and the energy dissipated by the system.
The energy dissipated by the spacer can be calculated by
the relationship:
E
d , spacer
=
T
1
[H ] X
X
2
2.5-45
where X is a vector defining the displacement at the
spacer clamps, and [ H ] is proportional to the spacer
stiffness matrix through the damping parameter of the
elastic elements of the spacer already defined.
Examples
As an example, the case of the Drake conductor, already
worked out in Section 2.5, is solved, for different bundle
configurations and damping systems.
Data common to all the simulations are:
When a cylinder is in the wake of another, the exciting
force on the cylinder in the wake is due to the effect of
vortex shedding on the cylinder itself plus the effect of
the wake of the upstream cylinder. As seen in Section
2.2.5, experimental tests were carried out in a wind tunnel to define the force on the conductor in the wake.
From these experimental tests, it was possible to define
in a similar way as for a single conductor, the energy
input from the wind with constant velocity on a pair of
conductors with one in the wake of the other.
• The tensile load of the bundle conductors is 26,545 N.
• A low turbulence wind is always considered.
• A 366-m span with six spacers is always considered,
being the subspan lengths (m) sequence as follows:
40.0, 55.0, 63.0, 51.0, 64.0, 55.0, and 38.0.
• The results are given in terms of vibration amplitude
and strains as a function of frequency. Antinode
Some comments and results of these tests have been
reported in Section 2.2.4, in Figure 2.2-16 and here in
Figure 2.5-47, where the curve relevant to one conductor of a pair of conductors of a generic bundle (curve b)
is compared to the single conductor curve (Diana and
Falco curve in Figure 2.2-15) and to bundle curves relevant to two different turbulence levels. These last curves
have been evaluated using the same procedure as for the
case of the single conductor, as discussed in Section
2.5.1 (Diana et al. 1979), reducing the low-turbulence
curve through a simplified approach.
Recent measurements (see mainly Figure 2.2-16) have
shown that, for the case of twin bundles, the energy input
in the conductor in the wake is greater or at least equal to
that of a single conductor, while for other types of bun-
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Figure 2.5-47 Wind power input from the wind on a
conductor bundle. (c) and (d) are the reduced wind
power input curves, (b) is the low-turbulence curve, and
(a) is the single–conductor, low-turbulence curve
(Diana and Falco 1971; Diana et al. 1982).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
vibration amplitude in the most vibrating subspan is
reported together with the maximum vibration
amplitude at the spacer and the damper clamp (mm
0-peak). Strains at the suspension clamp and at the
Chapter 2: Aeolian Vibration
damping devices clamp are reported (microstrains
0-peak).
• In all the figures, a reference curve relevant to a single
conductor equal to those of the bundle and at the
same tensile load is reported.
Case (a):
Twin bundle equipped with standard spacer-dampers (same type as the quadruple spacer reported in Figure 2.5-42) (see Figure 2.5-48). Torsional stiffness of the spacer hinges measured as a function of frequency according to the method described in Section 2.4.6:
5 Hz: TORS.STIFFNESS 168.00 [N*m/rad]
30 Hz: TORS.STIFFNESS 331.00 [N*m/rad]
TORS.DAMPING H/K
TORS.DAMPING H/K
0.335
0.29
Figure 2.5-48 Twin bundle equipped with Drake conductors at 26,545 N and standard spacer-dampers.
Comments: Due to the physiologic low inertia of the spacer central body, the spacer alone is not in
condition to damp aeolian vibrations of the bundle at low frequency (in this case below 20-25 Hz).
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Case (b):
Twin bundle equipped with standard spacer-dampers (see Figure 2.5-49). In this case, a very
low torsional stiffness of the spacer hinges, constant with frequency, is simulated:
Figure 2.5-49 Twin bundle equipped with Drake conductors at 26,545 N and standard spacerdampers: hinges with low torsional stiffness.
Comments: A very low (compared to the standard values previously considered) torsional
stiffness of the spacer hinge (with the same mass and moment of inertia of the central
body) improves the spacer behavior at low frequency, but the spacer behavior at high frequency becomes worse.
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EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 2: Aeolian Vibration
Case (c):
Twin bundle equipped with the standard spacer-dampers of case (a), but the central body
mass and moment of inertia are increased with respect to standard values: the mass is
nearly doubled, and the moment of inertia is nearly ten times greater (see Figure 2.5-50).
Figure 2.5-50 Twin bundle equipped with Drake conductors at 26,545 N and standard
spacer-dampers: central body mass and moment of inertia increased.
Comments: As already explained, a suitable increment of the central body inertia
(compared to the standard values previously considered) allows for moving the spacer
natural frequencies toward low frequencies. Then the spacer has a good behavior at
both low and at high frequencies.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Case (d):
Quad bundle equipped with standard spacer-dampers (see Figure 2.5-51). Torsional
stiffness of the spacer hinges as for the twin spacer in case (a).
Figure 2.5-51 Quadruple bundle equipped with Drake conductors at 26,545 N and
standard spacer-dampers.
Comments: Due to the physiologic high inertia of the spacer central body, the quad
spacer damper alone is generally in condition to damp aeolian vibrations of the bundle, for standard applications.
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EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 2: Aeolian Vibration
Case (e):
Twin bundle equipped with standard rigid spacers (see Figure 2.5-52).
Figure 2.5-52 Twin bundle equipped with Drake conductors at 26,545 N and standard rigid spacers.
Comments: As can be observed, the spacers do not dissipate energy, and then the vibration
amplitudes are similar to those of the single conductor in the whole aeolian vibrations frequency range.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Case (f):
Twin bundle equipped with standard rigid spacers and two suitable dampers per
each subconductor, one at each side of the span (see Figure 2.5-53).
Figure 2.5-53 Twin bundle equipped with Drake conductors at 26,545 N and standard
rigid spacers and two dampers per each sub-conductor, one at each side of the span.
Comments: Adequate dampers placed at the span extremities can control the aeolian vibrations of a twin bundle equipped with rigid spacers, because the twin
spacer allows for the transmission of vibration from one subspan to the other for
modes typical of the bundle. This holds true if the spacer inertia is not substantially
higher than that typical of a twin spacer.
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EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 2: Aeolian Vibration
Case (g):
Twin bundle equipped with standard spacer-dampers (same as in case [a]) and one suitable
damper per each subconductor, at only one side of the span (see Figure 2.5-54).
Figure 2.5-54 Twin bundle equipped with Drake conductors at 26,545 N and standard
spacer-dampers and one damper per each sub-conductor, at only one side of the span.
Comments: Only one damper per subconductor ensures an adequate control of the
aeolian vibration level in the whole frequency range of interest.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Case (h):
Triple bundle equipped with rigid spacers (see Figure 2.5-55).
Figure 2.5-55 Triple bundle equipped with Drake conductors at 26,545 N and standard rigid
spacers.
Comments: The spacers do not dissipate energy; many modes of vibration present vibration
amplitudes similar to those of a single conductor.
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EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 2: Aeolian Vibration
Case (i):
Triple bundle equipped with rigid spacers and two suitable dampers per each subconductor, one at each side of the span (see Figure 2.5-56).
Figure 2.5-56 Triple bundle equipped with Drake conductors at 26,545 N and standard rigid spacers and two
dampers per each sub-conductor, one at each side of the span.
Comments: In the case of triple and quadruple bundles, the rigid spacer does not allow for the transmission of vibration from one subspan to the other for modes typical of the bundle, and this fact causes
the end subspans to have low amplitudes of vibration. This fact compromises the possibility of controlling the bundle aeolian vibration level through dampers installed close to the span extremities. This is
shown by the software results: vibration amplitudes remain high between one spacer and the other,
while vibration amplitudes at the spacer clamps are close to zero (spacers create nodal points in the
deflection shape); strains at the suspension clamp are very low due to the fact that end subspans are fitted with dampers, while strains on the conductor at the spacer clamps remain high.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Case (j):
This situation is typical of triple and quadruple bundles equipped with rigid spacers and
becomes even worse, increasing the span length—i.e., increasing the spacer number. This is
shown in case (j), relevant to the same situation as case (h), except for the span length, which
is now 500 m, divided in 10 subspans (see Figure 2.5-57).
Figure 2.5-57 Triple bundle equipped with Drake conductors at 26,545 N and standard rigid
spacers: the case of a 500m span instead of a 366m span is considered.
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EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 2: Aeolian Vibration
This is true for all conductor systems, whether they are
used as single conductors or in bundles, and whether or
not they are fitted with damping and/or spacing devices.
Therefore, there is a need to set an upper limit to conductor unloaded tension that may prevail for a significant period of time.
Figure 2.5-58 Relationship between the Scruton number
and the vibration amplitude due to vortex shedding.
As already reported for the case of the single conductor
and the single conductor plus damper, an alternative
method to the EBP used in other sectors of engineering
is to use the relationship between the Scruton number
and the vibration amplitude due to vortex shedding
found by different authors.
For the case of the single damped and undamped conductor, the points computed through the EBP software
for all the considered cases have been reported on a
Scruton – A/d plane ( A/d is the antinode vibration
amplitude normalized to the conductor diameter), and
it has been observed that all the points define a single
curve (see Figures 2.5-15 and 2.5-31). The results of the
simulations performed in Section 2.5.4 for the twin bundle equipped with Drake conductors and spacer-dampers or rigid spacers have also been processed to be
reported on the same graph. Figure 2.5-58 reports the
obtained result: the new points also stay on the same
curve previously defined, thereby confirming the existence of a one-to-one relation between the Scruton number and the vortex-shedding amplitude of vibration
expressed in normalized form.
In this case, the log-decrement δ in the Scruton relation
(Sc = δ mL/(D2 ρ)) refers to the cable + spacers system,
and the considered amplitude of vibration is the maximum antinode amplitude found in the different subspans.
2.6
IMPACT OF VIBRATION UPON LINE
DESIGN
2.6.1
Introduction
It is well known that stranded conductors become more
vulnerable to aeolian vibration as tension is increased.
Unarmored, unprotected single conductors of the most
common types are considered in the first part of this
section, starting with a critical examination of the socalled EDS (everyday stress) concept, which was put
forward in 1962 by CIGRE SC 6, with the intent to provide guidance on such conductor safe design tensions
with respect to aeolian vibration (Zetterholm 1960).
This question has been addressed recently again by
CIGRE (22.11 TF4 2005), which proposed adopting
H/w, the ratio between the initial horizontal tensile load
H and conductor weight w per unit length, as the limiting parameter, depending on terrain roughness. The
addition of dampers calls for the introduction of
another parameter, which rates the protective capacities
of the damping system. The rating parameter that was
selected is LD/m, the ratio of the product of span length
L and conductor diameter D to conductor mass m per
unit length, which together with the limiting parameter
H/w defines certain application zones. Finally, based on
field experience and full-scale test line data, a single,
probably conservative, value for H/w has been proposed.
This is applicable to bundled conductor lines, particularly twin horizontal bundles, triple apex-down bundles,
and quad horizontal bundles made up of conventional
stranded conductors fitted with either damping or nondamping spacers or a combination of nondamping
spacers and span-end Stockbridge-type dampers. This
new CIGRE approach is also compared with other
design procedures commonly used today. Finally, in the
last part of this chapter, the impact of conductor tension
selection on the capital line costs is highlighted.
2.6.2
Historical Background
1924-1945
As early as 1924, the first wire failures were observed in
the Unites States, and a few years later also in Germany.
At that time, systematic examinations of overhead
transmission lines were carried out (Nefzger 1933; Ryle
1935), as well as the first scientific studies (Varney 1928;
Pape 1930; Monroe and Templin 1932), and by 1932,
test lines were erected to observe natural conductor
vibrations and to test the effect of various damper
designs (Margoulies 1935; Caroll and Koontz 1936).
The risk of accumulating damage of individual wires
and thus of the conductors in the course of line service
was soon recognized (Davidson et al. 1932; Caroll
1936). In the same period, the first wind tunnel measurements of wind power input (Bate and Callow 1934)
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
and the first measurements of conductor self-damping
(Bate 1935) took place.
In 1931, a factor F was introduced as the rate for the
vibration hazard (Holts 1931), as an attempt to relate it
to line and conductor parameters:
F=dT/w≈dσ/γ
Where
d = conductor diameter (mm).
w = weight of conductor (N/m).
T = conductor tension (N).
γ = specific weight (N/mm3).
σ = stress (N/mm2).
2.6-1
In Germany, the Studiengesellschaft für Höchstspannungsanlagen e.V. (Research Association for Extra-High
Voltage Installations) endeavored to clarify the vibration problem by a number of meetings and reports (Studiengesellschaft 1927-1950). Scientists, too, participated
actively in the investigations of this problem with
extended analytical studies (Maas 1933; Pipes 1936;
Dahl and Blaess 1950; Helms 1964). Valuable collections and analyses of historical data on existing lines relative to their design tensions and the incidence of
fatigued strands have also been published by Zetterholm
(1960), Rawlins et al. (1961), Hautefeille et al. (1964),
EPRI (1979), and Dulhunty et al. (1982). The bending
amplitude method for recording vibration in the field
(Tebo 1941) and corresponding fatigue tests on conductors (Bolster and Kanouse 1948) were introduced conceptually at an early stage.
CIGRE Activities 1925–1965
For almost 60 years, great importance was attached to
the problem of conductor failures due to wind-induced
vibrations by the CIGRE organization (CIGRE 22.11
2004). In 1953, the CIGRE Study Committee No. 6
(now B2), overhead lines, set up a special group called
the EDS panel, and in 1965, as successors, the Working
Group 01 (conductor vibration theories) and the Working Group 04 (endurance capability of conductors) were
established (Bückner 1988).
EDS Panel Results up to 1961
The EDS panel published reports of the fatigue behavior, based on operational experiences of mainly single
conductor lines, and recommended (Zetterholm 1960)
certain values for the everyday stress (EDS) (see Table
2.6-1).
Although more than 200,000 km of lines were investigated, the predominant detrimental influence of the tensile stress was not detectable in all cases, as is evident
from Table 2.6-2. For example, relatively low EDS values of 15% do not guarantee a 100% vibration-damage-
2-104
free line. This table summarizes the results of over
40,000 km of lines, and indicates the percentage of damage for the respective line lengths that have been
observed, listed by conductor cross-section and EDS
range. In total, damage was found on 6.5% of the
41,565 km of line examined here—i.e., on 2702 km of
line.
Some doubts as to the validity of the EDS recommendation were published quite early (Bovallius et al. 1960;
Bückner 1960; Dassetto 1962) and were expressed in the
discussions during the CIGRE SC 22 main meetings
held in 1960/61.
This is to be expected, since the likelihood of fatigue
damage is influenced by a number of other variables
than EDS. They include: conductor construction and
manufacturing process; effect of topography on incident
winds; effect of terrain on wind turbulence; and effects of
support structure dynamics and hardware configuration.
Survey of Service Failures after 1975
After 1975, the successor of the EDS panel within
CIGRE, working group 04 (endurance capability of
conductors) of Study Committee 22 (overhead lines),
carried out an extensive survey in order to assess conTable 2.6-1 CIGRE EDS Panel Recommendations for
Safe Design Tensions in Percent UTS (Zetterholm 1960)
Lines Equipped with
Unprotected
Lines
Copper conductors
26
ACSR
18
Aluminum
conductors
17
Aldrey conductors
18
Steel conductors
1. Rigid clamps
2. Oscillating
clamps
11
13
Armor
Armor
Rods and
Rods Dampers Dampers
22
24
24
26
Table 2.6-2 Evaluation of Vibration Damages 1940-1960
(numbers in parentheses indicate total line length in km)
ACSR Conductor Failures in % of Line Length
Everyday
Stress in %
UTS
50-160
160-300
300-600
Total
10-15%
18% (1035)
42% (820)
0% (200)
30% (2055)
15-20%
35% (1150) 3% (29,000)
0% (600)
3% (30,750)
20-25%
100% (40)
12% (6800) 14% (7760)
Conductor Cross Section (total mm2)
23% (920)
25-30%
0% (1000)
0% (1000)
Total
30% (2225) 4% (30,740) 10% (8600)
6.5%
(41,565)
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
ductor damages due to aeolian vibrations. The evaluation of reported damage shows the influence of
parameters other than the EDS on conductor safety
(CIGRE 22.04 1979). This was also documented within
the WG04 work by closely monitored tests on dedicated
test lines, as described below.
The tests entailed continuous monitoring of the
dynamic bending strains at the conductor supports with
strain gauges, and was carried out on a test line, actually
a non-energized section of an actual line. The tests give
a good indication as to which factors influence the
vibration stress in the conductors. Figure 2.6-1 demonstrates the relative levels of measured dynamic stress. A
single ACSR 560/50 conductor, a size very frequently
used for 220- and 380-kV transmission lines, with an
EDS of 20.5% was tested for a period of operation of 8
months in a hilly terrain with a span of 400 m. The
dynamic stress of this conductor under these conditions
was established as the 100% value. Based on the measured data, the percentage changes of the corresponding
dynamic bending stresses with the different parameters
were then plotted. More details can be found in (Philipps et al. 1972).
For example, an increase of EDS from 20.5 to 27.1%
results in an increase of the dynamic stress by 21% (see
column 1 of Figure 2.6-1. For the conductor in question, the stress during the first month amounted to
170% of the dynamic stress after 8 months (column 2).
This effect differs from conductor to conductor and can
be caused by wire creep, which then causes an increase
in self-damping, although this latter assumption has
been questioned (Hard and Holbein 1967). The design
of suspension clamps also influences the stress: the
three-point suspension clamp decreases the stress to
52%, and the armor grip suspension to 82% (columns 3,
4, and 5). The type of terrain has a strong influence,
being a determinative factor for the wind uniformity
(column 6). And also the design of the conductor (alu-
Chapter 2: Aeolian Vibration
minum/steel ratio, number, and diameter of aluminium
wires) plays an important role (columns 7, 8, and 9 of
Figure 2.6-1).
Research and testing performed since 1960 have provided information that was not available to the EDS
Panel. Self-damping tests on conductors showed that
the ratio H/w between the horizontal tensile load and
the conductor weight per unit length was a more appropriate parameter than the % of RTS. This may not have
been evident to the EDS Panel, because the vast majority of the lines up to 1962 were built with the classical
30/7, 26/7, and 54/7 stranded ACSR. With such conductors, the increase of RTS due to an increase of the conductor diameter also resulted in an equal increase in the
conductor weight.
The EDS Panel classified the lines on the basis of terrain, (flat, hilly, mountainous, etc.), but it is now well
known that surface roughness of the ground, which creates turbulence, influences the wind power. It follows
that a parameter often ignored is the occurrence of dangerous winds on the line. In some locales, the occurrence
and direction of these winds are only related to general
meteorological conditions, but in other locations, the
line experiences daily air flows from both directions.
Under such conditions, the rate of dynamic stress accumulation can be significantly more than in other areas.
All this information better explains the dispersion of the
time-to-failure of the lines investigated by the EDS
panel and, in general, of present similar lines in service.
Design Guides Based on Field Experience
Over the years there have been several approaches to
improving the EDS rule. Several factors, which are
known to influence conductor endurance in the recommendation and selection of a safe design tension, were
considered. For example, Rawlins (1962) developed
from the analysis of the vibration performance—i.e.,
Figure 2.6-1 Various influences on the dynamic stresses of ACSR.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
strand failures or not—of existing lines, a system of
plotting results by the use of two factors: one related to
the wind power input and the other related to the conductor self-damping.
boundary between the two is, therefore, logical. The
important point to notice, however, is the zone where
failures have not occurred. A line constructed with
parameters falling within the “no failure” zone should
not experience trouble, even in severe exposures.
The parameter that was keyed to wind input was
L xd
kLs = s
RS x m
2.6-2
Where
Ls = length of span.
d = conductor diameter.
RS = conductor rated strength.
m = conductor mass per unit length.
The factor related to self-damping ability was line tension, expressed as a percent of conductor rated strength.
The “k” factor is determined from conductor properties, and can thus be calculated for each size and stranding, as has been done in some of the ACSR Conductor
Tables included in Appendix 1. Because comparable
field experience is not available for other conductors, the
listing has been restricted to ACSR.
Sample plots are shown in Figures 2.6-2 and 2.6-3. The
system cannot be expected to yield precise results for
several reasons. Ruling span length has been used rather
than span length. Terrain factor is not included, and
because of this factor alone, we could expect an intermingling of lines having apparently similar characteristics, some of which have shown failures while others
have survived without damage. The lack of a precise
Dulhunty et al. (1982) proposed the use of a Nomogram
with the wind direction, terrain type, number of dampers, span length, clamp type, and EDS as parameters for
lifetime estimation. Similarly, but in more detail, the use
of so-called danger factors for a conductor lifetime
assessment for bundles was also proposed (CIGRE
22.04 1988).
This question has recently been addressed again by
CIGR E 22 .11 TF4 200 5, which foll owed a new
approach, as will be described in Sections 2.6.3, 2.6.4,
and 2.6.5 below.
2.6.3
Single Unprotected Conductors
This section aims at recommending safe design tensions
for unarmored, unprotected single conductor lines.
Methodology
Two approaches were followed to determine calculated
vibration levels (the span response) with regard to the
endurance capability of the conductor to vibration. In
the Endurance Limit approach, vibration levels are considered to result in an infinite lifetime of the conductor
if they do not exceed a defined limit value (the endurance limit in terms of fymax). Conductor tensions that
lead to vibration levels below the endurance limit are
regarded as safe.
Figure 2.6-2 Relative incidences of fatigue failure and survival of ACSR
lines, plotted as (k x span length) vs. percent of rated conductor strength.
(ACSR lines with armor rods.) (EPRI 1979).
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EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
All theoretical models that were employed to estimate
safe tensions rely basically on the Energy Balance Principle (CIGRE 22.01 1989) to predict steady-state vibration
in terms of fymax (the product of vibration frequency and
maximum vibration amplitude at antinodes). That is the
response of a span when excitation by the wind is balanced by the internal damping of the span.
In the Cumulative Damage approach, a certain proportion of fatigue damage is assigned to each vibration cycle.
These small fractions of fatigue damage are assumed to
accumulate at a certain rate during the service life of the
conductor, until fatigue breakage occurs. The usual
assumption is that of linear damage accumulation
(Miner 1945). This approach requires assumptions on
the recurrence of fatigue-inducing stress levels to determine the number of occurrences at different stress levels.
Data on the probability of vibration exciting wind also
has to be introduced into the model. Probabilistic considerations may be expanded to the S-N-curves that define
the fatigue-inducing intensity of different vibration levels,
and different S-N-curves may be surmised for different
levels of probability of survival. Safe conductor tensions
that are calculated on this basis thus relate to a particular
predicted fatigue life of the conductor.
Lastly, it may be observed that the Cumulative Damage
approach leads to a more permissive H/w than the
Endurance Limit approach. This is to be expected,
because the former approach allows for a certain number of vibration cycles above the conductor endurance
limit, while the latter does not.
Chapter 2: Aeolian Vibration
Comparison with Field Experience
Since tension, H, for any span is not constant but varies
with temperature, ice or wind loading history, and creep,
a reference condition has to be selected for determining
H. Therefore, the average temperature for the coldest
month has been defined as the reference temperature,
and the tension, H, has to be determined for initial conditions—i.e., before wind, ice loading, and creep.
In doing this, it became evident that the most significant
design parameter influencing the probability of fatigue
is conductor tension, because of the impact of tension
upon conductor self-damping (see Section 2.3.6). However, tension can be expressed in various forms, such as
force, stress, % of rated strength, and others. In order to
gather as many field cases into each class as possible, the
necessity arose to choose a ranking parameter that was
not dependent on factors such as conductor diameter.
The parameter that was selected was H / w, with H the
conductor tension in N, and w the conductor weight per
unit length in N/m, so the dimension of H/m is m. It is
worth noting that the chosen parameter H/w is, in fact,
the catenary constant described in Appendix 3.
Field experience cases were collected for undamped
spans—i.e., spans equipped with neither dampers nor
armor of any type. This database was used to verify the
predictions of maximum safe design tensions based on
the Energy Balance Principle.
Recommendations
The maximum safe design tensions with respect to aeolian vibrations of undamped and unarmored conductors are shown in Table 2.6-3 as a function of terrain
Figure 2.6-3 Relative incidences of fatigue failure and survival of ACSR lines,
plotted as (k x span length) vs. percent of rated conductor strength. (No armor
rods or dampers.) ([EPRI 1979).
2-107
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
category. The table uses H/w, the ratio of horizontal tension in the span to conductor weight per unit length, as
the tension parameter. It is important to note that, as
explained above, this horizontal tension refers to initial
horizontal tension, before wind and ice loading and
before creep, at the average temperature of the coldest
month on the site of the line.
Recommended safe tensions apply to the following
round strand conductors: all aluminum A1 /AAC) conductors; all aluminum alloy A2 or A3 (AAAC) conductors; aluminum/aluminum alloy A1/A2 or A1/A3
(ACAR) conductors; and steel-reinforced aluminum
A1/Syz /ACSR) conductors. It was decided to give a
uniform recommendation for all types of conventional
conductors using aluminum and/or aluminum alloy.
Although a lower fatigue endurance of A2 (AAAC)
conductors may be surmised from (EPRI 1979), there is
no well-documented field evidence to support a more
pessimistic tension recommendation for these conductors. Also there were not enough cases to indicate safe
tension limits using this “new” approach for steel
ground wires or OPGW.
Terrains have been divided into four categories according to general characteristics. Should there be any doubt
about real terrain category, the lowest class should
always be selected. The maximum safe design tensions
thus recommended should be suitable most of the time.
However, special situations require specific attention.
Such is the case for extra long spans, or spans exposed
to pollutants that may decrease the self-damping or the
fatigue endurance of the conductor, or spans often covered with ice, rime, or hoarfrost, or spans operated at
high temperature.
Generally, the damping of spans is inexpensive and is
certainly preferable to risking conductor fatigue breaks.
Moreover, use of damping may allow higher tensions,
resulting in significant cost savings in line construction
(see Section 2.6.6).
Table 2.6-3 Recommended Safe Design H/w Values for
Single Unprotected Conductors (CIGRE 22.11 TF4 2005)
The use of armor rods or special supporting devices,
such as cushioned clamps and helical elastomer-lined
suspensions, may justify higher design tensions on otherwise unprotected conductors. When these devices are
employed, information on safe tensions should be
obtained from their suppliers (see Section 2.3.6). In
addition, in some countries, the maximum safe design
tension may be governed by the maximum climatic loading, such as heavy ice loads, rather than by aeolian
vibration.
Table 2.6-4 compares the safe design tension (CIGRE
22.11.4 2005) with the original EDS values (Zetterholm
1960) and the values arising from the European norm
EN 50-341-3-4 (EN 2001), for various strandings of
ACSR conductors and also AA and AAA conductors.
The recommended safe H/w values (CIGRE SC22
WG11 TF4 2005) may thus appear overly conservative.
Nevertheless, it should be noted that they generally
exceed the 17-18% of RTS recommended by the EDS
Panel for all aluminum A1 (AAC) conductors and low
steel-content aluminum conductors A1/Syz (ACSR),
and evidently they are not intended to replace operational experience and engineering judgment. For
instance, good operating experience with higher H/w
values could be used for a new line in the same area if
engineering judgment concludes that this is justifed.
In this context, it is also interesting to note, that as far
back as 1934, the following “rule” was formulated by
Maria Artini (Artini 1934; Niggli 1969):
“When the value of the everyday tensile stress of conductors (expressed in kg/mm 2) lies below the value of
their specific weight (expressed in kg/dm3), these conductors do vibrate so seldom and so weak, that failure is
not to be expected.”
That means exactly H/w < 1000 in today’s units.
Table 2.6-4 Recommended EDS in Percentage of RTS for
Unarmored, Unprotected Conductors (after Kiessling et al.
2003)
Conductor Type CIGRE 1960 EN 50 341-3-4
CIGRE 2005
Terrain
Category 3
AL1/ST1A
2-108
4.3:1
18
18.5
13
6.0:1
18
18.5
14
7.7:1
18
19.0
15
11.3:1
18
18.4
16
Aluminum
17
18.8
20.8
AlMgSi
18
15.0
11.3
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
2.6.4
Damped Single Conductors
This section seeks to recommend safe design tensions
for single conductor lines protected by means of Stockbridge-type vibration dampers installed at the span
extremities, since currently, this is the type of damping
most widely used on conductors.
Chapter 2: Aeolian Vibration
the ice and wind load conditions are 12.6 mm radial glaze
ice with a 380 Pa wind at -20oC (CIGRE 22.12 2006).
Other typical values accepted internationally, as well as
in IEC 60826 (2003), are the following:
• 60 to 75% RTS under maximum climatic load conditions
One of the several sets of parameters that have been
applied to ACSR conductors in connection with selective damping is based on anticipated climatic conditions
for the region where the line is constructed. It restricts
the conductor tension to the conditions shown in Table
2.6-5, depending upon which becomes the limiting factor. It will generally be true that the third condition governs. The values shown should be adjusted to agree with
the likelihood of occurrence. If long periods of low temperature are common, the 27% figure should be reduced
(EPRI 1979).
Other sets of values for these parameters have been
employed.
The National Electric Safety Code (NESC) (NESC
1987) recommends limits on the tension of bare overhead conductor as a percentage of the conductor’s rated
breaking strength. The tension limits are: 60% of RTS
under maximum ice and wind loading, 35% initial
unloaded (when installed) at 60°F, and 25% final
unloaded (after maximum loading has occurred) at
60°F. It is common, however, for lower unloaded tension limits to be used. Except in areas experiencing
severe ice loading, it is not unusual to find tension limits
of 60% maximum, 25% unloaded initial, and 15%
unloaded final. This set of specifications could result in
an actual maximum tension on the order of only 35 to
40%, an initial tension of 20%, and a final unloaded tension level of 15%. In this case, the 15% tension limit is
said to govern (Southwire Company 1994). The NESC
is silent on the need for vibration dampers.
This is clearly demonstrated in Table 2.6-6, which shows
some results of sag-tension calculations as a function of
the initial installed stringing tension. The conductor is
403-A1/S1A-26/7 Drake, the ruling span is 300 m, and
Table 2.6-5 Conductor Tensions for Different Climatic
Conditions
Condition
Maximum allowable % of RTS
(Rated Tensile Strength)
Initial unloaded, no ice or wind,
at minimum temperature during
stringing
32
Final unloaded-after creep, no
ice or wind at 15°C
24
Final unloaded, no ice or wind,
at minimum temperature for area
27
Maximum load, worst conditions
35
• 20 to 30% RTS with no ice or wind at 15oC, when the
conductor is initially installed under tension.
• 15 to 25% RTS with no ice or wind at 15oC, the conductor being in its final condition (after the conductor has been exposed to a heavy ice and wind loading
event or has been in place for many years).
To avoid conductor system tensile failure under high ice
and wind loads, the conductor tension under maximum
ice and wind is often limited to between 50% and 60% of
RTS in areas experiencing heavy ice and wind loads.
In the recent CIGRE work (CIGRE SC22 WG11 TF4
2005), another approach is proposed. Therein, the similarity in damping efficiency levels indicated a particular
parameter to use in rating the protective capabilities of
dampers. This rating parameter, LD/√(Hm), (where L is
actual span length, D is conductor diameter, H is horizontal tension in the conductor, and m is mass of the
conductor per unit length) has been already in use in the
analyses of collections of field experience data on the
fatigue of overhead conductors (Rawlins et al. 1961). So
spans have been ranked according to the difficulty in
damping them, based on the line design variables span
length, conductor size, and tension. The parameter is
also proportional to the damping efficiency required to
control vibration amplitude to a given level. Since the
Task Force had adopted the parameter H/w (where w is
weight of the conductor per unit length) to rate the
effect of tension on conductor self damping, it was able
to simplify the set of rating parameters L D H m and
H/m to LD/m and H/w. Field experience has been substantiated by calculating so-called safe boundaries
according to the endurance limit approach explained in
Section 2.6.3 (see Figure 2.6-4).
Table 2.6-6 Tension under Maximum Ice and Wind
Loading as a Function of the Initial Stringing Tension for
Drake ACSR.
Initial Unloaded
Tension at 15oC
(%RTS)
Max. Design
Tension under Ice
and Wind Load
(%RTS)
Max. Design Tension
under Ice and Wind
Load (kN)
10
22.6
31.6
15
31.7
44.4
20
38.4
53.8
25
43.5
61.0
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
missive than the corresponding EDS values for low steel
content, medium steel content, or high steel content
A1/Syz (ACSR) conductors. However, for Aldrey conductors, the calculated safe design tension is definitely
much more conservative over the full span range than
the value recommended by the EDS Panel—i.e., 26% of
RTS or about 3000 m, which correlates well with operating experience (Niggli 1969).
Figure 2.6-4 Predicted safe boundaries according to
endurance limit approach (CIGRE SC22 WG11 TF4
2005).
The safe tensions recommended by the EDS Panel,
translated in terms of H/w for different damped A1/Syz
(ACSR) and Aldrey (AAAC) conductors are also shown
in Figure 2.6-4. As the Panel did not account for the
span length, their recommended tensions appear as
straight vertical lines in the graphics. For the common
range of span parameters, 5 < LD/m < 15 (m 3 /kg), it
may be observed that the safe design tensions, as calculated by the endurance limit approach are, respectively,
more permissive, about equally permissive, or less per-
Recommendations
The design recommendations of CIGRE SC22 WG11
TF4 2005 are depicted in Figure 2.6-5 in the form of
four sets of curves, each set associated to a particular
terrain category described in the legend. The corresponding information is provided in Appendix 2.7 in
algebraic form. Terrains have been divided into four categories according to their general characteristics (see
also Table 2.6-3). Should there be any doubt about real
terrain category, the lowest category should be selected.
The “Basic Safe Design Zone–No Damping” applies to
undamped and unarmored single conductors, as already
shown in the previous section. This zone is defined in
terms of the H/w parameter only, and it is unlimited in
the LD/m parameter.
The “Safe Design Zone–Span End Damping” constitutes a zone where full protection of single conductors
against aeolian vibration is achieved by means of one or
more Stockbridge-type dampers installed at span
extremities. Hence, within the limits of this zone, aeolian
vibration should not be a constraint on design tension.
For line parameters in the “Special Application
Zone”—for example, long spans— aeolian vibration is
most probably a constraint, and it is recommended that
line designers determine the availability of adequate
protection before finalizing the design.
As an application example, these recommendations are
applied to an ACSR Drake conductor.
For unprotected (no armor rods or AGS clamps), round
strand single conductors (not bundles nor protected single conductors), the recommended H/w parameter constraint, where vibration dampers are not used, depends
on terrain. Recommended maximum values of H/w in
Table 2.6-3 range from 1000 to 1425 m, say at -20oC. As
can be interpolated from Table 2.6-7, for the Drake
ACSR in a 300 m span, this would correspond to an
unloaded initial tension of between 11 and 15% RTS.
Figure 2.6-5 Recommended safe design tension for
single conductor lines. H: initial horizontal tension; w:
conductor weight per unit length, L: actual span length,
D: conductor diameter, and m: conductor mass per unit
length (CIGRE SC22 WG11 TF4 2005).
2-110
If dampers are used, then a higher H/w level would be
acceptable. For the example case, LD/m is 5.2 m 3 /kg,
and from Figure 2.6-5, the corresponding H/w value for
Category 4 terrain is about 2500 m. This corresponds to
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
an unloaded initial tension of 24%RTS. Normal dampers should be adequate up to that tension in this terrain.
Maximum safe H/w is smaller for the other terrain categories, as indicated in the figure.
2.6.5
Bundled Conductors
This section seeks to recommend safe design tensions
for bundled conductor lines. The recommendations
cover twin horizontal bundles, triple apex-down bundles, and quad horizontal bundles made up of conventional stranded conductors fitted either with damping
or nondamping spacers or a combination of nondamping spacers and span-end Stockbridge-type dampers.
Numerous field tests have demonstrated that bundled
conductors respond less to aeolian excitation than single conductors of the same size and at the same tension
as those of the bundle (Leibfried and Mors 1964; Liberman and Krukov 1968; Phillips et al. 1972). For example, Figure 2.6-6 shows results of simultaneous
recordings at an outdoor test line. Bundling reduced
vibration amplitudes by about half, with and without
dampers on the span.
Table 2.6-7 H/w Values for Drake ACSR in a 300 m Span
Tension at
Initial, Unloaded Initial Unloaded
-20oC with Tension at
Conductor
H/w at Avg Temp Max Ice and Max Ice
Tension at 15oC for Coldest Month) Wind Load and Wind
Load (kN)
(m)
(%RTS)
(%RTS)
10
900
22.6
31.6
15
1500
31.7
44.4
20
2100
38.4
53.8
25
2700
43.5
61.0
Chapter 2: Aeolian Vibration
The benefits of bundling are attributed to the effects of
mechanical coupling between the subconductors interfering with the vortex excitation mechanism.
Initially, Edwards and Boyd (1965) at Ontario Hydro
investigated the effect of damping introduced into spacers. They found that damping at a particular level
reduced amplitudes by a factor of 5 in a twin bundle,
and by a factor of 20 in a quad bundle relative to a comparable single conductor. The advantage of damping
was confirmed by Diana et al. (1982) at the Porto Tolle
Test Station in Italy. The effect of bundle configuration
on the advantage offered by damping was investigated
by Hardy et al. (1990) at the Magdalen Island Test Station. Damping in spacers is advantageous in all bundle
configurations, but seem most effective in those having
vertically related subconductors, such as triple and quad
bundles.
Recommendations
For bundled conductors, the safe H/w value is recommended as a matter of prudence to be limited to 2500,
although there is evidence that quite a few bundle lines
have operated for many years safely at higher H/w values.
It should be noted that this safe design tension limit is
supposed to be valid also for bundled conductors fitted
with spacer dampers, independently of the span parameter LD/m used for damped single conductors (see Section 2.6.4), because the benefits of damping in the case
of bundled conductors are usually well distributed over
the span length.
Use of armor rods or special supporting devices, such as
helical elastomer-lined suspensions, may justify higher
design tensions. When these devices are used, information on safe design tension should be obtained from
their suppliers.
2.6.6
Effect of Tension on Line Costs
Before leaving this section on safe design tension, it
should be remembered that in today’s extremely competitive environment in the power industry, the impact
of vibration upon line design is an important cost issue,
and this is highly dependent on the line tension.
Figure 2.6-6 Comparison of vibration in single versus
bundled conductors Drake ACSR in 1200-ft span. (MILS
= in. x 10-3; CPS = Hertz) 1 – Single conductor. 2, 3 –
Subconductors in horizontal two-conductor bundle. A –
No dampers. B – One Stockbridge damper at end
opposite recorder (Rawlins and Harvey 1960).
From experience of fatigue damage with a number of
lines throughout the world with high tension, it was
found that lines strung at tensions higher than 20% of
rated strength were difficult to maintain, since as discussed in Section 2.2.6, if the tension is increased, the
self-damping of the conductor is reduced. This will lead
to higher vibration levels. Surveys by CIGRE and others have shown that vibration fatigue breaks are more
likely to occur with high conductor tensions, even when
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
protective measures are applied. This experience generated an attitude of caution throughout the industry. As
a result, a great many lines probably exist that might
have been constructed with decreased tower height and
decreased sag, at considerable cost savings.
On the other hand, the adverse consequences of deviating too far from accepted and normal practice can be
significant. Once span length, sag, and ground clearance
have been established, it becomes more difficult to find
satisfactory solutions if fatigue problems develop. In
many cases, careful use of available damping systems
has made it possible to use higher tensions than those
normally considered. For instance, in Russia, the guidelines for components of electrical installations allow values for the initial conductor stress at mid annual
temperature (EDS) of up to 30% of RTS for AAC,
AAACSR, ACSR, and up to 35% of RTS for steel conductors and earth wires (Shkaptsov 2006). The potential
savings that might be realized through the use of higher
conductor tensions have been reviewed by Fritz (1960),
who found that they could be substantial. On the other
hand, it should not be forgotten that there are risks and
associated costs of extra maintenance, due to the natural ability of the vibration to develop damage at points
of poor installation, associated with these higher tensions. Unnecessary caution can thus be costly. This is
illustrated by the results of various studies. Two such
studies are described below.
The findings of an investigation, which has been carried
out in order to determine the optimum conductors and
conductor tensions for a twin-bundle 220-kV line, are
presented in Figure 2.6-7. It shows the costs of towers,
Figure 2.6-7 Initial costs of a 220-kV line (twin
conductors ACSR 300/...) versus conductor tension at
10°C (EDS) for different ACSR conductors. Solid lines are
valid for 20% tension towers, dotted lines for 10%
(Bückner 1966).
2-112
foundations, and conductors related to the EDS. The
conductors shown have the same aluminum cross section, 300 mm 2 , but a variable steel content from 9 to
20% of the aluminum cross section (corresponding to
the ratios 4.3:1 to 11:1 shown in the figure). Solid lines
show the costs for 20% tension towers, and dotted lines
show those for 10%. The curves start at a “normal”
value for the EDS and end at EDS values that are 20%
higher than the CIGRE EDS panel recommendations
for unprotected conductors (see Table 2.6-1). It should
be noted that these are initial costs, and do not reflect
the costs of extra maintenance should vibration control
prove inadequate.
Important savings can be realized for a low steel content. For instance, the optimum steel-to-aluminum ratio
for a 220-kV line is 11:1. Similar calculations have
shown that, for 110-kV lines, the optimum aluminiumto-steel ratio is 7.7:1.
For all conductors, with the exception of the 4.3:1 ratio
conductor, the costs of the 220-kV line decrease slightly
with higher EDS values and particularly for the 11:1
ratio conductor. The cost also decreases for a lower proportion of tension towers. For 110-kV lines, the cost savings by increasing the conductor tension are significant.
This is true to an even greater extent for 20-kV distribution lines.
In a more recent investigation, this trend of decreasing
line costs with increasing EDS has been confirmed also
for 380-kV lines (Figure 2.6-8).
For longer span lengths, the influence of conductor tension on the costs of the line is also high. Figure 2.6-9
shows, as an example, the calculated costs of a river
crossing against the EDS.
Figure 2.6-9 Costs of the line for a river crossing
versus the EDS (Kiessling et al. 2003).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Conclusion
The examples above have shown that the choice of the
conductor tension plays a major role in both in the
proper “utilization” of the mechanical properties of the
conductor and in the total costs of the line. Current
understanding of the various parameters influencing the
vibration behavior of a conductor has improved, as well
as the knowledge of how to apply vibration-damping
measures. Additionally, economies of scale and globalization have resulted in extremely price-competitive
vibration-damping hardware. So a possible “economic”
approach could be to base the mechanical design of the
conductors on both the maximum wind and ice loads
and the total line costs, and then, using the recommendations for safe design tension outlined in the previous
sections, select the proper damping hardware (see also
Section 2.4.) and, if required, check its performance on
the actual line, as described in Section 2.7.
2.7
ASSESSMENT OF CONDUCTOR
VIBRATION SEVERITY
2.7.1
General
Among the various wind-induced motions (EPRI 1979),
those due to vortex shedding, called “aeolian vibrations,” are the most recurrent and the most dangerous
for conductor integrity.
Figure 2.6-8 Influence of conductor tension (EDS)
on transmission-line costs for various 380-kV
configurations (cost base 1991) (Bückner 2002).
Chapter 2: Aeolian Vibration
For this reason, great efforts are devoted to the assessment of aeolian vibration severity. Four main methods
are available for this task:
1. Analytical prediction of conductor vibration severity
2. Field vibration tests on outdoor experimental spans
3. Vibration test on laboratory spans
4. Vibration measurements on actual lines
Each offers its own contribution to the total picture.
Although they are inter-related, their limitations and
concepts are somewhat different.
2.7.2
Analytical Prediction
Analytical prediction (Claren et al. 1974; Claren and
Diana 1969a; CIGRE SC22 WG01 1989b; CIGRE
SC22 WG11 TF1 1998; Ervik 1981; Hagedorn 1990;
Tompkins et al. 1956) is mainly used during the design
of the line to anticipate the performance of single and
bundled conductors under aeolian vibration and to
evaluate, when necessary, the amount of additional
damping required to maintain the vibration amplitudes
within safe limits. Analytical methods to assess conductor vibration behavior are covered in Section 2.5.
2.7.3
Outdoor Test Spans
Outdoor experimental spans exposed to natural wind
(Annestrand and Parks 1977, Cloutier et al. 1974,
Houle et al. 1987) have been built in several countries
worldwide for research purposes and for the comparative evaluation of conductor damping systems proposed
for important projects. Some test stations have been
used also for the evaluation of new damping systems
and for the assessment of the vibration behavior of new
line configurations. Figure 2.7-1 shows the Hydro Quebec test station at Varennes, Canada, formerly installed
at Magdalen Island and widely used for many years.
Figure 2.7-1 Outdoor test line of Hydro Quebec at
Varennes, Canada.
2-113
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
These test stations represent an accurate means for the
investigation of vibration phenomena; however, the considerable costs involved can be afforded only by power
authorities, research institutes, and major manufacturers (Rawlins and Harvey 1960) or justified in some large
transmission project.
Outdoor spans are normally not energized, and can,
therefore, be instrumented in a sophisticated fashion
with a large array of recording and monitoring systems.
If constructed specifically for testing, they are always
available and can closely duplicate actual line construction. Convenient access platforms are possible. Wire
links can be used to connect transducers on the line with
ground-based recorders, making this phase of the operation less expensive than it would be if telemetry were
necessary.
One of the disadvantages of an outdoor test span built
for a specific project is the cost of constructing a system
that may have no use beyond the test program. The generation of significant data is at the mercy of the elements, but the total amount of data can be very large.
Improvements in data reduction may make it possible to
achieve a balance between data generation and reduction to a useful form. However, it is generally true that
total use of the available information is not realized.
In order to reduce the travel time required for maintaining the line and gathering its data, the test span may not
always be located in a high vibration area, or in an area
typical of line construction. Vandalism can be a problem with installations of this type. Outdoor test spans
are useful for testing advanced line concepts. Tests can
be very rigorous, since line failure will not result in a service interruption. In some high-power laboratories, outdoor test spans have been used for short-circuit
simulation. Research on galloping and ice drops
(Mather and Hard 1958; Cassan and Nigol 1972; Van
Dyke and Laneville 2004) have also been performed.
Outdoor test spans can be useful for long-term product
demonstration, and for the investigation of fatigue and
wear of line hardware under natural conditions.
2.7.4
Indoor Test Spans
Laboratory spans for vibration tests are generally 30-50
m (100-165 ft) long. In few cases, spans of 90-100 m
(295-330 ft) have been built (Figure 2.7-2). Laboratory
test spans can provide important information on the
conductor dynamic characteristics such as self-damping
(CIGRE 1979a) and dynamic bending stiffness. For special conductors and/or unconventional suspension
clamps, the laboratory test spans can be used to establish the relationship between bending amplitude and
2-114
bending stress or strain (see Section 2.7.8). Moreover,
intensive tests are performed to assess the fatigue behavior of various conductor–clamp systems (CIGRE SC22
WG04 1985) and the effectiveness of vibration dampers
(IEEE 1993).
Indoor test spans are generally about one-tenth of the
length of the average outdoor span. This means that,
within the normal range of frequencies, the natural
responses of the indoor span are similarly reduced in
number, and the frequency difference between two natural responses will be much greater. Because the indoor
span is readily accessible and rarely presents problems
of height, precise measurements are normally possible
at any point throughout its length. The prime advantages that it offers are the facts that the frequency of
excitation can be precisely controlled, and since the excitation depends on a shaker mechanism, the span can be
driven with a pure single frequency, completely free of
beats. Tension adjustment and measurement can usually
be accomplished with relative ease. Although singlefrequency vibration does not duplicate the response
normally observed on outdoor spans (see Figure 2.7-3),
it does simplify analysis and interpretation of results.
The shaker system used for excitation normally provides
independent control of frequency and amplitude, so
that practically any span response can be observed without waiting for proper weather conditions. Many
measurements not possible in other test situations can
be made on an indoor span.
However, indoor spans cannot realistically replicate
low-frequency motions such as galloping or wakeinduced bundle oscillations. Moreover, they cannot be
used to reproduce the vibration behaviour of conductor
bundles because it is too complex and they are not suit-
Figure 2.7-2 Laboratory test span at the University of
KwaZulu-Natal (85 m).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
able for investigations involving the mobility of a suspension clamps because it is impossible to completely
simulate the motions of an insulator string between two
spans. For example, the evaluation of the influence of
the vibration recorder mass attached to the suspension
clamp on the conductor vibration shape has been performed by Heics and Havard (1993) on a full-scale outdoor test line.
Other important limitations of indoor span testing are
related to its shorter length and to the presence of the
shaker attached to the line. One problem that may be
encountered with indoor testing is that levels of excitation can be achieved far beyond those experienced
under natural conditions. The danger here is that a particular device, which may show high performance
indoors, may not fare as well in actual use. This could be
the case for concepts that rely on high acceleration or
displacement for their performance. In this respect, the
indoor test span should be guided by results from outdoor testing in order to achieve reasonable results. The
ability to overdrive is useful in some cases, as a means of
demonstrating extreme conditions, or of accelerating
damage.
Damper tests must account for the fact that a single
damper on a short indoor test span may be much more
effective than it is when assigned the task of damping a
longer actual span. Static bending tests are also possible
on an indoor span. Because of the array of measuring
equipment that can be brought to bear on the problem,
static and dynamic effects induced by various suspension devices, clamps, and armor rods can be investig a t e d . I n d o o r t e s t s p a n s o p e r a t e d b y fi t t i n g
manufacturers are used extensively for product development testing to demonstrate that a new concept or
device is more effective than another currently being
used. Much of this work is fatigue testing, with the end
point being determined by the number of cycles that a
component will withstand without breaking or showing
signs of excessive wear. Feedback control systems can be
used to maintain a uniform level of excitation for periods of weeks or months.
The fatigue testing of some components can be conducted at very high frequencies in order to shorten the
test time. This is not possible with conductor fatigue
tests, because so many variables are involved. A frequency increase will result in a shorter loop length, and
probably a higher level of conductor self-dissipation, so
that the test results could fall completely outside normal
conductor experience. Conductor fatigue testing is,
therefore, very time consuming. A certain degree of time
compression is obtained by virtue of the fact that the
span can be excited continuously over the full 24-hour
Chapter 2: Aeolian Vibration
period, whereas the actual span might experience many
quiet periods during the course of the day. Fatigue tests
on fittings are generally performed between 10 and 100
megacycles, while the fatigue curve of conductors are
determined up to 500 megacycles and above. The
megasecond is approximately 11.6 days. A conductor
being vibrated at 30 Hz would accumulate 30 megacycles in one megasecond. Performing fatigue tests on an
indoor span at 30 Hz would require roughly 4 days for
10 megacycles and 193 days for 500 megacycles.
2.7.5
Actual Lines
The third major type of testing employs actual lines
under operating conditions. Vibration measurements on
overhead lines are commonly performed as a final
acceptance test of the conductor damping system, at the
end of the line construction, and on lines in operations
for assessment of vibration intensity of the conductors.
For research purposes, this avoids special construction
costs, since the lines are not originally constructed for
testing. Areas in which tests are conducted can be
selected on the basis of previous experience and observation. The use of actual lines, in many cases, makes it
possible to experiment with conductor that has been in
service for several years and has experienced long-term
static creep and extremes of temperature. Since these
lines are in operation, the installation of instruments
usually requires a line crew, and possibly an outage, during the installation period. Measurements on the line
itself require battery-operated equipment that is selfcontained, or involve the use of telemetry. The limitations of this type of equipment are that it usually
requires some form of time sampling, which may miss
the recording of significant, but short–term, events. The
recording equipment itself generally runs on a time
basis and does not predetermine whether the vibration
level being recorded is significant or not. As a result, a
considerable amount of the recorded information contains insignificant levels of data. Interesting test areas
are not always easily accessible, so travel costs for servicing the equipment and gathering the recordings may be
relatively high.
Vandalism can be a problem only when ground instrumentation is required. The primary advantage in using
actual lines for test purposes is that they provide an
opportunity to evaluate the designs under conditions of
use. For example, if the line had been erected in an area
that could be vibration-prone and has been equipped
with an insufficient damping system, the test program
can indicate the advisability of adding dampers. Damping studies are a common activity on lines used in this
way, because it possible to simultaneously test conductors with and without additional damping.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
For these measurements, a variety of instruments have
been employed. Among the different test procedures,
the “bending amplitude method,” involving a specific
live-line vibration recorder, has been widely used for the
last 40 years.
2.7.6
Aeolian Vibration
The aeolian vibration phenomenon has already been
described in Section 2.1. As observed in Section 2.5, and
as in many naturally excited systems, two or more vibration frequencies that are close together are often
induced simultaneously by the wind in a conductor
span. The presence of two or more closely spaced vibration frequencies causes beats at any vibrating point of
the conductor, which result in a continuous variation of
the vibration amplitude, as shown in the recordings of
Figure 2.7-3.
The awareness of this aspect of the conductor vibration
is necessary for the correct interpretation of the data
collected by a specific recorder and for the evaluation of
conductor lifetime.
2.7.7
result from galloping and subspan oscillation, but is not
the main problem associated with those motions.
Fatigue of conductor strands, of any type, is caused by
the alternating stresses produced by the vibration at
points where the motion of the conductor is constrained—i.e., where the conductor is secured to fittings.
Thus, typical locations are: suspension clamps, deadend
clamps, splices, and clamps of spacers, dampers, warning devices, and antigalloping devices. Among these
locations, the most critical is at the suspension clamp,
because of its rigidity in the direction of aeolian vibration (mainly vertical) and the cumulative static stress
due to the conductor curvature, tensile load, and clamping effect. All the other fittings show a certain degree of
mobility, but poorly designed units, especially spacers
and dampers, may produce strand failures at their location (Figure 2.7-5) or may fail themselves under vibrations (Figure 2.7-6).
Some inspection procedures are available to assess
strand failure or to estimate whether fatigue failures on
Vibration Assessments
In overhead conductors, fatigue failure of strands is the
most common form of damage resulting from aeolian
vibration (Figure 2.7-4). Conductor fatigue may also
Figure 2.7-4 Strand failures due to aeolian vibration
(courtesy U. Cosmai).
Figure 2.7-3 Records of natural aeolian
vibrations (courtesy U. Cosmai).
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Figure 2.7-5 Strand failure on both sides of a spacer
clamp (courtesy U. Cosmai).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
strands may eventually occur during the economic life
of the conductor: The most common are:
1. Visual inspection of conductor surface
2. Radiographic inspection
3. Conductor vibration measurement
The need to apply one of these procedures may be indicated by certain “early warnings.”
Generic information about excessive vibration levels on
an overhead transmission line can be gathered by means
of line-crew reports about noise (rattling sounds) from
conductor, hardware, or tower members, and visible
damage or looseness of hardware components, crossarm members, and conductor fittings. Nevertheless,
these reports should be carefully evaluated, since they
do not necessarily indicate danger to the line. Further
investigation is necessary to clarify whether the damage
is isolated to a single event or to a single component, or
it is an indicator of a major design problem.
Strand failures of Stockbridge-damper messenger cables
and loss of damper weights are among the warning
signs (Figure 2.7-7). Nevertheless, this symptom should
be carefully analyzed, because it can indicate a poor
unit design or it can be the result of low-frequency
vibrations, unprotected by the damper (e.g., aeolian
vibration on conductor covered with hoarfrost or ice).
Chapter 2: Aeolian Vibration
Hardware components having natural responses in the
frequency range of conductor aeolian vibration may
face fatigue failure. Conductor vibration can excite
vibration of hardware components even if the conductor
vibration is damped at levels that can be easily endured
by the conductor. Slender components such as lattice
tower members can also vibrate from the direct action
of the wind (Carpena and Diana 1971; Havard and
Perry 2000). Hardware components showing signs of
chafing or rotation may provide evidence that vibration
had occurred. Fretting at the interstrand contact points
within conductors produces black metal oxide powder.
The appearance of this powder at the surface of the conductor indicates vigorous vibration activity.
Visual inspection is appropriate when there is strong or
specific evidence that damage has occurred, but it is not
usually performed systematically during periodic maintenance or line survey. In any case, strand failures may
be difficult to detect, because they occur near the last
point of contact between the conductor and clamp. For
example, failures at suspension clamps generally occur
on the lower side of the conductor inside the clamp
mouth. Reliable inspections require that the conductor
be separated from the clamp. When armor rods or elastomer-lined clamps with helical rods are used, the
search of strand failures requires the removal of these
components.
Moreover, aluminum-based conductors, having more
than one layer of aluminum strands, may show the first
strand failure either in the outer layer or in the layer
below (EPRI 1979).
Figure 2.7-6 Strand failures in the messenger cables of
vibration dampers (courtesy U. Cosmai).
Since visual inspection allows the detection of outerlayer damage only, it may overlook evidence of excessive
vibration severity until significant damage has already
occurred.
Radiographic inspection can give some results, but it is
not a common practice since it is costly and rather complex. Moreover, the interpretation of the radiographs is
sometimes difficult, and the failure detection may be not
completely reliable.
Figure 2.7-7 Vibration dampers with detached weights
(courtesy U. Cosmai).
Thermographic inspection is not suitable for the detection of strand failure on normal conductors. Tests and
calculations conducted in Italy on an ACSR (54/7) conductor (D’Ajello et al. 1994) showed that no difference
in temperature can be detected for failure of one and
two outer-layer strands and a difference of only one
degree for three-strand failure.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Another problem related to conductor vibration is the
loosening of the clamps of spacers, dampers, warning
devices, etc. Loosening of spacer clamps causes serious
damages to the conductor. It can be due both to aeolian
vibration and subspan oscillation. Initially, the movement of the loose clamp causes abrasion on the conductor surface (Figure 2.7-8), and then increasing looseness
allows hammering between the conductor and the
clamp that leads to complete failure of the conductor
(Figure 2.7-9). Looseness of single clamp fittings allows
the progressive slipping of the units along the conductor
toward the center of the span.
Considering the above, and as stated in EPRI 1979,
“attentiveness to early warnings and use of vibration
recordings” are the most suitable methods for the early
detection of conductor failure or risk of failure.
2.7.8
Vibration Measurements on Actual Lines
Measurements of aeolian vibration on actual lines can
be made in different ways using a variety of instruments
that can be classified into four groups:
• Generic transducers
• Vibration detectors
• Optical vibration-monitoring devices
• Vibration recorders (bending amplitude recorders)
Generic Transducers
Generic transducers—such as accelerometers, velocity
pick-up, contactless displacement transducers, anemometers, and thermometers—connected to a groundsite data acquisition system, are normally used in outdoor test stations. In the past, they have also been used
on several transmission lines to assess the vibration
severity or for research purposes (Hard 1958; Elton et
al. 1959; Falco et al. 1973; Diana et al. 1982). With the
advent of commercial bending amplitude recorders, this
practice has been limited to test stations.
Vibration Detectors
The first conductor vibration recorders, such as Zenith
and Servis recorders and Jacquet counters used about
50 years ago, were simply vibration detectors able to
provide a quite rough relative index of vibration activity.
Modern vibration recorders have replaced them.
However, the use of vibration detectors of low cost,
lightweight construction and easy installation can be
still of interest. One of these devices, for example, has
been proposed recently by the Rand Afrikaans University (DuPlessis and Pretorcus 1995).
Optical Vibration-monitoring Devices
Optical devices are sometimes used to assess the vibration level on overhead line conductors.
Two systems are known so far:
1. Opto-electronic recorder (Figure 2.7-10)
2. Laser recorder
Figure 2.7-8 Conductor abrasion caused by the
loosening of spacer clamps.
Figure 2.7-9 Strand failure caused by the loosening
of spacer clamps.
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Figure 2.7-10 Opto-electronic recorder (courtesy
Pfisterer).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Two German companies have developed a similar optoelectronic vibration-monitoring device.
Both types are mobile noncontact equipment that consists of three parts:
• vibration-monitoring unit
• wind-measuring unit
• computer-based data acquisition system
An electro-optical camera equipped with a telephoto
lens is usually directed at the vibrating object from the
ground. The camera transforms the vibration images
into electrical signals whose frequency spectrum and
time history can be displayed on an oscilloscope and
stored in the computer system.
A dedicated software allows the presentation of the
recorded data in terms of time history of the vibrations
and antinode amplitude Ymax or angle of vibration versus frequency. The device is normally placed between 40
and 100 m (130 and 330 ft) from the line and oriented
perpendicularly to the conductors. When the telescope
targets the conductor, the angle of observation to the
horizontal introduces an error in the measurements of
the vertical vibration amplitude that can be easily corrected. Errors are also introduced by air turbulence and
soil vibrations.
This device is not suitable for long-term recordings. It
can be used only when daylight and favourable weather
conditions are present. However, it can be conveniently
employed for short measurements of the antinode vibration amplitude, especially on bundled conductors with
spacers or shield wires with warning devices, where it
allows a comparison between the vibration levels of the
various subspans.
Chapter 2: Aeolian Vibration
The first measurements of this quantity were performed
applying strain gauges as near as possible to the points
of maximum bending (Steidel Jr. 1954; Hard 1958;
Buckner et al. 1968). However, this method, which is
suitable for laboratory tests, presents serious application
problems on the field.
Edwards and Boyd 1963 proposed the use of a vibration
amplitude called “bending amplitude” as a parameter
directly related to the bending strain at the mouth of the
suspension clamp and more accessible to measurements.
This practice had been used successfully by Ontario
Hydro for some 25 years, and the same authors introduced the first live-line recorder to be installed on the
suspension clamp and suitable for these measurements.
Bending amplitude (Y b ) was defined as the total displacement peak-to-peak of the conductor, measured relative to the suspension clamp, at a point 3.5 in. (89 mm)
from the last point of contact between the clamp and
the conductor (Figure 2.7-11a). It was found that a linear correlation existed between bending amplitude and
the strain measured on the surface of the conductor
adjacent to the clamp.
In 1966, the IEEE Task Force on the Standardization of
Conductor Vibration Measurements, recommended the
bending amplitude method (IEEE 1966) as a practical
method of assessing the severity of fatigue exposure of
overhead conductor in all conventional suspension
clamps. A simple but approximate equation was suggested to convert the bending amplitude into bending
strain, and evaluation criteria based on the maximum
allowable bending strain were proposed.
A prototype of a laser-based vibration recorder was
developed by ENEL, Italy, in 1984 (Corti et al. year).
The device consists of ground equipment emitting a
low-power laser beam directed to a “scotchlite” target
installed on the conductor. The laser light reflected by
the target returns to the instrument and is analyzed by a
computer-controlled opto-electronic system. Vibrations
of amplitude from 50 micron to 7 m in the frequency
range 0-150 Hz can be measured and recorded. Thus,
the recorder is suitable for any kind of conductor
motion.
Bending Amplitude
The parameter more closely related to conductor fatigue
is the dynamic bending strain measured at the mouth of
suspension clamps.
Figure 2.7-11 Bending amplitude and inverted
bending amplitude.
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Later, Poffenberger and Swart (1965) formulated the
dynamic deflection field of the conductor in the vicinity
of a fixed clamp and provided relationships to convert
the bending amplitude into dynamic curvature and
bending stress in the outer-layer strands at the mouth of
the suspension clamp. This relationship is considered
valid only for conventional conductors in solid metalto-metal suspension clamps without armor rods. For
other conductor and conductor clamp combinations,
the relationship between bending amplitude and bending stress or strain must be determined through laboratory tests or provided by the clamp manufacturer.
An alternative method, known as the “inverted bending
amplitude” (Figure 2.7-11b) method, was proposed in
1981 (Hardy et al. 1981; Hardy and Brunelle 1991),
together with a relevant measuring device (Figure
2.7-15). According to this method, a lightweight
recorder is fixed onto the conductor, where it senses the
motion directly above the last point of contact between
the conductor and the clamp. The measured inverted
bending amplitude can be converted to either bending
amplitude or bending stress, in order to express the
measurement results in accordance with the IEEE standardization, by means of the Poffenberger and Swart
theory.
The standardization of conductor vibration measurements provided the industry with the possibility of comparing results obtained from different operating
conditions.
In 1979, CIGRE WG 22-04 recommended a method to
determine the lifetime of conductors under the effect of
aeolian vibration (CIGRE SC22 1979). The method
makes use of the bending amplitude measurements, and
based on Miner’s rule, permits the estimation of the lifetime of a conductor subjected to complex bending strain
spectra. However, such estimates are subject to considerable uncertainty, as noted below under “Evaluation
Criteria.”
Bending Amplitude Recorders
The commercial bending amplitude recorders can be
divided into two categories: analog and digital devices.
The analog recorders are the oldest and can be selfcontained (Ontario Hydro) or require ground instrumentation (Hilda and similar). They can provide the time
history of the conductor vibration, which is valuable data
but generally involves time-consuming analysis.
Digital recorders are microprocessor-based, battery–
powered, self-contained devices with a built-in memory
in which the data are stored in digital form. They can be
connected to a computer for the setup of recorder
parameters and functions, before the measurements,
and to read out, display, and print measured data after
the test. Below, the most common bending amplitude
recorders are described.
Although some of these recorders are still in use, only
two models are currently manufactured and supported
by the manufacturers. These are the Vibrec and Pavica
recorders.
Ontario Hydro Recorders
These analog vibration recorders (Figure 2.7-12), developed by Edwards and Boyd (Edwards and Boyd 1963),
are no longer available on the market. However, they
have been widely used all over the world for many years.
The recorder contains an internal clock and is timed to
obtain one-second recordings every 15 minutes. The
recording system uses a tungsten carbide stylus that
marks a trace on a clear 16-mm cellulose film. The trace
is mechanically amplified five times.
The film is moved by a battery-powered mechanism
during the one-second recording at the speed of
6.4 mm/sec. The maximum countable frequency is
150 Hz, and the maximum allowable amplitude is
50 mils (1.27 mm) peak-to-peak.
In 1995, another CIGRE document (CIGRE SC22
WG11 TF2 1995) was published to provide a comprehensive guide to vibration measurements on overhead
conductors performed by means of bending amplitude
recorders.
At the time of publication, IEEE was intending to publish a “Guide for Aeolian Vibration Field Measurements of Overhead Conductors.” The draft edition 22.0
of this standard, dated June 2005, was made available
for the purposes of this work.
2-120
Figure 2.7-12 Ontario Hydro recorder (courtesy U.
Cosmai).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
The instrument autonomy is about three weeks in a temperature range of –20° to +40°C. The recorder must be
taken down to retrieve the data. The weight of the
instrument is 4.5 kg (7.8 kg with standard fittings).
HILDA (High Line Data Acquisition System)
The HILDA analog vibration recorder comprises a sensor/transmitter mounted on a suspension clamp (Figure
2.7-13) and a ground station consisting of a weatherproof cabinet enclosing a high-frequency receiver and
recording devices, such as magnetic recorder, paper
recorder, etc. The receiver collects the radio signals containing the vibration data, which are sent by the transmitter via a coaxially connected antenna installed on the
tower. A wind direction sensor and cup anemometer can
be coupled to the vibration sensor to give simultaneous
readings.
The maximum recordable bending amplitude is
2.54 mm peak-to-peak in a frequency range 1 to 100 Hz.
The autonomy of the transmitter is more than 200 days.
The weight of the line unit, excluding the attachment
clamp, is 0.64 kg. The recorder does not need to be
removed to gather vibration information because it is
telemetered to the ground station.
Extensive data analysis capability is incorporated.
Sistemel Recorders
Designed in Argentina, this analog vibration recorder
has been used for many years but only inside that country. The basic design principles and the performance
characteristics are similar to those of the HILDA
recorder. The wind velocity and direction transducers
and temperature sensor are standard accessories.
Scolar III Recorders
The Scolar III digital vibration recorder (Figure 2.7-14),
made in the United States, uses a rotary encoder as the
Figure 2.7-13 HILDA recorder (courtesy U. Cosmai).
Chapter 2: Aeolian Vibration
vibration sensor. Recorded data can be read with a standard audiocassette, through a plug-in connector built
into the unit and processed by a computer compatible
with the data format. Read-out time is 65 seconds. The
recorder is equipped with a liquid crystal display (eight
digits, 1 in. high), which can be read from the ground by
means of binoculars or a telescope. The display shows
the content of each memory cell in sequence.
The maximum measurable bending amplitude is
2.54 mm peak-to-peak in a frequency range 1 to 100 Hz.
The memory matrix contains 21 amplitude and 10 frequency classes. The autonomy of the recorder is about
three months. The weight of the instrument is 3.1 kg
(6.1 kg with standard fittings).
Pavica Recorders
The digital vibration recorder known as the Pavica
(Figure 2.7-15) is the last version of a series of Canadian
vibration recorders designed to be installed directly on
the conductor for the measurement of the inverted
bending amplitude. Its lightweight construction enables
the recorder to perform measurements at locations
other than suspension clamps (Figure 2.7-20).
A single bolt clamp and a gauge for the correct positioning incorporated into the recorder allow its fast and
easy installation without the need of any further adjustment on the line.
The vibration sensor is a blade equipped with strain
gauges. A built-in serial interface (RS232) allows direct
connection to a personal computer. A utility program,
supplied with the recorder, is used to set up recorder
parameters, and to read out, display, and print measured data. Moreover, it allows additional graphical presentations and conductor lifetime estimation in
Figure 2.7-14 Scolar III vibration recorder installed on an
AGS clamp (courtesy D.G. Havard).
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
accordance with the CIGRE WG 22-04 method for
some conductor-clamp configurations.
the ambient temperature. Previous versions still in operation are Vibrec 100 and Vibrec 300.
The maximum measurable inverted bending amplitude
is 1.3 mm peak-to-peak in a frequency range 1 to
255 Hz (127 Hz in the latest version). The memory
matrix contains 64 amplitude and 64 frequency classes.
Temperature recordings are also available, and a version
with a split vibration sensor is available for measurements on small conductors.
A recorder version with a vibration sensor split from the
main body is available for use on shield wire and small
conductors (Figure 2.7-17).
The autonomy of the recorder at the standard sampling
rate is between one and three months, depending on the
battery type and the environmental temperature. An
automatic start/stop function is included. The recorder
must be taken down to retrieve the data. The weight of
the instrument is about 0.5 kg, and it varies according to
the size of the clamp to be used.
Vibrec 400 Recorders
The digital vibration recorder, Vibrec 400 (Figure
2.7-16), from Switzerland can be used to measure the
vibrations of transmission-line conductors as well as the
wind velocity component perpendicular to the line and
A built-in serial interface (RS232) allows direct connection to a personal computer. A utility program supplied
with the recorder is used to set up recorder parameters,
and to read out, display, and print measured data.
Moreover, it allows additional graphical presentations
and conductor lifetime estimation. Time histories of the
recorded bending amplitude signal are also available. A
tridimensional matrix shows recording of amplitude/frequency data associated with the relevant wind speed.
The maximum measurable bending amplitude is 2 mm
peak-to-peak in a frequency range of 1 to 200 Hz. The
memory matrix can be formed by a maximum of 36
amplitude and 36 frequency classes. An automatic
start/stop function is included. The autonomy of the
recorder is about six months. The recorder must be
taken down to retrieve the data. The weight of the
instrument is 1.7 kg; with the fittings needed to attach to
the suspension clamp, the mass is increased by 0.5-1 kg.
A special version of the Vibrec 400 recorder has been
designed for subspan oscillation measurements.
Figure 2.7-15 Pavica recorder (courtesy U. Cosmai).
Figure 2.7-16 Vibrec 400 recorder (courtesy
Pfisterer Sefag).
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Figure 2.7-17 Vibrec 400 recorder with split
sensor installed on a shield wire (courtesy U.
Cosmai).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
LVR Vibration Recorders
This recorder (Figure 2.7-18), made in Germany, has
basic design principles and performance characteristics
similar to those of the Vibrec 400. The vibration sensor
is an opto-electronic type. No wind and temperature
measurements are provided. A built-in serial interface
(RS232 C) allows direct connection to a personal computer. A utility program, supplied with the recorder, is
used to set up recorder parameters, and to read out, display, and print measured data. The memory matrix contains 16 amplitude and 16 frequency classes. An
automatic start/stop function is included. The recorder
must be taken down to retrieve the data.
Data Sampling and Reduction
It has been common practice, since the early application
of the bending amplitude method, to perform measurements of a few seconds at regular intervals. The first
analog recorders were timed to obtain a 1-second
recording every 15 minutes. The Hilda recorder allowed
a choice of 1- and 3-second recordings every 15 minutes,
while the Scolar III can be set up for 1 to 4 seconds
every 10 minutes. Other digital recorders allow the setting up of different measuring and waiting periods. The
most commonly used interval is that of a 10-second
recording every 15 minutes.
The digital recorders perform on-line data reduction
because of storage limitation in the self-contained memory. The analog signal is sampled and reduced in digital
form. Then the frequency and the amplitude of each
vibration cycle are measured by suitable algorithms and
stored in a memory matrix according to the procedure
suggested by IEEE (IEEE 1966). The matrix contains a
number of frequency and amplitude classes forming
“cells” in which each amplitude/frequency combination
is stored as a single event (Figure 2.7-19). Each cell can
contain a practically unlimited number of events.
Figure 2.7-18 LVR vibration recorder (courtesy RIBE).
Chapter 2: Aeolian Vibration
Data relevant to temperature and wind speed perpendicular to the conductor, where available, are stored in separate arrays.
Recorder Positioning
Bending amplitude recorders are generally installed on
the suspension clamp. The only exception is the Pavica
recorder, which is designed for direct installation on the
conductor. The “lever arm”—i.e., the distance between
the sensor tip position and the last point of contact
between conductor and the suspension clamp is preferably maintained at the standard position of 89 mm
(3.5 in.). This may not be possible, for example, on elastomer-lined clamps with helical rod attachment and on
long suspension clamps for crossing spans.
When rods are used, forming a cage around the clamp,
the sensor is located outside the cage area, and a longer
lever arm (up to 300 mm [12 in.]) must be used, depending on conductor size (see Figure 2.7-14).
Applications of the Pavica recorder along the helical
rods and at their extremities, as well as near vibration
damper and spacer damper clamps (Figure 2.7-20), have
been reported.
In the event that the lever arm is set up at a distance
other than 89 mm, the measured amplitudes can be converted to the corresponding bending amplitude or bending strains values using the Poffenberger and Swart
formula and considering the actual distance of the sensor tip from the suspension clamp.
Correction curves are provided with the Ontario Hydro
and Scolar III recorders for these cases. Other digital
recorders can do this conversion during data elaboration by means of the relevant utility software.
Figure 2.7-19 Example of memory matrix (16 x 18
classes).
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Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
The IEEE guide (Draft 22, 2005) suggests that the effect
of a shift in the lever arm distance may be approximately corrected by multiplying all recorded amplitudes
by (89/xb)2, where xb is the actual lever arm distance. It
should be considered that the distance of 89 mm has
been chosen to get a measurable displacement while
maintaining the sensor tip in a conductor zone whose
shape, during vibration, is mainly governed by the conductor stiffness. Outside this zone, the Poffenberger and
Swart theory cannot be used to correlate the measured
vibration amplitude with the bending stress at the clamp
mouth.
Installation of the Vibration Recorders
The installation of the vibration recorders is a delicate
operation. It must be performed or witnessed by an
engineer with suitable experience in this field. Generally,
these engineers do not directly install the recorder,
unless the conductor under test can be reached with a
suitable bucket truck. In most of the cases, the engineer
instructs linemen to do it. Quite often linemen do not
speak English, and the training becomes difficult. The
best solution is to arrange a conductor/clamp assembly
for installation training at ground level. Each linesman
should be invited to install the recorder on the assembly,
during which the correct sequence of operations can be
carefully explained. In the installation manual, the technique is generally shown by photographs rather than
described by text.
Generally, the installation and removal of the live-line
recorder are done during an outage of few hours. In
some cases, the installation has been made on energized
lines using hot sticks or the bare-hand technique (Figure 2.7-21).
Figure 2.7-20 Pavica recorder installed near a
spacer-damper clamp (courtesy U. Cosmai).
2-124
When available, the use of the automatic start/stop function is advantageous, since it prevents the recording of
the conductor movements during the linemen’s operations and does not require the manual switching of the
recorder after the installation and before the removal.
Measurements at Clamps Other than Conventional
Suspension Clamps
The bending amplitude method has been established for
conventional metal-to-metal clamps. It has proved to be
reliable for clamps with mouth radii ranging from 0.4
mm to 152 mm (0.015 to 6 in.) (IEEE 1966). However,
this method has also been applied to measurements for
other suspension clamp types, as well as for tension
clamps and some fitting clamps.
Elastomer-lined suspension clamps, either bolted or
with helical rod attachments, do not behave like metallic
clamps, and for them, the relationship between bending
amplitude and bending strains should be determined by
laboratory vibration tests. The clamp manufacturers
should provide recommendations regarding the optimum positioning of the vibration sensor and for the
interpretation of the measurements.
The CIGRE guide (CIGRE SC22 WG11 TF2 1995) and
one manufacturer (Poffenberger et al. 1971) suggest, for
practical reasons, that the Poffenberger and Swart formula also be used for clamps incorporating elastomeric
inserts by considering the centerline of the suspension as
the last point of contact between the conductor and the
clamp.
Dangerous dynamic bending strains can occur, also, at
tension clamps and at the clamps of other fittings such
as dampers, spacers, warning spheres, and so on. For
these locations, measurements performed at the suspension clamps cannot provide reliable information. Mea-
Figure 2.7-21 Installation of a vibration recorder
on an energized line using the bare-hand
technique (courtesy LITSA, Argentina).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
surements of dynamic bending amplitudes, at these
clamps, are not as simple as the suspension clamp measurements, because they require light recorders or a different measurement approach. Moreover, the fatigue
endurance limits of the specific conductor/clamp combination as well as the relationship between bending
amplitude and bending stress or strain, if required, have
to be determined by laboratory tests.
Measurement Inaccuracies
In bending amplitude measurements, there are several
possible sources of measurement inaccuracies that
should be duly considered and, if possible, reduced to a
tolerable value.
Measurement errors can arise from the instrument performance—e.g., calibration inaccuracy, linearity deviation, electrical noise including corona, magnetic field
interference, temperature effect on electronic components, and so on. The recorder manufacturer should
provide evidence of the good performance of each unit,
together with the individual calibration certificate, and
be available for maintenance and periodic recalibration
services.
Errors can arise from the recorder attachments to the
suspension clamps. These mountings are specially
designed for each type and size of clamp, and should be
as light as possible but also rigid. Cases of resonance of
the recorder mountings at frequencies within the measurement range have been reported (Cigada and
Manenti 1995). It is advisable to perform a laboratory
vibration test on any type of recorder mounting assembly prior to the installation at the site.
Chapter 2: Aeolian Vibration
mass depends on the vibration frequency and is less at
low frequency. The phenomenon seems to be more pronounced with small conductors and large additional
inertia. For these reasons, the recorders should be as
light and compact as possible.
The recordings obtained by the bending amplitude
recorders should be analyzed in the context of the operating characteristics of the equipment and the variety of
conductor motions that occur during the tests. The
memory matrices of the digital bending amplitude
recorders quite often show entries at frequencies well
below the minimum aeolian vibration frequency calculated using the Strouhal formula.
The data stored under the lower frequency intervals (0.2
to 3 Hz) may show high amplitudes but for a limited
number of cycles. These entries are generally due to
transient oscillations of the cable that can occur under
the effect of high-speed wind gusts. In these cases, the
cable is subjected to variable drag forces inducing transversal oscillations, whose vertical component is detected
by the vibration sensor of the recorder. Moreover, the
effect of the transverse oscillations increases when the
axis of the displacement transducer deviates from its
vertical position (Figure 2.7-22).
Other causes include movements caused by the linemen
when the recorder is switched on manually, after the
installation on the line and switched off manually, before
the removal. Also, the presence of amplitude filters built
into the data reduction algorithm to avoid a great num-
Severe imprecision can be caused by the incorrect positioning of the recorder. The distance of the vibration
sensor from the clamp must be measured accurately.
Errors in evaluating this parameter translate into errors
in the resulting bending amplitude. Some recorders are
provided with gauges for the correct positioning of the
sensor.
Distortion of bending amplitude measurements can be
caused by loss of mechanical contact between the sensor
tip and the conductor or from an excessive reduction of
the measurement range due to an incorrect adjustment
of the sensor rest position.
The mass and moment of inertia of the recorder and relevant mountings may influence the bending amplitude
measurements. This effect has been theoretically analyzed, as well as tested in the laboratory and field
(Krispin 1992 and 1993; Heics and Havard 1993; Sunkle
et al. 1995). The influence of the recorder and mounting
Figure 2.7-22 Effect of transverse oscillations
on a recorder not vertically positioned
2-125
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
ber of entries because of signal noises can have an effect.
In this case, vibrations with amplitude below a specific
value are ignored, but this may cause entries with higher
amplitude and lower frequency with respect to the actual
vibration parameters as explained below.
The measured vibrations are classified using the socalled “peak-valley” algorithm (Figure 2.7-23).
When point “A” is passed, a change of the slope of the
signal is detected. This causes the time and amplitude of
point “A” to be temporarily stored. When point “B” is
passed, a change of the slope is detected again. Now the
amplitude value “a” is calculated from the difference of
the amplitude of point “B” and the amplitude stored for
point “A”. The same way, the period of the half-cycle
“T/2” is calculated as the difference of the time between
point “B” and point “A”. The reciprocal value of the
time “T” leads to the frequency of the equivalent fullcycle. In the presence of the amplitude filter, the situation described in Figure 2.7-24 may happen.
The algorithm recognizes peak A, ignores all the peaks
with an amplitude below the filter value—i.e., B, C, D,
E, F, G—and measures the peak H. The frequency measurement is calculated considering the time interval
between peak A and peak H. This leads to a frequency
value lower than the actual one and to an amplitude
value corresponding to the difference between the level
A and the level H, which is bigger than the actual amplitudes A-B and G-H.
Such low frequency entries have generally no influence
on the calculation of conductor lifetime for their limited
number of cycles. On the contrary, they are not considered, if they exceed the maximum allowable bending
amplitude, when this criterion is used for the evaluation
of vibration severity. This misconstruction of the peakvalley algorithm does not affect the reliability of the
measurements, since the most significant bending
amplitudes for the assessment of vibration severity are
measured correctly.
Test Locations
Vibration measurements are generally performed on a
few spans of a transmission line. When, in some locations of the line, there is evidence of conductor strand or
fitting failures or doubt of possible damages, the measurements are taken on these points.
As a final acceptance test of the conductor damping system, the vibration recording is generally performed on
one or two spans of the line, in which the greatest exposure to the vibration-inducing wind can be anticipated.
Those are generally the longest suspension spans, with
the highest supports, which are stretched in flat desert
areas or in open and plain lands, particularly near water,
with low and sparse obstacles (trees, buildings, etc.), in
areas where the predominant wind direction is perpendicular to the conductors, and where a wide range of
wind speeds is likely to occur. Very long spans crossing
rivers, channels, and valleys, designed with structural
characteristics and parameters different in respect to the
rest of the line, are tested separately.
Test Period
The test period is chosen in accordance with the purpose of the measurements.
If the purpose of the test is to measure the maximum
bending amplitude, the IEEE standardization (IEEE
1966) suggests a minimum period of two weeks.
Figure 2.7-23 “Peak-valley” algorithm.
Figure 2.7-24 Effect of amplitude filter.
2-126
For final acceptance testing of the conductor damping
system at the end of the line construction, most of the
utilities’ specifications require a minimum period of one
month. For comparative analysis of different damping
systems, the test period is not important, providing the
units under examination are tested simultaneously. To
obtain results that are statistically meaningful, a minimum period of three months is deemed necessary
(CIGRE SC22 WG11 TF2 1995).
In areas where seasonal conditions change significantly—e.g., different wind characteristics, different
ambient temperature ranges, changes in ground roughness due to cultivation and snow—measurements
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
should include these differing conditions. Alternatively,
the test period should be established taking into account
the yearly distribution of wind and ambient temperature
in order to experience the most severe meteorological
conditions during the tests
In any case, the vibration measurements should be associated with wind velocity measurements to verify that,
during the test period, the whole range of wind velocities able to excite significant aeolian vibrations was
present. If not, the test should be repeated.
Interpretation of Recorded Data
The bending amplitude measurement is, without doubt,
the easiest way to investigate the causes of damage
already found or to resolve doubts determined by “early
warnings.” However, the following must be considered
regarding the reliability of these measurements in determining the risk of future fatigue damage.
The inherent concept of these measurements is to take,
for a few weeks, on one or a few spans, samples of the
conductor vibrations. In general, the measurements are
performed for about 10 seconds every 15 minutes for a
period of one month. This means that information is collected for about 1% of the time elapsed in a month, which
covers about the 0.002% of the transmission-line life.
Such information is supposed to establish whether or
not the conductors in the spans under test will face
fatigue risks during their expected service lives (30 to 50
years), and if the conclusion drawn for those conductors
and spans can be extended to all the other spans of the
line. It must be pointed out that to achieve reliable conclusions, it is necessary that the vibration samples taken
do, at least, really represent the predominant conditions
that will exist on that line during its service life. Therefore, the correct choice of the test locations and the definition of the test period and duration are of primary
importance.
Evaluation Criteria
The following criteria are commonly used to assess the
vibration severity on transmission-line conductors:
• IEEE maximum allowable bending strain
• EPRI endurance limits
• CIGRE WG 22-04 method
The IEEE Task Force on the Standardization of Conductor Vibration Measurements suggested, together
with the bending amplitude method, a general evaluation criterion based on a maximum allowable bending
strain. More precisely, (IEEE 1966) states that: “The
maximum bending strain that can be tolerated in ACSR
Chapter 2: Aeolian Vibration
conductors without eventually inducing fatigue damage
cannot yet be stated precisely. . . . It is speculated that the
value of 150 μ inch/inch (microstrains) peak to peak,
which is given here only as a guide, is somewhat conservative and the strains of the order of 200 μinch/inch (peak to
peak) may well prove to be safe.”
With accumulating experience, this criterion proved to
be rather conservative. However, many utilities, in many
different countries, still require this procedure for the
assessment of vibration severity as an acceptance test of
the damping systems for new lines.
Since the previous edition of this book (EPRI 1979) has
provided the values of the bending amplitude or bending stress that can be endured indefinitely for various
types of conductor. (See Chapter 3 of this edition.)
These values, defined as “endurance limits,” are valid
for combinations of conductors and rigid metallic
clamps, without reinforcing rods and with smooth internal profile. The list of conductors includes mainly
ACSR conductors, but also some AAAC, steel, and
copper conductors are considered.
EPRI also suggests that a general endurance limit for
multilayer ACSR conductor at the bending amplitude
value of 9 mils (0.23 mm) could probably be used, as
well as a bending stress value of 8.5 MPa. These limits
can be applied to homogeneous aluminum conductors
of 1350 and 5005 alloy also, while for 6201 and similar
alloys, a lower limit of 5.7 MPa is suggested.
Endurance limits for other conductors and for clamps
other than metallic suspension clamps are not available
in the literature. Bending amplitude measurements on
combinations of these conductor and clamps can be
evaluated only when the actual endurance limits have
been defined by means of laboratory tests.
The evaluation of the conductor fatigue danger based
on the evidence that the maximum recorded bending
amplitudes, or bending stress/strain, do not exceed the
above-mentioned safety limits may be considered excessively cautious. In fact, these limits can be exceeded up
to a certain level and for a limited number of times with
no effect on the conductor integrity. For these reasons,
the strict interpretation of the endurance limit criterion
is relaxed to reduce the severity of the method. For
example, the following empirical limits are proposed in
the IEEE guide (draft 22.0, June 2005) as widely used
criteria:
• The measured bending amplitude may exceed the
endurance limit for no more than 5% of the total
cycles.
2-127
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
• No more that 1% of the cycles may exceed 1.5 times
the endurance limit.
• No cycles may exceed 2 times the endurance limit.
The CIGRE method (CIGRE SC22 WG04 1979) for the
evaluation of the lifetime of aluminum-based conductors considered the cumulative effect of all the recorded
vibration cycles. For this, the bending amplitude data,
stored in the recorder memory matrix, are converted
into bending stresses and then extrapolated to one year.
Finally, the data are presented as an “accumulated stress
curve,” showing, for each stress level”σi”, the number of
cycles “n i” to be expected in one year. Using Miner’s
theory about cumulative damage on structure subjected
to alternating stresses, this stress curve is compared with
a “universal” fatigue curve worked out by CIGRE WG
22-04 on the basis of the data collected from a large
number of laboratory fatigue tests on conductors (Figure. 2.7-25). This fatigue curve, known as “safe border
line,” is an S-N curve showing, for each stress level”σi”,
the maximum number of cycles “N i ” that can be
endured by the conductor without strand failures. The
partial damage at each stress level “σi ” is determined
from the ratio n/N. Supposing that the damage accumulation is linear and not influenced by the order in which
the different stresses occur, the conductor damage D in
one year would be
tests leading to the “safe border line” was based on
stresses determined from bending amplitude (CIGRE
1979c)—that is, on the basis of the Poffenberger-Swart
relationship. Thus, uncertainty surrounds the use of the
“border line” in estimating expected lifetimes of field
spans. (See also Chapter 3, Appendix 3.2.) The actual
S-N curve of the conductor clamp system under examination obtained by laboratory tests can be used in lieu
of the CIGRE safe border line.
Survey on the Evaluation Criteria
A survey on the evaluation criteria adopted by the
industry for the assessment of vibration severity on
transmission-line conductors has been performed by
reviewing 80 technical specifications issued by the main
utilities worldwide in the past 20 years (Figure 2.7-26).
The survey shows that for the evaluation of the vibration severity (Figure 2.7-27):
i
ni
1 Ni
D = ∑
and the lifetime L, in years, of the conductor will be
L=
1
n
∑1 Ni
i
i
=
1
n
n1 n2 n3
+
+
+ ..... n
N1 N 2 N 3
NN
Figure 2.7-26 Review of technical specifications
(courtesy U. Cosmai).
One of the difficulties in applying data from bending
amplitude recorders in this process is that none of the
Figure 2.7-25 Example of accumulated stress curve
and S-N curve.
2-128
Figure 2.7-27 Assessment of vibration severity
(courtesy U. Cosmai).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
• 58% of the specifications adopt the bending strain as
endurance limits.
• 16% adopt the bending amplitude endurance limits
proposed by EPRI.
• 6% adopt the CIGRE method for the evaluation of
the lifetime.
• 20% do not specify any criterion.
Among the utilities adopting the bending strain endurance limits (Figure 2.7-28):
Chapter 2: Aeolian Vibration
No utility’s specification requires laboratory tests, which
are very expensive and time consuming, to determine
the actual endurance limits when they are not available.
It is evident that many utilities are not aware of either
the development or inherent limitations in the assessment of conductor vibration severity.
CIGRE SC22 B2 WG11 and IEEE WG on Conductor
Dynamics are committed to provide the industry with
detailed and comprehensive guides on the subject.
27% prescribe 150 microstrain peak to peak.
18% prescribe 200 microstrain peak to peak.
4% prescribe 247 microstrain peak to peak (corresponding to 8.5 MPa).
51% prescribe 300 microstrain peak to peak.
It was evident during the survey that, in the industry,
evaluation criteria of vibration severity are frequently
prescribed with no consideration of whether the relevant
reference limits available in the literature are applicable
or not to a specific conductor-clamp combination. For
example, endurance limits for aluminum-based conductors in metallic clamps have been adopted for steel
shield wires or OPGW or for measurements taken at the
spacer clamps.
Figure 2.7-28 Maximum bending stress for aluminumbased conductors (courtesy U. Cosmai).
2-129
Chapter 2: Aeolian Vibration
2.8
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
HIGHLIGHTS
Causes and Effects of Aeolian Vibration
• When a conductor is not fitted with a suitable damping system, the aeolian vibration level can cause
fatigue damage in the conductor at the suspension
clamp or at the clamps of the damping devices or
other accessories attached to the conductor.
• In overhead conductors, fatigue failure of strands is
the most common form of damage resulting from
aeolian vibration: examples of conductor damage at
suspension clamps and spacer-damper clamps are
provided in Sections 2.1 and 2.7.
• The cause of aeolian vibration is the alternating
forces from vortices shed in the wake of the conductor during steady transverse winds. The vibration
occurs when the frequency of the alternating forces is
close to one of the conductor natural frequencies.
The vortex-shedding frequency f (Hz) is given by the
Strouhal formula: f = 0.18 V/D, where V is the wind
velocity (m/s) and D is the conductor diameter (m).
The conductor natural frequencies fn (Hz) are given
by:
fn =
n T
where n = 1, 2, 3 …, L is the
2 L mL
span length (m), T is the conductor tensile load (N),
and mL is the conductor mass per unit length.
Design Factors Affecting Aeolian Vibration
• The parameter indicating the sensitivity of an
undamped conductor to aeolian vibrations is the T/w
(m) parameter; the ratio between the conductor tensile load (N) and the conductor unit weight (N/m).
When T/w exceeds 1000 m, suitable damping devices
are required in order to safely control the aeolian
vibration level and avoid fatigue damage of the conductor. Therefore, conductors at greatest risk of
fatigue are those tensioned to relative high levels.
Long spans, such as crossings, due to different causes
(high tensile load, low level of wind turbulence), are
also generally in a critical condition with respect to
aeolian vibrations.
• The wind turbulence plays an important role in the
aeolian vibration phenomenon: flat terrains are characterized by a low turbulence, while turbulence
increases with the terrain roughness. Transmission
lines crossing a flat terrain, due to the low turbulence,
will be more sensitive to aeolian vibrations than
transmission lines crossing a terrain characterized by
high vegetation: due to high turbulence, they will be
generally subjected to a low level of vibration.
• In the recent years, CIGRE has produced different
guidelines for safe tension levels to be assumed for
2-130
conventional conductors in single undamped, single
damped, or twin, triple, and quad bundle configurations, according to terrain class. These guidelines are
described in Section 2.6.
Conductor Construction
• Different conductor constructions and materials are
used for overhead transmission lines. Their main
characteristics are summarized in Section 2.3.
Smaller diameter conductors and ground-wires are
generally more sensitive to aeolian vibrations than
others.
Single Conductor versus Bundle Conductors
• Spacered bundle conductors, except for twin bundles,
undergo lower levels of aeolian vibration than the
same-size single conductors. When spacer-dampers
are installed, they can contribute to control of the
aeolian vibration level.
Dampers
• Dampers can be added to most conductors to keep
vibration levels within safe levels, and thereby avoiding
fatigue problems in the conductors. The dampers have
to be suitably selected, in relation to the actual application, and correctly positioned on the conductor.
• If the damper is not suitable for the application, the
conductor may be under-damped and fatigue failures
of the conductor and damper will be possible.
• Stockbridge-type dampers are the most commonly
employed dampers and those for which the main testing procedures have been developed. Techniques for
measuring Stockbridge-type damper damping on a
shaker and on an indoor test span have been developed and are presented in Sections 2.4 and 2.7. These
techniques allow assessment of the damper dynamic
performance and evaluation of its suitability for a
certain application.
• Sample Stockbridge-type damper energy absorption
characteristics are provided in Sections 2.4 and 2.5.
• Alternative types of dampers—including impact
types and Bretelle and festoon dampers—are
described in Section 2.4, together with typical applications for these types of dampers.
• In Sections 2.4, 2.5, and 2.7 criteria are presented for
choosing a damper for a certain application, together
with tests and analytical simulations to verify the
behavior of the cable plus damper system with respect
to aeolian vibrations.
Energy Balance Principle
• The Energy Balance Principle (EBP) has been used to
give an estimate of an upper bound to the expected
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
vibratory motions in single conductors and bundles.
This principle is briefly introduced in Sections 2.1
and 2.2 and described in detail in Section 2.5.
According to the EBP, the steady-state amplitude of
vibration of the conductor or bundle due to aeolian
vibration is that for which the energy dissipated by
the conductor and other devices used for its support
and protection equals the energy input from the
wind.
Wind Energy Input
Chapter 2: Aeolian Vibration
several researchers: the agreement among the different curves is fair.
Conductor Self-Damping
• Procedures for determining conductor self-damping
in an indoor test span are described in Section 2.3,
together with the empirical relations used to approximate the measured self-damping curves.
• Sample self-damping data for several conductor sizes
are provided in Section 2.3 and Appendix 2.3.
• Wind energy input to conductors has been determined from several sets of wind tunnel measurements. The maximum energy input curve is
determined by the envelope of all the curves obtained
when the test parameters are varied, as shown in the
Figure 2.2-14. Figure 2.2-15 shows the experimental
data of the maximum power coefficient measured by
Conductor Vibration Measurement
• Methods of measurement of amplitude of vibration
on operating lines are reviewed in Section 2.7
• Procedures for interpreting vibration recorder data
are presented in Section.2.7, together with a review of
the available vibration recorders and their main features.
2-131
Chapter 2: Aeolian Vibration
APPENDIX 2.1
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
NUMERICAL VALUES OF FIGURE 2.2-15
Table A2.1-1 Numerical Values of Figure 2.2-15
[W-m^{-1}/m^{4}Hz^3]')
BATE
(1930)
A/D
BRIKA &
LANEVILLE
(1995)
CARROL
(1936)
DIANA &
FALCO
(1971)
FARQUHARSON &
MC HUGH (1956)
PON et al.
(1989)
0.02
0.04
RAWLINS
(1958)
RAWLINS
(1983)
0.01
0.03
0.03
0.17
0.11
0.23
0.11
0.20
0.18
0.18
0.49
0.40
0.70
0.40
0.60
0.50
0.60
0.85
1.80
0.84
0.06
0.65
0.10
1.60
1.10
0.20
3.90
3.20
1.50
1.20
1.60
5.00
3.00
3.20
4.00
4.50
0.30
5.50
9.00
0.40
6.00
14.00
9.00
6.50
0.50
18.00
10.10
0.60
20.00
10.70
0.70
21.00
10.80
0.80
20.00
Table A2.1-2 Polinomial Approximation of Curves in Figure 2.2-15
Pinput max (W-m-1/m4-Hz3) = B1x(A/d)+ B2x(A/d)2+ B3x(A/d)3+ B4x(A/d)4+ B5x(A/d)5+ B6x(A/d)6+ B7x(A/d)7+ B8x(A/d)8
Coefficient
Farquharson
and McHugh
(1956)
Brika and
Laneville
(1995)
Carroll (1936)
Rawlins (1958)
Bate (1930)
Diana and
Falco (1971)
B1
B2
B3
B4
B5
B6
B7
B8
1,57307
6,51807E-4
114,04078
171,04611
-804,62761
-1746,41902
4979,35418
14889,22968
-87265,23358 -22730,02552
330860,20086 68022,20996
-720484,66135 -117502,97968
678441,92498 88282,53536
0,23555
184,80587
-1166,87118
6226,3429
-25617,4015
71498,14106
-117476,06111
84876,93378
5,51021
144,83611
-879,82668
5524,75028
-29042,90344
97156,06605
-180845,34278
143111,15515
3,12858
208,972
-1048,68829
3894,56424
-8396,67235
9919,9573
-6137,30905
1573,9704
2,26894
88,81312
1,79838
134,82029
-1605,93248
118,93429
312,71115
16034,61109
-432,36754
2188,63016 -80429,61866 -8038,40839
31926,38
-11857,16738 220728,70434
39612,62833 -336499,34504 -40289,96769
79,97553
68607,57765 267919,86997
-40,25253
-87077,79986
45073,019
range
0,01≤A/d≤0,17 0,027≤A/d≤0,26
0,026≤A/d≤0,26
0,04≤A/d≤0,26
0,01≤A/d≤0,85
0,01≤A/d≤0,4
2-132
Rawlins
(1983)
0,025≤A/d≤0,7
Pon et al.
(1989)
0,01≤A/d≤0,3
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
APPENDIX 2.2
CALCULATION OF THE BENDING STIFFNESS FOR A 795 KCMIL DRAKE ACSR
CONDUCTOR
EImin -English units
Es = 3 x 107, ns = 7
Ea = 1 x 107, na = 26
ds = 0.136, ds = 0.1749
EI min = 7 x 3 x107
π 0.1364
64
π 0.17494
+26 x107
64
EImax -English units
Steel
n
EImin -SI units
Es = 2.068 x 1011 Nm2
Ea = 6.895 x 1010 Nm2
6
10
16
in.
0.1360
0.1360
0.1749
0.1749
R
in.
0
0.1360
0.29145
0.46635
E
lb/in.2 x
107
3
3
1
1
I
in.4 x 10-3
0.0168
0.907
10.66
42. 54
EI
lb.in.2 x
103
0.503
27.2
106.6
425.4
d
Elmax. = 559,700 ibin.2
EImax -SI Units
Steel
n
Aluminum
1
6
10
16
d
m x 10-3
3.45
3.45
4.44
4.44
R
m x 10-3
0
3.45
7.395
11.835
20.68
20.68
6.895
6.895
6.95 x 10- 3.76 x 10- 4.4243 x
12
10
10-9
1.7655 x
10-8
d s = 3.45 x 10-3 m
E
d a = 4.44 x 10-3 m
I
m4
EI
Nm2
7 x 2.068 x 1011π x (3.45 x 10−3 ) 4
64
26 x 6.895 x 1011π x (4.44 x 10−3 ) 4
+
64
= 44.3Nm 2
Aluminum
1
EImin = 15,469 lb•in.2
1 lb•in.2 = 2.87 x 10-3 Nm2
15,469 lb•in.2 = 44.4 Nm2
EI min =
Chapter 2: Aeolian Vibration
n/m2 x
1010
1.438
77.88
305.1
1217.3
Elmax. = 1602 Nm2
2-133
Chapter 2: Aeolian Vibration
APPENDIX 2.3
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
CONDUCTOR SELF-DAMPING
DATA
Data on the measured self-damping of several conductors and OPGWs were collected by the task force. These
data are presented in Tables A2.3-2 through A2.3-21. In
all cases, the measurements were in general conformity
with IEEE Standard 563-1978. However, the full range
of amplitude, frequency, and tension recommended by
the standard were not covered in most of the data sets,
apparently due to the difficulty of the measurements.
Both test procedures recommended by the IEEE standard—the Power Method (PT) and the Inverse Standing
Wave Ratio Method (ISWR)—are represented in the
data sets, some sets employing one and some the other.
The standard points out that dissipation at the test span
terminations contributes an error when the power
method is used. However, this error can be minimized
by the use of flexible pivots, which are illustrated in Figure 4 of the standard. Several of the data sets are from
tests where this was done, and that is noted in the head-
ings for those sets by the comment “End-point damping
minimised.”
Several data sets are from tests that used the ISWR
method. The organizations that contributed these sets
applied a correction to the data, a correction not
described in the IEEE Standard. The correction subtracts from the measured dissipation that part of it that
is due aerodynamic damping—i.e., fanning of the still
air of the laboratory by the vibrating test conductor.
The use of this correction is noted in the headings for
the data sets in question by the comment “Aerodynamic
damping removed.”
Table A2.3-1 lists the conductors and tensions covered
by the collection of data sets. Details of the construction
of the non-standard conductors are given in the headings of the data sets.
Figures A2.3-1 to A2.3-3 show examples of plots of the
data sets.
Table A2.3-1 Data Sets
2-134
Table
Conductor
Condition
Tension
(% UTS)
Figure
A2.3-2
7.3 mm Fiber Optic Ground Wire
new
9
A2.3-1
A2.3-3
13.8 mm Fiber Optic Ground Wire
new
15
A2.3-4
17.9 mm Fiber Optic Ground Wire
new
16
A2.3-5
400 sq mm Aldrey (61x 2.9 mm)
new
23
A2.3-6
400 sq mm Aldrey (61x 2.9 mm)
new
27
A2.3-7
400 sq mm Aldrey (61x 2.9 mm)
old
23
A2.3-8
400 sq mm Aldrey (61x 2.9 mm)
old
27
A2.3-9
240/40 sq mm ACSR (26/7)
new, greased core
10
A2.3-10
240/40 sq mm ACSR (26/7)
new, greased core
20
A2.3-11
240/40 sq mm ACSR (26/7)
new, greased core
30
A2.3-12
240/40 sq mm ACSR (26/7)
old, greased core
10
A2.3-13
240/40 sq mm ACSR (26/7)
old, greased core
20
A2.3-14
240/40 sq mm ACSR (26/7)
old, greased core
30
A2.3-15
1840 kcmil ACSR (72/7)
new
20
A2.3-16
3/0 ACSR (6/1) “Pigeon”
new
20
A2.3-17
35.6 mm ACSR (48/7) “Bersfort”
new
15
A2.3-18
35.6 mm ACSR (48/7) “Bersfort”
new
20
A2.3-19
35.6 mm ACSR (48/7) “Bersfort”
new
25
A2.3-20
35.6 mm ACSR (48/7) “Bersfort”
new
30
A2.3-21
1033.5 kcmil ACSR (54/7) “Curlew”
new
22
A2.3-2
A2.3-3
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Table A2.3-2 7.3 mm Fiber Optic Ground Wire
Chapter 2: Aeolian Vibration
Table A2.3-3 13.8 mm Fiber Optic Ground Wire
7.3 mm Fiber Optic Ground Wire
13.8 mm Fiber Optic Ground Wire
23 x 1.3 mm Galvanized Steel
15 x 2.34 mm Alumoweld
1 x 2.1 mm Stainless Steel Tube
Extruded aluminium Tube:
Outside diameter 9.14 mm
Dia = 7.3 mmNew
Inside diameter 5.90 mm
Mass = 0.222 kg/m
UTS = 41023 N
Dia = 13.82 mm New
Test Tension = 3825 N (9% UTS)
Mass = 0.57 kg/m
Test Method: Power. Test Span: 92 m
UTS = 76500 N
Source: ENEL
Test Tension = 11474 N (15% UTS)
Frequency (Hz)
Ymax/D (pk-pk)
Pc (mW/m)
74.90
0.205
19.80
40.54
74.90
0.356
35.41
0.685
12.10
35.45
1.027
32.23
Figure A2.3-1 7.3 mm fiber optic ground wire.
Test Method: Power. Test Span: 92 m
Source: ENEL
Frequency
(Hz)
20.82
24.10
24.10
24.10
31.04
31.04
34.28
34.28
34.28
38.87
38.87
38.87
38.87
45.48
45.48
45.48
51.30
51.30
51.30
51.30
55.32
55.32
55.32
62.43
62.43
62.43
62.43
62.43
Ymax/D
pk-pk
1.035
0.144
0.406
0.759
0.546
0.607
0.333
0.720
0.827
0.197
0.197
0.215
0.217
0.228
0.409
0.535
0.067
0.198
0.253
0.287
0.114
0.174
0.365
0.030
0.124
0.194
0.224
0.260
Pc
mW/m
16.70
0.96
5.77
22.25
25.00
31.02
19.46
94.37
141.78
10.49
11.53
15.32
12.94
20.62
99.16
182.84
2.04
19.29
45.03
68.30
7.19
17.97
126.33
1.95
20.67
57.96
90.04
132.48
2-135
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Table A2.3-4 17.9 mm Fiber Optic Ground Wire
Table A2.3-5 400 sq mm Aldrey (61 x 2.9 mm), New
Condition, 23% UTS
17.9 mm Fiber Optic Ground Wire
23 x 2 mm Aldrey
400 sq mm Aldrey (61 x 2.9 mm)
18 x 2 mm Alumoweld
Dia = 26 mmNew
Extruded aluminium Tube:
Mass = 1.111 kg/m
Outside diameter 9.9 mm
UTS = 118500 N
Inside diameter 5.7 mm
Test Tension = 26800 N (23% UTS)
Test Method: Power. Test Span: 28 m
Source: RIBE
Dia = 17.9 mmNew
Mass = 0.755 kg/m
Frequency
(Hz)
UTS = 91060 N
Test Tension = 14710 N (16% UTS)
Test Method: Power. Test Span: 92 m
Source: ENEL
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
10.00
0.279
0.52
10.00
0.559
2.10
2-136
Ymax/D
pk-pk
Pc
mW/m
13.2
0.185
0.108
13.2
0.371
0.59
20.7
0.118
0.368
1.997
20.7
0.237
31.85
0.077
1.18
31.85
0.154
6.419
44.7
0.055
2.968
44.7
0.110
16.08
15.84
0.615
13.64
15.84
0.838
28.20
19.31
0.279
4.63
19.31
0.447
14.30
400 sq mm Aldrey (61 x 2.9 mm)
26.67
0.196
10.57
26.67
0.419
52.18
Dia = 26 mmNew
26.67
0.642
107.74
Mass = 1.111 kg/m
Table A2.3-6 400 sq mm Aldrey (61 x 2.9 mm), New
Condition, 27% UTS
31.27
0.419
83.86
UTS = 118500 N
31.27
0.503
98.79
Test Tension = 31900 N (27% UTS)
31.27
0.726
229.80
41.81
0.168
41.05
Test Method: Power. Test Span: 28 m
48.90
0.101
43.16
End –point damping minimized
48.90
0.140
62.25
Source: RIBE
Frequency
([Hz)
Ymax/D
pk-pk
Pc
mW/m
14.37
0-170
0.11
14.37
0.341
0.611
22.55
0.109
0.382
22.55
0.217
2.07
30.67
0.080
0.88
30.67
0.160
4.77
44.6
0.055
2.428
45
0.109
13.15
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Table A2.3-7 400 sq mm Aldrey (61 x 2.9 mm), Old
Condition, 23% UTS
Chapter 2: Aeolian Vibration
Table A2.3-9 240/40 sq mm ACSR (26/7), New Condition,
Greased Core, 10% UTS
400 sq mm Aldrey (61 x 2.9 mm)
240/40 sq mm ACSR (26/7)
Dia = 26 mmOld
Dia = 21.9 mmNew
Mass = 1.111 kg/m
Mass = 0.987 kg/m Greased
UTS = 118500 N
UTS = 86400 N
Test Tension = 26800 N (23% UTS)
Test Tension = 8640 N (10% UTS)
Test Method: Power. Test Span: 28 m
Test Method: Power. Test Span: 28 m
End–point damping minimized
End –point damping minimized
Source: RIBE
Source: RIBE
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
13.2
0.185
0.116
10.3
0.191
0.067
13.2
0.371
0.564
10.4
0.381
0.503
20.7
0.118
0.389
10.3
0.768
2.35
20.7
0.237
1.888
13.3
0.148
0.159
31.85
0.077
1.237
13.4
0.395
1.01
31.85
0.154
6
13.3
0.595
7.64
44.7
0.055
3.075
19.3
0.102
0.52
44.7
0.110
14.92
19.2
0.206
2.99
19.3
0.410
14.7
Table A2.3-8 400 sq mm Aldrey (61 x 2.9 mm), Old
Condition, 27% UTS
22.3
0.088
0.939
22.3
0.177
4.71
22.3
0.355
25
400 sq mm Aldrey (61 x 2.9 mm)
25.5
0.077
1.53
Dia = 26 mmOld
25.3
0.156
6.77
Mass = 1.111 kg/m
25.4
0.312
40
28.6
0.069
2.24
UTS = 118500 N
28.5
0.139
9.77
Test Tension = 31900 N (27% UTS)
28.5
0.278
65.3
Test Method: Power. Test Span: 28 m
31.9
0.062
3.16
End –point damping minimized
31.7
0.125
12.6
31.7
0.250
98.4
35.2
0.056
3.73
34.8
0.114
17.5
34.8
0.227
124
Source: RIBE
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
14.37
0-170
0.122
14.37
0.341
0.59
22.55
0.109
0.409
22.55
0.217
1.98
30.67
0.080
0.935
30.67
0.160
4.54
44.6
0.055
2.556
45
0.109
12.41
2-137
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Table A2.3-10 240/40 sq mm ACSR (26/7), New
Condition, Greased Core, 20% UTS
Table A2.3-11 240/40 sq mm ACSR (26/7), New
Condition, Greased Core, 30% UTS
240/40 sq mm ACSR (26/7)
240/40 sq mm ACSR (26/7)
Dia = 21.9 mmNew
Dia = 21.9 mmNew
Mass = 0.987 kg/m Greased
Mass = 0.987 kg/m Greased
UTS = 86400 N
UTS = 86400 N
Test Tension = 17280 N (20% UTS)
Test Tension = 25920 N (30% UTS)
Test Method: Power. Test Span: 28 m
Test Method: Power. Test Span: 28 m
End –point damping minimized
End –point damping minimized
Source: RIBE
Source: RIBE
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
Frequency
(Hz)
10.6
0.263
0.0838
7.9
0.432
0.105
10.6
0.528
0.503
8
0.857
0.419
2-138
Ymax/D
pk-pk
Pc
mW/m
10.6
1.056
2.51
8
1.714
3.7
14.9
0.187
0.168
13.1
0.261
0.209
14.9
0.376
0.921
13.2
0.519
0.628
14.9
0.751
4.54
13.3
1.031
4.36
19.2
0.145
0.398
18.4
0.186
0.272
19.2
0.291
1.88
18.5
0.370
1.17
19.3
0.580
10.2
18.6
0.737
6.88
23.5
0.119
0.586
23.7
0.144
0.482
23.5
0.238
2.76
23.8
0.288
2.22
23.6
0.474
15.9
23.9
0.574
12.2
27.9
0.100
0.963
29
0.118
0.796
27.8
0.201
4.71
29.2
0.235
3.73
28
0.400
31.6
29.3
0.468
20.6
32.3
0.086
1.49
34.4
0.099
1.24
32.2
0.174
7.78
34.5
0.199
6.14
32.4
0.345
53.6
34.7
0.395
36.1
36.8
0.076
2.24
39.8
0.086
1.99
36.6
0.153
11.8
39.8
0.172
10.2
36.8
0.304
88.8
40.2
0.341
59.5
41.3
0.068
3.31
45.3
0.075
2.79
41.1
0.136
18.6
45.3
0.151
16.4
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 2: Aeolian Vibration
Table A2.3-12 240/40 sq mm ACSR (26/7), Old Condition,
Greased Core, 10% UTS
240/40 sq mm ACSR (26/7)
Dia = 21.9 mmOld
Mass = 0.987 kg/m Greased
UTS = 86400 N
Test Tension = 8640 N (10% UTS)
Test Method: Power. Test Span: 28 m
End –point damping minimized
Source: RIBE
Figure A2.3-2 240/40 square mm ACSR
Figure A2.3-3 3/0 ACSR (6/1).
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
15.2
0.130
0.38
15.2
0.260
2.02
15.2
0.521
11.3
18.7
0.105
0.81
18.7
0.212
4.65
18.6
0.426
24.7
22.2
0.089
1.36
22.16
0.179
8.14
22
0.360
41.1
25.8
0.076
2.13
25.7
0.154
14.3
25.6
0.309
71.9
29.5
0.067
3.11
29.3
0.135
22
29.2
0.271
122
33.2
0.059
6.47
32.8
0.121
39
32.7
0.242
165
7.78
37.1
0.053
36.1
0.110
263
40.8
0.194
10.8
40.1
0.049
432
2-139
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Table A2.3-13 240/40 sq mm ACSR (26/7), Old Condition,
Greased Core, 20% UTS
Table A2.3-14 240/40 sq mm ACSR (26/7), Old Condition,
Greased Core, 30% UTS
240/40 sq mm ACSR (26/7)
240/40 sq mm ACSR (26/7)
Dia = 21.9 mmOld
Dia = 21.9 mm Old
Mass = 0.987 kg/m Greased
Mass = 0.987 kg/m Greased
UTS = 86400 N
UTS = 86400 N
Test Tension = 17280N (20% UTS)
Test Tension = 25920N (30% UTS)
Test Method: Power. Test Span: 28 m
Test Method: Power. Test Span: 28 m
End –point damping minimized
End –point damping minimized
Source: RIBE
Source: RIBE
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
11.5
0.487
0.38
14
0.244
0.052
11.6
0.965
2.21
14
0.490
0.52
16.2
0.172
0.07
14
0.979
4.15
16.2
0.345
0.86
19.5
0.175
0.13
0.83
2-140
16.2
0.691
5.53
19.7
0.348
20.8
0.134
0.22
19.5
0.703
8.3
20.7
0.270
2.18
25.1
0.136
0.24
20.8
0.538
12
25.4
0.270
2
25.6
0.109
0.48
25.2
0.544
13.5
0.67
25.7
0.218
3.39
31.1
0.110
25.4
0.441
22.5
31.05
0.221
4.15
30.4
0.092
1.07
31.7
0.432
29.2
30.5
0.183
6.08
36.9
0.093
1.1
30.6
0.366
47
36.7
0.187
7.26
35.2
0.079
1.24
36.9
0.371
50.1
35.3
0.159
10.2
42.8
0.080
1.69
35.4
0.316
84
42.5
0.161
11.6
40.16
0.069
3.07
42.7
0.321
85
40.2
0.139
15.5
48.6
0.070
3.25
40.3
0.278
142
48.4
0.142
19.4
45.15
0.062
3.75
48.5
0.283
138
45.2
0.124
23.6
45.4
0.247
225
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Table A2.3-15 1840 kcmil ACSR (72/7)
Chapter 2: Aeolian Vibration
Table A2.3-16 3/0 ACSR (6/1) “Pigeon”
1840 kcmil ACSR (72/7)
3/0 ACSR (6/1) “Pigeon”
Dia = 40.6 mm New
Dia = 14.31 mm New
Mass = 2.91 kg/m
Mass = 0.4334 kg/m
UTS = 200.6 kN
UTS = 27410 N
Test Tension = 40.1 kN (20% UTS)
Test Tension = 5890 N (20% UTS)
Test Method: Power. Test Span: 24 m
Test Method: SWR. Test Span: 36 m
Source: Ontario Hydro
Corrections: Aerodynamic damping removed
Source: Alcoa
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
9.3
0.42
48
9.3
0.27
8.6
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
3.27
9.3
0.11
1.34
35
0.398
1.07
70
0.139
13.9
0.28
86
40
0.199
0.38
70
0.199
9.80
13.9
0.18
23
40
0.279
1.15
70
0.289
39.64
13.9
0.06
2.4
40
0.378
2.55
70.2
0.448
167.14
19.7
0.24
310
45
0.120
0.18
75.3
0.112
2.59
19.7
0.12
41
45
0.227
1.08
75.1
0.175
10.98
19.7
0.07
10
45
0.283
2.39
75.3
0.259
56.16
26
0.17
480
45
0.382
3.88
75.5
0.339
164.81
26
0.1
112
50
0.112
0.29
75.9
0.442
419.98
26
0.042
11
50
0.191
1.04
80
0.090
2.13
32.5
0.14
825
50
0.335
6.28
80.1
0.171
17.22
32.5
0.094
256
50
0.408
15.08
80.1
0.239
67.10
32.5
0.041
49
55
0.145
0.95
80
0.359
312.01
55
0.209
2.40
80
0.422
553.42
55
0.279
8.05
84.9
0.088
3.85
55
0.378
21.21
84.9
0.125
12.55
60
0.124
0.88
84.9
0.169
43.76
60
0.199
4.24
84.9
0.203
97.38
60
0.299
16.55
91
0.052
1.52
60
0.452
73.61
91
0.092
10.24
65.2
0.139
1.88
91
0.143
45.12
65.2
0.205
5.05
91
0.199
173.82
65.2
0.299
22.55
65.2
0.398
65.87
2-141
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Table A2.3-17 35.6 mm ACSR (48/7) “Bersfort,” New
Condition, 15% UTS
Table A2.3-19 35.6 mm ACSR (48/7) “Bersfort,” New
Condition, 25% UTS
35.6 mm ACSR (48/7) “Bersfort”
35.6 mm ACSR (48/7) “Bersfort”
Dia = 35.6 mm New
Dia = 35.6 mmNew
Mass = 2.37 kg/m
Mass = 2.37 kg/m
UTS = 180.1 kN
UTS = 180.1 kN
Test Tension = 27 kN (15% UTS)
Test Tension = 45 kN (25% UTS)
Test Method: ISWR. Test Span: 63 m
Test Method: ISWR. Test Span: 63 m
Corrections: Aerodynamic damping removed
Corrections: Aerodynamic damping removed
Source: IREQ
Source: IREQ
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
6.82
0.328
0.213
6.593
0.339
0.0547
6.82
0.656
1.07
6.593
0.678
0.233
9.46
0.236
0.614
9.91
0.226
0.158
9.46
0.473
3.33
9.91
0.451
0.756
14.9
0.150
2.1
14.406
0.155
0.539
14.9
0.300
10.9
14.406
0.310
2.74
21.6
0.103
6.38
20.2
0.111
1.47
21.6
0.207
37.8
20.2
0.221
7.57
30.1
0.074
16.8
29.85
0.075
5.1
30.1
0.149
93.3
29.85
0.150
27.2
Table A2.3-18 35.6 mm ACSR (48/7) “Bersfort,” New
Condition, 20% UTS
Table A2.3-20 35.6 mm ACSR (48/7) “Bersfort,” New
Condition, 30% UTS
35.6 mm ACSR (48/7) “Bersfort”
35.6 mm ACSR (48/7) “Bersfort”
Dia = 35.6 mmNew
Dia = 35.6 mmNew
Mass = 2.37 kg/m
Mass = 2.37 kg/m
UTS = 180.1 kN
UTS = 180.1 kN
Test Tension = 36 kN (20% UTS)
Test Tension = 54 kN (30% UTS)
Test Method: ISWR. Test Span: 63 m
Test Method: ISWR. Test Span: 63 m
Corrections: Aerodynamic damping removed
Corrections: Aerodynamic damping removed
Source: IREQ
Source: IREQ
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
Frequency
(Hz)
6.89
0.324
0.091
6.89
Pc
mW/m
7.22
0.310
0.0287
0.453
7.22
0.619
0.218
0.232
0.0911
9.9
0.226
0.286
9.653
9.9
0.452
1.26
9.653
0.463
0.388
1.11
14.52
0.154
0.344
5.32
14.52
0.308
1.55
2.85
20.73
0.108
1.04
0.216
4.98
15.04
15.04
20.35
0.149
0.297
0.110
20.35
0.220
14.5
20.73
29.42
0.076
10.1
29.84
0.075
2.92
46.8
29.84
0.150
14.1
29.42
2-142
0.649
Ymax/D
pk-pk
0.152
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 2: Aeolian Vibration
Table A2.3-21 1033.5 kcmil ACSR (54/7) “Curlew”
1033.5 kcmil ACSR (54/7) “Curlew”
Dia = 31.5 mmNew
Mass = 1.951 kg/m
UTS = 168400 N
Test Tension = 37270 N (22% UTS)
Test Method: Power. Test Span: 92 m
Source: ENEL
Frequency
(Hz)
Ymax/D
pk-pk
Pc
mW/m
10.45
0.898
14.74
20.12
0.562
78.26
20.30
0.457
45.21
23.10
0.411
71.02
23.10
0.384
44.68
23.10
0.444
91.34
23.25
0.319
30.81
23.30
0.319
48.23
29.60
0.225
59.63
29.80
0.221
59.23
29.80
0.221
59.23
29.80
0.221
47.77
30.70
0.209
49.37
30.80
0.174
30.61
30.80
0.207
51.28
30.80
0.191
49.50
2-143
Chapter 2: Aeolian Vibration
APPENDIX 2.4
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
DEAM METHOD
we find,
The Damping Efficiency Amplitude Measurement, or
DEAM, procedure is a method for measuring the flow
of vibration power along a vibrating span. It has been
used chiefly for evaluating the efficiency of dampers on
laboratory spans (Rawlins 1988), but has also been
applied for measuring dissipation by damping arrangements in situ in field test spans (Leblond et al. 1997).
The DEAM procedure takes advantage of the fact that
aeolian vibration, whether natural in field spans or simulated in the laboratory, takes the form of travelling
waves. These waves are a form of energy, and it is their
movement that conveys the energy of vibration to
damping arrangements at the end of the span.
Neglecting the effect of the flexural rigidity of the conductor, the waves are governed according to the differential equation,
H ⋅ y′′ = m ⋅ y,
where the primes indicate differentiation with respect to
position x along the conductor, and the dots indicate
differentiation with respect to time t. Solutions to this
equation take the form,
y1 = F1 ( t − x / c )
y2 = F2 ( t + x / c ) ,
where c = H / m is the wave velocity. F1 and F2 are
arbitrary functions describing the profiles of waves moving in the positive and negative directions along the x
axis.
Suppose a signal y were available representing the
motion of the conductor at location x , resulting from
these waves:
y = y1 + y2 = F1 ( z1 ) + F2 ( z2 ) ,
where
z1 = t − x / c
z 2 = t + x / c,
Suppose also that a signal were available representing
the time integral of the slope y’ at the same location x.
This signal Is can be expressed in the following manner:
I s = ∫ y′dt = ∫ F ′( z1 )dt + ∫ F ′( z2 )dt.
However, using the identities,
z1 = z2 = 1,
2-144
1
z1′ = − ,
c
1
z2′ = ,
c
1
I s = ⎡⎣ − F1 ( z1 ) + F2 ( z2 ) ⎤⎦ .
c
The equations for y and Is may be solved simultaneously
to obtain,
⎛ x ⎞ y − cI s
,
F1 ⎜ t − ⎟ =
2
⎝ c⎠
⎛ x ⎞ y + cI s
.
F2 ⎜ t + ⎟ =
2
⎝ c⎠
Now, in the laboratory span, vibration takes the form of
steady, single-frequency travelling waves, and the functions F1 and F2 become
F1 = A cos ( t − x / c ) ,
F2 = B cos ( t + x / c ) .
Their signals give the amplitudes of the two travelling
waves. These may be used to calculate the amounts of
power carried by those waves,
PA =
1
Z 0ω 2 A2 ,
2
PB =
1
Z 0ω 2 B 2 ,
2
where Z 0 = H ⋅ m , the characteristic impedance of
the tensioned conductor. They may also be used to calculate damping efficiency,
Y
P
A− B
= min =
Pmax Ymax A + B
The flexural rigidity of the conductor affects the above
development. In addition, practical measurement may
employ pickups such as accelerometers for signal acquisition, whose mass can distort the shape of the cable.
Corrections for these effects are given in Rawlins 1988.
As the above equation for damping efficiency suggests,
the DEAM approach is closely related to the Inverse
Standing Wave Ratio Method. It improves on that
method by avoiding the need to seek out the locations of
the nodes and antinodes for the measurement of Ymin
and Ymax. In the DEAM method, the signals for amplitude and slope are derived from a pair of sensors spaced
a short distance apart along the conductor. The sensors
may be accelerometers or optical displacement transducers. The span-wise location of the pair is arbitrary
vis-à-vis the location of nodes and antinodes. Their signals are conveniently processed by analog circuitry.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
APPENDIX 2.5
CHARACTERIZATION OF THE
ELASTIC AND DAMPING
PROPERTIES OF SPACERDAMPERS
To characterize the spacer-damper articulations, their
elastic and damping properties are defined using one or
more of the following methods.
1. Stiffness-Damping Method at low frequency and different arm displacement
2. Stiffness Method
Chapter 2: Aeolian Vibration
Stiffness Method
The spacer is held by two adjacent clamps onto horizontal rods, which are free to rotate.
One rod is held in position, and a force is applied to the
other rod to move the clamp arms to their stops in tension—i.e., increasing the spacing from Xnom to Xmax,
which shall be recorded.
The above is repeated for the arms in compression for
Xmin to be recorded.
3. Damping Method
4. Stiffness-Damping Method at constant velocity and
different frequencies
Methods 1, 2, and 3 are proposed by the IEC Standard
61854, while Method 4 is used in some computer programs for the formulation of the analytical model of the
spacer-damper.
Stiffness-Damping Method at Low Frequency and
Different Arm Displacement
With the central frame restrained, sinusoidal movements at a frequency between 1 and 2 Hz are applied to
one clamp at different values of the angle of deflection
Φ of the arm (Figure A2.5-1).
For each value of the angle Φ, the force F applied to the
clamp and the arm deflection are measured, and the relevant signals used to obtain the hysteresis cycle, which
area A represents the energy dissipated by the articulation in one oscillation cycle.
The phase angle α, between the force and arm rotation,
is calculated as follows;
α = arcsin
A
F ⋅ l ⋅π ⋅ Φ
Where:
A = the energy dissipated in one cycle (J)
F = the peak force (N)
l
= the arm length (m)
Φ = the peak arm deflection angle (rad)
Spacings Xt and Xc shall then be determined, where:
Xt = Xnom + 0.9 (Xmax - Xnom)
Xc = Xnom - 0.9 (Xnom - Xmin)
The spacer arm is then moved in the following cycle:
Starting at Xnom, the spacing is increased to Xt at a
uniform rate and held for 60 s before recording the
force Ft required to hold this spacing.
The spacing is then decreased at a uniform rate to
Xnom and then to Xc, where after 60 s, the force FC
required to hold this spacing is recorded.
The stiffness shall then be determined as (Ft +
Fc)/(Xt - Xc).
To illustrate the above, assume that the test is carried
out on a 400-mm twin spacer, which has stops at spacings of 420 and 370 mm. It will then be necessary to
record the tensile force Ft (N) necessary to maintain a
spacing of 418 mm and the compression force Fc (N)
necessary to maintain a spacing of 373 mm. The stiffness will then be (Ft + Fc) / 45 (N/mm).
Damping Method
The body of the spacer is fixed rigidly, and mass is
added to one arm such that the natural frequency of free
From the measurements of F and α, the torsional stiffness Kt and the damping constant Ht can be calculated
as follows,
F ⋅ l ⋅ cos α
( Nm / rad )
Φ
F ⋅ l ⋅ sinα
Ht =
( Nm / rad )
Φ
Kt =
Figure A2.5-1 Sketch of the setup for the measure of the
torsional stiffness and damping of the spacer hinges at
low frequency and different vibration amplitudes.
2-145
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
oscillation is between 1 and 2 Hz. The arm is then
moved to one of the end stops and, after one minute,
suddenly released. The movement of the arm is recorded
for at least two complete cycles. If the initial swing (from
starting position to maximum deflection in the opposite
direction) is Y1 and subsequent swings (peak to peak)
are Y2, Y3, and Y4, the log decrement is taken to be
equal to:
⎡1⎛Y
Y ⎞⎤
ln⎢ ⎜ 1 + 2 ⎟⎥
⎣ 2 ⎝ Y3 Y4 ⎠⎦
This definition is different from the conventional one
(ln[Ao/An]/n), but is less sensitive to measurement error
and does not require the zero deflection position to be
determined.
A suitable test device is illustrated in the sketch of Figure A2.5-2.
Stiffness-Damping Method at Constant Velocity and
Different Frequencies
With the central frame restrained, a spacer clamp is
connected to a shaker (see Figure A2.5-3). The spacer
arm is vibrated at constant velocity of 100 mm/s in a frequency range of 1-100 Hz.
The frequency is changed automatically, with a maximum variation speed of 0.5 Hz/s, or manually with steps
of maximum 1 Hz, checking the steady-state condition
for each frequency. A sketch of the measurement setup
is shown in Figure A2.5-3.
The dynamometer in the position indicated in Figure
A2.5-3 measures the force F developed between the
shaker and spacer arm.
The result of the test is a curve giving the force per unit
of displacement F/x and the phase ϕ between force and
displacement as a function of frequency. The inertia
forces due to the masses between dynamometer and
spacer clamp is subtracted from the measured force. In
this way, the “corrected” force per unit of displacement
of the spacer clamp Fd/x can be evaluated.
The torsional stiffness Kt and damping Ht of the hinge,
as a function of the circular frequency ω (rad/sec), can
be calculated with the equations below:
Fd
J
K
cos ϕ = −ω 2 20 + 2t
x
l
l
Fd
sinϕ
Ht
x
=
Fd
J
Kt
cos ϕ + ω 2 20
x
l
In these equations the Ht and Kt values are obtained,
respectively, from the real and imaginary part of the
“corrected” force (Fd/x cos ϕ and Fd/x sin ϕ); Jo is the
inertial moment of the spacer arm with respect to the
center of the spacer hinge, and l is the arm length (from
the center of the arm clamp to the center of the spacer
hinge).
An example of spacer-damper hinge stiffness and damping as functions of the frequency is given in the diagrams of Figure A2.5-4.
Figure A2.5-2 Device for logarithmic decrement
tests on spacer-dampers (courtesy Damp).
2-146
Figure A2.5-3 Sketch of the setup for the measure of
the torsional stiffness and damping of the spacer
hinges at different vibration frequencies.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
APPENDIX 2.6
Chapter 2: Aeolian Vibration
NATURAL FREQUENCIES AND
MODES OF VIBRATION OF THE
CABLE PLUS DAMPER SYSTEM
As explained in Section 2.5.2, dealing with the single
conductor, if the damping of the conductor is ignored,
the well-known partial differential equation governing
the motion of the conductor would be that of a taut
homogeneous beam (Claren and Diana 1969a)— i.e.:
∂ 4u
∂ 2u
∂ 2u
EI 4 − T 2 = −m 2
∂x
∂x
∂t
A2.6-1
In this equation, EI and T could be complex quantities
in order to take into account the internal damping of
the conductor.
A steady-state harmonic solution is: u(x,t) = W(x)ψ(t)
where: ψ(t) = ψ0 eiλt
with:
λ = α + iω
and W(x) = ASh(zx) + BCh (zx) + Csin(ax) + D
cos(ax)
being:
Figure A2.5-4 Example of spacer-damper hinge
stiffness and damping as functions of the frequency.
z=
T
T2
λ2
m
+
+
EI
EI
(2 EI ) 2
a= −
T
T2
λ2
m
+
+
EI
EI
(2 EI ) 2
A2.6-2
A2.6-3
In λ, the term α is related to the system overall damping
and has a negative value, while ω is the vibration circular frequency.
This solution holds true in each one of the sections into
which the span is divided by the various dampers.
If we suppose that m dampers are applied to one of the
conductor extremities and n are applied to the other, it is
possible to write p equations of the type (Falco et al.
1973):
Wi(xi) = Ai Sh(zxi) + Bi Ch (zxi) + Ci sin(axi) + Di
cos(axi)
A2.6-4
where p = m + n + l and A i , B i , C i , D i , are complex
quantities.
2-147
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
End conditions for the first and the last part are found
by imposing the condition of rigidly clamped extremities, that is:
W1(0) = 0;W’1 (0) = 0;
Wm+n+1( m+n+1) = 0; W’m+n+1(
where, for simplicity sake: Wi ' =
m+n+1) = 0 A2.6-5
dWi
dx
A2.6-6
Equilibrium and congruence equations for each one of
the dampers are found by imposing that displacement,
rotation, and bending calculated at the left side of the
damper equal those ones calculated at the right side of
the damper. (The bending moment is equal at the right
and left side of the damper if the torque transmitted by
the damper is neglected.) Then, that the share computed
at the right side of the damper equals the share at the
left side of the damper, plus the force transmitted by the
damper itself:
W i ( i) = Wi+1 (0)
(i=!, 2,….m + n)
’
i) = W i+1(0)
W’i(
-EIW”i (
i) = -EIW”i+1(0)
A2.6-7
- EIW”’i ( i) + SW’i( i) =
-EIW”’i+1(0)+SW’i+1(0)+Fai
where Fai is the force transmitted by the damper and can
be evaluated as
Fai = (FRi+iFIi)Wi+1(0)
A2.6-8
where FRi is the real part of the force per unit displacement, while FIi is the imaginary part as measured by the
experimental tests described in the preceding paragraph,
and refers to a unit displacement of the damper clamp.
By imposing Equation A2.6-5 in Equations A2.6-6 and
A2.6-7, we obtain an homogenous system of -4(m + n +
1) variables - Ai, Bi, Ci, Di – and by zeroing the determinant of this system, the λi = αi + iωi are found.
The modes of vibrations are defined through the Ai, Bi,
C i , D i constants, corresponding to each one of the λ i
eigenvalues.
2-148
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
RECOMMENDED CONDUCTOR SAFE DESIGN TENSION WITH RESPECT TO AEOLIAN
VIBRATION
TableA2.7-1 Recommended Conductor Safe Design Tension with Respect to Aeolian Vibration
APPENDIX 2.7
Chapter 2: Aeolian Vibration
2-149
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
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Studiengesellschaft für Höchstspannungsanlagen. 1927.
1928. 1932. 1950. Technische Berichte Nos. 20, 44, 45,
150.
Sturm, R. G. 1936. “Vibrations of Cables and Dampers—I and II.” Electrical Engineering. Vol. 55. pp. 455466. May. and pp. 673-688.
Sunkle, D. C., J. T. Tillman, D. Schroeder, and D. Brakenhoff. 1995. “Effect of Vibration Recorder Mass on
Field Vibration Measurement.” Seventh International
Conference on Transmission and Distribution Construction and Live Line Maintenance. ESMO-95 CP-22.
Tavano, F. et al. 1994. “Conductor Self-Damping.”
CIGRE Report. SC22-94(WG11)-126.
Tebo, G. 1941. “Measurement and Control of Conductor Vibration.” AIEE Transactions. Vol. 60. pp. 1183-93.
Tompkins, J. S., L. L. Merrill, and B. L. Jones. 1956.
“Quantitative Relationships in Conductor Vibration
Using Rigid Models.” IEEE Transactions. pp. 879-94.
October.
2-157
Chapter 2: Aeolian Vibration
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
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United States. ISBN 0-915760-02-9.
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377-380. July.
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Oxford, England. ISBN 0-19-856396-5.
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Williamson, C. H. K., and A. Roshko. 1988. “Vortex
Formation in the Wake of an Oscillating Cylinder.”
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2-158
Zetterholm, O. D. 1960. “Bare Conductors and
Mechanical Calculation of Overhead Conductors.”
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Ziebs. 1970. “Über das mechanische Verhalten von Aluminium-Stahl-Freileitungsseilen als Beispiel für Verbundseile.” BAM report no. 3.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
CHAPTER 3
FATIGUE OF OVERHEAD
CONDUCTORS
Louis Cloutier
Sylvain Goudreau
Alain Cardou
The chapter covers the fatigue that can occur in overhead conductors. Included in
the discussion is information on fatigue mechanisms and characteristics, results
from high-amplitude tests and tests with spacer clamps, spectrum loading, inspection of operating lines, and remedial measures.
Dr. Louis Cloutier completed Ph.D. studies in mechanical engineering
at Laval University, Québec, Canada, in 1966 and pursued postdoctoral
work at Cambridge University, England in contact mechanics for a
year. He held different functions in research laboratories (National
Research Council of Canada and IREQ [Hydro-Quebec's research institute]), industries (Gleason Works, Roctest Ltd., and Sogequa Inc.), and
universities (Laval and Sherbrooke). His professional experience of
more than 40 years led him to work in several projects related to
mechanical power transmission, medical instrumentation, and electrical power transmission. In that last field, his interests have been mainly devoted to problems related to transmission line mechanics: conductors, insulators, spacers, accessories, and more recently
line supports. He is the author or coauthor of several publications in related fields and
holds two patents. Professor Cloutier is presently chair holder of the industrial chair
recently created by Hydro Québec TransÉnergie in collaboration with the Natural Sciences and Engineering Research Council of Canada for studies of the structural and
mechanical aspects of overhead transmission lines. He is a member of l'Ordre des ingenieurs du Quebec (OIQ), an active member of several technical and learned societies, a
Distinguished Member of CIGRE, and Fellow of the Canadian Society for Mechanical
Engineering (CSME).
Dr. Sylvain Goudreau is a professor at the Department of Mechanical
Engineering at Laval University, Québec City, Canada and principal
researcher of GREMCA (Groupe de REcherche en Mécanique des
Conducteurs Aériens) research group. He received his bachelor and
master degrees in mechanical engineering from École Polytechnique de
Montréal, Canada, in 1977 and 1980, respectively, and his Ph.D. degree
in mechanical engineering from Laval University in 1990. He is a registered professional engineer in the Province of Québec. Before beginning
his Ph.D. studies, he worked at National Research Council of Canada (Institut du génie
des matériaux, Montréal), where he was involved in development of a mechanical testing
laboratory and in studies on composite materials. In 1988, he joined the Mechanical
Engineering Department at Laval University. His research activities are in the field of
mechanical behavior of overhead line conductor and their related fatigue problems. He is
the author or coauthor of many technical reports and papers on these subjects.
3-1
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Dr. Alain Cardou is adjunct professor
and, formerly, head of the Department
of Mechanical Engineering at Laval
University, Quebec City, Canada. He
graduated in mechanical engineering
from École Nationale Supérieure de
Mécanique, now École Centrale de
Nantes, France. He received his M.S.
and Ph.D. degrees in mechanics and materials from the
University of Minnesota at Minneapolis. His general
research interests are stress and strength analysis, on
which he is the author or coauthor of more than 90
3-2
papers. For several years, in collaboration with some
power utilities, and within the GREMCA research
group, he has been working on overhead electrical conductor fatigue problems. A registered professional engineer in the Province of Quebec (OIQ), he is a Fellow of
CSME and a member of the American Academy of
Mechanics.
Collaborators and internal reviewers
John Chan, Claude Hardy, André Leblond, Charles B.
Rawlins, Dave Sunkle and Pierre Van Dyke.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
3.1
INTRODUCTION
Fatigue failure of strands in overhead conductors is the
most common form of damage resulting from aeolian
vibration. Conductor fatigue may also result from galloping and from wake-induced oscillation, but is not the
primary penalty associated with those motions. Aeolian
vibration may also cause fatigue of other line components such as armor rods, dampers, ties, insulators, and
tower members.
Fatigue of conductor strands occurs at points where
motion of the conductor is constrained against transverse vibration, such as the vertical motion of aeolian
vibration. These points include: support locations, suspension clamps, clamp-top and pin insulators, and deadends. They also include damper and bundle conductor
spacer clamps, hot-line taps, splices, and armor rod end
clamps. Fatigue failures have occurred on occasion at
each of these locations.
The incidence of fatigue relative to the above locations is
directly associated with the rigidity with which conductor motion is restrained. The vast majority of fatigued
strands are found at tangent supports where structural
stiffness in the vertical direction is required to support
the load associated with the weight span. At the other
locations listed above, there is some vertical mobility of
the clamp or compression device that grips the conductor. This mobility is often reduced by resonances of the
parts involved. For example, fatigue at deadends often
involves a resonance of the insulator string and jumper
system. Fatigue at damper locations is usually associated with a poorly-damped resonance of the damper, or
resonance of the segment of conductor between the
damper and the adjacent support.
Fatigue failures of strands have occurred in all basic
conductor types: Aluminum Conductor Steel Reinforced (ACSR), all-aluminum whether EC (Grade Aluminum) or alloy, copper, copperweld, and steel, whether
galvanized or aluminum-clad, as well as in Optical
Ground Wire (OPGW) ground wires.
Fatigue of conductor strands is caused by the cyclic
bending of the conductors where their motion is
restrained. However, that fatigue is not a bending fatigue
situation, as found in standard fatigue tests on smooth
specimens. Rather, it is a case of fretting fatigue occurring at strand surfaces because of the cyclic microslip
induced by the conductor motion. This microslip occurs
locally at contact points whenever a tangential force
acts between the contacting bodies. That small relative
displacement may be of the order of a few microns up to
tens of microns before gross slip occurs between contacting bodies.
Chapter 3: Fatigue of Overhead Conductors
Although fretting fatigue life decreases with increasing
bending amplitude, beyond a certain amplitude, fretting
fatigue gives way to fretting wear, which is generally less
critical. Yet, if fretting wear is occurring at some points
in a particular conductor, restrained by a particular
clamp, fretting fatigue is certainly occurring at other
points where relative slip is more restrained (closer to
the clamp, or deeper in the conductor). Thus, in a conductor, fretting wear, with the corresponding debris
(black powder), is a good indicator of fretting fatigue, a
crack propagation phenomenon that is otherwise difficult to detect.
Thus, the notions of high-cycle (low-amplitude) and
low-cycle (high-amplitude) fatigue found in standard
fatigue situations should not be used here. Conductor
bending amplitude is merely the controlling factor for the
type of slip regime occurring between wires or between a
wire and the suspension clamp. Wire breaks occurring at
high-bending amplitudes are not different from those at
low amplitudes. Cracks will again start at contact points
and will propagate more rapidly. Also, at high amplitude, microslip extends to inner layers, which are then
involved in the fatigue process.
More importantly, for a given conductor-clamp system,
there is apparently an amplitude of bending that, if not
exceeded, can be endured almost indefinitely. This
amplitude corresponds to an endurance limit for the
clamp/conductor combination. Because of the complex
stress state in a contact area at which microslip occurs,
there is no direct relationship between the endurance
limit of the material, as found in material handbooks,
and that of the clamp-conductor system (Cloutier et al.
1999). A good example of that can be found in (EPRI
1987), where fatigue tests on an Aluminum Conductor
Alloy Reinforced (ACAR) conductor are reported. In
that conductor, the outer layer is made of 1350-H19 aluminum, while inner strands are made of 6201-T81 alloy,
whose reported classical fatigue limit (at 500 Mc—i.e.,
million of cycles) is almost double the outer one. However, 80% of strand failures were found to be inner
strand failures.
If the endurance limit is exceeded in a particular line,
the rapidity with which failures appear is determined by
the degree to which that limit is exceeded, and by the
rate at which cycles of high-amplitude accumulate. In
some cases, fatigue has appeared within a few months of
stringing, while in others, failures have been discovered
only after years of service. Figure 3.1-1 shows the distribution of the times for discovery of fatigue, based on a
study of U.S. experience made by Alcoa Laboratories in
1962 (Alcoa 1979).
3-3
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
bending, as measured by the amplitude of the conductor
relative to the clamp at a distance of 89 mm from it, was
0.61 mm (24 mils). This particular bending amplitude is
a practical parameter used in practice to predict conductor damage and will be analyzed in Section 3.2.2.
The nearly linear accumulation of conductor damage
with cycles of vibration, shown in the figure, is just an
example of that found in such tests and should not be
generalized.
Figure 3.1-1 Elapsed years between date of construction
and date when damage discovered.
Severity of damage, in terms of number of broken
strands at any location, is also determined by the amplitudes of bending experienced, and their accumulated
cycles. Fatigue, once initiated at a location, often
spreads to more and more strands if the vibration continues unabated, and can eventually result in fracture of
all strands of the same material as that which failed first.
Then, if the conductor is an ACSR, fatigue may halt
when only the steel core is left. In most cases, however,
line current is great enough to heat the steel core and
anneal it at the location where it is the only remaining
current path. When that happens, the steel core may fail
in tension.
The progress of fatigue through the aluminum strands
under continued vibration is illustrated in Figure 3.1-2.
The figure is based on data from a laboratory fatigue
test of 795 kcmil ACSR (45/7) (Silva 1976). Conductor
tension was 26% of rated strength, and the severity of
Figure 3.1-2 Progress of fatigue in 795 kcmil ACSR
(45/7). (Silva 1976).
3-4
In multilayer ACSRs, those having more than one layer
of aluminum strands, the first strands to break may be
in the outer layer or in a layer below it. An example of a
line in which initial failure in the outer layer predominated is represented in Table 3.1-1 (Alcoa 1979). The
table is based on inspection of all support points at the
time that the line was reconditioned after about 25 years
of service, and shows the number of support points having various combinations of inner- and outer-layer
strand failures. The conductor had two aluminum layers, the outer with 18 strands and the inner with 12.
Note that there were no instances in which failures were
found in the inner layer when the outer layer was intact.
There were no complete conductor failures in the line.
In contrast, there have been cases in other lines where
inner-layer strands failed before outer-layer strands.
This sequence of failure has been reproduced in laboratory fatigue tests of ACSR. For example, Table 3.1-2
shows the sequence of failure by layer in a test on 954
kcmil ACSR (45/7) at Alcoa Laboratories (Alcoa 1979).
Conductor tension was 25% of Rated Strength, and the
bending amplitude was 0.88 mm (34.5 mils), a rather
high amplitude for that size of conductor. In general, on
multilayer conductors, bending amplitudes slightly
above the endurance limit generate failures on the outer
layer or on the next one. Inner-layer failures only occur
at higher amplitudes.
The lag between first inner-layer failure and first outerlayer failure, and the number of inner strands that break
before outer-layer failure occurs, are important relative
to inspection of operating lines. Visual inspections
detect only outer-layer damage and thus may overlook
evidence of inadequate vibration protection until significant damage has already occurred.
In the series of tests from which Table 3.1-2 is taken,
there were five in which the first outer-layer failure followed inner-1ayer failure. For those tests, the ratio of
cycles required to cause outer-layer failure to cycles to
cause first inner-layer failure averaged 3.8. The maximum number of inner failures preceding outer failures
was 13, as represented in Table 3.1-2. The average for
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 3: Fatigue of Overhead Conductors
Table 3.1-1 Relative Occurrence of Broken Strands in Inner and Outer Layers of ACSR Cable a
Conductor: 397.5 kcmil ACSR (30/7)
Broken Inner-layer Strands
Broken Outer Strands
0
1
2
3
4
5
0
117
1
55
1
2
66
4
3
53
19
3
4
16
21
13
5
14
8
14
6
2
6
10
8
17
12
3
7
7
6
15
14
3
8
7
5
6
7
7
3
9
4
1
4
8
5
1
1
4
10
11
3
12
2
8
9
10
11
12
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
2
14
15
7
1
1
13
6
1
1
1
1
16
17
18
a. All strand breaks were found at support clamps after line had been in service for approximately 25 years.
Table 3.1-2 Sequence of Strand Failure in Multilayer ACSR
Megacycles of Vibration
Layer in Which Failure Occurred
5.29
Middle
6.99
Middle
7.56
Middle
8.47
Middle
8.62
Middle
8.81
Middle
9.03
Inner
9.05
Inner
9.25
Inner
11.00
Middle
11.49
Middle
11.79
Middle
11.87
Inner
11.96
Outer
the five tests was 5.4, or about 12% of the aluminum
strands.
In a series of 23 fatigue tests on 397.5 kcmil ACSR (26/
7) reported by Seppä (Seppä 1969) outer-layer failure
followed inner-layer failure in seven tests. In these seven
tests, the average ratio of cycles at first outer-layer failure to cycles at first inner-layer failure was 2.4, and the
average number of inner breaks preceding outer failure
was 1.86 or about 7% of the aluminum strands. There
were three additional tests in this series that were terminated before outer-layer failure occurred. Had it
occurred just at the time that each of these tests was terminated, then the average ratio of outer- to inner-layer
cycles to failure, in the tests where inner failure occurred
first, would have been 3.2, and the average number of
inner strands broken before outer-strand failure would
have been 2.7, or 10% of the aluminum strands. Based
on these data, the average time lag between first fatigue
and first visible evidence of it may be by a ratio on the
order of 3 or 4, and the average loss of aluminum area
preceding first outer-layer failure may be about 10 or
15%. The maximum lag in any test was by a ratio of 12
to 1, and the maximum aluminum area loss preceding
outer visible evidence was 29%. These figures pertain to
conductor-clamp combinations and amplitudes that
favor inner-layer failure. In a significant fraction of
cases, when amplitude is not too far above the conductor-clamp system endurance limit, outer-layer failures
occur first.
Transmission engineers are faced with several practical
questions with respect to fatigue damage in existing
lines.
a. Are failures likely to occur?
b. Have they occurred yet?
c. If so, what should be done?
3-5
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
These questions are discussed in the following sections,
and practical answers based on experimental data are
given for a wide range of cases.
Section 3.2 describes how to characterize a conductor
bending amplitude at a suspension clamp, based on
parameters that can be measured in an operating line
(see Chapter 2). Fatigue test data obtained under constant vibration amplitude are presented. Endurance limits are found—that is, vibration amplitudes under which
a conductor sees practically no fatigue damage. Such
values can then be used by the utility engineer to evaluate the critical vibration amplitude for a given conductor at a suspension clamp.
High amplitudes such as those found in galloping conductors pose a special problem. Section 3.3 reports data
from high constant-amplitude fatigue tests carried out
on various suspension clamps. Section 3.4 reports on
fatigue tests carried out using spacer clamps instead of
suspension clamps. Section 3.5 examines how constant
amplitude data can be used in the variable amplitude
case (so-called spectrum loading). Section 3.6 discusses
testing and inspection of operating lines.Section 3.7
reviews remedial measures. Finally, Section 3.8 presents
a synopsis of the practical results of these studies for the
benefit of the utility engineer audience.
3.2
FATIGUE ENDURANCE OF CONDUCTORS
Relating the measurable vibration of an overhead span
of conductor to the likelihood of fatigue of its strands is
a complicated matter. The complications arise primarily
from two facts. First, the stresses that cause the failures
are complex and not related in a simple way to the gross
motions of the conductor involved. Second, the failures
originate at locations where there is surface contact and
fretting between components.
Inspection and failure analysis of a large number of
fatigue breaks from field and laboratory spans indicate
that fatigue cracks always originate at places where the
strand that broke was in contact with another strand,
with an armor rod, or with the clamping device (Fricke
and Rawlins 1968; Seppä 1969; Möcks 1970, Silva 1976,
Cardou et al. 1994). The stresses at these locations are
combinations of static stresses due to conductor tension, bending, and the compressive force between the
members, and of dynamic stresses due to bending, fluctuation of tension, and traction between the contacting
members.
Theoretical and numerical models are available to evaluate a conductor global bending behavior at a point of
fixity such as a suspension clamp, a spacer clamp or a
dead end clamp (Papailiou 1997, Rawlins 2005). The
3-6
interested reader will find a summary of such bending
behavior analysis in the (CIGRE Task Force B2.11.07
2006) report. Also, cyclic stresses at points of contact
between the outer layer and the next have been
obtained, under purely elastic behavior hypothesis, and
with simple boundary conditions (Leblond and Hardy
2005). However, a realistic analysis relating all these
stresses—including contact stresses and microslip for a
specific conductor-clamp system—to the vibration of
the conductor has yet to be published.
The endurance of metals to combined stresses has
received considerable attention in recent decades, and
several criteria for rating such stresses relative to fatigue
have been developed and are in use. A similar effort has
been made to obtain criteria for fretting damage to the
contacting surfaces (Hills and Nowell 1994; Fouvry et
al. 2000). Application of these criteria is generally
restricted to specific materials, contact conditions, and
loadings.
No satisfactory criterion is available yet to analytically
evaluate the fatigue behavior of conductors from the
fatigue properties of the materials used in their construction and the stresses that occur in them. Thus
fatigue characteristics of conductors must be determined
by fatigue tests of conductors themselves. These tests
should be performed on conductor-clamp systems, reproducing as closely as possible the field loading conditions.
In such tests, the fatigue life of the conductor must be
determined as a function of some measure of vibration
intensity, rather than of the stress or stress combination
that causes the failure, since that stress is not accessible
to measurement.
Several measures of vibration intensity have been
employed:
a. Free-loop amplitude of vibration, ymax (Little et al.
1950; Alcoa 1961; Hondalus 1964; Smollinger and
Siter 1965)
b. Angle through which the conductor is bent at the
clamp by the vibration, β (Seppä 1969; Bolser and
Kanouse 1948; Helms 1964)
c. Bending amplitude (amplitude of conductor relative
to clamp, measured a short distance from the clamp),
Yb (Tebo 1941; IEEE 1966; Josiki et al. 1976;
Cloutier et al. 1999)
d. Dynamic strain in an outer-layer strand in the vicinity of the clamp, ε (Yamagata et al. 1969; Nakayama
et al. 1970)
Fatigue curves have been developed through tests in laboratory spans using each of these parameters as the
measure of vibration intensity.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Four problems arise in applying such fatigue curves in
order to assess vibration of field spans. One is that the
parameter expressing vibration intensity may be inconvenient to measure reliably in the field (a, b, d) or does
not do justice to the complicated behavior found there
(a) (Hard 1958; Rawlins and Harvey 1959). Also, a
parameter based on global conductor behavior should
be preferred to a “local” one, such as dynamic strain on
a strand (d), which depends on the selected strand, on
the suspension clamp geometry etc. It is because of
these problems that bending amplitude (c) is the most
widely used parameter for measurement of vibration of
operating lines (IEEE 1966).
The second problem is that vibration fatigue test data
are available for only a small fraction of the conductor
sizes and types that are in use, and such data are expensive to acquire. Since none of the above parameters is
simply related to the fatigue-initiating stresses, results
from tests on one conductor size are not necessarily
applicable to others.
The third problem is that fatigue tests have to be performed with a particular clamp, which may differ from
the one at hand. Although clamps of a generally similar
design yield similar results, it has been found that different types of clamps may yield quite different fatigue test
results.
Finally, the fourth problem arises when field vibration
amplitude is not a constant, while available fatigue tests
are performed keeping the selected amplitude parameter
constant.
The second problem has been dealt with in practice by
assuming that there is some idealized strain or stress that
can be calculated from vibration amplitude, and that correlates well enough with conductor fatigue life to permit
its use in establishing a single endurance limit for a range
of conductor sizes. To the extent that the approach is
valid, fatigue information on one size can be applied
throughout that range, or piecemeal fatigue data scattered over a number of sizes within the range of validity
can be combined by putting them on a common basis:
the calculated stress. Use of such an idealized stress, at
present, lacks a fundamental analytical basis. However,
ranges of conductor size and support arrangement have
been found where its use gives results that are reliable
enough to be usefully applied.
There is no solution yet to the third problem. The general hypothesis is that, within a given type, clamp geometry is not a primary factor. Some tests, however, have
shown that this is not quite the case (McGill and Ramey
Chapter 3: Fatigue of Overhead Conductors
1986; EPRI 1987). The best solution is to have fatigue
tests performed with the same clamp as the one considered in the application.
The fourth problem, variable amplitude, or spectrum
loading, will be dealt with in Section 3.5
3.2.1
Conductor Fatigue Mechanisms
Before taking up the calculation of idealized stress and
its correlation with fatigue, some discussion of actual
fatigue mechanisms is worthwhile.
Standard overhead conductors consist of concentric layers of helically-laid strands. The tensions of the strands
of each layer cause them to embrace the layer or core
below with a certain amount of pressure. This pressure
lends structural stability to the conductor. It also results
in friction forces between strands, and thus impedes
their sliding motion relative to one another during
vibration.
If there were no interstrand friction, there would be no
possibility of variation in the tension in a strand along
its length. If a conductor having frictionless strands
were flexed, the strand tensions in a layer might or
might not change. For example, the strand represented
at (a) in Figure 3.2-1 would undergo no tension change
because its arc length would not be affected by the
bending. The arc length of the strand represented at (b)
would change, however, resulting in a change in its tension. If the conductor were many lay lengths long, the
change in arc length would be dissipated over a great
length of strand, and the change in tension would be
slight. Thus, for long conductor lengths, in a frictionless
conductor, individual strand tensions would not be
changed by flexure of the conductor at its ends. In the
absence of tension changes in the strands, the flexural
rigidity of the conductor would simply be the sum of
individual strand flexural rigidities. Dynamic stresses
would be only those associated with bending of each
strand about its own neutral axis.
Figure 3.2-1 Effects of conductor bending
upon movement of outer strand.
3-7
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Note that when the cable of Figure 3.2-1 (a) is bent, the
strand slides along the core in the direction indicated by
the small arrow. Sliding also occurs in the cable at (b),
indicated by the arrows.
Real conductors do not have frictionless strands, and,
for the small amounts of flexure experienced due to
vibration waves out in the span, the friction present
between strands is normally great enough to prevent
gross sliding between them. The relative axial movements of the strands are absorbed in largely-elastic
shear strains around the small areas of interstrand contact indicated in Figure 3.2-2. However, very small
amounts of sliding, called microslip, do take place at the
peripheries of the interstrand contacts where the contact
pressure tapers to zero.
Near supporting clamps, conductor curvatures caused
by vibration are much larger than in the free span. The
attendant sliding forces there overcome frictional
restraint much more readily. Microslip amplitude
increases, and even gross sliding may occur, as indicated
by the arrow in Figure 3.2-3.
A noteworthy situation arises when the interstrand tractions are almost large enough to cause sliding. The
interstrand contacts are nominally line contacts
between the core and the innermost layer of strands,
and point contacts between strands of adjacent layers.
Actually, the line contacts expand into strip contacts,
and the point contacts into ellipses of finite size because
of the bearing forces acting upon them. The sizes of the
contact areas expand, mainly through plastic deformation of the strands. Contact pressure distribution is
more or less uniform at a value corresponding to the
bearing yield strength of the strand material, between
two and three times the material yield strength, of about
170 MPa (25 ksi) for conductor-grade aluminum. That
pressure decreases to zero on the boundary of the contact region. The tangential surface traction required to
cause sliding is this normal stress multiplied by the static
coefficient of friction, which is about 0.7 between aluminum strands. Under tangential surface traction, there
always is a microslip region near the contact zone
boundary (for a circular region, it would be an annulus).
That region increases when bending amplitude
increases. Then the dynamic shear stresses at the threshold of sliding may become quite high. Because of the
cyclic bending of the conductor, microslip direction is
reversed, as is the shear stress in the contact region. This
cycling often generates small cracks, which propagate
up to a certain point. Because of the contact pressure,
many cracks are stabilized. However, if the vibration
amplitude is large enough, some cracks grow beyond the
compression zone and enter in the region where the
dominating stress is the tensile stress from the conductor axial load. The small variation of that stress then
suffices to grow the crack up to complete strand fracture. The process is easily observed on the broken wire:
a crack starts at a small angle with the strand surface
(mode II, or normal shear, cracking). Then it rotates
and becomes normal to the strand axis (mode I, or
opening mode, cracking).
Shear stresses are reduced when amplitudes are large
enough to cause gross sliding at a contact. In this case,
fretting wear occurs instead of fretting fatigue. Wear
expands the area of contact, and the tangential tractions
are further reduced by the lubricating effect of wear
products. In such cases, strand fracture occurs at inner
layers where sliding is impeded by the higher contact
pressures. Thus, in a conductor-clamp system, occurrence of fretting wear is a definite sign that fretting
fatigue is also occurring, if not at the same points of
contact.
As noted earlier, all fatigue breaks of conductor strands
appear to originate at strand contacts where fretting has
occurred. There are numerous such contacts in the
vicinity of a clamp, between the various strands, and
between the outer-layer strands and the clamp or armor
rods, if any. Figure 3.2-4 shows the second layer of
Figure 3.2-2 Area of interlayer strand contact.
Figure 3.2-3 Strand motion adjacent to clamp.
3-8
Figure 3.2-4 Fretting and fatigue of second layer of
strands 795 kcmil ACSR (54/7) (Alcoa 1961).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
strands in a sample of 795 kcmil ACSR (54/7) fatigue
tested in the laboratory (Alcoa 1961). The region shown
was adjacent to a fixed clamp, and numerous fretted
contact points and several fatigue failures are visible.
Closer examination of the breaks permits identification
of the origins of the cracks. For example, the pattern of
radiating ridges and the texture variation in the failure
surface of Figure 3.2-5 identify the fretted region as the
origin of the crack.
Microscopic examination of cross-sections of fretted
zones, such as that of Figure 3.2-6, shows a surface layer
of highly disordered structure containing a fine lacework of cracks, heavily loaded with aluminum oxide.
This layer is created by repeated welding of the high
points or asperities of the contacting surfaces, and
breaking of virgin metal adjacent to the welds, under
Chapter 3: Fatigue of Overhead Conductors
repeated small tangential movements of the two surfaces relative to each other. Eventually, a crack may be
formed, as in the figure. Depending on the vibration
amplitude, it may remain stable in the compression
zone, or it may grow beyond that region and become the
origin of a fatigue break (Ouaki et al. 2003).
As a matter of observation, fatigue breaks in conductor
favor those strand locations where movements have
caused crack initiation and propagation (fretting
fatigue) but not gross wear (fretting wear). The reason
for this is that the latter removes material from the
strand surface faster than young cracks can propagate,
so that the stress raisers are destroyed at inception.
Besides, wear debris may act as a lubricant, leading to a
decrease in the coefficient of friction, and consequently
to smaller contact tangential stresses (Zhou et al. 1992).
The cracks created from the zone of fretting drastically
reduce the fatigue strength of the strand relative to its
unfretted strength. Some tests on individual strands
have shown a decrease by a factor of two (Lanteigne et
al. 1986). The magnitude of the effect is not the same in
all aluminum alloys. In fact, because of the difference in
crack propagation properties, the reduction in fatigue
strength is greater the stronger the alloy.
3.2.2
Figure 3.2-5 Failure surface of fatigued strand (Alcoa
1961).
Calculation of Idealized Stress
The mechanisms described above are complex enough
that any analysis of the vibration stresses in a conductor
has to be approximate. It is generally sufficient, however,
to determine one indicator that can be used in conjunction with fatigue tests. The following one, which is based
upon convenient assumptions has been employed to
arrive at a nominal stress for rating the fatigue-inducing
intensity of vibration. The particular stress that is customarily nominated for this purpose is the alternating
stress in the topmost fiber of a strand, at the point
where the conductor enters, or becomes restrained by,
the clamp.
There are several ways to assess this stress. One is measurement by strain-gage. Figure 3.2-7 shows fatigue
curves for 25.3 mm diameter ACSR (26/7) at three levels
of conductor tension, when the conductor was supported
by a rigid, square-faced aluminum bushing (Yamagata et
al. 1969). The dynamic stresses shown were determined
from measured strains on outer layer strands.
Figure 3.2-6 Microscopic cross section of fretted strand
(Alcoa 1979).
Because of the inconvenience of strain measurements
(and because it has been found to vary significantly
from one strand to the other), it is more common to use
a value of the nominal stress that is calculated from an
easily-measured vibration amplitude, a characteristic of
3-9
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
loop is short compared with the loop length, as indicated in the figure. The shape in this region is shown in
more detail in Figure 3.2-9, in which a dashed line represents the end of the sine-shape loop, from which the
conductor departs. The dashed line is almost straight in
this region. The conductor axis, which is assumed to be
horizontal at the clamp, becomes asymptotic to the sineshaped loop with increasing distance from the clamp.
Figure 3.2-7 Results of fatigue tests on 25.3-mm
diameter ACSR (26/7), based on measured outer-layer
dynamic strain (Yamagata et al. 1969).
the whole conductor. In such calculations, the conductor is treated as a solid rod under tension for purposes
of determining the alternating curvature of the conductor at the clamp caused by vibration—i.e., the variation
in curvature about the static curvature associated with
sag. Some value of flexural rigidity, constant along the
conductor, is assumed in the calculations. Dynamic
strain is estimated from the alternating curvature
The value customarily used for flexural rigidity is the
sum of the flexural rigidities of the individual strands,
where each strand is assumed to be straight (lay angle is
neglected) and to bend about its own neutral axis. Thus,
all strands are assumed to undergo the same alternating
stress, independently of their distance from the conductor effective neutral axis, a rather drastic assumption.
Several similar analyses of the shape of a vibrating stiff
wire, rigidly clamped at its ends, have been published
(Morse 1948, p. 166 et seq.; Steidel 1959; Scanlan and
Swart 1968; Seppä 1969; Claren and Diana 1969). The
following simplified analysis takes advantage of several
approximations that introduce errors that are generally
small enough to be neglected.
Assume that the conductor is straight and vibrates in
standing waves, as in Figure 3.2-8, and that the supporting clamp is rigidly fixed. Assume further that the
region adjacent to the clamp where the shape of the conductor departs significantly from that of a sine-shaped
Figure 3.2-8 Standing wave vibration, with rigidly fixed
supporting clamp at left end of section (a).
3-10
If the dashed locus is taken to be indeed straight, and
the amplitudes of motion are small enough in region (a)
that inertia forces can be neglected, then the dashed line
may be taken as the line-of-action of the conductor tension. If this is the case, the bending moment acting at
any cross-section is equal to the tension H multiplied by
the departure yt of the conductor's axis from that line of
action, as in Figure 3.2-10.
Now the curvature of the conductor is given by:
d 2 yt M
=
dx 2
EI
3.2-1
where M is local bending moment and EI is flexural
rigidity.
Since M = Hyt,
d 2 yt H
=
yt
dx 2
EI
3.2-2
and yt = Ae±px + C1x + C2 where p = H / EI , and A,
C1 and C2 are constants of integration to be determined
Figure 3.2-9 Enlargement of section (a) (from Figure
3.2-8).
Figure 3.2-10 Departure (yt) of conductor centerline from
sine-shaped loop, as conductor approaches fixed
supporting clamp.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
by boundary conditions. Since y t approaches zero for
large x, yt = Ae-px is the admissible solution.
The slope of the conductor axis relative to the line of
action of the tension is:
dyt
= − pAe − px
dx
⎛ d 2 yt ⎞
H
⎜ 2 ⎟ = pβ = β
dx
EI
⎝
⎠ x =0
3.2-4
The angle β may be determined from the frequency and
amplitude of motion of the span. For standing wave
vibration, the amplitude y at any location in the span
remote from region (a) is:
2π f
y = ymax sin
( x − x1 )
VT
3.2-5
in which VT = H / m is the velocity of traveling waves
on the conductor, and x1 is the distance from the clamp
to the point where the line of action of conductor tension intercepts the x axis. The node angle β is equal to
the maximum of dy/dx, and this turns out to be:
2π fymax
β=
H /m
Now the curvature and bending moment at the clamp
may be calculated on the basis of an amplitude other
than ymax. If that amplitude is measured within region
(a) of Figure 3.2-8, the calculation is particularly simple.
It can be seen from Figures 3.2-9 and 3.2-10 that this y
of the conductor relative to the x axis, assuming a small
angle β, is:
y = − ya + βx + yt
3.2-3
From Figure 3.2-9, the value of the slope at x = 0 (at the
clamp, with respect to the line of action) is equal to the
angle β , and the curvature of the conductor as it
emerges from the clamp is:
3.2-6
Chapter 3: Fatigue of Overhead Conductors
3.2-9
Now, from Equation 3.2-4:
β=
1 ⎛ d2yt ⎞
⎜
⎟ = pA
p ⎝ dx 2 ⎠ x =0
3.2-10
Also, ya = A, so:
y = − A + pAx + Ae − px
3.2-11
⎛ d2yt ⎞
p2 y
2
⎜ 2 ⎟ = p A = ( − px )
− 1 + px
e
⎝ dx ⎠ x =0
3.2-12
and:
Although the general principle of the calculation of
y t (x) is due to Isaachsen (Isaachsen 1907), Equation
3.2-12 was first reported by J. C. Poffenberger and R. L.
Swart (Poffenberger and Swart 1965) and is called the
Poffenberger-Swart Formula.
The industry standard position for measuring y is at x =
89 mm (3.5 in.) (IEEE 1966) and, when measured at that
position, its peak-to-peak value is called “bending
amplitude,” Yb. ( Y = 2 y .)
b
Thus the conductor curvature at the clamp becomes:
⎛ d2yt ⎞
m
fy max
⎜ 2 ⎟ = 2π
EI
⎝ dx ⎠ x =0
3.2-7
and the bending moment at that location is:
⎛ d2y ⎞
M o = EI ⎜ 2 t ⎟ = 2π mEI fy max
⎝ dx ⎠ x =0
3.2-8
It is interesting to note in this equation that the bending
moment Mo is independent of conductor tension H. The
reason is that, referring to Figure 3.2-9, Mo = Hya, but
the greater the tension, the more sharply the conductor
is curved as it emerges from the clamp, so the smaller ya
is. In fact, they vary in inverse proportion, so their
effects upon Mo cancel.
Equations 3.2-4, 3.2-7, and 3.2-12 provide three means
for calculating conductor curvature at the clamp, based
upon node point vibration angle, frequency and freeloop amplitude, or bending amplitude, respectively. In
practice, the vibration angle β is usually calculated from
measured values of f and y max according to Equation
3.2-6.
Estimated dynamic strain in the conductor strands at
the clamp is calculated by multiplying the dynamic curvature there by an assumed distance from the neutral
plane of bending to the outermost fiber. Half of strand
diameter, or d/2, is the value usually assumed. Again
this is equivalent to assuming that a strand bends with
respect to its own neutral axis. Thus the three bases for
estimating curvature at the clamp lead to the following
3-11
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
three equations for estimating the alternating stress in
the top surface of a strand at the clamp:
σa =
dE a
2
H
β
EI
m
fymax
EI
dE p 2 / 4
σ a = − px a
Yb
e − 1 + px
σ a = π dEa
3.2-13
3.2-14
3.2-15
in which Ea is Young's modulus for the strand material.
3.2.3
Comparison of Calculated with Measured
Stress
The correlation of calculated with measured values of
σ a may appear to be somewhat academic, since the
stresses that initiate fatigue failures are located at metalto-metal contacts, and σ a is a free-surface stress. The
comparisons do, however, provide some measure of the
sensitivity of the analysis to the degree of idealization
involved in the assumptions employed. For example, the
nominal value of EI used here, and by many workers, is
the sum of the flexural rigidities of the individual
strands, which is its minimum theoretical value (EI)min
(if one neglects the strand lay angle). However, dynamically-derived values of EI are sometimes 10 to 50 times
as great (Sturm 1936; Scanlan and Swart 1968). Indeed,
in small amplitude vibration, there is practically no
interlayer slip. Thus, one would expect EI to take a
value near its maximum (EI) max , when the section
behaves as in a solid beam, plane sections remaining
plane. However, microslip does occur at points of contact. Besides, elastic tangential compliance at these
points also plays a role in lowering the flexural rigidity
(Hardy and Leblond 2003). Thus (EI) max is never
obtained.
In view of these departures from reality, there is a surprising degree of correlation between measurement and
prediction. For example, Figure 3.2-11 shows the alternating stress determined by strain-gage measurement
versus fy max from a series of tests of 1/0 ACSR performed at Alcoa Laboratories (Alcoa 1979). The conductor was supported in a square-faced aluminum
bushing. The measurements cover tensions of 15%,
25%, and 35% of rated conductor strength, and frequencies ranging from 10 to about 115 Hz. There is a clear
one-to-one correspondence between σa and fymax. The
factor of proportionality is 0.147 MPa per mm/s, which
compares well with the calculated value of 0.171. The
ratio of measured to calculated σa/fymax is 0.86.
3-12
Similar measurements on multilayer conductors show
some scatter in this ratio, but the scatter is small, considering the crudeness of the assumptions noted above.
Table 3.2-1 shows this ratio for several published series
of measurements.
In the tests by Helms (1964), the clamp was allowed to
rock, and an effective bending angle, corresponding to
the sum of β and the angle of rocking, was reported.
For Table 3.2-1, this angle was treated as β in Equation
3.2-6 to obtain the equivalent fymax.
Good correlation is also found between measured σa
and that calculated on the basis of bending amplitude
Yb using Equation 3.2-15. Comparison between theory
and experiment found in the experiments of Poffenberger and Swart (Poffenberger and Swart 1965) is
shown in Figure 3.2-12, in which solid points pertain to
high conductor tensions, and open points to low tensions. Agreement is excellent, with measured stresses
generally being slightly smaller than predicted by theory, except for one “wild” point. However, in a separate
series of measurements, Claren and Diana (Claren and
Diana 1969) obtained experimentally-determined
stresses averaging 30% higher than predicted by Equation 3.2-15, with the total range, found in tests on 13
combinations of conductor size and tension, running
Figure 3.2-11 Dynamic bending stress based on
strain-gage measurement as function of fymax. 1/0
ACSR (6/1) supported by square-faced bushing.
Tensions 15%, 25%, and 35% of rated strength.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 3: Fatigue of Overhead Conductors
Table 3.2-1 Ratio of Measured to Calculated Values of σa/fymax
References
Conductor
Diameter
(mm)
Type
Stranding
Clamp
σ a ⎛ Meas. ⎞
⎜
⎟
fy max ⎝ Calc. ⎠
Hard 1958
28.14
ACSR
26/7
Susp.
0.43
Seppä 1969
28.14
ACSR
26/7
Sq. Bushing
1.00
Helms 1964
28.0
AACSR
28/19
Deadend
0.43
Claren and Diana 1969
30.45
ACSR
18/19
Sq. Bushing
0.61
30.45
ACSR
18/19
Sq. Bushing
0.65
30.51
ACSR
42/7
Sq. Bushing
0.59
31.5
ACSR
54/19
Sq. Bushing
0.76
31.5
AACSR
54/19
Sq. Bushing
0.51
35.0
ACSR
42/7
Sq. Bushing
0.78
understood as equivalent to being a life of 500 Mc without a strand failure. These are expressed in the respective sections as fymax and as Yb.
The data of these two sections pertain to unarmored
conductor. In Section 3.2.7, data from fatigue tests of
armored conductor are presented. These data indicate
that the relationship between fatigue life and bending
amplitude is not greatly changed by the presence of
armor rods. It is suggested that bending amplitude
endurance limits for unarmored conductor be applied
where armor rods are present.
Figure 3.2-12 Comparison of theory and
measurement for Poffenberger-Swart Formula
(Poffenberger and Swart 1965).
from 14% low to 73% high. They also found that strain
measurements varied a lot from one wire to the other. In
either event, correlation with experiments is rather good
considering the assumptions under which theoretical
stress is calculated, and because of these assumptions,
the calculated stress level should be considered as an indicator of conductor vibration severity rather than the
actual dynamic bending stress in the strands.
3.2.4
Use of Conductor Fatigue Test Data
The two following sections present data from fatigue
tests of various conductors in the form of σa-N curves,
in which σa is calculated from free-loop amplitude,
using Equation 3.2-14 in Section 3.2.5 and on the basis
of bending amplitude using Equation 3.2-15, in Section
3.2.6. In both sections, the σa-N curves are used to estimate endurance limits in terms of σa, applicable to certain ranges of conductors. These endurance limits are
then used to calculate the corresponding amplitudes
that can be endured “indefinitely,” which is usually
The results of Section 3.2.5, based on fymax as the measure of vibration, cannot be directly applied in determining whether the vibration of a particular field span is
safe, since one of the assumptions underlying Equation
3.2-14 is that the clamp is rigidly supported, and this is
seldom the case in the field. That assumption is not
inherent in Equation 3.2-15, which is keyed to bending
amplitude Yb. Furthermore, ymax is somewhat more difficult to measure on operating lines than is Yb. The curves
of Section 3.2.5 are included in spite of these limitations
because endurance limits in terms of fymax are available
for some conductor types for which endurance limits in
terms of Yb are not. These fymax endurance limits may
be converted to Yb endurance limits through laboratory
determination of the relationship between fymax and Yb
as the need arises. That determination entails a cost that
is only a very small fraction of the cost of running a new
series of fatigue tests. One should also note that, for
some types of suspension clamps, it is difficult to determine the “last point of contact” (see Section 3.2.6) of
conductor with supporting clamp and hence the appropriate plane at 89 mm, used as a reference for the measurement of bending amplitude Yb. It is preferable to use
parameter fymax even if assumptions underlying Equation 3.2-14 are not fully met.
3-13
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
One should not combine Equations 3.2-14 and 3.2-15 to
arrive at a theoretical relationship between fymax and Yb,
to convert the fymax endurance limit because, in these
equations, bending stiffness EI is given a value a priori,
which yields different values for the maximum curvature,
using Equation 3.2-14 or 3.2-15. Ratio Yb /fymax should
be obtained experimentally for a given axial load. In fact,
it may be found that, for a given conductor, it also varies
with specimen and vibration amplitude.
As a corollary, the σa endurance limits estimated in Section 3.2.5 through use of Equation 3.2-14 should not be
used to establish Yb endurance limits through the use of
Equation 3.2-15. The values of σ a obtained from the
two equations are different surrogates for the actual
fatigue-initiating stress at the strand contacts where failures originate. The effects of the simplifying assumptions in Section 3.2.2 can be expected to cancel only if
the same equation is used to take endurance limit information out of a σa vs N curve, as was used to put fatigue
test information in.
3.2.5
Fatigue Performance Relative to fymax
Data for the fatigue curves of this section derive from
tests in which ymax was measured or could be determined
from reported information. The idealized dynamic stress
was thus calculated using Equation 3.2-14.
σ a = π dEa
m
fymax
EI
3.2-14
All of the data employed derive from laboratory vibration fatigue tests of conductors supported by rigid
clamps. The tests were run with constant amplitude.
Analysis of σa-N curves employing available data indicates several things that will be brought out in graphs
below. First, the level of tension in the conductor seems
to have little effect upon the σa-N relationship, given the
conductor and its supporting clamp. Second, the number of layers appears to have some influence upon the
σa-N relationship within broad ranges of strandings,
given the conductor material and the supporting clamp.
Third, the general σa-N relationship is relatively insensitive to clamp contour. However, no conclusion can be
drawn from this set of data with respect to the endurance limit, as no run-outs (tests with no strand breaks)
were obtained with the square-faced bushings.
In the figures that follow, the tests are grouped according to:
a. Conductor material
b. Stranding class
c. Clamp type
3-14
The cycles to failure N is intended to refer to failure of
the first strand. Even when such failure occurs inside the
conductor, several techniques are available to record it.
However, in some tests, detection of failures was made
by periodic visual inspection of the conductor outer surface, and in some tests, involving multilayer ACSR, failures were found in inner-layer strands when the
conductors were inspected upon discovery of outerlayer fatigue. The multilayer sizes in which this occurred
were 397.5 kcmil Lark ACSR (30/7), and 795 kcmil
Condor ACSR (54/7). The values of N for these sizes are
thus biased on the high side relative to failure of the first
strand. Since inner-layer failure occurred in less than
half of these tests, the amount of bias is probably less
than 2:1 (EPRI 1979).
As with all fatigue tests, the number of cycles to first
strand failure N at a given amplitude shows a wide scatter, yielding a “cloud” of data points, rather than a
“fatigue curve”. As shown in Appendix 3.2, such a curve
may be obtained through statistical analysis. Even there,
results still depend on the assumptions made with
respect to data probability distribution and regression
analysis.
Multilayer ACSR
Figures 3.2-13a and b show calculated σa versus cycles to
failure (N) for several sizes of two- and three-layer
ACSR, respectively. Two-layer data lie slightly above
those for three-layer ACSR, indicating that the connection between calculated σa and the actual fatigue-inducing stresses is different for the two types of stranding. The
conductor sizes and the clamps used are indicated. The
suspension clamps were common commercial, shortradius clamps (Figures 3.2-14 a and b), generally with 5°
tilt to simulate sag angle. The clamps identified as “BM”
were aluminum bell-mouthed clamps (Figure 3.2-14c).
In Figure 3.2-13a, the groups of points at the same
stress represent groups of tests made under identical
conditions: clamp, clamping pressure, axial load, and
sag angle. This holds true except for the set at 39 MPa.
That set (Seppä 1969), containing 15 tests, encompassed
variations in sag angle from 0° to 10° and variations in
clamp bolt torque from 0 to 54 N-m. It also included
tests with the clamp keeper removed.
As noted previously, in the tests of 397.5 kcmil Lark
ACSR (30/7) and 795 kcmil Condor ACSR (54/7), failures were detected by visual inspection, so the fatigue
lives N are biased on the high side, probably by a factor
less than 2 (EPRI 1979). In the other tests, failure was
detected by distortions of the conductor in the vicinity
of the clamp. Seppä (Seppä 1969) used strain-gages
attached to several strands to reveal the shift of tensions
among strands that follows each strand break. A
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 3: Fatigue of Overhead Conductors
Figure 3.2-13a Fatigue tests of two-layer ACSR.
Figure 3.2-13b Fatigue tests of three-layer ACSR.
3-15
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 3.2-14a Typical common commercial
short-radius suspension clamp.
Figure 3.2-14b Typical common commercial
short-radius suspension clamp.
Figure 3.2-14c Sketch of a typical aluminum bell-mouthed clamp.
method devised at Alcoa laboratories (Silva 1976) is
based on monitoring the rotation of the conductor, at
the node nearest the clamp, that rotation resulting from
loss of torque in a layer due to strand failure. Other laboratories have also used this method (EPRI 1981, Cardou et al. 1994).
Figures 3.2-13a and b indicate the scatter among identical tests and show a generally consistent pattern for the
several conductors and clamp combinations involved.
At high amplitude, for a given conductor, scatter is
rather small—lives to first strand failure being in a maximum ratio of about three, at a given amplitude. At
lower amplitudes, scatter is much larger, that ratio
reaching 25 in some cases. It also shows, for Seppä's
data at the 39 MPa stress level, a rather small influence
by the variations in clamp tilt and bolt torque. It will be
noted, however, that for data encompassing several conductors, scatter is even larger.
been obtained at amplitude σa ≈ 24 MPa, showing that
endurance limit is not far from this value. In Figure 3.213a (two-layer ACSRs), several run-outs have also been
obtained for 100 Mc tests and beyond:
• Two 500 Mc run-outs with the Drake ACSR
(GREMCA 2001, 2006a; Dalpé 1999) for σa ≈ 33
MPa
• One 400 Mc run-out with the Lark ACSR for σa ≈ 28
MPa (Alcoa 1979)
• Several 100 Mc run-outs with the Drake ACSR
(EPRI 1987; GREMCA 2001, 2006a; Dalpé 1999)
for σa in the 29 to 33 MPa range
Moreover, in the same stress range, several tests (Alcoa
1979; GREMCA 2001, 2006a; Dalpé 1999) gave first
strand failure between 20 and 300 Mc. All these results
indicate that two-layer ACSR endurance limit is in the
region of σa ≈ 30 MPa.
In Figures 3.2-13a and b, BM clamp test data are shown
with a “+” mark (first strand break). One can see that
these points, even though some points are biased on the
high side, lie markedly to the right of other data points,
thus indicating a better performance of the BM clamp
with respect to the suspension clamp. Because of the
lack of run-outs with the BM clamp (only one in the
three-layer case), no conclusion can be drawn, however,
with respect to the endurance limit.
The data from (EPRI 1979) are shown again in Figure
3.2-15, with each group of tests represented by a single
point at the logarithmic mean cycles (i.e., mean value of
the logarithm of life N) to failure. The number beside
each point is the conductor tension, in percent of rated
strength, used in the tests of that group. It is evident that
the σa-N relationship is influenced slightly, if at all, by
conductor tension.
In Figure 3.2-13b (three-layer ACSRs), three 500-Mc
run-outs (Crow ACSR) (GREMCA 2002, 2005a) have
Figure 3.2-16 shows results of fatigue tests in which
square-faced aluminum or steel bushings were used as
clamps. The points for suspension and bell-mouthed
3-16
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 3: Fatigue of Overhead Conductors
Figure 3.2-15 Fatigue tests of multilayer ACSR. 68 tests represented. σa calculated
from Equation 3.2-14. Numbers indicate tension in percent of rated strength.
Figure 3.2-16 Fatigue tests of multilayer ACSR. σa calculated from Equation 3.2-14.
3-17
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
clamps are included in the figure for comparison. The
conductors that were tested in the square-faced bushings were as shown in Table 3.2-2.
with short, medium, and large exit radius—indicate
some influence of that radius.
Nevertheless, considering:
Tensions ranged from 18 to 63% of rated strength.
A small but consistent difference between the two
groups of data is evident in Figure 3.2-16. The stress
required to cause failure at a given number of cycles is
slightly less with the square-faced aluminum bushings.
In addition, one “sport” occurred at a stress of 28 MPa,
failing at about one Mc. At levels down to 28 MPa, Figure 3.2-16 indicates that clamp characteristics have relatively small influence upon the σa versus N relationship.
However, although suspension and BM clamps show an
endurance limit around 26 MPa, no such conclusion
can be drawn for square-faced bushings for lack of data
points. Other preliminary fatigue tests reported in
(EPRI 1987), using three generic suspension clamps—
Table 3.2-2 Conductors in Square-Faced Bushings
Size
Bushing Material
References
397.5 kcmil 30/7
Aluminum
Alcoa 1979
477 kcmil 30/7
Aluminum
Alcoa 1979
566.5 kcmil 26/7
Aluminum
Alcoa 1979
795 kcmil 30/19
Aluminum
Alcoa 1979
795 kcmil 54/7
Aluminum
Alcoa 1979
1780 kcmil 84/19
Steel
Hondalus 1964
• the practical case of suspension and BM clamps,
• that fatigue data from two-layer ACSR tests do not
show a clear endurance limit value,
• that no data are available for four-layer ACSR,
it is suggested that the three-layer endurance limit of
22 MPa be taken (Figure 3.2-13b) for multilayer ACSR
when calculated on the basis of Equation 3.2-14.
Single-Layer ACSR
Figure 3.2-17 presents fatigue data (Alcoa 1979) for
single-layer ACSR—i.e., the 6/1 and 7/1 strandings,
supported in bell-mouthed clamps and suspension
clamps. The sizes tested in bell-mouthed clamps were
No. 4 (6/1), No. 4 (7/1), and 3/0 (6/1). Log mean (i.e.,
mean value of the logarithm of life N) cycles to failure
are shown for groups of identical tests. Tensions ranged
from 20% to 70% of rated strength. Only 1/0 ACSR
(6/1) was tested in suspension clamps, and the tension in
those tests was 25% of rated strength. For the 1/0
ACSR, a point is shown for each individual test. As in
the tests of multilayer ACSR, the bell-mouthed clamps
were well-fitted to the conductors involved, and the
clamp exits were generously radiused. The suspension
Figure 3.2-17 Fatigue tests of single-layer ACSR in bell-mouthed or suspension clamps
σa. calculated from Equation 3.2-14.
3-18
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
clamp used with the 1/0 ACSR was not well-fitting. Its
seat was designed to accommodate conductors up to
18.3 mm in diameter, substantially larger than the
10.1 mm diameter of 1/0 ACSR. Clamping pressure
caused noticeable distortion of the conductor strands.
It is evident from Figure 3.2-17 that all of the data are
encompassed by a single σa-N relationship, and a curve
has been drawn to represent it. It can be used to compare these single-layer test data with two-layer (Figure
3.2-13a) and three-layer (Figure 3.2-13b) data. It is seen
to lie slightly above those for two-layer ACSR, and
markedly above those for three-layer ACSR, again indicating that the connection between calculated and the
actual fatigue-inducing stresses is different for different
types of stranding. The 22 MPa endurance limit, which
has already been suggested for the two and three-layer
ACSR, can thus be considered as a conservative value
when applied to single-layer ACSR .
Chapter 3: Fatigue of Overhead Conductors
Figure 3.2-18 compares the curve of Figure 3.2-17 with
results of several tests of single-layer ACSR supported
in square-faced bushings (Alcoa 1979). The conductor
sizes represented are those in Figure 3.2-17 (open circles), plus a special 28.6 mm diameter 6/1 ACSR (open
triangle). Use of square-faced clamps with single-layer
ACSR markedly shortened fatigue life in a number of
tests, especially those with the lower levels of σa.
Aluminum and Aluminum Alloy Conductors
Little data are available on stranded aluminum conductors of conductor-grade metal (1350 alloy), from tests in
which failure of the first strand, or first few strands were
detected. What data there are correlate best with the
multilayer ACSR pattern of Figures 3.2-13a and b, even
though they pertain to a seven-strand conductor. Multilayer all-aluminum conductors would be expected to
follow the same multilayer ACSR pattern. Thus, it
seems reasonable to assign the same σa endurance limit
to all stranded aluminum conductors: 22 MPa.
Figure 3.2-18 Fatigue tests of single-layer ACSR in square-faced bushings σa. calculated from
Equation 3.2-14.
3-19
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
smaller concentrations. Available data on these two
types are collected in Figure 3.2-20. For comparison, a
curve is drawn in Figure 3.2-20; it represents the mean
curve passing through the ACSR multilayered data (BM
and suspension clamps and square-faced bushings),
shown in Figure 3.2-16. All points represent individual
tests. The data for 7-strand 6201 alloy conductor indicate greater dispersion in fatigue behavior than found in
other conductor types, and a lower endurance limit, than
for ACSR or 5005 alloy conductor. Only a rough estimate of that endurance limit is possible. Taking a margin
of safety, a value of 15 MPa (2.2 ksi) is suggested.
Aluminum alloy 5005 has been used to a limited extent
in overhead conductors. Fatigue data on multilayer 5005
suitable for construction of a σa-N curve are not available. However, conductor fatigue tests comparing severity of damage after equal numbers of cycles of vibration
indicated little difference between 61-strand 5005 alloy
conductor and 1780 kcmil ACSR 84/19 of about equal
diameter (Hondalus 1964). This result is consistent with
vibration fatigue test data (Alcoa 1979) on single-layer
123.3 kcmil 5005 alloy 7-strand conductor shown in
Figure 3.2-19, where the ACSR curve from Figure
3.2-17 is based on log mean N values. The tests were
made at a tension of 25% of ultimate strength, and utilized the same ill-fitting suspension clamp used in the
tests of 1/0 ACSR discussed above. It thus appears reasonable to apply the σa endurance limit for ACSR to the
5005 alloy conductor.
The data are not extensive enough to clarify whether
Aldrey and 6201 conform to the same σ a -N relationship. Nevertheless, it is suggested that the same endurance limit be applied to both.
Few data appear to be available on conductors utilizing
heat-treatable aluminum alloys such as 6201 and Aldrey.
Aldrey has the same alloying constituents as 6201, but in
Fatigue tests on an ACAR 18/19 are reported in (EPRI
1987). The controlling amplitude being Yb, first strand
failure data points cannot be included in Figure 3.2-20.
Figure 3.2-19 Fatigue tests of 5005 alloy conductor (7-strand) in suspension clamps. σa
calculated from Equation 3.2-14.
3-20
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Besides, amplitude levels are quite high and yield very
short lives, thus giving no indication on endurance limit,
which was not the objective of the tests.
Steel and Alumoweld Ground Wires
Figure 3.2-21 shows data from tests of 5/16-in.
(7.94 mm) diameter extra-high-strength galvanized steel
ground wire (Little et al. 1950), 5/16-in. (7.94 mm)
diameter aluminum-coated steel (“Beth-alume”)
(Smollinger and Siter 1965), and 7 No. 8 Alumoweld
(Alcoa 1979). The ground wires were supported in standard suspension clamps in all cases.
The σa endurance limit for the EHS steel appears to be
about 192 MPa (28 ksi). It is of interest that shorter
fatigue life would be inferred for lower tension, based
upon Figure 3.2-21, for equal values of σa as calculated
by means of Equation 3.2-14. The difference is not great
enough to justify assignment of different σa endurance
limits for different tensions, however.
The points representing aluminum-coated steel and
Alumoweld are based upon the calculated stress in the
steel component of the strand. The two groups of data
seem to conform to the same σa -N relationship when
plotted on that basis. A common σa endurance limit of
about 135 MPa (19.5 ksi) is suggested.
Chapter 3: Fatigue of Overhead Conductors
Copper, Copperweld, and Copper-Copperweld
Figure 3.2-22 summarizes results of vibration fatigue
tests (Alcoa 1979) on No. 6A Copper-Copperweld (2/1),
3 No. 12 Copperweld, 4/0 HD copper (7 strand), 1/0 F
Copper-Copperweld (6/1), and 500 kcmil MHD copper
(37 strand). Bell-mouthed clamps were used in all tests.
Test tension was 25, 30, 45, and 60% of rated strength.
In the test of No. 6A Cu/Cw, which has two copper
strands and one Copperweld strand, fatigue behavior
was largely determined by the copper strands. In a series
of 49 tests, the Copperweld strand failed first in only 6
of the tests.
The test series represented in Figure 3.2-22 did not
extend to low enough values of σa to establish knees in
the σa-N relationships, so endurance limits are difficult
to estimate. However, 35 MPa (5 ksi) is suggested for
both 3 strand and 7 and more strand groups.
Trapezoidal Wires
A few fatigue tests have been reported on trapezoidal
ACSR conductors. Sanders (1996) compares the relative
fatigue performance of two constructions of three-layer
1431 kcmil ACSR, with an Alumoweld steel core. One
was made of trapezoidal wires (Bobolink/AW/TW),
while the other was a standard round wire conductor
(Bobolink/AW). They were tested with a standard shortradius (6–in.) suspension clamp. The same fymax = 252
mm/s was imposed. According to Equation 3.2-14,
Figure 3.2-20 Fatigue tests of Aldrey and 6201 alloy conductors. σa calculated from Equation 3.2-14.
3-21
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 3.2-21 Fatigue tests of steel and Alumoweld ground wires. σa calculated from Equation 3.2-14.
Figure 3.2-22 Fatigue tests of copper, Copperweld, and Copper-Copperweld
conductors. σa calculated from Equation 3.2-14.
3-22
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
applicable to the round wire case, this corresponds to a
bending stress amplitude σa, of 47 MPa, more than
double the endurance limit. Two variations of
ACSR/AW/TW using different stranding methods were
manufactured and tested. In each case, three specimens
were tested. Strand break occurrences were recorded, up
to nine breaks. It was found that, on average, for the
imposed fymax amplitude, trapezoidal wires yielded a
better fatigue response than round ones. However, compared with data points in Figure 3.2-13b, reported average first wire breaks did occur in the expected range for
that amplitude.
Endurance Limits Expressed as fymax
In the equation used for calculating the idealized
dynamic stress (Equation 3.2-14),
σ a = π dEa
m
fymax
EI
3.2-14
the factor preceding fymax on the right is nearly constant
within each conductor type. In fact, for homogeneous
conductors of a given material in which all strands are of
equal size, the calculated ratio σ a /fy max , is constant,
regardless of the number of strands and their size. This
constancy arises from the simplified assumption that
each strand bends independently with respect to its own
neutral axis. Thus, EI is proportional to nd4, while m is
proportional to nd2, n being the number of strands, and
the ratio σa/fymax, only depends on material parameters.
For ACSR, σa/fymax ranges from 0.171 to 0.200 MPas/mm for the standard strandings, except for 7/1. That
range of variation is small within the context of the
assumptions used in deriving the equation, and of the
indirect connection between σa and the actual fatigueinducing stresses. It is therefore reasonable to represent
all ACSRs, except the 7/1 strandings, by a single value of
σa/fymax.
Table 3.2-3 lists, for various conductor types, their
σa/fymax factors and the resulting fymax endurance limits.
Note that σa pertains to the material of the conductor
surface, except in the cases of EHS steel and Alumoweld, where σa pertains to the steel component.
The endurance limits listed in the table should be
treated with a caution commensurate with the weight of
data and inference leading to them. For example, data
on Aldrey and 6201 alloy conductor are quite thin.
Also, application of the steel and Alumoweld endurance
limits to multilayer strandings rests primarily upon evidence in the ACSR data that the single- and multilayer
strandings have about the same endurance limit.
Chapter 3: Fatigue of Overhead Conductors
It should be emphasized that fymax is preferred over σa for
expressing endurance limits, since both frequency and
amplitude were measured in the fatigue tests. In contrast, the stress σa is a derived parameter.
3.2.6
Fatigue Performance Relative to Bending
Amplitude
The idealized bending stress may be calculated from
bending amplitude by means of the Poffenberger-Swart
Formula (Equation 3.2-15):
dEa p 2 / 4
σ a = − px
Yb
e − 1 + px
3.2-15
in which Yb is measured 89 mm (3.5 in.) from the last
point of contact of conductor with supporting clamp.
Since p = H / EI , the calculated σa/ Yb is a function
of conductor tension.
Data from vibration fatigue tests in which Yb was meas u re d a re ava i l abl e fo r fo u r AC S R c o n d u c t o r s
(GREMCA 2006a, 2005a, 2002, 2001, 2000b; Lévesque
2005; Dalpé 1999; EPRI 1987). Several tests of Section
3.2.5 (Multilayer ACSR and Single-layer ACSR) in
which only f and ymax were measured can also be used.
Such previously-run fatigue tests have been reconstructed and run long enough to permit measurement of
Yb, and this has made several sets of data (Alcoa 1979)
available for construction of σ a -N relationships. The
procedure introduces an additional source of scatter,
since no test can be reproduced with exactly the same
conditions.
Fatigue Characteristics of ACSR
Data are available only for ACSR in sufficient quantity
to construct σa-N curves. These data are shown in Figures 3.2-23, 3.2-24, and 3.2-25. Most data are plotted
with respect to N cycles to first strand failure, although
some data from (EPRI 1979) are plotted with respect to
log mean N. They indicate that the single-layer, twolayer, and three-layer ACSR constructions have different σa-N relationships, when σa is calculated from bending amplitudes according to Equation 3.2-15. Within
each of these groups, however, there appears to be no
significant influence of stranding upon the σa-N relationship. The tests represented in the figure had tensions
ranging from 16% to 70% of rated strength. The quality
of the correlations within each group indicates that
Equation 3.2-15 takes tension effects into account adequately.
Figure 3.2-23 (single-layer ACSRs) suggests that the single-layer endurance limit of 22.5 MPa be taken when
calculated on the basis of Equation 3.2-15.
3-23
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Table 3.2-3 Endurance Limits for Various Types of Conductors* (SI Units)
Endurance Limit
σa/fymax
σa
Conductor Type
MPa-s/mm
MPa
fymax
mm/s
All-Aluminum
0.172
22
128
All-5005 Alloy
0.172
22
128
All-Aldrey or 6201
0.172
15
87
ACSR (Except 7 / 1)
0.186
22
118
149
ACSR (7 / 1)
0.148
22
Copper (Cu)
0.409
35
86
Copperweld (Cw)
0.299
35
117
6 Cu/1 Cw
0.377
35
93
2 Cu/1 Cw
0.359
35
97
EHS Steel (Galv.)
0.499
192
385
EHS Steel (Aluminized)
0.497
135
272
Alumoweld
0.498
135
276
English Units
Endurance Limit
σa/fymax
σa
Conductor Type
ksi-s/in.
ksi
fymax
in./s
5.04
All-Aluminum
0.633
3.19
All-5005 Alloy
0.633
3.19
5.04
All-Aldrey or 6201
0.635
2.18
3.43
ACSR (Except 7 / 1)
0.687
3.19
4.65
ACSR (7 / 1)
0.544
3.19
5.87
Copper (Cu)
1.499
5.08
3.39
Copperweld (Cw)
1.102
5.08
4.61
6 Cu/l Cw
1.386
5.08
3.66
2 Cu/l Cw
1.329
5.08
3.82
EHS Steel (Galv.)
1.837
27.85
15.16
EHS Steel (Aluminized)
1.828
19.58
10.71
Alumoweld
1.802
19.58
10.87
* In these fatigue tests, conductors were supported by rigid clamps. They were common commercial short-radius suspension clamps or aluminum bell-mouthed
clamps. For more specific information about fatigue tests, refer to the subsection
corresponding to the type of conductor. Endurance limits listed in this table apply
to this type of conductor-clamp combination.
In Figure 3.2-24 (two-layer ACSRs), several run-outs
have also been obtained for 100 Mc tests and beyond:
• Two 500 Mc run-outs with the Drake ACSR
(GREMCA 2001, 2006a; Dalpé 1999) for σa ≈
19 MPa
• One 400 Mc run-out with the Lark ACSR (Alcoa
1979) for σa ≈ 13 MPa
• Several 100 Mc run-outs with the Drake ACSR
(EPRI 1987; GREMCA 2001, 2006a, Dalpé 1999)
for σa in the 22 to 26 MPa range.
Moreover, in the range of 15 to 18 MPa, several tests
(Alcoa 1979; GREMCA 2001, 2006a; Dalpé 1999) gave
first strand failure at N values exceeding 100 Mc. These
results do not permit establishing an accurate endurance
3-24
limit but tend to show that the two-layer endurance
limit is higher than the three-layer one.
In Figure 3.2-25 (three-layer ACSRs), several run-outs
have been obtained for 320 Mc and beyond:
• Three 500 Mc run-outs with the Crow ACSR
(GREMCA 2002, 2005a) for σa ≈ 13 MPa
• One 500 Mc run-out with the Tern ACSR (Alcoa
1979), for σa ≈ 12 MPa
• One 320 Mc run-out with the Rail ACSR (Alcoa
1979) for σa ≈ 10 MPa.
Moreover, in the same stress range, several tests (Alcoa
1979) gave first strand failure at N values exceeding
80 Mc. All these results indicate that the three-layer
ACSR endurance limit is in the region of σa ≈ 10 MPa.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 3: Fatigue of Overhead Conductors
Figure 3.2-23 Fatigue tests of single-layer ACSR.
Figure 3.2-24 Fatigue tests of two-layer ACSR.
Nevertheless, considering
• the practical case of suspension and BM clamps,
• the uncertainty on endurance limit for two-layer
ACSR,
• that no data are available for four-layer ACSR,
it is suggested that the three-layer endurance limit of
8.5 MPa be taken (Figure 3.2-25) for multilayer ACSR
conductors when calculated on the basis of Equation
3.2-15.
Results of a few tests performed in Poland (Josiki et al.
1976) conflict with the multilayer data of Figure 3.2-25.
3-25
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 3.2-25 Fatigue tests of three-layer ACSR.
The tested conductor was similar to a three-layer Curlew ACSR. Although the applied tensile load was not
specified, if one assumes a 25% RTS load, their three
data points would yield failure points located at about
three times the level shown in Figure 3.2-25. The cause
of this conflict is not known.
In Figures 3.2-24 and 3.2-25, it is interesting to compare
test results obtained with BM and suspension clamps. In
the two-layer case, BM endurance limit is markedly
lower than with suspension clamps. On the contrary, in
the three-layer case, BM clamps, even though some tests
are biased on the high side, yield a better finite life than
with the suspension clamps, although no difference can
be detected on the endurance limit. Such results underscore the influence of the type of clamp on conductor
fatigue strength.
Bending Amplitude Endurance Limits for ACSR
The above estimated endurance limits are convertible to
Yb by means of Equation 3.2-15. When this is done, the
Y b endurance limits turn out to fall generally in the
range 0.5 to 1.0 mm endurance limits (20 to 40 mils) for
single-layer ACSRs, and 0.2 to 0.3 mm (8 to 12 mils) for
multilayer ACSRs. In the latter case, the precision with
which the σa endurance limit can be estimated, and the
quality of correlation in the σa -N relationship, do not
justify an inference of great precision in the calculated
Yb endurance limits. This is why only two uniform conservative values of σ a = 22.5 MPa and 8.5 MPa have
3-26
been selected for single-layer, and all standard multilayer ACSRs, respectively, and the corresponding calculated Yb endurance limits are included in Table 3.2-4. If,
in a given application, a more realistic value becomes
available based on future fatigue tests, the Yb endurance
limit given in the table should be multiplied by the
appropriate factor, which is simply the ratio between the
adopted σa value and the table value (22.5 or 8.5 MPa).
Conversion of fymax to Yb Endurance Limits
As noted above, endurance limits that have been established in terms of fymax may be converted to Yb endurance limits by experimental determination in a
laboratory span of the value of Yb that corresponds to
the fymax endurance limit. This should be done at the
fymax endurance limit. It may not be sufficient to determine the ratio Yb/fymax at some arbitrary combination
of f and ymax, since Yb does not always vary linearly with
fymax.
Several determinations of this kind, resulting in the Yb
endurance limit values, are shown in Table 3.2-5 (EPRI
1979). They are considered applicable where conventional suspension clamps are employed.
Safe Border Line Method
Based on a number of experimental data sets, the Safe
Border Line method has been proposed in (CIGRE SC
22 WG 04 1979) and (CIGRE SC 22 WG 04 1988). Its
objective was to replace the corresponding (σa vs N)
fatigue curves by a single conservative line. In (CIGRE
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 3: Fatigue of Overhead Conductors
Table 3.2-4 Maximum Safe Bending Amplitudes For ACSR1
Tension in Percent of Rated Strength2
15%
Yb
25%
Yb
35%
Yb
Name
Conductor
Size (kcmils)
Stranding
mm
mils
mm
mils
mm
Turkey
#6
6/1
0.97
38.
0.79
31.
0.69
27.
Swan
4
6/1
0.92
36.
0.76
30.
0.67
26.
Swanate
4
7/1
1.01
40.
0.84
33.
0.74
29.
Sparrow
2
6/1
0.86
34.
0.73
29.
0.64
25.
Sparate
#2
7/1
0.94
37.
0.80
31.
0.71
28.
mils
Robin
#1
6/1
0.82
32.
0.70
28.
0.63
25.
Raven
# 1/0
6/1
0.79
31.
0.68
27.
0.61
24.
Quail
2/0
6/1
0.75
30.
0.66
26.
0.59
23.
Pigeon
3/0
6/1
0.71
28.
0.63
25.
0.57
22.
Penguin
# 4/0
6/1
0.67
26.
0.59
23.
0.54
21.
Waxwing
266.8
18 / 1
0.33
13.
0.28
11.
0.26
10.
Owl
266.8
6/7
0.22
9.
0.20
8.
0.18
7.
Partridge
266.8
26 / 7
0.32
12.
0.26
10.
0.23
9.
Merlin
336.4
18 / 1
0.31
12.
0.27
11.
0.24
10.
Linnet
336.4
26 / 7
0.30
12.
0.26
10.
0.23
9.
Oriole
336.4
30 / 7
0.32
13.
0.27
11.
0.24
9.
Chickadee
397.5
18 / 1
0.30
12.
0.26
10.
0.24
9.
Brant
397.5
24 / 7
0.29
11.
0.25
10.
0.22
9.
Ibis
397.5
26 / 7
0.30
12.
0.25
10.
0.22
9.
Lark
397.5
30 / 7
0.31
12.
0.26
10.
0.23
9.
Pelican
477.O
18 / 1
0.29
11.
0.25
10.
0.23
9.
Flicker
477.0
24 / 7
0.28
11.
0.24
10.
0.22
9.
Hawk
477.0
26 / 7
0.28
11.
0.24
10.
0.22
9.
Hen
477.0
30 / 7
0.30
12.
0.26
10.
0.23
9.
Osprey
556.5
18 / 1
0.27
11.
0.24
10.
0.22
9.
Parakeet
556.5
24 / 7
0.27
11.
0.24
9.
0.21
8.
Dove
556.5
26 / 7
0.28
11.
0.24
9.
0.21
8.
Eagle
556.5
30 / 7
0.29
11.
0.25
10.
0.22
9.
Peacock
605.0
24 / 7
0.27
10.
0.23
9.
0.21
8.
Squab
605.0
26 / 7
0.27
11.
0.23
9.
0.21
8.
Teal
605.0
30 / 19
0.26
10.
0.22
9
0.20
8.
Swift
636.0
36 / 1
0.32
13.
0.28
11.
0.26
10.
Kingbird
636.0
18/ 1
0.26
10.
0.24
9.
0.22
9.
Rook
636.0
24 / 7
0.26
10.
0.23
9.
0.21
8.
Grosbeak
636.0
26 / 7
0.27
11.
0.23
9.
0.21
8.
Egret
636.O
30/ 19
0.26
10.
0.22
9.
0.20
8.
8.
-
653.9
18/3
0.26
10
0.23
9.
0.21
Flamingo
666.6
24 / 7
0.26
10.
0.23
9.
0.21
8.
Gannet
666.6
26 / 7
0.26
10.
0.23
9.
0.21
8.
8.
Starling
71 5.5
26 / 7
0.26
10.
0.23
9.
0.21
Redwing
71 5.5
30/ 19
0.25
10.
0.22
9
0.20
8.
Coot
795.0
36 / 1
0.31
12.
0.27
11.
0.25
10.
Tern
795.0
45 / 7
0.30
12.
0.26
10.
0.24
9.
Cuckoo
795.0
24 1 7
0.25
10.
0.22
9.
0.20
8.
Condor
795.0
54 / 7
0.32
12.
0.27
11.
0.24
10.
1. Calculated safe bending amplitudes listed in this table are based on tests performed with common commercial
short-radius suspension clamps and aluminum bell-mouthed clamps.
2. For other tensions, interpolate between values given.
3-27
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Table 3.2-4 Maximum Safe Bending Amplitudes For ACSR1 (Continued)
Tension in Percent of Rated Strength2
15%
Yb
25%
Yb
35%
Yb
Name
Conductor
Size (kcmils)
Stranding
mm
mils
mm
mils
mm
Drake
795.0
26 / 7
0.25
10.
0.22
9.
0.20
8
Mallard
795.0
30 / 19
0.25
10.
0.21
8.
0.19
8
mils
Ruddy
900.0
45 / 7
0.30
12.
0.26
10.
0.23
9
Canary
900.0
54 / 7
0.31
12.
0.27
10.
0.24
9
Catbird
954.0
36 / 1
0.29
11.
0.26
10.
0.24
9
Rail
954.0
45 / 7
0.29
12.
0.26
10.
0.23
9
Cardinal
954.0
54 / 7
0.30
12.
0.26
10.
0.24
9
Ortolan
1033.5
45 / 7
0.29
11.
0.25
10.
0.23
9
Curlew
1033.5
54 / 7
0.30
12.
0.26
10.
0.23
9
Bluejay
1113.0
45 / 7
0.28
11.
0.25
10.
0.22
9
Finch
1113.0
54 / 19
0.28
11.
0.24
9.
0.22
9
Bunting
1192.0
45 / 7
0.28
11.
0.24
10.
0.22
9
Grackle
1192.0
54 / 19
0.27
11.
0.24
9.
0.21
8
Bittern
1272.0
45 / 7
0.27
11.
0.24
9.
0.22
9
Pheasant
1272.0
54 / 19
0.27
11.
0.24
9.
0.21
8
Dipper
1351.5
45 / 7
0.27
11.
0.24
9.
0.22
9
8
Martin
1351.0
54 / 19
0.27
11.
0.23
9.
0.21
Bobolink
1431.0
45 / 7
0.26
10.
0.23
9.
0.21
8
Plover
1431.0
54 / 19
0.26
10.
0.23
9.
0.21
8
Nuthatch
1510.5
45 / 7
0.26
10.
0.23
9.
0.21
8
Parrot
1510.5
54 / 19
0.26
10.
0.23
9.
0.21
8
Lapwing
1590.0
45 / 7
0.26
10.
0.23
9.
0.21
8
Falcon
1590.0
54 / 19
0.26
10.
0.23
9.
0.20
8
Chukar
1780.0
84 / 19
0.29
11.
0.25
10.
0.23
9
—
2034.0
72 / 7
0.28
11.
0.25
10.
0.23
9
Bluebird
2156.0
84 / 19
0.28
11.
0.24
10.
0.22
9
Kiwi
2167.0
72 / 7
0.27
11.
0.24
10.
0.22
9
Thrasher
2312.0
76 / 19
0.27
11.
0.24
9.
0.22
9
Joree
2515.0
76 / 19
0.26
10.
0.23
9.
0.21
8
1. Calculated safe bending amplitudes listed in this table are based on tests performed with common commercial
short-radius suspension clamps and aluminum bell-mouthed clamps.
2. For other tensions, interpolate between values given.
Table 3.2-5 Estimated Bending Amplitude Endurance Limits
for Various Types of Conductor
Yb Endurance Limit
Conductor
Tension
(%)
(mm)
(mils)
7 No. 8 Alumoweld
25
0.96
38
7 No. 6 Alumoweld
25
0.96
38
123.3 kcmil 5005 (7 strand)
25
0.59
23
123.3 kcmil 6201 (7 strand)
25
0.40
16
¾ in. EHS Steel (7 strand)
25
1.96
77
½ in. EHS Steel (7 strand)
25
1.67
66
SC 22 WG 04 1988), for multilayer ACSR conductors, it
was approximated by the equation system:
3-28
σ a = 450 N −0.20
for
N ≤ 1.56 × 107 cycles
σ a = 263 N −0.17
for
N > 1.56 × 107 cycles
3.2-16
where σa is in MPa and N is the number of cycles. For
single-layer ACSR conductors, a conservative Safe Border Line is given by:
σ a = 730 N −0.20
for
N ≤ 2.0 × 107 cycles
σ a = 430 N −0.17
for
N > 2.0 × 107 cycles
3.2-17
For multilayer conductors, for a 500-Mc life, the second
of Equations 3.2-16 yields a safe alternating bending
amplitude of 9.1 MPa, which is supposed to apply to
any aluminum or aluminum alloy conductor with “welldesigned clamps.” This value is not too far from the
8.5-MPa limit for multilayer conductors proposed in
Section 3.2.6 (Bending Amplitude Endurance Limits for
ACSR). For single-layer conductors, the same calculation is performed using the second of Equations 3.2-17.
For a 500-Mc life, one gets a safe alternating bending
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
amplitude of 14.3 MPa, which looks rather conservative
when compared with the 22.5 MPa limit given in Section 3.2.6.
A more rigorous comparison of (EPRI 1979) data with
the proposed Safe Border Line has been reported by
Hardy and Leblond (2001). A summary of their statistical analysis and some of their results are shown in
Appendix 3.2. Lines corresponding to a given probability of failure have been drawn. The Safe Border Line is
compared with the log mean curve (the 50% survival
curve), and with a Safe Limit line corresponding to the
95% survival curve. For multilayer conductors, they find
that the Safe Border Line is in fact closer to the log
mean curve than to the 95% curve (Figure A3.2-1). For
single-layer conductors, on the contrary, and as already
found in the 500-Mc case, the Safe Border Line is found
to be even more conservative than the 95% curve (Figure A3.2-2).
It should be emphasized that, with the Safe Border line
approach, there is no endurance limit. For example, for
1000 Mc, a safe bending amplitude would be 7.8 MPa
and 12.7 MPa for a multilayer and single-layer ACSR
conductors, respectively. However, it should be noted
that the Safe Border lines given by Equations 3.2-16 and
3.2-17 are based on fatigue tests, most of which were
quite different from those represented in Figures 3.2-23
to 3.2-25.
3.2.7
Effects of Armor Rods
Application of armor rods to conductors at tangent
supports imparts a small but useful amount of addi-
Chapter 3: Fatigue of Overhead Conductors
tional damping to vibrating spans. The original intent in
use of armor rods, however, was to reinforce the conductor against the dynamic bending caused by aeolian
vibration. Their effectiveness as reinforcements has
turned out to be small, except for small conductors, and
not consistently realized, even there. Until more comprehensive series of laboratory tests are run, the same
fymax and Yb endurance limits as determined for bare
conductors may be applied to armored conductors without serious risk of significantly overestimating or underestimating the likelihood of fatigue occurring in a
particular span.
Under laboratory conditions, substantial increases in
the number of cycles required to cause strand failure
may be achieved by application of armor rods if the test
parameter is fymax. The presence of armor rods indeed
decreases the bending deformation of the conductor
where the fretting fatigue occurs and where the amplitude Yb is measured. On the other hand, tests conducted
with Yb taken as parameter will show no significant difference between the two conditions with or without
armor rods.
This point is illustrated in Figures 3.2-26 and 3.2-27, in
which data on two- and three-layer ACSR, respectively,
with and without armor rods, are plotted. Although a
better fatigue resistance for armored conductor is evident, the fy max shows an increase no more than 15%
greater than that for unarmored conductors. In contrast, a decrease in amplitude vibration, and thus in
fymax by a factor smaller than 0.5, is sometimes achieved
Figure 3.2-26 Effect of armor rods on fatigue of two-layer ACSR (fymax basis).
3-29
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
in spans of moderate tension by application of armor
rods, through damping effects.
Figure 3.2-28 shows a corresponding plot for ACSR
having 6/1 stranding and supported in bell-mouthed or
suspension clamps (Alcoa 1979). Although use of rods
Figure 3.2-27 Effect of armor rods on fatigue of three-layer ACSR (fymax basis).
Figure 3.2-28 Effect of armor rods on fatigue of single-layer ACSR (fymax basis).
3-30
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
introduces additional scatter, which always goes in the
direction of increased fatigue life, no clear difference in
the fymax endurance limit can be observed between the
armored and unarmored cases.
Both wrench-formed and preformed rods are represented in Figures 3.2-26, 3.2-27, and 3.2-28. There
appears to be no significant difference in their effects
upon fatigue resistance for equal fymax values.
In the fatigue tests with armor rods discussed in this section, conductor strand breaks were detected by different
means. In some tests involving multilayer conductors,
failures were detected by periodically stopping each test
and unlaying the rods for visual inspection of the conductor surface. If failures were not found, the rods were
relaid and the test resumed. In the GREMCA tests
(2005b), the failures were detected using the Alcoa
method—that is, by recording conductor rotation.
In most of the tests of single-layer conductor, failures
were detected without disturbing the armor rod assembly—for example, by monitoring conductor resistance
across the supporting clamp, or by detecting the transfer
Chapter 3: Fatigue of Overhead Conductors
of tension to armor rods when a strand fails, by straingages attached to the rods.
Figure 3.2-29 presents results by Little et al. (Little et al.
1950) on effects of steel preformed armor when applied
to 5/16 in. (7.9 mm) EHS steel (7 strand). These data
indicate a small but consistent improvement in fatigue
resistance, caused by the rods. In this case, the armor
rod data do not extend to a long enough fatigue life to
show whether the fymax endurance limit with rods is significantly different from that without.
Figures 3.2-26 to 3.2-29 showed effects of armor rods
for equal values of fymax.
Those effects may also be assessed for equal values of
bending amplitude Yb. Such comparison indicates little
or no improvement in fatigue resistance through use of
armor rods. For example, Figures 3.2-30 and 3.2-31
compare armored data for two- and three-layer conductors, with unarmored data, with conductors supported
by bell-mouthed or suspension clamps. All of these sizes
have about the same Yb endurance limits without rods.
All data in Figures 3.2-30 and 3.2-31 derive from tests in
which conductor tension was between 25 and 35% of
Figure 3.2-29 Effect of armor rods on fatigue of steel conductor (fymax basis)
3-31
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 3.2-30 Effect of armor rods on fatigue of two-layer ACSR (bending amplitude basis).
Figure 3.2-31 Effect of armor rods on fatigue of three-layer ACSR (bending amplitude basis).
ultimate. There is little to distinguish the armored and
unarmored groups. Comparisons for other size groupings for which data are available gave the same indication. Unfortunately, these data are restricted to ACSR.
Calculation of σa using Equations 3.2-13 to 3.2-15 cannot be applied to armored conductor, since two regions
3-32
should be considered in the analysis, each having its own
flexural rigidity. Besides, armor rod diameter, with its
corresponding bending stiffness, should have an influence on test results. Unfortunately, there appears to have
been no systematic study of that influence. Thus fatigue
test results have to be presented in terms of Yb. It seems
logical that the same amplitude, near the clamp, will
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
induce practically the same fretting fatigue phenomena
within the conductor, with or without armor rods. It
remains to be seen if the influence of tension, which is
normalized when using σ a , will be noticeable in such
presentation.
3.2.8
clamps (i.e., saddle and keeper type, Figures 3.2-14a and
3.2-14b), as well as BM (bell-mouth) clamps (Figure
3.2-14c), under alternating stress amplitudes of σ a
(fymax) < 70 Mpa and σa (Yb) < 45 Mpa, which correspond to fy max < 400 mm/s and Y b < 1.1 mm, respectively.
Other Supporting Devices
Several special devices for supporting conductors are
available that are said to allow higher vibration levels
than do conventional suspension clamps without
fatigue. Armor-Grip suspensions, long-radius clamps,
and “Formula” clamps are among such devices. Information on maximum safe vibration levels, when these
devices are used, should be obtained from their supplier.
A review of various supporting devices has been published by Cloutier and Hardy (1987).
Although not strictly a supporting device, spacer clamps
may also be a location for conductor fatigue and strand
breaks. Some laboratory fatigue tests have been conducted to compare various clamp designs and are
reported in Section 3.4.
3.3
Chapter 3: Fatigue of Overhead Conductors
HIGH-AMPLITUDE FATIGUE TESTS
Transmission-line conductors are normally installed
under such conditions that they vibrate at levels below
their endurance limit. However, there are conditions
where conductors may experience unusual high bending
amplitudes, such as the possible time lapse between
their installation and the installation of dampers when
they are required, a hoarfrost episode, or galloping conditions. For the former case, a bare conductor without
damper installed at H/w of 2300 m may experience
bending amplitudes as high as 0.5 mm peak-to-peak
(Van Dyke et al. 1997). Regarding hoarfrost, Rawlins
(1988) pointed out that ice accretion increases the cable
diameter and, given the same frequency, aeolian power
increases to about the fourth power of diameter, with a
corresponding increase in vibration severity. Recent
measurements on a full-scale test line (Van Dyke and
Laneville 2005) have shown that during galloping
events, fymax may reach amplitudes as high as 1200
mm/s. Fortunately, such conditions seldom happen, and
the number of accumulated cycles may not be sufficient
to harm the conductors. However, the possible hazard
associated with those events must be evaluated on a statistical basis.
There is apparently very little fatigue data available at
such amplitudes. For example, Sections 3.2.5 (Fatigue
Performance Relative to fymax), 3.2.6 (Fatigue Performance Relative to Bending Amplitude) and 3.2.7 (Figures 3.2-26, 3.2-27, 3.2-30, and 3.2-31) presented results
obtained for ACSR conductors with short commercial
In order to study conductor fatigue beyond these limits,
a test program with 81 fatigue tests has been conducted
at these high amplitudes (GREMCA 2005a). Clamps,
however, were of a different kind than short commercial
and BM clamps. The test benches used were of the resonance type. Imposed amplitude reached Y b = 3.0 mm
and a corresponding fymax < 880 mm/s. The conductor
was the 48/7 Crow ACSR. Imposed tensile load was
25% RTS, with a sag angle of 5.5° (except in the case of
a spacer clamp, where it was 0°). Depending on the target amplitude, specimens were vibrated at their second,
third, or fifth mode (i.e., the mode shape consists,
respectively, in two, three, and five loops within the
active length of the specimen, see Appendix 3.1).
It should be emphasized that the objective of the test
program was not to simulate complex dynamic galloping conditions but, rather, to explore the high amplitude
range of motion of a conductor in the vicinity of a rigidly held clamp on a resonance type fatigue bench test.
It was assumed, however, as it has been eventually verified, that higher bending amplitude would induce more
slip at inner layer contact points, thus increasing the
proportion of first wire breaks occurring at inner layers.
Further studies are still needed to determine how these
results relate to the kind of damage incurred by actual
galloping conductors.
In spite of its limitations, a summary of the results
obtained from this test program may be of interest and
is given below. For conciseness, each clamp used in the
program is referred to using the following codes:
• Suspension clamp S1 (Figure 3.3-1): a short metallic
suspension clamp with two hinged shells. Internal
bore is cylindrically shaped with a small exit radius
(92 mm). It can be adjusted to fit any conductor
diameter within a given range.
• Suspension clamp S2 (Figure 3.3-2): a short metallic
clamp made of two hinged shells with a cylindrical
internal bore that is made to fit one overall diameter
assembly. The clamp has a very small exit radius
(12 mm), and it comes with preformed armor rods.
• Suspension clamp S3 (Figure 3.3-3): similar to S2,
plus elastomer cushions at the clamp exit.
• Suspension clamp S4 (Figure 3.3-4): a short bellmouth clamp, made of two hinged half-shells. It is fitted with elastomer cushions over its whole length. It
3-33
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
comes with preformed armor rods, which are
installed between the elastomer cushion and metal
half-shell.
• Spacer clamp P1 (Figure 3.3-5): a short hollow circular half-cylinder, with an elastomer lining over the
“inner” side of the cylinder. It is held in place on the
conductor with four preformed tie rods.
Fatigue test data are presented in Figures 3.3-6 and
3.3-7, giving bending vibration parameter fymax (mm/s)
vs. number of cycles to first strand break (Mc). In these
figures, each solid data point corresponds to the first
wire break in each test carried out, and data points with
right-facing arrows represent run-out tests.
Tests were perfor med on the resonance benches
described in Appendix 3.1. A clamp was installed at one
end, while the taut specimen was vibrated with an electromagnetic shaker located at the other end. A clamp was
rigidly bolted to the stiff bench framework. Therefore,
clamp translation and rotation displacements were negligible. To simulate a conductor sag angle, the clamp was
given a tilt angle of about 5.5°. Shaker frequency was
adjusted to a selected resonance frequency of the span.
Figure 3.3-1 Suspension clamp S1.
Figure 3.3-3 Suspension clamp S3.
Figure 3.3-2 Suspension clamp S2.
3-34
Figure 3.3-4 Suspension clamp S4.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Because of their cylindrical bore, the conductor may be
considered as perfectly clamped at the S1, S2, and S3 suspension clamp. For these metallic clamps, it was possible
to define a so-called last point of contact between the
clamp and the conductor. It should be noted, however,
that the last point of contact was accessible for the S1
and S2 clamps only. Accessibility to the last point of contact is necessary in order to use the Yb amplitude parameter, as it has to be measured at a distance of 89 mm from
the last point of contact. For this reason, Figure 3.3-6
Chapter 3: Fatigue of Overhead Conductors
uses the fymax vibration parameter in order to plot S1, S2,
and S3 data points in the same figure.
The situation was quite different with elastomer-lined
clamps, like S4 and P1. Because of the elastomer cushions, and also because of the P1 clamp system, perfect
clamp conditions were not met. Vibrations could occur
on the other side of the clamp, that side being where the
test specimen was anchored to the frame through a deadend clamp. Thus, a system had to be devised to hold
the conductor rigidly, at least on the dead-end side of
the clamp (see Figure 3.4-5). However, it was not possible to find a clearly defined fixed section on the vibrating span side of the clamp. In such a case, where the last
point of contact could not be found, vibration parameter fy max had to be used. Fatigue test data with the
clamps S4 and P1 are presented in Figure 3.3-7.
Furthermore, with armor rods, and for a given antinode
amplitude y max, bending amplitude near the clamp is
reduced. Thus, as mentioned in Section 3.2.7, the fymax
amplitude parameter is the appropriate parameter in
order to compare relative performance between clamps
with and without preformed armor rods.
Figure 3.3-5 Spacer clamp P1 as assembled on the
resonance bench (the conductor is rigidly held on the
right side).
The reported 81 fatigue tests generated 292 wire breaks.
Of these, 23 occurred in the S4 clamp armor rods. In all
cases, one or more fretting marks were observed at or
near the broken section. In most cases, the broken section cut across such a mark; in some cases, it originated
at the tip of the mark. In a small number of instances,
Figure 3.3-6 Fatigue strength at high amplitude vibration.
3-35
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 3.3-7 Fatigue strength at high amplitude vibration.
the broken section cut across several fretting marks; in
such cases, it may prove difficult to determine which was
the crack initiation point. In any case, such observations
confirm that, even at high amplitude, conductor fatigue
is still a fretting fatigue problem, rather than a standard
low-cycle fatigue case induced by alternating plastic
strains.
During galloping events, conductors are subjected to a
combination of bending and axial loads at the clamp.
(See Chapter 4 for data on dynamic loads during galloping.) In the present fatigue tests the axial load on a specimen also undergoes a small cyclic variation when the
specimen is vibrated. Calling Tmax , Tmin , and Tav the
maximum, minimum and average values, respectively, of
tension T, this variation amplitude (half the peak-topeak variation) may be defined percentagewise as:
Δτ = 100 × (Tmax-Tmin) / (2Tav) = 100 × (Tmax-Tmin) /
(Tmax+Tmin).
This variation occurs at twice the bending vibration frequency. When bending amplitude increases, Δτ also
increases and may have some influence on the fatigue
process. In order to quantify that effect, a series of 17
fatigue tests with the Crow ACSR conductor and the S1
clamp only were performed at the same bending amplitude Yb = 1.5 mm (fymax ≅ 440 mm/s). Two tensioning
systems were used in order to vary Δτ. The recorded
maximum value for Δτ was 10%. Results obtained from
3-36
these 17 tests did not show any correlation between the
number of cycles to first wire break and Δτ. Therefore, it
seems safe to conclude that the axial load variation
influence on fatigue test data, at least at this level, is
small and can be neglected. It is well known, however,
that field galloping conditions may induce higher alternating tension amplitudes. Generating such amplitudes,
together with the high bending amplitudes, would
require completely different fatigue test benches.
Because of the high stiffness of their bolting on the
bench frame, the S1, S2, and S3 data points are shown
in Figure 3.3-6, allowing a comparison of their respective performance. For that purpose, three straight lines
are drawn. Thirty-nine tests were run with the clamp S1.
Line S1 is based on the first breaks obtained only from
those 29 tests that correspond to an amplitude fy max
higher than 450 mm/s. Lines S2 and S3 use the nine first
wire breaks obtained from the nine tests with each
clamp. Using these straight lines, and in the fymax range
of 450 to 700 mm/s, the best performance in terms of
fatigue strength is obtained with the S3 clamp, followed
by the S2 and S1 clamps in that order.
However, it is noted that the advantage yielded by the
more elaborate design (such as shell geometry, armor
rods, elastomer cushions) of clamps S3 and S2 tends to
decrease at higher vibration amplitudes. There is indeed
a crossover between lines S1 and S2 at an amplitude
fymax of about 650 mm/s, and the figure also suggests a
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
crossover of line S1 with the projection of line S3 at
about 750 mm/s.
Test data obtained with clamps S4 and P1 are plotted in
Figure 3.3-7; it should be recalled that these clamps
present special problems because of their flexibility.
Conductor exit angle for those clamps was 5.5° and 0°,
respectively. With clamp S4, the first recorded break was
always an armor rod break, and a wire break followed
much later (a wire break usually happened as the third or
the fourth break). In Figure 3.3-7, for the clamp S4,
armor rod breaks and wire breaks are given a different
symbol. Three straight lines are shown. Line S4W is
based on the seven recorded first wire breaks (not considering the armor rods) from the ten tests carried out on
clamp S4. Line S4A is based on the ten first armor rod
breaks obtained from the ten tests. In the fymax range of
450 to 650 mm/s, one can see that lines S4A and S4W are
not parallel, indicating that the fretting fatigue on the
armor rods is less severe as fymax decreases.
Of the 14 tests performed with clamp P1, only 12 have
given wire breaks (the two remaining tests were stopped
before the first wire break). First wire breaks are shown
in Figure 3.3-7. Straight line P1 is based on these 12
breaks. These results are also shown in Section 3.4.
Chapter 3: Fatigue of Overhead Conductors
dard suspension clamps. Such extrapolation seems risky,
however, for at least two reasons:
• There is an inherent uncertainty when no experimental point is available in the extrapolation range and
nothing can be said about the precision of the results
so obtained.
• Fretting fatigue mechanisms may be quite different in
each case, depending on the type of clamp and on the
vibration amplitude.
Instead, it is believed that more tests should be done in
order to have a significant overlap between the corresponding fymax amplitude ranges and to see if these supplementary test results are consistent with the results
mentioned above.
To conclude, it should be emphasized that clamps used
in the above high-amplitude test program were of a
quite different design (geometrical characteristics and
material compliance properties), and such differences
may have a notable impact on the conductor fatigue
performance. For any other commercially available
clamp, priority should be given to information provided
by the manufacturer.
3.4
SPACER AND SPACER-DAMPER CLAMPS
Additional data (Van Dyke and Laneville 2005) are also
available from galloping tests performed on a full-scale
test line using artificial ice profiles. The test line consists
of three suspension spans and two deadend spans. In
one test, a S4 clamp was installed at one end of the central span where galloping was induced and a S1 clamp
was installed at the other end. The adjacent spans are
about of the same length for both clamps. Moreover, the
two clamps were protected against aeolian vibrations by
dampers located at each end of each span. Hence, both
clamps were exposed to the same galloping amplitudes
from the middle span as well as to the reflection of the
galloping waves from the adjacent spans. During this
test, the conductor was tensioned at 41% and 51% RTS
depending on the weight of the D profiles installed on
the conductor. During the test, the first aluminium layer
of the conductor was broken under the S1 clamp. This
portion of the conductor was then replaced, and the test
was resumed. At the end of the test, six broken wires
were found under the S1 clamp, while there was no damage under the S4 clamp, indicating a better fatigue performance of the S4 clamp over the S1 clamp.
Spacers and spacer-dampers (see Chapter 5) are fitted to
bundled conductors primarily to maintain the geometry
of the bundle and secondarily to control wind-induced
vibrations. They usually comprise a number of arms
connecting a central frame to each of the subconductors
by means of attachment devices or clamps, as they are
identified hereafter. As a rule, spacer clamps are much
less sturdy than suspension clamps. However, they may
give rise to subconductor fatigue in their close vicinity,
because the masses of the spacers can induce nodes at
these clamps if the vibration of the subconductors is
uncontrolled.
Looking at Figure 3.3-6, one may wonder if high-amplitude fatigue data could simply be extrapolated from
data at lower amplitude, such as those found in Figures
3.2-13a, 3.2-13b, 3.2-26, 3.2-27, and obtained with stan-
Resonance bench data are shown in Figure 3.4-4. Three
spacer clamp models have been tested:
In order to characterize the fatigue performance of some
specific spacer clamps, tests have been performed using
two different types of fatigue test bench. One type is a
slider-crank mechanism, in which the clamp is given a
small, calibrated cyclic motion, normal to the conductor
axis (Cardou et al. 1990). The other type is a resonance
system, such as the one described in Appendix 3.1. In
both setups, one spacer arm and its clamp are used, the
other end of the arm being bolted to the bench frame.
• The first clamp, identified as spacer clamp P1 (Figure
3.4-1), is made of a short, open circular half-cylinder
3-37
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
covered with an elastomer lining on the inner conductor side. The clamp is attached to the conductor
by means of preformed helical tie rods.
• The second clamp, identified as P2 (Figure 3.4-2), is a
conventional metal-metal clamp fitted onto the conductor with a bolted keeper (GREMCA 2000a).
• The third clamp, identified as P3 (Figure 3.4-3), is the
same as the P2 clamp, except for an elastomer lining
covering both the clamp and the bolted keeper
(GREMCA 2000a).
The conductor used with the P1 and P2 clamps was a
Crow 54/7 ACSR and for the P3 clamp, it was a Curlew
54/7 ACSR. In all cases, the sag angle was 0°, and the
tension was 25% of the rated tensile strength. With the
P1 clamp, tests were run at a frequency of about 25 Hz,
while tests with the P2 and P3 clamps were run at about
62 Hz.
As already mentioned in the previous section, it may be
difficult on the resonance system to keep those clamps
using armor rods or elastomer linings from moving
when the conductor is vibrating. In such cases, it is
almost impossible to define a fixed section. The same
problem may also occur with metal-metal spacer clamps
in the following situations:
• The clamp-arm connection is too compliant, and no
stiffener can be added without drastically modifying
the clamp behavior
• The clamp itself, and/or the keeper, are too compliant.
In order to eliminate residual vibrations on the deadend side of these clamps, the conductor is held fixed by
means of a deadend clamp, as already explained in Section 3.3 for the P1 clamp tests.
Figure 3.4-1 Spacer clamp P1 as assembled on the
resonance bench (the conductor is held rigidly on the right
side).
Figure 3.4-2 Spacer clamp P2 (without deadend
clamp).
3-38
In Figure 3.4-4, comparison of the data for the P2 and
P3 bolted clamps shows the beneficial influence of the
elastomer lining on the conductor fatigue life. As for the
P1 clamp, the test amplitudes were in the range of 440 to
770 mm/s in terms of fymax, which is above the range of
amplitudes applied to the P3 clamp. (These test results
are also shown in Figure 3.3-7 [GREMCA 2005a]).
Even if the set of points relevant to each clamp shows a
consistent trend, extrapolation of the results from one
range to another is questionable. Thus, more tests
should be carried out in order to have a significant overlap between the corresponding amplitude ranges. It
should also be noted that, in all these fatigue tests with
Figure 3.4-3 Spacer clamp P3 (without deadend
clamp).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 3: Fatigue of Overhead Conductors
Figure 3.4-5 Spacer clamp fatigue test data (resonance test bench).
the P1 and P3 clamps, except for barely visible wire
marks, no sign of degradation of the lining was
observed. In fact, no particular effort was made to characterize the changes in the elastomer lining surface conditions with respect, say, to cycling frequency. However,
and in spite of the apparent lack of degradation, a new
lining was used in each test.
The slider-crank bench data are shown in Figure 3.4-7
in terms of Yb bending amplitude, as the (fymax) parameter does not apply here. The conductor was the 48/7
Bersfort ACSR, the sag angle of conductor was 0°, and
the tension was 25% of the rated tensile strength. Tests
were run at a 10-Hz frequency. The results of four series
of tests are shown:
Figure 3.4-6 Spacer clamp P4 (without elastomer
cushions).
• In the first test series, a clamp differing slightly from
the previous P1 was used. It is identified here as P1b
(GREMCA 1988, 1989).
• The clamp used in the second test series is identified
as P4 (Figure 3.4-5); it is made of two hinged halfcylindrical shells, confining complete elastomer cushions (GREMCA 1991). The locking system between
the shells may be adjusted to yield more or less pressure on the conductor. The P4 series corresponds to a
lower pressure.
• The third test series used the same P4 clamp, but a
higher locking pressure was applied. The corresponding data are identified as P4b (GREMCA 1991).
• The fourth test series, identified as B1, uses a square-
Figure 3.4-7 Square-faced bolted aluminum bushing B1.
faced bolted aluminum bushing having a small-radius
chamfer at the exit (GREMCA 1988, 1989) (Figure
3.4-6).
3-39
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 3.4-8 Spacer clamp fatigue test data (slider-crank test bench).
From Figure 3.4-7, it is seen that clamps with an elastomer lining (P1b, P4, P4b clamps) yield a slightly better
performance than the bare-metal B1 clamp. The good
performance of the P1b clamp should be noted. However, the rather crude metal-metal B1 design could probably be improved to provide a fatigue performance
equivalent to the lined clamps. As for the elastomer lining behavior, the same remarks made above for the P2
and P3 clamps still apply, that is, practically no degradation is observed, except for small wire marks.
3.5
SPECTRUM LOADING AND CUMULATIVE
DAMAGE
Up to this point, the fatigue strength of conductorclamp systems was obtained through tests using constant amplitude cycling; Sections 3.2, 3.3, and 3.4 provide the corresponding fatigue properties for several
conductor-clamp combinations, under constant amplitudes typical of aeolian vibration and even higher
amplitudes such as those found in galloping conductors.
Such fatigue test data are shown in fatigue diagrams
similar to a material S/N diagram. Most of them indicate that there exists an endurance limit below which
wire breaks may possibly only occur at very high numbers of cycles. Since it is not practical to test for very
long lives, the endurance limit is generally based on a
500-Mc life without a wire break.
Since actual conductors undergo variable amplitude
vibrations, one may wonder how such constant amplitude tests may be of any use to assess their reliability
and “life expectancy.” Indeed vibration amplitude can
3-40
be recorded only at a few suspension clamps on a given
transmission line; it is impossible to assess the exact
vibration conditions at all suspension clamps, and thus
the true fatigue loading of that line. Using a “fictitious
line” concept, Rawlins (2004) showed how such constant amplitude test data could be applied, provided the
data are statistically sound.
To go from the constant to the variable amplitude situation, the usual approach is to use a “cumulative damage
law.” Rigorously, such a law would have to take into
account, not only the load cycle amplitudes, but also the
order—that is, the sequence—in which these cycles occur.
The simplest cumulative damage law is the PalmgrenMiner law, also referred to, for brevity, as Miner’s rule.
Assuming a conductor specimen to be subjected to k
stress amplitude levels σi, this rule consists of calculating
an equivalent damage parameter D as follows:
k
ni
i=1 N i
D=∑
3.5-1
Where
ni is number of cycles at stress amplitude σi.
Ni is number of cycles to failure if the specimen was
subjected to constant amplitude level σi; Ni is
obtained from the S/N diagram of the material
being tested
According to Miner’s rule, failure occurs when D = Df =
1 (Df being the value of D at failure), which should be
satisfied when only one load level (k = 1) is applied.
However, Miner’s rule has the following two limitations:
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
• It is independent of the cycle sequence (the load history).
• Stress levels below the endurance limit of the material
do not contribute any cycle ratio ni / Ni in the calculation of D (Ni being infinite).
Tests have shown the shortcomings of Miner’s rule
(Schütz and Heuler 2000), and many improved cumulative damage laws have been proposed (Schütz and
Heuler 2000). In spite of its limitations, Miner’s rule is
widely used because of its simplicity. Its validity for conductor fatigue has been tested to some extent. Details of
several test programs with the corresponding results can
be found in (EPRI 1987; Cardou et al. 2002; GREMCA
2002, 2006b; Goudreau et al. 2003, 2005; Lévesque
2005; and Luc 2006). Its use has also been recommended in (CIGRE 1979), where it is recognized that
the critical value Df may vary from 0.5 to 2.
3.6
TESTS AND INSPECTIONS
Four general procedures are available that are suitable for
assessing the likelihood of the occurrence of damage
from conductor fatigue serious enough to threaten the
security of a line during its economic life. The different
procedures have strengths and weaknesses that help
determine when each is appropriate. The procedures are:
•
•
•
•
Recording vibration of the line
Visual inspection of the conductor surface
Radiographic inspection
Electro-magnetic-acoustic transducers (still in development).
The need to apply one of these procedures may be indicated by certain “early warnings.”
3.6.1
Early Warnings
Several types of information can indicate that the safety
of an existing line should be questioned due to possible
damage caused by fatigue.
One source of information is past experience with lines
in the same location. If a line of similar design is located
in an area where damage has not been experienced previously, then that line is almost certainly safe. If it is in
an area where damage has been experienced, then it may
or may not be in danger, depending primarily upon
local terrain conditions, and an investigation may be
appropriate.
Another source of early-warning information is reports
by line patrols of visible vibration of the line. A line may
display amplitudes large enough to be visible even from
Chapter 3: Fatigue of Overhead Conductors
the ground, especially at the low frequencies that occur
in light winds. Mere visibility does not indicate danger
to the line. A rough measure of the potential for damage
can be obtained, however, if the frequency of the
observed vibration can be inferred from the wind velocity or from observed loop lengths, and multiplied by the
observed free loop amplitude to obtain fymax. Reference
to Table 3.2-3 can then permit a quite approximate estimate of whether dangerous amplitudes are being experienced. The fact that the fymax endurance limits of Table
3.2-3 pertain to conductors supported by rigid clamps
tends to exaggerate the estimate of danger, especially
where armor rods are the sole means of vibration protection in the line. The fact that the observed fy max is
based upon spot observations tends to cause underestimates of danger.
Evidence of possibly damaging vibration sometimes
appears in components of the line other than the conductor. Loss of cotter pins, loosening of tower bolts,
fatigue of redundant tower members, dampers slipped
from their original position, and loss of damper weights
are among warning signs. Damper weights are dropped
more often as a result of galloping or aeolian vibration
of conductors when they are covered with hoarfrost.
3.6.2
Measurement of Vibration Intensity
Testing methods described in Chapter 2 may be
employed to determine the levels of bending amplitude
that occur in a line. The estimated endurance limits
given in Section 3.2 may then be used to estimate
whether fatigue of strands in the conductor may eventually occur.
This procedure has one major advantage. It permits an
assessment of the likelihood of damage before any damage has occurred. The procedure may be applied any
time after the line is sagged and clipped. It affords the
greatest lead time during which any needed remedial
action may be decided and scheduled.
The procedure has several disadvantages. First, it may
be economically applied only at a limited number of
points in the line. There is considerable dispersion in the
vibration activity among the spans of most lines. There
is thus a risk that the most active span will not be
among those tested, and that the “weak link” in the line
will be overlooked. Judgment and experience are important in minimizing this risk.
The second disadvantage is that the wind and temperature conditions that cause the most severe vibration will
not always occur during the period of recording. For
example, in a study of a series of two-week recording
3-41
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
periods on a 230-kV line in North Dakota, Poffenberger
and Komenda found considerable variation in the maximum alternating stress σ a recorded period-to-period
(Poffenberger and Komenda 1971). The average of these
maxima over 24 two-week periods was 10.3 MPa (1.49
ksi), as calculated from Yb using Equation 3.2-15. However, the maxima ranged from 7.7 to 15.2 MPa (1.12 to
2.17 ksi) over the 24 periods, with standard deviation of
2.2 MPa (0.33 ksi). A similar evaluation reported by
Rawlins illustrates the seasonal variation of maximum
Yb during 15 successive two-week recording periods, as
shown in Figure 3.6-1 (Rawlins 1971). Judgment and
experience are required in deciding when and for how
long to conduct field measurements. The test period
should be representative of the conditions causing the
effects to be evaluated.In many instances, a measuring
period of three months is sufficient to obtain results that
are statistically meaningful. In areas where seasonal
conditions change significantly (e.g., high/low temperatures, changing ground surface due to cultivation,
snow/ice, etc.), then measurements should include these
differing conditions (CIGRE 1995).
Each of these disadvantages affects the precision
involved in comparison of actual vibration amplitude
with that which can initiate failure of a conductor. The
smaller the measured amplitude is with respect to the
estimated endurance limit, the more confidently the
future safety of the line can be viewed. Prolonged
recordings on ACSR and single-layer ground wires at
selected line locations may permit reasonable confidence
in the long-term safety of a line, when maximum
recorded amplitudes are only about 20% (EPRI 1979)
below the estimated endurance limit of ACSR given in
Section 3.2.
The other significant disadvantage of vibration measurement as a means for assessing likelihood of fatigue
failures is the limited precision of the estimated endurance limits that must be used in interpreting the measurements. That precision is probably great enough in
the case of ACSR, for example, that errors associated
with estimation of its endurance limit are small compared with those likely to arise from choice of test location in the line, or choice of test period. The confidence
that can be assigned the estimated endurance limits for
some other conductors, such as ACAR and multilayer
steel and Alumoweld, is substantially less, and that
lower confidence must reflect upon the reliability
assumed for this procedure, where those conductors are
involved.
• No cycles may exceed two times the endurance limit.
When some recorded amplitudes are above the endurance limit, the revised version of the IEEE 1966 “Standardization of Conductor Vibration Measurements”
(draft 20.0, June 2005) proposes a “widely used empirical set of criteria”:
• The bending amplitude may exceed the endurance
limit for no more than 5% of total cycles.
• No more that 1% of the cycles may exceed 1.5 times
the endurance limit.
This view is supported by the authors of (CIGRE 2006)
where it is stated that: “The evaluation of the conductor
fatigue danger based strictly on the maximum allowable
bending amplitude corresponding to the “endurance
limit” may be considered excessively cautious. In fact,
these limits can be exceeded up to a certain level and for
a limited number of times with no practical effect on the
conductor integrity. To reduce the severity of the
method, some concessions are granted.”
For other conductor types, however, some margin of
safety is appropriate. No general rules can be given.
Study of data contained in (Poffenberger and Komenda
1971; Ruhlman and Poffenberger 1957), and the data of
Section 3.2 is useful in dealing with this problem.
3.6.3
Visual Inspections
In all but a few cases, a climbing inspection is required
to detect fatigue of outer-surface strands or of armor
rods or Armor Grips. Reliability of detection for unarmored conductors is about doubled if the conductor can
be bare-handed. Fully reliable inspection requires that
the conductor be lifted from the clamp. If armor is
present, it must be laid back, after the clamp has been
removed. If the clamp cannot be removed, the keeper
should be.
Figure 3.6-1 Maximum bending amplitudes recorded
during 15 successive two-week periods. 477 kcmil ACSR
(26/7) in a 457 m span (Rawlins 1971).
3-42
Visual inspection has several advantages. First, it lends
itself to wholesale inspection of support points more
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
readily than the other procedures. Second, the condition
of the conductor reflects all of its service to date, not
merely a sample acquired during a limited recording
period. Third, it provides information that is useful in
deciding which corrective measures are appropriate,
tower-by-tower. In fact, if a repair policy has been formulated, it is often possible to carry it out concurrent
with the inspection.
There are several disadvantages. First, the cost of the
procedure is generally high, and it entails an extended
period of scheduled outages. Second, information on
the extent of damage is incomplete and somewhat speculative relative to damage to inner layers, since only the
outer layer can be thoroughly inspected.
Finally, the most useful inspections require fortuitous
timing. The period between first appearance of visible
damage and the first serious threat to the line's integrity
due to extensive damage may be viewed as an inspection
“window.” An inspection is most valuable when it falls
near the beginning of this window. If no damage is
found, reliable operation of the line extends at least for
the duration of the window. If damage is found, the full
period of the window is available for taking corrective
action.
The duration of this window is not known, but it certainly is influenced by the likelihood of core annealing
by line current, and by whether or not the conductor is
armored. It is thought to vary from two to ten times the
period of service preceding the first occurrence of
fatigue in the outer layer.
Chapter 3: Fatigue of Overhead Conductors
splice. The outer aluminum sleeve (arrow 1) should be
centered over the steel-core splice (arrow 2).
Radiographic inspections are normally conducted by
companies having special capabilities in that area. This
type of inspection has several advantages. First, it is
capable of revealing damage that would not be detected
by visual inspection: failures of inner-layer strands. As
noted in Section 3.1, inner- layer failure may precede
outer-layer failure by a substantial margin in some lines.
In those lines, use of radiographic inspection moves the
leading edge of the inspection window forward, thereby
improving the chances of early detection of danger to
the line. The opportunity to use the most economical
remedial measures is less likely to have been foreclosed
in such a case.
Another advantage of radiographic inspection is the
opportunity, in many cases, to conduct the inspection
with the line energized. Figure 3.6-3 shows such an
inspection in progress.
Figure 3.6-2 Radiograph of a conductor splice. (Courtesy
Preformed Line Products).
The actual timing of visual inspections is determined in
almost all cases by evidence that the line is experiencing
excessive levels of vibration. The evidence may be
chance discovery of damage in the line or in a similar
line, records of high bending amplitudes from a test at
some location in the line, or line crew reports of visual
observations of excessive vibration. The timing of the
inspection may be viewed as fortunate if this evidence
comes to light early in the inspection window, when
damage is still small.
3.6.4
Radiographic Inspections
Radiographic inspections (Ruhlman and Poffenberger
1957; Elton 1961; Broschat and Sherman 1967) may be
made using X-ray or gamma-ray sources, and have been
successfully conducted on energized lines (Elton and
Batiste 1965). A sample X-ray of a splice is shown in
Figure 3.6-2 (Elton 1961). The splice inspection made
on an energized line revealed an incorrectly applied
Figure 3.6-3 Radiographic inspection procedure
(Courtesy Preformed Line Products).
3-43
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Finally, as with visual inspection, the condition of the
conductor reflects all of its service, not merely that
occurring during a limited period of recording.
There are three important disadvantages. First, the cost
is too great to permit inspection of large numbers of
supports. Second, processing of films introduces a time
lag between their exposure and actual detection of damage. Unless films are processed and read in the field,
inspection and repair cannot be done concurrently.
Finally, failure detection is not completely reliable, due
to the difficulty of interpreting the radiographs. Failures
are sometimes overlooked. In other cases, films indicate
failures that, in fact, are not present.
3.6.5
Electro-magneto-acoustic Transducers
(EMAT)
Figure 3.6-4 Signature of sound waves traveling on a
conductor, with healthy strands and with broken
strands.
More recently special efforts have been focused on the
feasibility of developing portable, nondestructive monitoring and health assessment systems for live line applications.
In 1997, the Electric Power Research Institute (EPRI)
undertook the development of a device to identify broken conductor strands for Tri-State Generation and
Transmission, Electricité de France, Western Area
Power Administration, and Nebraska Public Power District. Working through a research group from the
School of Engineering and Computer Science of Denver
University (Shoureshi et al. 2004), the project constructed a prototype of the Electro-magneto-acoustic
transducer (EMAT) device. It was then tested in the laboratory under simulated environment. The concept of
the device is based on the notion that the shape of
reflected sound waves traveling downward a conductor
with healthy conductor strands is different from that
with broken conductor strands (Figure 3.6-4). Since
then, the device has been validated from extensive field
data collected from the above utilities as well as Southern Company, Tennessee Valley Authority, and New
York Power Authority. The EMAT device generates,
transmits, and receives electromagnetic waves that allow
the lineman to readily identify broken strands under a
suspension clamp while the line is energized. In addition
to detecting broken conductor strands, the technology
can be extended to detect conductor corrosion and
poorly installed conductor splices. A picture of the
EMAT device is shown in Figure 3.6-5.
A similar approach was reported by a research group of
Huazhong University of Science and Technology,
Wuhan (Rao et al. 2001). In their case the device uses
eddy currents to examine the aluminum strands and the
3-44
Figure 3.6-5 Prototype Electro-magneto-acoustic
transducer (EMAT) device for detecting broken
conductor strands.
magnetic flux leakage (MFL) to test the steel core. This
transducer also relies on signature analysis techniques
to interpret its results.
3.6.6
Discussion
Generally speaking, the above procedures are applied
only when existing evidence (or lack of it) raises a question with regard to vulnerability of a line or span to
fatigue caused by aeolian vibration. The urgency of that
evidence tends to determine which procedure is viewed
as most appropriate in any particular case. Recording
vibration amplitude is preferred when the evidence is
speculative, or when the line has been in operation for
only a short time. Radiographic inspection appears to
be favored for intermediate levels of urgency, perhaps in
response to results of vibration recordings indicating
large bending amplitudes. Visual inspection is appropriate when there is strong or specific evidence that damage
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
has occurred. Such evidence may stem from radiographic inspections or from discovery of actual damage
in the line or in a similar line.
When there is a fracture, the immediate priority is to
repair or replace the conductor, damper, or other hardware on a like-for-like basis. The broken conductor or
hardware needs to be preserved and labeled for further
inspection and analysis to interpret the failure.
3.7
REMEDIAL MEASURES
Remedial measures include repairs of damage already
experienced and changes in vibration arrangements.
Conductor damage may be repaired by addition of suitably chosen armor rods, or by cutting out the damaged
area and splicing in a segment of new conductor. In certain cases, armor rods or compression repair sleeves are
placed over damaged areas, and the conductor is shifted
several meters along the line to bring undamaged conductor into the supporting clamps.
The extent of damage that may be repaired using particular armor rod or compression sleeve devices may be
determined through enquiry directed to their suppliers.
Control of the vibration that occurs may be improved
through reductions in conductor tensions, if clearances
permit; through addition of vibration dampers; by substitution of damping spacers for non-damping types; or
by replacing conventional conductor with self-damping
conductor. Ordinarily, one of these steps must be taken
if fatigue has already been experienced, or is anticipated. Exceptions occur when the extent of damage is
small and the line is scheduled for retirement or reconductoring in a few years.
Timeliness in taking remedial action can have a strong
influence upon the cost involved, since the cost of repair
increases rapidly with the extent of damage. For example, it may be sufficient to apply or retain standard
armor rods over conductor having a few broken strands,
and to prevent continued breakage, except where cracks
have already formed, by reducing vibration levels experienced through application of dampers. Laboratory
HI-LO fatigue tests bear on this procedure (Silva 1976;
EPRI 1981; EPRI 1987), which consists in cycling at
high amplitude until one or more strand failures are
obtained, then reducing sharply the amplitude, generally below the endurance limit, and continuing the
fatigue test up to a predetermined number of cycles,
unless a maximum number of new strand failures is
observed.
Chapter 3: Fatigue of Overhead Conductors
Silva tested 795 kcmil ACSR (45/7) supported by a rigid
suspension clamp and tensioned at 26% of rated
strength (Silva 1976). In one test the conductor was
vibrated at Yb of 0.61 mm until one strand broke at 1.7
million cycles. Y b was then reduced to 0.18 mm, or
about 70% of the estimated endurance limit given in
Table 3.2-4, and vibration was continued for another
30.3 million cycles. No further failures occurred, and
none were discovered in subsequent visual inspection. In
a second test, vibration at 0.61 mm was maintained
until, at 5 million cycles, four strand failures had accumulated. Bending amplitude was then again reduced to
0.18 mm, and vibration continued for an additional 29
million cycles. Three additional strands failed after 9,
10, and 11 million additional cycles, respectively, but
none failed thereafter, nor were cracked strands discovered when the sample was dismantled. The three breaks
that occurred after amplitude was reduced are thought
to have resulted from cracks that were formed prior to
the amplitude reduction.
Similar HI-LO tests on three different ACSRs (EPRI
1981) and one ACAR (EPRI 1987) are found in the
EPRI reports yielding similar results. These tests suggest that, where damage is slight, and effective damping
can be applied, armoring of the damaged areas can be
foregone. In a majority of cases the damage is not discovered at such an early stage, and repair, in the form of
armoring, is required, along with addition or improvement of damping. In a significant number of cases, damage had progressed to the point where splicing of new
conductor is required at some supports. Attentiveness to
early warnings, and use of vibration recording appear to
be the best defense against such experience, even if their
use to obtain a complete overhead line damage evaluation is still quite limited (Rawlins 2004).
3.8
HIGHLIGHTS
• Causes of Fatigue Strand Breakages. Fatigue of conductor strands occurs at points where the conductor
is constrained against its motion. Most of the
reported cases have been related to conductor motion
due to aeolian vibrations. However, more recent work
indicates some possibility of fatigue strand breakages
in presence of galloping.
• Location of Fatigue Strand Breakages. At suspension
clamps in most cases. However, due attention must
also be given in particular to spacer, damper clamps
and to marker ball clamps.
• Evaluation of Lines. Sections of lines can be evaluated for their susceptibility to fatigue of conductors
by evaluation of the likelihood of conductor motion,
when at the design stage of the line. For lines in ser-
3-45
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
vice, vibration recorders can be installed to monitor
conductor motions in sections of a line exposed to
favorable wind conditions favorable to aeolian vibrations.
• Acceptable Limits of Conductor Motion. Several measures of vibration intensity have been employed (Section 3.2). The bending amplitude, Yb, offers the
advantage of being practical both for in situ and laboratory measurements. S/N curves (Section 3.2) and
Table 3.2-4 are available to analyze the most common cases of ACSR conductors supported in short
metallic clamps with keepers. For those cases it is
possible to establish the degree of severity of conductor motion with respect to the fatigue breakages of
conductor strands. Extrapolation of these results to
other cases must be done with caution, and the
advice of manufacturers is highly recommended.
Table 3.2-3 reviews endurance limits for various
types of conductors and ground wires, both in SI and
English units.
Laboratory results mostly relate to tests carried out
at constant amplitudes. When S/N curves are available, it is possible to determine an endurance limit
applicable to the cases studied.
On actual lines, the conductor motion is not of constant amplitude. The systematic use of the endurance
limit as the maximum value acceptable represents a
safe design choice but could imply an unnecessary
margin of overdesign. An exact and complete analysis of this aspect is yet to come. Some empirical solutions are proposed in Section 3.6.2.
• Mechanics of the Phenomenon. In order to correctly
apply the results presented in this chapter, it is important to carefully read Section 3.2.1. All fatigue breaks
of conductor strands originate at strand contacts
where fretting has occurred, implying a fretting
fatigue situation. Further analytical considerations
are presented in Chapter 2, Section 2.6.
• Detection of Fatigue Breaks on Actual Lines. Detection of fatigue breaks is an important subject for the
transmission line engineer responsible for the integrity of a line. Sections 3.6.3, 3.6.4, and 3.6.5 review
that aspect. New developments, under way, show
promise.
APPENDIX 3.1 LABORATORY DETERMINATION
OF FATIGUE ENDURANCE CAPABILITY
Background
Either at the design stage or for an evaluation of the
residual life of a line, there is a need to relate the potential level of vibration of an overhead conductor to the
likelihood of fatigue of its strands. For an endurance
assessment, as well as for an improvement of clamp
design, fatigue tests are advantageous. The exact modelling of the actual system and of the field conditions is a
complicated matter. The failures originate at interlayer
strand contacts or at contacts between the outer strands
and the line accessories where conditions for fretting are
present. The definition of a more appropriate model
than the one presently proposed (Section 3.2.2) to represent the actual phenomenon remains to be completed.
Thus, it is still necessary to note not only that fatigue
characteristics of conductors must be determined by
fatigue tests of conductors themselves (EPRI 1979), but
also that these tests should be conducted with clamps
having similar characteristics to those of the conductor/clamp system being characterized. A guide for
endurance tests of conductors inside clamps was prepared by CIGRE WG 22-04 (1985) where it is stated
that to arrive at comparable results in different laboratories an agreement on important test parameters and on
an uniform method is necessary.
Laboratory Conditions
Different systems have been developed to simulate conductor motion (Monroe and Templin 1932; Elton et al.
1959; Philips et al. 1972; Goudreau et al. 2003), each
presenting specific advantages. However, a test bench of
the resonance type imposing a conductor motion in a
vertical plane should be preferred. It is important
indeed to reproduce as closely as possible the actual situation and to be able to control the parameters evaluated in the tests. Thus only this approach will be
described in detail, applied to the case of a conductor
supported in a “standard” metallic clamp, normally a
short clamp. The limitations of that approach relate to
the ability to reproduce the actual conditions experienced by the conductor, the clamp supports, and the
range of bending amplitudes associated with the phenomenon reproduced.
Figures A3.1-1 and A3.1-2 show a typical installation of
a resonance type test bench. The active length of the
conductor specimen must be long enough—at least 5 m
between the clamp and the point of excitation—to
ensure a good distribution of the load within the strands
at the test end where the clamp is held. It is placed in a
position to reproduce the static bending angle of the
conductor. Typically, this angle is 5° to 10° for suspen-
3-46
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
sion clamps, and 0° for spacer clamps. The length of the
conductor specimen is chosen to ensure that the length
of the clamp is still small relative to the wave length
induced. The minimum distance between the clamp
under test and the back deadend of the conductor
should be at least 2 m, again to ensure an adequately
uniform load distribution in the conductor strands.
That section of the conductor experiences no motion.
Although suspension clamps in actual lines are generally free to rock, holding the clamp in a fixed position
results in a simpler test procedure, because it eliminates
the difficulties associated with the dynamic response of
a rocking clamp and the ensuing complex motion that
remains to be adequately interpreted (Cardou et al.
1990). Of course, the transverse pressure between the
clamp keeper and the conductor should be evaluated by
a proper measuring device and controlled during the
tests.
Chapter 3: Fatigue of Overhead Conductors
At the other end of the test bench, a load is applied
through some tensioning device. The load is held constant within ±2.5% during the test. The load may be
applied in different ways, such as dead weight loading
with a cantilever, hydraulic piston, or with a pneumatic
tensioning device, as shown in Figure A3.1-1. It is advisable to introduce a dynamometer to be able to continuously monitor the tension applied or to have its value
checked periodically. It also simplifies the process for
the initial setting. The tension level in the conductor
should be representative of the actual prevailing line
conditions, in order to induce a somewhat similar mean
static stress in the system (CIGRE SC22 WG04, 1985).
However, according to results reported in (EPRI 1979),
this parameter apparently has little effect on the fatigue
test data, given a conductor and its supporting clamp. It
is noteworthy to add, though, that it is a question that is
not yet settled. An attempt was made to include the conductor tension as a conductor fatigue parameter (Cardou et al. 1990). The large scatter of test results makes it
difficult to arrive at a conclusive statement. The actual
Figure A3.1-1 Resonance fatigue test bench (GREMCA 2005a).
Figure A3.1-2 Resonance Fatigue Test benches (GREMCA)
3-47
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
knowledge of the fretting phenomenon and of the conditions of contact favoring microwelds and crack initiation, however, warrants the requirement for adequate
control of a constant tension during a test campaign.
An electrodynamic shaker is a good choice as a device
to impose conductor vibration in the system because of
characteristics well suited for such tests, particularly
when they last for several months. Most tests are carried
out at constant amplitude and frequency. A frequency
in the range of 10 to 50 Hz best fits the field experience
and thus simulation of the actual field conditions. But it
is optional. However, one should avoid much higher frequencies to avoid strong possibilities of altering the
interlayer strand contact conditions responsible for the
initiation of the microcracks and their propagation leading to strand failures. Fretting fatigue is a contact phenomenon resulting in wear, as seen in the areas where
cracks are initiated. Wear produces debris, which can
modify the tribological conditions, and is a function of
the sliding velocity at the contact, and hence of the frequency of excitation. In fatigue tests it is important to
try to reproduce as closely as possible the actual conditions. Frequencies normally chosen, within that range,
are those corresponding to a resonant mode of the tautconductor system. It makes it easier to achieve constant
amplitude conductor vibration for long-duration tests.
Test Parameters
In such tests, the fatigue life of the conductor must be
determined as a function of some measure of vibration
intensity. The stresses or stress combinations that would
characterize the conditions favoring strand failures are
not easily accessible to direct measurement.
Several measures of vibration have been employed, as
previously mentioned in Section 3.2: vibration bending
angle β, dynamic strain in an outer-layer strand in the
vicinity of the clamp, free-loop amplitude of vibration
ymax, and bending amplitude Yb (amplitude of conductor motion relative to clamp at 89 mm from the last
point of conductor/clamp contact).
Bending amplitude Yb is the most widely used parameter for measurement of vibration in the field (see Chapter 2), and it is recommended to use it as well in
laboratory tests to avoid the necessity of converting this
bending amplitude into any of the other parameters.
That conversion depends strongly on the proper choice
of the bending stiffness of the actual conductor (EPRI
1979). However, it is advisable to also measure the free
loop amplitude ymax to facilitate the correlation of the
test results of conductors supported with clamps of different configuration and also to permit their use in
establishing an endurance limit for a range of conductor
3-48
sizes. However, results from tests on one conductor size
are not necessarily applicable to all the others of the
same size. Two conductors of similar size but of different geometry e.g., two layers of coarse strands as compared to three layers of finer strands, could lead to
different fatigue curves (Section 3.2, Fatigue Characteristics of ACSR).
The concept that there is some idealized strain or stress
that can be calculated from vibration amplitude and
that correlates well enough with conductor fatigue life
has given the engineer a useful tool to overcome the
complexity of the problem and find results that are reliable enough to be usefully applied.
The number of cycles to failure N generally refers to
failure of the first strand (EPRI 1979). However, in
(CIGRE SC22 WG04 1985), one reads that “three broken wires or 10% of the aluminium wires – whatever is
smaller – should be used as the damage criterion in
respect of the relationship between the stress amplitude
and the number of cycles.” In practice it is not a problem, suffice to indicate clearly to what situation one
refers to when reporting test results. Due consideration
should be given to that point when comparing results
from different laboratories.
Detection of failures by periodic visual inspection of the
conductor outer surface was made in some early tests. It
is well established that failures often occur at inner-layer
strands, so that this practice is certainly not preferred.
The strand failure detector is a solution to this problem.
A simple method developed at Alcoa Laboratories
(Silva 1976) has been extensively used (Cardou et al.
1994). It consists of a small arm attached to the conductor in order to amplify its relaxation in torsion when a
strand failure occurs. The rotational motion of the arm
is detected by any suitable sensor (LVDT [Linear Variable Differential Transformer], proximity sensor, optical
sensor), and it results in a step signal that may be associated with N, the number of cycles applied. Tests conducted until three and more strand failures have
occurred are providing much more useful information,
taking into account the inherent scatter of such test
results (Hardy and Leblond 2001).
Tests should be carried out with different values of the
vibration parameters to obtain fatigue endurance curves
(similar to the so-called S/N curves or Wöhler curves for
a material). Those curves also provide a value for the
endurance limit, an amplitude of bending below which a
particular clamp-conductor combination will endure
almost indefinitely. The endurance limit is defined, as
currently accepted for aluminum, as the highest amplitude with no break at 500 Mc. In practice a test is inter-
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
rupted when N failures are observed, it is a choice left to
the laboratory responsible of the tests as stated above,
or else when 500 Mc are reached. Because of the scatter
of fatigue data, three tests per level of vibration amplitude should be considered as a minimum, and four
amplitude levels are barely enough to define the fatigue
diagram with sufficient accuracy. A good example of a
completed S/N diagram for one “ACSR Conductor –
short metallic suspension clamp” system is represented
by the data of the ACSR Crow conductor (34 points
including five 500 Mc run-out points) in Figure 3.2-13b.
Analysis of Results
After completion of a test, the clamp region of the conductor should be submitted to a dissection process that
will permit correlating the strand failures observed with
those indicated by the strand failure detector and to
produce a map of the failures in the transverse plane as
well as in the longitudinal plane (the position of the failure relative to the clamp support). This information is
very helpful to improve our comprehension of the complex mechanism responsible for conductor fatigue. In
several instances laboratories conducting such tests will
further their analysis by a closer examination of the
interlayer strand contact area where fretting occurred.
This is particularly useful when tests are performed to
compare or improve the design of clamps and to evaluate the use of lining materials.
The most common form to present conductor fatigue
test results is the semilogarithmic fatigue endurance
curve mentioned previously as the S/N curve. It is possible to superpose, on the same graph, points indicating
the first, second, third, and k th strand failures for a
series of tests. It then shows the dispersion of the results
and certain particular anomalies when, for instance, an
early first failure occurs but is not followed by a second
one within the 500-Mc duration of the test.
To assist in the interpretation of available data on fatigue
endurance of certain conductor/clamp system, a statistical analysis (Hardy and Leblond 2001) was presented
that led to the determination of various S/N curves on a
sound probabilistic basis (see Appendix 3.2).
Fatigue Testing with Other Supporting Devices
It is indeed important to be able to use the database
available for the evaluation of the performance of “standard” metallic clamps when evaluating the performance
of special supporting devices.
The temptation to rapidly define an “equivalent” Yb is
strong but not necessarily easy. To illustrate the point, let
us consider the evaluation of the fatigue endurance characteristics of a special clamp lined with a resilient material between the clamp itself and the conductor. One can
see easily that the “last point of contact” between the
Chapter 3: Fatigue of Overhead Conductors
supporting clamp and the conductor defined to establish
a reference length (89 mm) at which one measures the
bending amplitude Yb does not exist in the way that it
was defined for the standard case of a conductor supported in a short metallic clamp. Moreover, the resilient
lining supporting the conductor is likely to affect the
profile of deformation of the conductor being flexed and
hence the conditions of fretting fatigue. The analysis of
such cases requires specific tests that will respect conditions such as the appropriate modelling of the actual situation on the line and the choice of test parameters that
could be related to the situation in the field. To compare
the performance of these special supports to the one of
standard metallic clamps, the fymax vibration parameter is
likely to be the best choice.
Some special supporting devices use armor rods, which
give a longer equivalent contact length of the conductor
with the support. This point has to be taken into consideration when designing a test bench for those devices. An
active length of 7 m was indicated as a typical value in
Figure A3.1-1. It is possible that the length of any special
support (e.g. armor rods) imposes a longer active length
to satisfy the requirement of a minimum of 5 m between
the “support” and the point of excitation at the shaker.
APPENDIX 3.2 A STATISTICAL ANALYSIS OF
FATIGUE DATA
Hardy and Leblond (2001) have presented the following
statistical analysis of conductor fatigue test data. A
detailed account of the formulas may be found in any
elementary book on statistics and, in particular, in the
(ASTM 1963) publication.
Each data point corresponds to first strand failure at Ni
cycles, the alternating stress σa,i being a PoffenbergerSwart stress calculated with Equation 3.2-14 or 3.2-15.
A mean life curve is calculated using the so-called
Strohmeyer relationship:
⎛ A⎞
σa = σd + ⎜ ⎟
⎝ N ⎠
C
A3.2-1
where σd corresponds to the endurance limit, if it exists,
and A and C are constants to be estimated. Ñ is
assumed to be the mean life at stress level σa.
Equation A3.2-1 may also be written in the form:
ln( N ) = a + b ln(σa − σd )
A3.2-2
where a = ln (A) and b = -1/C. These constants are estimated using the least squares method on a linear-log
scale.
3-49
Chapter 3: Fatigue of Overhead Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure A3.2-1 Multi-layer ACSR conductors.
It is assumed that all observed fatigue lives N i for a
given class of conductors follow a log-normal distribution centered around the predicted life Ñ1 corresponding to the applied Poffenberger-Swart stress σ a,i . The
standard deviation, s, is then given by:
∑ ⎡⎣ln( N ) − ln( N )⎤⎦
s=
i
2
i
n−2
A3.2-3
where n is the number of data points.
Safe Limit Line
At alternating stress level σa, one may determine the
number of cycles Ñα that corresponds to a probability
of failure α (5%, for example). It is given by the following expression:
ln( N α ) = a + b ln(σa − σ d ) − stα ,n − 2
A3.2-4
where the term tα,n-2 is the αth quantile in the student’s t
distribution with (n - 2) degrees of freedom.
Application
This analysis has been applied to the test data shown in
Figure 2-25 of (EPRI 1979), which correspond mostly
to the (Alcoa 1979) data of this chapter. Data for singlelayer and multiple-layer have been treated separately.
3-50
First, it has been found by Hardy and Leblond that a
best fit for Equation A3.2-1 was obtained by taking σd =
0—that is, no endurance limit. With their own published
figures, the resulting log mean curves have been redrawn
in Figure A3.2-1 (multilayer ACSR conductors) and
Figure A3.2-2 (single-layer ACSR conductors). Also
shown in each case are the 95% survival probability Safe
Limit Line, as well as the CIGRE Safe Border Line
given by Equations 3.2-16 and 3.2-17.
As noted in Section 3.2.6 (Safe Border Line Method),
for multilayer ACSR conductors, the Safe Border Line
is found to lie above the 95% Safe Limit Line. For single-layer ACSR conductors, it is found to lie well below
that line.
In order to compare with endurance limits suggested in
Section 3.2.6 (8.5 MPa for multilayer and 22. 5 MPa for
single-layer ACSR conductors), one can use the 95%
Safe Limit Lines shown in Figures A3.2-1 and A3.2-2
for a 500-Mc life. They yield 6.5 MPa and 20.2 MPa,
respectively. On the other hand, the 95% Safe Limit
Lines intersect the 8.5 MPa and 22.5 MPa levels at
about 125 Mc and 245 Mc, respectively. Thus, if it is
considered that these Safe Limit Lines are too conservative at longer lives, it could be considered to replace
them with composite lines having a horizontal plateau
beyond these values of N.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 3: Fatigue of Overhead Conductors
Figure A3.2-2 Single-layer ACSR conductors.
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Scanlan, R. H. and R. L. Swart. 1968. “Bending Stiffness and Strain in Stranded Cables.” IEEE Conference
Paper C68 43-PWR.
Philips, W., W. Carshem, and W. Buckner. 1972. “The
Endurance Capability of Single and Bundle Transmission Line Conductors an its Evaluation.” CIGRE
WG22.04 Report 22.05. Paris, France. August. 18 pages.
Schütz, W. and P. Heuler. 2000. “Miner’s Rule Revisited.” Jahrg. 42, 6, MP Materialprüfung, pp. 245-252.
Poffenberger, J. C. and R. A. Komenda. 1971. “LongTerm Vibration Study with the Live-Line Recorder.”
IEEE Conference Paper C71 159-PWR.
Poffenberger, J. C. and R. L. Swart. 1965. “Differential
Displacement and Dynamic Conductor Strain.” IEEE
Transactions on Power Apparatus & Systems, Vol. PAS84. pp. 281-289.
Rao, G. A.,Y. H. Kang, and S. Z. Yang.2001. “Inspection of High Voltage Transmission Lines Using Eddy
Current and Magnetic Flux Leakage Methods.” Insight.
Vol. 43, No. 5. pp.307-309.
Rawlins, C. B. and J. R. Harvey. 1959. “Improved Systems for Recording Conductor Vibration.” AIEE Transactions, Vol. PAS-78. pp. 1494-1500.
Rawlins, C. B. 1971. Discussion of Poffenberger, J.C.
and R. A. Komenda. 1971.
Rawlins, C. B. 1988. “Research on Vibration of Overhead Ground Wires.” IEEE Transactions on Power
Delivery. Vol. 3, No. 2. April. pp. 769-775.
Rawlins, C. B. 2004. “A Perspective on the Interpretation of Field Recordings of Overhead Conductor Vibration with Respect to Fatigue.” CIGRE SCB2-WG11TF7-04-13, 2004.
Rawlins, C. B. 2005. “Flexure of a Single-Layer Tensioned Cable at a Rigid Support.” Sixth Intl Symp. On
Cable Dynamics. Charleston, S.C.
Ruhlman, J. R. and J. C. Poffenberger. 1957. “Vibration
Destruction Testing of Transmission and Distribution
Conductors -Part I.” Pacific Coast Electrical Association Meeting. March.
Sanders, E. T. 1996. “Comparison of Vibration-related
Fatigue Performance, Vibration-related Self-damping
Performance, and Wind Energy Input of ACSR/AW
versus ACSR/AW/TW.” Wire Journal International.
May. pp. 104-112.
3-54
Seppä, T. 1969. “Effect of Various Factors on Vibration
Fatigue Life of ACSR ‘IBIS’.” CIGRE Report 22-69.
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Transmission Lines.” ASME Transactions, Journal of
Dynamic Systems, Measurement and Control. Vol 126.
June. pp. 303-308.
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Compressive Forces on the Fatigue Performance of
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237.
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EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 3: Fatigue of Overhead Conductors
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Chapter 3: Fatigue of Overhead Conductors
3-56
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
CHAPTER 4
Galloping Conductors
Jean-Louis Lilien
David Havard
Pierre Van Dyke
This chapter describes galloping of overhead conductors. It includes an overview on
the phenomenon, with information on its characteristics, types of galloping, damage
resulting from it, and causes. The chapter also covers the mechanisms of galloping
and reviews protection methods.
Professor J. L. Lilien, Ph.D., is the head of the unit Transmission and
Distribution of Electrical Energy at the Montefiore Institute of Technology, University of Liège, Belgium. He has more than 30 years experience
solving the electrical and mechanical engineering problems of power systems. His work involves analysis of problems in “cable dynamics” in general and on overhead power lines in particular. His major activities have
been devoted to: (i) vibrations on transmission lines, in particular galloping, including its control; (ii) large movements of cables, such as shortcircuit (both in substations and power lines); (iii) health monitoring of power lines (sag and
vibrations); and (iv) low-frequency electric and magnetic field effects on human beings.
Jean-Louis is a long-time active member of IEEE and CIGRE, where he has served as convenor of several task forces of CIGRE study committee B2, “Overhead Lines” and B3
“Substations.” He has published more than 100 technical papers in peer-reviewed publications. Since 1995, he has been the initiator and organizer of the CABLE DYNAMICS conference.
Dr. David Havard, president of Havard Engineering Inc., has over 45
years experience solving the mechanical and civil engineering problems
of power delivery systems. His work involves analysis of problems and
finding solutions on station structures, underground cables, overhead
distribution and transmission conductors, hardware, and structures. As
a senior research engineer in the Mechanical Research Department of
Ontario Hydro, he coordinated Ontario Hydro's assessment of older
transmission lines for the provincewide refurbishment and upgrading,
and he has worked closely with design and maintenance staff to solve problems on vibration and galloping of overhead lines.
Since establishing his own company, Dr. Havard continues to provide engineering services
to utilities on control of vibration and galloping, and testing and analysis of components
of transmission systems, as well as providing training of staff in these topics. Dave is a
long-time active member of IEEE, CEA, and CIGRÉ, where he has served as Convenor
of CIGRÉ Study B2, “Overhead Lines,” Working Group 11 “Mechanical Behaviour of
Conductors and Fittings.” Dr. Havard has authored over 190 published papers and
reports and is a Registered Professional Engineer in the Province of Ontario.
4-1
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Pierre Van Dyke received his engineering degree and his M.A.Sc. in 1983
and 1985, respectively, from École
Polytechnique de Montréal (Canada).
He completed a masters certificate in
project management at Laval University (Canada) in 2005. While working
at IREQ, he is about to complete his
Ph.D. at Sherbrooke University (Canada).
After working in the field of vibrations at the Quebec
Industrial Research Center (CRIQ), he joined, as a
researcher, the Hydro-Québec Research Institute
(IREQ) in 1990, where he is now project leader. His
fields of interest are galloping, aeolian vibrations, wakeinduced oscillations as well as conductor self-damping,
fatigue, aerodynamics, and ice accretion. He has con-
4-2
ducted many studies on a full-scale overhead test line
and a laboratory test span. He also developed the
Hydro-Quebec vibration damper and suspension
clamps that are sold throughout the world.
He is currently secretary of the CIGRE task force on
galloping and is involved in other task forces as well. He
represents Hydro-Québec on the scientific committee of
the industrial research chair on atmospheric icing of
power grid equipment (CIGELE). He has organized or
been involved in the organization of conferences related
to overhead line dynamics, he has also been invited
s p e a ke r a n d c h a i r m a n , a n d h e h a s p u b l i s h e d
30 technical papers.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
4.1
INTRODUCTION
• Numerous aerodynamic properties of conductors
Galloping of iced conductors has been a design and
operating problem since the early 1900s. The earliest
occurrences of galloping cannot be pinpointed, since a
connection between the observed low-frequency, highamplitude motions and the aerodynamic effects of ice
deposits on conductors was not recognized until the late
1920s and did not achieve general credibility until 1932,
when Den Hartog presented his classic analysis of the
mechanisms involved (Den Hartog 1932).
Since that time, numerous research programs throughout the world have been mounted, aimed at solving the
problem, and various devices and techniques have been
proposed for preventing galloping or at least minimizing
its effects. Some of these methods have been tested, and
many have been applied on operating lines with mixed
results.
Despite significant improvement in the understanding
of galloping since the first edition of this book in 1979,
no practical protection method has been developed that
is recognized as fully effective for all kinds of galloping
under any ice accretion and wind speed.
Progress, both in analytical approach to the problem
and development of countermeasures, was slow until
the 1980s, but has since received more support due to
the rapid growth of computer capability. This capability
has facilitated the rapid solution of complex systems
involved in the analysis of galloping behavior. However,
more than 75 years after the publication of Den Hartog’s analysis, important questions remain. Even when
all relevant parameters of weather and line construction
are known, there are still areas of uncertainty regarding
which mechanisms are significant in particular cases,
and validation of some parts of galloping theory is still
not fully satisfactory.
The progress that has been made has resulted from several factors:
• Quantitative data on field behavior has been collected
during a long campaign of observations, from many
test sites, and from some full-scale test spans with
natural or artificial ice, particularly in Japan and
Canada.
• International cooperation has been strongly supported inside CIGRE and IEEE,
exchanges of data between experts.
Chapter 4: Galloping Conductors
facilitating
• Analytical/numerical models have been compared to
dynamic wind tunnel tests, as well to actual observations on test lines with artificial ice of different shapes
or, more rarely, with natural icing.
with ice and wet snow have been obtained.
It has been demonstrated that any approach to galloping, in particular its analytical and numerical analysis,
has to consider a full section (from deadend to deadend
towers), inside which many different modes of galloping
may occur, with coupling between spans owing to suspension insulator movement. Tension variation during
galloping, which is a design load for both dead-end and
suspension towers, has been thoroughly investigated,
and comparisons between model and observations are
in good agreement, both as to magnitude and frequency
content. The modeling of tension variations is beyond
the scope of this book, but variations themselves are
treated in Section 4.3.4 and Appendix 4.4.
One major problem is that the varied character of ice
and wet snow deposits from one occasion or one location to another makes generalization from a few observations unreliable. Questions remain regarding how well
artificial ice sections represent natural ice, and regarding
how broadly tests with only a few artificial ice shapes
can be generalized with respect to the great variety of
natural ice shapes. But a data bank of ice shapes and
their aerodynamic characteristics has been obtained
with a large range of relative ice thickness. Their effects
have been evaluated by numerical simulation, and the
results compared with actual on-site observation of several hundred events. Moreover, some significant studies
have been performed to evaluate the processes of ice
accretion on conductors on a real span, taking into
account conductor torsional stiffness as well as the
influence of wind speed.
It is worth noting that some cases of motion similar to
galloping have been reported where ice could not be
involved. Some of these involve bundled conductor and
are most probably related to wake-induced oscillation.
These are generally of limited amplitude and with limited consequences on the line. They are discussed in
Chapter 5.
In rare cases, such as the famous ice-free galloping of
the crossing of the River Severn in England and Wales, a
yawed wind to the cable may also have induced significant amplitude at low frequencies. In this case, the
round wires of the conductor presented a slightly nonsymmetrical cross section to the oblique wind, which
caused the instability. The oscillations were suppressed
by taping the conductor, creating a smooth body.
There is no general agreement as to whether a fully reliable yet practical method for controlling galloping eventually can be found. It is extremely difficult to assess the
4-3
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
effectiveness of such countermeasures on a probabilistic
basis, because numerous observations need to be
obtained. Only one device (the eccentric mass) has
received enough study to reveal trends based on largescale results of observation. These observations could
be extrapolated to a range of devices based on similar
principles of use. It must be noted, nevertheless, that,
even for such devices, although the overall trend of performance is statistically positive, there are a few cases of
complete lack of effectiveness, even creating some galloping on treated lines in the vicinity of completely still
untreated phases. Also some devices have introduced
side effects, such as conductor damage related to unexpected strong aeolian vibrations.
Experts, today, may evaluate the efficiencies of some
antigalloping devices by simulation tools. But these
tools are complex. Simulations and other analytical
approaches are of interest to designers, because the
results can help to identify the types of behavior and
interactions that are at work in galloping. These
approaches—from analytical to finite element modeling—are aids to insight and understanding. But the
designer cannot apply them at this time.
Although there appears to be some consensus on bundle line protection methods, there is less common opinion on single-line protection methods, because the
mechanism of galloping is generally not the same.
Innovations have been made in conductor design, generally to control aeolian vibrations, but also to decrease
galloping risk, by changing conductor cross-sectional
shape, changing wire shape, or changing conductor
characteristics, such as torsional stiffness and self damping. Some of these new conductors may have some effect
on galloping, but the degree of benefit is unproven at
this time.
Galloping is observed on CATV (cable television)
cables, lashed fiber optics cables, and other types of
cables. In these cases, the ice is not necessary, since an
asymmetrical shape already exists. Some information
will be given about these cases.
Interphase spacers have been widely applied on single
and bundle overhead lines. They are designed to limit
the approach between conductors, and thereby limit
flashovers. However, they do not suppress galloping
motions, and dynamic loads and stresses can still cause
damage over time.
At present, line designers have available to them a menu
of protection schemes that differ widely in cost, effec-
4-4
tiveness, degree of evaluation, and level of usage. Several
of these schemes are discussed in some detail in Section
4.5, and described briefly in Section 4.2. None of these
schemes has been validated as fully effective; some are
known to be partly effective; some are thought to be
promising.
In sum, successful design to control galloping will
involve considerable good fortune, and it may involve
capital expenditures.
This chapter attempts to do four things:
1. Provide insight into the mechanics of galloping of
iced conductors and the factors that influence its
occurrence, type, and severity.
2. Provide an overview of galloping observation data
available.
3. Give a survey of protection methods.
4. Provide data from which new rules of antigalloping
clearance design may be developed for lines without
protection, including data on maximum amplitudes
of motion and dynamic variations of tension at both
dead-ends and suspension towers.
The chapter has six sections and eight appendices, and is
organized as follows: Section 4.2 provides an overview
on galloping, with information on its characteristics,
types of galloping motion, incidences of galloping,
damage resulting from it, the causes of galloping, and
protection methods. Section 4.3 covers the mechanisms
of galloping and the factors that influence it. Section 4.4
explores testing of galloping behavior. Section 4.5
describes protection methods. Section 4.6 provides a
summary of practical information for utility engineers.
4.2
OVERVIEW
4.2.1
Principal Characteristics of Galloping
Galloping is a low-frequency (from 0.1 to 1 Hz), largeamplitude (from ± 0.1 to ± 1 times the sag of the span,
some cases up to 4 times the sag on distribution lines),
wind-induced vibration of both single and bundle conductors, with a single or a few loops of standing waves
per span (Figure 4.2-1). It is usually caused by a moderately strong, steady crosswind acting upon an asymmetrically iced conductor surface. The large amplitudes are
generally—but not always—in a vertical plane, while
frequencies are dependent on the type of line construction and the oscillation mode excited. Winds approximately normal to the line with a speed above a few m/s
are usually required, and it cannot be assumed that
there is necessarily an upper speed limit.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
Figure 4.2-1 The three main types of power line vibration (after Orawski 1993), indicating
aeolian vibration, wake-induced oscillation and galloping, with their ranges of loop lengths
and amplitude.
Galloping has a major impact on the design of overhead
lines, both for clearances and in some cases (even if not
considered actually in most of utilities) tower load. The
clearances between conductors need to be sufficient to
limit to acceptable levels, contacts, and flashovers
between conductors, which are the most common effects
of galloping. Large, repeated load variations may occur
between phases and even between each side of a given
tower, causing horizontal and vertical bending as well as
torsional load on towers and crossarms. Due to the
repeated large amplitudes, critical loads may be reached,
causing wear and fatigue of conductor attachments, as
discussed in Section 4.2.2. Tower bolt failures have also
been observed, and wear has occurred at some locations
(yoke plate, pins of insulator, etc.), which may trigger
later more severe consequences.
Additionally, torsional motion of the phase or overhead
ground wire, single or bundle, may occur with very significant amplitude (up to bundle collapse, in some
c a s e s ) , c au s in g d a m ag e t o s p a c e rs a n d s u sp e n sion/anchoring hardware.
Types of Galloping Motion
Galloping takes one of two basic forms, standing waves
and traveling waves, or a combination of them. The
standing waves may occur with one, or as many as ten,
loops in a span. Data on observed galloping of operating lines, collected by the Galloping Task Force of EEI,
shows the distribution of loops in Table 4.2-1 (Edison
Electric Institute 1977).
Table 4.2-1 Galloping Reported Cases vs. Number of Loops
Cases Reported
No. of Loops
Phase
Grd. Wire
1
42
2
2
26
3
3
34
6
4 or more
2
1
Small numbers of loops are clearly favored.
Traveling waves are often observed in the course of
buildup of actual galloping. The waves may initially be
only tens of meters long, with amplitudes of a few centimeters. With repeated passage back and forth along the
span, they grow in length and amplitude, and eventually
interact with one another to form standing waves. If the
standing waves turn out to have a large number of loops
within the span, further traveling-wave action usually
leads to a shift to a smaller number of loops, and eventually the span settles on three or fewer loops.
On occasion, the shift from traveling waves to standing
waves does not occur, and a traveling wave with a length
of the order of one-fourth of the span length will persist
as long as wind conditions do not change. Such waves
may incorporate steep wavefronts, causing significant
dynamic loads on supports. There is one such example
in the accompanying compact disk. On other occasions,
standing-wave galloping builds up without travelingwave involvement.
4-5
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Observed peak-to-peak amplitudes of galloping are
often as great as the sag in the span and are sometimes
greater, especially in short spans. Amplitudes approaching in magnitude the sag have been observed with as
many as three loops in the span, but beyond that number, the amplitudes become smaller.
showed significant torsional motion to be present in two
out of five cases of natural galloping of single conductors that were analyzed.
Traveling-wave peak-to-peak amplitudes have magnitudes comparable to standing waves of the same
length—that is, the longest waves may have amplitudes
on the order of span sag, but the shorter waves have
smaller amplitudes.
Many such movements can be observed in the bundle
conductor galloping shown on the videos on the accompanying CD.
It must be noted here that a report of large traveling
waves by observers may be the superposition of oneand two-loop standing waves, which has a similar
appearance.
The predominant conductor motions are vertical in galloping, but there is often some horizontal component of
motion transverse to the line. The vertical and horizontal motions are often not in phase, so that a point on the
conductor near mid-loop traces an elliptical orbit. The
data collected by the EEI Task Force indicate that substantially elliptical orbits occur in about 30% of
observed cases. Figure 4.2-2 shows the percentage distribution of observed orbit shapes based upon two collections of galloping reports (Edison Electric Institute
1977; Oldacre 1949).
When galloping occurs with one loop in the span, there
may be significant movement of the conductor in the
direction of the line. Peak-to-Peak swings of the insulators on the order of 0.5 m have been observed. These
motions are most noticeable in long spans. Many observations in Japan on large bundle conductors showed
large horizontal movement. Some examples are shown
in Section 4.5.4.
Twisting motion is almost always observed during vertical galloping of bundled conductors (Anjo et al. 1974).
Incidence of Galloping
The frequency with which galloping occurs is, of course,
closely related to the frequency of icing, depicted, for
the United States, in Figure 4.2-3. Incidence is greatest
in the central region of the United States, between the
Rockies and the Appalachian Mountains, but not
including Louisiana and Arkansas and the states to the
east of them. Most utilities that experience galloping at
least annually lie in that region. Galloping also occurs
annually in parts of California. Utilities in the Northwest experience galloping about every two to five years.
Utilities in the Atlantic Seaboard States experience galloping rarely or never, except in New York and New Jersey, where galloping may occur every two to every ten
years.
Ice storms move with the frontal weather system. Little
data appear to be available on the dimensions of the
regions affected. Smith (Smith 1966) reports widths
from 40 km (25 miles) to 160 km (100 miles), and
lengths in the direction of storm movement from 160
km (100 miles) to 320 km (200 miles) in South Dakota.
The lengths of line affected by galloping vary from only
a single span to as many as 30 km (18 miles.)
Twisting motion of single conductors during galloping
is difficult to discern from the ground, but it has been
detected and measured by means of attachment of suitable targets to the span. Peak-to-peak rotations greater
than 100° have been observed, simultaneous with vertical motion. Edwards and Madeyski’s analysis (Edwards
and Madeyski 1956) of films of natural galloping
Figure 4.2-2 Percentage of observations of various
galloping ellipse shapes and tilts.
4-6
Figure 4.2-3 Total number of glaze storms observed
during the nine-year period of the Association of American
Railroads Study (Tattleman and Gringorten 1973).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
In Japan, Hokkaido Island as well as Honshu Island, on
both the west and east coasts, are very prone to galloping, as can be seen in Figure 4.2-4, showing 776 events
during the last 30 years. The frequency of galloping
events is related to major winds flowing either from the
Pacific Ocean or from the west depending on the period
of the year.
Chapter 4: Galloping Conductors
many observed during the 1998-1999 winter. There were
9 cases of galloping on single conductors, 22 cases on
twin bundle lines, and 16 events on quad bundle lines.
Germany as well as all of northern Europe is also very
prone to galloping. 570 cases were reported and collected in Germany between 1979 and 1999. Figure 4.2.5
shows the locations of the 47 galloping events in Ger-
Figure 4.2-4 Location of 776 cases of galloping reported
in Japan in the last 30 years (courtesy M. Mito).
Figure 4.2-5a Locations of 47 cases of galloping in
Germany during the 1998-1999 winter (courtesy
C. Jurdens).
Figure 4.2-5b 570 galloping cases reported in Germany during the 1980s and 1990s, classified
by year and month.
4-7
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
All these reported cases caused short circuits, and four
cases had permanent bundle collapse (through twisting).
4.2.2
are extracted from a video of a galloping event that
occurred in England in 1986 and lasted four days. The
video of this event is included on the accompanying CD.
Damage and Other Penalties
Galloping has caused various kinds of structural damage in overhead lines. Some types of damage result
directly from the large forces that galloping motion
applies to supports. For example, crossarms have failed
on wood and on metal structures. Ties on pin-type insulators have been broken. On rare occasions, support
hardware has failed. On others, cotter pins have been
damaged, permitting insulator strings to uncouple.
Repeated dynamic loads, such as the shock that occurs
when steep-fronted galloping waves are reflected at a
tower, have damaged vibration dampers, sometimes
snapping the weights off and sometimes fatiguing the
damper cables. The number of miles of line affected by
galloping in a particular storm occasionally can be surmised later from assessment of damper damage.
Dynamic loads have also caused loosening of crossarm
and fatigue of bracing bolts in tower structures (Figure
4.2-6a), and loosening of wood poles themselves in the
ground. Jumpers at deadend towers have been broken,
and sometimes tossed up on to crossarms (Figure
4.2-6b). Suspension insulator strings undergo heavy
dynamic loading, with hammering action that flattens
security clips and may permit the connection between
insulator units to unlatch (Figure 4.2-6c). These figures
The motion has been great enough in some cases to
cause broken strands in conductors, and to result in
complete failure of ground wires or even phase conductors (Figure 4.2-6d).
When galloping amplitudes are great enough to permit
flashover between phases or from phase to ground, the
resulting damage can include arcing damage to conductor surfaces and strand separation (Figure 4.2-6e).
Figure 4.2-6b Damage due to galloping on
jumpers in England (courtesy M. Tunstall).
Figure 4.2-6c Damage due to galloping
on a string of suspension insulators.
Figure 4.2-6a Damage due to galloping
on towers.
4-8
Figure 4.2-6d Damage due to galloping on a triple bundle
conductor in China.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Large-cycle fatigue damage can occur in the conductor
next to the suspension clamps. Figure 4.2-6f shows such
damage to an ACSR “Grackle” conductor, diameter
34 mm, next to the clamp of an inverted V-string, due to
galloping in the Netherlands in the 1978-1979 winter
(Leppers and Wijker 1979). The use of inverted
V-strings amplifies the dynamic bending stresses at the
clamps and accelerates the wear and fatigue processes.
The ice shape during that event has also been collected,
and is shown in Figure 4.3-4.
Chapter 4: Galloping Conductors
Such severe damage is rare, however, because faults are
usually brief, and the arcs usually travel, leaving only a
track of pock marks on the conductor surfaces
(Edwards 1970).
Forced outages caused by galloping result in loss of revenue and sometimes in other costs associated with reestablishing service. Those penalties are generally
considered to be more severe than direct damage to
lines. Published data on their magnitude do not appear
to be available, but a survey of utilities by the T&D
Committee of EEI (data courtesy of Transmission and
Distribution Committee of Edison Electric Institute)
developed the information shown in Table 4.2-2 on
effects of the worst ice and/or galloping conditions that
each utility had faced (costs in the 1970s).
Although line failures due to heavy ice loading may be
represented in Table 4.2-2, it is likely that galloping
cases predominate.
Frequency of outages caused by galloping has been
reported by few utilities. During a two-year period, the
Central Electricity Generating Board (CEGB) in the
United Kingdom experienced an outage rate of 0.24 per
100 km per year, on 132 kV and above (Lowe and Richards 1966).
Of 48 utilities reporting outages, in EEI’s collection of
galloping case, none reported phase-to-ground faults
(Edison Electric Institute 1977).
A number of utilities design lines with larger phase and
phase-to-ground wire clearances than would otherwise
be employed, in order to reduce the frequency with
which flashover occurs during galloping. The added
Figure 4.2-6e Broken strands resulting from short circuit
due to two-phase fault induced by galloping in the
Netherlands (Leppers 1981).
Figure 4.2-6f Damage to ACSR “Grackle” conductor,
diameter 34 mm, next to the clamp of an inverted V-string,
due to galloping in the Netherlands in the 1978-1979
winter (Leppers and Wijker 1979).
Figure 4.2-6g Damage to ACSR “Groningen” conductor,
diameter 22 mm, next to the suspension clamp due to
heavy galloping in the Netherlands during the 1978-1979
winter (Leppers 1979).
4-9
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Table 4.2-2 Utility Penalties Associated with Ice or
Galloping-Caused Outages
No. of Customers Affected
No. of Utilities
0-10,000
24
As a result, caution is needed in the “after-event” evaluation of the damages, so as not to decide to modify
design rules based on galloping when the true cause is
static loading.
11,000-50,000
9
51,000-100,000
3
4.2.3
More than 100,000
2
Length of Service
Interruption
No. of Utilities
1 hour or less
17
1-3 hours
9
3-6 hours
4
The Drag Force
The drag is a force induced by the wind on any structure
or conductor. It is oriented in the direction of the
wind—more exactly, in the direction of the relative wind
when the conductor is moving, as indicated in Figure
4.2-7 (See also Figure 4.2-15 and Appendix 4.1.) Fluid
forces, particularly the air pressure distribution around
the conductor, are the source of the drag force. The
static effect of the drag force is to displace the conductor
laterally until the wind force is balanced by the internal
tension in the conductor. Due to the conductor swing,
there is a tension component acting in the wind direction. The dynamic effect of the drag force is the periodic
elastic response of the conductor following variations in
wind speed and the die-down of these motions due to
the damping of the system. Any disturbance caused will
disappear after a while. That is because the drag force is
oriented in the direction of the relative wind speed,
which has a component opposite to the movement of
the conductor. There is no way, with constant drag
force, that instability can occur.
6-9 hours
5
9-12 hours
6
12-24 hours
5
1/
5
3 to
1/
2 days
4-8 days
4
9-11 days
1
Cost of Interruption
(thousands of dollars)
No. of Utilities
Less than 50
27
51-100
7
101-200
1
201-500
3
501-1000
3
4000
1
margins of clearance increase tower costs. Representative figures cited in 1966 for the additional cost were:
$8000/mile ($5000/km) for double-circuit 345 kV, and
about the same for double-circuit 230 kV in Canada
(McMurtrie 1966). Current figures for lines of similar
design are thought to be in the $40,000 to $60,000/mile
range in 2006. The difference in cost would be even
greater between conventional lines with clearances
increased because of galloping and compact lines (Barthold et al. 1973).
When forced outages due to galloping are anticipated,
extra transmission is often provided in the system to
make the outages more tolerable. This extra transmission adds to utility costs, and since the increased clearances usually employed do not eliminate all outages,
they do not entirely eliminate galloping costs (McMurtrie 1966).
Causes of Galloping: The Forces in Action
The drag force is given by the formula:
D=
1
ρ air .φ .CD .Vr2
2
C D, the drag coefficient, is in fact not a constant and
depends on the wind speed and “roughness” (k/h on
Figure 4.2-8) of the conductor surface. Moreover, if the
surface has an eccentricity due to an asymmetrical
Finally, confusion may arise in examining damages after
wind/snow events.
It is particularly difficult to allocate all of the damages
to one particu lar cau se, like galloping. Indeed
wind/snow events may also induce many other dangerous phenomena that have no relation with galloping.
For example, ice shedding and static wind loads are also
dramatic causes of ruptures in power lines.
4-10
4.2-1
Where
ρ a i r i s t h e d e n s i t y o f a i r ( ab o u t 1 . 2 k g / m 3
[0.075 lb/ft3] at standard conditions of temperature and pressure.
φ is the conductor diameter.
Vr is the relative wind speed.
Figure 4.2-7 Wind force on bare conductor.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
Once asymmetry exists, a new parameter has to be
defined—namely, the angle of attack. The angle of
attack is the angle between the relative wind speed direction and the direction of the asymmetry, generally taken
as a straight line joining the bare conductor axis and the
center of gravity of the ice coating. This is illustrated in
Figure 4.2-10 and designated by ϕ (More details are in
Appendix 4.3—e.g., Equation A4.3-2).
Figure 4.2-8 Variation of coefficient of Drag (CD) vs.
Reynolds number (Re) for smooth and classical stranded
conductors, compared to a pure cylinder. To the right, the
conductors’ cross-sections are shown. Bottom scale:
Equivalent wind speed, U, corresponds to conductor
diameter about 31 mm. For Aero-Z conductor k/h ~ 0.005,
and for Aster k/h ~ 0.02. Aero-Z: 31.5 mm and Aster: 31.05
mm (courtesy Nexans and EDF).
deposit (e.g., ice), C D will become dependent of the
angle of attack, which would refer to ice position relative to the wind direction (see Figure 4.2-10).
The Lift Force and the Pitching Moment
For galloping to occur, the conductor must be subjected
to more than just the drag force, which is a purely dissipative force at wind speeds encountered during galloping.
As soon as an asymmetric coating is present on a conductor and wind is blowing, lift and drag forces exist.
These two aerodynamic forces are effectively applied on
a point inside the conductor, which is called “aerodynamic center,” and which is not the center of the conductor (Figure 4.3-19). To facilitate the understanding,
measurements, and modeling, the shift of the application point of these forces is replaced by the same forces
applied on the axis of the conductor plus an additional
pitching moment. In Figures 4.2-9 a, b, and c, this
pitching moment is zero, clockwise, and anticlockwise
respectively.
Wind tunnel measurements are used to determine these
three components of the wind action on asymmetrical
shapes, giving curves such as those shown in Figure
4.2-10. There are then three aerodynamic coefficients
that all depend on the angle of attack.
There is also an aerodynamic lift force, which would be
able to create, in some particular conditions, negative
damping of the conductor motion. The lift force is generated by wind acting on an asymmetrical profile of the
conductor.
Figure 4.2-9 Lift and drag on iced conductor. Lift is a
force perpendicular to the wind direction, which may be
zero (a), negative (b), or positive (c), depending on ice
position.
Figure 4.2-10 Typical aerodynamic coefficients for a
conductor with an asymmetric ice accretion. Crescentshaped ice thickness 1.1 cm over a subconductor
diameter of 32.4 mm. Lift positive upwards; Pitching
moment and torsional angle positive anticlockwise. Zero
angle of attack when the ice is facing the wind and in the
horizontal position. The symmetry with angle of attack is
not perfect as the curves have been measured on a real
ice shape, which was not exactly symmetrical. In this
case all coefficients have values of the same sign as a
typical air-foil near zero angle of attack.
4-11
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
The two forces and the pitching aerodynamic moment
(all per unit of length) have been obtained by similarity
laws to be expressed as follows:
D=
1
ρ air .φ .Vr2 .CD (ϕ )
2
1
ρ air .φ .Vr2 .CL (ϕ )
2
1
M = ρ air .φ 2 .Vr2 .CM (ϕ )
2
L=
4.2-2
(Notice the square exponent of the conductor diameter
on the pitching moment.)
These definitions of aerodynamic forces and moment
are for single conductors. In the case of bundle conductors, it is generally considered that the values for the
bundle as a whole are simply the same formula multiplied by the number of subconductors. (Some screening,
due to wake effects, occurs in practice, and ice may not
be the same on each subconductor, but the proposed
approach is conservative and easy to manage.)
Figure 4.2-10 shows the variation of CD, CL, and CM, for
a particular ice shape, plotted against ϕ, the angle of
attack. The typical amplitudes of these wind actions on
power line conductors are, for a wind speed of 10 m/s
and a conductor diameter of 30 mm:
4.2.4
Causes of Galloping: How the Wind May
Transfer its Energy to Vertical Movement?
On-site wind speed is rarely constant, and constant wind
speed is not needed for galloping. Figure 4.2-11 shows
the wind speed component perpendicular to the line
from measurements during one galloping event on an
actual 400-kV line in the Ardennes in Belgium in February 1997. The galloping observed was a typical occurrence with large vertical amplitude, and was recorded
under 25% turbulent wind.
Galloping occurred with amplitudes around 6 m peakto-peak, in a single loop on a dead-end span, at around
710 minutes and another significant event occurred
around 830 minutes. The temperature was close to 0°C,
and the precipitation was freezing rain with strong wind.
One of the two events, for which only tension recordings
were available, has been reconstructed as shown in Figure 4.2-12. Tension variations up to 25 kN peak-to-peak
were recorded.
Based on the quasi-steady theory of fluids, and many
observations and simulations, it can be concluded that
turbulence level has limited influence on galloping. Galloping may easily occur during moderate to high winds,
irrespective of turbulence level. The ten-minute mean
wind speed is a good reference wind to evaluate galloping amplitude under steady conditions. (It must be
D = 2 to 3 N/m,
L = 0 to 1 N/m and
M = 0 to 0.03 N.m/m.
It is surprising that these small forces and moments are
able to generate the huge amplitudes observed during
galloping. The large motions are due to the very small
internal self-damping of conductors at the frequencies of
galloping, and that the aerodynamic forces, owing to
their derivatives (see Section 4.3.1 and Appendix 4.3),
will be able to change the system damping to negative
values. Under those conditions, energy can be transferred from the wind at each cycle of oscillation, thus
increasing progressively the amplitude to a maximum
level. Nonlinearities in the aerodynamic coefficients govern this maximum amplitude because the negative damping is effective over a limited range of angle of attack.
These aerodynamic coefficients of lift and drag are more
or less independent of wind speed in the range of Reynolds number for overhead power lines (this is less true
for pitching moment). These coefficients are considered
to be in the subcritical range of Reynolds number, where
the drag would have been constant on a bare conductor.
4-12
Figure 4.2-11 Mean wind speed in m/s measured at the
line location and appropriate height during all the day of
February 13, 1997. Abscissa is time in minutes.
Recordings at one-minute intervals. Turbulence was
quasi-constant around 25%.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
It is important to distinguish the conductor motions
and lift variations here from those involved in aeolian
vibration, discussed in Chapter 2. The frequencies
involved in galloping are generally less than 1 Hz, and
usually less than 100 times those for aeolian vibration
for about the same wind velocity. Conductor movement
amplitudes in galloping often exceed a meter, whereas
they rarely exceed a few centimeters in aeolian vibration. The two phenomena are not directly related.
Figure 4.2-12 Galloping orbits at mid-span, recreated by
simulation (10-minute records). The simulation was guided
by tension recordings.
noted that some authors [Nowak and Tanaka 1974;
Chadha and Jaster 1975; Laneville 1977; Hack 1981]
pointed out some wind tunnel evidence of turbulence
effects on the lift coefficient, particularly near zero angle
of attack.)
Galloping of iced conductors occurs when wind is able
to transfer its energy to vertical, and more rarely to horizontal or even to torsional, movement. This means that
a mechanism must be found to progressively inject more
energy than the mechanism that is dissipated by selfdamping, which is extremely low at low frequency, and
by the drag during each cycle of vibration.
But the mere presence of lift is not enough to cause galloping. To destabilize the system, that is to obtain negative damping, the lift force must be such that any
disturbance would augment the lift force in the same
direction as the starting movement, and the instability
condition is created. Disturbances always occur in practice—for example, a conductor movement rising due to
buffeting.
Thus the derivative of the lift force with respect to angle
of attack is a key factor. A mechanism by which the
periodic motion of a galloping conductor could cause
modulation of aerodynamic lift to sustain the motion
was first described by Den Hartog in 1932 and A. E.
Davison in 1930. These mechanisms will be detailed in
Section 4.3 and Appendix 4.3.
The Case of Pure Vertical Motion
This mechanism will be discussed with reference to the
idealized profile of an iced conductor and the variation
of aerodynamic lift with respect to angle of attack,
shown in Figure 4.2-13. Den Hartog (Den Hartog 1932)
pointed out that the conductor’s vertical velocity y·
could modulate the angle of attack of the apparent
wind, Vr, since, as shown in Figure 4.2-14, the vector Vr
is the true wind vector V, minus the conductor’s velocity
vector y· . Figure 4.2-14 shows the effect upon the apparent wind vector of upward and of downward velocity of
the conductor.
It is apparent that y· modulates both the magnitude and
the direction of the apparent wind. The magnitude variations are small enough that they can be ignored for
present purposes. The modulation in the vertical component of the apparent wind, indicated by V tan ß in
Figure 4.2-14, is significant, however.
Suppose that the iced conductor, when not galloping,
has zero angle of attack and thus experiences zero lift
Figure 4.2-13 Illustration of variation of lift with angle of
attack. Clockwise reference for angles. Zero angle facing
the wind. Lift values opposite to typical airfoil value near
zero angle of attack but valid for D-shape structure, as
shown.
Figure 4.2-14 Effect of vertical conductor motion on
apparent wind. The sign of the angle of attack is
obtained depending of reference choice.
4-13
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
according to Figure 4.2-13. If that conductor is given an
upward velocity as in Figure 4.2-14a, it experiences an
angle of attack with respect to the apparent wind of –ß,
and this results in positive lift corresponding to point a
in Figure 4.2-13. The upward velocity thus begets an
upward lift force on the conductor. A downward velocity, as in Figure 4.2-14b, results in a downward lift force,
such as at b in Figure 4.2-13.
If the conductor gallops sinusoidally in the vertical
direction, the lift force from the wind assists its motion
during each vertical stroke, imparting energy to the conductor to increase its amplitude of motion. In fact, if the
motion is given by
y = ymax sin ω t
.
so that y = ω ymax cost ω t
.
β = − y/ V = −
ω ymax
V
assuming that | y |<< V .
cost ω t,
4.2-3
.
If the excursions of ß are small enough that angle of
attack remains on the straight-line part of Figure 4.2-13
between a and b, then the lift is given approximately by
L = − Lα β = −
Lα .
y
V
4.2-4
where Lα = dL/dα, the slope of the lift curve of Figure
4.2-13, between points a and b. The slope illustrated is
negative, with the result that the lift is proportional to,
and in phase with the conductor’s vertical velocity y· . In
effect, the force L is a negative damping force.
Note that the lift force has the character of negative
damping, making self-exciting galloping motions possible, only when the slope Lα is negative. Were the operating point not at the origin, but at an angle of attack
where Lα, is positive, such as point c in Figure 4.2-13,
the variations in L resulting from y· would be such as to
oppose motions in the vertical direction, and the oscillations would decay.
Lift and drag are defined as the components of aerodynamic force, respectively perpendicular and parallel to
the relative wind velocity Vr. Consequently both the lift
L and the drag D forces have components acting in both
vertical and horizontal directions. Thus, when there is
vertical velocity, the directions of lift and drag are as
shown in Figure 4.2-15, where D is the drag vector. The
component of L that acts in the vertical direction is L
cos ß.
4-14
The other aerodynamic force that influences the conductor’s galloping in the y direction is the vertical component of drag, D sin ß. This force component always
opposes the conductor’s y motion and acts as positive
damping. The balance between the negative damping,
due to L α and positive damping, caused by D, determines whether galloping can build up or not. Specific a l ly, i f L α + D i s n e g at ive, i n t h e re g i o n o f t h e
conductor’s at-rest angle of attack, then galloping can
build up from small amplitudes. If Lα+D is positive, it
cannot build up. (The at-rest angle of attack is the angle
of the ice section with respect to the wind arising solely
from the ice’s position of deposit on the conductor.) It is
measured with respect to some convenient position in
the ice deposit, such as the middle of the ice crescent, as
in the insert to Figure 4.2-13.)
The preceding paragraphs sketch the elements of Den
Hartog’s analysis. Den Hartog also explained how the
maximum amplitude of galloping is determined by
energy balance considerations when large excursions in ß
bring into play parts of the lift versus α curve that have
positive slopes or, at least, slopes that are less negative
than those responsible for letting the galloping build up.
His analysis established a credible connection between
the motions observed in ice-coated conductors and the
changed aerodynamics resulting from the ice deposits.
Den Hartog’s analysis has since been studied, tested,
modified, and extended, as will be discussed in Section
4.3 and Appendices 4.1 and 4.3.
Coupled Motion
An alternative theory to that of Den-Hartog has been
developed and will be described in Section 4.3 and
Appendix 4.3. Numerous observations of galloping of
single and bundle conductors showed the presence of
clear torsional movement of the conductor at the same
frequency as the vertical motion.
This theory has improved the general understanding of
galloping under a range of conditions, enhanced the
ability to interpret most of observed cases, and facilitated the development and refinement of galloping control methods.
Figure 4.2-15 Lift and drag referred to apparent wind.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Many scientists through the world have contributed to
these new theories. The first published papers came from
the United States, Canada, and Japan in the early 1970s
(e.g., Richardson et al. 1963; Otsuki 1973; Nigol and
Clarke 1974; Otsuki and Kajita 1975; Nigol et al. 1977;
Matsubayashi et al. 1976; Richardson 1979). These theories have been deepened and modelled in the 1980s and
1990s owing to increased computer performances and
worldwide cooperation through organizations like
CIGRE, IEEE, and the Japan Association for Wind
Engineering (JAWE). The 1980s/1990s were particularly
fruitful with the work performed by (Nakamura 1980;
Ottens 1980; Havard and Pohlman 1984; Lilien and
Dubois 1989; Diana et al. 1991; Yu et al. 1991 and 1992;
Chan et al. 1991; Rawlins 1993; Wang 1996; Chabart and
Lilien 1998; Wang and Lilien 1998; Keutgen 1999; etc.).
This kind of galloping has been called, may be improperly, “flutter galloping” or “binary flutter” by similitude
with airplane and bridge engineering. In that domain
instabilities like this are very well known.
It is not the aim of this book to relate these theories in
detail, although some descriptions will be provided in
Section 4.3. Greater detail can be found in the literature,
or in the CIGRE brochure that will be published in 2007
on the subject. But it is important to consider the major
findings, which can be summarized as follows.
• Torsional movement may be the sole origin of wind
energy input into the vertical movement.
• Flutter galloping is strongly related to the initial ratio
of torsional to vertical frequency of the conductor,
and thus structural parameters have strong influence.
A frequency ratio close to one, within the range of +/30%, is needed to promote galloping.
Chapter 4: Galloping Conductors
• Flutter galloping is strongly influenced by the phase
shift between vertical and torsional movement. Thus
torsional damping will play a major role.
• The coupling between vertical and torsional movement is related to (i) aerodynamic lift and pitching
moment, (ii) torsional stiffness of the system, (iii) torsional moment of inertia of the system with ice, and
(iv) position of ice.
• The conductor span, or the ratio of conductor diameter to sag of the span, is a key parameter
When Den-Hartog-type motion, with no torsional oscillations, occurs, the system is unstable in all its modes—
that is, in one, two, three, or more loops. The amplitudes
of motion are controlled by Den-Hartog instability
range of the angle of attack, the wind speed, and the frequency concerned.
In the case of “flutter galloping,” this may be not the
case, as the modes with better vertical-to-torsional tuning will grow faster.
An example of stability and amplitude analysis for
“flutter galloping” is shown in Figures 4.2-16 and Figure 4.2-17.
4.2.5
Causes of Galloping: Factors Influencing
Galloping
We may summarize these influencing factors as follows:
• Environmental Effects
• Wind and Ice
Figure 4.2-16 The influence of torsional damping (2 and 4% of critical damping) on “flutter-type” galloping
on a bundle conductor line according to analysis (courtesy University of Liège). Left: Amplitude of
galloping vs. position of ice (0° is facing the wind, anticlockwise). Right: Amplitude vs. wind speed (ratio
vertical/torsion = 0.93, conductor/bundle diameter = 0.072, reduced ice inertia = 0.007, conductor span =
0.066), aerodynamic curves as in Figure 4.3-5.
4-15
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Certain localized areas, often near lakes or rivers, show
a much higher incidence of galloping than do nearby
regions.
The power line needs to be located in region where:
• Most galloping occurs at temperatures near 0°C (Fig-
Figure 4.2-17 The influence of detuning, same case as
in Figure 4.2-16 according to analysis. A 25% detuning is
able to suppress or limit to negligible value the galloping
for wind speed up to 10 m/s. The impact of extratorsional damping is clearly visible, as it helps to
suppress galloping or to limit its amplitude with fewer
detuning effects.
The ice profile determines the aerodynamic characteristics of the iced conductor, thus:
–Ice accretion type and shape (eccentricity, weight,
aerodynamic properties)
ure 4.2-18), but some galloping has been observed at
much lower values, even at -45°C in Siberia, and
some others have been observed at ground level temperature close to +3°C. Figure 4.2-18 shows data
from the AMeDAS (Automated Meteorological Data
Acquisition System) which records air temperature,
wind speed and direction, and sunshine duration at
more than 1,300 locations in Japan.
• The temperature must be negative on the surface of
the conductor, which must be able to accrete ice, wet
snow, or rime. Ice is thermally conductive, so that
light winds can extract heat from the conductor and
permit the deposit to solidify. Heat generated by electrical loads will impede this solidification. Section
4.5.2 reviews ice removal options.
• The power line is more or less perpendicular to wind
speed (range over 5 m/s) during winter time (Figure
4.2-19)
–Position of ice in the presence of wind
• Structural Properties
–Conductor properties—e.g., mass, diameter, stiffness, tension, self-damping
–Span lengths and sags in the line section, and section length between deadends
–Structure properties—e.g., longitudinal stiffness of
anchoring tower or at fixation point
–Yoke plate assembly geometries at anchoring and
suspension towers
–Bundle properties—e.g., number and arrangement
of subconductors, subconductor spacing
–Spacer properties—e.g., kind of spacer, locations,
stiffness and mass distribution
Figure 4.2-18 Number of galloping events vs.
temperature in Japan.
–Presence of retrofit devices
The effect of the ratio vertical/torsional frequency of the
span of conductor for each mode, in the presence of
wind, is detailed in Section 4.3.
Environmental Effects
A survey by EEI’s Galloping Task Force found terrain
to be “flat” in 71% of reported instances of gallop, “rolling” in 22%, and “mountainous” in 7%. However, the
location was described as “urban,” as opposed to
“rural” in about half of the cases (Edison Electric Institute 1977).
4-16
Figure 4.2-19 Number of galloping events vs. wind
direction in Japan.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Terrain Effects
• The wind acts similarly on most of the span(s) of the
same section (in the same direction) with no significant obstacle in the close vicinity (which would
induce turbulence in a part of the span). Very flat
areas like deserts, fields, large river, lake or fjord
crossings, and tundra are very sensitive to galloping.
• A terrain environment that favors wind acceleration,
and/or driving wind in a direction close to perpendicular of the power lines may be very sensitive to galloping. Examples are fjord crossings, power lines
down a hill from which transverse wind may arrive
from the top of the hill over a forest, power lines on
the top of hills subject to transverse wind, plateaus in
mountainous areas with enough distance (e.g., several hundreds of meters) for the wind to “re-arrange”
before arriving on the power lines.
• Winter conditions may drastically change from summer conditions as some obstacles may be hidden by
the snow.
• Near water courses (such as lakes, rivers, seas, or
oceans) perpendicular to dominant winds, which are
locations very prone to power lines icing, together
with significant wind coming, for example, from the
sea.
• Turbulence intensity may be quite high during galloping events. Records of tension and wind speed, supported by visual observation, during a galloping event
in Belgium showed turbulence up to 20% (Lilien et al.
1998). Turbulence may not impede galloping.
The Ice Deposit
Ice Forms
Galloping requires moderate to strong wind at an angle
greater than about 45° to the line (Figure 4.2-19), a
deposit of ice or rime upon the conductor lending it
suitable aerodynamic characteristics, and positioning of
Figure 4.2-20 Types of ice deposits (Kuroiwa 1965).
Chapter 4: Galloping Conductors
that ice deposit (angle of attack) such as to favor aerodynamic instability. The ice, wet snow, or rime deposit
has to have strong adhesion to the conductor.
A classification of icing forms has been proposed in
Technical Brochure No. 109 by a CIGRE working
group (CIGRE TB109 2000a). This divides icing into six
different types. The different appearances of some of
these types are also presented in Figure 4.2-20, and the
relevant ranges of temperature condition and droplet
diameter are shown in Figure 4.2-21).
Precipitation icing includes three types:
1. Glaze, density 0.7 to 0.9, also called “blue ice,” is due
to freezing rain. Pure solid ice, it has very strong
adhesion, sometimes forms icicles, and occurs in a
temperature inversion situation. The accretion temperature condition is -1°C to -5°C.
2. Wet snow, density 0.1 to 0.85, forms various shapes
dependent on wind speed and torsional stiffness of
the conductor. Depending on temperature, wet snow
may easily slip off or if there is a temperature drop
after accretion, it may have very strong adhesion. The
accretion temperature condition is +0.5°C to +2°C.
3. Dry snow, density 0.05 to 0.1, is a very light pack of
regular snow, which is easily removed by shaking.
In-cloud icing includes three types:
1. Glaze due to super-cooled cloud/fog droplets (similar
to precipitation icing).
2. Hard rime, density 0.3 to 0.7, has a homogenous
structure and forms a pennant shape against the wind
on stiff objects but forms as a more or less cylindrical
coating on conductors with strong adhesion.
3. Soft rime, density 0.15 to 0.3, has a granular “cauliflower-like” structure, creating a pennant shape on
any profile, with very light adhesion.
Figure 4.2-21 Relation between types
of ice and meteorological conditions
(Tattleman and Gringorten 1973).
4-17
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Hard rime and glaze deposits are tenacious enough, and
have sufficient strength and elasticity, that galloping
motions do not dislodge them.
Wind-driven wet snow may pack onto the windward
sides of conductors, forming a hard, tenacious deposit
with a fairly sharp leading edge. The resulting ice shape
may permit galloping.
Ice Incidence
The incidence (frequency of occurrence) of glaze icing
was studied by Bennett (see Tattelman and Gringorten
1973). Figure 4.2-3 shows the number of glaze storms
that occurred in various parts of the country during a
nine-year period. Almost all states experienced glaze,
but the highest incidences were found in the Northeast,
North Central, and Central States and certain localized
regions in West Coast states. Corresponding information on incidence of hard rime is not available. It occurs
most frequently, but not exclusively, in hilly or mountainous regions.
More information on incidences of icing in other countries is given in Technical Brochure No. 291, by a
CIGRE working group (CIGRE TB 291 2005).
Ice Thickness
The thickness of icing varies from storm to storm. Table
4.2-3 shows, to the nearest one-quarter inch reported ice
thicknesses, at point of maximum thickness, during 69
cases of galloping (Edison Electric Institute 1977).
Galloping has occurred with deposits so thin (1 or 2 mm
[0.04 or 0.08 in.]) that the contour of the strand surface
was not obliterated. It has also been observed with ice
thickness as great as 5 cm (1.97 in.).
Apparently quite a wide variety of shapes provide aerodynamic characteristics capable of causing galloping for
at least some range of angle of attack. A survey by J. J.
Ratkowski (Ratkowski 1968) of wind tunnel data on 18
simulated ice shapes found all but two of them capable
of causing galloping, according to Den Hartog’s theory,
when suitably oriented.
Japan has been particularly active in galloping observations from the early 1970s. 776 cases have been recorded
in some detail from all regions of Japan, most of them
occurring on Honshu and Hokkaido Islands, particularly in the Tokyo, Hokuriku, and Tohoku regions. The
statistics of these events such as single or bundle lines,
wind speed and orientation to the line, temperature, altitude, span length, etc. are available in a CIGRE brochure (CIGRE 2007, to be published).
Interesting additional details are also provided about ice
shape and its eccentricity for 125 cases:
• 53 cases were observed with eccentricity less than 1,
most of the cases with a crescent shape windward (23
cases). (Eccentricity is defined as the ratio ice thickness over conductor radius.)
• 48 cases were observed with eccentricity in the range
1 to 2—34 of these of the cases with a triangle shape
with a round tip to windward)
• 7 cases were observed with eccentricity in the range 2
to 4—most of these cases with a triangular shape
with a round tip windward.
• 16 cases were observed with eccentricity in the range
4 and over—12 of these cases with a triangular with a
round tip to leeward.
Wind tunnel testing of actual ice shapes, and of plastic,
metal or polymeric replicas of actual iced conductors,
has been largely developed since 1979 all around the
world. Examination of ice shapes involved in actual galloping indicates that numerous naturally-occurring
shapes have been involved.
Ice Location on the Conductor
Figure 4.2-22 shows the percentages of observations
when the ice was thickest in each of eight sectors around
the conductor’s girth, based upon two collections of
data on galloping transmission and distribution line
span (Edison Electric Institute 1977; Oldacre 1949).
Table 4.2-3 Thickness of Icing
No. of Cases
4-18
Ice Thickness (in.)
Ice Thickness (mm)
42
“Very thin,” “Not visible,” etc.
17
0.25
6
8
0.50
13
0
0.75
19
0
1
25
2
1.25
32
Figure 4.2-22 Percentage of observations in which
point of maximum ice thickness fell in various
sectors of the conductor surface (Edison Electric
Institute 1977; Oldacre 1949).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
duration of icing conditions. This “wrapped-on” ice
shape will be different from that near span ends where
little rotation takes place.
As ice builds up, the conductor could twist due to the
wind pressure, towards another angle α, going through
a range where CL α changes significantly in value and
sign. Thus, galloping could start during glazing and
could cease before glazing stopped.
Figure 4.2-23 Effect of rain impingement angle on
location of ice deposits.
The thickness of ice deposit appears to influence the
likelihood of galloping for certain types of span. Galloping is favored if the ice shape is uniform and of constant angle of attack along the span. Glaze ice is usually
deposited on the upper windward surface of the conductor as illustrated in Figure 4.2-23. In long single-conductor spans, the eccentric weight of the deposit (see
Figure 4.2-24) may be great enough to significantly twist
the conductor. Since the conductor span is fixed against
rotation at the ends, this eccentric ice load will twist the
conductor most at mid-span, and the angle of twist will
become progressively smaller going from that point
toward the supports. The angle of attack will thus vary
along the span.
The ice shape will also vary along the span. Near the
span extremities, the ice deposit on the top windward
surface will progressively thicken with continued
impingement of freezing droplets. Ice deposited on that
quadrant remains in that quadrant. Near mid-span,
however, continued deposition of ice causes progressive
rotation of the conductor, so that the ice coating is
“wrapped on” (Edwards 1970). Because of this rotation,
the first film of ice, which was initially in the upper
windward quadrant, may ultimately face directly to
windward, or down, or even directly to leeward, depending upon the torsional stiffness of the span and the
The twisting of the conductor, discussed above, may
have the effect of changing the conductor’s ability to
gallop as the ice storm progresses. Early in the storm,
the angle of attack of the ice deposit may be nearly constant along the span, and its value may be such that galloping may occur or such that it may not. Subsequent
twisting may change the angle of attack, remote from
towers, to values where the reverse is true. Ultimately,
ice shape and angle of attack may vary so greatly along
the span that galloping cannot occur. Thus galloping
behavior may change substantially during the storm,
even when the wind conditions remain constant. After
precipitation ceases, and as long as the ice coating
remains intact, galloping behavior should depend only
on wind conditions.
Galloping behavior may be influenced by the electrical
load being transmitted by a line, since a small temperature rise of the conductors can postpone the initiation of
deposition, and a large enough temperature rise may
prevent icing altogether.
There is considerable variety in ice deposits found in the
field. It can be expected that the varied deposits found
from storm to storm, line to line, and indeed span to
span will have different aerodynamic properties characterized by different combinations of CLα and eccentricity (among other parameters). Unfortunately, little data
exist on aerodynamic characteristics of conductors with
actual ice deposits (Yamaguchi et al. 2005).
The videos on galloping on the CD distributed with this
book include some good views of some of the events. A
recent Japanese overview of galloping observations during the last 30 years gives some additional data (Mito
2003).
In this overview, 124 cases of height and shape of the ice
were observed. Table 4.2-4 shows observation data of
shape of ice and height.
Figure 4.2-24 Eccentric ice deposit resulting in
torque on conductor.
There are not enough such data to develop probability
distributions of, for example, CLα. Yet it is such probability distributions, acting through the dynamic charac-
4-19
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Table 4.2-4 Number of Galloping Incidents over 30 Years,
versus Height and Shape of Ice (Japan)
Height of Ice/Conductor Diameter
0 ~ 0.5
Shape
0.5 ~ 1.0
1.0 ~ 2.0
2.0 ~
Wind Lee- Wind Lee- Wind Lee- Wind Leeward ward ward ward ward ward ward ward
Triangle
9
10
8
3
1
0
0
0
Triangle
with round
tip
3
1
34
2
4
0
0
12
Crescent
23
0
1
0
1
0
0
0
Others
7
0
1
4
teristics of exposed spans, that determine the likelihood
of galloping occurring.
The distribution of actual CLα,, eccentricity ε combinations influences the expected benefit of different galloping control devices. This is discussed in more detail in
Section 4.3.)
Influence of Torsional Stiffness on Galloping
Torsional stiffness (described in Section 4.3) effects are
thought to influence the number of loops that occur in
natural galloping. Spans with low torsional stiffness,
due to large span length or small conductor diameter,
tend to experience large rotation at mid-span resulting
in a shape of ice having aerodynamic characteristics
poorly suited to galloping (Burgsdorf et al. 1964). The
amount of rotation is less at locations nearer the towers,
such as the quarter points of the span. The distribution
of a “gallop-prone” ice shape along the span is thus better able to support two-loop than one-loop galloping. It
is, in fact, widely thought that single-loop galloping seldom occurs in long single-conductor spans.
However, significant conductor rotation during deposition of ice does not occur in bundled conductors
because of their much larger torsional stiffness. In some
quarters, bundled conductors are thought to be more
prone to galloping than single conductors. But the number of kilometers of single lines being much larger, there
are many observations on such cases, too.
In Japan, during the last 30 years, 776 case of galloping
were recorded, 326 of them being observed on single
line 66 kV, 231 cases observed on single conductors at
voltage between 66 and 220 kV, and 210 cases on bundle
lines of voltage of 220 kV and over, including 53 on 500
kV. These figures correspond to galloping occurrences
on about 30% of the 66-kV line route length and 20% of
the 275-kV line route length.
4-20
4.2.6
Protection Methods: Overview
There are three main classes of countermeasures
employed against galloping:
1. Removing, or preventing formation of, ice on conductors.
2. Interfering with the galloping mechanisms to prevent
galloping from building up or from attaining high
amplitude.
3. Making lines tolerant of galloping through ruggedness in design, provision of increased phase clearances, or controlling the mode of galloping with
interphase ties.
All of these are treated in detail in Section 4.5.
Several utilities have designed ice-melting schemes for
their icing prone lines, and mechanical ice removal techniques are practiced, and some novel devices are being
developed. Use of galloping-resistant conductors is
gaining acceptance in some utilities as part of the lineupgrading program.
Provision of increased phase-to-phase and phase-toground wire clearances is the most widely practiced
countermeasure against galloping. EEI’s T&D Committee survey (data courtesy of Transmission and Distribution Committee) found this approach employed by 39 of
the 48 utilities that reported taking active measures to
offset the effects of galloping. Vertical clearances are
increased the most. Most designers rely upon “galloping
ellipses” in gauging what clearances to use, and feel that
very significant reductions in outage rates are achieved.
These ellipses, first proposed by A. E. Davison of
Ontario Hydro, will be discussed in Section 4.5. New
data based on extensive field observations of galloping
may lead to improvements to that design approach.
Interphase ties are rigid or flexible, phase-to-phase,
insulating struts that are placed at one or more points in
a span to enforce phase separation. These are the most
widely used add-on galloping controls. Galloping is not
prevented, but the motion that occurs is forced into a
mode that reduces the relative motion of the phases, and
thus the likelihood of flashover. Interphase ties have
been in use for more than 40 years (Jongerius and Lewis
1970; Becken and Drevlow 1972; Kito et al. 1975), and
experience has been quite encouraging. They have been
used by 20 of the 48 utilities noted above that reported
taking active measures against galloping. Nevertheless,
some breakage of interphase spacers has occurred, as
well as cases of synchronized galloping of all phases.
Further details of field experience with interphase spacers are given in Section 4.5.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
Devices that have been developed in order to interfere
with the galloping mechanisms fall generally into three
groups:
• No control method can guarantee that it will prevent
• those that intervene in the energy balance of a galloping span to damp the motions, in a manner similar to
that by which Stockbridge dampers control aeolian
vibration,
will not occur, but do not necessarily prevent galloping or dynamic stresses at the suspension clamps.
Their usage is growing, and their design is undergoing further development.
• those that modify the aerodynamics of the conductor
• Mechanical dampers to stop vertical motion are still
or the ice shape, and
galloping under all conditions.
• Interphase spacers virtually ensure galloping faults
being pursued but only to a very limited extent.
• those that seek to control torsional vibrations of the
• Torsional devices that either detune or increase tor-
conductors in a manner that prevents large vertical
amplitudes from developing.
sional damping or both are being pursued and
actively evaluated.
Trials of various devices designed to increase the energy
absorption in vertical movement during galloping have
not succeeded.
Unsuccessful devices are not covered in this survey, but
have been listed in a recent CIGRE document (CIGRE
2000b).
Several devices have shown some success based on modifying the aerodynamics of iced conductors, including
the air-flow spoiler used mainly on single conductors,
the AR Windamper on single and bundle conductors,
and eccentric masses.
Several devices that seek to intervene in galloping mechanisms operate through control of the conductor’s torsional motion. Extensions of Den Hartog’s analysis to
include torsional effects, as well as other theories, have
led to hypotheses that vertical galloping can be controlled by preventing torsional motion from occurring,
or by inducing torsional motion having a certain phase
relationship with the vertical motion. A number of
devices have been developed for single and bundle conductors based on this approach. These effects will be
discussed further in Section 4.5.
Survey on Galloping Control Devices
A recent survey published in ELECTRA (CIGRE
2000b) showed the following results:
• The complexity of galloping is such that control techniques cannot be adequately tested in the laboratory
and must be evaluated in the field on real overhead
lines. This testing requires a coordinated approach,
with observer crews equipped and trained to record
the galloping events on their lines. Due to the difficulty in predicting galloping occurrences, this may
take years, and the results may be inconclusive.
• Analytical tools and field test lines with artificial ice
are useful in evaluation of galloping risk, control
devices, and appropriate design methods.
• Techniques that disrupt either the uniformity of ice
accretion by presenting a varying conductor crosssection or the uniformity of the aerodynamics by
inducing conductor rotation are being actively pursued.
• Methods of ice removal or prevention are not widely
used as specific antigalloping practices, but they are
in place in utilities where icing is frequent.
• For bundled conductors, despacering with hoop
spacers, adding vertical offsets to horizontal bundles,
or using rotating-clamp spacers are still used extensively in parts of Europe subject to wet snow accretions.
• For bundled conductors, the influence of the design
of suspension and anchoring deadend arrangements
on the torsional characteristics of the bundle and on
the occurrence of vertical/torsional flutter-type galloping has been recognized.
4.3
MECHANISMS OF GALLOPING
4.3.1
Basic Mechanisms of Galloping
The basic mechanism of galloping, described by Den
Hartog, was outlined in Section 4.2, for a springmounted model constrained to move solely in the vertical plane. Appendix 4.6 gives the sign convention, clockwise or anticlockwise, for the aerodynamic forces that
will help to better understand the following. Analysis of
that mechanism led to the criterion that galloping may
occur if:
La + D ≤ 0 with clockwise reference for positive angles
D – La ≤ 0 with anticlockwise reference for positive
angles
Figures 4.3-5 to 4.3-7 show the Den Hartog instability
zones (highlighted) with actual and artificial ice shapes.
Since the drag D and lift L are given by Equations 4.2-1
and 4.2-2 in Section 4.2, the criterion may be expressed
4-21
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
versus aerodynamic coefficients of lift and drag and
their derivatives
CLα + CD ≤ 0 (clockwise)
CD - CLa ≤ 0 (anticlockwise)
4.3-1
Where
CLα = ∂CL / ∂α
α = angle of attack.
Inequality 4.3-1 is known as the Den Hartog criterion.
Tornqist and Becker pointed out that this criterion had
actually been derived as early as 1919 in connection with
autorotation of airfoils (Tornquist and Becker 1947).
Applied to iced conductors of power lines, Equation
A4.2-7 (Appendix 4.2) includes the Den Hartog mechanism as already discussed.
Efforts have been made to verify the analyses against
tests in wind tunnels and on full-span test lines. On the
whole, correlation has been good where theory has been
tested against experiment in wind-tunnel simulations.
Correlation has been less evident where full-span galloping in natural wind is involved, however.
A detailed discussion of galloping theory is beyond the
scope of this volume, since line designers cannot usefully
apply very much of it. Some understanding of the main
mechanisms at work in galloping is useful, however, and
it is the intent of the present section to provide that.
Appendix 4.3 provides a more complete view of galloping instabilities, including other kinds of galloping
instability than the Den Hartog type.
It is helpful to approach the discussion with specific
questions in mind. The first part of this section will deal
with the question: when may galloping occur—i.e.,
under what conditions can galloping of small amplitude
build up, rather than decay and disappear? The second
part of the discussion will concern the question: if galloping can occur, how severe will it be, how great its
amplitudes? The first question involves behavior when
amplitudes are small and thus permits the simplifications afforded by linearization. The second question
requires consideration of nonlinear effects with their
complexities.
In much of the discussion, the conductor span, more
exactly a specific mode of a multi-span section, will be
modelled as a rigid rod hung from springs in such a way
that it has one or several of the three degrees of freedom:
vertical displacement y (plunging), horizontal displacement x (swinging), and rotation θ (torsion), as depicted
4-22
in Figure 4.3-1. In this lumped parameter representation, the springs k1 and k2 are chosen to give natural frequencies in the x and y directions equal to horizontal
and vertical natural frequencies for the span in question,
and the torsional spring k3 is chosen to reproduce in the
model the torsional natural frequency of the span. It
must be noted that such configuration has been used in
wind tunnels for dynamic testing, notably by (Mukhopadhyay 1979; Nakamura and Tomanani 1980; Hack
1981; Tunstall and Koutselos 1988; Yu et al. 1992; Chabart and Lilien, 1998; Keutgen 1999), using a rigid rod
simulating a piece of conductor by adding the outer
layer of strands fitted on to a piece of tube, and on which
ice accretion is reproduced by a synthetic material. The
same experiment, without springs, helps to determine
the aerodynamic coefficients.
In one sense, this model reflects one mode of oscillation
of a whole overhead line section, in its three degrees of
freedom; a fourth degree exists in longitudinal direction,
but—despite its dramatic importance for tension variation—we may temporarily neglect its influence on galloping onset mechanisms.
Aerodynamics of Some Ice Coatings and
Corresponding Potential Incidences of the Den
Hartog Instability Condition
The Den Hartog instability criterion needs a relationship between the drag and the derivative of lift. Many
investigations have been described in the literature on
the aerodynamic properties of replicas of actual ice
shapes. These shapes were obtained during galloping
observations, usually as pieces of ice dropped from the
line (Tunstall and Koutselos 1988; Koutselos and Tunstall 1988), or in a wind-tunnel experiment simulating
natural icing conditions. This last procedure used a
Figure 4.3-1 Lumped mass model of conductor span.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
piece of conductor fixed in the vertical and horizontal
directions but able to rotate with appropriate torsional
stiffness. Snow or ice was injected into or created in the
wind tunnel to produce the ice accretion shapes, which
are dependent on temperature, wind speed, duration of
the icing event, and conductor torsional stiffness. Afterward the ice shapes were reproduced and the aerodynamic forces measured in a classical wind tunnel. Most
of these complex tests were performed in Japan (Otsuki
and Kajita 1975) and Canada (Buchan 1977).
In the following, the eccentricity of the ice is defined by
similitude based on a quasi-elliptical ice profile. The
eccentricity ε is the ratio of the ice thickness to the conductor radius. For example, in Figure 4.2-16, 11 mm
(0.4 in.) of ice on 32.4 mm (1.28 in.) diameter conductor
gives ε = 0.67. As a general conclusion based on all such
tests performed during the last thirty years, the findings
can be summarized as follows:
Chapter 4: Galloping Conductors
Figure 4.3-2 Actual ice shapes causing galloping. Left:
on a quad bundle, as observed in Japan (Anjo et al.
1974) extracted from a video record from the KasatoriYama test line. Right: ice accretion on a rigidly reinforced
bundle conductor, with eccentric mass.
• For instability to occur, the ice shape may have to be
an airfoil with significant eccentricity, mainly on bundle conductors (Figures 4.3-2 and 4.3-3).
• The ice shape on single conductors, which can generate galloping, may be extremely thin glaze ice (Figure
4.3-4).
• The D-shape type of ice almost never occurs.
Figure 4.3-3 Freezing rain ice shape fallen from
quad bundle line during a galloping event in the
United Kingdom in 1986 (courtesy M. J. Tunstall,
CEGB, Corech meeting, September 1987).
Figure 4.3-4 Ice layers on ACSR conductors. Upper Left: Groningen, diameter 22 mm (0.87 in.).
Below: Grackle, diameter 34 mm (1.34 in.), during a galloping event (courtesy P.H. Leppers, Corech meeting 1979).
4-23
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
It has been shown by laboratory testing (e.g., Tunstall
and Koutselos 1988) that extremely thin deposits
behave, near the zero angle of attack, completely differently from other ice shapes. They show lift curves with
opposite slopes, compared to other thicker deposits,
greater than the drag indicating potential Den Hartog
instability, similar to D-shape but in a much more
restricted range of angle of attack.
The aerodynamic curves in Figures 4.3-5 to 4.3-8 have
been obtained by the methods described above. Ranges
of angles of attack with Den Hartog instability zones
are highlighted by a heavier line on the abscissa. The
angle of attack is measured in the anticlockwise direction for all curves presented.
The left-hand side of each figure shows lift and drag,
and the right-hand side shows drag and derivative of lift.
The Den Hartog instability zones occur when the curves
Figure 4.3-5 Aerodynamic properties of a conductor with ice eccentricity 0.33 (source: P. Buchan, OH report
78-205-K, 1978). Left: lift and drag versus angle of attack. Right: derivative of lift and drag versus angle of
attack. There is only one small range of Den Hartog instability zone near 180°.
Figure 4.3-6 Aerodynamic properties of a conductor with eccentricity 0.82 (source: Manitoba Hydro,
CEA report N°321, T 672, 1992). Left: lift and drag versus angle of attack. Right: derivative of lift and
drag versus angle of attack. There is only one small range of Den Hartog instability zone near 180°.
Figure 4.3-7 Aerodynamic properties of a conductor with eccentricity 1.39 (source: Fujikura, courtesy T. Oka).
Left: lift and drag versus angle of attack. Right: derivative of lift and drag versus angle of attack. There is only
one small range of Den Hartog instability zone near 180°, plus one asymmetric instability zone near -40°.
4-24
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
Figure 4.3-8 Aerodynamic properties of a conductor with a D-Shape accretion (courtesy University of Liège,
1999). Left: lift and drag versus angle of attack. Right: derivative of lift and drag versus angle of attack. There
is a large range of Den Hartog instability zone near zero and 90° angles of attack.
the Den Hartog criterion. For example, in Figure 4.3.7,
with an eccentricity of 1.39 at around -40°. This means
that a small asymmetry in the ice shape may create such
behavior, but the area of instability, which will be related
to the amplitude, is generally very small.
Figure 4.3-9 Typical artificial D-shapes (courtesy
Hydro Québec). The figure on the bottom has very
similar aerodynamic coefficients as in Figure 4.3-8.
cross, due to the choice of the anticlockwise sign convention. All curves are smoothed using a high-bandpass Fourier filter with 42 harmonic components.
Ice Shapes Tested in Wind Tunnels
Many teams have worked around the world to obtain
aerodynamic properties of ice shapes. Also, using the
quasi-steady hypothesis, they have applied the aerodynamic coefficients assuming that they are independent
of wind speed. For these measurements, static wind-tunnel tests are performed by installing the conductor with
its ice shape supported rigidly within a wind tunnel with
sensors to measure the lift, drag, and moment for the
chosen wind speed. The support system can rotate the
conductor to provide these aerodynamic properties at
each angle of attack. The conductor support must be
designed to enable measurement of the appropriate
pitching moment.
Some of these teams were trying to reproduce actual ice
shapes due to wet snow or freezing rain. To obtain these
shapes, two methods were used:
• Collect ice shapes fallen from the line following galIt must be noted that a conductor with a “classical” crescent-shaped ice coating, such as shown in Figures 4.3-5
to 4.3-7, with any eccentricity has similar aerodynamic
lift curves of different amplitudes. There is little or no
Den Hartog instability zone, except at 180°, which needs
wind from the opposite side to the ice coating.
The D-shape (Figure 4.3-8) shows the opposite behavior
near the zero angle of attack, and is very unstable
(Nakamura and Tomonari 1980). Figure 4.3-9 shows
artificial D-shapes used in test stations.
Rarely, for some ice shapes, there can be a small range
of angle of attack that can become unstable based on
loping events. Then they reproduce the ice shape by
creating a mold, using low-temperature curing silicone rubber, and further creating replicas of the ice
shape using that mold, which are then attached to a
simulated conductor for use in the wind tunnel
(Nigol and Buchan 1981).
• Create ice accretions in an icing wind tunnel in which
samples of conductors are placed across the wind
tunnel, and freezing rain or snow is deposited on the
conductors during a given time. The conductor samples are installed with end fixations able to rotate to
correspond to an appropriate conductor torsional
stiffness (Manitoba 1992; Fujikura personal communications; Nigol and Buchan 1981).
4-25
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Some examples are reproduced here at right.
It is useful to note that the aerodynamic lift, drag, and
moment are, in principle, reasonably independent of the
particular conductor diameter of the sample tested in
the wind tunnel. Only the relative size of the ice thickness to the conductor diameter and geometric shape of
the ice layer are important. Any other ice profiles that
can be obtained by simply a scale factor would have the
same aerodynamic coefficients. That is why aerodynamic curves are given by the “eccentricity” of the ice
shape, which is a dimensionless coefficient, as shown by
Figures 4.3-5 to 4.3-7.
Influence of Ice Location on the Conductor
The distribution of the actual CLα, eccentricity e combinations, influences the expected benefit of different galloping control devices.
The actual distribution of CLα, ε is of direct interest in
connection with predicting the probability of galloping,
and in connection with assessing proposed protection
methods. As noted, data are lacking. The opinion of
researchers in the field, although certainly not unanimous, is generally as follows:
1. Ice builds up on the top and windward side of the
conductor, unless the wind reverses direction.
2. The wind reverses direction in a small number of ice
storms. Then galloping can easily occur based on
Den Hartog type instability on any kind of ice. This is
a particularly difficult type of galloping to control.
From a survey of Japanese utilities (Mito 2003)
(Table 4.2-4), about 20% of the galloping occurrences
cases were observed with leeward ice.
3. The absolute value of ε is usually less than 0.5. In the
same Japanese survey noted above, as reported in
Table 4.2-4 in Section 4.2, 53 cases or 43%, had
eccentricities lower than 0.5 and 71 cases, or 57%,
had higher eccentricities.
4. Both positive and negative values of CLα occur, perhaps with about equal probability.
There are widely differing opinions as to the magnitudes
of CLα, both positive and negative, that are achieved in
nature. The rapid overview of typical cases can be seen in
Figures 4.3-5 to 4.3-8, all being in the eccentricity range
of the Japanese investigations. These cases show very few
windward positions of the ice or wet snow with the Den
Hartog instability criterion satisfied.
It is felt that CLα may change in a particular span during
the ice buildup, due to twisting of the conductor under
the eccentric weight of the ice deposit and the force of
the wind. This twisting is greatest at mid-span and negli-
4-26
Figure 4.3-10 Wet snow shape 1
(Koutselos and Tunstall 1988 and
1986) obtained on a Zebra ACSR
54/7, conductor diameter 28.6 mm, ice
thickness of 12.6 mm (aerodynamics
similar to Figure 4.3-6). Den Hartog
potential instabilities occur only near
180°—i.e., horizontal, leeward side.
Figure 4.3-11 Wet snow shape 2
(Koutselos and Tunstall 1988 and
1986) obtained on a Zebra ACSR
54/7, conductor diameter 28.6 mm, ice
thickness of 14.6 mm. Den Hartog
potential instabilities near 180°,
horizontal, leeward side, and a very
narrow zone near 40° windward,
which is either upper and lower
quadrant.
Figure 4.3-12 Thin freezing crescent
collected by Koutselos (Koutselos and
Tunstall 1986) obtained on a Zebra
ACSR 54/7 conductor, diameter 28.6
mm, ice thickness of 3 mm. Den
Hartog potential instability near 180°
and a very narrow zone near zero°
windward.
Figure 4.3-13 Ice shape obtained on
a 21.5 mm conductor diameter, ice
thickness 15 mm (Fujikura, personal
communication with M. Oka)
(aerodynamics identical to Figure 4.37).Den Hartog potential instabilities
near 180° (horizontal, leeward side)
and a very narrow zone near 60°
windward (upper quadrant).
Figure 4.3-14 Ice shape obtained on
a 35 mm conductor diameter, ice
thickness 38.5 mm (Fujikura personal
communication with M. Oka). Den
Hartog potential instabilities near 180°
(horizontal, leeward side) and a very
narrow zone near 60° windward
(upper quadrant and down quadrant).
Figure 4.3-15 Ice shape obtained on
a 13.5 mm conductor diameter, ice
thickness 5 mm (Fujikura personal
communication with M. Oka)
(aerodynamics similar to Figure
4.3-5). Den Hartog potential
instabilities near 180° (horizontal,
leeward side) only. This shape is
quasi-identical to Buchan 1978.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
gible near the supports. During a period of “natural” ice
accretion of progressively increased eccentricity, the initial angle of attack, early in the storm, would correspond to an angle of impingement of the droplets,
possibly about 60° above horizontal, where a region of
near instability exists. This corresponds to -60° angle of
attack with the positive anticlockwise sign convention.
In this vicinity, CLα would be positive, reference positive
anticlockwise. With buildup of ice and wind force, the
conductor could twist toward other angle α , going
through a range where CLα is changing significantly in
value and sign. Thus, galloping could start during ice
build up and could cease before icing stopped. A longer,
torsionally more flexible span might twist enough to
take α out of the “appropriate range” of the Den Hartog instability, and might thus experience a short galloping period. A shorter, torsionally stiffer span might not
twist enough to take α out of the dangerous zone near
-60°, and therefore might suffer prolonged galloping.
These observations are dramatically influenced by the
wind speed, which may shift the ice position away from
its position without wind, due to the aerodynamic pitching moment acting on it. For example, depending on
torsional stiffness, single conductors would behave completely differently from bundle conductors. It would
simply be impossible, in the case of “low” torsional stiffness, for the conductor to twist so that the ice shifts to a
position below the wind direction. This depends on a
complex mix of wind speed, ice eccentricity, that is,
aerodynamic properties and weight, and conductor torsional stiffness. Section 4.3.2 offers an overview of these
aspects.
Bundle conductors, generally have very strong torsional
stiffness, compared to the external forces, so that the ice
buildup will generally occur on the upper quadrant facing the wind. This is not true for single conductors.
4.3.2
Influence of Structural Factors
Conductor Torsional Stiffness
Some details of the torsional stiffness of bundle conductors are explained in Chapter 7 in relation to the bundle
rolling instability.
The torsional stiffness “GJ”, also called “τ”, is related
to the external applied load by Equation 4.3-2.
d 2ϑ
− GJ 2 = M ( z )
dz
4.3-2
where M (z) is a torque on the span at abscissa z, which
can be distributed or localized.
Chapter 4: Galloping Conductors
“GJ” is given by analogy with beam theory, where G is
the shear modulus and J the polar moment of inertia.
“GJ” is an intrinsic property of the conductor. For
power lines conductors, the conductor is made of
assembled wires, most often round wires, and J is determined experimentally. By analogy with beam theory, the
parameters involved in the torsional stiffness are: the
diameter raised to the power 4 for cylindrical beams, the
geometry of the section, and the shear modulus. Most
conductors have a round external shape, and their outer
layers are made of aluminum. These outer layers contribute most to the torsional stiffness. As a result, a simplified approach could consider the diameter at a power
“x” as the only variable of interest.
If that equation is applied to the simple case of a concentrated torque “C” applied at the middle of a span of
length “L”, the corresponding angle of rotation at midspan is given by the classical formula:
ϑL / 2 =
C .L
4GJ
4.3-3
This testing arrangement has been used to determine
the effective “GJ” value of both single conductors and
bundles. To avoid any reference to “G” or “J” this
apparent torsional stiffness is generally replaced by one
variable “τ”.
Single Conductor
The torsional stiffness measurements on single and bundle conductors have been reported in several technical
publications (Nigol et al.1977; Havard 1976, 1980;
McConnel and Zemke 1980; Richardson 1981; Douglass 1981; Tombeur 1984; Susab et al.1985; Wolfs 1988;
Wang 1996; Wang and Lilien 1998; Keutgen et al.1998;
Keutgen 1999).
There is a useful review covering the results of 87 experimental measurements performed in many different
countries (Wang and Lilien 1998), which is summarized
in Figure 4.3-16.
The torsional stiffness measurements are characterized
by scatter of the order on a factor of about ± 2 on the
average value at each diameter.
A good approximation for the torsional stiffness of
standard round strand conductors with a diameter
between 12 and 60 mm (0.47 and 2.36 in.) AAAC,
ACSR, can be estimated by the simple formula:
GJ = τ = 0.00028φ 4
4.3-4
4-27
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
This formula produces conductor torsional stiffness τ in
Nm2/rad when the diameter φ is given in mm.
Large discrepancies may occur for old conductors.
Some over 30-year-old conductor tests showed values
two times the value of new conductors. Conductors with
noncircular wires, such as trapezoidal or z shape, also
have much stronger torsional stiffness. The tests of new
conductors with z-shaped strands showed up to two to
three times higher torsional stiffness, depending on
stranding and the number of z-shaped layers.
As an example from Equation 4.3-4, a Drake ACSR,
470 mm 2 , diameter of 28.2 mm, conductor has a torsional stiffness of:
τ = 0.00028(28.2)4 = 177 Nm2 / rad
It is clear from Figure 4.3-16 that torsional stiffness
based on diameter raised to the power “4” remains
valid, as for the beam theory, but significant discrepancies may occur, in particular for old conductors.
Bundle Conductors
The basic minimum torsional stiffness, as explained in
Chapter 7, of a bundle of “n” subconductors is given by:
GJ = n(τ + r .T )
2
4.3-5
where “r” is the radius of the bundle. The diameter of
the bundle is the diameter of the circle on which all subconductors are placed, for the classical bundle layout,
and τ is torsional stiffness of one subconductor. T is the
mechanical tension in each subconductor. In the SI unit
system, τ is in Nm2/rad, r in meters, and T in Newtons.
Based on this simple formula, the torsional stiffness of a
bundle is a very much larger value compared to a single
conductor, because the conductor tension adds significantly to the stiffness.
As an example, a twin Drake conductor with 0.45 m
bundle diameter and a 40 kN tension in each subconductor will give a bundle torsional stiffness of:
2(177 + (0.45 / 2) 2 .40000) = 4400 Nm 2 / rad
which is 26 times larger than the single Drake conductor.
The torsional stiffness of a bundle conductor is unfortunately not so simple. It can even be larger, up to twice
that value, depending on end-span conditions, including
the yoke plate arrangement on dead end structures.
That is because tension differences may appear between
subconductors, depending on the yoke plate arrangement at the end of the span.
The physics are explained in Chapter 7, including the
subspan torsional collapse mechanism. In this section,
the discussion covers torsional angles less than the collapse value, because the design must be such than collapse has to be avoided. But it should be noted that
some galloping does cause bundle collapse due to large
torsional movement.
The torsional stiffness of bundle conductors is definitely
nonlinear. It depends on conductor tension, which
changes during galloping. But for small movement, in
any direction including torsion, the tangential stiffness
may be used. That is particularly applicable to evaluating the basic oscillation modes of the power line.
Influence of Eccentric Masses on the Line
On some overhead lines local concentrated masses in
the form of various galloping control devices may be
present on the single or bundle conductor arrangement,
at a number of locations in the span. These masses have
a marked impact on torsional stiffness of the conductor.
Figure 4.3-16 Torsional stiffness versus diameter for
single conductors including ACSR and AAAC, with new
and up to over 30-year-old conductors. Based on 87
tests from Belgium, France, Canada, Japan, and the
United States. Only round wire conductors. Two curve fits
are shown (Lilien and Wang 1998).
4-28
To limit complexities, we will suppose that the additional mass is installed vertically below the conductor,
single or bundle, at a distance “lpi” m from the center of
gravity of the conductor, just like a pendulum. That
mass is rigidly fixed to the conductor, so that rotation of
the conductor will force all the system to rotate and the
mass will rotate through the same angle.
Some simplified evaluation of the additional torsional
stiffness on each different mode “k” due to different
“Np” masses “mpi” located at different place “zpi” on the
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
span “L” can be given by Equation 4.3-6, where g is the
gravitational constant = 9.81 m/s2:
kπ z pi
2
)
m pi l pi g sin 2 (
L
GJ add = ∑ L
2
1
⎛ kπ ⎞
⎜
⎟
⎝ L ⎠
Np
4.3-6
For example, a single vertical pendulum of 6 kg with an
arm of 0.2 m placed at mid-span, with span length L =
400 m, on a Drake ACSR single conductor, gives an
increase of the torsional stiffness for the first galloping
mode, k = 1, of about:
2
π 200
(6).(0.2).(9.81) sin 2 (
)
400
GJ add = ∑ 400
2
1
⎛ π ⎞
⎜
⎟
⎝ 400 ⎠
= 955 Nm 2 / rad
1
4.3-7
which is quite a large increment compared to the singleconductor intrinsic stiffness of 170 Nm2/rad.
The same case has obviously no impact on mode 2 torsional stiffness, because the mass is located at the central point of the span, which is a nodal point. The sine
term in Equation 4.3-6, with k = 2, will give a zero contribution.
This example emphasizes the importance of added
eccentric masses on power line conductors. It must be
noted that the same mass will also change the moment
of inertia by a significant amount.
Interaction of Ice with Conductor Torsional
Stiffness
Similarly to eccentric masses, a layer of ice coating adds
a moment along the span of the conductor and
increases the stiffness when the centroid of the ice is
below that of the conductor. Inversely, when the ice
accumulates on the top of the conductor, the torsional
stiffness is reduced. (Nigol and Havard 1978).
It must be pointed out also that the angle of attack of
the ice accretion—be it glaze, wet snow, or rime—is also
strongly dependent on the wind speed. The combination
of torsional stiffness of the span with aerodynamic
pitching moment causes some conductor rotation all
along the span. During moderate to strong winds, say 15
m/s, some positions of ice at mid-span are simply impossible because they are “statically” unstable. The cable
cannot maintain the position due to torque applied by
Chapter 4: Galloping Conductors
the wind. Typically a large highly eccentric ice accretion
cannot remain on the windward side of a single conductor in the presence of wind.
This points out some of the complexity of galloping and
some requirements of modeling. Not all positions of ice
are probable, and some are simply impossible depending
on wind speed. The inclusion of an appropriate torsional stiffness model is necessary, and this is not a simple exercise, especially for bundle conductors as detailed
in Chapter 7. A suitable model, verified by static test on
an actual span, can be used to explain bundle collapse in
all its aspects, subspan by subspan. The same theory led
to the identification of the major effect, of end-span fixation and yoke plates of bundle conductors at suspension and anchoring towers, on the torsional stiffness of
bundle conductors (Keutgen 1999; Wang 1996).
The influences of the mean wind speed and the inverse
pendulum effect are dramatic, even based on a purely
static approach.
In the following example, assume that ice accretion is
created instantaneously all along the span at the same
position ϑ = ϑice . Then consider gravity and the wind
acting on that accretion, to establish the equilibrium
position from a purely static approach. This assumes
that the wind is constant, and that there is no inertial
effect. Only torsion is considered here.
The equation governing the position of ice along a span
is given by:
−τ
d 2ϑ
= k M V 2CM (ϑ ) + mice gdice cos(ϑ )
2
dz
4.3-8
Where
τ is the conductor torsional stiffness.
z is the coordinate oriented from one end to the
other of the span (z = 0 at the origin and z = L
at the end).
ϑ is the actual position of ice at abscissa z (the
initial position of ice on a rigid structure =ϑice.)
1
2
kM a constant, --- ρ air φ (following Equation 4.2-2,
2
definition of aerodynamic pitching moment M)
The two right-hand side terms are:
First term, the aerodynamic pitching moment acting on
the ice, with CM the aerodynamic moment coefficient,
and V the wind speed.
Second term, the inverse pendulum effect of the ice
where mice is the mass of ice, dice is the distance between
4-29
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
the conductor shear center and the center of gravity of
the ice, and g is the gravity constant (9.81 m/s2).
It is relatively easy to solve that equation with the two
conditions:
ϑ (0) = ϑice
and the symmetry condition:
dϑ
= 0 , at mid-span; that is, at z = L/2
dz
The effects may be represented by two dimensionless
parameters:
P2 =
L2 k M V 2 and
π 2τ
P5 =
L2 mice gdice
π 2τ
The general view of the ice distribution along the span
can be seen in Figure 4.3-17, giving ice position at the
mid-span ordinates versus ice position at the end of the
span. CM coefficient is given by its aerodynamic curve
depending on the angle of attack; in this case, we chose
the same as shown in Figure 4.3-5.
Figure 4.3-17 shows the predicted twisting of the ice
layer of a 488-m span of single conductor Drake ACSR,
having an external diameter 28.2 mm, strung at 40 kN.
The Drake conductor has a torsional stiffness around
170 N.m2/rad. For lines 1, 2, and 3, there is assumed to
be no inverse pendulum effect—that is, term P5 is inactive. The simple existence of aerodynamic pitching
moment gives a value of P2 around 3 as soon as the wind
speed is over 2 m/s for an elliptical ice thickness near
10 mm.
That means, from curve 2 or 3, depending on wind
speed, that many positions of the ice cannot occur near
mid-span, for any accretion angle—i.e., the position at
the end of the span, as soon as the wind starts blowing.
These “potential” positions of the ice accretion, which
could exist in the absence of wind, would be moved by
the wind to another position.
The major influence of the inverse pendulum effect is
illustrated by case 2', that is with term P5 active.
The situation is completely different for bundle conductors as shown by curve 1. The bundle is at least one
order of magnitude stiffer in torsion. For example, a
twin Drake conductor with 45 cm separation would
have a torsional stiffness close to 4000 Nm2/rad. The P5
parameter has no effect on curve 1.
The general case would have to include the appropriate
ice accretion procedure, during which wind and gravity
are also acting, and which may also include some rotation of the conductor. In conclusion, the shape of the ice
accretion across the span is a very complex feature.
For a bundle with spacers rigidly connected to the subconductors, each subspan having a length around 40 to
60 m, the eccentricity of ice is probably rather uniformly
distributed owing to the much stronger torsional stiffness and distributed spacers.
The situation is much more complex on single-conductor
lines, where the ice position can differ according to the
presence or absence of the wind. Some devices attached
to the line, such as eccentric masses, may drastically
change the torsional stiffness of a single conductor, thus
completely affecting the accretion procedure and the possible position of ice in the presence of the wind.
Figure 4.3-17 Evaluation of ice position along the span
with an assumed aerodynamic pitching moment, using
the curve shown in Figure 4.3-26. Line 1 is for a twin
Drake conductor. Lines 2 and 3 are for single Drake
conductors with different wind speeds. Line 2 is for a
single Drake conductor with both wind and ice mass
inverted pendulum effects. In the abscissa, the ice
position at the end of the span, on the ordinate, the ice
position at mid-span. Angle positive anticlockwise.
4-30
Thus the mechanics of conductor galloping are strongly
dependent on the torsional behavior of power line conductors.
There is one particular exception for almost all ice profiles—that is, when there is a reverse wind speed, or the
ice position is leeward at about the opposite position
compared to the wind direction. All known measured
aerodynamic coefficients—for example, any of Figures
4.3-5 to 4.3-8—on any ice shape, have a potential Den
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Hartog instability under these conditions. Moreover,
this ice location undergoes very limited influence of
either the wind speed or the torsional stiffness of the
conductor.
Modified Den Hartog Conditions Owing to Torsional
Movement
Torsional response can expand the ranges of angle-ofattack where Den Hartog type galloping can occur, and
in fact open such ranges where the Den Hartog criterion
would fail in the absence of torsional response
The Den Hartog mechanism of galloping may be significantly influenced by the torsional behavior of the whole
span, in the presence of wind and ice. As detailed in
Appendix 4.3, the torsional movement, if in phase with
the vertical velocity which is typical for a single conductor line, may modify the Den Hartog criterion into a
much more complex interaction, depending on structural data which influence the amplitude of torsion. The
criterion is then “modified” as the derivative of lift
needed to create instability must have the same sign as
in Den Hartog evaluation, but its value is now multiplied by a factor that is dependent not only on aerodynamics. That multiplication factor is dependent on
pitching moment derivative, ice eccentric mass effect,
and some others.
Field data (Figure 4.5-22) show that galloping on single
conductors will occur mainly for very thin ice shapes,
thus with limited “modified Den Hartog” effect,
because both pitching moment and ice eccentric mass
effect will be negligible. Galloping on single conductors
is indeed possible and has been observed many times
with very thin windward ice, similar to the sample in
Figure 4.2-12. These thin ice shapes, with ice thicknesses
lower than about 10% of the conductor diameter, have
aerodynamics different from thicker ice deposits, and
Den Hartog galloping is possible only near zero angle of
attack.
The situation is completely different for a bundle conductor line, which is much stiffer in torsion. On these
lines, other mechanisms than Den Hartog, or modified
Den Hartog, may cause galloping, and torsional movement may not be in phase with the conductor vertical
velocity. More details of this mechanism are given in
Appendix 4.3. The ice layer generating galloping may be
any thickness or density.
Power Line Section Eigenmodes
Most of the structural factors influencing galloping, as
stated in Section 4.3.2, are coupled and can be analyzed
in relation to one basic physical property of the whole
section of the line—namely, the section eigenmodes.
Chapter 4: Galloping Conductors
The incidence of single-loop galloping appears to be
influenced not only by the twisting of the conductor due
to eccentric loading by the ice, as noted above, but also
by the sag ratio and the whole section data (from deadend to deadend towers). This needs further clarification.
The galloping motion may be correlated to some “eigenmodes” of the whole section. Eigenmodes are the free
vibration shapes that are possible in structures. These
modes have a clear physical sense. Galloping observed
on video or in the field demonstrates the nature of
vibration modes. Each mode is a synchronized motion
of the conductors in all spans and has a given frequency.
The lowest frequency is called the fundamental. For a
violin, the fundamental of a string, which is a taut
string, has a given frequency, and the corresponding
modal shape is a pure sine. For a conductor in an overhead line, the conductor is not a taut string because the
sag/span ratio is not negligible, generally 2 to 5%, compared to taut string structures, such as a violin, or a
stayed cable in a bridge. The full theory of cable dynamics has been developed, for example by (Irvine 1988). It
has introduced a parameter that indicates how far the
conductor behavior is from taut string theory. This
parameter has been extended to overhead lines (Lilien et
al. 1989; Dubois et al. 1991), including tower stiffness,
by introducing the following key parameter:
If
K
= tower stiffness (of the deadend towers that
terminate the line section (N/m).
EA = product of conductor Young modulus by
conductor cross-sectional area for one
phase, and for bundles, n times the cross section of one conductor, n being the number
of subconductors (N).
Ls = span length of the span considered in the
section (m).
L = the whole length of the multi-span section
(m).
a = the inverse of the catenary parameter (m-1),
which means the ratio between conductor
weight (product of mass per unit length
[kg/m] divided by the gravitational constant
g = 9.81 m/s 2 and conductor tension T in
Newtons).
r
= the radius of the bundle (m), all subconductors assumed to be on a circle.
σ = angular position of one subconductor, 0°
for horizontal twin, 90° for vertical twin.
h = the longitudinal dimension of the yoke plate
at deadend level, as defined in Figure 4.3-18
(m).
Figure 4.3-18 shows two very different yoke plate
arrangements for a twin-bundle deadend.
4-31
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
The following set of definitions will lead to Mv and Mθ
factors, this last only for bundle:
1
L
1
=
+
K v EA K
Ns
1
Kϑ ,twin
=
1 ⎛ (2r ) 2 L ⎞
+
⎜
⎟
cos 2 σ ⎝ 2hT EA ⎠
L = ∑ Ls
s =1
mg
a=
T
Ωv2 = (
π 2 T
Ls
).
2
m
8a .K .L
Mv = 2 v 2
π .m.Ωv
Ωϑ2 = (
Mϑ =
π 2 1
Ls
).
mr 2
(τ + r 2T )
8a 2 .Kϑ .L
π 2 .m.Ωϑ2
The correction factor based on “M” factors is the same
curve (right diagram of Figure 4.3-19) for vertical and
torsion, but refers to different basic formula (Ωv or Ωθ)
and different K factors.
Some surprising effects become apparent for twin-bundle conductors:
Horizontal twin bundles, σ = 0° compared to vertical twin, σ = 90°.
For vertical twin bundles, the yoke-plate has no
impact, Kθ is always zero as cos (σ) = 0.
For horizontal twin, the yoke-plate has a dramatic
impact:
The minimum value of the influence of the yokeplate on torsional frequency is obtained for h = 0
(full equilibrium between tension in the two conductors). Then Kθ is zero, and the horizontal bundle has
the same frequencies as for a vertical bundle, and
equal to fundamental theory.
The maximum value of the influence of the yokeplate on torsional frequency is obtained for h =
infinity, as is shown in the left-hand diagram of Fig-
Figure 4.3-18 Yoke-plate arrangements for deadends,
showing the definition of “h” and two typical
arrangements for a twin bundle. Left: with h quasi infinite.
Right: with a typical “h” around 0.1 m. Two cases that
would dramatically influence torsional frequencies.
4-32
ure 4.3-19. Kθ is equal to EA/L, which is very large
and may induce a significant increase of the pseudoone loop frequency in torsion. An increase of more
than 2 is possible.
Detuning—that is, separating the vertical and torsional
frequencies—is thus possible on horizontal twin bundles
by a simple rearrangement of the end-span details. This
is less valid for a multi-span section with a large number
of spans, because the end-span influence quickly
decreases with distance along the line section.
Comparing the taut string theory with the exact theory,
as detailed by Irvine, may help to draw the Figure 4.3-19
for the four first modes of a single span overhead line, as
detailed in (Lilien et al. 1989).
Figures such as these, which are for a level span, may
become more complex if there is a significant slope to
the span. The diagram on the right in Figure 4.3-19
shows that the two-loop mode may have lower frequency than the first mode with some geometries of
deadend hardware. This is particularly true for long
spans, and thus may explain why these are prone to twoloop galloping. For a span having Mv larger than about
2, the lowest frequency is the two loops mode, the first
to be unstable as wind speed increases. This will be discussed in more detail Section 4.3.5.
Another notable observation is that the shape of the socalled “one-loop” mode is not a pure sine wave. But it
has some “small loops” near the end of the span (Figure
4.3-19 left). This is called the “pseudo-one loop.” In deadend to deadend spans, the normal single- loop case is not
possible. This has been clearly observed, for example, in
the very detailed monitoring of a full-scale test line (Anjo
et al. 1974).
Another important feature of galloping is the behavior
of a multi-span section
An eigenmode of a power line section is the form of the
steady-state oscillation of a section of conductor, both
in the relative motion of each span, and in the natural
frequency. An eigenmode is normally calculated using a
linearized representation of the elastic properties of the
conductor. For a simulation of galloping, both the vertical and torsional motions are involved. Although a
span-by-span estimate may sometimes provide sufficient
accuracy in predicting motions, considering a line section between deadends gives a more realistic representation. This is because there is longitudinal motion of the
conductor at the suspension towers, due to the motion
of the suspension insulator strings. Also, for bundle conductors, the details of the fixity of the yoke plates at the
deadends can have an influence on the eigenmodes. The
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
Figure 4.3-19 Modal shape changes for pseudo-one loop galloping vs. Mv factor. Left: profile of possible single loop
galloping modes with different structural factor M. Right: frequencies of first three galloping modes versus different
structural factor M.
differences between the two estimates are greatest when
the span lengths are unequal.
Figure 4.3-20 illustrates the four lowest-frequency
modes for a line section having four suspension spans of
160, 180, 190 and 195 m between deadends. Calculations, using a linear analysis of the motions, show that
for the modes at 0.386 and 0.403 Hz, there is only small
variation in tension during galloping. This is because,
when one span is at its upward extreme of motion, there
is another span at the downward extreme. The variations in arc length of the two spans compensate each
other through swinging of the suspension support
between them.
In the mode at 0.516 Hz in Figure 4.3-20, all spans move
in phase, so there is less ability for arc length compensa-
Figure 4.3-20 Typical one-loop mode shapes in a fourspan line section. In the three first modes, alternate
spans move alternately up and down with minimum
variations in conductor tension due to insulator
movement. In the fourth mode, all spans move in the
same direction simultaneously. This mode involves large
tension variations, and its shape may deviate from
sinusoidal.
tion between spans to occur. As a result, this mode displays significant tension variations during galloping,
rather like the pseudo-fundamental in a deadended
span, which is discussed below.
The least common design of overhead transmission line
span is that with deadending at both ends. When the
galloping takes place in such a span, and if the structures are rigid, the motions are independent of what is
taking place in adjacent spans. The galloping may display modes with 1, 2, 3, etc. loops. The modes with even
numbers of loops conform in frequency and mode shape
to simple taut-string theory. The odd-numbered modes,
however, have higher frequencies than predicted by
string theory, and their mode shapes take the form of
sine waves with an offset, as illustrated in Figure 4.3-19
(left). They are called pseudo-modes, because of these
differences, as explained above.
These odd modes, especially the pseudo-fundamental,
are marked by significant variations in conductor tension, even for small galloping amplitudes. These variations occur because the galloping loops are
superimposed upon the curvature of the sagged conductor. This results in a difference in the arc length of the
conductor between its upper and lower extremes of
motion. Since the supports of a dead ended span are
nominally rigid, this variation in arc length must be
accommodated through conductor strain, with resulting
variations in tension. The lowest odd mode, the pseudofundamental, may have enough offset that it appears to
have three loops. Deadend spans experience the highest
forces applied to the structures during galloping.
4-33
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
There are certain modes that, even in suspension spans,
are autonomous to the span. These are the modes that
have even numbers of loops in the span. These modes
cause only slight variations in conductor tension, and
thus produce little motion at suspension supports. Thus
there is no significant coupling to adjacent spans.
Spans are often observed to gallop in a combination of
two or more of the modes that are available to them. For
example, a suspension span may move simultaneously in
a mode of the section and in its own autonomous twoloop mode.
The vertical component of galloping, and the longitudinal motions at suspension supports, are important relative to violation of electrical clearances, both in spans
and at supports. They are also closely associated with
the conductor tension variations, which can be large,
and the dynamic forces transmitted to insulators and
supporting structures.
The above discussion neglects the torsional component
of galloping motion, as well as motions lateral to the
span. Both of these also have normal modes by span
and by line section. Those components can have important effects in relation to aerodynamic mechanisms that
cause galloping, and they are discussed in the next part
of this section.
Further, if the ice formations in adjacent spans are not
at an unstable angle of attack, these spans may act as
dampers, reducing the amplitude or the likelihood of
galloping of the span having the gallop-prone ice formation. Some damping effect may also arise from the varying longitudinal load applied to the tower.
As a matter of observation, single-loop galloping of
large amplitude is a great deal less frequent in long spans
than in short, probably for both of the reasons cited.
Some order of magnitudes of frequencies for single
deadend spans and multi-span sections, both for single
and bundle conductors are given in Appendix 4.7.Torsional frequencies are also given in that appendix.
Effect of Vertical Damping
If the model of Figure 4.3-1 is constrained to purely vertical vibration, without torsional or horizontal motion,
then Den-Hartog’s criterion applies (Equation 4.3-1).
Note that the magnitude of wind velocity is not involved
in the criterion. The negative damping forces, due to CLa
of appropriate sign, and the positive damping, due to the
deflection of the drag vector, both vary directly with V2,
so if the negative damping overpowers the drag effect at
one wind velocity, it does so at all wind velocities. Care-
4-34
ful experiments in wind tunnels indeed show galloping
down to quite low wind velocities.
If mechanical damping is applied, for example, by paralleling the vertical springs with dashpots, a force that
does not vary with wind velocity comes into play, and
stability then depends upon V. The equation of motion
for the damped system is:
⎡ φ
⎤
my + ⎢q (CD − CLα ) + c ⎥ y + ky = 0
⎣ V
⎦
4.3-9
Where
m = mass per unit length of conductor.
q = ρV2/2 = dynamic pressure.
c = damping constant of dashpot.
k = system spring constant.
φ = conductor diameter.
Steady galloping is possible when the coefficient of the
y· term is zero, or
V =−
2c
ρ airφ .(CD − CLα )
4.3-10
This relationship is conventionally expressed in the
form:
V
2m
2δ
=−
•
2
f v .φ
ρ airφ (CD − CLα )
4.3-11
where δ is the logarithmic decrement of the system in
2
still air. The dimensionless parameter 2m/ ρ air φ is
roughly 3000 to 3500 for commonly-used ACSRs. To
illustrate, if the galloping frequency were 0.5 Hz, the
conductor were 25 mm in diameter, CD - CLα were -1,
and δ were 0.05, the threshold fvφ would be about 300,
and V would be about 3.75 m/s or about 8 mph. Doubling would double the threshold wind velocity.
Just how much damping, in terms of δ , a particular
span requires to prevent galloping depends very
strongly upon what wind speeds are anticipated and
upon the characteristics of the ice deposit, since those
characteristics determine C Lα and C D. Methods for
achieving useful levels of damping will be discussed in
Section 4.5. For practical reasons, nobody until now has
found any usable ways to increase the vertical damping at
galloping frequencies of an amount that could be of interest. Maybe one day active control could do that.
Dissipation within the conductor caused by its vertical
motion is too small to influence galloping behavior,
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
since the long loops associated with galloping result in
only slight flexing of the conductor.
As actual mechanical damping has been confirmed to
be very close to zero, the onset galloping wind velocity
should be extremely low. Practically no galloping has
been observed at wind speeds lower than roughly 4 m/s.
As this cannot be correlated to possible mechanical
source of damping, it must be recognized that another
cause may explain the observed onset galloping wind
speed. One possible cause is that a certain wind speed is
needed to maintain conductor surface at the negative
temperature required to retain a glaze ice, wet snow, or
rime deposit, despite the electrical load flow in the conductor. Some other causes could be: (i) the wind speed
needed to rotate the ice eccentricity to a location to generate galloping, which is seldom possible if it is located
at the bottom of the conductor, and (ii) some other
mechanisms beside the Den-Hartog instability exist, so
that the onset conditions will be different and will
depend on other structural data, which may be, due to
nonlinearities, influenced by the wind.
It must be understood that protection methods against
aeolian vibration, which are described in Chapter 2,
such as Stockbridge dampers, have absolutely no effect
on galloping, because this occurs mainly in a range of
frequencies much lower than aeolian vibration, and also
because the amount of energy in galloping is much bigger than the amount related to aeolian vibration.
The wind energy input during a galloping of a few
meters amplitude peak-to-peak is typically in the range
of several hundreds of Watts. By comparison, the maximum wind power input during aeolian vibration of
amplitude close to the conductor diameter on a span of
a few hundred meters is a very few Watts—between two
and three orders of magnitude less.
On the other hand, aeolian vibration dampers may be
subject to damage during galloping, despite their very
low response at galloping frequencies. The response may
be affected by snow accretion lowering the natural frequencies of the dampers, coupled with large-amplitude
motions that can lead to drooped and even fatigued
messenger wires.
As galloping is a low-frequency, high-power phenomenon, the control of it usually requires the use of systems
having significant mass. As shown in Section 4.5, preventive methods with more than 10% of the full-span conductor mass are sometimes used. The overhead line
designers have to be cautious about side effects that
could be induced by antigalloping devices. A heavy mass
Chapter 4: Galloping Conductors
in a conductor span acts as a fixed point at high frequencies, which may increase the magnitude of the vibratory
stresses due to aeolian vibration, and it may be necessary
to add damping or conductor reinforcement.
Influence of Conductor Self-Damping in Torsion
Stranded conductors possess significant self-damping
for torsional motion, even at the low frequencies
encountered in galloping. Edwards and Madeyski
(Edwards and Madeyski 1956) report experimentally
determined torsional log decrement in the range 0.15 to
0.20 in typical conductors, which corresponds to 2.2%
to 3.5% of critical damping. More recent testing presented in a CIGRE brochure on galloping, to be published in 2007, confirmed torsional damping from close
to 2% up to 4% of critical damping at galloping frequencies. The value is also dependent on conductor stranding.
The effect of this torsional damping is to make the rotational motions lag those that would occur in the absence
of damping. This effect is most noticeable for quasi-resonance between vertical and torsional movement.
As already stated, the limit cycle frequency is close to
the vertical frequency, and is also close to the torsional
frequency if quasi-resonance exists, which is very possible for bundle conductors. Small structural changes—
such as bundle orientation, end-span arrangement,
spacer type, subconductor separation, actual tension,
etc.—may shift the torsional frequency slightly. This
would then shift the ratio of limit cycle frequency to torsional frequency with dramatic consequences on phase
shift between movements owing to the torsional damping, which is the only significant structural damping
present.
For example, the response shown in Figures 4.3-21 and
4.3-22 could become that of Figure 4.3-23 with torsional
damping.
Figure 4.3-21 Combined vertical and torsional motion,
with amplitudes out of and in phase.
4-35
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
For ice leeward in Figure 4.3-23 (wind from right-hand
side), the rotation of the conductor is limited due to
wind action on ice and torsional damping is such that
torsional movement is delayed compared to vertical
one; the reverse is true for windward ice.
The importance of these rotational responses is that they
may shift the conditions under which galloping may
occur relative to those obtaining in the absence of torsional response. The rotational responses may, in fact,
permit entirely new instabilities. For example, the rotation component would reduce the excursions in angle of
attack of the ice section with respect to the relative wind
(effect of torsion on the angle of attack defined in
Appendix 4.1 and explained in Appendix 4.3–Equation
A4.3-7 and Appendix 4.5 Equation A4.5-6) more or less
as depicted in Figure 4.3-21, 4.3-22 and 4.3-23.
That reduction could reduce the amplitude of the lift
force shown in Equation 4.3-12 enough that the damping effect of CD could not be overcome, and galloping
might not be possible. A more positive value of C Lα
would be required to permit galloping with the torsional
motion indicated by Den Hartog’s criterion.
Conversely, if the ice lay to windward in the above case,
the excursions in would be amplified by the rotational
motion, and a less positive value of C Lα would be
required to establish the instability. That is the modified
Den-Hartog criterion. (See also Appendix 4.3.)
Instability in the form of flutter, not considered in the
Den-Hartog analysis, may arise from the mechanical
coupling of vertical to torsional motion. As noted in
Section 4.2, positive values of CD - CLα are stabilizing;
i.e., they tend to damp out purely vertical motions.
However, if the rotational .motion is in phase with and
large enough relative to y / V, as shown in Equation
4.3-12 and also detailed in Appendix 4.3, the phase of
the lift force L may be reversed, such that it sustains,
rather than damps, the motion in the y direction.
This has been established (Keutgen 1999) by the criterion
given in
(CD − CLα )
ω ymax
V
< CLα .ϑmax .sin ϕ
4.3-12
Where ϕ is the phase shift between torsion and vertical
movement.
The ability to modify the torsional motion, including its
damping, would certainly be beneficial for controlling
flutter-type galloping. This is the basis of galloping control methods based on torsion, which are described further in Section 4.5.
Figure 4.3-22 Combined vertical and torsional motion,
with amplitudes in quadrature.
Influence of the Ratio of Torsional to Vertical
Natural Frequency
For typical conductors, the positions of the stability
boundaries depend mostly upon wind speed, V, the ratio
of torsional to vertical natural frequency ft / fv, and upon
the conductor’s torsional damping.
Figure A4.3-3 in Appendix 4.3 shows these effects.
Figure 4.3-23 Combination of vertical and torsional
motion, resulting from eccentric ice load, when
torsional damping is present.
4-36
Although ft / fy for bare single conductors that are rigidly
supported at towers falls generally in the range 6 to 10,
several effects can reduce it (Nigol and Clarke 1974).
One is the “inverted pendulum effect” illustrated in Figure 4.3-24. Without ice or wind, the torsional natural
frequency is determined by the mass moment of inertia
of the conductor about the pivot and by the constant of
the torsion spring. With ice is deposited on the top of the
conductor, the center of gravity of ice plus conductor lies
above the pivot, and the torsional natural frequency is
reduced. See, for example, Equation A4.2-8 in Appendix
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
The aerodynamic moment has been defined, and its
interaction with torsional stiffness already pointed out.
It could cause an increase or a decrease of the torsional
natural frequency, depending on the ice location.
Figure 4.3-24 Model illustrating inverted pendulum effect.
4.2, with sin(θ0)=sin(-90°)=-1, which decreases the torsional stiffness, thus decreasing the torsional frequency.
If enough ice is deposited, the system may be statically
unstable and the conductor may twist to a new at-rest
position with the ice deposit’s center of gravity somewhere below the altitude of the conductor axis.
The inverted pendulum effect comes into play whenever
the center of gravity of the ice deposit falls above the
altitude of the conductor axis, and is strongest when the
deposit is directly on top. Calculations based upon a
derivation by Nigol and Havard (Nigol and Havard
1978) indicate that a deposit of only 4 mm thickness
over the top surface of a 25 mm diameter conductor
would halve the torsional natural frequency of a 250-m
(820-ft) span. The thickness required to do this varies
roughly as the square of conductor diameter and
inversely as the square of span length. Most ice deposits
do not fall exactly on top of the conductor, so the frequency reduction usually is more modest but may still
be significant.
Even with no inverted pendulum effect, the increase in
the mass moment of inertia from the ice deposit causes
some reduction in torsional frequency. The vertical natural frequency is also reduced by the mass of the ice, but
usually by a very small amount.
The aerodynamic moment varies with angle of attack α.
The effect upon the torsional vibration of the conductor
about its axis is the same as that of attaching a torsion
spring, additional to k3 in Figure 4.3-1, having a varying
spring constant (see also Appendix 4.2, Equation
A4.2-8, torsional stiffness term), M being already
defined in Section 4.2.5, α being the angle of attack:
-
dM
=-q.φ2 .CMα
dα
Where C
Mα =
moment.
4.3-13
dCM , the derivative of the pitching
dα
If CMα is positive, the net torsional spring constant will
be reduced, and thus the torsional natural frequency
will be lowered, as shown in Equation A4.2-8 (Appendix
4.2). To illustrate this effect, and compared to Nigol and
Havard’s derivation, the torsional natural frequency
about the conductor axis, with y motion restrained,
would be halved by a value of CMα of about 0.34 under
the following conditions:
V = 10 m/s, d = 25 mm, span length = 250 m.
Such values of CMα are apparently within the range of
practical interest (Figure 4.3-26).
The torsional coupling due to eccentricity not only
changes the boundaries of the regions of instability, but
also alters the degree of instability within regions. This
is also illustrated in results of wind-tunnel model tests
reported by Chadha (Chadha 1974). See Figures 4.3-27
and 4.3-28.
The frequency ratio ft / fy may also be altered by direct
aerodynamic action of the wind. This can occur when
the aerodynamic center, through which the drag and lift
forces act, does not coincide with the conductor’s axis.
This is illustrated in Figure 4.3-25, and the situation
depicted results in an aerodynamic moment about the
conductor axis. This effect is the “pitching aerodynamic
moment.”
The inverted pendulum and aerodynamic moment
effects are included in the galloping system Equation
A4.2-8 in the torsional stiffness term.
Figure 4.3-25 Illustration of displacement of aerodynamic
center from center of gravity of iced conductor.
4-37
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Purely Torsional Self-Excitation
A different torsion-effect mechanism than that outlined
above has been suggested by Nigol and Clark (Nigol
and Clarke 1974). The mechanism described above
relied upon coupling of the vertical and torsional
motions to produce either modified Den-Hartog galloping or flutter. In the former case, torsional motion
merely modified what is basically a vertical instability,
while in the latter case both vertical and torsional
motions were necessary for instability to occur.
Nigol and Clarke suggest that iced conductors may
become unstable and oscillate purely in torsion, without
the need for vertical motion. The existence of purely torsional instability has been demonstrated through windtunnel tests in connection with suspension bridges
(Scanlan and Tomko 1971) and for models of iced conductors (data courtesy of the Hydro Electric Power
Commission of Ontario), although the aerodynamic
mechanism bringing the instability about is not yet
clear.
testing, are based on the concept that CMa may introduce negative damping in the torsional motion (Wang
1996). If this may produce instability when torsional
damping is extremely low, this has no practical interest,
because on an actual line, torsional self-damping is usually large enough to avoid such situation.
Such movement, if any, could be suppressed by preventing the torsional instability through extra torsional
damping.
Horizontal Motion
We have considered above the interaction of torsional
and vertical motions of the conductor. Torsional motion
may also couple with horizontal swinging motion
through the variations in drag induced by CDα = dCD/dα.
Vertical and horizontal motions may also couple
through CMα, and in fact all three motions—vertical,
horizontal, and torsional—may become coupled.
The effects of horizontal conductor motions are thought
to have considerably less practical effect upon the likeli-
The recent view on these mechanisms, as far as it concerns power lines, actually only observed in wind tunnel
Figure 4.3-26 Typical aerodynamic pitching
moment and its derivative for a crescent ice shape,
eccentricity 0.33, angle positive anticlockwise.
Figure 4.3-27 Model of iced conductor. Very thin ice
deposit as used by Chadha. These shapes induce a
Den-Hartog area near zero angle of attack. (Chadha
1974).
4-38
Figure 4.3-28 Effect of small eccentricity of ice
deposit upon motion buildup rate at different angles of
attack, as found in wind tunnel model test. Negative
log decrement indicates buildup, positive indicates
decay.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
hood and expected severity of galloping than the vertical
and torsional motions, and will not be pursued here. The
reader is referred to the published work of McDaniel
1960; Richardson et al. 1963a, b; Chadha 1974; Keutgen
1999; Lilien and Dubois 1989; and Wang and Lilien
1994, 1998 for three-degree-of-freedom analysis.
the presence of ice and wind. Although this is easily
obtained for bundle conductors, it seems extremely difficult to obtain in the single-conductor configuration,
except for very particular ice shape and wind speed conditions (such effects in fact have been enhanced in Nigol
and Buchan 1981).
The recent view has been modified by the observations
done in the 1970s. In fact, numerous observations,
mainly in Japan, have pointed out natural galloping
with more horizontal movement, or figure eight, mainly
in the horizontal direction, galloping limit cycles, but
almost exclusively on large bundle conductors—that is,
on bundles of four or more conductors, sometimes with
large bundle diameters, up to 2 m in extreme cases. As
these cases occurred with bundle geometries that are not
widely used, the focus will remain on vertical galloping,
with some limited horizontal movement.
In the case of bundled conductors, there is wide agreement that torsional motion accompanies vertical galloping all or most of the time (Anjo et al. 1974; Liberman
1974; Nigol and Havard 1978; Matsubayashi et al.
1977). However, problems of properly modeling natural
ice are of significance even in the case of bundles. Anjo
et al. (1974) found that torsional motion led vertical
motion in phase during an episode of galloping with
natural ice, but lagged it during galloping with artificial
ice having a shape related to the D-section. The authors
were testing a four-bundle of 950 mm2 ACSR at the Mt.
Kasatori test line, in a series of two spans 310 and 315 m
(1017 and 1033 ft) long.
Some details are reproduced in Section 4.5.4
Perspective on Excitation Mechanisms
Questions surrounding the mechanisms still remain,
particularly for single conductors. Some experts are in
favor, for single conductors, of the collapsing of the frequencies in vertical and torsion due to the action of
wind and ice. But others cannot agree with that, based
on possible positions of ice in the presence of wind. In
this last case, (modified) Den-Hartog kind of galloping
would remain the sole possibility to get instability on
single conductors. In the former case, any kind of mechanisms would be possible. That question has a dramatic
effect on protection methods. We are sorry not to be
able to give a definite answer to that question. The following remarks can, nevertheless, be made:
Based on more recent experience and theoretical investigations, most observations on single-conductor test
lines can be explained as follows: torsional oscillation is
not needed to get Den-Hartog-type galloping. But torsional oscillations, nevertheless, very often appear due
to inertial coupling, the inverse pendulum effect, or the
presence of a significant pitching moment. In these
cases, the torsional oscillation is forced by the vertical
movement. Numerous cases of Den-Hartog galloping
on single conductor may be observed with very thin ice
shape, as shown in Figures 4.3-27, 4.3-28, and 4.3-12
thus with no or very limited inertial ice effect, and no
inverse pendulum or pitching moment effects. In these
cases, torsion may be very limited.
In the other form of galloping, the so-called coupled
flutter, torsion is a driven part of the phenomenon and
will always be present, but sometimes with very limited
amplitudes. These cases need, to be unstable, to have
similar values of vertical and torsional frequencies in
Adding to uncertainty, it must also be noted that some
authors (Nowak and Tanaka 1974; Chadha and Jaster
1975; Laneville 1977; Hack 1981) pointed out some
wind-tunnel evidence of turbulence effects on the lift
coefficient, particularly near zero angle of attack.
4.3.3
Estimation of Galloping Amplitudes
Natural galloping records exist, based on analysis of
motion picture film. An example of a waveform of vertical motions versus time is given in Figure 4.3-29.
There are some hundreds of field observations of galloping with estimates of the vertical motions, and will be
used as part of the input toward a new method of design
of clearances between phases (Figure 4.3-30).
The practical problem for power line engineers is determination of design clearances able to avoid an excessive
number of flashovers during galloping or to limit galloping effects by an appropriate retrofit method. In
Figure 4.3-29 Waveform of vertical oscillation during
natural galloping in a 256-m span of Grackle ACSR
conductor (34 mm diameter), determined from analysis of
motion picture film (Edwards and Madeyski 1956).
4-39
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
practice, these determinations are based on collections
of field observations, as described in Section 4.5.4,
“increase clearances.” However, methods for analytical
estimation of galloping behavior are of value for the
insight that they provide into galloping mechanisms.
Numerical and analytical tools have been developed to
study the complete interaction between all the degrees of
freedom involved in galloping of overhead conductors,
including all aspects of a multi-span line. An example of
this form of treatment is given in Figure 4.3-31. It is possible that the galloping can now be modelled completely
through these equations, which are well known and
defined, But the complexity of so many interactions and
the limited knowledge of many of the inputs dependent
on the nature of the ice accretion make it very difficult to
obtain a full understanding, even if it is possible to simulate any case with assumed values of the parameters.
As far as it concerns torsional amplitudes, Figure 4.3-32
is a record of an actual galloping (extracted from the
attached CD), clearly showing significant torsional
amplitude on a twin horizontal bundle. Figure 4.3-31,
obtained by simulations, is also giving access to tor-
sional amplitude and its phase shift with vertical one. In
all cases, as already discussed, both movements during
the galloping limit cycle are oscillating at the same frequency, but not necessary in phase.
Analytical Prediction of Galloping Amplitude
The current theory indicates that the nonlinearities of
the aerodynamic properties of the ice accretion may
determine the limit cycle amplitude. In dead-end span,
the mechanical tension variation in the conductor may
instead limit cycle amplitude. The aerodynamic nonlinearities can occur at several different angles of attack.
Indeed, lift curve, as can be seen in Figures 4.3-5, 4.3-6,
and 4.3-7, does not have the same slope for a large range
of angle of attack. Thus a growing amplitude corresponds to a change in angle of attack, depending on the
vertical component of the relative wind speed, and the
derivative of lift, which is the driven part in the instability, is not constant during all positions in the cycle.
As an example, consider a conductor with an ice coating
with a region of Den-Hartog instability, so that the system is unstable and the galloping amplitude is growing.
This condition is exemplified in Figure 4.3-5 around the
180° angle of attack. The wind speed is assumed to be
10 m/s.
Assuming, for example, that a span is galloping in a single
one-loop mode y (ymax is the maximum amplitude of the
mode, i.e. mid-span amplitude for the first mode, which is,
roughly speaking, a pure half sine wave on one span) at a
Figure 4.3-30 Maximum observed galloping
amplitudes versus 30-sec mean wind speed at the
Kasatori-Yama test line (Anjo et al. 1974). Bundle of 4
x 410 mm2 ACSR, two-span section, span lengths 312
and 319m, conductor mass = 6.7 kg/m, subconductor
diameter 26 mm, tension 123000 N/phase, sag at 0°C
= 6.5 m. Pseudo-one loop frequency at 0.36 Hz, twoloop frequency close to 0.46 Hz and three-loop
frequency close to 0.68 Hz. Conductor span
parameter 0.05.
4-40
Figure 4.3-31 A typical galloping ellipse in a quasivertical plane at mid-span, due to coupled flutter. Points
are at approximately 0.1 s intervals. The straight line
attached to each square point shows to the ice position at
each position in the limit cycle (calculated by University of
Liège using analytical tools).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
Figure 4.3-32 Galloping of a horizontal twin-bundle conductor under natural ice and wind
conditions. The vertical amplitude is estimated at 2.5 m, and the torsional amplitude is very
significant. A one-loop galloping at about 0.3 Hz. Other phases are also galloping.
frequency of about 0.5 Hz. The amplitude cycle is nominally to be a pure sine wave, in purely vertical motion—
that is, no torsional or horizontal movement.
y = ymax sin ω y t
.
then y =ωyymaxcosωyt
4.3-14
The excursions in angle of attack become
α = –tan–1 y. /V
4.3-15
These excursions grow with the vertical speed, which
means that, close to the initial angle of attack, say 180°
as stated above, any conductor position during the vertical oscillation has its own speed and thus its own angle
of attack:
Application:
ymax = 0.4m
ω = 2π f = 2π (0.5) = 3.14rad / s
y max = (3.14).(0.4) = 1.25m / s
α = 7°
In this example, the angle of attack (at mid-span)
changes from (180 - 7)° = 173° to (180 + 7) = 187°. In
that range the Den-Hartog instability criterion is still
violated, so that the energy transferred by the wind to
the vertical movement is still positive.
But as the amplitude grows further, there will obviously
be a range of angle of attack variation in which the DenHartog criterion will no longer apply, so that energy
transferred by the wind to the power lines starts decreasing, and progressively, as amplitude grows the net
energy input in each cycle becomes zero. At that point,
there are parts of the cycle during which energy is
injected in the system and other parts of the cycle during which energy is extracted from the system. The equilibrium of these two parts exists for a particular
amplitude, which is the limit cycle amplitude and the
major axis of the galloping ellipse.
In this rough approach, we have not discussed the variation of the angle of attack along the span, which could
easily be taken into account by appropriate integration
on the whole span. This does not qualitatively change
the former discussion but will have some quantitative
impact. For example, the fact that Den-Hartog instability criterion is met on only some part of the span may
not be enough to generate galloping, because the other
parts of the span will be dissipative, and only the whole
span energy has to be considered. Similarly, for the
amplitude evaluation, range of angle of attack changes
will not be the same all along the span, because parameters, like the vertical speed and torsional amplitude, are
4-41
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
not constant, thus a whole-span analysis always has to
be performed.
The analytical evaluation of galloping amplitude is presented in detail in Appendix 4.5.
Typical cycles of galloping, including both vertical and
torsional motion in twin-bundle conductor lines, are
shown in Figures 4.3-31 and 4.3-32.
As shown in Appendix 4.5, for a Den-Hartog type of
instability, the following maximum amplitude relationship exists:
α max = − tan −1 (ω ymax / V ) Eα =0
4.3-16
An implication of this result is that given fy and thus ω,
ymax will vary directly with wind speed V. That, in fact, is
found to be the case in wind-tunnel tests involving
purely vertical galloping (Novak and Tanaka 1974; Parkinson and Santosham 1967), except at such low wind
velocities that the galloping motion interacts with the
shedding of Karman vortices.
The linear relationship between ymax and V is also evident in tests of actual spans equipped with simulated
“ice” and exposed to natural wind. Figure 4.3-33, for
example, shows recorded values of ymax as a function of
the component of wind velocity normal to the conductor for a 244-m (800 ft) vertical two-bundle span of
336.4 kcmil all-aluminum conductor having a 20 x
20 mm (0.8 in. x 0.8 in.) square-shaped polyethylene
Figure 4.3-33 Measured single-loop vertical galloping
amplitudes vs. wind velocity (km/h). Vertical twoconductor bundle with artificial foils on the subconductors
to provide square profiles in a 244 m span. Solid line
shows predicted maximum amplitude that could be based
on Equation 4.3-16, for a given constant variation of the
angle of attack, the value of which being obtained owing
to integration of Equation A4.5-5 in Appendix 4.5 (data
courtesy Alcoa Laboratories).
4-42
covering (data courtesy Alcoa Laboratories). The conductors were oriented with the sides of the square horizontal and vertical. A bundle was employed with 406mm (16 in.) separation and rigid spacers every 17 m
(57 ft), to enforce that orientation. The span was fullydeadended to eliminate support point damping effects,
and tension was 50% RS.
Interestingly, galloping first occurred in a highfrequency mode with one loop between adjacent spacers. The top and bottom conductors moved vertically,
with opposite phase and equal amplitudes, leaving the
spacers stationary. Adjacent subspans did not interact,
and there was no low-frequency galloping. The top and
bottom conductors would sometimes clash.
This high-frequency mode was eliminated by applying
specially-designed Stockbridge-type dampers, tuned to
its frequency, to the bottom conductor in each subspan.
The span then galloped in the one-loop full-span mode.
Figure 4.3-33 pertains to that galloping. The straight
line in Figure 4.3-33 is the predicted relationship
between ymax and V based upon integration of Equation
A4.5-5 in Appendix 4.5.
Figure 4.3-34 shows results of another field test, this one
carried out by J. J. Ratkowski (Ratkowski 1963). The
“conductor” was a stainless steel ribbon with wooden
“ice” attached in the form of a semicircle, or “Dsection,” having 54 mm (2-1/8 in.) diameter. The flat
face was positioned vertically and facing the wind. The
Figure 4.3-34 Measured single-loop galloping amplitudes
in 8.7 m model span having D-shaped cross-section. Solid
lines show predicted maximum amplitudes based upon
Equation A4.5-5 in Appendix 4.5 (Ratkowski 1963).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
span was 8.7 m (28.6 ft) long, deadended through
springs. The two curves represent predicted ymax versus
V, using Equation A4.5-5 in Appendix 4.5, based upon
CD CL data published by Cheers (Cheers 1950) and by
Harris (Harris 1949).
Both field tests show reasonable correlation between
theory and experiment for purely-vertical galloping.
Section 4.4, “Testing in Natural Wind,” details some
additional testing in natural wind conditions, with artificial or natural icing.
Traveling-Wave Buildup
Ratkowski (Ratkowski 1963), observed that, in his span
equipped with flat-faced D-section, the initial stages of
buildup involved traveling waves moving back and forth
in the span. The waves were of short wavelength and
had small amplitude, so their energy was small. A gust
could have excited them. Because of their short wavelength, however, their passage over any location along
the span caused a brief, but quite significant, pulse of
vertical velocity, illustrated in Figure 4.3-35, the magnitude of that velocity being equal to the slope of the wave
front multiplied by the velocity of travel of the wave.
With enough slope, y could be great enough and permit
energy flow from the wind into waves, causing them to
build up when there is an appropriate ice shape and ice
accretion position.
Ratkowski’s observations showed that the small waves
did indeed increase in amplitude and length, with
repeated travel along the span. They eventually became
equal in length to some harmonic of the span and were
transformed to a standing wave in that harmonic.
Chapter 4: Galloping Conductors
When Eα is significantly positive at small amplitudes,
galloping can build up from rest without recourse to the
wave mechanism. This was the case with the tests using
square conductor represented in Figure 4.3-33. Such
buildup, without traveling waves, has been reported with
natural ice by A. T. Edwards (Edwards 1966).
Observations of actual galloping and forced galloping
using the ellipse shape of ice have shown that traveling
waves are not necessarily present during the buildup
procedure.
But some have been observed with traveling waves. One
is available on the CD accompanying this volume, with
no evolution to stationary waves.
Appendix 4.5 gives some insights about galloping initiation mechanisms based on observations.
Effect of Ice Thickness on Galloping Amplitude
Based on former discussions, particularly around Equation 4.3-16 (amplitude relationship), a certain ice shape
on a given span should produce different amplitudes
depending on wind speed V, but should produce similar
excursion in angle of attack α, and thus fYmax/V, independently of V. Thus that parameter is a good one for
exploring the effect of other variables, such as ice thickness, as in Figure 4.3-36.
Figure 4.3-36 shows the reported fY max /V versus ice
thickness from the EEI galloping field data base. It is
evident from that figure that galloping occurred much
more frequently with thin ice than with thick, and that
The process described above has been observed in some
cases of actual galloping, some involving natural ice and
some involving artificial ice. The process is evidently
required for ice shapes for which Eα(the energy per cycle
imparted to the conductor by the wind as defined in
Appendix 4.5) is small or negative for small excursions
in but significantly positive for large excursions. Some
shapes experience this condition for some initial orientations but not at others.
Figure 4.3-35 Vertical conductor velocity resulting from
passage of traveling wave.
Figure 4.3-36 Observed combinations of fYmax/ V and
maximum ice thickness, based upon field reports. Circled
points pertain to bundled conductors.
4-43
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
fYmax/ V tends to become smaller for thicknesses greater
than 6 mm (0.25 in.).
the conductor to go slack at some level of the galloping
cycle.
The tendency would be even more obvious, were the calculations of f based upon loaded sags, which were not
available. Frequency and sag D are related by the equations. (These equations are not accurate for single-loop
galloping of fully deadended spans with sag ratios
greater than about .01 to .015.)
If sag is shallow, the tension need not become zero
because the conductor passes through the zero sag position. Thus amplitudes of galloping can exceed the sag,
as can be seen in our videos of actual galloping. This is
particularly true for distribution lines where galloping
amplitudes several times the sag may be reached. (See
Appendix 4.5, Figure A4.5-1 [left].)
f = 0.56n / D for D in meters
= 1.00n / D for D in feet,
4.3-17
where n is number of loops. Use of loaded sags would
tend to lower the plotted positions of the cases involving
larger ice thickness more than those with thinner ice.
The apparently reduced aggressiveness of thick ice may
arise from several effects. A “wrapped-on” deposit with
its less effective lift characteristics would obviously be a
thick one. Torsional coupling effects could also be
involved.
The two cases having greatest fYmax/ V had ice thickness
of 6 mm (0.25 in.). In both of these cases, the conductors were fully coated, with the point of greatest thickness directly to leeward.
4.3.4
Tension Variations
When a span gallops with one loop in the span, the arc
length of the catenary tends to change, as illustrated in
Figure 4.3-37. If the span has suspension supports, the
supporting insulators swing in the direction of the line,
feeding the variations in the secant span length into
adjacent spans. If the span is fully-deadended, however,
such swings cannot occur, and the conductor experiences longitudinal strain with resulting significant variations in conductor tension. These tension variations are
great enough that high galloping amplitudes can cause
Figure 4.3-37 Single-loop galloping in span with: (a.)
small sag ratio and (b.) large sag ratio.
4-44
But, in general, most of transmission lines have their
amplitude limited to magnitudes about the same as the
sag. (This is not the case on distribution lines, where
amplitudes can reach up to five times the sag [see
Appendix 4.5].)
A deadended span can only go slack if its arc length can
be reduced by more than the elastic stretch in the conductor, by lifting it into a straight, zero sag, position.
Now the difference between the arc length Sa and the
secant length S of a shallow catenary is well approximated by Equation 4.3-18.
ea =
S a − S 8D 2
=
S
3S 2
4.3-18
where D is sag. ea, is the strain that a conductor would
undergo rising from sag D to the straight position. If ea
exceeds the elastic strain in the conductor in its at-rest
position due to tension, the conductor can go slack
before becoming straight. If ea is less, however, the conductor cannot go slack, regardless of amplitude.
Most lines are strung with unloaded 0°C tensions in the
range 20 to 33% of RS, and their elastic strains are generally in the range .0006 to .0016. These correspond, by
the above equation, to bare-wire sag ratios of 0.015 to
0.024. A span that would go slack in the no-sag position
with ice will also do it without ice, so the potential for
going slack can be judged from bare-wire sags. Thus, if
the approach of slackness does, in fact, limit galloping
amplitudes, most deadended spans with 0°C sag ratios
greater than 0.024 should be incapable of one-loop galloping at amplitudes approaching sag, while deadended
spans with sag ratios less than .015 should be capable of
much greater amplitudes in the one-loop mode.
Figure 4.3-38 contains data on a number of observed
cases of galloping, most of them collected by the Galloping Conductor Task Force of T&D Committee of
EEI (data courtesy Galloping Conductor Task Force).
The points in the figure represent galloping cases in
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
spans that were deadended at both ends, were on pintype insulators, or were supported from strut insulators.
The number identifying each point is the number of galloping loops observed in the span. The ordinate is the
observed ratio of peak-to-peak amplitude to bare-wire
sag, while the abscissa is the bare-wire sag ratio. The
data show that single-loop galloping was not observed
for sag ratios greater than 0.023. Amplitudes reached as
much as four times sag for sag ratios less than 0.018.
The slackness effect may come into play in long suspension spans, if the swing of insulator strings is great
enough to effectively “deadend” the spans at some point
in the galloping cycle. This is illustrated in Figure
4.3-41. The figure shows a three-span section between
deadends, and shows the galloping motion at the point
where the tangent span is at the top of its travel. At this
point the end spans are in effect fully deadended, and
the tangent span is slack.
Suspension spans may gallop to amplitudes greater than
sag without going slack. Figure 4.3-39 shows data similar to that of Figure 4.3-38, but for suspension spans
only. Several single-loop cases occurred for sag ratios
greater than 0.023, two of them with amplitudes slightly
exceeding sag.
This effect appears at lower amplitudes of galloping
when the insulator string or suspension linkage is short.
That fact probably accounts in part for the lower incidence of single-loop galloping in ground wires than in
phase conductors, indicated in Section 4.2 under “Types
of Motion.” The expected limitation on single-loop
amplitudes caused by the mechanism illustrated in Figure 4.3-41 has been used in estimating required phaseto-phase clearances (information courtesy of Commonwealth Edison Company). The slackness effect can be
achieved at lower amplitudes by use of inverted V-string
supports at tangent towers.
Figure 4.3-40 shows the same type of data for spans that
are deadended at only one end.
The patterns in Figures 4.3-38 to 4.3-40 are distorted by
the use of 16°C (60°F) final sags, which were available,
rather than 0°C sags existing at the time galloping was
observed.
Figure 4.3-38 Observed combinations of amplitude
divided by sag and sag ratio, for spans with fixed
supports.
Figure 4.3-39 Same as Figure 4.3-38 but for spans
supported in suspension at both ends.
4-45
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Order of Magnitude of Tension Variations
There are some interesting published papers on the subject of dynamic loads due to galloping, (Anjo et al.
1974; Bekmetyev and Jamanbaev 1985; Havard 2002
[see Tables 4.3-1 and 2]; Lilien et al. 1998; Escarmelle
1997; Krishnasamy 1984; Brokenshire 1979; Eliason
personal communication), including measurement on
site. Some of these measurements were on short deadended line sections and others cases were on long multispan line sections. The dynamic loads would be
expected to be higher for the former situation.
More is given in Appendix 4.4.
Figure 4.3-40 Same as Figure 4.3-38 but for spans in
suspension at only one end.
Figure 4.3-41 Illustration of large amplitude
galloping permitting a tangent span to go slack.
4-46
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Observations, field measurements, and simple modeling
show that the large galloping motions are not symmetrical about the rest position of the conductor. Analysis of
films of many galloping events showed that the upward
motion is typically three times the downward motion
during galloping (Havard and Pon 1994). The tension
variations during severe galloping are also asymmetrical
and depend on line parameters, especially the ratio of
the length of spans on each side of a suspension. The
tension deviation from the static value during the downward half cycle can be twice the deviation during the
upward half cycle (Havard 2002).
For many utilities, the dynamic loads under galloping
conditions are less than the maximum design loads, for
example, under the heaviest static ice weight or under
some ice level plus high wind. However, these dynamic
loads are repeated loads, and some rare occurrences of
fatigue damage to conductors, hardware, and even supporting structures have been documented.
4.3.5
How Many Loops Will Occur?
The several simplified methods described above and in
Appendices 4.3 and 4.5, for estimating galloping amplitude (energy balance and that of Hunt and Richards) all
lead to an estimate of the parameter fYmax/ V. Amplitude Ymax can only be estimated for some assumed wind
velocity if the frequency is known. The fundamental frequency of suspension spans can be calculated from sag,
but the actual frequency may be the fundamental or
some harmonic of it. The expected amplitude is strongly
influenced by the harmonic of the span in which galloping occurs. For example, if wind speed is 10 m/s and sag
is 5 m, then by Equation A4.5-9, f is .25 Hz max for oneloop galloping, and by Equation 4.32 in Appendix 4.5,
Ymax is 10.4 m. For two-loop galloping, f is 0.50 Hz and
Ymax is only 5.2 m.
Several effects influence how many loops will actually
occur.
• Deadending influences the number of loops, as discussed immediately above, tending to exclude the single-loop mode.
• Twisting of the conductor under the eccentric weight
(in the case of single conductor lines) of the growing
ice deposit tends to result in a more aerodynamically
stable ice shape at mid-span than near the ends, tending to favor two-loop galloping over single loop.
• The most important factor, for deadend spans and
for “up-up” modes in multi-spans, is, nevertheless,
the coefficient “Mv and Mθ” defined in Section 4.3-2
in the subsection on “power line section eigenmode.”
In fact, fundamental mode is not a pure sine wave for
typical (but not all) high-voltage power lines. It is
Chapter 4: Galloping Conductors
called “pseudo-one loop” (Figure 4.2-42). The frequency of the pseudo-one loop may be larger than
the two-loops mode. In such cases, the two-loop
mode is obviously more quickly excited because it
needs a lower wind speed to be launched.
• The modes that occur will obviously be those that are
unstable, and this may result from a complex mix of
structural and aerodynamic data, like torsion/vertical
frequencies detuning. It depends on the galloping
mechanism. In case of the Den-Hartog type, if the
wind speed is strong enough, all the modes are unstable below a certain frequency, which is not true for
the coupled flutter-type galloping.
• It can happen that the ice shape and wind conditions
are such as to favor galloping only in one span of a
section. Movements may, nevertheless, occur all
along the section, with that span supplying energy to
the others through coupling by insulator swing. In
bundle conductors, the instability of only certain
spans may be due to differences in torsional-to-vertical ratios.
With these effects aside, the number of loops appears to
be governed by chance, at least for Den-Hartog galloping. That is much less the case for flutter galloping,
where the required torsional/vertical frequency ratios
may occur in only one or a few of the available modes.
Consider a suspension span with uniform ice section
along its length, the section having such shape that DenHartog’s criterion is satisfied The statement that the criterion is satisfied means that small motions will grow in
amplitude, and the statement applies to motions in one
or two or any number of loops. Whatever mode is
present initially will grow. That mode will continue to
grow until a limit cycle is reached, such as one of the
type described by Myerscough (Myerscough 1975).
When such a limit cycle is attained, then other modes
cannot grow. The mode that has reached limit cycle has,
in effect, preempted the wind’s supply of galloping
energy and locked other modes out.
Note that there must be an initial disturbance in order
for galloping to build up. In field spans, such disturbances are thought to arise from gusts striking the span.
The choice as to the number of loops in which galloping
finally occurs is thought to be governed by two effects.
The first has to do with the combinations of modes that
are present in disturbances excited by gusts. The second
pertains to the relative rates of growth of the different
modes.
The simplest gust is one that is wide enough that it
strikes the whole span uniformly. Such gusts tend to
excite primarily the fundamental mode. For example, if
4-47
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
the operating point of the ice section (its angle of
attack) is such that the span experiences lift, then the
increase in wind speed that attends the gust will increase
that lift, giving the span an impulse in the vertical direction. The span’s response to this impulse will be largely
in the one-loop mode, with only small response in
higher modes.
Buildup is thus an “unfair” race among modes that are
given (usually) unequal starts. The outcome varies from
one occasion to the next, even in the same span. The
starting conditions tend to give the edge to the fundamental mode in short spans and to the two- and threeloop modes in longer spans. Deadending and conductor
twisting effects, noted earlier, modify the odds.
In natural winds, the gust fronts have randomly distributed widths, with many in the 20 to 100 m range at elevations above ground typical of overhead conductors.
These limited width gusts excite disturbances that contain several harmonics of the span simultaneously.
Which of these harmonics is dominant in any case
depends upon the width and spanwise location of the
gust, upon the length of the span, and upon the duration of the gust relative to the span’s fundamental frequency. Regardless of span length, the relative
intensities of the several harmonics that are excited vary,
gust-to-gust. However, in short spans the fundamental
one-loop mode is emphasized more often than the
higher modes, whereas in longer spans, the typical run
of gust sizes tends to excite the higher modes more
strongly.
Several of the methods being used or tried for preventing high-amplitude galloping appear to have the effect
of “fixing” the race. They prevent or retard the growth
of the fundamental, one-loop mode, giving the higher
modes a better chance to build up and preempt the limit
cycle. The lower amplitudes that attend the higher
modes, because of their higher frequencies, are less
likely to cause flashover.
When the mean wind speed and the ice deposit attain
conditions where galloping may occur, all of the gustexcited modes that exist in the span at that moment start
to build up. If the one-, two-, and three-loop modes are
present in the current gust-induced disturbance, all
three begin to grow independently of one another. They
do not, however, all grow at the same rate. Energy
effects governing their buildup are such that they all
experience the same percentage increase in amplitude
per cycle of motion; they all experience the same (negative) logarithmic decrement. Thus, if they all start from
the same amplitude, the two-loop mode grows twice as
fast per unit time as does the one-loop mode, and the
three-loop mode grows three times as fast, because of
their higher frequencies.
The different modes or harmonics grow independently
of one another as long as the angle-of-attack excursions
that result from their combined motions remain in the
linear range of the CL characteristic: region a-b of Figure 4.2-16, for example. When these excursions penetrate the nonlinear regions of the CL characteristic, the
energy supply to all modes is reduced, and all grow
more slowly. The mode that is dominant at this point is
affected least, however, and continues to grow. As it
does, it reduces the coherence of the lift forces acting on
the span with the motions in the other modes, and they
eventually die out. In the end, the mode that won the
buildup race settles alone into its limit cycle.
4-48
All of the galloping control systems that attach to and
restrain the motion of the conductor at discrete points
remote from the span ends (interphase spacers, aerodynamic drag dampers, seismic dampers and torsion control devices) are thought to be affected by this
mechanism.
4.4
TESTING IN NATURAL WIND
Tests of galloping behavior in full-scale spans exposed to
natural winds are normally directed at improved understanding of the phenomenon, at testing theories of galloping or at evaluation of proposed protection schemes.
Certain test programs are carried out on spans fitted with
artificial ice of some shape. Others are organized on
spans of operating lines on which icing is anticipated.
Tests motivated by research and development are usually performed on spans equipped with artificial ice,
whereas tests aimed at assessing effectiveness of protection methods that are in an advanced state of development are ordinarily carried out on operating lines. Use
of artificial ice permits much more rapid testing and better control of test variables.
Section 4.3 shows the aerodynamic characteristics of
some typical ice shapes, including the “D” shape, which
has been used frequently in galloping studies. D shapes
(Figures 4.4-1 and 4.3-9) and some “aerodynamicallysimilar” profiles (Figure 4.4-2) are found to be very
unstable when the vertical face is presented more or less
facing the wind, even when the wind is not necessarily
perpendicular to the span. These shapes show a very different aerodynamic behavior compared to crescent-type
eccentricity (Figure 4.4-3), particularly when the ice is
located on the windward side of the conductor.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
It is more difficult to create galloping-type instabilities
when testing with artificial, crescent-shaped profiles. Only
particular angles of attack would allow significant galloping amplitudes, and the specific angle of attack may be
dependent on structural properties. But actual ice shapes
are more close to these crescent-shaped profiles.
Figure 4.4-1 Simulated ice section employed by
Tornquist and Becker (Tornquist and Becker 1947).
Galloping can be strongly dependent on structural properties, such as torsional stiffness, moment of inertia, natural frequencies, the ratio between frequencies in different
directions of movement, etc. Test spans need be designed
to reproduce these properties, which is not always easy.
For example, testing on a single deadended span will not
be able to account for important influences, especially
span-to-span motions at suspension insulator strings. For
that reason, most of the existing test arrangements have
at least two spans in the test section.
Tests with artificial ice are usually viewed as not providing strong enough validation to support confident use of
proposed protection schemes. In-service testing is
required.
Finally, antigalloping devices that modify or interfere
with the galloping mechanism—which is practically all
of them, except perhaps, interphase spacers—should be
tested on lines with different conductor sizes and span
lengths and in different locations, and over a certain
period of time, since they may perform differently with
different densities and shapes of ice accretion.
4.4.1
Tests Using Artificial Ice
The artificial ice shapes, or airfoils, are generally reproduced in plastic, silicone rubber, or metallic foil in
lengths of about 1 to 2 m. These airfoils are fixed on the
conductor in a way that their orientation is sufficiently
constant on a significant part of the span, as shown in
Figure 4.4-4 using the air-foil of Figure 4.4-3. This is
particularly difficult on single conductors on long spans
Figure 4.4-2 Simulated ice section employed
by D.C. Stewart (Stewart 1937).
Figure 4.4-3 Typical crescent-type artificial airfoil
employed by Vinogradov (Lilien and Vinogradov 2002).
Figure 4.4-4 Artificial airfoil installed on twin bundle at
Talasker test station (Lilien and Vinogradov 2002).
4-49
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
because conductors tend to rotate during installation. It
must be noted that airfoil weight and center of gravity
may be of dramatic importance on instabilities, as
shown in Section 4.3.
As the instability may be limited to a small range of
angles of attack, it may be very cumbersome to change
airfoil all along the span(s) and then to wait for an
appropriate wind speed(s) and orientation. Some test
stations use rotational devices at the support points to
permit rotation of the conductor, whether single or bundle, on the whole span.
Galloping is readily obtained with many shapes, when
the airfoil is installed at an angle of attack of about
180°—that is, on the downwind side of the conductor.
The result is the Den Hartog type of galloping under
conditions that are rare on real lines, because it would
need a reversal of the wind speed compared to that
present during ice accretion. This is of limited practical
interest in evaluating the performance of antigalloping
devices.
To reproduce actual galloping conditions, it is strongly
recommended to install a crescent-shaped airfoil on the
windward side of the conductor. Generally, but not
always, unstable positions are found at about 0° and
90°, both upwards and downwards. Figure 4.4-5 shows
the zones of instability of a twin-bundle span using the
airfoil shown in Figures 4.4-3 and 4.4-4.
Figure 4.4-5 A polar representation of zones with no
instabilities observed, dark grey, and the three narrow
zones where instabilities were observed, light grey with
dots, on a twin-bundle span using an airfoil shown in
Figure 4.4-4. The radius coordinate indicates the ratio of
galloping amplitude/sag (Lilien and Vinogradov 2002).
4-50
It can also be very useful to install a D-shaped airfoil
because galloping would occur at lower wind speeds and
may be observed during more hours, which helps to
measure and to observe many details. Such testing procedure would, nevertheless, not be useful to test antigalloping devices based on the torsional mechanism. But it
would be valid to evaluate, for example, interphase spacers or mechanical damping devices.
Tests on Single-Conductor Lines with Artificial Ice
Shapes
The need to use simulated ice, in order to permit yearround controlled testing for research purposes, was evident to early investigators. The first successful test span
using artificial ice was apparently that described by D.
C. Stewart of Niagara Mohawk (Stewart 1937).
Stewart erected a single 32 m (104 ft) span of No. 4
ACSR (6/1) in 1936, and attached to it the wax section
shown in Figure 4.4-1. The span galloped in one loop.
The trajectory of the conductor was elliptical, with the
major axis vertical. Maximum amplitude was about 1 m
(3 ft). The motion that occurred included considerable
rotation of the conductor, more than 180° over the
course of a cycle of motion.
Stewart utilized the span for fundamental investigations, including an assessment of the energy balance of
the span during limit cycle motions.
In 1947, Tornquist and Becker of the Public Service
Company of Northern Illinois reported results of tests
on two test lines equipped with artificial ice (Tornquist
and Becker 1947). 3/0 copper conductor was employed
in both lines. The first line had a single 76 m (250 ft)
span, which was deadended through springs at each
end. The “ice” shape employed is shown in Figure 4.4-2,
and was chosen on the basis of extensive wind tunnel
model tests. The wooden sections were about 76 cm (30
in.) long and were fastened to the conductor with iron
tie wire. The span galloped in two, four, and six vertical
loops, generally without significant accompanying torsional motion. Galloping occurred only when the wind
struck the flat side of the section, and then only when
wind direction was more than 10° off perpendicular to
the span. There was no one-loop galloping.
Tornquist and Becker’s second line had four 76 m
(250 ft) spans and three phases. The middle three supports were in suspension. The same “airfoil” was
employed as in the first line.
The line galloped in one loop (Figure 4.4-6), in two
loops (Figure 4.4-7) and in a combination of these
modes. Amplitudes as great as 2.3 m (7.6 ft) were
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
with wooden D-sections and found, like Edwards and
Madeyski, that torsional tuning to encourage torsional
motion was needed in order to obtain high-amplitude
galloping. He concluded that such tuning does occur on
occasion with natural ice coatings, and is responsible for
the galloping that actually takes place. He investigated
use of torsional dampers for preventing galloping.
Figure 4.4-6 Coupled one-loop galloping of adjacent
spans (Tornquist and Becker 1947).
Figure 4.4-7 Two-loop galloping (Tornquist and Becker
1947).
achieved. Apparently significant torsional motion did
not occur.
One of the important problems in tests using artificial ice
concerns how well the behavior obtained represents that
occurring under conditions of natural icing. The presence
or absence of torsional motion, and its role in natural
galloping, is one of the central issues involved. Stewart
had torsional motion. Tornquist and Becker, in general,
did not, using the D-section. In an AIEE paper (Edwards
and Madeyski 1956) reported use of the D-section in a
span at Ontario Hydro’s Port Credit test line. The conductor was 336.4 kcmil ACSR (30/7) in a 126 m (412 ft)
span. They obtained only very small amplitude galloping
of the span when torsional motion was absent, but large
amplitudes when torsional motion occurred. In certain
tests, the torsional frequency was tuned to coincide with
vertical natural frequencies, and this had the effect of
broadening the conditions under which spontaneous galloping would occur. They interpreted the failure of the
span to display torsion-free galloping as an indication
that terrain in the vicinity of the Port Credit test line was
too obstructed to permit the smooth winds on which Dsection galloping was predicated.
Binder reported similar experience with D-sections in a
1962 article in Electric Light & Power (Binder 1962), but
drew a different conclusion. He had fitted six 76 m
(250 ft) spans of 3/0 and 300 kcmil copper conductor
However, Ratkowski also reported in 1963 (Ratkowski
1963) work on a short outdoor model span, demonstrating torsion-free galloping using the D-section. Ratkowski’s “conductor” was a flat steel strip 8.7 m (28.6 ft)
long with wooden quarter-rounds attached to its upper
and lower surfaces to form the “D.” He concluded that
conductor rotation is not required in galloping of iced
conductors.
Meanwhile, continued investigation at Ontario Hydro
pointed toward the damping effect of the wooden airfoils used by Edwards and Madeyski as the explanation
for the Port Credit test span’s failure to gallop in the
absence of torsional motion. In 1966, Edwards
(Edwards 1966) reported use of D-section airfoils of
extruded polyethylene on a test line at Scarborough,
Ontario. The plastic airfoils caused considerably less
damping than had the wooden airfoils. The test line,
comprising nine 335 m (1100 ft) spans of 795 kcmil
ACSR, displayed frequent high-amplitude galloping,
without the need for torsional tuning. Amplitudes as
great as 3 m (10 ft) peak-to-peak were obtained in the
two-, three-, and four-loop modes. A square-shaped section was also tried, with more limited success. The test
line has been used extensively in evaluating proposed
systems for controlling galloping.
More recently, at the Hydro-Quebec test line, Van Dyke
and Laneville (2004) observed that the D-section (Figure 4.3-9) was more prone to gallop with winds having
an angle of about 45º from perpendicular to the conductor. They concluded that, in that case, the wind flows
around an effectively thicker D-section—that is, it has a
different aspect ratio. For example, for a direction of
about 50º from the perpendicular to the line, the apparent aspect ratio of the D-section becomes 0.78 instead
of 0.5. Based on research by Nakamura and Tomonari
(1980), who have measured the aerodynamic characteristics of D-sections with different aspect ratios in a turbulent flow, D-sections with aspect ratios above 0.73
will experience galloping that starts spontaneously from
a resting state. This result emphasized the fact that a
mathematical model based on aerodynamic coefficients
corresponding only to the direction perpendicular to the
section considered will not provide adequate results for
other wind directions.
4-51
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
During the same tests, they also found that conductor
galloping may induce large bending amplitudes in the
conductor (Van Dyke and Laneville 2005). They measured bending amplitudes as high as 3.0 mm (0.1 in.)
peak-to-peak in the conductor adjacent to a metal-tometal clamp corresponding to fy max values as high as
1.2 m/s (4 ft/s) peak. Those results are covered with
more details in Chapter 3 on conductor fatigue.
The D-section’s apparently fickle behavior has roused
considerable debate among researchers concerned with
galloping. However, the D-section can be quite energetic
once it gets going, and the galloping behavior that then
occurs is very similar to that observed in natural galloping. This is a considerable virtue because, for a number
of years, the “D” was one of the few artificial sections
that enjoyed that distinction (square sections had also
performed well in a few tests). Attempts to produce
high-amplitude galloping with shapes more representative of natural ice had been largely unsuccessful
(Edwards and Madeyski 1956; Alcoa Laboratories.
In the 1970s, renewed efforts at Ontario Hydro to obtain
high-amplitude galloping with sections similar in shape
to natural ice have produced more fruitful results. Nigol
and Clarke (1974) made silicone rubber casts of actual
ice shapes taken from conductors (Figure 4.4-8) and,
based on them, had the extruded plastic shapes shown
in Figure 4.4-9 manufactured. The sections were fitted
to conductors in a test line at Kleinburg, Ontario, having three 244 m (800 ft) spans, the middle one supported
Figure 4.4-8 Silicone rubber casts of sections of ice
removed from conductor (Nigol and Clarke 1974).
in suspension. Extra care was taken to simulate natural
conditions, by applying ballast slugs to the span to make
up for the smaller density of the plastic shapes relative
to natural glaze.
Nigol and Clarke obtained high-amplitude galloping
similar to that of naturally-iced spans for certain ranges
of foil orientation (angle-of-attack). Galloping occurred
in one-, two-, and three-loop modes and in higher
modes. One-loop amplitude as great as 3 m (12 ft) was
obtained. The galloping always involved torsional
motion.
Nigol and Clarke viewed their experience with these
shapes as supporting the hypothesis that torsional
motion is required when natural galloping is to occur.
They, and later Nigol and Havard (1978), have pursued
development of devices to control the torsional motion
in such a way as to prevent high-amplitude galloping.
Tests with shapes not typical of natural ice (Tornquist
and Becker 1947; Ratkowski 1962; Edwards 1966; Alcoa
laboratories) have shown that torsion is not in principle
necessary. Analyses of films of natural galloping
(Edwards and Madeyski 1956) have shown that torsion
does not always occur. However, the results of Nigol
and Clarke (1974) indicate either: that the most commonly-observed ice shapes require torsional participation; that Nigol and Clarke’s models still do not
represent natural ice sufficiently well; or that some
important factor is not yet comprehended in existing
galloping theory or testing. Most workers pose the
question in terms of the percentage of occasions in
which torsional motion is crucial to instability. While
some have expressed the opinion that the answer is
“rarely,” and others that the answer is “always,” objective evidence permitting resolution of the question does
not appear to be available. This situation significantly
limits the usefulness of tests with artificial ice for evaluating protection methods for single conductors.
It seems that more or less all observations, except those
with tuning between vertical and torsional frequencies,
cited in this subsection on single conductor, are related
to Den Hartog type of galloping:
• either with a significant ice eccentricity, thus with significant torsion, clearly the case of Figure 4.4-2, but
also to a lesser extent with Figure 4.4-9, thus with significant contribution of inertial effect, inverse pendulum effect and pitching moment effect, or
• or with a very limited eccentricity, Figure 4.4-1, thus
Figure 4.4-9 Plastic test foils used to simulate natural
ice deposits (Nigol and Clarke 1974).
4-52
with limited torsion.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
In addition, Nigol and Buchan (1981) have observed
that some ice shapes showing Den Hartog conditions in
the quasi-static aerodynamic coefficients have not generated instabilities during dynamic testing. This observation tends to prove that, in some cases at least, the
quasi-steady theory used in all modeling today cannot
be considered as valid in all cases.
Tests on Bundle Conductor Lines
In the case of bundled conductors, there is wide agreement that torsional motion accompanies vertical galloping all or most of the time (Anjo et al. 1974; Liberman
1974; Nigol and Havard 1978; Matsubayashi 1977)
Problems of properly modeling natural ice are of significance even in the case of bundles. Anjo et al. (1974)
found that torsional motion led vertical motion in phase
during an episode of galloping with natural ice, but
lagged it during galloping with artificial ice having a
shape related to the D-section. They were testing a four
bundle of 950 mm2 ACSR at the Mt. Kasatori test line,
in a series of two spans 310 and 315 m (1017 and
1033 ft) long.
This observation is not a definitive claim against D
shape testing, as many parameters influence the phase
shift between torsion and vertical movement, e.g. ice
shapes, torsional damping, ratio between vertical and
torsional frequencies. Nevertheless it clearly shows the
vast field of possible galloping on actual lines, some of
them being easily observed by particular ice shapes,
such as the D shape. But these are not necessarily the
shapes to be controlled as they are special cases different
from actual observed ice profiles.
A modified D shaped artificial ice has also been used on
bundle conductors. Tsujimoto et al. (1983) conducted
tests using such an artificial ice accretion at the Juoh
test line to compare the galloping behavior of eightbundled and quad-bundled conductors.
Additional tests were also conducted on the eight-bundled conductors with natural ice accretion at the Tsuruga te st line. T he tests dem onstrat ed that the
fluctuations of mechanical tension for eight-bundled
conductors were similar under both artificial and natural ice conditions. The amplitude of the fluctuation in
tension, for eight-bundled conductors, increased less
rapidly than for quad-bundled conductors. Furthermore, the ratio of tension fluctuation over static tension
for eight-bundled conductors was about 80% of the
value for the quad-bundle. The maximum wind velocity
reached during those tests was 20 m/s (65.5 ft/s).
Asai et al. (1990) performed galloping tests on a deadended test line having a span length of 162 m (531 ft),
using modified D artificial ice accretions on a twin bun-
Chapter 4: Galloping Conductors
dle. With an average wind velocity of 15 m/s (49 ft/s),
they obtained a ratio of maximum dynamic tension
variation over static tension of the conductor of 2.6. It
has to be noticed that the variation in tension is not
symmetrical with respect to the average tension. The
same configuration was tested with one interphase
spacer in the span, and the ratio decreased to 2.0. Oura
et al. (1995) obtained the same ratio of dynamic conductor tension over static tension of 2.6.
Using a triangular-type artificial ice shape, Ozaka et al.
(1996) obtained peak-to-peak galloping amplitudes as
large as about 6 m (19.5 ft) on the Mogami test line.
Furthermore, horizontal large-amplitude, figure eightshaped galloping was observed. Variation of peak-topeak dynamic conductor tension during galloping
reached a maximum of 1.2 times the static tension.
Observations, Measurements, and Recordings
The procedures employed in conducting tests on spans
fitted with artificial ice vary with the purpose of the test
and the productivity of the span. Some testing employs
simple visual observation for acquiring data. Amplitudes are estimated with reference to known line dimensions, frequencies are timed with a watch, and wind is
measured with hand-held anemometers. More often,
suitably chosen transducers and recording systems are
employed.
Conductor motions have been sensed by attaching a
string to the conductor, the string being supplied from
spring-loaded reels at ground level. A multiturn potentiometer coupled to the reel shaft makes an electrical signal representing vertical amplitude available for
recording. This method was developed by A. S. Richardson and was utilized by Alcoa Laboratories.
Accelerometers have also been used for sensing vertical,
horizontal and torsional amplitudes (Edwards and
Madeyski 1956; Nigol and Clarke 1974). The conductor
displacement along the span may be inferred from two
accelerometers signals (Van Dyke et al. 2006). Bending
amplitude recorders of the type normally utilized in
aeolian vibration testing have been applied on occasion
for galloping recording. It should be noted that some of
these bending amplitude recorders have a lower limit to
the range of frequencies recorded, which may preclude
their registering normal galloping motions.
The amplitude of galloping, or its severity, can be
inferred from support point load variations and insulator string deflections if conductor tension is known. Clinometers may be added on the insulator string of
suspension towers to calculate the components of force
transmitted to the tower.
4-53
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
In addition to instrumentation of the above types, Anjo
et al. (1974) employed an optical tracker for studying
orbits of motion and for determining the space swept by
a conductor during an extended episode of galloping.
Finally, to relate the galloping recordings to mathematical models, it is important to measure the wind velocity
and direction as well as the temperature.
4.4.2
Tests with Natural Ice
Tests involving natural galloping of spans in operating
lines are usually aimed at validating the effectiveness of
proposed protection methods. Test programs entail the
selection of spans in areas that are likely to experience
glazing conditions, installation of devices to be tested on
one or several conductors in the spans, and provision of
the means for determining the behavior of the spans
when icing occurs.
The main advantage of testing under natural icing conditions is that it is realistic. The interpretation of results
does not depend upon theoretical assumptions about
which even experts may disagree. In addition, environmental effects found in actual service, such as icing-up
of moving parts, are present.
There are several disadvantages. The most serious is the
low productivity of such test programs. Glazing conditions conducive to galloping occur so infrequently, are
so localized, and have such random geographical distribution that a given test area may produce useful data
only once in several years.
The large number of variables that influence galloping
behavior aggravates this disadvantage. A protection
method may be used with confidence only if it is known
to be effective throughout the range of wind conditions
that is anticipated and against the variety of ice shapes,
thicknesses, and postures that are likely to occur. Thus a
large number of episodes of galloping are required in
order to properly evaluate a protection system.
A second disadvantage concerns acquisition of data.
The low productivity of individual test areas makes it
difficult to justify automatic data recording equipment.
Such equipment can sense motion at only one support
point. Even though a test area may experience galloping, on most occasions all spans or even phases do not
participate in it, and when they do, they do not participate to the same degree. Recording at only one support
point thus provides only a narrow sample of the activity
occurring in the area where it is located. Because of this
situation, the most effective method for data acquisition
is through observer teams who visit test areas when
4-54
glazing occurs. The observers are able to cover all
phases of a line over a length of several miles. This
important matter will be treated on Section 4.4.3
As mentioned earlier, most testing conducted with natural ice aims at the validation of antigalloping devices,
which are covered in Section 4.5. However, more general
results were gathered through such tests that are worth
mentioning here. Japanese researchers have been especially active in the field of galloping experimental tests.
Yutaka et al. (1998) summarized observations, measurements, and studies conducted in Japan. The authors
found that the country has 10 to 100 galloping cases
annually. Galloping happens at sea level as well as in
high-altitude areas. Galloping with ice accretion is
caused chiefly by strong winds. Galloping with snow
accretion is identified with a wide range of wind speeds.
At the Mt. Kasatori test line, observed oscillations, as
shown in Figure 4.3-30, were:
• one loop, or more correctly, pseudo-one loop mode
• mixed one loop “up and down” and two loops
• three loops per span.
It was found that large-amplitude oscillation occurs
when prevailing modes overlap. The dominant locus
drawn by the oscillations was a vertical oval shape. The
oscillation amplitude increases with wind speed, and it
was observed that the oscillation amplitudes tended to
reach a plateau at a certain wind speed.
At the Tsuruga test line, large-diameter bundled lines of
six conductors were tested, and unusual horizontal
oscillations were observed Figure 4.5-33)
Studies at the Mt. Sanpo test line found that super-large
bundled lines had a lower galloping frequency and
smaller oscillation amplitude than conventional quadbundle lines (Morishita et al. 1984).
Other tests conducted on the Tsuruga test line (Gurung
et al. 2003) have confirmed that galloping of bundle
transmission lines involves significant coupling of vertical and torsional motions. On bundles, the most likely
galloping mode in deadend spans is the two-loop mode
and large amplitudes of galloping occur when the torsion and vertical oscillations are in-phase.
Furthermore, deadend span line sections are more
prone to galloping than semi-suspension spans. According to Matsuzaki et al. (1991), observations have shown
that galloping occurs even in conditions that are stable
according to the Den Hartog criterion, and it is consid-
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
ered that this phenomenon is closely linked to the fact
that the twisting of conductors creates an unstable area.
Hokuriku Electric Power Company experienced galloping (Kasima et al. 1996), and they found that galloping
occurred with wet snow and most of the time at temperatures of -1 to +2ºC. Most galloping occurred at a wind
velocity of 5 to 7 m/s (16 to 23 ft/s), and the highest wind
velocity corresponding to galloping was 14 m/s (46 ft/s).
Galloping occurred on spans located at an altitude
below 100 m (328 ft) above sea level, but some galloping
was also observed at altitudes up to 700 m (2297 ft).
Based on the ratio of number of spans experiencing galloping over the total number of spans, it seems that bundles are more prone to galloping than single conductors.
In Belgium, a two-circuit 400 kV/220 kV operating line
in the Ardennes has been equipped for galloping detection, including instrumentation for recording tension
variations. The test length of this line occupies one deadend span and four suspension spans. The deadend
span is where an interesting case, with a 6 m (19.5 ft)
peak-to-peak galloping amplitude, was observed and is
illustrated in Figure 4.2-12. The four spans test section
has been studied by eigenmode analysis in Figure 4.3-13
and on which sample of galloping tension records can
be seen in Figure 4.4-10 and studied in the next subsection. The recording system was used between the 1980s
until end of the 1990s. Some interesting events have
been recorded and detailed in the literature and internal
reports, and some have been detailed in this book. The
dynamic tensions during the galloping event were measured on a twin horizontal bundle (Lilien et al. 1998).
Large tension variations of up to 100% peak-to-peak of
the sagging tension were recorded. Despite the fact that
the span was a deadend span, the galloping was mainly
in single loop. Many other observations were made at
other times, including some with all of the four spans of
the section galloping in one loop, some with two-loop
galloping located in only one span of the section, etc.
More details are given in a CIGRE galloping brochure
to be published in 2007.
A Typical Case Recorded on an Operating 220 kV
Line
A typical case of a recorded galloping event on an actual
operating 220-kV line is given here. It occurred on
March 4, 1986 in the Ardennes (Belgium) near Villeroux.
The galloping occurred on a twin horizontal bundle of
normal stranded conductors, 2 x 620 mm2 AMS, all aluminium alloy conductor, with standard spacers. The section of the line has four spans, as detailed in Figure. 4.413. The subconductor diameter was 32.4 mm (1.3 in.).
The tension at 0°C was 35000 N per subconductor.
Chapter 4: Galloping Conductors
There were load sensors at the same deadend tower on
five different arrangements of reference conductors or
conductors with galloping controls, with one sensor per
subconductor.
The wind speed during the galloping event was between
3 and 5 m/s (10 to 16 ft/s, measured at 10 m (33 ft) from
ground level. The wind direction was not purely perpendicular to the line, but precise data was not available.
The temperature was rising from -2.9°C up to -1.8°C
during the event. The precipitation was freezing rain.
There were several separate periods of galloping during
the episode. Tension records were obtained during two
of them. In the first, the maximum tension variation in
one subconductor observed was 27 kN peak-to-peak at
a frequency of 0.36 Hz during 15 minutes. It was very
similar in the other subconductor of the same bundle.
Much lower tension oscillations were observed in the
other phases, with a maximum of 4 kN in one phase and
14 kN in another.
The period of strong tension variations lasted for about
50% of the galloping period. The second period of galloping occurred with a maximum tension variation of
18 kN/subconductor but lasted for 30 minutes.
The buildup of galloping at the strongest value was in
two steps, as illustrated in Figure 4.4-10:
1. A period of about 10 minutes with limited amplitude,
10 kN peak-to-peak, with some beating phenomena.
2. The last “beat” wave was a little bit higher in amplitude,12 kN, and then it started to grow again, with no
Figure 4.4-10 A recorded initiation of galloping at the
Villeroux test station (courtesy Laborelec, Belgium) on
March 4, 1986. Twin spacered horizontal bundle 2 x
620 mm2 AAAC sagged at 35 kN/conductor, sag 7.7 m.
The figure shows changes of tension over time in one
subconductor at an anchoring tower. The main
frequency observed is 0.36 Hz. Natural icing. Two circuit
operating line at 400/220 kV.
4-55
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 4.4-11 Typical tension variation during actual galloping on untreated phase and phase with galloping control
device, as measured on an actual twin-bundle 400-kV line with permanent recording equipment. This recording of
tension fluctuations was made at an anchor tower at the Villeroux test station in Belgium. Only relative changes are
important. Upper oscillogram shows ±5 kN peak-to-peak for the phase with the antigalloping device. Lower trace shows
the tension fluctuation, ± 25 kN peak-to-peak, in the reference phase during the same period of observation.
further beating. It reached the maximum amplitude
of 27 kN in 5 seconds and stayed at that amplitude
for a long time, 20 minutes, without any beating.
The frequency was the same (0.36 Hz) throughout the
observed oscillations.
Galloping Observations by Measurement and Data
Analysis
In addition to the detailed case of the initiation of galloping on an operating line, illustrated by Figure 4.4-10,
many galloping events have been observed and motions
measured. Some of these events, which were observed
on operating lines under natural wind and icing conditions, will be discussed in this section.
Instrumented test lines and instrumented sections of
operating lines are particularly valuable in advancing
the understanding of galloping, since they produce
numerical records. Galloping can occur in a number of
different modes, and these often appear in combination
(Figure. 4.4-13). Recorded data on the variables that are
involved in galloping can be used to determine which
modes were present in particular galloping events, and
can often permit estimates of galloping amplitudes, even
if amplitude was not directly recorded. Doing this
requires detailed knowledge of the modes that can occur
in the span or line section involved.
Figure 4.4-11 shows an example of an oscillogram
obtained from a permanently instrumented section of
an operating overhead power line on which several types
of galloping control devices were installed.
4-56
Figure 4.4-12 Spectrum of conductor tension, Sensor
4, Villeroux, April 4, 1989.
Many such oscillograms were obtained during several
years in the same test station. One of them is treated
here in detail. The FFT (Fast Fourier Transform) of the
signal is reproduced in Figure 4.4-12. It was measured
in a section of four spans equipped with horizontal
twin-spacered bundle. The twin bundle was made of
AAAC 620 mm2 conductor of 32.4 mm (1.3 in.) diameter. The subconductors spacing was 0.45 m (1.5 ft). The
nominal tension per subconductor was about 35 kN at
around 0°C.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Figure 4.4-12 is a spectrum obtained during a galloping
episode at the Belgian test line at Villeroux. The
recorded variable was the conductor tension at one of
the deadends of the four-span section. The spectrum
shows 12 major peaks, suggesting that 12 different oscillation modes were active. This is not exactly true as
explained below.
Analysis of the possible normal modes of the section
was carried out using the procedures of Rawlins (Rawlins 2001). These modes are determined based on linear
elastic behavior, and several are pictured in Figure
4.4-13, identified by their frequencies. It should be
noted that the motions that occur in natural galloping
are not strictly identical to the undamped free normal
modes obtained from the procedures of (Rawlins 2001),
since aerodynamic forces are not taken into account.
However, those aerodynamic forces are small compared
with the inertial and elastic forces at work in the conductors. Thus, they cause only small perturbations in
Chapter 4: Galloping Conductors
the gross features of the normal modes—i.e., the frequencies and amplitudes of motion and tension variations. The free normal modes provide a good, if
imperfect, representation of the major features of actual
galloping.
Table 4.4-1 lists the major spectral peaks of Figure
4.4-12, and associates many of them with eigenmodes of
the section. Some of these peaks reflect the tension variations that are synchronous with the galloping motion,
such as the eigenmode at 0.357 Hz, and those at 1.111,
1.316, 1.406, and 2.072 Hz. Other peaks reflect tension
variation due to nonlinear effects. When galloping
amplitude becomes large enough, stretching of the conductor at its extreme displacements causes increases in
tension twice each cycle. This introduces a tension variation at double the frequency of the eigenmode. For
example, the peaks at 0.66 and 0.74 Hz arise from
autonomous two-loop galloping in the 397.3 and 361.4
m (1303 and 1186 ft) spans, which had resonant frequencies of 0.341 and 0.375, respectively. The eigenmode at 1.316 Hz causes a peak at 1.31 Hz directly, and
one at 2.63 Hz due to nonlinear effects.
The peak at 0.36 Hz could also be due to the 0.357 Hz
eigenmode directly, or to a nonlinear effect of the 0.1819
Hz eigenmode. It would require additional information,
such as from an insulator swing transducer, to distinguish between the two possibilities.
Figure 4.4-13 First six possible eigenmode shapes and
frequencies for the four-span test section at Villeroux.
The peaks at 1.53 and 1.89 Hz are not associated with
eigenmodes of the recorded phase. A 1.89 Hz peak was
present in the tension spectrum of another phase, and
probably caused motion in the deadend structure that
was reflected in the signal leading to Figure 4.4-12. The
1.53 Hz peak has the same frequency as subspan reso-
Table 4.4-1 Correlation of Spectral Peaks with Eigenmodes
Spectrum
Frequency
(Hz)
Eigenmode Frequency
(Hz)
Effect on Tension
Estimated. Maximum
Peak-to-Peak Amplitude
(m)
0.33
0.167 Hz
Nonlinear
2.42
0.36
0.182 Hz
Nonlinear
2.49
0.36
0.357 Hz
Direct
0.19
0.66
2 loops in 397.3 m span
Nonlinear
2.38
0.74
2 loops in 361.4 m span
Nonlinear
2.91
1.13
1.111 Hz
Direct
0.40
1.31
1.316 Hz
Direct
0.15
1.38
1.406 Hz
Direct
0.014
1.53
Subspan gallop in another phase?
1.89
Transfer from another phase.
2.07
2.072 Hz
Direct
0.64
2.63
1.316 Hz
Nonlinear
0.27
4-57
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
nance in another phase. It also corresponds to the longitudinal resonance of the four-span section (CIGRE
1989; Lilien et al. 1998). The peak may be associated
with this coincidence.
Detailed knowledge of the eigenmodes associated with
the spectral peaks permits calculation of the galloping
amplitudes from the spectrum ordinates. Table 4.4-1
shows these estimated amplitudes reported as the maximum peak-to-peak amplitude in the section. Note that
the source of the 0.36 Hz peak is ambiguous. That peak
may mean either 2.5 m (8 ft) in the 0.182 Hz eigenmode,
or 0.19 m (0.6 ft) in the 0.357 Hz eigenmode. Fortunately, on-site observers were present during the galloping and could not have failed see the 0.182 Hz mode.
Thus, the tension peak at 0.36 Hz must have been from
the 0.357 Hz eigenmode directly. The observers did
report seeing, and filmed, two-loop galloping in the
361.4 m span with an amplitude of 3 m (10 ft). This is
consistent with the 2.91 m (9.5 ft) calculated from the
tension spectrum.
The combination of recorded data from an instrumented test line, supported by observer reports, with
detailed analysis of the possible galloping modes permits greater insight into the complexity of galloping in
nature. In the example described here, there are three
different modes with amplitudes larger than 2 m (6.5 ft)
simultaneously present. The picture that emerges highlights the challenge faced by on-site observers in
attempting to describe galloping events verbally and the
great value of a video record of the event.
4.4.3
Observer Training
Providing trained personnel for the above purpose, during a period when service continuity is being challenged,
is a hardship for utilities, but appears at present to be
the most widely used method for acquiring data.
There has been a clear trend toward programs spanning
several utilities in order to speed field evaluations. A significant illustration of this trend has been EPRI’s
Research Project 1095, which involved 24 utilities and
about 56 test areas, and the Canadian Electrical Association’s similar field programs on control of galloping on
distribution lines and on bundle conductor lines. These
projects aimed at concentrating enough testing effort on
a few devices at a time to permit their speedy evaluation.
It appears that programs involving such wide involvement are necessary if in-service testing is to achieve useful objectives.
For participating utilities, programs of the above type
encompass the following elements, given the choice of
one or more protection systems to be evaluated.
4-58
Site Selection
The most important criterion in selecting a test area is
the expected incidence of galloping. Past experience is
the best guide. Smooth, unobstructed terrain is quite
desirable. Additional factors are: accessibility from
observer crew bases; number of circuits within an area
that a crew can reasonably cover; and availability of a
series of similar spans in similar terrain. The last of
these is important because adjacent suspension spans in
the same phase are coupled through support point
movements longitudinal to the line. A protection
method should be applied in a series of four or more
spans, unless deadends permit isolation of the test section from adjacent spans.
Installation
The particulars of device installation depend upon the
device involved, and supplier recommendations should
be followed if possible. A short length of pipe or of conductor should be hung parallel to the line from one
tower near ground level so that, later, ice thickness and
shape can be measured. This sample will not reflect the
effect of resistance heating of the conductors or of conductor rotation due to the eccentricity of the deposit,
but will probably provide the best available basis for estimating what is on the conductors. Sags should be
checked. If targets, such as spacer clamps, are to be
installed to aid in estimating amplitudes and modes, it is
convenient to do that at the same time devices are
installed. Convenient observation points should be
noted, along with reference dimensions of the line that
might be useful in estimating galloping amplitudes.
Choice of these locations may be influenced by whether
or not targets are employed. If local inhabitants are to
be recruited to report the existence of galloping, it may
be most convenient to show them the test area at this
time.
Observer Training
Observers should be provided with suitable report
forms, camera and tripod to produce a film record that
can be scaled, thermometer, and wind meter; they
should also be trained in obtaining the information that
is requested. The details of reporting forms vary from
case to case. Some or all of the following information
may be requested:
•
•
•
•
•
•
Identity of observer
Date and time
Identity of line, circuit, and phase
Voltage
Location in the line by tower number
Weather conditions, including precipitation, temperature, and wind speed and direction
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
• Mode of galloping: standing loops or traveling wave;
one mode or several; number of loops; adjacent
spans moving synchronously or not; subspan motion
in bundles or in spans divided by interphase spacers
or other devices
• Amplitudes of galloping: vertical, horizontal, and
torsional, for bundles and for singles fitted with targets; shape of galloping ellipse
• Support point motions longitudinal and lateral to the
line
• Location in the span where adjacent phases came
closest
• Frequencies of observed modes of motion
• Shape and thickness of ice coating on conductors
• Behavior of nearby circuits
If the crew can make a video recording of the galloping,
the form should include a map of the test area so that
camera positions can be noted. The form may provide for
later entry of line current and occurrences of trip-outs.
The most valuable form of report is a film of the galloping motion, and the observers need to receive guidance
on where to stand and point the camera. An effective
record of each of the directions of motion requires a different position, and the crew must be encouraged to
take all film from a tripod and to expose film that can be
scaled to determine amplitudes after the fact.
The most difficult items of requested information pertain to modes, amplitudes, and frequencies. It is advisable to use films of past galloping episodes in training
observers to assess these items. Modes are most easily
classified when viewing along the line where the entire
span falls within a narrow field of view, and adjacent
phases can be more readily distinguished. Amplitudes
are easier to estimate from a broadside position because
the middle of the loop can be more accurately located.
In addition, known line dimensions, such as insulator
string lengths, can be more easily employed because
effects of perspective are minimized. One useful technique (Hydro Electric Power Commission of Ontario) is
to stand about one span length to the side of the line,
hold a pencil vertically at arm’s length, and mark off
with the thumb a distance on the pencil that corresponds to panel height, insulator string length, or phase
spacing. The pencil is then swung, still at arm’s length,
to line up with the middle of the galloping loop, and
amplitude is estimated with reference to the known line
dimension.
Classification of modes is rendered difficult when several are present simultaneously. When observed motions
Chapter 4: Galloping Conductors
are too confusing, classification can sometimes be
achieved by associating each discernible frequency with
its amplitude. Later calculation permits the modes corresponding to the several frequencies to be identified.
Even when motions are simple and easy to classify as to
mode, frequency should be counted, since it permits the
loaded sag of the conductor to be calculated.
A methodology for collecting data from a galloping
event has been carefully described in a report prepared
by a CIGRÉ task force (CIGRÉ 1995). Some parts of
that document—including examples of galloping mode
shapes, how to measure galloping ellipses, and how to
install cameras during galloping observations—are
shown in Figure 4.4-14, and galloping reporting forms
are shown in Figures 4.4-15 to 17.
Since galloping instability depends not only on ice shape,
aerodynamic force coefficients, and wind conditions, but
also sometimes on structural characteristics, it is particularly important to evaluate them adequately. A review of
methods and systems for collecting icing data has been
completed recently (Fikke 2003). Moreover, there is still
some additional information that might be gathered during or after the galloping event, such as the possibility to
collect ice samples that have fallen from the cables. In
rare cases, because the line collapsed and the cables lie on
the ground, the ice samples may be still on conductors. In
either case, security of the personnel must be considered
first, but this will not be covered here. It should be noted
that the orientation of the ice samples remains problematic in either case.
When collecting ice samples, the following procedure
should be followed:
• Identify the conductor or ground wire or OPGW
from which the ice sample comes.
• Identify the span number.
• Measure the distance from the nearest tower, since
the ice shape may vary along the span due to the variation of torsional rigidity of the cable.
• Cut a section of the ice section and take a photograph with an object of known dimension (a rule is
ideal for that purpose).
• Make a sketch of the ice sample section with its main
dimensions, indicating the orientation of the ice section relative to the horizontal plane.
• Put the ice sample in a plastic bag to prevent loss by
sublimation and keep it in a cold place.
• As soon as possible, measure the mass of the ice sample to deduce its mass per unit length.
• Prepare plaster molds of the ice samples for future
aerodynamic characterization in a wind tunnel.
4-59
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Galloping observed on operating lines in the field often
shows variation between responses of apparently identical phases under the same conditions of ice and wind.
Table 4.4-2 shows the report of one event on one of
Ontario Hydro’s test sites during a freezing rain occurrence in 1977. The test site includes two parallel circuits.
One circuit has one phase with detuning pendulums
installed and two phases with no devices, while the other
circuit has no devices. The report shows that in a 30minute period some phases with no devices remain still
while others gallop with amplitudes between 0 and 3 m
(10 ft). In the same time period some phases have single
loop motion, while others undergo two-loop galloping.
Although most testing on operating lines employs
observer crews, remote sensing has been used in a few
areas experiencing a high incidence of galloping. A system was developed by Ontario Hydro in connection
with early detection of conductor icing (Kortschinski
1968). It employs a load cell in series with the suspension string at a selected tower. The signal from the load
cell is telemetered to the system control center.
Figure 4.4-14 Field observations of overhead line galloping: Guidance for filming galloping motions (CIGRÉ 1995).
4-60
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
Figure 4.4-15 Galloping reporting forms: On-site
observations (CIGRÉ 1995).
Figure 4.4-16 Galloping reporting forms: Line and site
information (CIGRÉ 1995)
The arrangement at the support is shown in Figure
4.4-18. The load cell is restrained against movement lateral to the line, so only the vertical load at the tower is
measured. The system is sensitive enough that as little as
1 mm (1/32 in.) of radial ice thickness can be detected.
As originally conceived, it served the same purpose as
monitoring carrier loss: detection of icing to permit
timely ice melting. However, it was found that the
dynamic loads caused by galloping in spans either side
of the support could be detected and recorded on an
oscillograph in the control center. With several load
cells located in the same area of high galloping incidence, it was possible to make comparisons between
protected and unprotected phases, without dispatching
observers.
was noted that several galloping events occurred without immediate impact on the operation of the lines,
especially on a horizontal circuit. In fact, galloping,
being comprised of mostly vertical motions, did not
result in any interphase faults, although galloping
events were observed. The authors concluded that the
dynamic forces associated with these galloping events
might contribute to progressive deterioration of the line
due to fatigue from the large cyclic motions.
In Norway (Halsan et al. 1998; Fikke 1999), a monitoring system using video cameras was installed in a
remote location to monitor galloping. Motion of the
image of the conductor across the video screen was
detected by optical sensors and used to trigger permanent recording of the motions for subsequent analysis. It
4.5
GALLOPING PROTECTION METHODS
4.5.1
Introduction
A variety of methods for protecting against galloping or
its effects are currently in use or under field evaluation.
They fall generally into the following categories:
• Ice buildup prevention, ice melting, or ice removal
• Special conductors with aerodynamic or ice phobic
properties
4-61
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
list of discontinued methods. This section focuses on
control devices that are considered to be practical, and
in use, at least on a trial basis, on operating lines. Where
possible, practical issues relating to ease of installation
and side effects attributable to the devices are summarized. At the end of this section, Table 4.5-8 compiles
the key information about the application of each of the
devices in current use.
The discussion of galloping protection in this section
includes, where possible, the following aspects:
Figure 4.4-18 Arrangement for sensing vertical load in
insulator string (Kortschinski 1968).
• Type(s) of weather exposure and line construction for
which each device has been tested and applied.
Galloping can be caused by a range of different conditions—namely, the type, density, and adhesion of
the ice (whether it is glaze, wet snow, or hoar frost),
and the speed, direction, and turbulence of the wind.
Most of the North American experience is with galloping due to wind acting on glaze ice accretions.
Galloping due to wind acting on wet snow has
received more attention in Japan and parts of
Europe. The type of icing under which each device
has been evaluated will be included along with known
practical details. Galloping also occurs differently on
small versus large single conductors, on bundle conductors versus single conductors, and on dead–end
spans versus suspension spans. There are even rare
conditions, with wind but without ice, in which other
mechanisms create galloping like motions. The common feature of all galloping is the excitation of the
• Increased clearances between phases and ground
wires
• Interphase
spacers
to
reduce
phase-to-phase
approaches
• Aerodynamic drag dampers to modify wind effects
during galloping
• Torsional motion control devices
• Limitation of longitudinal conductor motions
• Bundle geometry modification to decouple bundles
and to promote twisting of the subconductors.
A survey of the various known galloping control methods was recently completed under the aegis of CIGRE
and published in ELECTRA (CIGRE 2000b). The various control approaches were classified as “retrofit” or
“design” systems. The ELECTRA paper also includes a
Table 4.4-2 Sample Report on a Galloping Field Observation (extract from Ontario Hydro Research Division Report
No. 78-75-K, Chadha et al.1978)
GALLOPING OBSERVATION REPORT
OBSERVED BY:
PB & AV
TEMPERATURE:
-1×C
CONDUCTOR SIZE:
795 kcmil
DATE:
Dec 18, 1977
LOCATION:
MINDEN LINE
WIND DIRECTION:
WEATHER:
FREEZING RAIN
VOLTAGE:
230 kV
TIME
CIRCUIT
& TOWER NUMBERS
WIND SPEED
ESTIMATE
12:25
M9R
959-956
15-20 mph
24-32 km/h
12:25
12:50
12:55
4-62
M8R
959-956
M8R
958-956
M9R
959-956
15-20 mph
24-32 km/h
15-20 mph
24-32 km/h
15-20 mph
24-32 km/h
PHASE
CONTROL
DEVICE
GALLOP
MODE
PEAK TO PEAK
AMPLITUDE
ESTIMATE
TOP
NONE
1 LOOP
6ft
1.8 m
MIDDLE
NONE
-
0
BOTTOM
NONE
-
0
TOP
NONE
1 LOOP
6ft
1.8 m
MIDDLE
NONE
1 LOOP
0
BOTTOM
4 x 11.3 kg PENDULUMS
-
0
TOP
NONE
1 LOOP
6ft
1.8 m
MIDDLE
NONE
1 LOOP
5 ft
1.5 m
BOTTOM
4 x 11.3 kg PENDULUMS
-
0
TOP
NONE
1 LOOP
6ft
1.8m
MIDDLE
NONE
2 LOOP
10 ft
3m
BOTTOM
NONE
-
0
ELECTRICAL LOAD
COMMENTS
88 MW
ICE THICKNESS ~
1/16 INCH
~1.6 MM
88 MW
88 MW
88 MW
FREQUENCY 0.25
Hz
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Chapter 4: Galloping Conductors
Data from tests on scaled or full-size test lines, sometimes with airfoils to represent ice, are included where
available. More weight should be given to information obtained from observations on actual operating
lines—especially where there are systematic trials
including untreated phases similar to the phases with
the control devices—and such results are included
where possible. When galloping does occur in a span
of an overhead line, the individual conductors are frequently moving at different amplitudes and in different modes under nominally the same exposure to ice
and wind. During an ice storm the galloping amplitudes change as the speed and direction of the wind,
as well as the amount of ice deposited, changes. This
randomness and variability are inherent in the galloping phenomenon. Conclusions on the overall performance of a device need to be based on a number
of separate galloping events. The greatest confidence
can be placed on the devices that have been the subjects of the widest exposure and evaluations. At the
same time the control device needs to be installed on
one or more phases in the same span as nominally
identical phases without controls. Galloping motions
on all the phases need to be documented in order to
obtain statistically supportable conclusions on the
performance of the control devices.
Figure 4.4-17 Galloping reporting forms: Damage and
costs (CIGRÉ 1995).
lowest natural frequencies of the spans and the resulting large-amplitude, low-frequency motions.
• Proper locations for each galloping control device.
The number of devices required for control, or the
physical design of the devices, or the manner of application of the devices may also differ according to the
expected type of ice accretion and the physical details
of the conductor span. Where there are alternative
practices, these are identified. Although application
practices for some of the devices are public knowledge, these practices for other devices are considered
proprietary by the suppliers.
• Limitations and precautions required with each galloping control device.
The performance of a control device may be acceptable in one range of sizes of conductor while less
acceptable in another size range. Also the effectiveness in one weather condition may or may not indicate effectiveness in a different form of icing.
• Observed motions without and with each control
device.
Cautions to be Observed When Applying In-span
Galloping Control Devices
In-span hardware, including galloping control devices
and aircraft warning markers, are concentrated masses,
which can act as reflection points of traveling waves of
aeolian vibration. This vibration due to wind can occur
in the sections of the conductors or overhead ground
wires between the in-span devices, and these sections of
the span are isolated from any vibration damping systems, which are most often applied to the ends of spans.
For spans of conductors with low tension, this does not
cause any problems. However, extra precautions are
needed for spans with tensions approaching the safe tension limits with no dampers (Hardy et al. 1999). The
precautions required are to reduce the stresses concentrated at the metal clamps attaching the hardware to the
conductors. Two alternatives for reducing these stresses
are installing armor rods under the metal clamps or
replacing the metal clamps with elastomer-lined clamps
(Van Dyke et al. 1995). A further option is to add vibration dampers within each subspan between the in-span
hardware.
A second aspect requiring caution applies to galloping
control devices based on the control of torsional
motions. These are custom–designed, based on the
parameters of the conductor span. They are designed to
ensure that the torsional natural frequency, after adding
4-63
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
the devices and a chosen amount of ice and wind, falls
within a range necessary for the proper function of the
control device. The caution required for this is that the
actual parameters of the line need to be known, and that
may necessitate a line survey to confirm that the line is
installed according to the design. In particular, the tension of the conductors has been found to deviate from
the as-designed values, especially in regions where ice
loads have occurred thereby increasing the sag, or where
repairs have been made in the spans. There are ratios of
torsional to vertical oscillation frequency that make a
span more likely to gallop. Consequently, it is possible to
misapply the devices if they are designed with the wrong
input parameters, or if the resonant behavior is not
avoided by proper choice of device dimensions. It is,
therefore, highly recommended that the design of galloping controls be carried out by experienced practitioners.
4.5.2
Ice Prevention, Melting, or Removal
The methods of ice removal from overhead conductors
were summarized as part of a review of ice accretion
technology, and utility operating and design practices
with respect to ice, snow, and wind on overhead lines
(Pohlman and Landers 1982). The methods used to deice overhead conductors were categorized as “passive”
and “mechanical.” The passive approaches include icephobic coatings, which reduce the adhesion forces
attaching the ice to the conductor. However, at that
time, no coating would shed ice without additional
mechanical action such as abrasion or flexing. Heating
by electric current is identified as the commonest utility
practice. Guidelines developed in the 1930s suggested
that prevention of ice accretion required a current of
about 50% of the rating of the conductor, while ice
removal required about 125% of the rating. The survey
concluded that there was no practical means of ice prevention by coatings or mechanical means.
A review focused more tightly on ice and snow removal
alternatives (Laforte et al. 1996) covered a total of 28
technologies from other fields, which may be usable or
adaptable for use in the overhead line de-icing application. Of these, 13 methods have been adapted for use on
overhead conductors. Each deicing system was categorized according to its stage of development, whether it
removes or prevents icing, which types of ice it is
designed to control, the efficiency of deicing, difficulty
of application, and costs of infrastructure and operation. The methods reviewed include thermal, mechanical, passive, or miscellaneous techniques. The more
promising of these methods are described in more detail
below.
4-64
Ice Melting
The protection measure that was utilized earliest was
removal of ice, or prevention of its formation, by heating conductors electrically. One of the earliest applications was on the Pennsylvania Water and Power System
about 1915 (Shealy et al. 1952). Two of three lines connecting Holtwood Hydro Station and Baltimore were
removed from service and connected in series. One end
of this combined circuit was short-circuited, and voltage
was applied at the other to heat the conductors.
Early applications of this and similar procedures were
apparently aimed primarily at preventing failures due to
the weight of ice on conductors, and faults resulting
from contact between phases or a phase and a ground
wire when the sudden release of ice from a span caused
“sleet jump.” Trends toward larger conductors, and
stiffer supports for the smaller ones, and wider use of
flat phase configurations have lessened these problems.
Prevention of galloping has been the primary objective
in ice melting and prevention activities during the last
several decades. The procedures are still used by some
utilities, but ampacity constraints of the transmission
lines and substation equipment prevent their application in many cases. Also, there is a conflict between providing enough resistance in conductors to permit
effective heating, on the one hand, and minimization of
year-round system losses, on the other hand.
The amount of heating required depends upon whether
it is applied before icing begins, so that no actual melting of deposited ice is needed, or after some ice has been
deposited. In the latter case, the amount of heating and
its duration depend upon the thickness of the ice
deposit. In both cases, heating power requirements
depend upon ambient temperature and wind velocity.
The following equations were developed for calculating
the temperature rise of a bare conductor's surface over
ambient for winds greater than 1 m/s (3 mph) (Clem
1930).
ΔT = 4.43x10
−3
Rac I 2
dV
4.5-1
Where
ΔT is temperature rise in °C.
Rac is conductor ac resistance in ohms/km.
I is current in amperes.
d is conductor diameter in mm.
V is wind speed in m/s.
The constant in Equation 4.5-1 is 8.18 x 10-4 if R ac is
given in ohms/mile, d in inches, and V in mph. Equation
4.5-1 has been used to estimate currents needed to pre-
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
vent ice formation, and Clem suggests that a 9°C rise
may be adequate for most conditions.
If ice is already on the conductor, heat must be supplied
to melt through it and also to maintain the conductor a
few degrees above freezing. Clem gives the following
equations for estimating the power per unit conductor
surface area, for each of these:
d ( ti + 0.11d )
563m
ΔT
wc d =
d
14980
+ 877 log i
d
Vdi
wi d =
4.5-2
4.5-3
Where
wi is melt-through power in watts/mm2.
wc is power to maintain temperature rise in
watts/mm2.
ti is ice thickness in mm.
m is melt-through time in minutes.
di is diameter of conductor with ice in mm.
If wi and wc are in watts/in2; ti, di, and d are in inches;
and V is in mph:
29.1d ( ti + 0.11d )
m
ΔT
wc d =
d
175
+ 34.53l og i
d
Vdi
wi d =
4.5-4
ti
mRac
I = 64.6d 0.68
4.5-8
using the above metric units, or
ti
mRac
I = 3726d 0.68
4.5-9
using the English units above. The equation correlates
well with results of ice melting testing performed by E.
K. Lanctot of Alcoa Laboratories, as shown in Table
4.5-1.
Table 4.5-1 Currents to Remove 25.4 mm (1 in.) Thickness
of Ice in One Hour (Lanctot et al. 1959)
Conductor
Based Upon
Size
(kcmil)
Diameter
(in.)
From Test
(amp)
From Eq’n
(4.5-9)
(amp)
648a
1.093
1240
1355
795
1.108
1420
1517
954
1.165
1560
1721
1186a
1.60
2070
2382
1346a
1.75
2335
2695
1275a
1.60
2150
2470
1414
1.75
2395
2761
a. Expanded ACSR
4.5-6
in the above metric units, or
I = 446.15 ( wi d + wc d ) / Rac
ent temperatures near freezing and winds of 1.3 m/s
(3 mph) or less:
4.5-5
The current required for melt-through becomes
I = 1772.5 ( wi d + wc d ) / Rac
Chapter 4: Galloping Conductors
4.5-7
using the above English units.
Thus, the choice of current is influenced by wind velocity, how far ambient temperature is below freezing, how
quickly the ice must be removed, and how thick it is at
the beginning of thawing (Lanctot et al. 1959).
Another formula for estimating melt-through currents
has been developed by H. E. House of Alcoa for ambi-
The increased currents needed for ice prevention or
removal may be attained by routing load flow within the
system, by removing circuits from service and applying
short circuits, or by producing circulating currents
within the system by forcing phase shifts over the length
of the line (Shealy et al. 1952; Corey et al. 1952;
DeSieno et al. 1952; Oehlwein 1953). Each of these
methods requires special switching and, sometimes,
equipment specifically intended for that purpose. Protective relaying arrangements may have to be altered.
Prior arrangements and training are necessary.
Arrangements encompass: provisions for obtaining
early warning of possible icing conditions from meteorological services; detection of icing, usually by monitoring attenuation of carrier signals; and setting up
predetermined strategies to be followed by dispatchers
based upon the system load condition, location of icing,
and the trend in the weather.
The need to make prior arrangements, and limitations
on switching options, generally lead to preselection of
heating currents, and utilities base these selections upon
4-65
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
conditions in their own systems. Care must be taken
that conductors are not annealed or allowed to sag
below required clearances, and that connectors, buses,
and other components do not become overheated. An
example of a heating current table for sleet melting is
shown in Table 4.5-2.
Table 4.5-2 Heating Current for Sleet Melting Used at
American Gas and Electric System (DeSieno et al. 1952)
American Gas and Electric System
Range of Sleet Melting Currents for Various Temperatures
near 30ºF Ambient
Conductor Size
(circular mils)
Short Circuit Current
Minimum Amperes Maximum Amperes
200,000 Cu
475
366,400 ACSR
550
550
700
397,500 ACSR
550
750
800
477,000 ACSR
575
556,500 ACSR
600
900
636,000 ACSR
625
1000
There appear to be no data available on the extent of
usage of ice prevention and melting by electrical heating,
or on percent effectiveness where used. One utility system used such procedures 202 times in ten years, prior to
1952 (Corey et al. 1952), and another applied them 20
times during a single month in 1956 (Chadha 1974).
Utilities that still employ “sleet melting” also still experience galloping, but information is not available on how
much more galloping would have occurred without it.
An experience of Bonneville Power Administration in
the Cascade Mountains (BPA 1974) showed that lower
levels of current can still be effective in limiting ice deposition. During an extreme four-day storm, ice buildup
was monitored on two parallel lines. One line was
loaded at between 15 and 27% of its rating, while the
other was loaded at 24 to 43%. Ice buildup occurred 30
hours later on the more heavily loaded line, and that line
shed its ice 7 hours earlier. The maximum radial thickness of the ice was 1.9 cm on the heavier loaded line
compared to 4.3 cm on the other line.
Manitoba Hydro has been employing ice and snow melting as an organized practice for reducing loads on lines
for some time (Tymofichuk 1978; Farias 1999). This is a
region where serious ice storms are relatively frequent,
and the capital expense for additional switching, development of standard operating procedures, and training
of staff can be justified. About 60 ice storms of varying
severity, from minor to catastrophic, were documented
in a 37-year period. Switching equipment has been
incorporated into substations to allow sections of their
grid to be isolated and current to be circulated in
selected lines to melt off the accretion. Three-phase
4-66
shorts are created at predetermined locations. Short customer outages must be taken to enable these procedures.
A total of 2628 km (1633 miles) of 33 to 115 kV lines
was cleared of ice using ice melting during a major
storm period in February 1998. The voltages applied to
generate the currents for melting were from 8 to 33 kV.
The average duration of each melting period was 11
minutes. In addition to switching ac current, a scheme to
inject dc for ice melting is under consideration.
Ice-phobic Coatings
In the 1980s, EPRI sponsored a study of potential icephobic coatings (Baum et al. 1988). The various coatings were evaluated based on ice adhesion tests. In these
tests, a coated cable strand was embedded in a block of
ice, and the load required to pull the strand out was
measured in a tensile test machine. The test was conducted at a temperature of –10ºC. The shear stress was
determined from maximum load required to remove the
wire from the ice divided by surface area of the wire
embedded in the ice. The coatings with the lowest shear
strength were found to be silicones and elastomeric-type
materials. Teflon-type coatings were less effective. Several oil-filled coatings were also tested and found to
have low adhesive strength. Coatings with low inherent
strength could be easily damaged and are, therefore, less
suited to use on lines where a certain amount of handling is required.
Covered conductors, one example of which is shown in
Figure 4.5-1, have also been considered to reduce galloping through prevention of ice accretion. Such conductors consist of cross-linked polyethylene (XLPE)
jacketed round strand or compact ACSR or AAAC
conductors of various designs, and are used mainly for
low-voltage applications in residential areas. Field studies of ice buildup on this type of conductor over an
eight-year period (Wareing and Chetwood 2002)
showed that, when the conductors are new, they do shed
wet snow readily. But after some time exposed to normal weathering, pollution, etc., the surface becomes
rough, and the adhesion of wet snow is similar to that
on other types of conductor.
Figure 4.5-1 Sample covered conductor (Wareing
2002). 1. Compacted AAAC core. 2. Semiconducting
layer. 3. Polyethylene layer. 4. XLPE jacket.
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
An alternative method of testing to evaluate adhesion of
coatings was developed under contract to HydroQuébec (Laforte and Beisswenger 2005). Samples of
coatings were applied to the surfaces of flat blades,
which were spun at increasingly high speeds in a centrifuge. The speed at which the coating released was measured, and the shear stress at the surface determined, to
give the relative adhesion of different coatings. Eighteen
different coatings were evaluated. The results indicate
that the greases and nonpermanent coatings are more
effective than the solid coatings. Some coatings actually
increased the adhesion compared to bare aluminum.
Passive Snow Removal Techniques
In regions where wet snow accumulates on overhead
lines, the accumulation has been found to be reduced by
the addition of snow rings around the conductors
(Higuchi 1972; Saotomi et al. 1988). The snow tends to
form on the top surface of the conductor and slide down
in the direction of the strands, as indicated in Figure
4.5-2, top. With increasing accumulation the snow slides
around the conductor, following the direction of the
conductor stranding. The addition of rings (Figure 4.52, middle) or wires wound around the conductor in
opposite direction to the lay of the strands (Figure 4.52, bottom) causes the wet snow to fall off. The rings and
wires break the surface tension through which the snow
adheres to the bottom of the conductor.
Chapter 4: Galloping Conductors
counterweights, as shown in Figure 4.5-3. The effectiveness of the snow rings and rings plus counterweights was
determined, using automatic monitoring systems
installed on 12 sample locations, during wet snowstorms
during a period of two years. The instrumentation
included lights and video cameras, weather-monitoring
devices, and load cells to measure the weight of snow on
each conductor with different snow removal schemes.
The test program also included some conductors
wrapped with a low-Curie-point wire, as shown in Figure
4.5-4.
This low-curie point material undergoes a large increase
in resistance at a specific temperature, the “curie point.”
When aluminum wire with a low-curie-point alloy core is
wound around the conductor, and the temperature drops
to below this temperature, which is around the freezing
point, the induced current increases and heats the conductor locally, and melts any ice or wet snow buildup.
A sample of the results obtained on a 314m (1030 ft)
span of 52.8 mm (2.0 in.) diameter of TACSR1520 conductor on a 154kV line is illustrated by Figures 4.5-5
and 4.5-6. The conductors all carried a current of 230
amps during the period of the measurements. Figure
4.5-5 shows the snow profiles on the conductors with no
treatment, with rings and counterweights, and with lowCurie wires. Figure 4.5-6 shows the weight of snow ver-
In the Kanso region of Japan, about 50% of the overhead lines, concentrating on the areas where wet snow
most often occurs, have been treated with the snow rings,
(Saotome 1988). To improve the torsional stability of the
conductors, some are equipped with both rings and
Figure 4.5-3 Combination of rings and counterweights for
wet snow removal from conductors (Saotome 1988).
Figure 4.5-2 Top: Path of wet snow accretion sliding in
strand direction. Middle: Snow rings. Bottom:
Counterflow wires added to conductors to promote snow
shedding (Higuchi 1972).
Figure 4.5-4 Conductor wrapped with low-Curie-point
wire (Saotome 1988).
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Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
sus time for these three treatments, plus a sampler, a
short length of conductor rigidly attached to one of the
towers. The diagrams show that the sampler overestimates the snow loads on the conductors, that the highest loads are on the conductor with no treatment, and
there are improvements when rings and weights are
added. The greatest improvement was seen with the lowCurie wire wrap. In addition to the lower weights of
snow, the duration of snow accretion on the conductors
was also reduced slightly.
To summarize the use of the various methods of ice and
snow removal through melting, coatings, and add-on
passive devices, there is localized application of some of
these techniques. These are in place on lines in locations
where icing is frequent and the importance of the lines
can justify investment in the capital cost of the special
equipment needed. It is not likely that any utility would
apply any of these systems widely to their systems
because of the high capital costs involved.
Mechanical Removal Methods
A traditional method of removing ice from lines is by
rolling. Manitoba Hydro has used ice rolling routinely
for de-icing lines, as they typically have more than one
ice storm each winter (Farias 1999). A basic ice roller is
illustrated in Figure 4.5-7. The roller is placed over the
conductor by a lineman, and a rope attached to a loop
below the pulley is pulled along the conductor by hand
or from a vehicle. The pulley is aluminum to minimize
damage to the conductor. The techniques can be used
on live lines at 12 kV, and at 25 kV with an insulated
link in the stick. At higher voltages the lines must be
deenergized. The rolling method can be used under
most weather conditions, and can be applied to phase
conductors and overhead ground wires. The procedure
is highly labor intensive, time consuming, and expensive.
Damage can occur to insulators and conductors, and
the roller can get wedged on splices.
Figure 4.5-5 Snow profiles observed during field test of
snow shedding measures (Saotome 1988).
Figure 4.5-6 Measured snow weight during field test of
snow shedding Measures (Saotome 1988).
4-68
Figure 4.5-7 Basic Ice Roller (Farias 1999).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
The severe ice storm that crippled the power system of
the Canadian province of Québec in January 1998
caused a resurgence in the research on overhead line
icing and in the development of various means of
removing ice from conductors and overhead ground
wires in similar emergencies. One of these is a remotely
operated, mechanized version of the roller described
above. This has been developed for Hydro-Québec (Leblond et al. 2002), and Figure 4.5-8 shows this device
removing artificially formed ice deposits using the set of
steel blades, shown on the right of the vehicle. This
device is designed to de-ice overhead ground wires and
has evolved from a manually drawn prototype. It has
also been successfully tested on conductors of lines at
voltages up to 315 kV. The device can operate as far as
1 km away from the ground-based controller. The development of this device is continuing with inclusion of
other functions, such as photography of the conductor
to show burnt strands and other damage, and infrared
thermography to identify hot spots.
An impulse device under development (Leblond et al.
2002) takes advantage of the brittle nature of ice at cold
temperatures. This is a hydraulic cylinder that can be
installed from a helicopter or insulated boom truck. A
fast-acting release of gas within the cylinder imparts an
impulse to the conductor or overhead ground wire to
which it is attached. Figure 4.5-9 shows the device
installed on the 100 m (328 ft) 12.7mm (0.5in.) diameter
steel cable used as a test line, and Figure 4.5-10 shows a
sequence of images of the ice being removed from the
test line. The shock wave de-icer sends a traveling wave
along the conductor, which decays in energy with distance from the device. The development is continuing
toward increased power capacity, and repeated
impulses.
Figure 4.5-8 Remotely operated de-icing vehicle
(Leblond et al. 2002).
Chapter 4: Galloping Conductors
Another impulse-based device, which eliminates the
need for installation from a bucket truck or helicopter, is
shown in Figure 4.5-11 (Leblond et al. 2005). This
device consists of a piston, which is attached to the conductor, a revolver system carrying six blank cartridges,
and an electronic receiver circuit to charge a capacitor
on command and fire the cartridge. A ground-based
radio frequency system creates the signal used to trigger
the charge and explode the cartridge. The device is
attached to the line by firing a projectile with a light line
attached over the conductor or ground wire to be deiced, using a commercially available line thrower, a
device commonly used by Coast Guards during rescue
operations. This light line is used to pull a heavier pulling line over the conductor. That line is used to raise the
device into place around mid span, and to secure it
against the conductor.
The device includes a chamber of six cartridges, and one
cartridge within the device is fired remotely to produce
the desired impulse. The ice is removed by the traveling
wave emanating on each side. In field trials this has successfully removed artificially produced ice layers up to
12.7 mm (0.5 in.) thick from a 100m (328 ft) length of
12.7mm diameter steel ground wire. Multiple impulses
are recommended for longer lengths. The device has
also been investigated for use in de-icing optical ground
wires (OPGW). However, there is a concern that the
impulse might impair the ability to transmit data after
use. In simulated tests without ice, repeated firings were
applied, and although high strains were measured at the
suspension clamps, no optical degradation was
detected. Tests on de-icing OPGW showed that it has
Figure 4.5-9 Shock wave de-icing prototype
(Leblond et al. 2002).
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Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
higher mechanical impedance than normal overhead
ground wire, and the device needed multiple shots to be
fully effective.
A further alternative mechanical approach to ice
removal relies of the weakness of an ice layer in shear
created by twisting the conductor (Laforte et al. 2005).
The procedure is reported to have been successful in
removing naturally formed ice on cables on three occasions. A ratcheting device was developed to facilitate
twisting (Figure 4.5-12). The device is clamped to the
conductor, and one handle serves as a restraint, while
the second is used to turn the conductor. The procedure
required up to ten rotations on a 200-m (656-ft) span of
11-mm (0.4-in.) diameter overhead ground wire with
fixed ends, and removal was achieved in 2-3 minutes.
Figure 4.5-13 shows the ice being removed from a 15-m
(49-ft) test span of 11 mm (0.4-in.) diameter steel cable
with about 25 mm (1 in.) of radial glaze ice. The method
appears to be based on a weakness in the adhesion of ice
to conductors, and may be applicable to unenergized
conductors and overhead ground wires. The operator
needs to be close enough to the conductor to install the
Figure 4.5-10 Successive images of de-icing of a
100-m, 12.7-mm diameter steel test line using the shock
wave de-icer (Leblond et al. 2002).
Figure 4.5-12 Twisting device installed on an iced
test conductor (Laforte et al. 2005).
Figure 4.5-11 De-icer actuated by cartridge in
place on a test line (Leblond et al. 2005).
4-70
Figure 4.5-13 Removal of ice from a test conductor using
the twisting device (Laforte et al. 2005).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
clamp and turn the conductor using the handles. Mechanized versions of the device are being developed.
Although there is a significant research effort being
applied to the removal of mainly glaze ice by mechanical means, none of these new technologies can be considered practical for de-icing long lengths of operating
overhead lines. Melting of accreted ice through the
application of higher than normal currents is being used
by some utilities, and when suitable switching is in place,
fairly long lengths of line can be de-iced. Some utilities,
in countries where freezing rain is a regular wintertime
occurrence, have resorted to replacing overhead lines by
underground lines, but this option is limited to low-voltage circuits.
4.5.3
Alternative Conductor Designs
The T2 conductor, introduced in the 1980s, is specifically designed to reduce wind-induced motions, including galloping, through aerodynamic modification
(Douglass and Roche 1985) (Figure 4.5-14). A virtually
identical conductor design, distributed under the name
“VR” conductor, is essentially two smaller, standardconstruction, ACSR or AAC, conductors twisted
together with a lay length of about 2.7 m (9 ft). Based on
wind tunnel testing and some field trials, it was concluded that this type of conductor can be an effective
alternative to normal round conductors for suppression
of aeolian vibration and galloping. The presence of the
continuous twist in the conductor profile creates counterbalancing alternating upward and downward wind
forces, which resist the creation of coordinated wind
forces along the span necessary for galloping to occur
(Figure 4.5-15). At this time this type of conductor has
been used in smaller sizes of new low-voltage single conductor lines and a few twin bundle lines.
The T2 conductor was evaluated in comparative field
tests in Texas and Illinois, in which the twisted-pair con-
Figure 4.5-14 Twisted-pair conductor for vibration and
galloping motion reduction (Douglass and Roche 1985).
Chapter 4: Galloping Conductors
ductor and standard round conductors were mounted in
parallel phases of the same span and circuit on operating lines (Shealy 1980). The sizes of T2 ranged from 2 x
0.464 in. diameter to 2 x 0.885 in. diameter. Over a twoyear period, the lines were observed during eight galloping events in which the round strand conductors and the
shield wires were seen to gallop while the T2 conductors
were quiet. The galloping amplitudes on the standard
conductors varied from “very little,” through 1-1.5 to 8
ft, to “substantial.” There was also one event with an
estimated 2-in. thickness of ice, with 6–in. icicles, in
which all phases including the T2 conductor galloped
with up to 3 ft peak-to-peak amplitude. The field studies
were also used to assess the aeolian vibration levels
occurring with T2 compared to standard round conductors. Vibration recorder measurements showed significant reductions in the bending amplitudes, and the
author suggests that the T2 conductor can be safely
used without additional dampers.
This twisted-pair T2 conductor design has been used in a
vertical twin bundle 345-kV arrangement, without spacers or dampers, on a 345-kV line on wooden H-frame
structures, in New Mexico by the El Paso Electric Company (Hunter 1994). The line is exposed to seasonal
modest to high winds and occasional ice storms. Broken
overhead ground wires and extensive wear of the hardware were reported after a few years in service. This
damage was accompanied by shield wires pulled along
the line and twisted structures. Tower movement on the
order of 30 cm (1 ft) along the line, and excessive conductor twisting, were observed. Most of the damage
occurred on exceptionally long spans over a region of
rolling hills. Less damage was experienced on two other
segments of the line with spans lengths about 250 m
(800 ft). Vibration recorder traces indicated the presence
of high-amplitude vertical conductor motions in a wide
range of frequencies. Adding Stockbridge dampers
removed the excessive high-frequency vibration. On one
Figure 4.5-15 Variation of aerodynamic profile to the
wind from twisted-pair conductors (Kaiser 1979).
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Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
occasion, modest galloping was seen after an accretion
of about 13 mm (0.5 in.) of radial ice under light winds.
It is not likely that the damage in this line occurred due
to conductor galloping, although the vibration traces do
show low-frequency motions present. However, the case
is included here because the twisted-pair conductor can
be prescribed for galloping control. But all its peculiarities are not fully understood, and other forms of vibration appear to be possible.
The second conductor design that has been recently
introduced and is intended to counteract the wind
effects is the oval conductor (Sanders 1997). This design
also has a continuous twist along the length and consists
of strands with different areas and shapes to create the
desired outer profile. Figure 4.5-16 shows the crosssectional profile of this conductor. The extent of usage
and effectiveness of this design of conductor are
unknown at this time.
Smooth-body conductors have also been proposed for
improved antigalloping performance. These conductors
are composed of trapezoidally shaped strands, as shown
in Figure 4.5-17. Some limited laboratory measurements suggest that these have higher internal damping
than conductors with round strands. However, trapezoidal strand, smooth–profile, self-damping conductors
have been in use for several decades in the Canadian
provinces of Alberta and Saskatchewan, where galloping occurrences are frequent (Perry et al. 1992). There
appears to be no benefit from the smooth-body profiles.
Figure 4.5-16 Cross section of a “Linnet/OVAL”conductor
for vibration and galloping mitigation (Sanders 1997).
Covered conductors have also been considered as possibly less gallop-prone. These are discussed in Section
4.5.2.
4.5.4
Increased Clearances
In the absence of active methods to eliminate galloping,
the principal opportunity to reduce the effects of galloping occurs at the design stage. These effects are limited
by a passive approach, which is to include separations,
especially horizontal separations, between conductors,
that are sufficient to avoid most phase-to-phase contacts
and flashovers. These separations dictate the tower
shape that cannot be modified easily once the tower is
installed.
Many utilities have guidelines aimed at providing sufficient spacing within the tower heads to reduce the probability of overlapping of the galloping motions of the
phase conductors and overhead ground wires, thus
avoiding contacts between them. A summary of these
approaches is given in (EPRI 1980). The design
approaches are basically similar to the concepts introduced by Davison (Davison 1939). These are based
upon observations of amplitudes and mode shapes in a
number of cases of actual galloping. The design methods involve laying out elliptical envelopes around the
conductor positions under standardized conditions of
wind and ice loading. The envelopes are intended to represent the maximum excursions, during single-loop
motions, of the galloping orbits at mid-span. The conductor and overhead ground wire positions are the positions including the sag at mid-span under the chosen ice
and wind load. The ellipse sizes vary between the different design methods, but the ellipse axes are normally
scaled in terms of the sag under these chosen wind and
ice loads. Figure 4.5-18 shows the approach schematically. The symbols in the figure have the following significance, corresponding to Davison’s recommended
values:
A1 = D L
DL = sag under wind and ice load
A2 = A1/4
A3 = 0.3 m (1 ft)
θ = φ /2
φ = angle of conductor swing out under
A5 = 0.4A4
the selected loading
Figure 4.5-17 Smooth-body conductors with trapezoidal strands. Left: compact conductor
(McCullogh and Ralston 1981). Right: self-damping conductor (Aluminum Association 1989).
4-72
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
It had been observed that, when certain spans galloped,
the motion most often seen was the two-loop mode, and
the single-loop mode was rare. These observations were
on deadend–deadend spans and very long spans. For
these spans alternate lower values of the major, A4 , and
minor, A5 , axes of the ellipse have been proposed (Toye
1951). The proposed values are:
A4 ≈ DL / 2 2
4.5-10
A5 = 2 A4
4.5-11
These basic shapes for the clearance ellipses have been
modified by several utilities based on their own experience. Table 4.5-3 summarizes some of these variants. A
more complete description is given in (EPRI 1980).
Davison’s suggested value of θ in Figure 4.5-18 had the
ellipse tilted opposite to the blowout angle, φ. Other val-
Chapter 4: Galloping Conductors
ues have been used. It appears from the database of field
observations that tilts in both directions are regularly
experienced with perhaps a higher incidence of tilts that
are in the same direction as the blowout angle.
Given A 4 , dimension A 2 in Figure 4.5-18 is of minor
importance with respect to phase-to-phase clearances, if
all phases are assumed to gallop. An error in estimating
A 2 does not affect the relative positions of the phase
ellipses. A2 is important to phase-to-ground wire clearances, especially if the ground wire is assumed not to
gallop. Simultaneous phase and ground wire galloping
was observed in only about 10% of reported cases. For
galloping in two and more loops, the galloping ellipse is
very nearly centered on the conductor’s blown-out atrest position.
All of these galloping ellipse systems have apparently
served well in that they have resulted in reduced outage
rates. Statistical data on the degrees of reduction do not
appear to be available, but the reductions are generally
thought to be quite significant.
The issue of whether spans are more likely to undergo galloping in single- or two-loop mode was addressed by Anjo
(Anjo et al. 1974). From studies of two-and four-conductor bundle lines, the behavior was related to a parameter
M given by:
M=
m2A 2
EA
24T 3
4.5-12
Where
E is the final modulus of the conductor.
A is the area of cross section of the conductor.
A is the span length.
M is the mass per length of the conductor.
T is the conductor tension.
Figure 4.5-18 Generic galloping ellipse envelope
inscribed around sagged conductor at mid-span (EPRI
1980).
This parameter is equal to ea /e, in which ea is the excess
of catenary length over secant span length, expressed as
a fraction of the latter, and e is elastic strain of the con-
Table 4.5-3 Sample Dimensions of Galloping Clearance Ellipses
Source
A4
A5
A2
Comment
Davison 1939
1.25 DL + 0.3 m (1 foot)
0.4 DL
A1/4
Single-loop galloping
Toye 1931
DL/2√2
2√A4
DL/2
Two-loop galloping
REA 1962
DL + 0.6 m (2 feet)
0.4 DL
0.3 m (1 foot)
Single-loop galloping
AEP (EPRI 1980)
1.25 DL
DL + 0.3 m (1 foot)
0.33 A4
0.3 m (1 foot)
Single-loop galloping
Ontario Hydro
F.DL + 0.3 m (1 foot)
0.4 A4
A4/4
F is a galloping factor between
0.8 and 1.4
Commonwealth Edison
1.4 DL + 0.3 m (1 foot)
1.25 A4
0.4 DL
Single-loop galloping
Russia
(Baikov 1967)
35-220 kV: 0.45DL + 1m
300 kV: 0.9 DL
500 kV: DL
0.33 A4
A4/5
Single-loop galloping
4-73
Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Table 4.5-4 Guidelines for Galloping Clearance Ellipses Based on Anjo’s Method (Anjo et al. 1974)
Deadend Spans
Suspension Spans
A4
Sag
DL < D
0.58 DL
DL<0.83 D
1.25 DL
D1* < DL < D2*
0.37 DL + 1.3 m
0.83 D1* < DL < D1*
1.04 DL
D2* < DL < 27.3 m
0.45 D2*
D1* < DL < D2*
0.24 DL + 5.0 m
DL > 27.3 m
2.27 DL
D2* < DL < 32.8 m
0.54 D2*
DL > 32.8 m
0.27 DL
*
1
ductor due to its loaded tension. The guidelines developed from this approach differentiate between the
expected ellipse sizes for dead-ended and suspension
spans. The recommendations are presented in Table
4.5-4 in which D1* and D2* are the sags corresponding
to M = 1.5 and 4.0, respectively.
A similar approach was taken by the Bonneville Power
Administration (Winkelman 1974). Their approach
assigns values to the major ellipse axis, A4, according to
span length, single or bundle conductor, and dead-end
or suspension span type. The approach is summarized
in Figure 4.5-19. The asterisks identify span lengths
below which single-loop galloping, and above which
two-loop galloping, are assumed.
The ellipses surrounding the various conductors and
overhead ground wires need to be separated by sufficient air gap to eliminate flashovers at the corresponding phase-to-phase or phase-to-ground voltage. Table
4.5-5 shows the separations required.
Figure 4.5-19 Bonneville Power Administration
guidelines on galloping ellipse amplitude (Winkelman
1974).
4-74
A4
Sag
*
1
Table 4.5-5 Clearances Required to Avoid Flashovers
Between Conductors and Overhead Ground Wires at
Different Voltages (EPRI 1980)
Voltage
115 kV
138 kV
230 kV
345 kV
500 kV
PhasePhase
0.46 m
(1.5 ft)
0.46 m
(1.5 ft)
0.76 m
(2.5 ft)
1.07 m
(3.5 ft)
1.83 m
(6.0 ft)
PhaseGround
0.30 m
(1.0 ft)
0.30 m
(1.0 ft)
0.61 m
(2.0 ft)
0.76 m
(2.5 ft)
1.22 m
(4.0 ft)
Analyses of Field Data of Conductor Galloping
Data from 81 galloping events were gathered over several years by the “Galloping Conductor Task Force” of
the Edison Electric Institute (EEI) and documented in
the chapter on galloping in the EPRI “Orange Book”
(EPRI 1980). The reports include the basic design
parameters of the line and the weather and galloping
activity on lines without any control devices installed,
but not all data were collected in every case.
Figure 4.5-20 shows the plot of these results in the form
of peak-to-peak galloping amplitude, Ymax, versus span
length, S, for conductors supported in spans that are in
suspension at at least one end, along with several cases
for which the support conditions were not reported.
Figure 4.5-21 shows the equivalent values for conductors supported at both ends by dead-end structures. In
Figures 4.5-21 and 4.5-22, the small numbers indicate
the number of galloping loops reported, and circled values are for bundled conductors. These two plots provide
field data for comparison with each of the above design
methods. The maximum galloping amplitude reported is
about 12 m (39.3 ft). Also there is a slight tendency for
more galloping loops in the longest spans and in deadended spans.
It is of interest to compare the amplitudes reported in
the EEI’s collection of galloping cases, and in previous
reports and papers, with the suggested values of A4 discussed above. Unfortunately, the comparison cannot be
done in a rigorous manner, since the loaded sags that
exist during galloping are usually quite difficult to deter-
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
mine and are rarely reported. Comparison must be
based upon bare-wire sags and, since most of these have
been referred to 60°F (16°C), that reference temperature
has been used.
Influence of Ice Thickness and Wind Speed
The observed ice thicknesses during 21 different glaze
ice galloping events are shown in Figure 4.5-22. This
and Figure 4.5-23 show data extracted from reports that
include more than one phase and span, and so there can
be several points plotted from each event. This figure
Figure 4.5-20 Field data from galloping events: Peak to
peak galloping amplitude versus span length for
suspension spans (EPRI 1980).
Figure 4.5-21 Field data from galloping events: peak-topeak galloping amplitude versus span length for deadended spans (EPRI 1980).
Chapter 4: Galloping Conductors
shows that the majority of galloping events occur with
thin layers of ice, and consequently, use of bare-wire
sags should be acceptably close in most cases, except
where small conductors or short spans are involved.
The wind speeds recorded during the same set of 21 galloping events are shown in Figure 4.5-23. This figure
shows that most events occur with wind speeds between
Figure 4.5-22 Data from 21 galloping events from
database compiled during field studies showing that
most events occur with low ice thickness (Havard and
Pohlman 1984).
Figure 4.5-23 Data from 21 galloping events from
database compiled during field studies showing that
most events occur with wind speeds between 15 and 35
mph (24 and 56 km/h) (Havard 1979).
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Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
15 and 35 mph (24 and 56 km/h). The corresponding
wind pressure is then in the range of 0.6 to 3.1 pounds
per square foot (29 to 148 Pa). The value of 2 pounds
per square foot (96 Pa), which is the pressure due to a
28-mph (45 km/h) wind, used in the REA guide (REA
1962) then appears to be a reasonable intermediate
value. When the area of the conductor including the ice
accretion is being considered, the relative positions of
phases would be the same, but there could be different
positions relative to the overhead ground wire.
Influence of Span Parameters
There are several dimensionless, or other, ratios between
the various parameters that can be used to describe a
span of conductor and its galloping behavior. Based on
adequate data from observations from the field, the galloping amplitude can be correlated with these various
parameter ratios. Some of these are shown below.
The same database of field observations of galloping
was used in an analysis to relate maximum galloping
amplitude to line parameters (Rawlins 1981, 1986; with
additional data courtesy of C. B. Rawlins). The resulting
set of trend lines is presented in Figure 4.5-24 in the
form of curves of equal peak to peak galloping amplitude / span length, Ymax / S, versus catenarity factor, M',
and tension / unit weight of conductor, T/w. M ' is
expressed by Equation 4.5-13. Here EA' is an adjusted
longitudinal stiffness including the flexibility of insulator strings of different length, or deadend strings.
M '=
w2 S 2
EA'
24T 3
Figure 4.5-24 Estimated maximum peak-to-peak
galloping amplitude/sag versus catenarity factor
and tension/weight (Rawlins 1986).
4-76
4.5-13
The above database was augmented by additional data
from extensive field trials of galloping (Havard and
Pohlman 1984; Havard 1996), increasing it to a total of
166 observations of galloping on single, twin, triple, and
quad bundle lines. The field observations in the database cover the range of line parameters as follows:
• sag/span ratio in the range 1-5%
• conductor diameter between 1 and 5 cm (0.4 and
2 in.)
• single-conductor span lengths 50 to 450 m (160 to
1500 ft)
• bundle conductor span lengths 200 to 450 m (650 to
1500 ft)
Conventional expectations of galloping behavior are
exceeded, for maximum galloping motions on short
spans, and through the existence of single-loop galloping on long spans.
Plots of the maximum galloping amplitudes and maximum galloping amplitudes divided by sag, for single
conductors, as observed in the field from the above
database, are shown as functions of span length, in Figure 4.5-25. Both plots show continuous envelopes
around the maximum values.
This expanded database has been subjected to further
study aimed at improved guides to maximum expected
amplitudes. These studies have sought to correlate various parameters, some dimensionless, for expressing
amplitude with others expressing aspects of the span’s
design. Some of these further analyses are included in a
manual for “Gallopmode3” software (courtesy of C. B.
Figure 4.5-25 Envelopes encompassing maximum
peak-to-peak galloping amplitude and peak-to-peak
galloping amplitude/sag versus span length from 95
galloping events on single conductors (Havard 1998).
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
Rawlins). Two examples from that source are shown
here as Figures 4.5-26 and 4.5-27, which are plots of galloping amplitude divided by span length versus tension
divided by mass for single and bundle conductor lines,
respectively.
The various correlations are, of course, empirical. Not
surprisingly, they lead to somewhat different estimates
of maximum expected galloping amplitudes. Natural
galloping involves too many variables for its essence to
be captured by only two parameters. Thus, the different
correlation patterns are simply limited views of the same
mass of data taken from different perspectives
This diversity of estimates presents a problem to the
designer: which to use in designing clearances? In applying the envelopes of these various plots of the same data
bank to the development of design guidelines for clearances between phases and overhead ground wires within
tower heads, the smallest estimate of amplitude from the
various presentations is closest to the true maximum,
but also some statistical estimate of variance needs to be
applied. While the database, having over a hundred
observations, may appear quite large, on examination,
the data for lines close to any particular set of parameters is sparse, and the extreme values observed may not
reach the potential true maximum for that class of line.
Consequently it is prudent to include some margin to
account for possible higher galloping motions under
exceptional weather conditions.
An alternative analysis of the same database (Lilien and
Havard 2000) employs the reduced amplitude, which is
the ratio of peak-to-peak galloping amplitude (Apk-pk)
over conductor diameter (φ), both in m:
A pk − pk
Figure 4.5-27 Plot of galloping amplitude/span length
versus conductor tension/mass for bundle conductor
lines (courtesy of C. B. Rawlins).
4.5-14
φ
From the observed field data in the database, this
reduced amplitude has a range between 0 and 500.
The conductor span parameter is a combination of the
catenary parameter with the ratio of conductor diameter (φ) over the square of the span length (L), which can
also be expressed as the ratio of conductor diameter
over the sag (f). The conductor span parameter is
dimensionless:
100
T .φ
100.φ
=
2
8f
mg.L
4.5-15
This conductor span parameter has been used to normalize the maximum galloping amplitudes in the database. The parameter shows a clear distinction between
single and bundle conductors, and a similarity among
all types of bundle conductor. For the field data from
single conductors, this parameter has a range of 0 to 1.0
with tension in N, mass in kg/m, and span length, sag,
and diameter in m. For the bundle conductor field data,
this span parameter has the range of 0 to 0.12, in the
same units. The dimensionless conductor span parameter is useful, because it shows clear trends on the global
database. For single conductors, the fitted curve to the
maximum amplitude over conductor diameter, which is
included in Figure 4.5-28, is given by:
A pk − pk
Figure 4.5-26 Plot of galloping amplitude/span length
versus conductor tension/mass for single-conductor
lines (courtesy of C. B. Rawlins).
Chapter 4: Galloping Conductors
φ
= 80. ln
8f
50.φ
4.5-16
Figure 4.5-28 Variation of observed maximum peak-topeak galloping amplitude/diameter on single conductors
as a function of the conductor span parameter (Lilien
and Havard 2000).
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Chapter 4: Galloping Conductors
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
For bundle conductors, the corresponding fitted curve,
which is reproduced in Figure 4.5-29 as the estimated
maximum, is given by:
A pk − pk
φ
= 170 . ln
8f
500 .φ
4.5-17
It may be noted that the expressions have the same
form, but single conductors have up to about 2.5 times
larger values of galloping amplitude/diameter for values
of the conductor span parameter between 0.015 and
0.10.
Figure 4.5-30 shows the variations of peak-to-peak galloping amplitudes/conductor diameter versus sag/conductor diameter for single and bundle conductors based
on the fitted curves describing the maximum observed
galloping motions from the field data. These are the
same curves, expressed in Equations 4.5-16 and 4.5-17,
plotted on semi-logarithmic scales as shown in Figures
4.5-28 and 4.5-29. The points superimposed on the fit-
ted lines indicate the extent of the actual field data on
which they are based. As shown in those figures, the
curve representing the maximum galloping motions on
single conductors is a better fit to the data than that for
the bundle conductors. These curves offer a contribution toward a potentially improved approach to designing clearance ellipses to accommodate galloping
motions within tower heads.
Orbit Shape and Orientation
The U.S. and Canadian field trials of galloping control
devices (Havard and Pohlman 1979; Havard and Pohlman 1984; Havard 1996) produced an extensive archive
of films of the events reported. Since that program finished, the clearest of these films were selected for further
analysis (Pon and Havard 1994). A total of 44 films were
used, showing galloping events on single conductors and
twin, triple, and quad bundle lines. The films were carefully scanned and motions scaled to give statistical data
on actual conductor orbits during galloping.
The key characteristics of the galloping motions
extracted from the films were:
• peak-to-peak vertical amplitude
• peak-to-peak horizontal amplitude
• position of the motion relative to the median position
of the conductor
The main results of this analysis were that, based on
films of 12 galloping events, the vertical motions of single conductors were up to 1.7 times the loaded sag. On
bundle conductors, the vertical motions extended up to
0.93 times the loaded sag from 17 different films.
Figure 4.5-29 Variation of observed maximum peak-topeak galloping amplitude/diameter on bundle
conductors as a function of the conductor span
parameter (Lilien and Havard 2000).
The horizontal motions for the both single and bundle
conductors were always less than one-tenth of the
loaded sag, and always less than one-fifth of the vertical
motions. Thus the observed motions are almost all in
the vertical plane.
The position of the center of the galloping motion was
found to be close to the static position in half of the
records. In the other half of the records, the static position was found to be in the lower third of the motion. A
compromise average of the film records places the static
position at the lower quartile point of the motion.
Figure 4.5-30 Peak-to-peak galloping
amplitude/conductor diameter versus sag/conductor
diameter based on maximum values of field observations
on single and bundle conductors.
4-78
These film analyses led to a possible new galloping
clearance envelope. Figure 4.5-31 shows this profile,
which consists of two ellipses, each with a width that is
10% of the height, and inclined at 5° each side of vertical. They are attached to the sagged position of the
conductor at the lower quartile point in the ellipse. The
height would be chosen according to the current prac-
EPRI Transmission Line Reference Book—Wind-Induced Conductor Motion, Second Edition
tice of the utility. In default, the maximum galloping
amplitude given as a function of span length, as shown
in Figure 4.5-24 can be used. It should be noted that the
envelope around the field data does not show lower
galloping amplitudes for two-loop galloping than for
single-loop galloping.
The effect of this profile compared to existing ellipses
would be to reduce the amount of horizontal offset
between tower crossarms, resulting in lighter tower
shafts and foundations because of the lessened requirement for resisting twisting under unbalanced, broken
conductor, load.
The results of the analysis of films of galloping,
described above, are from events due to freezing rain
accretion on the conductors. The terrain in most cases
was relatively flat. There are some regions where there
are transmission lines, which are subject to wet snow
accretion, and galloping does occur in those regions.
These are often regions in mountains and where there
are frequent periods with cold wet winds from a nearby
sea. It is unlikely that the orbit shown in Figure 4.5-31
would be appropriate in those locations.
Several field sites have been established in regions where
galloping is caused by wet snow, with the test sites set up
mainly to study the effects of the weather conditions
before constructing a new transmission line. Some of
these studies are summarized in a comprehensive
CIGRÉ paper (Morishita et al. 1984). That paper is
mainly focused on the behavior of bundled conductors
using three test sites in the mountains. Test lines com-
Figure 4.5-31 Clearance envelope derived from
analysis of films of galloping (Pon and Havard 1994).
Chapter 4: Galloping Conductors
prising single conductors, and two-, four-, six-, eightand ten-conductor bundles were installed. The sites
included instrumentation and cameras to record loads
and movements during galloping events. Results of
three winters at two sites and four winters at the other
site are summarized. The terrain is irregular, and the
winds have significant vertical components rather than
being mainly horizontal as in flat terrain.
One significant result of this research, from the perspective of design of clearances between conductors, is the
extent of conductor motions during galloping in these
locations with wet snow accretion. The excursions of the
four- and six-bundle conductors are exemplified by the
orbits included in Figure 4.5-32. These recordings were
obtained under naturally accreted wet snow, with winds
of 12 m/s (27 mph), by Chubu Electric Company at their
Mount Ryuo test site. The conductors cross a valley
between mountains at an elevation of 830 m (2720 ft)
and are boldly exposed to transverse winds. The orbits
recorded contain much larger horizontal motion than is
usually seen during galloping under freezing rain conditions in flat terrain.
The tests with an eight-conductor bundle showed an
even more elongated orbit as shown in Figure 4.5-33.
This record was obtained at an elevation of 750 meters
(2460 feet) above sea level at the Mount Tsuruga test site
by the Kansai Electric Power Company, under natural
wet snow accretion with a wind speed of 18 m/s
(40 mph).
Some research was conducted by the Tokyo Electric
Company at the Mount Takahashi test site with simulated wet snow accretion on six- and ten-conductor bundles. This test site is at an elevation of 1500 m (4920 ft)
Figure 4.5-32 Orbit shapes obtained on six- and fourconductor bundles during galloping due to wet snow
with a wind velocity of 12 m/s (27 mph) (Morishita et al.
1984).
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Chapter 4: Galloping Conductors
EPRI Transmi