Transmission Line Grounding
Volume 1
EPRI-EL—2699-Vol.1
EL-2699, Volume 1
Research Project 1494-1
DE83 900569
Final Report, October 1982
Prepared by
SAFE ENGINEERING SERVICES LTD.
12201 Letellier
Montreal, Quebec, Canada
H3M 2Z9
Principal Author
F. Dawalibi
Prepared for
Electric Power Research Institute
3412 Hillview Avenue
Palo Alto, California 94304
EPRI Project Manager
J. Dunlap
Overhead Transmission Lines Program
Electrical Systems Division
MASTER
anroimo# n> this mcukht » miMtrts
DISCLAIMER
This report was prepared as an account of work sponsored by an
agency of the United States Government. Neither the United States
Government nor any agency thereof, nor any of their employees,
makes any warranty, express or implied, or assumes any legal liability
or responsibility for the accuracy, completeness, or usefulness of any
information, apparatus, product, or process disclosed, or represents
that its use would not infringe privately owned rights. Reference
herein to any specific commercial product, process, or service by
trade name, trademark, manufacturer, or otherwise does not
necessarily constitute or imply its endorsement, recommendation, or
favoring by the United States Government or any agency thereof. The
views and opinions of authors expressed herein do not necessarily
state or reflect those of the United States Government or any agency
thereof.
D IS C L A IM E R
Portions of this document may be illegible in electronic image
products. Images are produced from the best available
original document.
ORDERING INFORMATION
Requests for copies of this report should be directed to Research Reports Center
(RRC), Box 50490, Palo Alto, CA 94303, (415) 965-4081. There is no charge for reports
requested by EPRI member utilities and affiliates, contributing nonmembers, U.S. utility
associations, U.S. government agencies (federal, state, and local), media, and foreign
organizations with which EPRI has an information exchange agreement. On request,
RRC will send a catalog of EPRI reports.
Copyright © 1982 Electric Power Research Institute, Inc. All rights reserved.
NOTICE
This report was prepared by the organization(s) named below as an account of work sponsored by the Electric
Power Research Institute, Inc. (EPRI). Neither EPRI, members of EPRI, the organization(s) named below, nor any
person acting on behalf of any of them: (a) makes any warranty, express or implied, with respect to the use of
any information, apparatus, method, or process disclosed in this report or that such use may not infringe private­
ly owned rights; or (b) assumes any liabilities with respect to the use of, or for damages resulting from the use
of, any information, apparatus, method, or process disclosed in this report.
Services Ltd.
, Canada
ISfC Tf’*'
.|fe
ABSTRACT
A generalized approach to transmission line grounding has been developed and is
presented in this report.
Dedicated interactive computer programs based on advanced analytical models
presented in the report have been developed and verified. Theoretical predictions
from the computer programs are in good agreement with several measurements
including data from transmission line staged fault tests conducted within the scope
of this project.
Typical problems are used to describe in detail the steps required to design
transmission line grounds using the computer programs and design charts developed
for this project.
Measurement equipment and techniques are described in depth. Recommendations
are provided to enhance the practicality, accuracy and usefulness of the transmission
line grounding measurements.
EPRI PERSPECTIVE
PROJECT DESCRIPTION
While considerable information is available on the design and analysis of substation grounding,
relatively little is known on an equally important design consideration "Transmission Line
Structure Grounding". Recent systems disturbances that may have been related to structure
grounding problems emphasize a need for better design methods. As fault currents continue
to grow, engineers need more accurate design methods that will assure continued safe
conditions near the structures in the case of a phase-to-ground fault. This project (RP 1494-1)
was initiated in order to formulate a state-of-the-art transmission structure grounding design
manual that would satisfy these needs. The final report is in two volumes. Volume 1 describes
analytic methods, measurement techniques, and design methodology. Volume 2 contains design
charts for typical structure grounds.
PROJECT OBJECTIVES
The four objectives of this project were:
•
To assemble comprehensive background information and to develop a design
methodology that would result in a complete understanding of structure grounding
problems and solutions.
•
To provide user-oriented graphic design techniques for typically occuring situations.
«
To provide versatile computer programs capable of handling complex conditions.
0
To verify the accuracy of these design methods by comparing them with field
test data.
v
PROJECT RESULTS
The above objectives were fully achieved, resulting in design information on transmission
line structure grounding that is superior to any previously available. This final report was
specially designed for both (1) the user requiring an in-depth analysis of complex or unusual
grounding problems and (2) the user wanting a quick, easy solution. The report provides
sufficient information to aid the reader in handling the most complex situations. Yet, for
typical designs, the charts and interactive computer program can be used by persons having
little previous experience in this technology.
John Dunlap, Project Manager
Electrical Systems Division
EPRI
ACKWOWLEDeEIVIEWTS
The following members of the EPRI Advisory Task Force are gratefully acknowledged for
their invaluable assistance and guidance throughout the project:
J.
Dunlap, Project Manager, Electric Power Research Institute
T. E. Bethke, Potomac Electric Power
A. C. Pfitzer, Tennessee Valley Authority
C. J. Blattner, Niagara Mohawk
G. B. Niles, Baltimore Gas and Electric
R. S. Baishiki, Pacific Gas and Electric
Mr. G. B. Niles is particularly thanked for his assistance in the testing and evaluation of
the software package GATE.
Especially acknowledged is the excellent cooperation provided by the Tennessee Valley
Authority (TVA) and Rochester Gas and Electric Company (RGE) who participated in the
planning and execution of the field test programs. Special thanks are extended to Mr. J. W.
Chadwick from TVA and Mr. J. Windsor from RGE.
Appreciation is extended to Electricite de France, Ontario-Hydro, American Electric Power
Company and Idaho Power Company for providing much data valuable for this project. The
following individuals are particularly thanked for their willingness to share information
and discuss subjects related to this project: P. Kouteynikoff, Electricite de France; E. A.
Cherney, Ontario Hydro; N. Kolcio, American Electric Power; W. G. Eisinger, Idaho Power.
Deserving of special acknowledgment for services and assistance provided during the project
is Mr. D. Bensted from David Bensted and Associates Ltd.. Mr. Bensted is the principal
author of Chapter 9 and was responsible for the coordination and execution of the field
tests.
All of the utilities that responded to the transmission line grounding survey questionnaire
are gratefully acknowledged for their invaluable contributions.
CONTENTS
Page
Chapter
1
2
INTRODUCTION
1.1
GENERAL
1-1
1.2
HISTORIC NOTES
1-1
1.3
PROJECT OBJECTIVES
1-2
1.4
USE OF THIS BOOK
1-3
1.5
CONCLUDING REMARKS
1-5
FUNDAMENTAL CONSIDERATIONS
2.1
GENERAL
2-1
2.2
TRANSMISSION LINE DISTURBANCES
2-1
2.3
EARTH
2.3.1 Simplified Methods
2.3.2 Computer Program RESIST
2-2
2-3
2-3
2.4
POWER SYSTEM
2.4.1 Conductor
2.4.2 Computer
2.4.3 Computer
2-3
2-5
2-7
2-7
2.5
GROUNDING PERFORMANCE OF TRANSMISSION LINE STRUCTURES
2.5.1 Simplified Formulas
2.5.2 Computer Program GTOWER
2-8
2-8
2-8
2.6
TYPE OF DISTURBANCE
2.6.1 Power Frequency Ground Faults
2.6.2 Lightning Strokes
2-9
2-9
2-9
NETWORK
Impedances
Program LIN PA
Program PATHS
REFERENCES
2-10
ix
CONTENTS (continued)
Page
Chapter
3
4
TYPICAL DESIGN METHODOLOGY
3.1
GENERAL
3-1
3.2
DESCRIPTION OF THE PROBLEM
3.2.1 Tower Footing
3.2.2 Power System Network
3.2.3 Transmission Line Conductor Data
3.2.4 Apparent Soil Resistivity
3-1
3-2
3-2
3-4
3-5
3.3
DESIGN METHODOLOGY
3.3.1 Two Layer Earth Model
3.3.2 Transmission Line paramaters
3.3.3 Tower Grounding Performance
3.3.4 Fault Current Distribution
3.3.5 Safety Evaluation
3-5
3-6
3-6
3-9
3-13
3-14
3.4
POTENTIAL CONTROL CONDUCTORS
3.4.1 Inner Potential Control Loop; Step 1
3.4.2 Leg Control Loop; Step 2
3-15
3-15
3-17
3.5
OTHER CASES
3-18
EARTH RESISTIVITY
4.1
GENERAL
4-1
4.2
ELECTRICAL PROPERTIES OF EARTH
4.2.1 Conduction by Electronic Process
4.2.2 Electrolytic Conduction
4.2.3 Electrical Conduction in Earth
4.2.4 Electrical Model of Earth
4-2
4-3
4-3
4-5
4-8
4.3
MEASUREMENT METHODS AND TECHNIQUES
4.3.1 Electrical Well Logging
4.3.2 Galvanic Resistivity Methods
4.3.3 The Wenner Method
4-8
4-9
4-11
4-12
4.4
DERIVATION OF THE EQUATIONS
4.4.1 Point Source Electrode in Uniform Soil
4.4.2 Multiple Source Electrodes
4.4.3 Nonuniform Soils
4.4.4 Point Source Electrode in a Two-Layer Earth
4.4.5 Point Source in Earth with Inclined Layers
4.4.6 Point Source Embedded in a Localized Discontinuity
4.4.7 Application of the Potential Functions to the Wenner Array
4-14
4-14
4-17
4-18
4-19
4-22
4-23
4-24
x
CONTENTS (continued)
Chapter
4.5
Page
INTERPRETATION OF THE MEASUREMENTS
4.5.1 Basic Considerations
4.5.2 Empirical Methods
4.5.3 Analytical Methods
4.5.4 Methodology
4.5.5 Logarithmic Curve Matching
4.5.6 Partial Curve Matching
4.5.7 Other Methods
4.5.8 The Steepest Descent Method
REFERENCES
5
4-27
4-27
4-28
4-30
4-32
4-33
4-35
4-38
4-39
4-42
POWER FREQUENCY PERFORMANCE OF TRANSMISSION LINE
STRUCTURE GROUNDS
5.1
GENERAL
5-1
5.2
TRANSMISSION LINE GROUNDING
5.2.1 Transmission Line Structure Grounding System
5.2.2 Equivalent Cylindrical Conductor
5-3
5-3
5-5
5.3
LOW FREQUENCY RESPONSE OF STRUCTURE GROUNDING
SYSTEMS
5.3.1 Grounding Performance of a Line Source
5.3.2 Analysis of a Structure Grounding System
5-7
5-7
5-12
5.4
LOCAL HETEROGENEITIES IN THE SOIL
5.4.1 Hemispherical Electrode Embedded in a Hemispherical Shell
5.4.2 Vertical Rod Embedded in a Cylindrical Shell
5.4.3 Vertical Rod Encased in an Elliptic Shell
5.4.4 Comparison Between the Equipotential Surface Methods
5.4.5 Extensions & Limitations of the Equipotential Surface Methods
5.4.6 Concrete Encased Grounding Elements
5-18
5-18
5-21
5-23
5-27
5-29
5-32
5.5
CONTINUOUS COUNTERPOISES
5.5.1 Performance of an Isolated Continuous Counterpoise
5.5.2 Counterpoise of Transmission Lines
5.5.3 Accurate Analysis of Counterpoises
5-35
5-36
5-41
5-47
5.6
SOIL HEATING EFFECTS
5.6.1 Heating of the Soil Around a Grounding System
5.6.2 Steady State Performance
5.6.3 Transient Heating
5-50
5-50
5-51
5-52
REFERENCES
5-54
xi
CONTENTS (continued)
Chapter
6
Page
POWER FREQUENCY FAULT CURRENT DISTRIBUTION
6.1
GENERAL
6-1
6.2
IMPORTANCE OF FAULT CURRENTDISTRIBUTION
6-2
6.3
CONSTANT LINE PARAMETERS
6.3.1 Long Transmission Lines
6.3.2 Long and Short Transmission Lines
6-3
6-3
6-6
6.4
VARYING LINE PARAMETERS
6.4.1 Sebo's Method
6.4.2 The Single and Double Sided Elimination Methods
6.4.3 The Generalized Double Sided EliminationMethod
6.4.4 Practical Considerations
6-12
6-13
6-16
6-23
6-30
REFERENCES
7
6-33
LIGHTNING PERFORMANCE OF TRANSMISSION LINE STUCTURES
7.1
GENERAL
7-1
7.2
EFFECTS OF LIGHTNING ON POWER LINES
7.2.1 The Lightning Flash
7.2.2 The Back Flashover Mechanism
7-1
7-1
7-2
7.3
ANALYTICAL MODELS FOR BACK FLASHOVERCOMPUTATIONS
7.3.1 Simplified Models
7.3.2 Travelling Wave Models
7.3.3 Electromagnetic Field Models
7-5
7-5
7-8
7-13
7.4
UNCERTAINTIES IN THE ANALYTICAL MODEL OF A STRUCTURE
7.4.1 Lossless Conducting Elements
7.4.2 Earth Resistivity
7.4.3 Analytical Models of Extended Grounding Systems
7.4.4 Soil Ionization Mechanism
7-19
7-19
7-20
7-21
7-23
7.5
FREQUENCY DOMAIN APPROACH
7.5.1 Frequency Effects on Electrical Constants of Materials
7.5.2 Clarity and Precision
7.5.3 Hybrid Models
7.5.4 Conclusion
7-25
7-25
7-26
7-27
7-27
REFERENCES
7-27
xii
CONTENTS (continued)
Chapter
8
Page
SAFETY
8.1
GENERAL
8-1
8.2
THE ELECTROCUTION EQUATION
8.2.1 The Electrocution Mechanism
8.2.2 Thresholds of Current
8.2.3 Parameters Influencing Heart Fibrillation
8.2.4 The Electrocution Theories
8.2.5 The Electric Shock
8.2.6 Safe Impulse or Surge
Current
8-2
8-3
8-3
8-3
8-7
8-8
8-14
8.3
PROBABILISTIC CONSIDERATIONS
8.3.1 The Probability of an ElectrocutionIncident
8.3.2 The Statistical Probabilistic Approach
8.3.3 The Selective Deterministic Approach
8-16
8-16
8-16
8-19
8.4
SAFE DESIGNS AND MITIGATION TECHNIQUES
8.4.1 Evaluation of the Safety Level
8.4.2 Improving Safety Around TransmissionLine Structures
8.4.3 Ground Potential Mitigating Conductors
8.4.4 Other Safety Measures
REFERENCES
9
8-20
8-21
8-22
8-25
8-27
8-27
FIELD MEASUREMENT TECHNIQUES
9.1
GROUND RESISTANCE MEASUREMENT
9-1
9.2
TEST METHOD
9.2.1 Two-Point method
9.2.2 Three-Point Method
9.2.3 Fall-of-Potential Method
9.2.4 Theory of the Fall-of-Potential Method
9.2.5 Interpretation of Fall-of-Potential Data
9.2.6 Overhead Ground Wires
9-2
9-2
9-2
9-3
9-4
9-6
9-9
9.3
GROUND RESISTANCE MEASUREMENT INSTRUMENTATION
9.3.1 Portable Ground Testers
9.3.2 Voltmeter/Ammeter Method
9.3.3 High Frequency Portable Instruments
9.3.4 Other Measurement Systems
9-10
9-10
9-11
9-12
9-12
xi i i
CONTENTS (continued)
Chapter
Page
9.4
MEASUREMENT TECHNIQUES
9-13
9.5
EARTH RESISTIVITY TESTS
9.5.1 The Four Point Method
9.5.2 Driven Ground Rod Method
9.5.3 Resistivity MeasurementInstrumentation
9.5.4 Measurement Techniques
9-16
9-17
9-18
9-19
9-20
9.6
SAFETY PRECAUTIONS
9-21
REFERENCES
10
9-22
COMPARISON BETWEEN MEASUREMENTS AND COMPUTATIONS
10.1
GENERAL
10-1
10.2
THE RGE 115 kV TRANSMISSION LINE MEASUREMENTS
10.2.1 Test Site
10.2.2 Test Equipment
10.2.3 Earth Resistivity Tests
10.2.4 Analysis of the Resistivity Tests
10.2.5 Ground Impedance Measurements
10.2.6 Analysis of the Ground Impedance Measurements
10-2
10-2
10-5
10-6
10-7
10-11
10-13
10.3
THE TVA 500 kV TRANSMISSION LINE MEASUREMENTS
10.3.1 Test site
10.3.2 500 kV Staged Fault Test Description
10.3.3 Low Current Tests
10.3.4 SES Test Procedure
10.3.5 Earth Resistivity Tests
10.3.6 Analysis of the Resistivity Tests
10.3.7 Earth Potential and Ground Impedance Tests
10.3.8 Analysis of the High Frequency Tests
10.3.9 Analysis of the Low Frequency Tests
10.3.10 Analysis of the TVA Staged Fault Current Measurements
10-16
10-19
10-20
10-22
10-23
10-24
10-28
10-31
10-33
10-35
10-42
10.4
THE OH/AEP 500/765 kV TRANSMISSION LINE MEASUREMENTS
10.4.1 The AEP Measurements
10.4.2 The OH Measurements
10-50
10-50
10-54
10.5
THE EDF ROCKET TRIGGERED LIGHTNING MEASUREMENTS
10.5.1 Equivalent Circuit of the Tower Structure
10.5.2 Equivalent Circuit of the Grounding Electrodes
10-59
10-62
10-63
REFERENCES
10-64
xiv
CONTENTS (continued)
Chapter
11
Page
SURVEY OF NORTH AMERICAN TRANSMISSION LINE GROUNDING
PRACTICES
11.1
OBJECTIVES OF SURVEY
11-1
11.2
SURVEY DISTRIBUTION
11-1
11.3
RESPONSE TO THE SURVEY
11-2
11.4
QUESTIONNAIRE FORMAT
11-2
11.5
ANALYSIS OF THE RESPONSES
11.5.1 General
11.5.2 Measurements
11.5.3 Engineering
11.5.4 Safety Considerations
11.5.5 Construction/Measurements/Maintenance
11.5.6 Typical Design and Data
11-3
11-3
11-4
11-4
11-5
11-6
11-7
11.6
SUMMARY OF COMMENTS RECEIVED
11-11
11.7
CONCLUSION
11-14
APPENDIXES
A
COMPUTER PROGRAM LIN PA
A-l
B
COMPUTER PROGRAM RESIST
B-l
C
COMPUTER PROGRAM GTOWER
C-l
D
COMPUTER PROGRAM PATHS
D-l
E
LIST OF SURVEY RESPONDENTS
E-l
F
RGE 115 KV TRANSMISSION LINE GROUNDING TEST RESULTS
F-l
G
TVA 500 KV STAGED FAULT AND TOWER GROUNDING TEST RESULTS
G-l
ILLUSTR AXIOMS
Page
Figure
2.1
Equivalent Power System Network
2-4
3.1
345 kV Four Leg Lattice Tower
3-2
3.2
Grillage Foundations
3-3
3.3
Power System Network
3-3
3.4
Design Methodology
3-7
3.5
Logarithmic Curve Matching Technique
3-8
3.6
Worst Touch and Step Voltages
3-9
3.7
Fundamental Tower Grounding System Dimensions
3-11
3.8
Earth Surface Potential Profiles
3-12
3.9
Simplified Circuit
3-13
3.10
Ground Potential Control Loops
3-16
4.1
Soil Resistivity Versus Temperature
4-5
4.2
Soil Resistivity Versus Temperature for Typical Soil Samples
4-6
4.3
Resistivity Map of the United States
4-7
4.4
Geoelectric Model of Earth
4-8
4.5
Operating Principle
4-10
4.6
Commonly Used Arrangements
4-10
4.7
Typical Log Resistivity Curve
4-11
4.8
Galvanic Resistivity Methods
4-12
4.9
Wenner Arrangement
4-13
4.10
Point Source Electrode in Uniform Soil
4-15
4.11
Hemispherical Electrode
4-16
4.12
Schlumberger-Palmer Array
4-18
4.13
Two-Layer Earth Model
4-19
xv ii
ILLUSTRATIONS (continued)
Page
Figure
4.14
Vertical Fault
4-22
4.15
Localized Discontinuity
4-24
4.16
Wenner Array
4-25
4.17
Vertical Fault (Top View)
4-25
4.18
Uniform Earth
4-27
4.19
Sudden Changes
4-28
4.20
Current Density in Earth
4-29
4.21
Assymptote's Rules
4-31
4.22
Logarithmic Curve Matching
4-34
4.23
Horizontal Two-Layer Earth Master Chart
4-35
4.24
Vertical Fault Master Chart
4-36
4.25
Multi-Layer Earth
4-37
4.26
Partial Curve Matching
4-37
4.27
The Method of Steepest-Descent
4-39
5.1
Equivalent Cylindrical Conductor
5-5
5.2
Equivalent Linear Current Source
5-7
5.3
Point Source Below Earth Surface
5-8
5.4
Infinite Number of Point Sources
5-9
5.5
Segmentation Process
5-10
5.6
Tower Grounding System
5-13
5.7
Average Potential and Center Methods
5-17
5.8
Local Soil Heterogeneities
5-18
5.9
Hemispherical Configurations
5-19
xv i i i
ILLUSTRATIONS (continued)
Page
Figure
5.10
Effects of a Hemispherical Heterogeneity
5-20
5.11
Tower Foundations
5-20
5.12
Small Cylindrical Heterogeneous Material
5-21
5.13
Effects of a Cylindrical Heterogeneity
5-23
5.14
Elliptic Shell
5-24
5.15
Ellipsoid
5-24
5.16
Effects of an Elliptic Heterogeneity
5-28
5.17
Equal Volume Base
5-28
5.18
The Equipotential Metallic Sheet Principle
5-29
5.19
Illustration of a Typical Problem
5-30
5.20
Typical Concrete Foundations
5-32
5.21
Dynamic Resistance of Concrete
5-33
5.22
Arcing Process in a Concrete Distribution Pole
5-35
5.23
Isolated Continuous Counterpoise
5-36
5.24
Infinitesimal Counterpoise Element
5-36
5.25
Ground Impedance of a Counterpoise
5-41
5.26
Effects of Frequency on Counterpoise Impedance
5-42
5.27
Transmission Line Counterpoise
5-43
5.28
Equivalent Conductor Pair for a Counterpoise
5-44
5.29
First Iteration
5-45
5.30
Last Iteration
5-46
5.31
Computer Solution of Counterpoise Ground Impedance
5-48
5.32
Current Distribution Along a Counterpoise
5-49
xix
ILLUSTRATIONS (continued)
Figure
Page
5.33
Heating of the Soil Around a Grounding Electrode
5-51
5.34
Temperature Variation with Time
5-53
6.1
Conventional Circuit Reduction
6-2
6.2
Fault Current Distribution
6-3
6.3
Distributed Parameters Method
6-4
6.4
Lumped Parameters Method
6-7
6.5
Distributed & Lumped Method - ConstantTower Resistance
6-11
6.6
Currents in Ground Wire
6-13
6.7
Circuit of One Span of a Line
6-15
6.8
Ground Fault at Span n From the SourceTerminal
6-16
6.9
Equivalent Network - General Case
6-17
6.10
Fundamental Loops of the Network
6-18
6.11
Fundamental Loops of the Network
6-24
6.12
A Phase-to-Ground Fault on a Transmission Line
6-31
6.13
Effects of Ground Resistance Values
6-32
7.1
A Typical Transmission Line Back Flashover
7-3
7.2
Travelling Waves After a Lightning Stroke toa Structure
7-4
7.3
Simplified Models
7-6
7.4
Approximation of a Current Surge
7-7
7.5
Lightning and Travelling Waves
7-9
7.6
Illustration of a Typical Problem
7-12
7.7
Typical Structure Top Potentials
7-12
7.8
Moving Wave of Electric Charges
7-13
xx
ILLUSTRATIONS (continued)
Figure
Page
7.9
Integration Path of Vector Potential
7-16
7.10
Voltage Across Insulator String
7-16
7.11
Wave Reflection and Refraction Technique
7-18
7.12
Earth Resistivity and Earth Potentials
7-20
7.13
Dynamic Resistivity-Impulse Current Curve
7-23
7.14
Frequency Dependence of Material ElectricalConstants
7-26
8.1
Strength-Duration Stimulus Curve
8-4
8.2
Equivalent Circuit of a Typical Cell Membrane
8-5
8.3
Threshold of Ventricular Fibrillation for a 50Kg Man
8-6
8.4
Safe Body Current Versus Time
8-8
8.5
The Electric Shock Circuit
8-9
8.6
Simplified Equivalent Electric Shock Circuit
8-11
8.7
Body Resistance Versus Applied Voltage
8-12
8.8
Ground Resistance of Feet
8-13
8.9
Nonfatal Surge Capacitor Discharge Currents
8-14
8.10
Perception Current as a Function of Frequency
8-15
8.11
Approximate Equivalent Transmission Line Circuit
8-22
8.12
Body Current Versus Resistivity
8-24
8.13
Resistivity of Gravel
8-25
8.14
Typ ical Ground Potential Mitigating Rings
8-26
9.1
Principle of Ground Resistance Measurement
9-2
9.2
Fall-of-Potential Test Schematic Diagram and Typical
Test Results
9-4
ILLUSTRATIONS (continued)
Page
Figure
9.3
Required Potential Probe Location in Fall-of-Potential
Measurements
9-6
Required Potential Probe Location in a Two-Layer
Structure
9-8
9.5
F all-of-Potenti al Profile Results ofan Actual Test
9-9
9.6
Voltmeter/Ammeter Test Set-Up
9-11
9.7
Functional Schematic - High Current Frequency Selective
Ground Resistance Test Set-Up
9-12
General Instrumentation Arrangement for the Measurement
of Ground Impedance Using a FFTDigital Analyzer
9-13
Field Calibration Check or Ground Resistance Measuring
Equipment
9-17
Four Point Method of Earth ResistivityMeasurement
9-19
9.4
9.8
9.9
9.10
10.1
Rochester Gas and Electric Test Site
10-3
10.2
115 kV Wood Structures
10-3
10.3
Curent (Cl) &
10-4
10.4
Test Equipment
10-5
10.5
Functional Schematic of the Test Set-Up
10-6
10.6
Rochester Gas and Electric Measurement Site 115 kV
Transmission Line
10-7
10.7
Earth Resistivity Traverse RGE 01-1
10-8
10.8
Earth Resistivity Traverse RGE 01-2
10-9
10.9
Earth Resistivity Traverse RGE 03
10-9
Potential (PI) Test Lead Connections
10.10 Earth Resistivity Traverse RGE 04
10-10
10.11 Equivalent Circuit of Grounding Connections at
Double-Pole Structures
10-13
xx ii
ILLUSTRATIONS (continued)
Figure
Page
10.12 Frequency Dependence of Transmission Line Grounds
10-14
10.13 Measured and Computed Apparent Impedance
10-16
10.14 Test Site; Tower 130 and Fault Structure
10-17
10.15 Arc Initial at Fault Structure
10-17
10.16 Staged Fault Tests Measurements
10-19
10.17 Topography of the Test Site
10-20
10.18 Potential Transformers and Crossbow
NearTower 130
10-21
10.19 Resistivity Measurements
10-23
10.20 Resistivity Traverse TVA 1-1
10-24
10.21 Resistivity Traverse TVA 2-2
10-23
10.22 Resistivity Traverses TVA 1-2 and TVA 10
10-26
10.23 Resistivity Traverses TVA 2-1 and TVA 03
10-27
10.24 Resistivity Traverse TVA 04
10-28
10.25 Potential Profile Measurements (Ground Wires Connected to
Tower 130 & 10 Adjacent Towers on Each Side of Tower 130)
10-31
10.26 Potential Profile Measurements (Ground Wires Disconnected
From Tower 130)
10-32
10.27 500 kV Tower Leg
10-33
10.28 Equivalent Circuit with Ground Wires Connected
10-34
10.29 Measured and ComputedGroundImpedances
10-35
10.30 A Typical TVA 500 kV Tower
10-36
10.31 500 kV Tower Leg Earth Anchor
10-37
xxiii
ILLUSTRATIONS (continued)
Figure
Page
10.32 Equivalent Earth Anchor Grounding Model
10-37
10.33 Measured and Computed Potenti al Profiles (Ground Wires
Connected to Tower)
10-38
10.34 Computed Potential Profiles (soil Models 1 to 5)
(Insulated Ground Wires)
10-40
10.35 Measured and Computed Potential Profiles (Insulated
Ground Wires)
10-40
10.36 Measured and Computed Potential Profiles Compatible
Soil Models (Insulated Ground Wires)
10-41
10.37 Equivalent Positive and Zero-Sequence Network
10-42
10.38 Equivalent Faulted Transmission Line Circuit
10-43
10.39 Transmission Line Conductor Impedance
10-44
10.40 Current and Voltage Oscillograms Measured at Tower
Site
10-47
10.41 Current and Voltage Oscillograms Measured at
Cumberland Station
10-48
10.42 Current and Voltage Oscillograms Measured at
Johnsonville Station
10-49
10.43 The AEP 765 kV Test Sites
10-50
10.44 Plan View of Guyed-Vee Towers
10-51
10.45 Average Apparent Soil Resistivities Around Guyed-Vee Towers
10-52
10.46 Earth Potential Profiles for Tower 13
10-53
10.47 Earth Potential Profile for Tower 36
10-53
10.48 Plan View of 765 kV Lattice Tower Footing
10-54
10.49 500 kV Tower Leg
10-54
at Kleinburg
10.50 Plan Cross Sectional View Views of the 500 kV Tower Footing
XXIV
10-55
ILLUSTRATIONS (continued)
Figure
Page
10.51 Earth Surface Potential Measurements pads
10-55
10.52 Resistivity Measurements at Kleinburg Test Site
10-56
10.53 Earth Surface potential Profiles for Ground Rods
and GPC Ring
10-57
10.54 Earth Surface Potential Profiles for Rebar Cages
and GPC Ring
10-57
10.55 Earth Surface Potential Profiles for Ground Rods With
Rebar Cages and GPC Ring
10-58
10.56 Tower Structure at St. Privat d'Allier
10-59
10.57 Ground Level Rocket-Launching Area
10-60
10.58 Tower Base and Insulator Supports
10-61
10.59 Electrode Configuration Subjected to Surge Tests
10-61
10.60 Tower Structure Impedance
10-62
10.61 Ground Impedance of Hemispherical, Double Loop and
Horizontal Electrodes
10-63
10.62 Ground Impedance of a Ground Rod and a TwoBranch Star
10-63
11.1
Size of Utilities Which Answered the Questionnaire
11-2
11.2
Distribution of Fault Current Between Structure and
Skywires
11-5
11.3
Additional Cost of Grounding
11-6
11.4
Average Useful Life of Grounding Conductors
11-7
11.5
Grounding Arrangement
11-9
11.6
Transmission Structure Resistance
11-10
11.7
Lightning Rate of Failure
11-10
F. l
RGE'S 115 KV Transmission Line Test Site
F-l
G. l
TVA'S 500 kV Johnsonville-Cumberland Transmission Line
G-l
TABLES
Table
Page
3.1
Apparent Soil Resistivity
3-3
3.2
Computed Impedance matrix
3-8
3.3
Permissible Contact Voltages
3-15
4.4
Typical Resistivity Values
4-4
6.1
Round-off Errors in Computations
6-20
6.2
Initial Values
6-22
9.1
Resistance Measurement Equipment Check List
9-14
9.2
Mutual Impedance Between Two Parallel Conductors on
the Surface of the Earth
9-16
10.1
Equivalent Two-Layer Soils
10-8
10.2
Pole and Structure Ground Resistances
10-14
10.3
Frequency Response of Transmission Line Structures
10-15
10.4
Equivalent Two-Layer Soils
10-29
10.5
Origin of Soil Models Analyzed
10-30
10.6
Ground Wire Impedance
10-34
10.7
Computed Ground Resistances
10-39
10.8
Bonded Ground Wires Test Results & Computations
10-45
10.9
Insulated Ground Wires Test Results
10-46
10.10 Guyed-Vee Tower Resistances
10-52
10.11 Kleinburg Tower Ground Resistance
10-56
11.1
Maximum Tower Ground Resistances
11-8
11.2
Transmission Line Lightning Failure Rates
11-8
xx vi i
TABLES (continued)
Table
Page
F.l
Resistivity Measurements - Traverse RGE 01-1
F-3
F.2
Resistivity Measurements - Traverse RGE 01-2
F-3
F.3
Resistivity Measurements - Traverse RGE 03
F-4
F.4
Resistivity Measurements - Traverse RGE 04
F-4
F.5
Potential Measurements - Profile
RGE 02-1
F-5
F.6
Potential Measurements - Profile
RGE 02-2
F-5
F.7
Potential Measurements - Profile
RGE 02-3
F-6
F.8
Potential Measurements - Profile
RGE 02-4
F-6
F.9
Potential Measurements - Profile RGE 02-4
F-7
F.10
Potential Measurements - Profile
RGE 02-5
F-7
F.ll
Potential Measurements - Profile
RGE 02-7
F-8
F.12
Potential Measurements - Profile RGE 02-8
F-8
F.13
Potential Measurements - Profile
RGE 02-9
F-9
RGE 02-10
F-9
F. 14 Potential Measurements - Profile
G. l Resistivity Measurements - Traverse TV A 1-1
G-3
G.2
Resistivity Measurements - Traverse TV A 1-2
G-3
G.3
Resistivity Measurements - Traverse TV A 2-1
G-4
G.4
Resistivity Measurements - Traverse TV A 2-2
G-4
G.5
Resistivity Measurements - Traverse TV A 03
G-5
G.6
Resistivity Measurements - Traverse TV A 04
G-5
G.7
Resistivity Measurements - Traverse TV A 10
G-6
G.8
Potential Measurements - Profile TV A 01
G-7
G.9
Potential Measurements - Profile TV A 01
G-7
G.10 Potential Measurements - Profile TV A 02
G-8
xxviii
TABLES (continued)
Table
Page
G.ll
Potential Measurements - Profile TV A 11
G-8
G.12
Potential Measurements - Profile TV A 05
G-9
G.13
Potential Measurements - Profile TV A 06
G-9
G.14
Potential Measurements - Profile TVA 07
G-10
G.15
Potential Measurements - Profile TVA 08
G-10
G.16
Potential Measurements - Profile TVA 09
G-ll
G.17
Ground Resistance Measurements
G-13
G.18
Ground Resistance Measurements
G-13
G.19
Ground Resistance Measurements
G-14
xxix
SUMMARY
OBJECTIVES
The primary goal of this Electric Power Research Institute (EPRI) project has been to
develop a transmission line grounding reference book which consolidates ail available
information on the subject and describes a systematic and practical design methodology. In
meeting this objective, two volumes have been written and a software package
developed.
RESULTS
Volume 1 of the final report describes analytical methods, measurement techniques and
design methodologies related to transmission line grounding. A summary of survey responses
from North American utilities on the state-of-practices of transmission line grounding is
included. Volume 1 also contains instructions for using the software package. Volume 2
contains an extensive set of design curves intended to provide an alternative design
methodology to the computer analysis approach.
The software package GATE (Grounding Analysis of Transmission Lines) consists of four
FORTRAN programs developed to provide simple and accurate tools for the analysis and
design of transmission line grounding systems and ground potential mitigation electrodes.
CONTENTS
A significant portion of the information contained in this report has come from published
work. This information has been grouped in a manner convenient for use by transmission
line engineers. New methods and techniques are also presented. Examples of original research
work include earth resistivity analysis and interpretation techniques, an analysis of concrete
encased electrodes, computer generated counterpoise impedance curves and transmission line
fault current distribution analysis. New concepts and approaches have also been introduced
in the areas of field measurement techniques and safety.
S-1
VOLUME 1
The first part of the report presents practical information on transmission line grounding
design techniques. A detailed description of the design data required by GATE or by the
design graphs of Volume 2 is provided. Techniques for interpreting the results obtained from
the programs and from the charts are described.
The middle portion of the report describes advanced analytical methods relating to transmission
line grounding. Recommendations for earth resistivity measurement and interpretation
techniques are given. Equations that predict the power frequency performance of a transmission
line grounding system are supplied. The subjects of concrete encased electrodes, counterpoises
and soil heating are also discussed. Methods for calculating the current distribution between
a faulted structure and the overhead ground wires are provided. The report analyzes the
response of transmission line structures to lightning strokes and discusses existing analytical
theories.
The latter portion of the report describes modern theories on the effects of body
currents and introduces the probabilistic and deterministic approaches to safety in the vicinity
of transmission line structures. Measurement techniques and equipment are described. Actual
field tests, including staged fault tests conducted during this EPRI project are also reported.
The purpose of these tests was to provide a comparison of measured and computed results.
Good agreement was obtained between field measurements and results of the calculations.
VOLUME 2
Volume 2 contains design curves, derived primarily from the results of the GATE computer
program. Charts permit the user to convert resistivity measurements into equivalent earth
models, to design grounding systems, to determine the current distribution in a faulted line
and to perform safety analysis.
SOFTWARE PACKAGE GATE
GATE consists of four programs: LINPA, RESIST, GTOWER and PATHS. LINPA calculates
the self and mutual impedances of transmission line conductors, RESIST interprets earth
resistivity measurements, GTOWER analyzes the performance of transmission line grounding
systems and PATHS calculates the distribution of fault current in the transmission line.
CONCLUSION
The two volumes of the reference book and the GATE computer programs form an integrated
package which meets the widely varying needs of researchers and designers. They also serve
as a comprehensive reference document for engineers with little or no grounding experience.
S-2
iWTRODUCTiOW
1.1 GENERAL
This book is the culmination of several years of design and research work in the field of
grounding. Much of the work was completed by Safe Engineering Services Ltd (SES) and
other organizations prior to the start of the project. All available research results were
combined and adapted to a transmission line design perspective in convenient reference
volumes. These documents contain the information and tools necessary to conduct an
engineering study that fully utilizes the capabilities of today's computer technology.
1.2 HISTORIC NOTES
The traditional approach to transmission line grounding design is highly empirical. Practices
vary widely from one utility to the other as evidenced by the results of a North American
utility survey summarized in Chapter 11 of this report.
The design of a power system reguires that both normal and abnormal conditions be considered
in order to correctly determine the design reguirements and characteristics of the installed
power equipment. Of the abnormal conditions which can occur on a power transmission line,
the two most frequent are:
•
Lightning strokes
•
Phase to ground faults
In both cases, the overhead network and the earth path, including buried metallic conductors
such as counterpoises and ground electrodes, are part of the circuit in which the surge or
fault current circulates. Generally, an analysis of these abnormal conditions is based on a
reasonably accurate representation of the overhead circuit. The earth path, however, is
usually modelled as a perfect conductor or in a very simplified form. This seldom leads to
realistic results. The apparent inconsistancy of these engineering approaches can be explained
by the mathematical difficulties involved in the analysis of three dimensional current flow
in earth. Often, the wide variations observed in the characteristics of earth, generally
described as a semi-infinite nonhomogeneous medium, are used as justification for not pursuing
detailed modelling of the earth path for fault currents.
Thirty years ago, the lack of suitable high-speed digital computers was a serious obstacle
to accurate modelling of the earth. Now, there are no computational limitations to the
development of an accurate model of the structure of the earth. Recently published analytical
works on power system grounding describe accurate, computer based computational techniques
for the design of grounding systems.
1-1
Large variations in earth resistivity need not be an obstacle to the development of detailed
earth structure models. Relatively simple equivalent earth models can be effectively used
to accurately predict transmission line grounding performance, as evidenced by the field
measurements described in Chapter 10. Finally, the earth structure at any particular site
can be accurately determined by a suitable selection of test methods and equipment.
Tremendous increases in energy consumption coupled with environmental constraints which
limit the availability of right of ways, have introduced a particular need for accurate and
practical methods for the analysis and design of cost effective transmission line grounding
systems and potential gradient mitigation schemes.
1.3 PROJECT OBJECTIVES
The objectives of the project have been to provide to the Electric Power Industry the
following items consolidated into a single, convenient packages
•
A reference document including a comprehensive description of advanced theories
and techniques pertaining to the analysis, design and measurement of transmission
line grounding systems, with a particular emphasis on safety and mitigation
techniques to improve safety around exposed structures.
•
A field measurement report on actual transmission lines including high current
staged fault tests in order to prove the effectiveness of the advanced analytical
methods described in the report.
•
A practical and concise design manual which clearly describes the various steps
of transmission line grounding system design using realistic examples.
•
A series of dedicated computer programs which can be used in a batch or
interactive mode and require a minimum of grounding expertise on behalf of the
user, while delivering a maximum of computed information based on the sophisticated
theories and concepts described in the final report.
•
An appropriate selection of design charts for those who do not have access to a
computer terminal, or wish to obtain quick estimates of transmission line grounding
parameters for standard transmission line grounding systems.
In achieving these challenging objectives, new methods and techniques, not previously available
in the literature, have been introduced. Examples of such new developments include earth
resistivity interpretation techniques, concrete encased electrode design, computer generated
counterpoise impedance charts, and transmission line fault current distribution analysis by
the generalized double-sided elimination method. Original contributions have also been made
in areas such as safety and field measurement techniques.
Much of the information contained in this report comes from published research work. This
has been conveniently regrouped from a transmission line engineering viewpoint.
1-2
1.4 USE OF THIS BOOK
To simplify the use of this book, it has been organized in two volumes. Volume 1 contains
the bulk of the text while Volume 2 contains the design charts. Each chapter is generally
self-contained and includes the necessary background information for the chapter. In a very
few cases, references are made to pertinent sections of other chapters inorder to improve
the comprehension of the text and avoid excessive repetition.
Except for Chapter 11 which summarizes the transmission line grounding practices of North
American utilities, this book can first be divided into five major blocks, namely:
•
Fundamental Considerations and Practical Design Methodology
•
Computer Programs
•
Design Charts
•
Measurement Techniques andTest Equipment
•
Concept, Theories andAnalytical
Development
These blocks overlap in that the same chapter is sometimes referred to in more than one
block. Nevertheless, the block structure should satisfy the needs of most readers. For example,
the reader who is only interested in design applications need not read Chapters 4 to 8. If
an application involves the use of the computer programs, Volume 2 need not be used.
The following describes the contents of the five major blocks and explains the interrelations
between the blocks and their parts. This should permit the reader todecide where to start
in order to best fit his immediate and, perhaps, longer term needs.
Fundamental Considerations and Practical Design Methodology
Chapters 2, 3 and major portions of Chapter 10 contain practical information regarding
transmission line grounding design. These chapters clearly explain how to determine and
gather the necessary data required by the four computer programs forming the software
package GATE (Grounding Analysis of Transmission Lines) or by the design charts of Volume
2.
The reader interested in an immediate application but with insufficient exposure to grounding
problems, must first read Chapter 2 on basic concepts and general information. He then
should proceed directly to Chapter 3 where a realistic but not overly complex design problem
is examined in full detail. The user should participate actively while reading this chapter
by personally repeating the computer sessions and/or using the referenced design charts.
Once the reader has become familiar with the design methodology, computer programs and/or
design charts, he may proceed to Chapter 10 where he will gain additional expertise in using
the design tools to analyze more difficult and subtle problems.
If necessary, the user should not hesitate to refer to the pertinent sections of the other
chapters to enhance his understanding of the issues. Chapters 8 and 9 which deal with
measurements and safety aspects respectively, may be of great value to the users of the
computer programs and design charts.
1-3
Computer Programs
The software package GATL (Grounding Analysis of Transmission line Grounding) is an integral
part of this EPRI project. It consists of four independent computer programs; LINPA, RESIST,
GTOWER and PATHS. These programs are logically interrelated through the design methodology
steps. Instructions for the use of these programs are given in Appendices A to D. Sample
computer generated printouts are also provided in these Appendices. Although the programs
are very simple to use, Chapters 2, 3 and 10 are a prerequisite for their effective use in
the design of grounding installations.
Design Charts
Volume 2 contains a large number of design charts representing several standard North
American transmission line designs. These are intended to provide the reader who is not
using the computer programs with an alternate tool to predict transmission line grounding
performance with reasonable engineering accuracy.
It must be realized that the accuracy of the desi gn charts will decrease as the actual design
problem parameters depart from those used in the reference example of the charts. Chapter
3 describes how correction factors can be applied to improve the accuracy in such circumstances.
It is clear however, that the use of the design charts are restricted to cases si mil ar to the
base examples used to generate the charts.
Measurement Techniques and Test Equipment
The reader who is interested in the practical aspects of measurement techniques and test
equipment should read Chapters 9 and 10 for a complete discussion of this subject.
Concepts, Theories and Analytical Development
The concepts and theories on which this book and the related software package GATL are
based, are described in Chapters 4 through 8. A good knowledge of these chapters is essential
for those who wish to improve their analytical expertise in grounding problems or are planning
to maintain and enhance the GATL package.
It is strongly suggested that the nontheoretical sections of these chapters be read by those
who wish to acquire a general understanding of the subject without getting overly involved
in the analytical development.
Chapter 4 deals with the earth resistivity measurement interpretation techniques. Chapter
3 presents analytical methods to predict the power frequency performance of transmission
line grounds while Chapter 6 concentrates on the calculation of the distribution of fault
current between structures and overhead ground wires. Chapter 7 is a tutorial on the subject
of the response of transmission line structures to lightning strokes. Finally, Chapter 8
describes modern theories relating to the passage of electric current through the body of a
living creature and introduces deterministic and probalistic approaches to safety around
transmission line structures.
1-4
1.5 CONCLUDING REMARKS
Although this book is reasonably complete, there are certain aspects of the problem
which require further research work. Lightning performance of transmission line structures
is one typical example.
Also, the problem of coexistence of transmission lines and pipelines along the same corridor
has not been addressed. This exclusion was specified in the Request For Proposal. Because
this subject is a natural extension of this project, the analytical methods and computer
programs were developed with the possibility in mind of making future enhancements to
handle transferred potentials from transmission line structure grounds to neighbouring buried
metallic structures such as pipelines.
As these lines are written, active research on grounding continues throughout the world. The
tremendous capabilties of modern computers have virtually eliminated all of the computational
constraints which have severely restricted the progress of power system grounding research
for nearly half a century.
1-5
FUNDAMENTAL CONSIDERATIONS
2.1 GENERAL
At an early phase of an engineering analysis, it is of utmost importance that all significant
parameters influencing the problem be correctly identified. This is particularly true in
transmission line grounding studies where a large number of parameters, many of which may
vary over wide limits, have a significant influence on the response of a structure during
power frequency and lightning fault current events.
Consequently, the power system engineer must carefully examine each problem in order
to avoid oversimplified or unnecessarily complex analyses. In many cases, simple calculations
and sound engineering judgment may be all that is needed to design a transmission line
grounding system. In some problems however, the design will require careful
measurements and elaborate computer calculations using programs such as those developed
for this EPRI project. In both cases however, the engineer must first determine the complexity
of the problem in order to decide which methods to use. This initial design step requires
some preliminary calculations, using simple formulas, to determine the orders of magnitude
of the problems involved. It also requires a knowledge of the fundamental influencing
parameters and the capabilities and limitations of the computerized methods likely to be
used if accurate calculations are necessary.
This chapter contains general information related to transmission line grounding and describes
the four computer programs developed for this EPRI project.
2.2 TRANSMISSION LINE DISTURBANCES
Ideally, the current in the earth and the current in the neutral conductors of a perfectly
balanced three-phase power system are equal to zero during normal operating conditions. In
practice however, phase voltages are not perfectly balanced and the transmission line conductor
configuration and characteristics are not perfectly symmetrical because of the unequal
distances between the phase conductors and earth. Also, various loads on the system are
often significantly unbalanced. This means that even during normal conditions, all power
systems will have some continuous current in the earth and neutral circuits. This "unbalance
current" is generally a few percent of the total transmission line load current. The distribution
of this current depends on the particular geometry of the line, number of neutral conductors,
and resistance of the ground connections such as substation and transmission line
structure grounds.
2-1
In practice, most of the unbalance current enters substation ground grids and returns to the
generating source ground system. Very little current normally flows in the neutral wires and
transmission line structures because the impedance of the path offered by the structures
and neutral wires is typically one or two orders of magnitude higher than a typical station
ground resistance. Since the value of a substation's ground resistance is generally a fraction
of an ohm, there are usually no safety hazards associated with the unbalance current.
The majority of power system disturbances result in the circulation of large currents in the
earth. The power system response to such disturbances is largely dependent on the grounding
system design and earth characteristics. Two of the transmission line disturbances which
occur most frequently are:
•
Phase to ground faults
•
Lightning strokes
The analysis of a power system subject to a lightning stroke or phase to ground fault at a
transmission line structure requires specific data on the overhead network, earth path and
nature of the disturbance. Understandably, it is not possible to consider all the parameters
which will influence system performance. Rather, those parameters which have significant
effects on the electrical response of the power system should be retained.
The following variables define the parameters which, according to the recent literature on
the subject, play a critical role in the grounding performance of transmission lines. These
variables have been grouped into four major categories:
•
Earth
•
Power system network
•
Grounding system
•
Nature of fault
The accuracy of the analyses depend on the accuracy of mathematical models developed
from these variables.
2.3 EARTH
The development of a mathematical model to represent the electrical properties of earth
can be a formidable task because of widely nonuniform characteristics.
Fortunately for transmission line grounding purposes, the earth can be reasonably approximated
by a two-layered soil structure. This soil structure is characterized by the layer resistivities
P i, 92 and the upper layer thickness h. The lower layer is considered infinite. In some
cases, the thickness of the upper layer is large enough for the earth model to be
considered fairly uniform.
The variables Pj, P2 and h are generally determined by interpreting the apparent resistivity
values measured using the Wenner (or four probe) array.
2-2
2.3.1 SIMPLIFIED METHODS
There are no simple formulas which will define an equivalent two-layer model of a complex
earth structure from measurement data. Some useful graphical techniques are explained in
Chapters 3 and 4.
An equivalent uniform soil is not easy to determine. There is no basis for assuming that a
uniform soil model with a resistivity equal to the average measured apparent resistivity
will give more accurate results than one using a resistivity value arbitrarily selected from
the measured results. The appropriate choice is greatly dependent on the real earth structure
and grounding system configuration. Thus, the experience and judgment of the engineer are
critical to the development of an equivalent uniform earth model of a complex earth
structure.
2.3.2 COMPUTER PROGRAM RESIST
The resistivity measurement interpretation process is considerably simplified when program
RESIST is used. Detailed information on the use of this program is included in Chapters 3,
4 and 10 and in Appendix B.
Because RESIST requires a minimum of data from the user, it can be used by engineers
with very little exposure to power system grounding. The input data consist of the probe
spacings and apparent resistances (or resistivities) measured using the Wenner method. RESIST
automatically selects and calculates all the other data needed to proceed with the final
computations.
The simplicity and accuracy of program RESIST has been achieved by restricting the
applicability of RESIST to transmission line grounding problems. Attempts to apply this
program to other types of grounding problems may not lead to optimal solutions. This remark
applies equally well to GTOWER and PATHS and, to a lesser extent, to LINPA.
For example, RESIST must select initial values for the upper layer thickness and layer
resistivities before starting its iterative search algorithm. The initial values retained are
appropriate for relatively small grounding systems such as those employed in transmission
line structures.
Finally, it is paramount to remember that the performance of RESIST depends largely on
the number of measurements and extent of the resistivity traverse. A small number of data
points or short traverses inevitably lead to a multiplicity of equally probable earth models.
Very long traverses unnecessarily emphasize the influence of the deep layers which have
very little effect on transmission line grounding performance. In practice, 10 to 20 measurements
along a traverse extending 5 to 10 times the transmission line structure base dimension will
usually lead to reasonable success.
2.4 POWER SYSTEM NETWORK
Throughout this report, it is assumed that the fault or disturbance is at a structure on a
transmission line section between two substations. Each substation and the power system
network to which it is connected is designated as a terminal. Figure 2.1 illustrates such a
typical network.
2-3
PHASE r
PHASE q
PHASE p
TERMINAL
Figure 2.1
LOCATION OF
FAULT
Equivalent Power System Network
The terminals can be described by the equivalent circuit of the network which exists at
either extremity of the transmission line. The variables which identify the terminal are:
V
Phase to ground voltage of the terminal power source (if not a power source the
voltage is set to zero)
Zs
Equivalent source impedance of the terminal
Zn
Equivalent neutral impedance of the terminal
Rt
Equivalent ground impedance of the terminal
The term "equivalent" is used because the substations at the transmission line extremities
are always interconnected with other substations. In practice it is usually possible, through
suitable circuit reduction, to obtain an equivalent Thevenin circuit which reduces the problem
to the basic two terminal circuit shown in Figure 2.1. At times, this reduction is not possible
without judicious approximations. Usually, a valid approximation is to replace the network
driving the step-down transformer, which feeds the transmission line under consideration,
by an infinite source with zero neutral and ground resistances. Because of the distances
involved, the effect of this procedure will usually be insignificant at the location of the
disturbance. Moreover, if the distance between the origin and extremity terminal is great
enough, the terminal busses can be considered as infinite busses (i.e., zero equivalent source
impedances) and the equivalent neutral and ground impedances will be equal to those of
the terminal transformers feeding the line.
The transmission line is assumed to consist of several zones, 1,2,3—m. Each transmission
line zone (TLZ) consists of one or more sections. All the structures within a given zone
have the same ground impedance value. A transmission line section (TLS) is defined by; the
phase conductors, the ground wires between two grounded transmission line structures, and
one of these two grounded structures. By convention, the structure which is defined in a
given TLS is the structure which is further from an observer as he moves from the point
of fault to any terminal.
Each TLZ, and consequently, any TLS belonging to this zone is characterized by the following
parameters:
Zp
Self impedance of phase conductor p
Zpq
Mutual impedance between phase p and phase q
Zg
Self impedance of ground wire g
Zpg
Mutual impedance between phase p and ground wire g
R
Ground impedance of a transmission line structure. The reactive part of this
impedance is generally negligible compared to its resistive part.
R can be determined from measurements or can be calculated from the structure grounding
system configuration and soil characteristics. More will be said about this resistance in
Section 2.5.
The self and mutual impedances of the overhead conductors of the TLS are very seldom
measured directly. Generally, these values are determined from tables and charts or are
calculated from simplified formulas or computer programs, usually designated as line parameter
programs.
2.4.1 CONDUCTOR IMPEDANCES
The self and mutual impedances of parallel cylindrical conductors located above or below
the surface of a uniform soil are given by Carson [1] and Pollaczeck [2]. Clarke [3] expresses
the self and mutual impedance of two overhead conductors with common earth return as
follows:
1=1. + Z
P
Z
«
(2-1)
ep
(2-2)
z
epg
In (2-1) Z; represents the internal impedance of the conductor. This impedance can be
determined from conductor data provided by the manufacturer. Zep represents the resistance
and reactance of the component of self impedance with earth return external to the conductor
p. In (2-2) Zgpg represents the resistance and reactance of the mutual impedance with
common earth return between conductors p and g. These impedances are generally expressed
in ohms per unit length of conductor, generally a kilometer or a mile. In Equations 2-3, 2-4,
2-6 and 2-7, the impedances are given in ohms/meter.
pg
Zep
and Zepg can be computed accurately from Carson's formulas which involve the
summation of tne terms of an infinite series. For frequencies of 60 Hz or less, only a small
number of terms is necessary to obtain accurate calculations. Clarke [3J provides simplified
formulas and charts for the computation of the external self and mutual impedances at
power frequencies.
Recently, Deri et al [4] have shown that the Dubanton's [5] simplified analytical expressions
for the external earth return self and mutual impedances Zep and Zepg are accurate to
within a few percent over a wide range of frequencies. They also analytically relate Dubanton's
formulas to those of Carson by showing that the concept of an equivalent complex ground
return plane is analytically sound. The Dubanton-Deri formulas are:
2-5
y<3
1 n
ep = jw —
2tt
2 (h +D)
E
J(h
epg
= ju) —
2ir
1
n
(2-3)
+h +2D)2 + h2
J__ E_J_________E9
(2-4)
V(h -h )2 + h2
f p g
pg
where
w
= Z-rf ; f being the frequency in Hz
M0
=
47tx10-7
is the magnetic permeability of free space
r
is the conductor radius
hp
is the height above the surface of the earth ofconductor
hpg
is the distance between conductors p and g
p
D
is the complex depth of the equivalent groundreturnplane. If P is the uniform
soil resistivity, then D equals:
V?
D =
(2-5)
VJWPo
The above formulas are convenient for computations using hand calculators and are applicable
to low as well as high frequencies. Therefore, they also can be used to calculate the high
frequency impedance of counterpoises buried close to the surface (hp ~ 0).
If the depth d of the counterpoise is such that the counterpoise can not be considered as
lying on the surface or if the counterpoise resistivity and permeability are to be taken into
consideration, then the following formulas, described by Wedehpohl [6], are preferable:
!
Z. =
wy.
r
j wyj' i
V
j —coth jO.777^1 j —— r
irr
2
jmy
ep
1
f
/jwy ' r -i
~ ' 1n Y\----- ~
2
Lip
d
-1*
2 J
0. 356p:
+ —
•nr
/jojy ‘ "
-----
3fpJ
where
y
= 1.781.... (In 7
is Euler's constant)
Mi
is the magnetic permeability of the conductor
Pi
is the resistivity of the conductor
M
is the magnetic permeability of earth
P
is the resistivity of earth
2-6
(2-6)
(2-7)
2.4.2 COMPUTER PROGRAM LINPA
Power utilities and consultants usually have access to a line parameter computer program
which provides the self and mutual impedances of power conductors arranged in any
configuration. Quite often however, the computer results available to the engineer are limited
to the equivalent phase sequence parameters. That is, the values obtained after the overhead
ground wires have been eliminated by a suitable circuit reduction technique. Because the
ground wire impedance and its mutual impedance with the faulted phase conductor play a
critical role in the fault current distribution between the ground wire and the faulted
structure, it is essential that these impedances be known and represented during the fault
calculations. This information is readily obtained from the computer program LINPA
which was specifically developed to serve as a convenient and accurate tool for the computation
of the impedances required by the fault current distribution computer program PATHS.
LINPA is described in Appendix A and is also discussed in Chapters 3 and 10. Computer
program LINPA is valid for any configuration of overhead parallel conductors over a uniform
earth. The conductors are grouped into different phases, belonging to one or several circuits.
If a group of conductors are to be replaced by an equivalent single conductor, the conductors
are assigned the same phase number and circuit number. For example, in a transmission line
consisting of three phase conductors and two ground wires, the ground wires may be assigned
the phase number 4 and LINPA will produce a 4x4 matrix where conductor number 4 will
be the equivalent conductor representing the original ground wires.
2.4.3 COMPUTER PROGRAM PATHS
PATHS is a short-circuit analysis program which calculates the distribution of current between
the overhead ground wires and the faulted structure during transmission line ground faults
at that structure. Optionally, PATHS will provide the fault currents in the ground wire spans
and in the structures adjacent to the faulted structure. PATHS is described in Appendix
D and is discussed in detail in Chapters 3, 6 and 10.
Theinput
data to PATHSconsist of thevariables illustrated
in Figure 2.1. Thesevariables
werediscussed earlier. One salient feature ofPATHS
isthat it uses the actual 3-phase
representation of the circuit, not the zero, positive and negative sequence representation.
Thus, when only the sequence impedances are known, these must be converted back to the
actual values according to the following equations:
1
Z
(2-8)
= - (Z0+2ZO
s
3
1
Z
m
= - (Zo-Zi)
(2-9)
3
Where Zs and Zm are the actual self and mutual impedances, respectively. Zg and Z\
represent the zero and positive sequence impedances, respectively (assuming equal positive
and negative impedances).
PATHS provides accurate computation results for single, double and three phase-to-ground
faults at any structure along the transmission line being considered. If PATHS is not readily
available or if approximate results are desired, then Equations 6-15 and 6-34 of Chapter
6 may be used. These equations provide convenient analytical expressions for the calculation
of the fault current in the structure, as a fraction of the total single phase-to-ground fault
current.
2-7
2.5 GROUNDING PERFORMANCE OF TRANSMISSION LINE STRUCTURES
The distribution of fault current between a structure and the overhead ground wires connected
to it is greatly dependent on the ground resistance of the structure. As stated, this resistance
R can be either measured or calculated. Knowledge of surface potentials around the faulted
structure may also be needed to assess the overall grounding performance of the structure.
These earth potentials are usually calculated for local soil characteristics.
2.5.1 SIMPLIFIED FORMULAS
The ground resistance of a structure and the earth potentials around it may be calculated
using simplified analytical expressions under the assumption of uniform soil resistivity P and
simple structure grounding systems such as a hemispherical electrode, a vertical rod and
a horizontal cylindrical conductor. These expressions also assume that the current in the
electrode discharges into earth uniformly along its length. If these assumptions can be
tolerated in a practical design situation, then it is possible to use a variety of approximate
formulas available from various publications. Important work on this subject is described in
Dwight's paper [7] and Tagg's book [8]. Useful summaries are also provided in IEEE guide
80 [9].
A very useful approach to transmission line grounding design is to initially consider the
structure base and associated grounding elements as equivalent to a hemispherical electrode
with an appropriate radius r. Under these assumptions, the ground resistance R of the
structure is:
P
R = ----2Trr
and the surface potential V at a distance
a current I in the earth is:
(2-10)
x
pi
V = -----
from the center of the hemisphere injecting
(2-11)
2ttx
2.5.2 COMPUTER PROGRAM GTOWER
In most practical cases where the earth structure and grounding configuration are complex,
simplified formulas based on a uniform soil approach often fail to predict the results,
sometimes even within an order of magnitude.
The agreement between calculated and measured results are considerably improved when
computer programs such as GTOWER are used to determine the transmission line grounding
performance. This is well illustrated in Chapter 10 of this report. GTOWER is described in
Appendix C and is discussed further in Chapters 3, 5 and 10.
GTOWER calculates the performance of a transmission line structure grounding system made
up of horizontal and vertical cylindrical conductors located arbitrarily in a uniform or
two-layer soil. An optional feature of the program expedites the data entry procedure for
the case of a symmetrical grounding arrangement. The program automatically subdivides the
conductors into sub-elements to accurately calculate the nonuniform current distribution
along the grounding conductors.
2-8
The input data to the program consist of the soil structure data, ground conductor coordinates
and earth profile specifications. The output of GTOWER gives the ground resistance and the
surface potentials along specified profiles. These profiles can also be plotted if desired.
There is one restriction in the program which may not always be identified by the program
error-detection routines. Because the potentials are defined only in earth and at the surface
of a conductor, requests to calculate potentials just above the center of a ground rod buried
at zero depth will cause an arithmetic error. The possibility of this happening will be
eliminated if a very small burial depth is assigned to the ground rod.
Limits are imposed on the radius of the ground conductors. The radius can not exceed 0.5
m (1.6 ft) for horizontal conductors and 2 m (6.5 ft) for ground rods. There are two good
reasons for these limits. Firstly, such a large radius is very uncommon in practice and the
error detection capabilities of GTOWER are enhanced by such a limitation. Secondly, the
fault current distribution at the surface of a very large radius conductor is not symmetrical
because of the proximity effects to other ground conductors. This is contrary to the
assumptions on which GTOWER is based. If necessary, this limitation can be alleviated by
replacing a large radius conductor with several smaller ones regularly spaced along the
surface of the original conductor. In fact this procedure is recommended for a conductor
radius above 0.5 m if improved accuracy is desired.
2.6 TYPE OF DISTURBANCE
The disturbance is assumed to be localized at a specific structure (structure 0) of the
transmission line. This disturbance could be a surge, caused generally by a lightning
stroke to the structure, or a power frequency ground fault at the structure. The ground
fault could be initiated by various causes such as insulator pollution or a backflash resulting
from a lightning stroke.
2.6.1 POWER FREQUENCY GROUND FAULTS
Structure faults may be of the single, double or three phase-to-ground type. The overwhelming
majority of transmission line power frequency ground faults are single line-to-ground. The
type of fault in program PATHS is selected by simply assigning a suitable value to the shunt
impedance between the phase conductor and the faulted structure. This impedance may be
regarded as the impedance of the arc path developing between the faulted phase and the
structure. In most cases, the arc impedance is negligible compared with the other impedances
of the circuit. Healthy phases are modelled by simply selecting a shunt impedance high
enough to represent an open circuit condition between the phase conductor and the structure.
2.6.2 LIGHTNING STROKES
The lightning response of transmission line structures is certainly one of the most difficult
subjects in the area of transmission line design. The basic difficulty in calculating lightning
performance of structures is due not only to the mathematical effort required to obtain
accurate results, but to the uncertainty in the identification of all parameters which have
a significant influence on this performance. Moreover, unlike the other subjects considered
in this project, there are a number of unresolved controversial issues relating to this matter.
2-9
Unfortunately, recent extensive artificially-triggered lightning test programs have not been
capable of resolving the controversies, despite the wealth of new information which is
significantly broadening our knowledge on the subject of lightning. Moreover, some of the
new evidence may very well be a source of vigorous discussion and additional disagreement
as explained in Chapter 7.
Chapter 7 contains a brief but complete description of the transmission line structure response
to lightning stroke currents. The most widely used analytical approaches are described and
commented upon. From this chapter it can be concluded that despite its incompleteness and
some deficiencies, the so-called "transient surge impedance" of a structure as given by
Wagner [10] remains the most accepted way to represent the lightning response of the
structure:
Z$ = 60 In [V5 (ct/a)]
(2-12)
where
c
is the velocity of light (3x108 m/s)
t
is the time in seconds
a
is the radius of the equivalent structure in meters
Zs
is the surge impedance in ohms
Further research work in this area is clearly needed. Accurate methods appear feasible.
However, these methods will require the use of advanced and sophisticated techniques only
suitable for treatment by digital computers.
REFERENCES
1 - J. R. Carson, "Wave Propagation in Overhead Wires With Ground Return", Bell System
Technical Journal, No. 5, October 1926.
2 - F. Pollaczek, "Ueber das Feld Finer Unendlich Langen Wechselstrom Durchflossenen
Einflachleitung", Elektrische Nachrichten Technik, No. 3, September 1926.
3 - E. Clarke, "Circuit Analysis of AC Power Systems, Volume 1; Symmetrical and Related
Components", Book published by General Electric Company, 1961.
4 - A. Deri, G. Tevan, A. Semi yen, A. Castanheira, "The Complex Ground Return Plane; A
Simplified Model for Homogeneous and Multi-Layer Earth Return", IEEE Transactions on PAS,
Vol. PAS-100, No. 8, August 1981, pp. 3686-3693.
2-10
5 - G. Gary, "Approche Complete de la Propagation multifilaire en haute frequence par
Utilisation des Matrices Complexes", EDF Bulletin de la Direction des Etudes et Recherches,
Serie B, No. 3/4, 1976, pp. 3-20.
6 - L. M. Wedepohl, D. J. Wilcox, "Transient Analysis of Underground Power Transmission
Systems", Proceedings of the IEE, Vol. 120, No. 2, February 1973, pp. 253-260.
7 - H. B. Dwight, "Calculation of Resistances to Ground", Electrical Engineering, Vol. 55,
December 1936, pp. 1319-1328.
8
- G. F. Tagg, "Earth Resistances", George Newnes Ltd., London 1964 (book).
9 - Guide IEEE 80 (1976), "Guide for Safety in Substation Grounding", published by IEEE,
New York 1976.
10- C. F. Wagner, "A New Approach to the Calculation of the Lightning performance of
Transmission Lines. Ill- A Simplified Method: Stroke to Tower", AIEE Transactions on PAS,
Part III, Vol. 79, October 1960, pp. 589-603.
2-11
TYPICAL DESIGN METHODOLOGY
3.1 GENERAL
There is a wide variety of transmission line grounding problems requiring thorough
analysis by power system engineers. Some of these problems can not be fully addressed
without concepts and analytical methods not within the original scope of this EPR1 project;
transferred potentials (or resistive coupling) to nearby pipelines, structures and buried low
voltage circuits, for example. However, most problems can be accurately examined using
the analytical methods developed in Chapters 4 to 7.
It is recommended that Chapters 4 to 7 be carefully read, although it is not necessary to
become familiar with the analytical theories in order to effectively use the computer programs
developed from these theories. It is, however, exceedingly important to follow an appropriate
methodology when applying the various computer programs to the design of optimum
transmission line grounding systems.
In this chapter, a typical transmission line grounding design problem is examined in detail
using the computer programs developed during this EPRI project. Solutions to the problem
based on the design charts of Volume 2 are also provided.
Obviously it is impossible to include in this example all the possible variations which emerge
in practical problems. However, the design problem of this chapter and the various problems
examined in Chapter 10 constitute a good starting point in gaining the necessary experience
for effective use of the computer programs and design charts developed during this EPRI
project.
3.2 DESCRIPTION OF THE PROBLEM
The four-legged lattice tower shown in Figure 3.1 is a typical structure for a planned 345
kV transmission line. One of these towers will be erected near a schoolyard. For this reason,
it was decided to design a grounding system which will maintain safe step and touch voltages
around this tower.
3-1
AVERAGE HEIGHTS
USED TO
CALCULATE LINE
PARAMETERS
21.5'
Figure 3.1
345 kV Four-Legged Lattice Tower
3.2.1 TOWER FOOTING
The foundation of each tower leg is of the grillage type shown in Figure 3.2. The grillages
provide a good grounding system for the tower. This grounding system can be accurately
modelled by equivalent cylindrical elements based on the GMR concept or the approximate
"equal cross-section" approach of Chapter 5 (Section 5.2.2). It is assumed that the "equal
cross-section" approach leads to an equivalent grillage made of cylindrical elements with a
diameter as shown in Figure 3.2(c).
3.2.2 POWER SYSTEM NETWORK
The "schoolyard" tower is 3.7 km (2.3 miles) from substation LEFT and 20.9 km (13
miles) from substation RIGHT. The average span between towers is 243.8 m (800 feet). A
short-circuit occurs between phase A of circuit No. 1 and the "schoolyard" tower as shown
in Figure 3.3. There are 14 towers on the left of the faulted tower and 85 towers on its
right. Circuit No. 2 of the transmission line will become operational only 15 years after
circuit No. 1 is energized.
3-2
PROFILE
LEGEND
SOIL SURFACE
5.V
VERTICAL ROD
i—- a • •
JL
V
CYLINDRICAL
CONDUCTOR
<p = 0.08'
b)
Figure 3.2
cj
SECTION “DD"
EQUIVALENT LEG
Grillage Foundations
FUTURE
Z ~ O.Hl -f j 1.169 fi/mile
= 0.09+J0.53 S2/mi
Z
= 0.808 +
a/m] I
2-3 miles
15-3 miles
TERMINAL
"LEFT"
Figure 3.3
TERMINAL
"RIGHT"
Power System Network
3-3
The phase-to-ground short-circuit levels at both substation busses have been determined,
using a conventional short-circuit program, as 8000 MV A for substation LEFT and 3000 MVA
for substation RIGHT. These short-circuit levels are converted into approximate equivalent
source impedances (as seen from the substation bus) of the network feeding a current
into the fault via the substations:
(345 kV)2
Z I
a1
14.878
Q
8000 MVA
(345 kV)2
39.675 ft
3000 MVA
It is further assumed that the inductance to resistance ratio of the equivalent source
impedance is 15. Therefore:
Za =
0.99 + j14.85 ft
Zb =
2.64 + j39.59 ft
Generally, the substation transformers at each end of the transmission line will contribute
the major portion of fault current which will return to the transformer neutral points through
the overhead ground wires and substation grounding grids. In many cases however, significant
fault current contribution is also provided by other substations. Consequently, the ground
impedances Ra and R5 shown in Figure 3.3 are the equivalent ground impedances of all
current sources on the left and right of the faulted tower. In practice Ra and R5, typically
0.5 ohm or less, will have a negligible effect on the fault current magnitude and its
distribution between the faulted tower and the overhead ground wires. This is why Ra and
Rb are assumed equal to 0.01 ohm in this example.
The above determination of the equivalent source and ground return impedances is an
approximation which leads to accurate results in most cases where the primary source
substations are interconnected to a large power network. If a source substation is not
connected to other substations, then the source impedance is the equivalent impedance of
all power transformers in parallel and the ground return impedance is the substation grid
impedance. Finally, it is always possible by use of a circuit reduction algorithm, to reduce
the source substations and their interconnections into an equivalent source as shown in Figure
3.3.
The equivalent left and right source networks will be designated as "terminal LEFT" and
"terminal RIGHT" respectively to distinguish them from the actual substations "LEFT" and
"RIGHT".
3.2.3 TRANSMISSION LINE CONDUCTOR DATA
Each phase is a bundle of two 954 MCM ACSR conductors as shown in Figure 3.1. The
conductors have a radius of 3.04 cm (1.196") and are characterized as follows:
Code : Cardinal
Stranding : 54x0.1329" aluminum
Number of layers :
;
7x0.1783" steel
4
Resistance : 0.0620 ft/Km at 60 Hz and 25 °C (0.0998 ft/mile)
GMR :
0.0123 m (0.0404 ft)
Reactance at 1 ft radius : 0.242 ft/Km at 60 Hz (0.389 ft/mile)
3-4
There are two 19 No. 10 alumoweld overhead ground wires which have the following
characteristics:
Conductor diameter : 1.29 cm (0.509")
Resistance : 0.893 fl/Km at 60 Hz and 25 °C (1.437 ft/mile)
GMR : 0.000841 m (0.00276 ft)
Reactance at 1 ft radius : 0.444 ft/Km at 60 Hz (0.715 ft/mile)
The average height above ground of the phase conductors and ground wires is assumed equal
to the height at the tower (see Figure 3.1) less half the average conductor sag which is
about 22 ft.
Finally the average soil resistivity along the transmission line right of way is estimated at
150 ft-m.
3.2.4 APPARENT SOIL RESISTIVITY
The apparent soil resistivity around the "schoolyard" tower was measured using the Wenner
method. The results of the measurements are given in Table 3.1.
PROBE
SPACING (m)
Table 3.1
APPARENT
RESISTIVITY (ft-m)
2.5
320
5.0
245
7.5
182
10.0
162
12.5
168
15.0
152
Apparent Soil Resistivity
3.3 DESIGN METHODOLOGY
The main objective is to design a tower grounding system which limits the touch and step
voltages around the tower to safe values. This can be accomplished by following the steps
shown in the flowchart of Figure 3.4. In this flowchart, the bracketed names on the right-hand
side refer to the computer programs which can be used to perform the necessary calculations
(see Appendices A to D for a description of these programs), while the left-hand bracketed
descriptions refer to design charts contained in Volume 2 of this report or to simple equations
described in this volume.
The flowchart describes the three principal methods which can be used to mitigate step and
touch voltages. The subjects of safety and mitigation measures are discussed in Chapter 8.
3-5
3.3.1 TWO-LAYER EARTH MODEL
Table 3.1 clearly shows that the soil around the tower is not uniform. Therefore, an equivalent
two-layer earth model must be determined to improve the accuracy of the tower grounding
performance calculation.
The resistivity values of Table 3.1 were used as input data to computer program RESIST as
shown in Appendix B. This appendix provides instructions for preparing the input data file
(for batch mode processing) and the input data dialogue when the interactive mode is selected
to run the program. The computer printout of this appendix shows that the equivalent earth
structure determined by RESIST corresponds to a 2.56 m (8.4 feet) thick first layer with a
resistivity of 383 fi-m underlain by a second layer with a lower resistivity value of 147.7
Q-m.
An almost identical two-layer earth model can be determined using the logarithmic curve
matching technique described in Chapter 4. The field resistivity curve is plotted on a
transparent logarithmic graph and is then compared directly to the set of theoretical Master
curves provided in Volume 2 (Figure 1.1). The comparison process, illustrated in Figure 3.5,
consists of obtaining a satisfactory match between the measured and theoretical curves
through a series of appropriate horizontal and vertical translations of the transparent graph
sheet. When this is accomplished, the thickness of the upper layer is the value of the abscissa
on the vertical line passing through the Master chart abscissa corresponding to a/h = 1.
From Figure 3.5 it is found that the upper layer thickness is approximately 2.5 m (8.2 feet).
Similarly, the upper soil resistivity is the value of the ordinate on the horizontal line passing
through the Master chart ordinate corresponding to Pa/P| = 1. Figure 3.5 shows that the
upper soil resistivity is about 390 fi-m. Finally, this figure indicates that the measured
apparent resistivity curve corresponds to a reflection factor in the range of -0.4 to -0.45.
This leads to a lower resistivity value between 148 and 167 Q-m.
3.3.2 TRANSMISSION LINE PARAMETERS
The self and mutual impedances of the transmission line phase conductors and ground wires
are important parameters for the calculation of the fault current and its distribution between
the faulted tower and the overhead ground wires. In particular, the self impedance of the
ground wire and its mutual impedance with the faulted phase conductor have a significant
influence on the portion of fault current which flows down the faulted tower. These impedances
are not always readily available to the design engineer and must be calculated using
transmission line parameter computer programs, charts or approximate formulas such as those
given in Chapter 2.
Computer program LIN PA is a line parameter program specifically developed to calculate
the line parameters required by the computer program PATHS, which determines the fault
current and its distribution between towers and ground wires. Appendix A provides the
instructions to use LINPA in a batch or interactive mode. It also gives the complete printout
of the LINPA run based on the design problem data described in Section 3.2.3. The results
of this run are summarized in Table 3.2 which gives the symmetrical impedance matrix
(excluding circuit No. 2) after the conductors of a bundle and the ground wires have been
reduced to an equivalent conductor. The bundle and ground wire reductions are essential
since the computer program PATHS uses the self and the mutual impedances of the equivalent
phase conductors and equivalent ground wire.
3-6
APPARENT SOIL
MEASUREMENTS
VOLUME 2
PART 1
DETERMINE
EQUIVALENT
TWO-LAYER
EARTH MODEL
RESIST
TOWER
CONFIGURATION
AND CONDUCTOR
CHARACTERISTICS
VOLUME 1
CHAPTER 2
DETERMINE
TRANSMISSION
LINPA
PARAMETERS
CONFIGURATION
OF TOWER
GROUNDING
VOLUME 2
PARTS 2,3,
AND k
DETERMINE TOWER
GROUNDING
PERFORMANCE
GTOWER
CURRENT IN
TOWER
USE LOW
IMPEDANCE
OVERHEAD
GROUND WIRES
iVOLUME 2)
;PART 3
/
VOLUME 1 1
^CHAPTER 6'
DESIGN
COMPLETED
DETERMINE
FAULT CURRENT
IN TOWER AND
IN OVERHEAD
GROUND WIRES
OPTIMIZE
GROUNDING SYSTEM
CONFIGURATION
(GROUND POTENTIAL
CONTROL RINGS,
COUNTERPOISES, ETC.)
PATHS
IS TOWER
GROUNDING SYSTEM
\ SAFE ? /
LAYER ON
SURFACE OF SOIL
SELECT
MITIGATION
MEASURES
Figure 3.4
Design Methodology
As can be deduced in Appendix A, conductors to be reduced to an equivalent conductor by
program LINPA are assigned the same phase number (phase No. 4 for the two ground wires
of this design problem) to indicate that these conductors are at the same potential with
respect to remote ground. Therefore, the word "phase" in LINPA has a broad meaning.
Note that the transmission line impedance values shown in Figure 3.3 and used as input data
for the program PATHS (Appendix D) are average values determined from Table 3.2.
3-7
r
r
I
r
(ooo-
l
f
t
it
390 ft-m
b
f
i
b
b
l
i
r
i
i
F
[
v
\
F
i
f
Ff
i
J2.5 m
Figure 3.5
ijml
Logarithmic Curve Matching Technique
EQUIVALENT
CONDUCTOR
SELF AND MUTUAL IMPEDANCE
A1 *
0 1 2
+ jl.168
B1
0.092
+ jO.611 0.141 + jl.169
Cl
0.091 + j0.527 0.091 + j0.599 0.141 + jl.169
0.091 + j0.485 0.090 + j0.521 0.090 + j0.602
* A1 = Phase A of Circuit No. 1
GW = Ground Wire
Table 3.2
GW*
Cl
B1
A1 *
GW*
. A
(IN OHMS/MILE)
Computed Impedance Matrix
3-8
0.808
+ 1.234
3.3.3 TOWER GROUNDING PERFORMANCE
The response of a grounding system conducting power frequency current into earth is
proportional to the current magnitude unless soil breakdown occurs due to very high current
densities in the ground conductors. This situation very seldom occurs at transmission line
structures subject to power frequency faults. It is therefore possible to analyze the performance
of a grounding system assuming a 1 per unit (p.u.) current and applying appropriate
proportionality factors to determine the response of the grounding system to actual or
predicted currents.
The grounding performance of the tower footings illustrated in Figure 3.2 was determined
using the computer program GTOWER described in Appendix C. The same results were
derived from the charts provided in Volume 2. In each case the actual current in the tower
was not yet known. A value of 1 kA was assumed in the GTOWER run. The design charts
are normalized (in %) with respect to the tower current, upper soil resistivity and transmission
line configuration and dimensions.
The computation results of GTOWER provide the tower ground resistance and earth surface
potentials along the profile shown in Figure 3.2 (Appendix C shows the complete printout
of a GTOWER run relating to a grounding system consisting of the tower footings and a
square ground potential control loop). The worst touch and step voltages occur 0.9 m (3
feet) from the tower leg as illustrated in Figure 3.6. The computed results are as
follows:
Tower ground resistance : 31.67 ohms
Touch voltage Vq (also step voltage VS]J) : 69.1%
Touch voltage Vt2 (also step voltage Vs2) : 67.2%
The step and touch voltages are expressed in percent of the tower potential rise which is
the product of the tower ground resistance and the fault current injected into earth by the
tower. Step and touch voltages at other locations around the tower can be determined from
GTOWER results if appropriate potential profiles are specified.
3'
--
3'
TOUCH VOLTAGE
Figure 3.6
STEP VOLTAGE
Worst Touch and Step Voltages
3-9
Similar results can also be determined with reasonable accuracy from the charts of Volume
2 (Part 2) because the tower footings correspond to one of the two types provided in Volume
2. It should be noted, however, that although the general shape is the same, the various
dimensions between the actual and example towers are not in the same proportion. More
will be said about this later. For the moment however, it is assumed that all dimensions of
the actual tower footings are proportional to those of the reference tower used to develop
the charts of Volume 2. This dimension scale factor Xjj, is defined as the ratio of the tower
base dimension (51.8 feet) in the example, to the tower base dimension of the actual tower
(28 feet). Therefore
is equal to 1.85.
A close examination of the equations of Chapter 5 reveals that if all dimensions, including
the thickness of the upper soil layer, are scaled up or down by a factor X£ , the response
of the grounding system remains inversely proportional to the scale factor Xjj, . It also shows
that this response is proportional to the upper layer resistivity P i, provided that the reflection
factor is the same. These observations are summarized by the following expression:
p
actual
= p
model
_
X
(1-1)
u
P
where
P is the ground resistance or the earth potential (i.e.,response of the grounding system).
X£ is the dimension scale factor as defined earlier.
Xp is the resistivity scale factor and is the ratio of upper layer soil resistivities in
the example and the actual case.
The upper layer soil resistivity of the example used in Volume 2 is 100 fl-m. Thus the
resistivity scale factor for the design problem is 0.261, reducing the above expression to:
P
actual
=7
?26
P
model
Ground Resistance
The ground resistance for the example (base) tower is obtained from the chart of Figure
2.3 in Volume 2. The upper layer of the actual soil is 2.56 m deep. This corresponds to a
4.7 m (2.56x1.85) thick upper soil layer in the example. From Figure 2.3, the ground resistance
of the tower footings without a potential control conductor in a two-layer soil with a
reflection factor of -0.44 (as computed by RESIST) is about 3.4 ohms. Hence, the actual
tower resistance is:
R
aCT.Ua I
= 7 • 085x3 . k = 24.1 ohms
The resistance value has been derived assuming that all dimensions of the actual tower are
proportional to those of the base tower. This is not the case, as can be concluded from an
examination of Figure 3.2 and Figure 2.1 of Volume 2. Thus, a correction factor should be
applied to account for the nonuniform scaling between the actual and base towers. A logical
way to determine this correction factor is to calculate an average dimension scale factor
based on the dimensions of the fundamental elements of the grounding system. In the case
of this problem the following average scale factor is selected:
,
A£a =
1 /
Li mode 1
3 \
L i actual
-I Wi
,
L? model
L3 model
Lz actual
L3 actua1
----------- + w2 —------------ + w3 —r-----------
1 / 5L! t J0JL t ju8 \
3 \ 28
5A
1.6 /
3-10
)'
2 26
(3-2)
where Lj_, L2 and L3 are the dimensions shown in Figure 3.7 and wj, W2, W3 are weighting
coefficients which describe the relative influence of a ground element and its effect on the
variable being calculated. For tower ground impedance, it is considered that the three
dimensions selected have equal influence w^ = W2 = W3 = 1.
Figure 3.7
Fundamental Tower Grounding System Dimensions
The correction factor is therefore 2.26/1.85 = 1.22. The tower ground resistance thus becomes:
"actual " 21,.1x1.22 = 29.; ohms
The derivation of correction factors to account for minor differences between actual and
base tower ground systems will generally be based on experience and engineering judgement.
For example, the same weighting coefficient should be applied to all grounding elements if
the tower ground resistance is being calculated. If however, a surface potential is being
investigated, then it may be more appropriate to apply different weighting coefficients
depending on the distance between an element and the point where the potential is calculated.
It is important to be cautious when correction factors are used to account for significant
differences in scale. Above a value of 1.5, correction factors are suspect, suggesting that
the charts of Volume 2 can not be used for such cases.
Touch and Step_Voltages
The touch (and step) voltages Vq and
can similarly be determined from the normalized
potential profiles of Figure 3.8 which is also Figure 2.8 of Volume 2.
A distance of 0.9 m (3 feet) from the leg of the actual tower becomes 0.9x1.85 = 1.7 m
(5.5 feet) from the base tower leg. This is because the earth surface potentials, expressed
in percent of the tower potential rise, are the same for two geometrically equivalent points
3-11
of the actual and base towers. Thus, from Figure 3.8 the following values are determined:
vt1 = Vs1 = 100^
-35% = 65%
Vt2 = VS2 = 100^ "38^ = 62^
Because the above voltages represent the difference in surface potentials at points very
close to the tower leg, the influence of differences between the footing grillage of the
model and actual towers is negligible. Consequently, the correction factor to be applied on
the above voltages is:
1 ) 51.8 + 10.5
2 1
28
5.4
(1.85) = 1.025
735 kV (QH)
TRANSMISS ON LINE STRUCTURE
SOIL STRUCTURE: Un i form
h =
5
U
Two- layerLx.1
m
POTENTIAL CONTROL RING: YES □
POTENTIAL PROFILE No. :
NO
SI
(Leg)
POTENTIAL
i
r
0
5
,
i
1
10
TOWER LEG
■
r
'
15
20
25
Distance from Origin of Profile
Figure 3.8
Earth Surface Potential Profiles
(in meters)
3.3.4 FAULT CURRENT DISTRIBUTION
The magnitude of the fault current and its distribution between the faulted tower and the
ground wires was determined by computer program PATHS described in Appendix D. The
input data file, the input data dialogue and the computer program results related to this
design problem are presented in this appendix. The input data used by PATHS have been
described previously and is summarized in Figure 3.3. Note that the tower ground resistance
^e> has been determined by GTOWER and is equal to 31.67 ohms. Note also that the self
impedance of the phase conductors as used by PATHS is the average value of phases A, B
and C.
The computation
with only 377 A
the soil directly
volts. The worst
potential rise or
results from PATHS show that the fault current magnitude is 15,321 A
flowing down the tower. Therefore, only 2.46% of the fault current enters
at the faulted tower and the tower potential rise is 377x31.67 = 11,940
touch (and step) voltage previously calculated was 69.1% of the tower
0.691x11,940 = 8,250 volts.
A similar result can be obtained using the design charts of Volume 2, Part 5. However,
these charts provide the tower current in percent of the total fault current which, if not
known, must be calculated by conventional short circuit programs or by other means such
as the one which follows.
If the coupling between the phase conductors and the ground wires is neglected and if
the influence of the nonfaulted phases are also neglected, a simple circuit reduction of the
network of Figure 3.3 leads to the equivalent circuit of Figure 3.9. The total fault current
If can easily be calculated from this circuit. A further simplification can be introduced by
considering that the impedance of the current return path is zero (Re in parallel with Zi
and Z2 is negligible). This last assumption is reasonably valid for this problem and leads to
a total fault current of about 14,800 A.
0.99+j14.8Q
0.33+j2.7^
+j 18.0^
2.1 7
3^5 kV
/3
345
/3
0
2.64+j 39.6f2
ft
Figure 3.9
0
n
Simplified Circuit
The current It in the tower depends on the ground resistance of the adjacent towers, the
impedance of the overhead ground wires and their mutual impedance with the phase conductor.
The self and mutual impedances of the ground wire match reasonably well those of the 500
kV transmission line example of Volume 2 (Part 5). As it can be concluded from Chapter
6, the voltage of the transmission line is of no consequence when the current in the tower
is expressed in percent of the fault current. Of primary importance are the ground wire
self and mutual impedances and the ground resistances of the faulted tower and the
immediately adjacent towers. The average span distance and the average ground
resistance of the remote towers do influence the results but only slightly.
3-13
The charts which are most applicable to the case being analyzed are Figures 5.41, 5.43 and
5.44 of Volume 2 Part 5. These charts are directly applicable to a 20 mile long transmission
line.
From Figure 5.41, it can be determined that for an average tower resistance of 20 ohms,
the current Ij- in tower 14 would be about 3.6% of the total fault current for a fault at
that tower. This result assumes that the faulted tower resistance Re is equal to the average
resistance R. Since this is not the case, a correction factor is needed. This factor can be
determined from Figures 5.43 and 5.44 of Volume 2. A close examination of these two
figures indicates that for R < Re, the following relationship is applicable:
It(R<Re) = — It(R=Re)
(3-3)
R
e
Thus, the correction factor is, 20/31.67 = 0.63, and the adjusted tower current is, 3.6x0.63
= 2.3%, a value which compares favorably with the results of the PATHS run.
Once more, the importance of appropriate correction factors is clearly illustrated. These
factors are needed whenever a design problem is different from the reference problem of
Volume 2.
3.3.5 SAFETY EVALUATION
At this point, the hazard level around the tower can be examined. There are several
approaches which can be followed to conduct a safety evaluation. These are explained in
Chapter 8. In the case of this problem, Dalziel's well known formula is used to illustrate
the design concept:
0.116
(3-4)
A
where ij-, is the maximum permissible body current in amperes and t is the fault duration
in seconds. If Vt designates a touch voltage and Vs represents a step voltage, then safety
is achieved when:
V <
s
116 + °-»2
a
= u
*f
.
s
(3-5)
„.6)
/t
The above expressions assume that the resistance of the human body is 1000 ohms (see
Chapter 8). Rf is the resistance of one foot of a person standing on a thin semi-insulating
layer covering the soil surface. From Equation 8-8 of Chapter 8, the value of Rf for a 200
cm2 foot (31 in2) is:
Rf = 50eps
(3-7)
where e is the thickness of the semi-insulating layer (in m) and Ps the resistivity of this
layer (in ft-m).
Table 3.3 shows tolerable step and touch potentials for several values of the fault duration
t, resistivity ps, and surface layer thickness e.
No
TIME
(s)
TOUCH
VOLTAGE
ut
(VOLTS)
STEP
VOLTAGE
us
(VOLTS)
Table 3.3
GRAVEL
(ps = 3000 -m)
SURFACE
e=5cm
LAYER
(p
ASPHALT
> 10,000 Q-m)
e=10cm
e=15cm
e=20cm
e=15cm
e=20cm
0.1
367
1742
3118
4494
5869
4952
9537
14123
18708
0.2
259
1232
2205
3177
4150
3502
6744
9986
13228
0.3
212
1006
1800
2594
3388
2859
5506
8154
10801
0.5
164
779
1394
2010
2624
2215
4265
6316
8366
0.1
367
5869
11371
16874
22376
1 8708
37049
55390
73732
0.2
259
4150
8041
11932
15822
1 3228
26198
39167
52136
0.3
212
3389
6565
9742
12919
10801
21390
31980
42569
0.5
164
2625
5085
7546
10007
8366
18525
24771
32974
e=5cm
e=10cm
Permissible Contact Voltages
The zone within the heavy line of Table 3.3 identifies the cases where safety criteria are
not satisfied based on the 8,250 volt worst case touch and step voltages determined from
the computer runs related to this problem. It is clear that safety is achieved only
through the use of a thick high resistivity surface layer such as asphalt. It is also clear
that permissible step voltages are significantly higher than the permissible touch voltages
when there is a semi-insulating surface layer.
3.4 POTENTIAL CONTROL CONDUCTORS
A touch or step voltage of 8000 volts may not be tolerable in some cases. Potential control
conductors could then be used to reduce the voltage to a more acceptable value.
In the following paragraphs, the mitigating effects of the square potential control loops
of Figure 3.10 are analyzed as these loops are installed in a three step sequence, illustrated
in Figure 3.10. The methodology of the analysis is a repetition of what has been described
in Sections 3.3.3 and 3.3.4. Note that the design charts of Volume 2 (Part 2) can only be
applied to step number 1, i.e., when the potential control loop shown as a solid line in
Figure 3.10 is installed. For the next two steps, the computer program GTOWER must be
used to analyze the performance of the tower grounding system.
3.4.1 INNER POTENTIAL CONTROL LOOP; STEP 1
Appendix C gives the input data instructions, input data file and computer printout of a
GTOWER run based on a tower grounding system consisting of the footings and an inner
potential control loop. The computation results show that the tower ground resistance is
reduced to 12.17 ohms and the touch and step voltages defined in Figure 3.6 are:
vtl = vsl = icm -74.4% = 25.6?
Vt2 = VS2 = ]00Z "63.0% = 37.0%
Comparable results are obtained from the design charts of Volume 2 by following the same
technique used in Section 3.3.3.
3-15
OUTER POTENTIAL CONTROL LOOP (STEP 3)
INNER POTENTIAL CONTROL LOOP (STEP 1
LEG POTENTIAL CONTROL LOOP (STEP 2)
TOWER LEG
CENTER OF TOWER
Figure 3.10
Ground Potential Control Loops
From Figure 2.3 of Volume 2, the tower ground resistance of the example for a 4.7 m thick
upper layer and a reflection factor of -0.44 is about 1.23 ohms. The actual resistance is
therefore:
'383
x(l.85)x(1.25) =7-085x1.25 = 8.85 ohms
100
This resistance should be further multiplied by the following correction factor:
1 HA + J£i5 + 4-8 +_95
4 1 28
5.4
1.6
37
(1.85) = 1.26
In the above expression 95/37 represents the ratio of the inner potential loop dimensions of
the base and actual towers. The adjusted ground resistance of the tower is therefore 8.85x1.26
= 11.2 ohms which is in reasonable agreement with the value computed by GTOWER. Note
that it is also possible to account for the influence of the potential control loop dimension
by using Figure 2.4 of Volume 2.
The results of program PATHS for a fault at the tower with only an inner potential control
loop show that the total fault current has remained practically constant at about 15,346 A.
The current in the tower has increased to 938 A, however. This corresponds to a potential
rise of 938x12.17 = 11,415 volts, i.e., slightly less than the case with no inner loop. The
worst touch and step voltage is 37%x 11,415 = 4224 volts, about half the value computed
without the loop. If the fault clearing time is known, Table 3.3 can be used to select the
thickness and material type of the semi-insulating surface layer which should be used to
insure safety around the tower.
A similar worst case touch voltage value can be determined from Figures 2.24, 2.17,
5.42, 5.43 and 5.44 of Volume 2. The methodology is identical to that followed in Sections
3.3.3 and 3.3.4.
3-16
3.4.2 LEG CONTROL LOOP; STEP 2
As shown in the previous section, a person touching the leg of the tower while standing
underneath the tower, 3 feet from the leg will be subject to a touch voltage of 37% of the
tower potential rise. The touch voltage will be only 25% if the person is on the outside (see
Figure 3.6). The addition of L-shaped conductors at each leg improves this situation as can
be concluded from the following computer results:
GTOWER
Resistance of tower : 11.03 ohms
Touch and step voltages (in % of tower potential rise)
Vti = Vsi = 20%
Vt2 = Vs2 = 18%
PATHS
Total fault current : 15,350 A
Current in tower s
1,026 A
Tower potential rise : 11,324 volts
The worst touch voltage has been reduced to 20%xll,324 = 2,265 volts.
3.4.3 OUTSIDE POTENTIAL LOOP; STEP 3
The addition of the outer ground potential loop leads to the following results as computed
by GTOWER and PATHS.
GTOWER
Resistance of tower : 7.34 ohms
Touch and step voltages (in % of tower potential rise)
Vtl = Vsl = M.2%
Vt2 = VS2 = 14.6%
PATHS
Total fault current : 15,369 A
Current in tower :
1,482 A
Tower potential rise : 10,876 volts
The worst touch voltage is now equal to 14.6%x 10,876 = 1,588 volts. This value is significantly
less than the unmitigated value of 8,250 volts computed in Section 3.3.4.
3-17
3.5 OTHER CASES
It is obvious that despite the large number of charts available in Volume 2, their use is
restricted to cases which belong to the same category as the referrence example used to
develop the charts. Deviations from the reference example can be handled by use of a
variety of appropriate correction factors, but the judicious choice of a correction factor is
essentially a matter of experience.
In contrast, the computer programs offer the possibility of analyzing a large variety of
configurations without the need for correction factors. GTOWER can be used to explore new
potential control loop designs and PATHS, which is valid for single or double circuit
transmission lines, can be used to analyze ground faults on any phase; single, double, or
three-phase to ground and at any tower.
3-18
CHAPTER
4
EARTH RESISTIVITY
4.1 GENERAL
The ability of a group of buried metallic conductors such as transmission structure grounds
and counterpoises, to conduct current into the soil is significantly dependent on the resistivity
of the soil. Other factors, such as the impedance of power cables and overhead conductors,
are influenced by earth resistivity. Earth resistivity can even affect the susceptibility of a
particular location to lightning strikes [1,2]. Thus, a knowledge of soil resistivities is of
fundamental importance in accurate prediction of transmission line performance during ground
fault or lightning conditions.
Unfortunately, it is not practical to determine soil resistivity everywhere along the route
of a transmission line. There are certain circumstances, identified in Chapter 8, which require
that accurate knowledge of soil structure be determined at specific sites. At most other
sites, accurate values are not necessary and an order of magnitude estimate is sufficient.
Fortunately, there are usually indirect sources of information from which it is possible to
secure a qualitative knowledge of the soil structure. This chapter is directed at the
measurement and interpretation techniques most generally used to determine soil structure
and resistivity.
The complexities of most classical methods used by geologists to measure and interpret earth
resistivity are beyond the scope of this report. The objectives of a power system design
engineer are quite different from those of a geologist, however. Electrical exploration of
the earth for geophysical purposes is directed at a determination of soil structure and
composition at great depths. In contrast, the electrical engineer needs to know the soil
structure at relatively shallow depths and over comparatively short distances, because the
performance of grounding structures is influenced mainly by the characteristics of the soil
surrounding the grounding electrode.
The only information required for grounding purposes is the actual soil structure or an
equivalent model resulting in similar performance. This is fortunate because the actual earth
can often be modelled as an equivalent two-layer soil structure [3-5], or in some cases, a
three or four-layered structure. Because of the complexity of the mathematics required
to handle models with more than two-layers, these cases will not be analysed in detail. A
two-layer earth model is usually more suitable than an approach based on uniform soil models
because the only cases where uniform soil models can lead to accurate answers are those
cases where measurements confirm that the earth is in fact fairly uniform.
Unlike most engineering problems, interpretation of earth resistivity measurements is an
"inverse" problem; i.e., from the electrical response to impressed current at specific locations
on the earth surface, the electrical properties of the conducting media (earth) are to be
determined. In contrast, conventional electrostatic problems determine the electrical response
or the excitation current sources, based on the known properties of the conducting material.
These are known as the Laplace and Dirichlet problems. Obviously, the inverse problem,
where the physical constants of the material are unknown, presents more difficulties than
those problems where the physical constants of the material are known functions of position.
4-1
Geophysical prospecting is an example of the inverse problem, because of the enormous
variety of soil structures and characteristics. Moreover, the number of parameters required
to represent a model of the earth structure is usually so great that it is difficult to choose
initial values to these parameters and have a computer algorithm converge to an acceptable
solution within a practical time frame. Consequently, the selection of initial values becomes
a fundamental task in the interpretation process. Perhaps this is why geoeiectrical sounding
is still considered an art accessible only to experienced geophysicists despite the intricate
mathematical theories developed to support this engineering science.
Success or failure in this important initial assessment is generally dependent on the experience
of the engineer and the knowledge of earth electrical properties available to the engineer
responsible for the interpretation of the measurements.
There is one further problem with the inverse solution of resistivity measurements. It is not
always possible to obtain a unique solution to a data interpretation problem. Because of
inaccuracies in the measurements {usually ±5% with classical geoelectric instruments), several
models of earth structure can be found to give satisfactory agreement with the measured
results. These models will usually differ in the characteristics of the deep soil layers.
The above discussions are not presented to discourage the power system engineer from
performing a scientific interpretation of resistivity measurements, but rather to make him
aware that this task requires careful preparation, investigation, and engineering judgment.
The difficulties mentioned previously, while imposing a considerable challenge to the geologist,
have significantly smaller impact on the electrical engineer. Firstly, the existence of multiple
solutions to the substratum structure is of little consequence in determining the response of
ground electrodes, particularly those of the transmission line structure grounds. Secondly, a
two-layer earth model is generally sufficient for modelling transmission line structure grounding
systems. Finally, there are numerous charts, algorithms, and simple engineering visual
estimation techniques which can be used to determine an equivalent two-layer
earth model with reasonable accuracy. The following paragraphs are intended to provide the
electrical engineer with the basic knowledge and engineering tools required to properly
interpret earth resistivity measurements.
Initially, the basic electrical properties of earth materials will be described and discussed,
since these are fundamental to the interpretation process. Next, measurement methods will
be introduced and the classical Wenner method will be examined in detail. The fundamental
equations governing the response of the current- carrying electrodes used in the Wenner
configuration will then be derived. These equations are essential to the derivation of an
accurate earth model. Several interpretation methods will be described using actual
measurement results from various sites. Finally, measuring equipment will be described
together with problems likely to be encountered in the field. Solutions to the problems will
be proposed.
4.2 ELECTRICAL PROPERTIES OF EARTH
The conduction of electricity in earth may take place by electronic or ionic current flow.
The resistance offered by a material to current flow is expressed in terms of resistivity.
This resistivity p is defined by the mathematical expression of Ohm's law:
E = pJ
(^-l)
where E is the electric field strength expressed in V/m and J is the current density in A/m2.
4-2
The unit for resistivity is the ohm-meter. The two opposing faces of a 1 meter cube of a
material will exhibit an ohmic resistance corresponding to the value of resistivity of the
material. That is a cube of 10 ohm-meter material will have a 10 ohm resistance in this
configuration.
4.2.1 CONDUCTION BY ELECTRONIC PROCESS
Electronic conduction is characterized by the movement of free electrons in a metallic or
semiconductor material when a dc field is impressed on it. Although electrons in semiconductors
are only mobile over relatively short distances, no other atomic particles participate in the
conduction process. Gold and copper are typical metallic conductors. Another conductor is
carbon, which occurs commonly in the form of graphite. The resistivity values of some
common refined and unrefined metals are listed in Table 4.1.
Because of differences in atomic structures, the resistivities of semiconductors are higher
than those of metals. A clearer dishinguishing feature dividing semiconductors and metallic
conductors is their temperature behavior. With semiconductors, resistivity decreases with
temperature rise at least within a certain temperature range, while the opposite is true with
metals. Also, the resistivity of semiconductors varies over a wide range of values. Some
typical semiconductors and their average resistivity values are also given in Table 4.1.
Metals and semiconductors occur infrequently, when compared to the amounts of other
materials in earth. Nonetheless, their occurence in small amounts, particularly in a pure
metallic state, may significantly influence the results of apparent resistivity profiles. However,
it would be unusual to discover disturbing effects due to native metals during surveys for
power engineering applications. This is because the extent of the resistivity traverses is
generally too short to penetrate into the deep soil. In the majority of cases, if the presence
of a metallic mass is a problem, a man-made metallic structure buried in the vicinity (pipes,
etc.) will be the cause.
4.2.2 ELECTROLYTIC CONDUCTION
All rocks at the surface of earth are at least slightly porous, and the degree of this porosity
helps determine the electrical properties of the rock. Igneous and dense carbonate rocks are
not very porous, generally less than 1% of total volume. Other highly porous rocks such as
poorly compacted mudstones may be up to 50% porous. The voids are usually completely or
partially filled with water having some concentration of salt, and thus can be highly conductive.
Depending on the water content, salt concentration, type of metal and its concentration in
the rock, the electrolytic conduction process in rocks will be variable. Typically, for surface
rocks, electrolytic conduction will be the predominant factor. However, in completely frozen
rocks or in deep rocks subject to high overburden pressures, electronic conduction becomes
significantly more important than ionic electrical conduction. Also, the presence of magnetite,
graphite or pyrite, even in quantities of only a few percent, may reduce the resistivity of
a rock to less than 1 ohm-meter if suitably distributed throughout the rock volume.
As a general rule however, the resistivity of materials near the earth's surface is dependent
on water content and the nature of the salts dissolved in the water. That is why it is
not possible to assign a single value for the resistivity of the rock and soil materials shown
in Table 4.1.
4-3
TYPE
RESISTIVITY
Q-m
MATERIAL
REFINED
METALS
TYPE
SI 1ver
1.5x10'8
Chemiccally clean water
25x101'
1.6xl(f8
Distilled water
5000
Gold
2.0x10~6
Rain water
100 to 1000
Surface water (1ake,rivers)
100 to 500
Aluminum
2.5x10-8
WATER
8.5x10’8
Sea water
0.1 to 1
1 ron
9-xlo"8
Loams, garden soils
5 to 50
Lead
19.x10‘8
Clay, cha1k
10 to 70
Bismuth
100.xio"8
Clay, sand 5 gravel
mixtures
L0 to 250
Copper
1.2xl0'8 to 30x10~8
Peat, marsh soil &
cult!vated sol 1
50 to 250
Diabase, shale, limestone
& sandstone
100 to 500
Sand, Cambrian limestone
& sandstone
lx103 to 3x103
Graphite depending
on direction of
current flow with
respect to
cleavage
CONDUCTING
MINERALS
*Note:
Table 4.1
TYPICAL
VALUES
28x1o'8 to
o
5.5xto“8
LIthium
o
Z i nc
(FeS ) Pyrite
-6
-8
0.3x10 to 50x10
1.2x10"3to 600x10'S
(MoS ) Molybdenite
0.08 to 7.5
Igneous, rocks granite
3x105 to 4x107
(CU 0} Cuprite
10 to 50
Wet concrete
50 to 100
(Fe 0 ) Magnetite
52x!0*6
Dry concrete
2x103 to 1xIO4
(CUO) Malaconite
6000
(PBS) Galena
SEMI-
Ground water, well and
spring water
o
k. 3xl0~8
SOILS
MINERALS
RESISTIVITY
Q-m
Copper
Sod 1um
NATIVE
MATERIAL
Moraine, quaternary surface
Ix103 to lx104
coarse sand 6 gravel
The larger range in values is due to the variations in the
composition of the materials.
Typical Resistivity Values
However, this is not of immediate interest to the power system engineer. The important
point is that the absence of water in rocks results in very high resistivities. The rock
resistivity will continue decreasing with increasing volume of water, approaching that of the
water in the rock for higher porous rock conditions. Temperature variations also affect the
resistivity of surface rocks. If the temperature changes so that it becomes high or low
enough to evaporate or freeze the water contained in the voids, the resistivity may be
expected to increase manyfold. If no evaporation occurs, an increase in the temperature will
generally result in a slight decrease in the rock resistivity, due to the increased mobility
of the ions in the water solution. Figures 4.1 and 4.2 show the effect of temperature on
the resistivity of soils and rock. It should be noted that the resistivity variations of rocks
with temperature will not follow those of pure water, since the presence of dissolved salts
and the confining effect of small pores tend to lower the freezing point of the water in
the rock.
For accuracies within an order of magnitude, Hummel's empirical formula, is useful to
estimate the resistivity of most soils materials which conduct electricity principally by the
electrolytic process:
where Ps is the soil resistivity in
volume of water contained in soil.
-m, Pw is the water resistivity and C is the relative
BIOTITE GRANITE
....
SAND & GRAVEL
SILT
TEMPERATURE
Figure 4.1
(°C
Soil Resistivity Versus Temperature (Redrawn from [6])
4.2.3 ELECTRICAL CONDUCTION IN EARTH
Among the electrical characteristics of the earth, only the relative permeability ^r may be
considered as constant and equal to unity. The relative permittivity er and the resistivity
p vary within wide limits, although the variations of p (typically in the range of 1 to 10,000
Q-m) are considerably more important than the variations of £r (typically in the range of
1-100). The permeability and permittivity are not important parameters in the context of
direct and low frequency current conduction.
The dielectric strength of the soil is of importance in phenomena, involving the passage of
very high currents in the soil such as lightning surges. Dielectric strength however, remains
within fairly narrow limits. This characteristic of earth is analysed in Chapters 5 and 7.
We have analyzed the conduction properties of various earth materials. Typically, earth which
is investigated by electrical methods is comprised of a combination of a number of materials
in varying shapes and sizes and of differing resistivities. Because the conduction of current
in the earth is largely electrolytic, the differences in the resistivity values are caused by
variations in the amount of, and the nature of the solutes in the water contained in the
material. In spite of this usual heterogeneity, there are cases where large, relatively uniform
volumes of earth surround a power grounding electrode. A uniform earth assumption is often
a reasonable approximation and is a good starting point in helping to understand the
fundamentals of grounding.
The earth can be broadly modelled as having a voluminous core (3500 km in radius; 2200
miles) consisting of a low resistivity hot magma and surrounded by a 2850 km (1800 miles)
thick layer of hot but solid low resistivity material. Another thin layer (50 km below
continents; 30 miles; zero to a few km, below oceans) of relatively higher resistivity rock
surrounds the thick and hot solid crust. This thin layer consists of strata of different rocks
overlain in places by a wide variety of materials. Since large power system ground electrode
dimensions are considerably less than the upper crust thickness of earth (0.5 km compared
to 50 km), and because the response of ground electrodes is influenced minimally by the
nature of soil at distances of more than 10 times their maximum dimension, one may conclude
that approximately 1/10 of the uppermost and thinnest earth crust plays a role during current
conduction through the electrode. Unfortunately, the widest variations in earth resistivity
exist in this surface layer. Figure 4.3 shows an average resistivity map of this upper layer
in the United-States.
COARSE-GRAINED
MATERIAL
FINE-GRAINED
MATERIAL
TEMPERATURE 6 (° C)
Figure 4.2
Soil Resistivity Versus Temperature for Typical Soil Samples (Redrawn from [7])
Geologists have measured the apparent resistivity of earth for very large spacings between
test electrodes [7,8] (deep penetration of the test current into the soil) and have developed
a three-layer earth model, in which the middle layer exhibits a significantly higher resistivity
than the adjacent layers, and which gives results in reasonable agreement with measurements.
This earth model is reasonably consistent w|th the geological model described previously.
The differences are a direct consequence of the distinction which must be made between
geological and geoelectric structures.
A single geological structure often presents different resistivity values (see Table 4.1) and
thus, incorporates several geoelectric structures. The reverse can also occur. Two volumes
of different materials may be equal in resistivity and therefore will appear as a uniform
geoelectric structure to the geologist. In many cases however, the geological structure will
match its geoelectric counterpart.
LOW
RESISTIVITY
< 100 fl-m
Figure 4.3
MODERATE
RESISTIVITY
HIGH
RESISTIVITY
100 to 500 fi-m
> 500 fi-m
Resistivity Map of the United States (Adapted from [7])
While both the geological and geoelectric models are of importance to the geologist, only
the geoelectric model is of significance to the power system engineer. Based on the three-layer
geoelectric model given previously, the earth can be considered to consist of:
1- A surface layer consisting of several varieties of soil and rock in which a
great number of pores or cracks of various sizes are saturated with water containing
dissolved salts. The conductivity of this layer is largely electrolytic in nature and
its average resistivity is moderate although the actual value varies within wide
limits (10 - 10,000 Q-m). The thickness of this layer is in the order of 2 to 5
km (1 to 3 miles).
2- A middle layer, 10 to 40 km thick (12 to 25 miles), characterized by a
very high resistivity value (10^ to 10^ Q-m) which results from the considerable
pressure impressed on the rocks and the absence of pores and cracks which
can retain water.
3- A lowermost layer, consisting of very hot rocks or magma which is highly
conductive despite the absence of moisture (10-100 Q-m).
This model illustrated in Figure 4.4, is inadequate for modelling power system ground
electrodes however, since the significant soil structure surrounding the electrode is represented
by a single layer of average resistivity. The thickness of this layer (a few km), although
very thin with respect to earth diameter, is nonetheless considerable when compared to the
electrode dimensions. To create a suitable earth model for grounding designs, it is necessary
to construct one by further subdividing the uppermost layer into additional layers, as required
to accomodate the local resistivity values which have the most influence on the response
of the grounding system.
4-7
4.2.4 ELECTRICAL MODEL OF EARTH
This modelling procedure, which consists of introducing as many horizontal layers of uniform
resistivity as necessary, is very attractive since it allows vertical changes in resistivity to
be considered as additional layers. In addition, the theory of earth resistivity measurements
in multi-layer soils is well understood and solution techniques are available using modern
computers. The inverse problem (modelling the earth from measurements) requires considerably
more effort and computer time however, and is seldom justified, even for complex geophysical
problems. Usually, the computer resources are used in association with empirical methods
in order to arrive at a satisfactory approximation.
The multi-layer earth model is incapable of recognizing lateral variations in earth resistivity
such as vertical faults, or localized volumes of materials with resistivity values different
from the surrounding soil. In such cases, suitable equivalent earth models must be
derived. Quite often, in practice, various earth models are analyzed separately to approximate
a real earth structure. The results are then combined empirically to interpret the measurements.
This method generally leads to satisfactory results. For example, a three-layer earth model
can be analyzed using the combined results of two different but suitably selected two-layer
earth models. This subject will be further discussed in Section 4.5.6.
For most power system grounding problems, it has been found in practice [3-5] that a
two-layer stratification is a good approximation to the real earth structure, even when
measurements indicate that a more complicated structure exists. For the cases where either
uniform earth or two-layer models are considered to be unacceptable simplifications, it is
necessary to use adjustment algorithms and engineering judgment to predict the performance
of a grounding installation.
DENSE ROCKS
(i n4 - i n 8 n-.
Figure 4.4
Geoelectric Model of Earth
4.3 MEASUREMENT METHODS AND TECHNIQUES
Because of the wide variations in the structure and properties of earth materials, there are
numerous methods and techniques for determining the structure of earth. These methods can
be classified into two broad classes:
1- Direct measurements
2- Indirect measurements
Direct measurements are based on the extraction, from various depths, of samples of earth
materials which are then examined in specialized laboratories. This method is accurate and
straightforward provided that the material is not disturbed by the extraction process. However,
it requires that expensive borings be made at a large number of representative locations to
cover the site being investigated. This kind of investigation is usually performed after indirect
measurements have confirmed that the site offers promising results. Such direct
geological surveys are used extensively for pre-construction studies.
Indirect measurements determine the earth structure from the measurement of the earth
response R to certain impressed excitation E. The measured earth response R is a physical
quantity which is a function of earth resistivities and a number of other earth parameters.
From the known relation between R and earth parameters, the probable earth structure is
determined. There are a great variety of indirect methods. These methods can be grouped
into the following categories:
abcdefgh-
Seismic methods
Gravitational methods
Radio-wave methods
Telluric and magneto-telluric methods
Induced-polarization methods
Induction methods
Electrical well logging methods
Galvanic resistivity methods.
Methods c to h are based on the earth response to electrical excitation sources. A description
of all these methods, is beyond the scope of this report. However useful information on
them can be found in [7] and [9-15]. The only methods which will be described here are the
last two; electrical well logging and galvanic resistivity methods. These tests are used widely
throughout North America and typical results are readily available in the literature or from
various organizations utilizing the methods.
When apparent resistivity measurements (using galvanic resistivity methods) at a transmission
or substation site are not available, electric well logs may be available. In the United States
and Canada, many hundred of thousands of oil and water wells have been electrically logged.
Where this information is not available, civil engineering reports will usually contain borehole
log data which can be very useful.
This information should be obtained even when resistivity measurements have been performed.
By correlating results, the interpretation task will become easier and more accurate.
4.3.1 ELECTRICAL WELL LOGGING
Several alternatives exist in the techniques employed and instruments used to measure
resistivity. The principles are essentially the same however, regardless of the technique used.
Figure 4.5 shows a simplified illustration of the measurement method. A number of small
electrodes are lowered into a drilled cylindrical hole. The function of these electrodes is
either to inject current into the soil or to measure the potential caused by the flow of
electric current through other electrodes. This method is therefore a galvanic resistivity
method. It is traditionally considered as a nonconventional method because, the measurements
involve a very small volume of soil within the vicinity of the electrodes. Thus, only local
changes in resistivity values are recorded. By exploring the well over its length, the vertical
earth structure in the vicinity of the well is determined.
The differences in the various techniques employed during electrical well logging lie in the
arrangement and location of the electrodes. Some commonly used arrangements are depicted
in Figure 4.6.
4-9
Power Supply
Recorder
Lowering
Equipment
Movable Electrode
x
(or Array of Electrodes]
Figure 4.5
Operating Principle
a- SINGLE ELECTRODE
LOGS
Figure 4.6
Return Current
Electrode
b- SPACING
LOGS
c- FOCUSED
LOGS
d- MICRO
LOGS
Commonly Used Arrangements
A typical resistivity curve obtained from electric logs is shown in Figure 4.7 along with the
corresponding geological structure. Accurate interpretation of the apparent resistivity curve
requires sufficient expertise to account for the electrode arrangement used and distortion
effects caused by the mud in the well. However, an inspection of the curve, based on the
knowledge that the apparent resistivity measured is a distorted image of the local volume
of earth material, can yield useful information.
The interpretation of electric logs has problems similar to those encountered with conventional
galvanic methods. However, it is unlikely that this method will ever be used by electrical
engineers as a primary measurement technique. Interpreted results will normally be available
to the engineer through geological survey reports.
Thus, interpretation techniques for this method are not presented. The reader interested in
more information should consult [14]
4-10
RESISTIVITY (fi-m)
^tOO
800
1200
DRILL
HOLE
SECTION
Figure 4.7
Typical Log Resistivity Curve
4.3.2 GALVANIC RESISTIVITY METHODS
Most commonly used methods for measuring resistivity are based on galvanic contacts between
the earth and an array of electrodes. This array typically consists of four electrodes, a
generalized arrangement of which is depicted in Figure 4.8. Current is injected into the soil
through one pair of electrodes (current electrodes Cl, C2) and the potential established
at the surface of the earth by the test current is measured at the second pair of electrodes
(potential electrodes PI, P2).
As Figure 4.8 suggests, a great variety of arrangements can be used to carry out the
measurements. As a general rule however, practical arrangements consist of electrodes driven
into soil along a straight line and symmetrically positioned about a central point. Three
categories of probe arrangements are generaly used.
1- Potential difference arrangements (measurement of the difference in potential
between widely spaced electrodes, PI and P2).
2- Potential gradient arrangements (PI and P2 are closely spaced to measure the
local earth gradient).
3- Potential curvature arrangements (both pairs of electrodes closely spaced in
order to measure the curvature of the earth surface potential function.
All these arrangements can be used to detect vertical or horizontal resistivity changes.
4-11
a - TOP VIEW
C2
Figure 4.8
Galvanic Resistivity Methods
When vertical resistivity variations are being investigated, the spacing between the current
electrodes is increased in steps, thus forcing the test current to penetrate progressively
deeper into the lower layers of the earth. Current flow through the earth at greater depths
decreases the effect of the surface materials on the potential between PI and P2. Thus, it
may be concluded that large spacings between current electrodes are required to determine
deep layer resistivities while close spacings are used to determine surface layer resistivities.
If horizontal changes in earth resistivity are being explored, the measurement technique
consists of moving the entire array with constant electrode spacings along a traverse line.
Ideally, this traverse line should be at right angles to the suspected discontinuity which
interfaces the two areas of unequal resistivity. The first type of measurement, to locate
vertical strata, or layers, is usually designated as "horizontal profiling", while the second
type is called "vertical sounding".
4.3.3 THE WENNER METHOD
Most resistivity measurement techniques are variations of the four equally-spaced electrode
arrangement originally described by Frank Wenner [16]. Variations have been introduced to
eliminate or decrease certain difficulties encountered with the Wenner arrangement,
particularily at large electrode spacings. Difficulty is caused by very low potential differences
which are developed between the potential probes PI and P2 at large electrode separations.
Since resistivity surveys for power engineering applications require only moderate
spacings, the Wenner method is extensively used. Its simplicity and accuracy are key factors
in its popularity. It is essential, however, that appropriate instrumentation be used to mitigate
the effect of stray currents in earth. This arrangement, which is of the "potential difference"
type, will be reviewed in detail.
4-12
It is more than sixty years since Wenner first described the four probe equal spacing technique
for earth resistivity measurements, usually called the Wenner method. Many modifications
have been proposed, but the underlying principles are the same. In modern geoelectric
surveying, the Wenner method is seldom employed because at large inter-electrode spacings,
high sensitivity measuring equipment is required. Moreover, the apparatus used must be
capable of discriminating between the measured signal and stray currents in the soil. This
problem can be controlled at small inter-electrode spacings by increasing the magnitude of
the test current until the noise level is insignificant.
In power system engineering applications, the Wenner method is used almost exclusively for
resistivity measurements. It is our opinion that this method, when used with suitable test
equipment, will provide sufficient data for an accurate earth structure model for the analysis
of transmission line structure grounding systems. Because of the relative simplicity of results
interpretation and widespread availability of test equipment supporting the use of this method,
it is recommended as an effective and suitable standard test procedure. Therefore, the
remainder of this chapter will deal almost exclusively with the Wenner electrode arrangement
for measuring earth resistivity.
The Wenner four-electrode arrangement is shown in Figure 4.9. Four electrodes are driven
into the earth along a straight line. The electrodes are uniformly spaced and the burial
depth of the electrodes is usually less than 10 per cent of the spacing between two adjacent
electrodes. Thus, each electrode will appear as a point with respect to the distances involved
in the measurement.
A current I is injected into earth via two outer electrodes and the earth surface
potential difference V is measured by the two inner electrodes. The outer electrodes are
called the current electrodes and the inner pair, potential electrodes. It can be shown that
the role of the electrode pairs can be interchanged without changing the electrical response
of the array, the ratio V/I. This ratio, with dimension of resistance, is proportional to a
variable described as the apparent resistivity pa at spacing a. The proportionality factor
between V/I and Pa is called the array geometric factor a . Thus the following equation
can be written:
(4-3)
-if
P2
C2
C‘
PI
Tijffr
a
Figure 4.9
a
a
Wenner Arrangenent
4-13
A similar relation can be written for other arrangements of electrodes. Generally, the
geometric factor is different from one arrangement to the other. Interchanging the roles of
the electrode pairs does not change the value of the geometric factor.
The test current is generally provided from a dc source such as a battery. However, due to
polarization at the metal electrodes, a polarity reversal mechanism is used to periodically
reverse the direction of current flow between the current electrodes resulting in a chopped
dc vaveform. The instrumentation and field measurement techniques are discussed in Chapters
9 and 10. It is also possible to use alternating currents at low frequencies where induction
effects and attenuation can be neglected. In such cases, the measured apparent resistivity
value is identical to the direct current measured value. Care should be taken to insure that
the mutual impedance between test leads is negligible compared to the test electrode ground
resistance. This problem will seldom exist at small or moderate inter-electrode spacings.
4.4 DERIVATION OF THE EQUATIONS
4.4.1 POINT SOURCE ELECTRODE IN UNIFORM SOIL
Initially, the case of a completely homogeneous isotropic earth and a single point source of
current buried at the surface of earth will be considered. The point current source injects
a current I in the soil. This current returns to the power source through a return electrode
sufficiently remote from the point current source so that its effects can be neglected. The
return electrode is assumed to be at "remote" ground. The problem to be analyzed is shown
in Figure 4.10.
The current source must obey Ohm's law, i.e.:
E = pj
(4-4)
where
E is the potential gradient (V/m)
J is the current density (A/m2)
P is the earth resistivity (fl-m)
Since it is assumed that there are no other current sources in the volume of earth, the
divergence condition requires that:
(4-5)
AJ = 0
Combining Equations 4-4 and 4-5 leads to Laplace's equation:
AJ =—AE = — v2U
P
P
(4-6)
where U is the scalar potential function defined as:
3U=F
jU _
3x
x ’ 3y
3U
y ’ 3Z
z
or in a more compact form:
U = -grad E
(4-7)
4-14
In polar coordinates, the Laplace equation is given by:
9
(/ r 2 -------- )\ +.
9r
9r
9
,
92U
. 0 9U x
— (sin6 ___) +
90
90
r2sinf
r2sin2f 9B2
=
0
(^-8)
Because of the complete symmetry of the current flow with respect to the angular coordinates
6 and /?, the derivatives with respect to these variables are zero and (4-8) reduces to:
JL (r2 2H)
9r;
9r v
=
(b-S)
0
SOURCE
REMOTE
GROUND
Figure 4.10 Point Source Electrode in Uniform Soil
The solution of this differential equation is straightforward:
(4-10)
U (r) = - — + B
r
A and B are constants which are determined from boundary conditions, i.e.:
U =
/
0
, when r ->- <»
Jds = I
where s is the surface of a hemisphere concentric to the current source,
thus, B = 0 and A is obtained from:
/E
P dS ~
I
r9U
Js
r2^
dS
~JQ
A
Pr:2
pr
dr =
2 itA
p
which leads to:
A = Pi
2tt
consequently:
PI
U =
(4-11)
27rr
4-15
It is possible to obtain Equation 4-11 directly using a hemispherical electrode and simple
physical considerations rather than Laplace's equation.
Consider a hemispherical electrode having a diameter c and buried at the surface of a
uniform earth (Figure 4.11)
Figure 4.11 Hemispherical Electrode
Because of the spherical symmetry, the equipotential lines are shells concentric to the
hemisphere. The voltage drop between two equipotential surfaces located at a distance r
and r + dr is:
(4-12)
IdR = (U + dU) - U = dU
where dR is the resistance
equipotential surfaces, i.e.:
length
dR - p
of
the
volume
of
earth
enclosed
the
two
dr
- p
surface
between
(4-13)
Zirr2
Since dR can be as small as desired, the two equipotential surfaces can both be made equal
to ZtitZ.
From (4-12) and (4-13) the following equation is derived:
pI 1
dU ----------- dr
2ir r2
(4-14)
Equation 4-14, integrated between r and «, leads to Equation 4-11.
Although convenient for simplified cases, the last derivation can not be generalized to solve
more complex problems. In such cases, the first method is required.
4-16
4.4.2 MULTIPLE SOURCE ELECTRODES
Since the potential function is a scalar quantity the superposition principle can be
applied. The algebraic sum U^ + U2 + ~ + Un of the potentials, established by independent
point sources, at a point M is equal to the total potential U which exists when these sources
are acting simultaneously.
Therefore, the total potential at a point M, due to n point sources at the surface of a
uniform earth is:
(4-15)
M
where
is the current injected by point source i and rj is the distance between the source
and the point M.
When Equation 4-15 is applied to the Wenner array, the following potentials are determined
at the potential electrodes, (assuming that current at Cl is positive and negative at C2):
P I
U
= ----4iTa
p
(4-16)
PI
U
p2
4Tia
Measured between the inner electrodes, the ratio of the potential difference V, to the test
current, I is:
V/i
=
---- -Sl-L.
I
p =
(4-17)
Tra
2
Zira------
(4-18)
I
Thus, lira is the geometric factor a introduced earlier in this section. This factor is a linear
function of the electrode spacing a. Since earth is assumed uniform, a is a linear function
of a and the ratio V/I must decrease with increased spacing a. If I is held constant as a
is increased, the measured potential V will decrease to a level where stray currents and/or
equipment sensitivity will introduce large measurement errors. A straightforward solution
would be to increase the value of the test current I. In practice, however, power sources
are voltage or power limited and the only feasible way to increase the current is to decrease
the ground resistance of the current electrodes.
In order to increase the magnitude of the measured voltage V at large probe spacings, one
may use the so-called Schlumberger-Palmer array shown in Figure 4.12. This is a symmetrical
four probe arrangement with the potential probe moved closer to the current probes than
with the Wenner technique.
4-17
Figure 4.12
Sclilumberger-Palmer Array
Simple algebraic calculations will show that in this case:
]I
The geometric factor
a
(**"19)
of this array is thus
r(a2/b - b/4).
7
An increase in the spacing a will not result in a proportional increase of a since b can be
increased also. Based on a constant test current I, the measured potential V will decrease
more slowly than in the case of the Wenner array.
4.4.3 NONUNIFORM SOILS
The concept of a completely uniform earth is useful in defining the apparent resistivity
function and its relation to the geometric factors for various electrode arrangements.
This concept has also served to establish the fundamental equations which govern the
performance of point source electrodes. The analysis of this simple problem can be extended
to more complicated earth models, and will serve as a reference for the interpretation of
real earth measurements.
When resistivity measurements are made at a given site, the measured ratio V/I can be used
to define a fictitious apparent resistivity pa as:
p
V
= a(a) a
I
(4-20)
where a is the geometric factor introduced earlier. This geometric factor is a function
of the spacing a, when the Wenner arrangement is used. We have shown that a was proportional
to a when the earth is uniform. By convention we will assume that a(a) is independent of
the earth structure (a(a) = 27ra for Wenner method). The apparent resistivity, so defined,
has no physical meaning except when soil is uniform and Pa equals the true earth resistivity.
In practice however, the apparent resistivity represents the weighted average resistivity
of the earth at the site, up to a depth in the order of the electrode spacing a.
4-18
The apparent resistance R, the ratio of the measured potential difference V to the test
current I, is given by Equation 4-17 when earth is uniform. When earth is nonuniform , R
is a complicated function of the spacing a and other parameters such as the thickness and
resistivity of earth layers:
R = ip(a,Ax ,X2................... ,A................... An)
(4-21)
where Aj is one of the n parameters which define the earth structure. If Paj is the measured
apparent resistivity then:
Paj " 2Traj^(aj >Ai,A2............... Aj ................An) =0
(4-22)
Theoretically, when n measurements are made at various spacings nj, it is possible, to solve
the n simultaneous Equations 4-22, to determine the n unknown parameters Xj of earth. This
task is not as straightforward as it seems because of several problems which will be discussed
in Section 4.5. Before proceeding with this analysis, it is necessary to establish expressions
for certain idealized earth structure models which are suitable for the analysis of power
system ground electrodes, including transmission line structure grounds.
4.4.4 POINT SOURCE ELECTRODE IN A TWO-LAYER EARTH
There are several mathematical approaches which have been used to calculate potentials in
a layered soil structure [3,5,17-19]. The method which is adopted here is to search for a
particular solution to Laplace's equation which satisfies the boundary conditions of the
problem.
One of the simplest and most important earth structure models is the two-layer earth model.
It can be shown that the potential in earth can be always expressed as the sum of a normal
potential (uniform soil), and a disturbing potential, which accounts for the deep layers of
soil. Therefore, the two-layer model can be used as the simplest equivalent earth structure
for interpreting practical resistivity measurements.
We shall analyze the problem of a surface layer of resistivity P} and thickness h, overlaying
a second layer of resistivity P2, which extends to an infinite depth (see Figure 4.13).
■
1
y
y'
y
y
s
s'
s'
X
;
Tjjjp
h
^
p1
wv\
r
z
M(x,y,z)
ipfj
1
^2
1
Figure 4.13
Two-Layer Earth Model
4-19
The potential U at point M must satisfy Laplace's equation. Since there is cylindrical
symmetry, Laplace's equation reduces to:
3ZU
1 3U
32U
3r2
r 3r
3z2
----- +-------- + ------ =
(4-23)
0
Assume now that a solution can be found in the form of a product of two independent,
single variable functions namely:
U =
0
(r) 4>(z)
Substituting U in Equation 4-23 and rearranging, leads to
32i|j
------- =
3z2
320
1
(4-24)
0
30
----- + -—-+a20 = O
3r2
r 3r
(4-25)
The solution of (4-24) is
>p(z)
= A(ct)
e°Z + B(o) e~OZ
The solution of (4-25) contains terms with Bessel's function of zero order of both the first
and second kind
0(r) = C(a) J0 (or) + D(ct) Y0 (ar)
The function Y0(<rr) can not be retained in this case, since it tends to become infinite when
r is small. Consequently, its coefficient D must be set identically to zero. The solution
of Laplace's equation is therefore:
X
'
y
u =
2tt
>[3(a) Jo(ar)
+ 0(a) J0(ar)
e°z
(4-26)
L
where
Pil
3 =---- A C
2tt
PjI
and 0 = ------ B C
2fT
Since any linear combination of terms in (4-26) is acceptable, the general solution of Equation
4-23 may contain an infinite number of terms with different values of a. Since a is arbitrary
and thus, can vary continuously, the general solution must be given by:
U
3(a) Jo(ar)
eOZ
da +
4-20
J0 (ar)
-crz
da
(4-27)
The values of
0
and
constants are determined from the boundary conditions:
9
1- The potentials of the upper and lower layers must be equal at
the surface boundary of the two layers:
Ux(z) = U2 (z)
;
z = h
(4-28)
2- At the interface between the two-layers (z = h), the normal
component of current flow must be continuous:
1
3Ux
1
3UZ
----------- = _ ----pi 3z
p2 3z
;
(4-29)
(z = h)
3- No current can flow accross the upper layer and air boundary:
3Ui
----3z
;
=0
(z =
)
(4-30)
0
4- As z goes to infinity, the potential must go to zero:
z -s- co
Uz(z) = 0 ;
(4-31)
The upper and bottom layer potentials
and U2 are given by Equation 4-27 where /3 and
6 are replaced by j8x, #1 and 182, @2 respectively. When Ui and U2, as given in (4-27),
are replaced in the boundary Equations 4-28 to 4-31, a set of 4 equations with four unknowns,
namely, @1, 02, 9y and #2 are obtained. The solution of the simultaneous equations is
straightforward but lengthy and has been omitted. Since all the integrations are carried out
through the same limits, the integrands are identically zero when the integral is equated to
zero. The following results are obtained:
1
0i (a)
1
-ke
ke
(a) =
-2ah
1
-2ah
- ke
-2ah
(4-32)
+ k
-2ah
1 -ke
1
62(a)
;
62(a) = 0
where k is designated as the reflection coefficient:
p2 - Pi
K = ------------P2 + Pi
(4-33)
The fraction:
1
, - ke-20h
can be expanded as:
1
-ke
1
-2crh
- y>n«
-2nat)
(4-34)
n=1
4-21
noting that:
— = (r2 + z2) ^ =
I
e az J0(ar)da
r1
J0
and then replacing
and 0^ by their expansions as given in (4-34), into Equation 4-27 and
integrating, the following expression for the potential at a point M on the earth surface
(z=0) is obtained:
U:
= PLifi
27rr
(^-35)
C1+(2nh/r)
Thus the potential consists of two parts:
a- The normal potential (PiI)/(2 tit) which exists if the soil was uniform (infinite
layer of resistivity P i).
b- A disturbing potential caused by the presence at finite depth of a layer having
a different resistivity P 2 than the upper layer.
4.4.5 POINT SOURCE IN EARTH WITH INCLINED LAYERS
If the boundary separating two regions of earth with different resistivities is not horizontal,
but inclined at an angle to the surface, an exact mathematical solution for the potential
function is arduous to obtain. The potential function is obtained through a double integration
process on two dummy variables, of a complicated function containing hyperbolic sines and
Bessel functions of the second type [3,20,21].
When the angle of dip is 90°, a simple solution can be obtained. Figure 4.14 illustrates this
case. The case where a vertical interface between two dissimilar earth resistivity areas
exists, will be referred to as a vertical fault structure. In practice, this effect can be the
result of a number of different mechanisms, including, but not limited to, geological faulting.
S
I
I
I
f
b - TOP-VIEW
a - SIDE-VIEW
Figure 4.14
Z
Vertical Fault
4-22
3
The potential about a current source embedded in earth at a distance d from the boundary
separating two media of different resistivities Pi and P2, may be found by an analysis which
follows the same lines developed for the case of two horizontal layers. Equations 4-23 to
4-27 are also applicable in this case. By transforming the original semi-infinite medium into
an infinite medium symmetrical about the earth surface plane, the potential function U given
by (4-23) must satisfy the following boundary conditions:
a- Ui must go to zero as z goes to - »
b- U2 must go to zero as z goes to
00
c- At the surface between the two media (z=h):
U1 (z) = U2(z)
d- At the surface between the two media (z=h):
1
SUj
Pi 9z
1
pa
9U2
9z
These boundary equations are suffieient to determine the unknown constants 6^,
82 and
02* Simple algebraic manipulations will show that the potential at any point of the earth
surface is given by one of the following expressions, depending on whether M is in region
1 or 2.
(4-36)
(4-37)
If the current source is embedded in region 2, the above expressions are also applicable
provided that Pj and P2 are interchanged.
4.4.6 POINT SOURCE EMBEDDED IN A LOCALIZED DISCONTINUITY
Thus far, we have analyzed the case of a nonuniform earth consisting of two layers extending
to infinite distances. In practice, there are circumstances where the current source is buried
in a small volume of material having a resistivity significantly different from the average
earth resistivity of the site considered. In such case, neither the horizontal nor the vertical
layered earth models are suitable to model the real situation. Examples of these cases are
electrodes buried in a small lake, or electrodes in a small volume of soil artificially treated
to lower resistivity.
This kind of problem is easily solved if it is assumed that the current source is embedded
at the center of a hemispherical volume of soil of resistivity Pj different from the resistivity
P2 of the rest of the earth (see Figure 4.13).
4-23
Figure 4.15
Localized Discontinuity
This earth structure has spherical symmetry and therefore Equation 4-10 is applicable:
U = - ^ + B
(4-38)
The boundary conditions are:
Ui = U2
j_ 3U
Pi 3r
U2 “
;
r = R
_ J__ 9U .
p2 3r ’
when r
0
(4-39)
r
R
(4-40)
(4-41)
00
X'
pi Jids = I
The solution
of
Pil
Ux =----2ir
(4-42)
Equations 4-58 to 4-42 leads to:
1
L r
Pz~Pi
(4-43)
pi R
Pzl
U2 =
(4-44)
irr
2
It should be noted that once again, the potential Uj in the upper layer consists of two
terms, the normal potential and a disturbing potential. In this case however, the "disturbance"
is constant regardless of the location of the point M.
4.4.7 APPLICATION OF THE POTENTIAL FUNCTIONS TO THE WENNER ARRAY
The apparent resistivity pa, as measured using the Wenner method, is obtained easily from
the surface potential function
previously derived for various earth structures. The Wenner
arrangement consists of two current sources of opposite polarities separated by a distance
3a, and two potential probes, located between the current electrodes at distance a from
4-24
each other and from a current source. Applying the superposition principle to a group of
current sources, the apparent resistivity pa is determined as (see Figure 4.16):
+ U
Pa
+1
Cl
1
Cz
t
i
i
• P2
♦pi
i
a
(Pj) - U
Cl
(P2)
(4-45)
-I
C2
i
a
2
Figure 4.16
Wenner Array
Two-Layer Earth (Horizontal Layers)
From Equations 4-35 and 4-45, the following expression is obtained for pa;
Pa = Pi
, .
co
'Ey?
n=1
r
[ ---------L
(4-46)
L [1+((2nh/a)2r
2nl
[4+(2nh/a)J.
Vertical Fault (Vertical Layers)
Equations 4-36, 4-37 and 4-45 are used to derive the expression for Pa. In this case however,
several expressions are necessary for each location of the center of the array O whose
direction is at an angle « to the line of fault (see Figure 4.17).
Line of Fault
Figure 4.17
Vertical Fault (Top View)
4-25
Let M be the center of the array and O the point of intersection between the array direction
and the line of fault. The distance between M and the line of fault is h. The following
geometric relations exist between h, « and the distances dj and 62 between the current
sources and the line of the fault:
: S COSO)
(4-47)
s sinoi
(4-48)
1
3
= h + — a s 1 nto
(4-49)
2
3
= h-----a
(4-50)
s t no)
2
By convention, we will assume that Cl is the positive current source, located in the medium
of resistivity p^. Furthermore, the center of the array is also assumed to be in region 1.
This arrangement is symmetrical with respect to the vertical line OX. The results which
are obtained using this assumption will also be applicable in region 2 by interchanging
and P2 in the equations.
Therefore there are three possibilities:
1- P2, C2 in region 2
2- P2 in region 1, C2 in region 2
3- P2, C2 in region 1.
In the first case, we have:
U(Pi) = UnCPj) + U2i (Pi)
(4-51)
U(P2) = U12(P2) + U22(P2)
(4-52)
where Uj; is the potential at a point in region j due to a source in region i. From Equations
4-35 , 4-37 , 4-45 and 4-47 to 4-52, the following expression is determined:
Pi
PA = --------3
K(1-K)
1
K(1+K)
(4-53)
+ k2 +
(1-k)
[4(sinw+h/a) 2+cos2w]
2
[4(s inoj-h/a) 2+cos2(jo] 2.
Similar expressions can be obtained for the other cases.
Localized Discontinuity
In Section 4.4.6, the derived potential expression applies only when the current source is at
the center of the hemispherical discontinuity. In a typical resistivity measurement array, a
current source is unlikely to be located at this center. In this case, the potential calculations
are significantly more difficult. It is possible however, to obtain an approximate solution for
the apparent resistivity function by initially considering a combination of the following cases:
a- current source located far from the discontinuity
b- current source located close to the discontinuity center and then, through
appropriate interpolations, completing the apparent resistivity function.
4-26
4.5 INTERPRETATION OF THE MEASUREMENTS
The information contained in this section will provide a base of knowledge from which the
results of apparent resistivity measurements can be correctly interpreted. There are a variety
of interpretation methods and techniques used by geologists. Not all of these methods are
applicable to power system grounding problems. The methods which we believe to be most
useful to power system engineers are presented and discussed in detail.
4.5.1 BASIC CONSIDERATIONS
The simplest interpretation problem is the case where the measured apparent resistivities
Pa vary minimally around an average value p. This indicates that earth at the measurement
site is reasonably uniform and has a resistivity p. Typical apparent resistivity curves peculiar
to this situation are shown in Figure 4.18(a).
SPACING
a- QUASI-UN I FORM SOIL
Figure 4.18
SPACING
b- ERRATIC MEASUREMENTS
SPACING
c- THIN UPPER-LAYER
Uniform Earth
Observed resistivity variations can be attributed to small local discontinuities, which may
be neglected, or to inaccuracies in the measurements due a number of factors such as stray
currents in earth or inadequate sensitivity of the measuring equipment.
Unfortunately, such cases rarely occur in practice. In most cases, apparent resistivity, plotted
as a function of the electrode spacing shows large variations with probe spacing. This indicates
that the earth is nonuniform.
In general, apparent resistivity curves change smoothly and do not exhibit sudden changes.
When the latter occurs, it is a clear indication that the array has just crossed a vertical
fault or a local discontinuity close to earth surface. The magnitude of the jump is an
indication of the difference between the resistivities of the two adjacent earth materials.
The presence of buried pipes or other structures close to the surface is a typical cause of
sudden changes in apparent earth resistivity (see Figure 4.19).
4-27
SPACING
Figure 4.19
a
Sudden Changes
The method used for interpreting the measurements can be grouped into two simplified
categories:
•
Empirical interpretation
•
Analytical interpretation
Analytical interpretation is, in theory, independent of the person conducting the interpretation.
In contrast, the results of an empirical interpretation are significantly influenced by the
background and experience of the interpreter.
It is preferable to use a combination of both approaches for maximum accuracy and a
minimum of uncertainty. For example, when analytical methods indicate that two or more
earth models are reasonable, the most realistic choice can be determined from empirical
considerations or visual inspection of the curves. In any case, it should be emphasized that
experience is of paramount importance in the interpretation process.
4.5.2 EMPIRICAL METHODS
Empirical methods are based on experience gained through numerous measurement and
interpretation exercises. Thus, such methods can be described as statistical in nature.
Essentially, it is observed that the shape of an apparent resistivity curve is closely related
to the earth structure and its characteristics at the site. Therefore, certain properties of
the measured curve are used to deduce the resistivity and thickness of the earth layers.
Although there may be inherent inaccuracies in some of these methods, they are of less
consequence to the design engineer than they are to the geologist. Empirical methods
may be useful for on site interpretations and serve as a good starting point for more rigorous
methods.
4-28
The Gish and Rooney Rule
Based on their work, Messrs Gish and Rooney [22J concluded that apparent earth resistivity
measurements give the average resistivity of earth material to a depth approximately equal
to the electrode spacing. Based on this assumption, a change in the formation can be detected
quickly when a significant variation of the apparent resistivity value or a change in the
curvature of the data is observed.
This rule implies that the test current does not penetrate to a depth greater than the
electrode separation. This is incorrect as can be seen from Figure 4.20 which shows the
magnitude of the current density as a function of depth, computed for the case of uniform
soil. In soil with a low resistivity bottom layer, the current densities in this layer are even
greater.
3 $ a
Figure 4.20
H •
Current Density in Earth
Consequently, the empirical rule established by Gish and Rooney should be used with caution
as it may lead to false conclusions, and is, at best, a coarse approximation.
The Lancaster - Jones Rule
Quite often, the apparent resistivity curve indicates the presence of two major electrically
distinct layers. These layers are described as electrically distinct to distinguish them from
the geological structures which may be comprised of more than two distinct layers.
In such cases, the apparent resistivity curve contains a point of inflection somewhere between
the small spacing values, where the upper layer resistivity value primarily influences the
measured values, and the large spacing values, where the bottom layer resistivity primarily
influences the measured values. Messrs Lancaster-Jones [23] have suggested that this point
of inflection occurs when the spacing between the electrodes in the Wenner array is
approximately equal to 3h/2, where h is the thickness of the upper layer.
4-29
While the theory of two-layer earth shows that there is a relation between the point of
inflection, the thickness h and the spacing a, it also shows that this relation is dependent
on the reflection factor K (i.e., contrast between the upper and bottom layer resistivities)
and varies between two close limits. Only the upper limit is close to 3h/2 and corresponds
to the case where the bottom layer is significantly more resistive than the upper one. Based
on Tagg's work [3], it appears that a more appropriate relation between the spacing a and
h at the point of inflection is:
a = (0.7K + 1)h, when K > 0
(h-5b)
a = (0.15K + 1.15) h , when K < 0
(4-55)
and
It should be pointed out however, that the exact location of the point of inflection is not
easily determined by visual inspection. This difficulty further reduces the accuracy of the
Lancaster-Jones Rule or its improved version. Nevertheless, this rule can be useful in many
cases, particularly whe'n the knowledge gained is used to select the most suitable location
for the next resistivity traverse.
The Asymptote's Rules
This method is applicable when the bottom layer is significantly more resistive than the
upper layer. This interpretation procedure is illustrated in Figure 4.21 which shows the results
of a typical apparent resistivity measurement. Note that the resistivity curve is usually
drawn on bilogarithmic graph paper.
This method [7] is based on the knowledge that an apparent resistivity curve will rise at a
45° angle if the deep layer is an insulator and if the spacings are large enough. First, a
horizontal line (horizontal asymptote), passing through the measured point at short spacings,
is drawn. The point of intersection with the resistivity axis gives the upper resistivity.
Secondly, a 45° line (asymptote) passing through the last measured point(s) is drawn. The
ratio of spacing to apparent’resistivity for any point along the 45° line, C, is constant and
is used to determine the thickness of the upper layer. The value of C/(21n2) represents the
columnar conductance, in ohms, of the upper layer. The thickness of this upper layer, when
the Wenner arrangement is used, is:
C
a
------------ = --------------px
21n (2)
2paln{2)
(4-56)
The resistivity of the bottom layer is indeterminate, since this method is valid only if
the bottom layer resistivity P2 is much greater than the top layer resistivity Pj. In practice,
this means that P2 can be anywhere between approximately 50 P^ and 00.
4.5.3 ANALYTICAL METHODS
The word "analytical" can be misleading as it is often interpreted as meaning "accurate" or
"rigorous". Earth resistivity measurements are rarely accurate to within 1%, even when
sophisticated equipment is used. Usually, careful measurements with conventional equipment
are accurate to within about 5%. Careless measurements, inexperience or poor equipment
can lead to measured results significantly different from the real values. Even measurements
taken by an experienced crew under the best of conditions, will never give a perfect match
with analytical results computed from the optimum earth model derived from the measurement
data. The reasons for this were briefly explained in the introduction and in Section 4.4.3.
We will now elaborate on these effects.
4-30
>00
00
LU
C£
CC
<
CL.
CL.
<
SPACING
Figure 4.21
Asymptote's Rule
It was shown in Section 4.4.3 that the relation between the measured apparent resistivity
Paj at spacing aj is given by Equation 4-22 which is now rewritten:
PaJ- = ZtiajiMaj >
> *2 ........... -X.----- ------ »An)
(4-57)
Xi,....,Xn are n parameters which completely describe the real earth structure and its
characteristics. In theory, n measurements at different spacings are sufficient to uniquely
solve the n unknown parameters of the n simultaneous equations given in (4-57). Unfortunately
not only the values of the parameters are not known, but their nature, number and influence
on the measurements are also unknown. Since one can not see the various materials contained
in the earth, it is not possible to define which variables describe the shape, location and
resistivity of the material. One possible solution to this difficulty is to consider the resistivity
of earth as a function of space, i.e., P(x,y,z). Unfortunately, even if an analytical solution
to this problem was possible, it would not be very useful, since the real function is generally
discontinuous at the interface between two volumes of different materials. This returns us
to our first difficulty, which is to determine the location and shape of the boundaries where
the resistivity discontinuities exist.
It is in this determination where the fundamental difficulty associated with earth resistivity
measurement lies. It is necessary to propose an earth model and see whether or not the
computed apparent resistivities of the proposed model fit those measured. It is obvious that
a perfect match will seldom occur. Even if satisfactory agreement is obtained between the
measured and calculated results, measurement inaccuracies always make it possible that
results from another earth model could be matched equally well with the measured results.
4-31
4.5.4 METHODOLOGY
Based on the discussion of the preceding section, it can be concluded that what we have
termed "analytical methods" follow a constant methodology, i.e.:
Step 1
The measured results are examined and preliminary interpretation is performed, typically
based on the empirical methods described previously.
Step 2
One or several possible earth models are proposed.
Step 3
The measured results are compared with those calculated from the proposed models.
Step 4
The most suitable model is retained. If more that one model is suitable, these are considered
to be equivalent.
Step 5
The selected model is optimized. Often the optimization process is based on engineering
judgment. Sometimes one may choose to conduct additional surveys in order to check the
validity of some assumptions or to eliminate uncertainties. However, in power system design
this step is generally omitted.
The differences in techniques employed to interpret the results are essentially due to:
1- Complexity of the earth model selected.
2- Availability of apparent resistivity Master reference curves based on the
proposed model.
3- Techniques used to make the comparisons between measured and calculated
values.
Two different techniques are used to match calculated and measured results:
a- Complete-curve matching
b- Partial-curve matching.
In some cases, prepared apparent resistivity curves are used to compare measured and
calculated results. When these reference curves are not available, computer programs are
normally used.
There are many difficulties which, in practice, limit the complexity of the earth model
to a small number of layers. In this report, only the two-layer earth model is considered in
detail. Three or more layers are studied briefly using the technique of partial-curve matching
for two-layer earth models.
First, the use of precalculated curves is described. Computer methods based on the method
of steepest-descent are then described. A computer program (RESIST) based on the method
of steepest-descent is described in Chapters 3, 10 and Appendix B.
4-32
4.5.5 LOGARITHMIC CURVE MATCHING
The apparent resistivity functions which were derived in Section 4.4.7 (Equations 4-46 and
4-53) may be written in terms of the dimensionless ratios K, Pa/
and h/a:
Horizontal Two-Layer Earth
CO
= 1 + 4 ^ ' Kn^[l + 4n1
2 (h/a)2] 2 - [4 + 4n2 (h/a)2] 2]
(4-58)
P-/Pi
n=1
Vertical Fault
j/Pj
- (l_K)
1 + K2 + K(1-K) [ 4(sino) + h/a)2 +
- K(1 + K) [4(sinoj - h/a)2 + Cos2oj]
Cos2oj
2 J
] 2
(4-59)
If one of the above dimensionless apparent resistivity functions Pa = pa/is plotted in
logarithmic coordinates, i.e., ln(Pa/ P^) = F(ln(a/h)), the coordinates of a point on the resistivity
curve will be:
Y = lap
a - 1npi
x = 1na - Inh
on the y axis
(4-60)
on the x axis
(4-61)
If we now assume that a number of apparent resistivity reference curves, designated as
Master curves, are plotted for various reflection coefficients K, then:
y° = Inp
(4-62)
3
x° = Ina
(4-63)
assuming that Pi = 1 fi-m and h = 1 m.
Where Pi and/or h are not equal to unity, resistivity curves derived for two-layer earth
structures will be shifted by -ln(Pi) vertically and -ln(h) horizontally, with respect to the
corresponding Master curves as shown in Figure 4.22. The shapes of the curves are thus
preserved. This property of the apparent resistivity curve is the basis for the logarithmic
curve matching method.
Thus, a field curve can be compared directly with a set of theoretical Master curves, through
a series of appropriate translations of the field curve plotted on transparent paper. If a
satisfactory match is found between the field and a theoretical curve, then the real earth
reflection factor K, is equal to that of the computed curve. Pi and h are then determined
as follows:
1- Pa/ Pi = 1 on the Master chart, corresponds to 12 fi-m on the field chart.
Therefore:
12/Pi = 1
and
Pi = 12 fi-m
2- a/h =1 on the Master chart, corresponds to 30m on the field chart. Thus:
30/h = 1
and
h = 30 m.
4-33
^__ L
*
t_ MEASURED
VALUES
HORIZONTAL
t*
VERTICAL
Figure 4,22 Logarithmic Curve Matching
This method requires that a set of precalculated Master reference curves be available to
the interpreter. Such curves can be easily determined based on Equation 4-58 for horizontal
layers and Equation 4-59 for a vertical fault. Figure 4.23 is a set of Master curves for the
case of a two-layer earth. When a field curve falls between two curves, the correct values
can be interpolated. If more precision is required, additional curves for closer K values
should be constructed.
Figure 4.24 is a set of Master curves applicable to vertical faults when the direction of the
traverse is at 0° angle with the line of fault. It should be noted that additional charts
(different angles w) are required for a complete set of master charts. The construction of
such charts is straigthforward with a programmable calculator. Reference charts for 30, 60
and 90° angles are provided in Volume 2 of this report.
At this point, a word of caution is necessary. The apparent resistivity curve measured when
a traverse does not cross the line of a fault (for example, when the direction of the
measurement array is parallel to a line of the fault) is very similar to a typical horizontal
layer curve. In practice, it may be very difficult to distinguish between the two situations.
This difficultiy can be readily overcome if two traverses, at right angles, are made available.
In the case of horizontal layers, no significant differences will be found between the two
traverses. If the earth exhibits vertical discontinuities, the curves of each traverse will
be different. The differences may be significant if the vertical fault is close to the traverses
and/or the resistivity difference between the regions is marked. If one of the traverses is
more or less orthogonal to the fault and crosses the discontinuity, then one curve will have
a shape similar to the curves shown in the figures of Volume 2 (w = 60° or 90°).
TWO-layer
Figure 4.23
earth
Horizontal Two-Layer Earth Master Chart
4.5.6 PARTIAL CURVE MATCHING
The logarithmic curve matching method is a complete curve matching technique. That is,
the best fitting theoretical curve is used as a reference to calculate the unknown parameters
of the real earth. The occurence of more than two-layers in earth is quite common. In many
cases, however, it is necessary to average the apparent resistivity values in the zone which
indicates the presence of a middle layer and use the new adjusted curve as the reference
field curve (see Figure 4.25).
4-35
9£-*?
VERTICAL FAULT
10
Figure 4.24
Vertical Fault Master Chart
-5
SPACING
SPACING
Figure 4.25
Multi-Layer Earth
Unfortunately, if the difference in resistivities between adjacent layers is significant, this
approximation may be unacceptable.
Even though multi-layer earth problems are not analyzed here, it is necessary to evaluate
the nature of multiple layer structures in order to choose the best approximate two-layer
model. The partial curve matching technique is recommended as appropriate for this evaluation.
This technique, illustrated in Figure 4.26, is essentially a complete curve matching process,
conducted in two (or more) consecutive steps on given zones of the apparent resistivity
curves.
Connecting
Zone
SPACING
Figure 4.26
Partial Curve Matching
4-37
Once the earth model for each portion is determined, the models are overlaid to arrive at
a suitable multiple layer earth model. It is not practical to develop rules to define the
resistivities or the thicknesses of the layers. Engineering judgment and experience must
be the major guiding factors. A typical example of this technique is described in Chapter
10.
Alternatively, partial curve matching can be performed using a two-layer resistivity
interpretation computer program, simply by submitting the data for zone 1 to the computer
followed by the data for zone 2. The rest of the interpretation task is identical whether
Master curves or computer programs are used. In grounding problems where a maximum of
two-layers are considered, one more step is necessary. The three (or multi) layer earth model
derived using the partial fitting technique, must be converted to an equivalent two-layer
model by combining the effects of adjacent layers. The major difficulty is in the selection
of those layers which can be combined without seriously affecting the accuracy of the
grounding analysis.
If we restrict ourselves to the case of three layers, then the main problem is whether the
mid-layer should be combined with the upper or bottom layers. Theoretically, the answer
will depend on a number of factors such as the ratio of the grounding system dimension to
the upper and mid-layer thicknesses, the contrast between the resistivities and the presence
of ground rods in the mid or bottom layers. Generally however, it is preferable to combine
the mid and bottom layers because, as explained in Chapter 10, the surface potentials above
the grounding system are particularly sensitive to the characteristics of the upper layer,
which usually encloses the ground conductors. The influence of the deep layers should not
be significantly different whether the deep layers are represented discretely or as a lumped
equivalent layer. This observation is also applicable to the calculation of resistance value
of the grounding system [24-26].
Similar observations and reasoning can also be applied to multi-layer earth.
4.5.7 OTHER METHODS
There are many other methods which have been proposed and used to interpret apparent
resistivity curves. These methods use graphical or computation techniques based on the known
properties of idealized earth models [27-29]. Tagg has proposed two techniques which could
be adapted to either graphical or computerized approaches [3].
Most computerized methods are essentially of the curve fitting type using a known reference
function. The selection of a suitable curve fitting technique is based on considerations such
as speed of computations, stability of the algorithm, convergence and ease of programming.
The following method was used as the basis for the computer program RESIST (see Appendix
B) developed by SES. This method was selected for the following reasons:
•
A more elaborate version of the method has been operational for several years
and has been extensively tested in practical cases. It has proved to be a very
stable, reliable method which requires a minimum amount of input data. Initial
values for the presumed earth model are not required from the user. Therefore,
it can be used by engineers with limited experience in resistivity interpretation.
•
The method is easy to implement
•
The program is particularly suited to transmission line structure grounding design
where very large spacings between the electrodes of an array are not necessary.
This program is based on the method of steepest-descent described in the following section.
4.5.8 THE STEEPEST-DESCENT METHOD
General
The method of steepest-descent [30] is most readily vizualized by an analysis of the
two-variable function ^(x,y), illustrated in Figure 4.27.
The gradient of this function is calculated at an initial point M0 defined by x0, y0. The
values of x and y are then selected so that the function decreases along the direction defined
by the gradient vector. The process is repeated until the function along the initial direction
starts to increase. The process will stop when all possible directions of the gradient indicate
that the present (x,y) coordinates corresponds to a minimum of the function (zero gradient).
MINIMUM
Figure 4.27
The Method of Steepest-Descent
This process will normally converge to a minimum of the function. However, there is no
guarantee that the minimum obtained will be the only one nor that it is the minimum of
the minima. Experience shows that when a secondary minimum is obtained, the initial starting
point was most likely within the zone of influence of this minimum. In this case another
pair of initial x and y values should be selected and the process started again.
Analytical Description
Let p°(aj), j = 1, n be the series of apparent resistivity values as measured at a given
by the Wenner method for n different inter-electrode spacings aj.
site
Let p(ap, j = 1, n be the calculated apparent resistivity value, based on a two-layer earth
model and the same spacings aj used during the measurements.
The interpretation task consists of finding the most suitable earth model for which the
difference between the set of measured and calculated values, according to certain criteria,
is a minimum. In theory anycriterion can be used (e.g., sum of the absolute value of the
differences). In practice, the classical least-square criterion is preferred.
4-39
Let
^(Pi,
K, h) be the square error function defined as:
'P°(ai)~p(al)'
(it-64)
ijj(pi, K, h) =
j=1
L
PUU.,
The best fit is obtained when ^ is minimum. The values of Pi, K, h which lead to this
minimum are determined by the steepest-descent algorithm.
The gradient vector is defined as:
/ 8^
8^
3^ \
\ 3pi ’ 3h ’ 9K /
Each component of the potential vector is determined from Equation 4-64. Thus:
8i|) - 3pi
dip
2
3p
E(pl'p)
1 V p02/
3pi
- - 2 t(p0-p)
3p
3^
3p
K
>
O
1 \ P02/ 3K
!
3K
II
(4-65(a ))
(4-65(b))
(4-65(c))
1 \ p02/ 3h
3h
Assume now that
represented as:
AP^,, AK,
Sip
Api =
(4-66 (a))
-T -------
Spi
3ip
AK =
(4-66(b))
-T --------
3K
Sip
Ah = -x---3h
(4-66(c))
where r is a positive value (expressed in p.u. of V), suitably selected to generate a smooth
search for the minimum. The above changes cause a small variation
in the error function
A<J> =-g- Api +4r"AK +lh~Ah
or
(4-67)
4-40
The sought for minimum is obtained when
= 0 or practically when:
|Ai|»| < e
(4-68)
where e is the desired accuracy.
The main steps in the steepest-descent algorithm are therefore:
1- Estimate initial values of
K and h (i.e., Pj , K° , h° )
2- Calculate a suitable value of r
3- Determine APj, AK and Ah
4- Estimate a new starting point:
+ Api
K<.)
h<'>
+ AK
hC-D + Ah
5- Calculate
[A'/']
and compare it with e:
a- if | A^|
< e , the fit is completed.
b- if |A^| > e , continue the process at step 2 (or step 3 if
maintained constant).
t
is
In order to calculate A\4 from Equation 4-67, the partial derivatives of \p must be known.
These are determined from (4-65) where the partial derivatives of the theoretical two-layer
earth apparent resistivity function are obtained from Equation 4-46. These calculations lead
to:
3p_
(1 - n(1 - K2)/2K) (A"
(4-69)
9pi
CO
3p ^ nKn_1
- B-i ^
(4-70)
3K
9p
3h
a2
(4-71)
n=1
where
A = 1 + (2nh/a)2
(4-72)
B = A + 3
4-41
REFERENCES
1 - B. L. Goodlet, "Lightning" IEE Journal, Vol. 81, No. 487, July 1937, pp. 1-56. (see
discussion by F. J. Miranda).
2 - A. Cimador, R. Fieux, B. Hutzier, "Influence des Resistances des Prises de Terre sur le
Foudroiement des Pylones d'une ligne 222 kV", E.D.F. Bulletin de la Direction des Etudes et
Recherches, Serie B, No. 4, 1974, pp. 29-42.
3 - G. F. Tagg, "Earth Resistances", George Newnes Ltd., London 1964 (book).
4 - E. D. Sunde, "Earth Conduction Effects in Transmission Systems", Dover Publications,
New York, 1968 (book).
5 - F. Dawalibi, D. Mukhedkar, "Influence of Ground Rods on Grounding Grids", IEEE
Transactions on PAS, Vol. PAS-98, No. 6, November/December 1979, pp. 2089-2098.
6 - P. Hoekstra, D. McNeill, "Electromagnetic Probing of Permafrost", Geophysics 1973, pp.
517-526.
7 - G. V. Keller, F. C. Frischknecht, "Electrical Methods in Geophysical Prospecting",
Pergamon Press, New York (1977).
8 - G. V. Keller, "Statistical Study of Electrical Fields From Earth Return Tests in the
Western States and Comparison with Natural Electrical Fields", IEEE Transmission on
PAS, Vol. 87, April 1968, pp. 1050-1057.
9 - G. E. Backus, J. F. Gilbert, "Numerical Applications of a Formalism for Geophysical
Inverse Problems", Geophysics J. R, Astr. Soc.13 (1967), pp. 247-276.
10- L. C. Cham, D. L. Moffat, L. Peters Jr., "A Characterization of Subsurface Radar
Targets", Proceedings of the IEEE, Vol. 67, No. 7, July 1979, pp. 991-1000.
11- M. Cauterman, J. Martin, P. Degauque, R. Cabillard, "Numerical Modeling for
Electromagnetic Remote Sensing of Inhomogeneities in the Ground" Proceedings of the IEEE,
Vol. 67, No. 7, July 1979, pp. 1009-1015.
12- V. I. Dimitriev, M. N. Berdichevsky, "The Fundamental Model of magnetotelluric Sounding"
Proceedings of the IEEE, Vol. 67, No. 7, July 1979, pp. 1034-1044.
13- H. O. Seigel, "The Induced Polarization Method", Mining and Groundwater Geophysics,
1967, Published by the Geological Survey of Canada, pp. 123-137.
14- H. Guyod, "Interpretation of Electric Ray Logs in Water Wells", The Well Log Analysis,
January-March 1966.
15- L. B. Slichter, "An Inverse Boundary Value Problem in Electrodynamics", Physics, Vol.
4, December 1933, pp. 411-418.
4-42
16- F. Wenner, "A Method of Measuring Resistivity", National Bureau of Standards, Scientific
Paper 12, No. S-258, 1916, p. 499.
17- S. Stefanesco, C. & M. Schlumberger, "Sur la Distribution Electrique Potentielle Autour
d'une Prise de Terre Ponctuelle dans un Terrain a Couches Horizontales Homogenes et
Isotropes", Journal de Physique et Radium, Vol. I, Serie VII, No. 4, 1930, pp. 132-140.
18- M. Muskat, "Potential Distribution About an Electrode on the Surface of the Earth",
Physics, Vol. 4, No. 4, April 1933, pp. 129-147.
19- H. M. Mooney, E. Orellana, H. Pickett, L. Tornheim, "A Resistivity Computation Method
for Layered Earth Models", Geophysics, Vol. XXXI, No. 1, February 1966, pp. 192-203.
20- K. Maeda, "Apparent Resistivity for Dipping Beds, Geophysics, Vol. XX, No. 1, January
1955, pp. 123-139.
21- L. S. Palmer, "Examples of Geoelectric Surveys", IEE Journal, Vol. 106, part A, June
1959, pp. 231-244.
22- O. H. Gish, W. J. Rooney, "Measurement of Resistivity of Large Masses of Undisturbed
Earth", Terrestrial magnetism and Atmospheric Electricity, Vol. XXX, p. 161.
23- E. Lancaster-Jones, "The Earth Resistivity method of Electrical Prospecting", The Mining
Magazine, June 1930.
24- F. Dawalibi, D. Mukhedkar, "Parametric Analysis of Grounding Grids", IEEE Transactions,
Vol. Pas-98, No. 5, September/October 79, pp. 1659-1668.
25- F. Dawalibi, D. Mukhedkar, "Influence of Ground Rods on Grounding Grids", IEEE
Transactions, Vol. PAS-98, No. 6, November/December 79, pp. 2089-2098.
26- J. Endreyni, "Evaluation of Resistivity Tests for Design of Station Grounds in Nonuniform
Soil", IEEE Transactions on PAS, Vol. PAS-84, No. 12, December 1963, pp. 966-970.
27- L. B. Schlichter, "The Interpretation of the Resistivity Prospecting Method for Horizontal
Structures", Physics, Vol. 4, September 1933, pp. 307-322.
28- A. F. Stevenson, "On the Theoretical Determination of Earth Resistance from Surface
Potential Measurements", Physics, Vol. 5, April 1934, pp. 114-124.
29- A. A. R. Zohdy, "Automatic Interpretation of a Resistivity Sounding Using Modified Dar
Zarouk Functions" Geophysics 38, pp. 644-660.
30- F. Scheid, "Numerical Analysis", Shaum's Outline Series, McGraw-Hill Book Company,
New York 1968.
CHAPTER
5
POWER FREQUENCY PERFORMANCE OF
TRANSMISSION LINE STRUCTURE GROUNDS
5.1 GENERAL
Ideally a power system should not conduct any ground currents when only one energized
element in the system is grounded. In practice, however, all elements of a power system
have a capacitance to ground due to the finite distance between each element and the
earth's surface. Therefore, there is always an earth return path for the current through the
distributed capacitance of the power system during normal operation. The earth acts as a
return conductor during faults, whether these faults are initiated by natural causes such as
lightning or by system malfunctions or disturbances.
The use of ungrounded power circuits was commonplace at one time, and a number of
distribution systems have been operated ungrounded for many years. Operating experience
has shown, however, that grounded systems have better service continuity than ungrounded
systems. The two main reasons for this will be discussed.
While a phase to ground fault on an ungrounded system generally does not immediately result
in a service interruption, the fault can cause sustained system overvoltages and, possibly,
resonant conditions or restriking ground faults. These conditions will increase the likelihood
of a second ground fault on one of the other phases, and subsequent power outages.
Direct lightning strokes to an ungrounded power system may cause serious damage to vital
equipment. The lightning current can cause severe transient overvoltages and flashovers,
sometimes at several different locations on the power system. Often, these flashovers are
followed by power frequency backflashes which may remain uncleared.
Power system performance is not the only factor which favours grounded power systems.
Ground faults on ungrounded systems can present a severe or lethal shock hazard. This is
because in ungrounded systems the probability of exposure to such faults is much greater
due to the longer time between the occurence of a fault and detection and removal of the
faulted circuit.
The importance of adequate grounding is continuously increasing with the increases in both
voltage and short-circuit current levels of modem power systems. While there are still a
few ungrounded distribution systems, all high voltage power systems in North America are
effectively grounded. The earth is used as a return path for power frequency fault and
unbalanced currents, as well as for lightning and switching surge currents.
A grounding electrode performs several essential functions during normal and faulted power
system conditions:
5-1
m
A grounding electrode maintains the potential rise of the power system neutral
below a critical value.
•
The grounding electrode provides an alternate path, or the only path for unbalanced
faults and lightning currents. This is achieved by designing a low impedance
connection between the power system neutral points and the earth.
•
A grounded system permits fast and sensitive detection of fault currents. By
monitoring a solidly grounded system for neutral current magnitudes above a
certain value, faulted circuits can be detected and isolated in the minimum amount
of time.
©
Finally, a suitable grounding electrode is the only feasible means of maintaining
the various noncurrent carrying metal structures of a power installation at safe
potential levels and keeping the earth surface potential gradient in the vicinity
of the electrode within tolerable values.
The critical role played by a grounding electrode has not always been recognized. Many
electrocutions and equipment problems may have resulted from a lack of adequate knowledge
of grounding system behaviour.
There are many reasons why power system grounding has been neglected as power system
technology has developed. There are two factors, however, which have been the principal
obstacles to the development of a thorough understanding of power system grounding. Firstly,
the physical process of current conduction in the earth is three-dimensional in nature and
very complex mathematically, even when point electrodes are considered. When practical
power system grounds are analysed, hand calculations become impossible, unless extensive
simplifications are introduced. Furthermore, it is not possible to derive empirical formulas
or rules based on previously installed grounding electrodes. The reason for this lies with the
complexity of the earth's structure which varies with geographical location and climatic
conditions. Also the size and configuration of grounding electrodes vary within wide limits.
The availability of digital computers has permitted a renewed interest in the subject of
power system grounding. Numerous papers [1-22] describing computerized analytical methods
for grounding analysis have been published in the last decade. Moreover, the spectacular
advances in electronic technology is leading to the development of significantly improved
grounding measurement equipment [23-27] which will permit a fast and accurate determination
of the equivalent "electrical" earth structure and the impedance of installed grounding
systems.
In this chapter, the basic mathematical equations defining the behaviour of a grounding
electrode injecting power frequency current into a uniform or two-layer earth structure will
be derived and discussed. The analytical methods described in this chapter, although general
in nature, are concerned primarily with small ground electrodes of the type usually encountered
on transmission structures not equipped with continuous counterpoises. The continuous
counterpoise is analyzed separately at the end of this chapter.
The theory presented in this chapter is the basis for the grounding computer program
GTOWER, described in Appendix C. This program was used to analyze several grounding
structure configurations buried in various earth structures. It also determines the effectiveness
of ground potential control conductors designed to reduce step and touch potentials
around transmission structures in densely populated centers, where the probability of exposure
of the public to the structure is high and should be considered.
5-2
The results of the analysis, performed using computer program GTOWER, are presented in
several design charts which can be used to directly determine the performance of structure
grounding systems.
5.2 TRANSMISSION LINE GROUNDING
The insulation requirements of transmission lines are determined by lightning or switching
surge transients and not by the power frequency voltage.
In case of a severe surge, such as a direct lightning stroke on a structure, the voltage built
up across a phase conductor insulator at that structure is the product of the lightning current
i(t) in the structure and the structure impedance Z(t) where t represents time. The dynamic
(time-varying) impedance function Z(t), is difficult to determine because of the mathematically
complex structure geometry, structure footing and grounding configurations, and often, the
complex nature of the soil structure. In Chapter 7, an attempt is made to derive the function
Z(t). In this chapter, however, our interest is directed at the resistive part of Z(t) and, more
precisely, at the structure ground resistance. Except in rare cases where soil breakdown
occurs due to very high structure currents, this resistance is constant and is dependent only
on the structure grounding configuration and soil characteristics.
Structure ground resistance plays a major role in transmission line design. Experience and
statistical data have shown that there is a definite relation between lightning outage rates
and structure resistance. Consequently, the classical method for determination of transmission
line outage rates caused by lightning [28,29] uses structure ground resistance as a fundamental
parameter in the calculations. The importance of structure grounding has also been confirmed
by measurements and theoretical analyses as discussed in Chapter 7. Analysis [28-30] shows
that the potential rise of a transmission line structure struck by lightning depends mainly
on the structure ground resistance, when the wavefront duration of the current is sufficiently
longer than the propagation time of the surge in the structure. With very steep wavefronts,
the surge response of the complete structure, including its grounding system, may influence
the potential at the top of the structure, especially when the footing resistance is relatively
low.
In addition to the major influence it has on transmission line lightning performance, the
grounding system of a transmission structure also contributes to the effective dissipation of
power system ground faults. When a ground fault occurs on a transmission line equipped with
overhead ground wires, a significant portion of the fault current is diverted to the structures
on each side of the faulted structure. Consequently both the fault current and potential rise
at the faulted structure are decreased. This has favorable effects on both transmission line
performance and safety.
5.2.1 TRANSMISSION LINE STRUCTURE GROUNDING SYSTEMS
The grounding system of a transmission structure consists of the following elements:
•
All metallic elements of the structure buried in the soil or in the concrete of
the foundations. These include rebars, stub angles, guy anchors or anchor bolt
cages, buried portions of structure legs, etc..•
•
Any supplemental grounding electrode, such as ground rods, horizontal rings,
counterpoises or any combination of these ground conductors.
5-3
Although the subject is discussed in greater detail later in this chapter, it should be noted
that metal structures encased in concrete usually contribute significantly to a reduction
in the structure ground resistance. Often, the concrete of the foundations alone provides a
suitable grounding system for the structure. This is especially true in low resistivity soils
where the structure resistance may well be below 10 ohms for high voltage four-legged
lattice structures, or their equivalent.
The structure grounding arrangements most widely used by utilities can be grouped in two
basic types (reference is made to the supplemental grounding only):
•
Concentrated type.
•
Extended or continuous type.
The extended type, generaly called continuous counterpoise, consists of one, and sometimes
two horizontal cylindrical conductors buried in the soil along the transmission line and
connected to each structure of the line. This type of grounding system is analysed later in
this chapter.
The concentrated type can be subdivided into a number of categories, each characterized
as an arrangement of one or more of the following basic grounding elements:
a)
A vertical ground rod.
b)
An horizontal cylindrical conductor segment.
c)
A ring or closed cylindrical loop.
In the following sections, analytical expressions which govern the behaviour of the concentrated
types of electrodes, consisting of interconnected elements of one or more categories will
be derived.
Although it is possible to consider a continuous counterpoise as an interconnection, along a
rectilinear path, of a large number of elements from the b
category, a fundamental
theoretical difference, exists between the continuous counterpoise and the concentrated
grounding system. While it is valid to assume that all parts of a concentrated ground are
at the same potential with respect to a remote reference point, i.e., the ground conductor
elements have zero self impedance, it is inaccurate to neglect the self impedance of a
continuous counterpoise. For a sufficiently long counterpoise, the point of current injection
is at a maximum potential while at least one extremity is at zero potential. The zero
potential is due to the total voltage drop that is caused by the finite value of the self
impedance of the counterpoise. This is true for dc currents as well as ac or impulse currents.
In order to apply the following equations to a complete structure grounding system, some
further assumptions are required. Firstly, it is assumed that small volumes of concrete buried
in earth assume the resistivity of the local soil. When this assumption is not realistic, an
equivalent structure can be defined whereby, the volume of concrete is replaced by an
equivalent volume of the surrounding soil (see Section 5.4). Field and laboratory measurements
confirm the validity of this approach, although certain restrictions must be observed when
dealing with long duration currents (minutes, hours or days depending on the current magnitude)
or short duration currents of very high magnitude. This restriction is due to some
peculiar properties of concrete and is discussed in more detail in Section 5.4 of this chapter.
The next assumption is an approximation. Since all buried metallic parts of a structure have
relatively short lengths and are usually close to vertical or horizontal in orientation, they
can be equated to one of the a, b or c categories identified previously, provided that any
noncylindrical structures are replaced by equivalent cylindrical conductors. In addition, it is
5-4
suggested that any metallic part whose dimension is small compared to the total length of
the structure grounding system be ignored, unless it represents a significant portion of
the total length of the ground conductors which are buried in a low resistivity volume of
soil (for instance, rods buried in a low resistivity bottom layer).
5.2.2 EQUIVALENT CYLINDRICAL CONDUCTOR
The buried metal parts of a structure are generally cylindrical conductors (rebar cage, anchor
bolts, etc.) or metallic beams with L, T or U shapes (lattice structure legs, foundation
beams, etc.).
In order to find the equivalent cylindrical conductor of these metallic structures, the
well-known concept of the geometric mean radius (GMR) for n closely spaced parallel
conductors [31,32] will be applied. The GMR concept, in this context, is not exact. However,
it provides a convenient and accurate means of reducing a group of ground conductors to
an equivalent single conductor. This technique should be used only when the distance between
the conductors is small compared to their length. The GMR concept is a valid approximation
because theoretical analysis shows that the effect of the ground conductor radius on structure
grounding performance is minimal, even for a 4:1 change on conductor radius. Thus, even
though the proposed approach is not exact, deviations from the results of a precise calculation
will be insignificant for practical purposes.
Figure 5.1, illustrates the principle of the proposed technique. In this figure, re is the
equivalent cylindrical conductor radius, rj is the radius of the cylindrical conductor i of the
group of n conductors, R is the rebar cage radius (cage center to rebar center) and djj is
the distance between two conductors i and j of the group of conductors.
Figure 5.1
Equivalent Cylindrical Conductor
The applicable relations are as follows:
Equation 5.3 is the general form of the geometric mean radius formula. The n symbol in
the equation represents the cumulative product operand, i.e.;
5-5
n
II a. = a* x a2------------------------x a
—i s
n
a) Rebar Cage (assuming that
rj = r):
n
r
n
e
i=2
(5-1)
‘1 i
b) Regular Beams (assuming that rj = r):
(5-2)
If the beams are regularly spaced along a straight line (spacing s), Equation 5-2 reduces to:
------------------------- 1
f:-fr
r
1)l(n-2)!
e
3! 2!]2
c) Irregular Shape:
r
(5-3)
e
It is also possible to determine an equivalent cylindrical conductor using the following
approximate formula:
re = ( 7 S)2
(5-4)
Here S is the cross section of the metallic element and re is the equivalent conductor radius.
This equation is only applicable to single elements and can not be used for a group of
conductors such as the rebar cage.
In summary, the following fundamental assumptions are made in the analysis of concentrated
structure grounding systems:
1- The grounding system is an equipotential surface (infinitely conductive ground
conductors).
2- Concrete resistivity is equal to the surrounding soil resistivity. If this assumption
is not realistic, the concrete encased conductors can be replaced by equivalent
conductors using the approximation techniques presented in Section 5.4. Therefore,
this assumption is not restrictive but is made here only to avoid mixing the
problem of encapsulated electrodes with the general theory of grounding electrode
performance.
3- All noncylindrical elements of the real grounding system are replaced with
suitable equivalent cylindrical conductors.
Also, since most elements of practical transmission line grounding systems are horizontal,
vertical or can easily be considered as such, the analysis assumes vertical or horizontal
elements. Although there are no theoretical difficulties in dealing with oblique conductors,
in the context of transmission line grounding it has been concluded that such refinements
are unnecessary since they will rarely be applied in practice and will have a negligible
impact on results.
5-6
5.3 LOW FREQUENCY RESPONSE OF STRUCTURE GROUNDING SYSTEMS
When a dc or low frequency ac current is injected into a concentrated grounding electrode
consisting of interconnected cylindrical conductors, the current flows in all conductors and
is injected into earth along each conductor's surface. When the conductor diameter d is small
compared to its length l and spacing D between any two conductors of the ground system,
the surface current density at a given location of the conductor is, for practical
purposes, uniform over the surface of the conductor (see Figure 5.2).
d
i—r
Line Source
Figure 5.2
Equivalent Linear Current Source
Thus, it is possible to replace the conductor with a line source (filament). The linear density
5 of the earth leakage current in the equivalent line source is related to the surface current
density a of the real cylindrical conductor according to Equation 5.5:
6 (A/m) = a(A/m2)/2irr
(5"5)
The linear current density is usually nonuniform over the length of the line source, being
dependent on the grounding system configuration and earth structure. 8 can therefore be
expressed as a function of the space coordinates x , y and z . Reference [21] provides an
easy explanation of why the current distribution is generally nonuniform.
5.3.1 GROUNDING PERFORMANCE OF A LINE SOURCE
In Chapter 4 of this report, the potential at an observation point, M(x,y,z), in a uniform or
two-layer soil was derived for a point current source buried at the suface of the soil (Equation
4.35). This solution was obtained from Laplace's equation and appropriate boundary conditions.
The solution is valid only when displacement currents in the air and in the earth are negligible.
This is the case for dc or low frequency ac curents.
The earth potential function describing the performance of a line source can be deduced
from the expression for the potential due to a point source buried at a depth e below earth
surface. This potential is obtained using an approach identical to the one used in Chapter
4 (point source at surface of soil). The results for a two-layer earth structure are (see
Figure 5.3):
5-7
a) Point source in top Layer (e < h):
ipi F
4>(0)+ip(e)
Un(r) == -----J
kn
L
r
+
Kn
n=1 L
ipid+K) r
U12 (r) = -----------kn
where
and
respectively.
Uyi
L
-|‘
^(nh)+^(nh+e) + ip(-nh)+^(-nh+e)
/
(5-6)
r
^
ij;(0)+^(e) +
J.
K
L
i/j
(nh)+^(nh+e)
(5-7)
are the earth potentials at a point M in the top and bottom layer
b) Point Source in Bottom Layer (e > h):
op
ip2
U21(r) = -----
ip(0)+ip(e)
EKn
n=1
kn
ip2
U22(r) = -----
^(0)+^(e)
r
^(-nh)+^(nh+e) - 4j(-(n-1)h)((n-1)h+e)
(5-8)
L
£■•[ ^(nh+e)
- ^((n-2)h+e)
4tt
(5-9)
where U21 and U22 are the earth potentials at a point M in the top and bottom layer
respectively.
In equations. 5-6 to 5-9 the function ^ is defined as:
^(a)
=jr2 + (2a+b)2 J
(5-10)
where r is the distance between the point source O and the observation point M, b is the
coordinate of M with respect to the vertical ow axis (see Figure 5.3) and a is the variable
used to define the function
W
K = (p2"Pl)/(P2+Pl)
Figure 5.3
Point Source Below Earth Surface
Multi-Layer Earth
The method used to derive the preceding equations can be extended to the n-layer earth
without difficulty. The earth potential, due to a current source buried in the ith layer, at
a point M in the jth layer has the general form of Equation 4-27 of Chapter 4:
5-8
•PI
U. .
u
J0(ar)ear + 0.J0(ar)e"arda
2ir
(5-11)
The j3\ and B\ are determined from the boundary conditions between two consecutive layers
(including air) and by the condition that the earth potential approaches zero at large distances
from the point source. Of course, the solution of 2n simulataneous linear equations is required
to obtain
and 6\. Even for the case of a three layer earth, the analysis has become
cumbersome [33-34].
Line Source
A line source can be considered as an infinite number of point sources placed si de by side
as shown in Figure 5.4.
w
Figure 5.4
POINT
SOURCE
SURFACE OF
GROUND
CONDUCTOR
Infinite Number of Point sources
Each point source located at a distance u from the origin of the line source injects a current
i(u) into earth. When I is the total current injected into earth by the line source, the
following relation holds:
(5-12)
I
The earth potential at any point of the surface of the ground conductor must be constant
since the conductor is a perfect conductor (assumption number 1). Therefore:
V =
o?vo
,wo)du
(5-13)
where
V is the constant potential of the conductor.
u0, v0, w0 are the coordinates of a point at the surface of the conductor.
U is the potential due to a point source.
U is given by one of the previous Equations 5-6 to 5-9. These equations are linear functions
of the source current i(u) which is unknown but can be determined from the knowledge that
the derivative of the potential function dU/du, for v2 +
= a^ (a is the conductor radius),
is zero (constant potential). Hence the current distribution i(u) must satisfy an integral
equation for which, as yet, there is no known closed-form solution. By successive approximations
a solution can be obtained. This process is already tedious for a simple horizontal conductor
buried in uniform soil. However, when the grounding configuration is more complex and the
5-9
soil is nonuniform the process for obtaining a solution becomes unmanageable. In such cases,
it is advisable to use other methods. The finite element technique is particularly well suited
to this problem.
Various algorithms have been proposed recently in the grounding literature. The most widely
used method is based on the segmentation-integration process originally proposed in [4].
Another process, also described in [4], is the summation method. It involves the summation
of the scalar potentials U of a finite number of point sources, which are suitably distributed
over the length of the ground conductors, and the subsequent solution of a set of simultaneous
linear equations to determine the unknown current distribution values i(u). This method has
several major disadvantages. One of the more serious is the large number of point
sources required to suitably model real-life grounding installations.
The Segmentation-Integration Method
This process, depicted in Figure 5.5, involves a division of the line source into a number of
segments, each small enough (with respect to the overall dimensions of the grounding system)
to allow the current distribution over each segment length to be considered uniform. The
srrialler the length, the more accurate the results will be. There are, however, practical
limitations related to computer time and memory capacity. Fortunately, experience [23] has
shown that excellent accuracy is obtained when the segment length is in the order of l/10th
of the maximum ground conductor length. Confirmation of this conclusion can be obtained
by comparing computer results made with the same grounding system divided into a variable
number of segments.
Recently, model tests [21] have confirmed the validity of the segmentation process. Moreover,
analysis of the test results has indicated that once a minimum number of segments is
attained, further subdivision of the ground conductor becomes an unnecessary refinement.
Finally, the minimum required number of segments (for a given accuracy) was found to
be greatly dependent on the way the conductor was divided. In other words, there is an
optimum subdivision (unequal segments) which leads to a minimum number of segments.
SEGMENT j
MICRO
SEGMENT
COORDINATES
Figure 5.5
Segmentation Process
Assume that the line source has been divided into a suitable number of segments. The current
distribution along each segment is uniform but may vary from one segment to the next.
There are a total of m segments, and each segment j injects a current Ij into earth.
5-10
Since I is the total conductor earth current, we have:
m
I = £l.
(5-14)
J-1 J
The linear current density gj (A/m) of segment j of length £ j is:
6
= I /£
(5-15)
Now consider an infinitely small length du on segment j of the line source (Figure 5.5). This
small element will be called a microsegment and, since it can be made infinitely small (du
—» 0), it can be considered as a point source. The contribution of the microsegment to
the potential at a point M (uQ, v0, w0) is therefore given by one of the Equations 5-6 to
5-9. for convenience, these equations will be represented by one single general equation:
U = IA [T*(a)]
(5-16)
where
i is the point source current.
A is a constant (A = PjMtt in Equation 5-6).
The special character T before ^(a) means, by convention for this chapter, the
appropriate sum of funtions of the type \p.
is the function defined by Equation 5-10.
&
a is used to represent the appropriate value of the parameter defining each function
^ of the sum.
The values of r and b in Equation 5-10 are determined from the following relations (refer
to Figures 5.3 and 5.5).
r2 =
(u-Uq)2
+ (v-v0)2 + (w-w0)2
(5-17)
b = w0
Thus, Equation 5-10 becomes:
ifKa) = j^(u-u0)2 + v-v0)2 + (w-w0)2 + (2a+w0)2J
2
The total current in the microsegment is:
i . = 6.du
J
J
and the potential contribution of the microsegment is, from Equation 5-10:
dU. = 6.A
J
J
du
The potential contribution of the segment is therefore:
5-11
(5"l8)
The integration of '/'(a) defined in Equation 5-18 is straightforward:
{&j _u o) + \ &j - u o)2 + Vo 2 + (2a+wo) 2
Uj = 6 j ATI n
(5-19)
■u 0 + Vuo2 +
Vo
2
+"
(2a+wo)'
For example, in the case of a segment j buried in the upper layer of a two-layer earth,
the potential at a point M is:
oo
6 jPi
Un =
4tt
■E.
(£j-u0) + ^(£j-u0)2 + v02 + (2nh+w0)2'
1n
- u0 + yj u02 + v02 + (2nh+w0)2
n=-
(5-20)
(£j-u o) + ^(£j-uo)2 + Vo2 + (2nh+2e+wo)'
1n
- u0 + yj u02 + v02 + (2nh+2e+w0)2
5.3.2 ANALYSIS OF A STRUCTURE GROUNDING SYSTEM
The structure grounding system of Figure 5.6 is divided into a suitable number of segments,
m. Thereafter, the potential Uj at a point M, caused by a segment j, is computed using the
general potential Equation 5-19 or the more explicit Equation 5-20 if the segment j and
point M are in the upper layer. Since the potential is a scalar quantity, the total potential
U caused by all segments (j = 1, m) of the grounding system becomes:
U =
m
X)u.
j=1 J
(5-21)
Note that in Equation 5-19, the coordinates uD, vQ, w0 are relative to a cartesian system
attached to the segment j and with the origin at one extremity of the segment. Moreover,
the u axis of the coordinate system coincides with the orientation of the segment, as shown
in Figure 5.6.
Therefore it is convenient to refer to only one coordinate system xyz as shown in Figure
5.6. This cartesian coordinate system is arbitrary, provided that the xy plane corresponds to
the surface of the soil. The relations between the u, v, w and x, y, z coordinates are as
follows:
Horizontal Conductors
x = xg + ucoscx - vs ina
y = yg + usina +■ vcosa
z = z
s
(5-22 (a))
+ w
5-12
Vertical Conductors
x = xg - w
y = ys + v
(5-22(b))
z = z +u
s
where
xs>
Ys
ar|d zs are the coordinates of the segment origin.
« is the angle between the x axis and the projection of the segment on the xy plane.
Earth
Surface
Figure 5.6
Tower Grounding System
Determination of the Segment Current Densities
Equation 5-21 contains one unknown quantity, the segment current density 6j. Because
the current density distribtion along the conductors of a grounding system is generally
nonuniform, 5; is different from one segment j to another. As a first approximation, one
may assume that the current distribution is uniform. Under this assumption the current
density is:
6. = I/L
(j = 1,m)
where I is the total current in the grounding system (I = Sip and L is the total length of
ground conductors in the grounding system (L = 2£p.
This assumption may lead to significant errors, however, except for a few grounding system
configurations such as ring electrodes buried in uniform soil. Therefore, in most cases where
accuracy is required, it is necessary to determine the values of the current densities 5j.
This is achieved by stating that the potential on the surface of all segments is constant and
5-13
equal to the potential rise V of the grounding system. Thus, if M is a point on the surface
of a ground conductor, the following condition must be fulfilled:
m
v = ]Cmm)
j=1 J
Since Uj
condition
m
E
j=1
is directly proportional to dj (see Equation 5-19), we can rewrite the preceding
as:
6,
—Rj(M) =
(5-23)
V
Rj/
can be defined as the
mutual resistance between segment j and point M, even though there is no real physical
meaning to this mutual resistance. Note that, if M is a point on segment k, and N a point
on segment j, generally, £(<Rj(M) ~ £jRk(N).
Rj(M) is now a known quantity and is expressed in ohm-meters
Equation 5-23 must be verified for each point M on the surface of all segments, i.e., an
infinite number of points in theory, and in practice, a very large number of points, say /x.
Consequently, one must solve m linearly independent equations with m unknowns 8\ (i =
1, m). Since ju can be as large as desired, the system is consistent only when n is equal
to m (V is assumed to be known). Now the question is which points among the many possible
points should be retained. Several alternatives are possible. However, only two are of practical
value.
The average Potential Method (AP)
In this method [35], no specific points M are selected. Rather, the average integral of
the function Rj is computed for all points M along the segment k, i.e.:
.fijk is the mutual resistance between segment j and segment k. In this case
=
The m linearly independent equations needed to determine the current densities
represented by the following equation:
E
j=1
I
£ v
j k
/ k Mm) = 1 for k = 1 ,m
Jo
Xkj‘
are
(5-24)
J
The AP method is very accurate since all points of the grounding system are indirectly
considered in the equations. This method however is not retained in this study because an
alternate method, which will now be discussed, is more convenient. A comparison between
the AP method and the alternate method, is presented later in this section.
The Center Potential Method (CP)
The m points on the surface of the conductors are selected at the center of each segment
j. The reader will recall that each segment j of the grounding system must have a length
St j small enough to allow the current density 5j along the segment to be considered uniform
and equal to the average real current density distribution 6(x, y, z). This requirement is
5-14
equivalent to saying that the values of the computed potentials at the points on the surface
of the segment should remain within narrow limits around the true potential rise value,
V. Since there are generally a large number of segments in a grounding system, and because
the center of the segments are considered as randomly distributed over the length of the
conductors, the limited number of point retained is, in fact, a statistical sample, representative
of all the points.
The current densities are therefore determined from the m linear equations represented by
Equation 5-23 where M is replaced by M^,
being the center of segment k (k = 1, m).
Determining the Potential Rise and Ground Resistance
So far we have assumed that the potential rise V is known, while it has, in fact, been
unknown. However, by considering in Equation 5-23, the variable Xj = 6j/V instead of 5j,
one can first determine the Xj using matrix inversion or other techniques [9,11-13]. V is
then easily determined as follows.
The total earth current in each segment is:
The total grounding system current I is related to the segment currents by:
m
I
m
-E I.
j=l
J
m
yE A.£.
J J
Therefore
(5-25)
V = I
Finally, the ground resistance of the grounding system is, by definition, determined from
the following formula:
R = V/I
(5-26)
Computation Methodology
In summary, the following procedure is required to analyze the grounding system:
a- Divide the grounding system into m small segments.
b- Select a cartesian coordinate system whose xy plane is the soil surface and
direct the z axis downwards toward the earth center.
c- Determine the coordinates of the segment extremities (xs, ys, zs) and (xp, yp,
Zp) with respect to the xyz coordinate system. Compute the angle a between
the x axis and the projection of a horizontal segment (if any) on the xy plane.
d- Calculate the so called mutual resistance R;^ = RjfM^) between a segment j
and the center point of another segment k. An m x m matrix can be formed
when j and k are varied between 1 and m. This matrix is then inverted and the
5-15
normalized current densities Xj = 6j/V are determined from the following matrix
equation (equivalent to Equation 5-23):
-1
1
R.,
X.
jk mxm
j m
-
-
„
_
—
The elements of the Rj^ matrix are determined using Equation 5-19 (with 5j set
equal to 1) where coordinates u0, vOJ wD are related to the corresponding x0, y0,
zQ coordinates according to Equations 5-22(a) or 5-22(b). The appropriate logarithmic
terms to be included in Equation 5-19 (T sign) are determined from Equations
5-6 to 5-9.
e- Compute the grounding system potential rise V and resistance R from Equations
5-24 and 5-26 respectively. Determine the current densities of each segment j
using Equation 5-25.
f- Select the coordinates (x, y, z) of the points in earth where potential calculations
are required.
g- Compute the potential Uj at a point (x, y, z) from a segment j. This is done
using Equation 5-19 with <5j replaced by its value as determined in step e and
Uqj v0, wq replaced by x0, y0, z0 according to Equations 5-22(a) or 5-22(b). The
appropriate logarithmic terms to be included in Equation 5-19 (T sign) are
determined from Equations 5-6 to 5-9.
h- Sum all the potentials Uj according to Equation 5-21 to obtain the total
potential at point (x, y, z).
Chapter 10 of this volume and Part 2 of Volume 2, give several figures and design charts
based on the results of computer program GTOWER. This program was designed to perform
the complete grounding analysis based on the above methodology. More information on
GTOWER is given in Chapter 3 and Appendix C.
Comparisons Between the Average Potential and the Center Methods
The main advantage of the CP method is that the same basic Equation 5-19 is used to
compute the current densities and the earth potentials. In practice, this represents a significant
programming simplification and, for small grounding systems such as structure grounds, it
also means reduced computer time.
The AP method requires Equation 5-19 to compute the earth potentials and the more
complicated Equation 5-24 to determine the current densities and ground resistance. However,
for large grounding systems such as those for HV substations, the inconvenience of a larger
computer program is compensated for by a reduction by one half of the array size required
to store the symmetric mutual resistance matrix, R^.
With respect to computation accuracy of the current densities, the average potential method
provides the best alternative. However, from a practical point of view, the accuracy of both
methods is more than satisfactory, as illustrated in the following example.
Consider a conductor of the grounding system shown in Figure 5.7(a). The true potential rise
Vt along each point on the surface of the conductor is constant and therefore can be
represented by a horizontal line as shown in Figure 5.7(b).
5-16
t
00
AP method
CP method
X—,—,—,—^
GROUND ELECTRODE
12345
ALONG CONDUCTOR SURFACE
(a)
Figure 5.7
(b)
CURRENT DISTRIBUTION
Average Potential
and
ELECTRODE CONFIGURATION
Center Methods
The AP method computes an average potential rise for each segment j of the 5 segments
considered. This average value Va is indicated by the dotted line. When the potential rise
at each point on the surface of the conductor is calculated using the computed average
current densities, the dotted curve is obtained. The average value of the dotted curve
function in each interval representing a segment is exactly Va and is represented by the
dotted straight line.
The CP method gives the potential Vc at the center of each segment. The value of the
potential Vc (identical for all segments) is represented by a mark,
When the potential
rise at each point on the surface of the conductor is calculated using the computed average
current densities, the broken line curve is obtained. This curve crosses the mark
at each
segment center location.
The continuous potential curves computed using the AP and CP methods oscillate around
the true potential rise value V^. The amplitude of these oscillations depends on the
nature and number of segments constructed. Experience shows that when a suitable, yet
practical, segmentation is realized, the maximum amplitude of the oscillations is less than
1% of the average potential value. Since the center potential values lies somewhere between
the maximum and minimum values calculated according to the continuous potential method,
it is concluded that the CP method also produces accurate results.
There is no analytical proof to the preceding qualitative discussion, since a direct solution
to the real current distribution function is not available. However, comparisons between the
computation results using the AP method [10] and the CP method [5] provide an indirect
confirmation of the previous discussions. Further proof is provided by the good agreement
obtained between computed and measured results on scale models [21] and real-life installations
[36]. In Chapter 10, some of these test comparisons and other recent tests conducted in the
context of this EPRI project are described and commented on.
5-17
5.4 LOCAL HETEROGENEITIES IN THE SOIL
Attention is now focused on the situation where a grounding system (or one ot its elements)
is embedded in a small volume of soil having a resistivity
different from the average
resistivity P2 of the bulk volume of soil.
This situation is quite common in practice due to either natural or man-made factors. Apart
from the case where the grounding system happens to be installed in a small localized volume
of different resistivity soil, a grounding system may be deliberately installed in small lakes
or marshy areas in order to lower its ground resistance. Another example is where the
resistivity of a small volume of soil around the ground electrode is decreased by chemical
treatment or replacement of the natural soil with a low resistivity material. Finally, there
are cases where metallic conductors, connected to the grounding system, are embedded in
concrete which serves as the foundation of a structure (structure footings, power equipment
supporting structures, etc.). Theses situations are illustrated in Figure 5.8.
GROUNDING SYSTEM
GROUNDING SYSTEM
GROUNDING
^ SYSTEM
— Pi
RANDOM HETEROGENEITY
DELIBERATE INSTALLATION
IN LAKE OR MARSHY AREA
CHEMICAL TREATMENT
OR SOIL REPLACEMENT
METALLIC
CONCRETE
STRUCTURE FOUNDATIONS
(b) ARTIE I CAL HETEROGENEITIES
(a) NATURAL HETEROGENEITIES
Figure 5.8 Local Soil Heterogeneities
A rigorous analysis of the performance of a grounding system totally or partially embedded
in a relatively small volume of soil whose resistivity p]_ is different from the bulk earth
resistivity P2, is only possible for simple ground systems and certain configurations of
soil heterogeneity. Fortunately, when an exact solution is not feasible, it is possible to gather
very useful information through judicious approximations. In order to make the appropriate
approximations, it is necessary to analyze the following fundamental problems. It is assumed
unless stated otherwise, that soil resistivity is independent of the injected current and its
duration.
5.4.1 HEMISPHERICAL ELECTRODE EMBEDDED IN A HEMISPHERICAL SHELL
This problem, depicted in Figure 5.9, was resolved in Chapter 4, Section 4.3.6, for a
point source. The potentials
in medium 1 and U2 in medium 2 are given by Equations
4-43 and 4-44 respectively. These equations are also valid for hemispherical electrodes. In
this case, the ground resistance R is obtained as follows:
IR = ll(r ->-«>) - U(r = a)=U2(r->00) - Ui (r = a)
From Equations 4-43 and 4-44, the following is obtained:
R
+
P2 " Pi
(5-27)
A
5-18
MEDIUM 2
Figure 5.9
MEDIUM 1
Hemispherical Configurations
The resistance of a hemispherical electrode in uniform soil of resistivity P2 is given as:
1
p2
R2 = — ( — )
2tt
a
Thus, the effect of the heterogeneity can be expressed as the ratio of R/R2. This ratio
a is less than unity when medium 1 is more conductive than medium 2. We then have:
a
a
1
+
P2
- (—
A
pi
Pi
0
(5-28)
—
p2
Figure 5.10 gives the value of a as a function of the ratio of the resistivities, for several
practical values of a/A. This figure shows that in order to reduce the resistance by half (a
= 0.5), it is necessary to reduce the resistivity of a hemispherical volume of soil of about
2.5 times the electrode radius by l/10th. Figure 5.10 can be used to determine the equivalent
radius ae of the electrode which, when buried in a uniform soil of resistivity P2, will have
the same resistance as the electrode embedded in the hemispherical heterogeneity of resistivity
Pl. This equivalent radius is:
a
e
= a/a
(5-29)
Of course, the earth potentials around the equivalent electrode will be different from the
potentials which exist around the original electrode, particularly at points close to the
boundary between medium 1 and medium 2. However, when the volume of the heterogeneity
is small with respect to the grounding system dimension, this concept of equivalent radius
can be used to approximate the effect of the heterogeneity. To illustrate this, let us consider
the transmission line tower shown in Figure 5.11.
In this figure, we have assumed that the concrete in the foundations has an hemispherical
shape. Other shapes will be considered later. We also assume that the resistivity in the
concrete is significantly different from that of the remainder of earth, although this is
seldom the case in practice for small volume of concrete.
Firstly, the metallic elements of the foundations are replaced by an equivalent hemispherical
electrode. This is accomplished using the following approximations:
a- The metallic elements of one leg are considered as buried in a uniform soil
of resistivity p^.
b- The resistance R of this leg is computed.
c- The equivalent hemispherical radius
Pl/27rR.
5-19
a
is deduced from the relation a =
RESISTANCE RATIO (p.u.)
Next, the resistance ratio a of the structure leg foundations (metallic elements and concrete)
is determined from Figure 5.10. Equation 5-29 gives the required equivalent radius ae-
HEMt SPHERICAL HETEROGENEITY
EQUIVALENT RADIUS
RESISTANCE RATIO
a/A=0
EQUIVALENT RADIUS
= a/a
Figure 5.10
Effects of a Hemispherical Heterogeneity
STRUCTURE
FOUNDATION
Figure 5.11
Tower Foundations
.2
5.4.2 VERTICAL ROD EMBEDDED IN A CYLINDRICAL SHELL
Hemispherical electrodes are rarely used in practice. Moreover, very few grounding systems
can be approximated by a hemispherical electrode. Most grounding systems consist of
cylindrical conductors with a radius significantly smaller than the conductor length or spacing
between conductors. In most cases, the buried elements of a metallic structure are connected
to the grounding system and therefore are part of it. These metallic elements are generally
linear and have a small cross-section relative to their length. Often, several vertical elements
of the structure are embedded in a small volume of concrete.
These comments suggest that the case of a vertical rod embedded in a small cylindrical
volume of a material with a resistivity different from that of the local soil, is of considerable
interest.
This problem has been thoroughly investigated in [37]. However, the proposed method did
not consider the distortion of the equipotential surfaces due to the lower extremity of the
rod. In the following analysis this distortion effect is approximated using the cylinder-hemisphere
concept originally proposed in reference [38]. This concept is illustrated in Figure 5.12. The
thickness of the material enclosing the vertical conductor is assumed to be small compared
to the conductor length. Thus, the earth current flowing out from the conductor surface can
be assumed to flow radially (perpendicular to the conductor surface) within medium 1, since
it is assumed that the rod and medium 1 surfaces are concentric as shown in Figure 5.12.
Thus, both surfaces, as well as any intermediate concentric surfaces, are equipotential. The
resistance between any pair of these surfaces can then be computed using the conventional
relation between resistance and resistivity.
Figure 5.12
Small Cylindrical Heterogenous Material
Assuming that the lower extremity of the vertical rod is hemispherical, the resistance dRj
between two infinitely closely spaced equipotential surfaces (located at r and r+dr respectively)
is given by the relation:
length
dr
dRi = resistivity ------------------------- = Pi -------------------cross-section
2Trr£ + 2 tit2
5-21
The total resistance between the conductor surface and the boundary surface between medium
1 and medium 2 is therefore:
A{a + H)
Pi
= ------ 1 n
Ri
(5-30)
a (A + £)
IttI
The difference between this resistance
and the resistance R2 obtained using Equation
5-30 with a different resistivity P2 (rod in uniform soil), is given as:
(Pi - P2)
A (a + l)
AR = Rj - R2 = -------------- In ------------2Tr£
a(A + £)
(5-31)
The ground resistance of a vertical rod with a radius a
given with excellent accuracy by the following equation:
much larger than its length £ is
p2
21
R = ------ In —
Ziri
a
(5-32)
This equation assumes a uniform soil of resistivity P2.
The actual resistance of the rod embedded in the material of resistivity P^ which in turn
is surrounded by the soil with a resistivity P2 is therefore:
2£
P2
R
1n
= R + AR =
2tt£
+
(pi “ P2)
- -------------- 1 n
(1 + £/a)
2tt£
_(1 + £/A).
(5-33)
Equation 5-33 can then be used to determine the equivalent radius of the vertical rod which,
when buried in a uniform soil of resistivity P2, will have a ground resistance equal to
Rt. This is achieved by equating (5-33) with (5-32) where a is replaced with ae. This leads
to:
1 + £/a
a
e
(1”Pl/p2)
(5-34)
a
1 + £/A
Inspection of Equation 5-34 reveals that when P]^ < P2, the equivalent radius is larger than
the actual vertical rod radius. The reverse is also true. This is as expected, since the
resistance decreases when the radius increases. Figure 5.13 shows plots of the ratio, /? =
ae/a, as a function of the resistivity ratio P2/P1 for several practical values of the radius
ratio a/A. The results of this figure are based on a rod length to radius ratio of 20 (£/a =
20). For a group of rods, the equivalent radius concept must be used prior to establishing
the ratio j8.
It is important to note that a number of assumptions and approximations have been made
in order to determine the equivalent rod radius as determined from Equation 5-34 or
from Figure 5.13. Careful examination of a problem, together with sound engineering judgment,
is the only reliable method of determining whether or not the preceding approximate techniques
are applicable. For instance, if the value Pj of medium 1 is only slightly different from
P 2, it is certainly more expedient in ignoring the disturbing medium, with a minimal loss
in accuracy.
5-22
a/A =
a/A = 1
EQUIVALENT RADIUS ae
RADIUS RATIO
RESISTIVITY RATIO p2/p
RESISTIVITY RATIO (p.u.)
Figure 5.13
Effects of a Cylindrical Heterogeneity
5.4.3 VERTICAL ROD ENCASED IN AN ELLIPTIC SHELL
The cylinder-hemisphere equipotential surface concept, presented in the previous section, can
readily be demonstrated to be a valid approximation. At large distances from the rod, the
equipotential surfaces are practically hemispheres. At short distances, these surfaces follow
the assumed cylindrical-hemispherical shape of the rod. At intermediate distances, however,
the shape of the equipotential surfaces around a cylindrical rod is, in fact, more complicated.
For this reason the analysis in Section 5.4.2 was restricted to small volumes of material in
medium 1. It is believed, however, that the method is still reasonably accurate when moderate
volumes are considered.
As will be shown, in a uniform and isotropic soil, the equipotential surfaces around a
cylindrical, vertical conductor can be represented with a high degree of accuracy as
semi-ellipsoids of revolution. This property has been used in [39] to investigate the effectiveness
of conventional chemical and mechanical treatment of the local soil around grounding
electrodes in order to lower their ground resistances.
A method based on the elliptic equipotential surface concept is not only more accurate than
the previous one, but is valid for any volume of medium 1, provided that the shape of this
volume corresponds, or can be approximated by, one of the equipotential ellipsoids. This case
is depicted in Figure 5.14.
5-23
Figure 5.14
Elliptic Shell
The equation of an ellipsoid with center at the origin of a rectangular coordinate system
xyz with semi-axes lengths C, D, B is (see Figure 5.15):
When C = B, i.e., the ellipsoid is an ellipsoid of revolution with respect to the axis y. In
this case we have:
x2/D2 + t2/B2 = 1
(5-35)
t
(5-36)
where
y2 + z2 '
We also have the following relation between the major and minor semi-axes D and B and
the distance from center o to focus F or F':
D2 = B2 + l2
Figure 5.15
(5-37)
Ellipsoid
5-2b
As has been shown, the earth equipotential surfaces around the vertical rod shown in Figure
5.14, are semi-ellipsoids of revolution. More precisely, the lower focus of the equipotential
surface is exactly at the lower extremity of the rod. Consequently, for each equipotential
surface defined by its minor semi-axis B (distance from the rod to the equipotential surface),
the major semi-axis D (depth of the equipotential surface) is related to B, and to the rod
length, according to Equation 5-37. The preceding statement will now be proved.
The potential caused by a segment of conductor at any point (u, v, w) in the first layer of
a two-layer earth, is given by Equation 5-20 where u0, v0, wQ are replaced by u, v, w.
When the conductor consists of the vertical rod of Figure 5.14 and its image with respect
to the earth surface plane, (assuming that the conductor is buried in an infinite medium of
uniform resistivity, as in the case of Figure 5.15), Equation 5-20 simplifies to:
pi
(L-u) + ^(L-u)2 + t2
U = ----- In -----------47TL
------
-u + \u2
(5"38)
+ t2
where, I is the total conductor current, L its length (L = 2 £),
resistivity and t is given by Equation 5-36.
P is the
medium
The equipotential surfaces around the conductor are defined as U(u,y) = constant, which is
equivalent to:
(L-u) +V(L-u)2 + t2'
Y = ------------ r
-u +\u
(5-39)
------+ t
This can be simplified to:
(Y-1)2
yl2
u(u-L) + ---------- t2 = ---------by
(y-1)2
Since, u = x + H and L = 2£, this last equation becomes:
Ky +
D
(y - D
iiyfy'
(y - 1)
Equation 5-40 has the same form as Equation 5-35, and therefore, we can conclude that:
•
The equipotential surfaces are ellipsoids of revolution.
•
The center of the ellipsoid is at the center of the conductor consisting of the
rod and its image. Since the problem is symmetrical with respect to the earth
plane, this center is also at the upper extremity of a ground rod.
•
The major and minor semi-axes of the ellipsoid, D and B, are related to the
constant y according to the following equations:
nyfT
B = ----------(y-1)
l{y + 1)
D = ---------------(y- 1)
5-25
(5-41)
from which:
D2 = B2 +
l2
therefore, from Equation 5-37 we can state that:
•
The lower extremity of the rod is a focus of the ellipsoid.
Consider now the vertical rod shown in Figure 5.14. The resistance of the soil between the
conductor surface and the boundary surface between medium 1 and medium 2 is:
Uc " Ub
cb
where Uc is the conductor surface potential and Uj-, is the boundary surface potential. These
potentials are determined from Equation 5-20, i.e., for a uniform soil and a ground rod
driven to a depth £ in the soil:
(£-u)
Pil
U = ----- In
+yj(£-u)2
-u + -^u2 + v2 + w2
2tt&
potential of the rod (u = o ;
£
Pil
= ----- In
c
2ir£
U
+ v2 + w2
+yjn2
v^ +
=
+ a2
(5“42(a))
a
and since a « £:
U
2£
Pil
= -----c
2ir£
(5-42(b))
In
La _
The potential at the boundary surface (u = o ;
Pil
Ub =
v^ + w^ = B^) is:
£ +VF + B"
1n
27r£
which, based on Equation 5-37 simplifies to:
Pil
Ub =
£ + D
In
(5-^3)
2ir£
therefore:
2£'
Pi
cb
1n
'£ + D
(5-44)
- 1n
27r£
B
The resistance between the boundary surface and remote ground (at zero potential) is:
£ + D
Pzi
boo
1n
2tt£
(5-45)
.
B
5-26
Thus, the total ground resistance of the encapsulated ground rod is:
R
Pi
------ 1 n
27t£
t
2£
—
a
(P2-P1)
+ ------------- In
2ir£
-1
(5-46)
B
J
The equivalent radius of the rod buried in a uniform soil of resistivity P2 has the same
resistance
defined as:
P2
R
= ----- In
27r£
2£
(5-47)
a
from this:
a
I" 2£/a
= a I ------------e
I (£+D)/B
(I-P1/P2)
The radius ratio /8 = ae/a is plotted in Figure 5.16 as a function of P 2/ P1, for several
values of a/B, and for the case where £/a = 20.
Equation 5.47 is valid provided that a « £ . When the rod radius can not be neglected with
respect to its length, the equivalent radius formula should be derived using Equation 5.42(a)
instead or 5.42(b).
5.4.4 COMPARISON BETWEEN THE EQUIPOTENTIAL SURFACE METHODS
In order to permit meaningful comparisons between the results of Figures 5.13 and 5.16, the
volume of medium 1 should be the same in each case, i.e.:
4
4
'irA2£ + — tiA3 = — ttET 4B2 + £2
6
6
This simplifies to the cubic equation:
c2y3-(£2/a2)y -1=0
(5~48)
where
y = (a/b)2
A2
/ 3£
A
c = 7U+r
Equation 5-48 has only one positive real root. This provides the approppriate minor axis B
for each value A of the radius of the cylindrical surface considered in Figure 5.16.
Figure 5.17 shows the radius ratio (/3 = ae/a) computed using the cylindrical (dotted curves)
and ellipsoid (solid curves) methods. These curves were derived using the equivalent volume
concept. As expected, there are significant differences between the results.
5-27
ft/a = 20
a/B =
a/B = 1
EQUIVALENT RADIUS ae
RADIUS RATIO
RESISTIVITY RATIO p2/p
RESISTIVITY RATIO (p.u.)
Figure 5.16
Effects of an Elliptic Heterogeneity
•0.155
- a/A
•0.722
a/A = a/A =
a/B = a/A - 1
EQUIVALENT RADIUS ae
RADIUS RATIO
RESISTIVITY RATIO p2/pi
RESISTIVITY RATIO (p.u.)
Figure 5.17
Equal Volume Base
5-28
The ellipsoid method is, in theory, more accurate than the cylindrical method. However, in
practice, the shape of the excavation containing medium 1 (concrete, soil replacement, etc.)
is generally rectangular or cylindrical. Consequently, the real equipotential surfaces in the
vicinity of the rod are distorted somewhat, and their shape is probably intermediate between
a cylindrical-spherical surface and an ellipsoid. Therefore, the radius ratio /3 should be
selected using the curve which represents the average of the shaded area.
The hemispherical approach is probably useful when chemical treatment of the soil around
the electrode is used to decrease the local soil resistivity.
It is clear from the previous discussion, that in practice, no method can be considered as
superior to the other. Depending on the problem, one method may be more appropriate than
the other. In many cases, the three concepts can be advantageously applied to determine a
suitable equivalent radius. Briefly stated, the three methods described in the preceding
sections should be considered as useful, but approximate, techniques, and should be
applied with good engineering judgment.
Additional curves based on different values of the ratio £/a are given in Volume 2.
5.4.5 EXTENSIONS AND LIMITATIONS OF THE EQUIPOTENTIAL SURFACE METHODS
The hemispherical, cylindrical, and ellipsoid methods are all based on a well-known technique
from electrostatic theory. This technique is derived from the principle which states that any
equipotential surface (U = constant) can be replaced with a thin metallic surface maintained
at the potential U, without altering the problem.
Thus, when the equipotential surface around a grounding system is known, the resistance of
the grounding system may be obtained. The resistance is equal to the resistance between
added to the resistance of
the grounding conductor surface Sc and the boundary surface
the equipotential boundary surface (assumed to be a thin metallic sheet) buried alone in the
natural soil. For application of this electrostatic principle, the equipotential surface boundary
between the material, in which the grounding system is embedded, and the remainder of
natural soil, must be assumed to be equipotential. This procedure is illustrated in Figure
5.18.
ELECTRODE SURFACE Sc
^ ACTUAL
1
BOUNDARY
SURFACE S
REMOTE
HEMISPHERICAL
EQUIPOTENTIAL
SURFACE
APPROXIMATE
BOUNDARY
SURFACE
(a) ACTUAL PROBLEM
(b)
Figure 5.18
EQUIVALENT PROBLEM
The Equipotential Metallic Sheet Principle
5-29
It should be noted that, although the equivalent problem depicted in Figure 5.18(a) cannot
provide the earth potential values in medium 1, the earth potentials in medium 2 remain
identical to the real case.
Thus, the problem reduces to determining the equipotential surfaces around the grounding
system. This is a complex problem in uniform or multi-layer earth structures and, in most
cases is impossible to resolve when localized earth heterogeneities are present. Our effort
is not vain, however, if we restrict ourselves to heterogeneities enclosing the ground system
conductors, particularly, as in the case of transmission line grounding, where concrete and
other backfill materials are used. In such instances, suitable approximations, together with
the analytical techniques presented in this chapter, yield reasonably accurate solutions.
We will now discuss the step-by-step procedure required to achieve this goal.
The type of problem to be analyzed is shown schematically in Figure 5.19. The problem
is limited by the following assumptions:
a) Except for the localized heterogeneities, the earth is a uniform or two-layer
structure. Multi-layer earth can be handled in a similar fashion, but the equations
are considerably more cumbersome and will require considerably more computing
time.
b) The earth potentials in the volume delimited by the heterogeneities are not
of interest in these calculations, but rather will be determined in a separate step
(step 8).
Figure 5.19
Illustration of a Typical Problem
The procedure is as follows:
Step 1- Analyze the problem as if there are no localized heterogeneities, using the analytical
methods provided in this chapter. Let Rc be the computed ground resistance.
Step 2- Determine the equipotential surfaces around the grounding system up to the
equipotential surface
which, approximately (on an average volume basis, for example),
encloses all the heterogeneities.
Step 3- Replace all materials which exist between the ground conductors surface Sc and the
equipotential surface Sfo, with an equivalent average resistivity pa based on the
respective resistivity and volume of each single material removed.
5-30
Step 4- Knowing that the earth current stream lines are orthogonal to the equipotential
surfaces, compute the total resistance Rcb between the grounding system surface and surface
S{-), by adding the elementary resistances calculated between two closely spaced equipotential
surfaces located at r and r + Ar. In this step, it may be necessary to subdivide the volume
between these closely-spaced surfaces into smaller regular volumes.
Step 5- Replace the equipotential surface
with a metallic cage consisting of cylindrical
metallic conductors. This cage should resemble, as much as possible, the shape of the
equipotential surface S^.
Step 6- Compute the ground resistance Rboo of this cage when buried in the earth free
of the localized heterogeneities. Let V^oo be the earth potentials at any point outside this
cage.
Step 7- The approximate resistance of the grounding system in the real earth structure is
then:
R,n = R cb, + R,b°°
The actual potential rise of the grounding system is therefore:
uh = y
where I is the grounding system current.
The actual potential value of the equipotential surface Sj-, is:
U:=U
t>
c
- R
cb
l
=
R
cb
J
and the earth potentials at any point outside this equipotential surface are:
“b - W(IRbJ = V(lW.-'>
Although this may appear to be a simple procedure, considerable computational effort is
required to determine the equipotential surfaces. Thus, unless the maximum possible accuracy
is required, the design approach should commence with the determination of an equivalent
model, based on the spherical, cylindrical or ellipsoid approximations. When these methods
are not applicable, the real problem should be simplified to a problem requiring a minimum
of computation in each step. Fortunately, transmission line grounding problems are, in practice,
amenable to such approximations.
As mentioned at the beginning of this section, one further step may be required in some
cases. This additional step is required to determine the earth potentials within the volume
delimited by the equipotential surface Sj-,. This is a very approximate procedure when dealing
with several isolated heterogeneities of dissimilar materials as illustrated in Figure 5.19.
The earth potential at a point M within this volume is approximated as follows, however:
Step 8- Determine the equipotential surface Sm which traverses point M. Sm is selected
from the surfaces already determined in step 1. Next, as in step 4, compute the resistance
Rcm between the grounding system surface and surface Sm (based on average resistivity
P a). The potential of surface Sm is:
This is also the earth potential at point M.
5-31
5.4.6 CONCRETE ENCASED GROUNDING ELEMENTS.
Most of the commonly used metallic transmission line structures are made of steel and are
of the four-legged lattice type (towers) or of the single shaft tubular type (poles). Typical
foundation arrangements for these structures are shown in Figure 5.20. The tower foundation
consists of a concrete pier where one leg of the tower is embedded. Depending on the
mechanical requirements, there may be reinforcing steel bars in the concrete. The steel pole
foundation usually consists of a cylindrical anchor bolt cage embedded in a concrete pier
and surrounded by a number of reinforcing bars, also embedded in the concrete.
Figure 5.20
Typical Concrete Foundations
There is considerable controversy on the current conduction properties of concrete
[41-44], The facts that concrete consists of a variable mixture of materials of different
grain sizes and that concrete may be buried in various types of soil, might explain why
contradictory results have been reported in the literature.
There is ample experimental evidence [40,41] which shows severe damage to concrete as
a result of sustained or short duration alternating currents flowing from concrete encased
conductors. However, other experimental tests and considerable operating experience [37,42-44]
shows, equally well, that concrete encased ground conductors have very substantial ground
current capability and, therefore, are as effective or sometimes superior to equivalent
conductors in direct contact with soil.
Both results are credible and differ only because of the duration and magnitude of test
currents and soil conditions. The moisture content is a particularly important factor. There
are other factors which influence the conduction process to a lesser degree.
As explained in Chapter 4, current conduction in earth is primarily a function of the
electrolytic content of soil, i.e., presence of water and salts, acids, etc. Similarly, concrete
resistivity is a function of its moisture content. However, due to its inherent alkaline
composition, hygroscopic nature and density, it is less sensitive to the content of salts or
acids in the soil moisture and thereby, is more dependent on its inherent water content.
Since concrete in the earth tends to draw moisture from the local soil, concrete resistivity
is comparable to or lower than the local soil resistivity, provided that the volume of the
concrete is moderate enough to permit water infiltration through the whole volume. When
wet, concrete resistivity values range from about 30 fi-m to approximately 300 fi-m. When
dry, concrete is a very poor conductor with resistivity values ranging from a few kfl-m to
more than 10 kf2-m.
5-32
Conduction Current Process in Concrete
Recent tests conducted in Poland concerning the effects of lightning and alternating currents
on reinforced concrete foundations [44] have identified three different mechanisms of electric
conduction through the concrete: (1) electrolytic, (2) spark discharges, (3) arc discharges.
The results of the tests show that concrete foundations are able to repeatedly conduct very
high lightning currents without noticeable damage, but may be severely damaged during high
momentary short-circuit currents or sustained low magnitude fault currents [40]. In general,
it appears that such damage is possible only when a certain critical energy distribution in
the concrete is attained during the current conduction process.
When the current density and the electric field gradient within the concrete are low, the
conduction process is purely of the electrolytic type and the ratio of voltage to current is
constant, i.e.:
v(t)
R (t) = ap (t) = ------- = constant
i(t)
where, v(t) and i(t) are the applied voltage and resulting current, R(t) is the dynamic
resistance, p(t) is the apparent resistivity, a is a constant depending on the means of injecting
test current into the concrete, and t is the time.
When the test voltage and current are progressively increased, the energy dissipated in the
concrete starts to evaporate the water contained in the voids and microcracks of the concrete.
As a result, the potential gradients at the location of the evaporation increase significantly
(5-8 kV/cm) and cause spark discharges which quickly propagate within the concrete volume.
Concurrently, a significant reduction in the electric field follows the occurence of spark
discharges. Therefore, the dynamic resistances and apparent resistivity of the concrete
decrease substantially.
If the test current is further increased, the least resistance spark channel will quickly
transform into an arc channel where most of the current will flow. This arc channel may
cause severe damage to the concrete foundation.
Figure 5.21 shows typical dynamic resistance curves, R(t), obtained during laboratory
experiments [44]. These curves clearly show the electrolytic conduction zone, a transition
zone where the dynamic resistance decreases rapidly, and the spark discharge zone, where
concrete behaves as if its resistivity is considerably reduced from the static value.
12
14
16
18
CURRENT IN KA
Figure 5.21
Dynamic Resistance of Concrete (Redrawn from [44])
5-33
Each curve shown in Figure 5.21 corresponds to a test current with a different peak value.
During these short duration current tests (which emulate lightning currents), no visible damage
to the concrete was observed. The concrete surface current density reached about 3 A/cm2
(20 A/in2). Other tests show that a current density from 5 A/cm2 to 10 A/cm2 (30-60 A/in^)
is required to cause visible damage.
When the current density exceeds 10 A/cm2, arcs initiate fusing of the concrete.The result!no
pressure build up due to excessive heat in the voids causes explosions which are directed
towards the outside of the foundation. These result in the formation of craters which
may be up to 4 to 6 cm in diameter (1.5-2.5 in) and 2 to 3 cm in depth (about 1 in) if the
current concentrates in a single arc channel.
All of these tests indicate that no damage to the concrete foundations should be
expected when the surface current density is below 5 A/cm^, that some damage will occur
at values ranging from 10 to 15 A/cm^ and, finally, severe damage can be expected when
the current density exceeds 15 A/cm^. It should be noted that the current density is not
the only criteria. The duration of the current is also critical. During impulse currents,
the safe limits are significantly higher, while under adverse conditions, substantially lower
sustained currents may cause considerable damage. The limiting current density values given
in this paragraph generally apply to power frequency short-circuit currents from 0.1 to 0.5
seconds duration.
Practical Situations
The results reported in the preceding section are based on laboratory measurements which
were not intended to duplicate conditions existing in actual installations. In the following,
the current densities which are likely to exist in the concrete foundations of a transmission
line structure during fault conditions are examined.
Impulse Current
Lightning currents rarely exceed 200 kA. Based on the dimensions of modern high voltage
structure foundations, the concrete current density will not exceed 20 A/cm2 if 0ne foundation
is considered and 5 A/cm2 when the four leg foundations are involved. Considering the facts
that high magnitude lightning currents are of extremely short duration, that concrete can
withstand a much higher voltage under impulse currents and that the transmission structure
usually has supplemental grounding elements and is often connected to a ground wire, both
of which can divert significant portions of the current, it can be concluded that concrete
damage due to lightning currents is unlikely except for relatively small isolated structures.
This conclusion is supported by many years of operating experience over thousand of
miles of transmission lines.
Momentary Currents
Short-circuit currents in the order of 100 kA are very possible now or in the near future.
Their duration is limited to few cycles by modern high-speed relays, however. Based on the
large dimensions of foundations required to support such high voltage structures, a concrete
surface current density of 2 to 4 A/cm2 is an upper limit, even when supplemental grounding
elements and overhead ground wires are disregarded. A more typical value of 1 A/cm^ is
significantly below the safe limits quoted previously. Consequently, no damage should result
from short-circuit currents flowing in the concrete foundations of high voltage lines. This
is also confirmed by operating experience.
There is a situation, however, which may lead to a considerable increase in the concrete
surface current density. This adverse situation occurs when metallic structures (such as
pipelines), not connected to the transmission structure, are buried close to one of the faulted
structure foundations. In this case, most of the fault current concentrates in a narrow channel
along the shortest path from the foundation to the metallic structure. Surface current
densitites may reach hundreds of A/cm2.
Sustained Currents
Sustained fault currents rarely occur on high voltage transmission lines. This type of fault
is likely to occur on distribution lines not equipped with overhead ground wires and when
the fault occurs at a large distance from the distribution transformer or when the faulted
structure is poorly grounded. Under these very unfavorable circumstances, the continuous
flow of current through the structure may cause severe damage to transmission line tubular
steel (or reinforced concrete) poles with relatively small concrete foundations. In some
documented cases, severe arcing has occured and resulted in the destruction of concrete
poles [40,41]. The arcing phenomena referred to is shown in Figure 5.22 for reference.
I- TRANSITION ZONE
REGION OF HIGH
TEMPERATURES
REGION OF SPARK DISCHARGES
REGION OF ARC DISCHARGES
Figure 5.22
Arcing Process in a Concrete Distribution Pole (Redrawn from [40])
As a general conclusion concerning the behaviour of the concrete foundations of transmission
line structures conducting fault currents, it can be safely stated that no damage is likely
to occur under any type of fault which causes current circulation in the foundations. Therefore,
no special precaution is required to separate the structural metallic elements or rebars in
the foundations from the supplemental grounding elements.
As a guide to allowable current densities, an upper limit (conservative) of 5 A/cm2 can be
used for current durations in the order of 0.1 second. It is suggested that below 0.1 second
the product of the current density in A/cm^ and the square root of the time in seconds,
should be kept below 2 to remain within the same conservative test result limits.
5.5 CONTINUOUS COUNTERPOISES
In the foregoing sections, the ground conductors have been assumed to be of such short
length that the voltage gradient along their length can be neglected. For lengthy
grounded conductors, it is necessary to consider the longitudinal voltage drop along the
conductor.
Cable sheaths, railroad tracks, pipelines and transmission line continuous counterpoises are
typical examples of long metallic conductors totally or partially in direct contact with soil.
The current flowing in such conductors will induce a voltage drop due to the internal
impedance of the conductor.
5-35
The continuous counterpoise consists of one or two conductors buried continuously under the
transmission line or along certain sections of the line. The conductors are interconnected to
the overhead ground wire and ground system (if any) at each transmission line supporting
structure.
5.5.1 PERFORMANCE OF AN ISOLATED CONTINUOUS COUNTERPOISE.
Figure 5.23 shows a continuous counterpoise of total length & =
buried in a
uniform soil at a depth e below the earth's surface. A low frequency alternating current 1°
= Ii + l£ is injected in the counterpoise at a point A corresponding to u = o and w = e
with respect to the uvw coordinate system, where the u axis is parallel to the counterpoise
and the plane defined by the u and w axes is the earth's surface. The return current electrode
is assumed to be located at a large distance from the counterpoise (remote earth) so as not
to interfere with its performance. Finally, it is also assumed that there are no other buried
metallic structures (isolated counterpoise).
U°
0
Mr
_______ ---------- “T-TPFT”
;
!
u
I
^!
a
!
♦
W
REMOTE
(POTENTIAL = 0 V)
Figure 5.23
Isolated Continuous Counterpoise
The current entering the left and right side of the counterpoise at the injection point A(u=o,
w=e) are I^ and if respectively. Let I(u) and U(u) be the current and earth potential
of the counterpoise at distance u . Figure 5.24 shows an enlargement of an infinitesimal
element of the counterpoise between distance u and u + du.
I(u+du)
I(u)
— *-
U(u)
—njuL—'wows'—
c =
■[]6
U(u+du)
u+du
Figure 5.24
Infinitesimal Counterpoise Element
5-36
The application of Kirchoff's laws to this elementary circuit leads to the following expressions
for the current and potential of the conterpoise at distance u + du:
dI(u) = l(u + du) - I(u) = - (G + jojC)duU(u)
(5-^9)
dU(u) = U(u + du) - U(u) = - (r + ja)A)dul(u)
(5-50)
where r, X, G and C are the electrical parameters of the counterpoise, i.e.:
r is the unit length resistance (ohms)
X is the unit length inductance (henrys)
G is the
unit length shunt conductance (to ground),(mhos)
C is the
unit length shunt capacitance (to ground),(farads)
The current I, or the potential U, can be eliminated from the pair of simultaneous Eguations
5-49 by differentiating with respect to u. When this procedure is applied to the counterpoise
current, the classical wave equation is obtained:
d2I
--------- a2I = 0
(5-51)
du
where
z = r + ja)A
Y = G + JojC
a is the complex propagation constant. The general solutions of the differential Equation
5-51, assuming that z and Y are independent of u , are:
T
au
,
-au
11 = aie
+ b1e
;
,
.
when u < 0
,
au
-au
12 = 826
+ b2e
;
.
. „
when u > 0
Two similar, but different, expressions are required for the counterpoise (longitudinal) current,
since this current is not defined at u = 0. It is defined, however, at u = ± e, where e is
an infinitely small positive number:
11 = Ii
;
atu=e
12
;
atu = + e
~
12
The constants are determined from the boundary conditions:
Ii = 0
9
when u = -Al
12 = 0
9
when u = £2
II = I?
when u = 0"
I2 = 1°
when u = 0+
and
Ui(u=-e) = U2(u=+e) = u'
when e
5-37
0
This last boundary condition states that unlike the current I, the counterpoise potential U
is continuous around u = 0. From Equation 5-50, this condition is equivalent to stating that:
/
1 dlA
/
1 dl2\
\
V du / u=+e
= U°
\ Y du / u=-e
when e
0
after some elementary algebraic transformations, the following solutions are obtained:
u < 0
cosh(aiz)
ii = -r
, i nh|a(Jli + u)J
(5-52)
i i nh(a£)
u > 0
cosh(a£i)
inhja(£2 " u)J
I2 = I1
(5-53)
s i nh (ail)
The counterpoise potential is now easily determined from Equation 5-49. The following
solutions are obtained:
u < 0
cosh(a£2)
r
-|
Ui = I°g --------------- cosh a(£j + u)J
sinh(a£)
(5-54)
u > 0
cosh(a£i)
U2 = I 0 (
....
T
cosh
j^a(£2 - u)]
(5-55)
a(iz
sinh(a£)
where
= 'Jz/Y
The potential rise of the counterpoise at the current injection point (u = 0) is therefore:
cosh(a£i) cosh(a£2)
U° = I°f
sinh(a£)
and the ground impedance of the counterpoise as seen from this current injection point
is:
cosh(a£i) cosh(a£2)
Z = U°/I0 =
s i nh |^a(£i + £2)J
Specific Cases and Practical Considerations
When the injection point is at one extremity of the counterpoise (£j^ = 0 ;
ground impedance is:
Z = 8 coth (a£) =
■^z/y'coth
zY£
£2
£), this
(5-56)
5-38
When the injection point is at the center of the counterpoise, (Equation 5-55
reduces to:
3
Z = — coth(a£/2)
V
(5-57)
z'/Y coth
2
where
z' =
z/k
A comparison of Equation 5-56 and 5-57 shows that energization of the counterpoise from
its center is equivalent to reducing the self impedance of the counterpoise by four times
when energized from one of its extremities. Thus, the counterpoise is applied more effectively
when energized from its center.
When the product VzY i is large, the hyperbolic cotangent is approximately equal to unity.
The counterpoise ground impedance is then:
Z =^/z/y‘
(5-58)
This is the case for very long counterpoises or when a = VzY is large. At power frequencies,
the counterpoise capacitance C can be neglected compared to its conductance G . Therefore,
Y ~ G = l/Rj, where Rj is equal to the counterpoise distributed ground resistance in
ohms/meter. Hence, the ground impedance given by 5-58 becomes:
z
The distributed ground resistance, Rj (per unit length), of a counterpoise can be calculated
using the general equations developed in Section 5.3, for a unit length of conductor. When
the counterpoise is buried close to the surface of a uniform earth, the ground resistance is
approximately:
P
21
R = —
In _
Ttl
■y 2ae
(5-59(a))
where l is the counterpoise length, a is the radius and e is the depth of burial. Therefore,
the counterpoise distributed ground resistance per meter of conductor is:
P
R
d
21
'
(5-59(b))
R£
TT
yfae
Figure 5.25 gives the modulus of the ground impedance of a counterpoise buried in a uniform
soil with respect to its length £, for several values of soil resistivity p and for injection
points at one extremity and the center of the counterpoise. Figure 5.26 shows the effect
of frequency on the ground impedance of a counterpoise of length £, buried in uniform soil
of 100 fl-m resistivity and for an injection point at one extremity. Additional ground
impedance curves are also provided in Volume 2 of this report.
The characteristics of the counterpoise are as follows:
Conductor: copperweld conductor
Radius a: 0.5 cm (0.2 inch)
Depth of burial e: 0.5 m (20 inches)
5-39
Capacitance C: 0.03 MF/km (0.03 MF/mi)
Resistance r: see next paragraph
Inductance X: see next paragraph
Distributed resistance Rj; as computed using Equation 5-59(b)
The self impedance of the counterpoise r + jwX has been computed using program LINPA
(see Chapter 3 and Appendix A) for each value of soil resistivity and current frequency.
Rigorously, the computations performed by LINPA are valid for very long overhead conductors.
However, the results provide a good estimate of the exact values. Additional information is
also provided in Chapter 2.
An examination of Figure 5.25 and 5.26 leads to several interesting conclusions regarding
the performance of counterpoises during steady- state conditions. Among these are:
a- There is an effective counterpoise length, £e, above which the ground impedance
is essentially constant. This is equivalent to stating that beyond £e, the current
flow in the counterpoise is nearly zero. This effective length is approximately 3
to 5 times l/a, i.e., £e — ^/a.
b- The effectiveness of a counterpoise increases as soil resistivity increases. When
the modulus of the counterpoise ground impedance is compared with the ground
impedance for a perfect conductor, it is clear that long counterpoises provide an
effective means of reducing ground impedance in high resistivity soils.
c- The performance of a counterpoise deteriorates very quickly as the frequency
of the current increases. Figure 5.26 clearly shows that the effective length of
the counterpoise decreases rapidly as the frequency increases. This illustrates the
effect of transient currents of very short durations. Other phenomena such as
soil breakdown and wave reflections also will significantly alter the transient
behaviour of the counterpoise.
d- As mentioned previously, it is preferable to inject the current from the center
of the counterpoise rather than from an extremity. Thus, several counterpoises
radiating from a center common point are apparently more effective than a single
counterpoise having the same total length and energized from one of its extremities.
This conclusion is based on the assumption that the distributed ground resistance
is constant over the length of the grounding system. This assumption, although
not generally valid for a single linear counterpoise, is a good approximation.
Unfortunately, the assumption becomes less and less accurate as the number of
conductors radiating from a common center point increases. In this case the
resistive coupling between the branches is not negligible and, therefore, should
be considered in the computations. As a result, the ground impedance of the
counterpoise system will increase as the number of branches is increased, while
the total length is kept constant.
Although not analyzed in this section, it is reasonable to assume that an optimized counterpoise
system of a given length should consist of a number of elements arranged such that the
resistive coupling is minimal and the system is energized from several points, suitably located
on each element. Unfortunately, the analysis of such a counterpoise system requires considerably
more computations than are required for an isolated linear counterpoise. Some typical results
from computer solutions of the counterpoise problem are discussed briefly in Section 5.5.3.
5-40
EXTREMITY INJECTION
CENTER INJECTION
FREQUENCY = 60 Hz
C = 0.0 and 0.03 jF/Km
10000 ft-m
10
n-m
PERFECT
CONDUCTOR
COUNTERPOISE LENGTH (meters)
Figure 5.25
Ground Impedance of a Counterpoise
5.5.2 COUNTERPOISES OF TRANSMISSION LINES.
Transmission line counterpoises do not usually extend beyond the narrow right of way corridor
of a line. Thus, continuous conterpoises follow the line and are connected at each structure.
Crow-foot (radial) counterpoises have short branches which rarely exceed 50m (150 feet) and
thus, can be considered as a concentrated grounding system whose performance can be
analyzed according to the method presented in Section 5.3. If the length of the counterpoise
branches are too great to permit this approach, the method presented in this section can
be used without any modification.
5-^1
p = 100 ft-m
Cl = EXTREMITY
C = 0.0 and 0.03 uF/Km
500 KHz
100 KHz
50 KHz
10 KHz
5 KHz
1000 Hz
500 Hz
100 Hz
.60 Hz
50 Hz
20 Hz
PERFECT
CONDUCTOR
0.01 Hz
COUNTERPOISE LENGTH (meters)
Figure 5.26
Effects of Frequency on Counterpoise Impedance
In Section 5.5.1 the performance of an isolated continuous counterpoise was investigated.
Unfortunatly, the equations which were developed can not be applied to transmission line
counterpoises without significant loss of accuracy for the following reasons:
a- The per unit length ground resistance of a transmission line counterpoise is
not constant over the length of the counterpoise. This results not only from the
variations in the mutual ground resistance between the various elements of the
counterpoise, but because there is also an additional ground resistance due to the
structure foundations or other supplemental grounding elements at each transmission
line structure. This situation is illustrated in Figure 5.27.
b- When the transmission line is equipped with overhead ground wires, as in most
high voltage lines, the counterpoise is energized from multiple points along its
length, i.e., at each structure on both sides of the faulted structure (see Figure
5.27).
c- The mutual impedance between the counterpoise and the overhead ground wires
and the mutual impedance between the phase wires and the counterpoise can not
be neglected as they both have a noticeable influence on the performance of the
transmission line, including the counterpoise conductor.
d- In many cases, there are two counterpoise conductors, one buried on each side
of the transmission line. The mutual ground resistance between the counterpoise
conductors must be considered, otherwise a significant error will be introduced.
5-42
Phase Conductor
Ground Wire
'
Counterpoise
(a) ACTUAL PROBLEM
Transmission Line
Structure Groundina
(b)
Figure 5.27
,
Distributed
{
Resistai
Counterpoise
EQUIVALENT UNDERGROUND NETWORK
Transmission Line Counterpoise
Clearly, the concise equations of Section 5.5.1 can not be extended to cover the case of
transmission line counterpoises. This is primarily because the distributed resistance R cannot
be assumed to be a constant in the wave Equation 5-51 and because there are several
injection points along the counterpoise length.
Fortunately, an accurate solution can be obtained with the following method which requires
that the computations be performed using suitable computer programs such as LINPA,
GTOWER, and PATHS, described in the Appendices. These programs are based on the analytical
methods presented in this report. This method will now be explained.
Since it is possible to accurately analyze the performance of concentrated grounding systems
using the equations of Section 5.3, extended grounding systems can also be accurately studied
if they are broken down into a number of suitable concentrated grounding system arrangements.
In the case of the counterpoise shown in Figure 5.27, this is achieved through the following
steps:
Step 1
First, it is desirable to separate the effects of the inductive mutual coupling between
overhead and buried conductors, from the purely earth conduction effects. Based on the
steady-state superposition principle, the counterpoise can be considered to be made of
two fictitious conductors: an insulated conductor characterized by self and mutual impedances
identical to the original counterpoise values; and a bare perfect conductor, i.e., having zero
self and mutual impedances. Thus, the insulated fictitious conductor can be considered as
an additional overhead ground wire. Since the second, bare conductor can not experience a
voltage drop along its length, it is necessary to make a small opening at the middle of the
conductor section connecting the two structures as shown in Figure 5.28. Each section
between two consecutive openings will be raised to the potential of the structure to which
it is connected. Since this structure is also connected to the middle point of the corresponding
section of the insulated, fictitious, counterpoise conductor, this potential is the average
potential experienced by the real counterpoise between the opening locations.
It is possible to improve the accuracy of this simulation by further subdividing both fictitious
counterpoise conductors into smaller elements, regularly interconnected by perfectly conductive
jumpers. However, the improvement in accuracy is marginal and cannot justify the significant
increase in required computations.
5-h3
Ground
Wire
Phase
Conductor
Fictitlous 0/H
Counterpoise
FICTITIOUS PERFECTLY
CONDUCTING COUNTERPOISE
Figure 5.20
Equivalent Conductor Pair For a Counterpoise
Step 2
Each section of the fictitious buried conductor can now be considered as a concentrated
grounding system. The performance of one of these sections can be analyzed using the
equations of Section 5.3, provided that sections are separated by distances large enough to
justify neglecting their mutual ground resistances. Since this is not the case for this problem,
it is imperative to take this proximity effect into account. Two approaches can be used to
meet this objective:
•
The iterative approach
•
The average proximity effect approach
The iterative approach can be as accurate as necessary but requires considerable computation
time. In practice, however, such high accuracy is of academic interest only, since the earth
structure is very seldom uniform along the length of a counterpoise and several data values
are not precisely known. This approach is qualitatively described in step 3a.
The average proximity coupling effect is an approximate method which has the advantage
of being relatively easy to apply to practical problems.
Step 3a
1- Firstly, the mutual ground resistances between the buried sections are ignored and the
ground resistance of the sections (TL structure ground resistance) is calculated assuming
that each section is isolated from the other. Assume that Rf is the ground resistance of
section i.
2- The fault current distribution among the various structure ground resistances R° is
determined using the equations developed in Chapter 6, (see Figure 5.29). Computer program
PATHS, described in Appendix D, can be used to perform these calculations.
3- A better estimate of the previously determined ground resistance Rf can be obtained
by considering the influence of the neighbouring structures j (j = 1, i-1 and j = i + 1, n) which
inject a current Ij° into the earth. In practice, only a limited number of structures on each
side of structure i need to be considered, since the effect of distant structures can be
neglected. A new set of ground resistance values Rf is therefore determined (iteration 1).
New structure ground currents If can now be calculated using program PATHS.
4- The iterative process described previously is continued in sequence until the calculated
ground resistance R* (or current if ) at iteration k is not significantly different from the
computed value at iteration k-1.
5- At this stage (iteration k), the performance of the transmission line counterpoise can be
accurately determined from the computation results illustrated in Figure 5-30. For example:
The counterpoise ground impedance is:
I
k
f
Z =
where f designates the structure where the fault occurs and Ig^, Ig2 are the ground
wire currents on each side of the fault location.
The counterpoise ground potential at each structure i is:
The counterpoise ground potential at any intermediate location is determined from
the interpolated portion of curve between the computed structure potential points
(Figure 5.30(b))
The average longitudinal current in the section of counterpoise between structures
i and i+1 is given by the current in the fictitious insulated section between these
structures.
The average ground leakage current in the section of counterpoise between structures,
i , and i + 1 , is:
and the ground leakage current at any intermediate point on the counterpoise
between the two structures is estimated from the curve joining the points representing
one half the ground current at each structure (Figure 5.30(b)).
Phase
Conductor
Ground
Fictitious
Wire + Overhead
Counterpoise
Figure 5.29
First Iteration
(b)
Figure 5.30
CURRENT AND VOLTAGE DISTRIBUTION
Last Iteration
Step 3b
The approach presented in step 3a requires a cumbersome iterative procedure which is only
feasible when the soil structure along the counterpoise is reasonably well known and when
the transmission line is short; i.e., when the distance between the transmission line terminal
substations is relatively short. In most practical cases, however, the structure proximity
effect can be estimated using the following procedure:
1- The ground resistance of the total counterpoise length L is calculated using Equation
5-59(a) which assumes that there is no voltage drop along the counterpoise length.
Assume that R|_ is the computed resistance.
2- The ground resistance of the portion of counterpoise at structure i (length £) is calculated
from 5-59(a). Assume that R.£ is the computed resistance.
3- If there were no mutual ground resistances between the n portions (assumed of equal
length i = L/n) of the fictitious counterpoise conductor, we would have:
R
l
nR
L
i.e., using Equation 5-59(a):
np
21
P
^2ae
7T&
ttL
21
1 n - ■ ....'
-y2ae
1
But this cannot be since L = n £ . Therefore, the actual resistance R £, at each transmission
line structure is determined from the relation:
i
where 7 is a factor (7 > 1) which takes the proximity effect into account. From the two
preceding relations, the factor 7 can be written:
nR,
Y =
2L
In — -1
yj 2ae
2£
In -==, -1
yj2ae
5-46
4- Using the corrected resistance values R 7 = Rjj,; the analysis can now proceed as if
these values are the values obtained at the final iteration k using the iterative approach
described previously. Thus, the final computations are identical to those presented in step
3a, items 4 and 5.
5.5.3 ACCURATE ANALYSIS OF COUNTERPOISES
Two of the simplifying assumptions used to derive the counterpoise Equations 5-52 to
5- 56 lead to unrealistic results as frequency and counterpoise length increase. Fortunately,
a simple adjustment can be made which will compensate for the inaccuracies introduced by
the assumptions.
The first assumption is that the value of distributed ground resistance Rj per unit length
of counterpoise is uniform along the counterpoise, i.e., independent of the location of the
section of counterpoise used to apply the distributed parameter analysis. The second assumption
is implicitly made when Equation 5-59(b) is used to calculate Rj. This equation is based on
the assumption that current flowing into earth from a cylindrical horizontal ground conductor
of length £ is uniformly distributed along the conductor. As previously discussed in this
chapter and in [14,15,21], the current density is generally significantly higher at the conductor
extremities than at the center.
These two simplifying assumptions are interrelated because of the necessity to accurately
calculate the conductor current distribution and earth potential distribution along the surface
of a ground conductor, in order to determine the ground impedance of the conductor as seen
from the point where the current is injected into the conductor. This kind of calculation
can only be carried out realistically using a computer program such as the SES program
MALZ [45].
Figure 5.31 shows the ground impedance of a counterpoise as a function of its length based
on the assumption that:
•
The counterpoise is a perfect conductor (zero internal impedance). In this case,
Equation 5-59(a) applies. This was used to generate the solid curve of Figure 5.31.
•
The counterpoise is made of small identical sections which can be analyzed using
the distributed parameter approach (Equations 5-52 to 5-59).
•
The counterpoise is made of a number of sections having a uniform surface
potential and earth current density on each section but not necessarily the same
from one section to the other. The potentials and currents of the sections are
determined by MALZ with the desired accuracy by subdividing the counterpoise
into an appropriate number of short sections.
Examination of Figure 5.31 reveals that as the length of the counterpoise is increased, the
ground impedance decreases, as expected, until a certain length is reached, after which the
impedance rises. This sudden impedance increase has no physical justification but is
simply the result of approximations on which the counterpoise resistance Rj is based. The
MALZ program generated curve also shows a similar but less pronounced behavior. This
effect virtually disappears as the number of counterpoise sections increases. The optimum
number and length of counterpoise sections is frequency and resistivity dependent.
It is interesting to note that the computer results consistently show that when the number
of sections is sufficient, the counterpoise ground impedance curve becomes almost horizontal
beyond the minimum impedance point on the distributed parameter curve (knee point). This
suggests that the distributed parameter curve can still be used, provided that the rising
portion of the ground impedance curve is ignored and replaced by a horizontal line. The
5-47
ground impedance curves of Figure 5.26 and 5.25 and those shown in Volume 2 were obtained
after this adjustment technique was applied.
Another difficulty associated with the distributed parameter approach arises when the
counterpoise current distribution is to be determined. Based on the Equations 5-52 and 5-53,
the current is proportional to the hyperbolic sine of the distance from the structure to the
location where the current is to be observed. This is different from the current density
curves of Figure 5.32 which are based on MALZ computations. This figure clearly shows
that the current distribution is dependent on the length of the counterpoise and that, for
short counterpoises, an end effect consisting of an increase in current density can be observed.
A closer examination of this figure and of Figure 4.17 of Volume 2 also reveals that the
current distribution and end effects are frequency and resistivity dependent. An accurate
calculation of current distribution along isolated counterpoises is of limited interest in
transmission line grounding problems. The so-called continuous counterpoise most common in
transmission line applications is buried in various soils and is regularly connected to the
structures and the overhead ground wires. Consequently, it is more effectively and accurately
analyzed using the methods described in Section 5.5.2.
P
CI
- 100 {2-m
(CURRENT INJECTION) = EXTREMITY
DISTRIBUTED PARAMETERS
-SES COMPUTER PROGRAM
MALZ
- assuming zero
IMPEDANCE COUNTERPOISE
__ 60 Hz
COUNTERPOISE LENGTH (meters)
Figure 5.31
Computer Solutions of Counterpoise Ground Impedance
5-48
LINEAR CURRENT DENSITY ALONG COUNTERPOISE (A /m )
£ = 10000 m
p = 100 ft-m
FREQUENCY = 60 Hz
CI = EXTREMITY
8000 m
6000 m
2000 m
1000 m
800 m
,—600 m
200 m
100 m
20 m
t—i"
i i [
COUNTERPOISE LENGTH (meters)
Figure 5.32
Current Distribution Along a Counterpoise
5.6 SOIL HEATING EFFECTS
The importance of soil moisture content has been discussed on several occasions in this
chapter and previously. It is now clear that a ground electrode should not be loaded
continuously, or even for short periods, without suitable provision for heat dissipation in the
earth. This is necessary for maintaining the temperature rise of the soil in the vicinity of
the electrode, safely below the 100 °C limit of water evaporation.
Fortunately, it is very unlikely that the duration or magnitude of high voltage transmission
line fault currents will exceed the maximum value above which soil mixture evaporation
becomes a real concern. Hence, the subject of soil heating will not be analysed in detail.
Nevertheless, there does exist the possibility that a fault occurs at a high resistance
transmission line structure not equipped with overhead ground wires or other zero-sequence
return paths. Generally, low voltage transmission or distribution lines are the most prone to
this danger, especially, when the support structure is a concrete pole with no supplemental
grounding elements [40,41]. In this situation, the fault current may be low enough to prevent
the operation of the protection system or, a long time may elapse before a protective
element is activated. Consequently, a sustained current may penetrate the soil via a relatively
small ground electrode surface. The resulting high current density will introduce localized
heating and a corresponding increase in soil resistivity. This, in turn, will cause a further
increase in the local soil temperature. This cumulative effect, may lead to a complete
evaporation of the moisture in the soil around the grounding system, followed by destructive
arcing and, ultimately, complete isolation of the grounding system from remote ground [40].
This process may take a few minutes to several hours or days, depending on the fault current
magnitude, earth structure, grounding system configuration and ambient temperature.
The following theoretical considerations will provide a means of assessing the seriousness of
the heating process, should it arise during the design stage of a transmission line project.
It will allow for an evaluation of alternatives in the design of an existing structure grounding
system subject to such heating stresses.
5.6.1 HEATING OF THE SOIL AROUND A GROUNDING SYSTEM
Since the steady-state heat and current flow obey the same mathematical law, namely,
Poisson's differential equation, the heat performance of any grounding electrode can be
determined from a knowledge of the earth electric field , provided that certain conservative
assumptions are made:
®
The atmosphere is a perfect insulator.
•
The electrode surface is an isothermal surface, i.e., there is no temperature drop
between any two points on the electrode surface.
From the preceding discussion, it follows that the temperature rise around a grounding
electrode can be determined by considering the temperature rise of a hemispherical electrode
where terms related to the electric field are replaced with values corresponding to the
grounding system under consideration [35,46-48]. In this section however, the analysis is
conducted for an arbitrary grounding system. Figure 5.33 shows a ground electrode injecting
a current I into a uniform soil. The differential equation of the temperature rise in the soil
is [35,47]:
36
Y------ X&0 = Q
(5-60)
3t
5-50
where
6
is the temperature rise at any point in the soil
X is the thermal conductivity of the soil (assumed constant)
y
is the specific heat of the soil (assumed constant)
Q is the energy (in joules) produced per second and per cubic meter
A is the Laplacian operator
The following average values of
y
y
and X are provided in [46]:
~ 1.5x106 J/m^.°C
X ~ 2.0 /m.°C
EQUI POTENTIAL AND
ISOTHERMAL SURFACES
Figure 5.33
Heating of the Soil Around a Grounding Electrode
The solution of Equation 5-60 is cumbersome, even for simple electrode configurations such
as the ground rod. Fortunately, a complete solution is necessary only when an accurate
knowledge of temperature variation with time is critical. In problems involving the heating
of soil by grounding electrodes, the results of practical interest are the steady-state
temperatures and sometimes, the initial (transient) temperature variations. Note that the
transition period between the transient and steady-state temperatures can be
approximated by interpolation, (see Figure 5.34).
5.6.2 STEADY-STATE PERFORMANCE
During the stationary condition, the time derivative term of Equation 5-60 vanishes and this
equation, expressed in cartesian coordinates, reduces to:
320
020
320
E2
9x2
3y2
9z2
Xp
(5-61)
5-51
where
E is the electric field intensity (Q = E2/p)
P is the average earth resistivity
Recalling that the electric field intensity components are:
3U
su
—
j
3x
E
= - ----y
By
*
3U
E
= - -----
z
3z
where U is the earth potential at an arbitrary point, and since AU = 0 is the equation of
the earth potentials, the solution of Equation 5-61 is given by:
9 = (AU - iU2)Ap
(5-62)
where A is a constant. Based on these assumptions, there is no temperature drop between
any two points on the electrode surface. Thus, on the surface, U = Us and therefore:
90
90
90
— = — = — = o
9x
9z
By
a condition which, after differentiation of 5-62, leads to A = Us.
The following remarkably simple equation is thereby obtained for the temperature rise of
the soil at the surface of a grounding system, regardless of its shape:
U2
R2!2
(5-63)
0 = — = ------2Ap
2Ap
where R is the ground resistance of the electrode.
Thus, the maximum continuous current which can flow in the grounding system without
exceeding the allowable temperature rise ^ is:
1
(5-64)
= - j2Ap6m
Assuming a maximum temperature of 100 °C, it is straightforward to conclude that the
allowable continuous current density of an electrode is relatively small, i.e., in the order of
few amperes per m2? considerably less current than the 5 A/cm^ considered in Section 5.4
for short duration currents.
5.6.3 TRANSIENT HEATING
During the initial period of current conduction into the soil, the heat does not have the
time to dissipate effectively into the soil by conduction. Thus, the thermal conduction term
in Equation 5-60 can be neglected with regard to the specific heat term. This approximation
is, of course, a conservative one. Equation 5-60 reduces to:
de
o.
e2
dt
y
YP
5-52
therefore
(5-65)
The maximum temperature rise occurs at the point of maximum field intensity Em, usually
a very short distance from the electrode surface.
The electric field intensity E and the earth current density J at an arbitrary point are
related according to the expression:
E = pJ
Consequently Equation 5-65 can be written as:
Vy
0
(5-66)
7 7
This equation can be used to determine the maximum short duration current density
which does not result in a temperature rise exceeding a safe value. For a time duration of
0.1 s, soil resistivity of 100 ^-m, and a temperature rise of 80 °C, the maximum density
is:
I.SxlO6
80
------------x ------
V
100
- 31(00 A/m2 - 0.3** A/cm2
0.1
This value is significantly lower than the 5 A/cm2 short duration current limit in concrete
foundation specified in Section 5.4. Since the value 5 A/cm2 is based on experimental
evidence [44], it is believed to be realistic. This is true provided that sufficient time passes
between conduction periods at the electrode, to permit moisture migration from neighbouring
soil back into the areas affected by water evaporation.
Figure 5.34 illustrates the variation of temperature with time for short duration and
steady-state currents (solid line). For intermediate times, the interpolated portion of the
curve provides a good estimate of temperature variations.
Iransient
Figure 5.34
Steady
State
Temperature Variation With Time
5-53
The time constant of heating r, i.e., the time required to reach the steady-state temperature,
is obtained (approximately) by equating 5-62 with 5-65. Thus:
u2
(5-67)
T
2E2
The time constant at the surface of a grounding electrode (U=US
E=ES) is:
_ 1 Y
Ts = I 7
For a hemispherical electrode of radius
U
pi
= -----5
2na
; and
E
a:
pi
= ------5
2ira2
hence
Y
T
S
a2
2\
This indicates that the time constant of a grounding electrode is a function of the square
of its average dimension. For a 5 m radius electrode, the time constant is:
1.5x106
= ----------- x 25 - 107 seconds ~
r
5
108
days 1
k
Although this is a long period, experience shows that periods in the order of 10 to 100 days
are typical values for practical grounding systems.
REFERENCES
1 - T. N. Giao. M. P. Sarma, "Effects of two-Layer Earth on the Electric Field Near HVDC
Electrodes", IEEE Transactions, PAS-91 No. 6, November 1972, pp. 2346 to 2355.
2 - F. Dawalibi, D. Mukhedkar, "Ground Electrode Resistance Measurements
Nonuniform Soils", IEEE Transactions, Vol. PAS-93, No. 11, January 74, pp. 109-115.
in
3 - A. I. Yacobs, P. I. Petrov, "On Allowing for the Longitudinal Impedance of Horizontal
Elements in Large Earthings", Electrical Technology USSR (GB) No. 1, 1974, pp. 9-22.
4 - F. Dawalibi, D. Mukhedkar, "Optimum Design of Substation Grounding in Two-Layer
Earth Structure - Part I, Analytical Study", IEEE Transactions, Vol. PAS-94, No. 2 March/April
1975, pp. 252-261.
5 - F. Dawalibi, D. Mukhedkar, "Optimum Design of Substation Grounding in Two-Layer
Earth Structure - Part II, Comparison Between Theoretical and Experimental Results", IEEE
Transactions, Vol. PAS-94, No. 2, March/April 1975, pp. 262-266.
5-54
6 - F. Dawalibi, D. Mukhedkar, "Optimum Design of Substation Grounding in Two-Layer
Earth Structure - Part III, Study of Grounding Grids Performance and New Electrode
Configurations", IEEE Transactions, Vol. PAS-94, No. 2, March/April 1975, pp. 267-272.
7 - J. G. Sverak, "Optimized Grounding Grid Design Using Variable Spacing Technique", IEEE
Transactions, Vol. PAS-95, No. 1, January/February 1976, pp. 362-374.
8 - A. M. Arakelian, R. O, Gabrielyan, D. V. Arytyunyan, "Quick Calculation of Parameters
of Earthing Rods in Inhomogeneous Media", Electrical Technology USSR (GB), No. 3, 1976,
pp. 58-61.
9 - F. Dawalibi, D. Mukhedkar, "Multi-Step Analysis of Interconnected Grounding Electrodes",
IEEE Transactions, Vol. PAS-95, No. 1, January/February 1976, pp. 113-119.
10- F. Dawalibi, D. Mukhedkar, "Resistance Calculation of Interconnected Grounding
Electrodes", IEEE Transactions, Vol. PAS-96, No. 1, January/ February 1978, pp. 59-65.
11- F. Dawalibi, D. Mukhedkar, "Transferred Earth Potentials in Power Systems", IEEE
Transactions, Vol. PAS-97, No. 1, January/February 1978, pp. 90-101.
12- R. J. Heppe, "Step Potential and Body Currents for Near Grounds in Two-Layer Earth",
IEEE Transactions, Vol. PAS-98, No. 1, January/February 1979, pp. 45-59.
13- H. N. Nunnally, R. P. Webb, E. B. Joy and A. P. Meliopoulos, "Computer Simulation for
Determining Step and Touch Potentials Resulting from Faults on Open Neutrals, in URD
Cable", IEEE Transactions, Vol. PAS-98, No. 3, May/June 1979, pp. 1130-1136.
14- F. Dawalibi, D. Mukhedkar, "Influence of Ground Rods on Grounding Grids", IEEE
Transactions, Vol. PAS-98, No. 6, November/December 1979, pp. 2089-2098.
15- F. Dawalibi, D. Mukhedkar, "Parametric Analysis of Grounding Grids", IEEE Transactions,
Vol. PAS-98, No. 5, September/October 1979, pp. 1659-1668.
16- F. Dawalibi, D. Mukhedkar, "Resistance Measurement of Large Grounding Systems", IEEE
Transactions, Vol. PAS-98, No. 6, November/December 1980, pp. 2348-2354.
17- D. L. Garrett and H. J. Holley, "Calculation of Substation Grounding Resistance Using
Matrix Techniques", IEEE Transactions, Vol. PAS-99, No. 5, September/October 1980, pp.
2008-2011.
18- F. Dawalibi, W. G. Finney, "Transmission Line Tower Grounding Performance in Nonuniform
Soil", IEEE Transactions, Vol. PAS-99, March/April 1980, pp. 471-479.
19- P. Kouteynikoff, "Numerical Computation of the Grounding Resistance of Substations
and Towers", IEEE Transactions, Vol. PAS-99, No. 3, May/June 1980, pp. 957-965.
20- A. P. Meliopoulos, R. P. Webb, E. B. Joy, "Analysis of Grounding Systems", IEEE
Transactions, Vol. PAS-100, No. 3, March 1981, pp. 1039-1048.
21- F. Dawalibi, D. Mukhedkar, D. Bensted, "Measured and Computed Current Densities in
Buried Ground Conductors", IEEE Transactions, Vol. PAS-100, No. 8, August 1981, pp.
4083-4092.
22- T. Takashima, T. Nakae, R. Ishibashi, "High Frequency Characteristics of Impedances to
Ground and Field Distributions of Ground Electrodes", IEEE Transactions, Vol. PAS-100, No.
4, April 1981, pp. 1893-1900.
5-55
23- D. Bensted, F. Dawalibi, A. Wu, "The Application of Computer Aided Grounding Design
Techniques to a Pulp and Paper Mill Grounding System", IEEE Transactions, Vol. IA-17, No.
1, January/F ebruary 1981.
24- D. S. Ironside, "Some Recent Developments in Portable Ground Resistance Test Instruments",
Paper presented at the High-Voltage Power System Grounding Workshop Sponsored by EPRI,
May 12-14, 1982, Atlanta, Georgia.
23- I. D. Lu, R. M. Shier, "Application of a Digital Signal Analyzer to the Measurement of
Power System Ground Impedances", IEEE Transactions on PAS, Vol. PAS-100, April 1981, pp.
1918-1922.
26- P. H. Reynolds, D. S. Ironside, A. H. Silcocks, J. B. Williams, "A new Instrument for
Measuring Ground Impedances", IEEE Paper A79 080-3, IEEE PES Winter Meeting, New York,
1979.
27- J. Ufermann, K. Jahn, "High Frequency Earth Resistance Measuring Instrument", Brown
and Boveri Journal No. 3/67, pp. 132-135.
28- M. Darveniza et Al, "Modelling for Lightning Performance Calculations", IEEE Transactions
on PAS, Vol. PAS-98, No. 6, November/December 1979, pp. 1900-1907.
29- AIEE Committee Report, "A Method of Estimating Lightning Performance of Transmission
Lines", AIEE Transactions on PAS, Vol. 69, pt.II, 1950, pp. 1187-1196.
30- Report of Joint IEEE-EEI Subject Committee on EHV Line Outages, IEEE Transactions
on PAS, Vol. PAS-86, 1967, p. 547.
31- E. Clarke, "Circuit Analysis of AC Power Systems, Volume 1; Symmetrical and Related
Components", Book Published by General Electric Company, 1961.
32- "Transmission Line Reference Book 345 kV and Above", General Electric Co., Published
by EPRI.
33- M. Muskat, "Potential Distribution About an Electrode on the Surface of the Earth",
Physics, Vol. 4, No. 4, April 1933, pp. 129-147.
34- H. M. Mooney, E. Orellana, H. Pickett, L. Tornheim, "A Resistivity Computation Method
for Layered Earth Models", Geophysics, Vol. XXXI, No. 1, February 1966, pp. 192-203.
35- E. D. Sunde, "Earth Conduction Effects in Transmission Systems", Dover Publications,
New York, 1968 (book).
36- E. A. Cherney, K. G. Ringler, N. Kolcio, G. K. Bell, "Step and Touch Potentials at
Faulted Transmission Towers", IEEE Transactions on PAS, July 1981, Vol. PAS-100, No. 7,
pp. 3312-3321.
37- G. B. Niles, "Using Transmission Foundation Resistance for Grounding Purposes and
Determining an Effective Earth Resistivity", IEEE Paper A78 126-5, IEEE PES Winter Meeting,
New York, February 1978.
38- M. Datta, A. K. Basu, M. M. R. Chowdhury, "Determination of Earth Resistance of
Multiple Driven-Rod Electrodes", Proc. of the I.E.E, Vol. 114, No. 7, July 1967, pp. 1001-1007.
39- S. A. Sokolov, "The Lowering of Earth Resistances in Rocky Areas and Permafrost
Regions" Electric Technology USSR (GB), Translation of Electrosvyaz, No. 6, 1959, pp. 65-70.
5-56
40- W. Bogajewski, F. Dawalibi, Y. Gervais, D. Mukhedkar, "Effects of Sustained Ground
Fault Current on Concrete Poles", IEEE Paper 82 WM 202-1, IEEE Winter Meeting, Atlanta,
1981.
41- W. K. Dick, H. R. Holliday, "Impulse and Alternating Current Tests on Grounding in Soil
Environment", IEEE Transactions, PAS-97, No. 1, January/F ebruary 1978, pp. 102-108.
42- E. J. Fagan, R. H. Lee, "The Use of Concrete-Enclosed Reinforcing Rods as Grounding
Electrodes", IEEE Transactions, Vol. Iga-6, No. 4, July/August 1970, pp. 337-348.
43- J. Preminger, "Evaluation of Concrete-Encased Electrodes, IEEE Transactions, Vol. IA-II,
No. 6, November/December 1976, pp. 664-668.
44- R. Kostaluk, "Effects in Concrete and Ground Caused by Passage of Lightning and
Short-Circuit Currents Through Foundations of Transmission Lines", Archiwum, Elektrotechniki,
Tom XXV, 1976, pp. 95-107.
45- F. Dawalibi, "User Manual for Program MALZ", Safe Engineering Services Ltd., Montreal,
1981.
46- E. W. Kimbark, "Direct Current Transmission" Volume I, Wiley Interscience, 1971 (book).
47- J. H. Neher, "The Temperature Rise of Buried Cables and Pipes", AIEE Transactions,
Vol. 68, Part I, 1949, pp. 9-21.
48- K. R. Rakhimov, "Thermal Analysis of Earthing Rods at the Ends of D.C. Lines". Electric
Technology USSR (GB), Vol. 4, July 1970, pp. 36-43.
5-57
FAULT CURRENT DISTRIBUTION
6.1 GENERAL
The majority of transmission line faults are to ground and generally occur between a phase
conductor and a transmission line structure, often, as the result of an insulator flashover.
In some cases, the presence of foreign objects between a phase conductor and the overhead
ground wire (birds, etc.) or a grounded structure (trees or the arm of a crane) may cause
a ground fault somewhere along one span of the transmission line. Occasionally, the ground
fault is caused by a broken phase conductor in direct contact with the overhead ground wire
or soil surface. In all these cases, the fault current return paths include earth and, therefore,
present an impedance which at most is equal to the equivalent ground impedance of the
grounded structures which carry the fault current (the ground impedances of the generating
sources are neglected). If in addition to the earth current, part of the total fault current
returns to the generating sources via metallic return circuits (such as overhead ground wires,
counterpoises, etc.) the impedance value will be even less.
In conventional short circuit calculation techniques, the ground impedance is usually neglected
by assuming a zero impedance return path. Because modern power systems are solidly grounded
and the current return path impedance is generally negligible with respect to the other
power network impedances, this zero impedance return path assumption is very accurate
for most engineering problems and leads to conservative results. When this assumption is
not realistic, it is possible to add the value of the return path impedance in the equivalent
power system circuit. This procedure allows the influence of the ground impedance on the
magnitude of the total fault current to be included in the calculations (see Figure 6.1).
In all these cases, the division of the fault current at the faulted structure between
earth and the metallic return conductors of the circuit remains unknown. This is because of
the simplification of the circuit resulting from the use of an equivalent return path impedance
(generally, an approximated conservative impedance value).
In problems where a proper knowledge of the distribution of the fault current among various
paths is necessary, the conventional short-circuit computation tools are inadequate and
alternative methods must be used. This chapter describes several of these alternative methods.
One of these methods was used as the basis for the development of the computer program
PATHS described in Appendix D.
The subject of transmission line ground fault current distribution is not extensively covered
in the technical literature. However, the existing work related to this subject [1-10] is
comprehensive, reasonably complete and reflects the two principal approaches used to analyze
the problem, i.e.:
•
Transmission Line with constant line parameters
•
Transmission Line with varying line parameters
Z
z
r
Z
s
se
Z
s
+ Zr
Conventional Equivalent
Circuit
Actual Circuit
Figure 6.1
Equivalent Return Path Impedance
Conventional Circuit Reduction
Selection of the most suitable computation technique depends on the type of problem being
analysed, the availability and accuracy of the input data and the required accuracy of the
results. Sometimes, simple hand calculations are all that is required to analyze the problem.
In other cases, complex computer programs are required to arrive at meaningful conclusions.
In this report, simplified and more complex calculation techniques are briefly discussed and
properly referenced. Particular emphasis is placed on the description and discussion of the
double-sided elimination method which is suitable for solving the problem of transmission
line fault current distribution in general. This method was used as the basis of the computer
program PATHS to address the widely variable needs of North American Utilities (see
Appendix D).
6.2 IMPORTANCE OF FAULT CURRENT DISTRIBUTION
In assessing the effects of a ground fault on a transmission line, it is apparent that the
transmission line performance at the faulted structure and/or at other locations on the
transmission line, is significantly influenced by the fault current distribution between the
structure and the neutral conductors connected to the structure.
Figure 6.2 shows a typical system which illustrates this aspect. R represents the faulted
structure ground resistance and Zs the equivalent power generation (source) impedance. It
is also assumed that the value of Zs is significantly higher than the structure resistance
value R so that the total fault current Ij ~ V/Zs is approximately constant when R
varies within a relatively narrow range.
Inspection of Figure 6.2 leads to the following conclusions:
a- If one of the ground wire impedances Z^ or Zr is smaller relative to R, then
very little current enters the faulted structure and the potential rise of the
structure is proportional to the metallic return circuit path impedance, i.e. Z^
in parallel with Zr.
b- If in contrast, R is small compared to Z^ and Zr, then most of the fault
current flow through the structure, causing a ground potential rise proportional
to the structure ground resistance R.
6-2
This example, although simple and perhaps unrealistic, illustrates the importance of fault
current distribution. In a real transmission line there are hundreds of grounded transmission
structures. The metallic return circuits are not only bonded to these structures but also are
electromagnetically coupled to the phase conductors. Moreover, the ground resistance of the
structures is not constant and generally varies between wide limits along the route of the
transmission line. The fault current distribution is therefore more complex to calculate and
will vary with the type of transmission line and location of the fault on the line.
Z
s
Overhead
Ground-wire
Fau1 ted
Structu re
Figure 6.2
Fault Current Distribution
6.3 CONSTANT LINE PARAMETERS
One of the most classical methods using uniformly distributed parameters was presented by
Endreyni in 1967 [1]. Alternative approaches have since been proposed [3-5], but in essence,
the techniques proposed are similar to Endreyni's method or to Rudenberg's earlier but more
approximate method [2]. In all cases however, the final equations developed by the authors
are valid only for "long" transmission lines.
6.3.1 LONG TRANSMISSION LINES
The full treatment of this concept is well covered by Desieno et al [3]. In this section, the
case of a ground fault fed from both terminals of a transmission line is described. Figure
6.3 represents the transmission line with the following uniformly distributed parameters:
Zg: Self impedance of the ground wire (or equivalent single ground wire); in ohms
per unit length (km or mile).
Zm: Average mutual impedance between a phase conductor and the (equivalent)
ground wire in ohms per unit length.
R
: Average structure footing ground resistance in ohms.
N
: Number of transmission line structures per unit length.
6-3
11
If
0
i(x+dx)
Figure 6.3
Distributed Parameters Method
It is assumed that the fault occurs at some distance from the terminals so that the
transmission line can be considered infinite in both directions. This is required to
maintain the validity of the distributed parameters approach. If this is not the case, then
the equations of this section should not be used. Instead, one should use the equations of
the method developed in the next section (6.3.2), or those related to methods based on
varying line parameters (see Section 6.4).
The length of the three-phase single ground wire transmission line of Figure 6.3 is v. A
phase to ground fault occurs at a distance d from the left terminal.
The current i in a transmission structure located at a distance x from the left terminal is:
-j---- = i (x) = l(x + 6) - l(x)
(6-1)
where I(x) is the ground wire current in the local span and I(x+ 5) the ground wire current
in the next span (see Figure 6.4). 5 represents the distance between consecutive transmission
line structures. Because a very long transmission line is assumed, the average ground resistance
R (ohms) of the N structures per km or mile of the line can be reliably approximated by
a large number 7/ of shunt resistances of R' where, R' = y R/N. The distance between any
two consecutive resistances is dx = I/17. Rewriting Equation 6-1 for this new but equivalent
line configuration leads to:
V(x)
R1
Ndx
V(x) = I(x + dx) - I (x)
Dividing both sides of the equation by dx and taking the limit of the right-hand side as dx
approaches zero leads to:
H V(x) = ■d.I(x).
R W
dx
(6-2)
The total drop of voltage in the circuit consisting of two shunt resistances R' and the short
segment of ground wire (of length dx) between these resistances must be zero (see Figure
6.4):
V (x
\ + dx) - V(x) - l(x)Z g dx +
f m dx = 0
Irl
6-4
Dividing by dx and taking the limit of the preceding eguation as dx approaches zero yields
the following relation:
Z I(x) - Z l'
g
m f
=
dx
(6-3)
By differentiating (6-2) and (6-3) with respect to x and then combining the resulting equations
together, the following second order differential equations are obtained:
d2l(x)
- cc2l(x) = - a2 ^ If
(6-4)
g
dx"
d2V(x)
- a2V(x) = 0
(6-5)
NZ
■t
(6-6)
dx"
where
a =
V
The general solutions of (6-4) and (6-5) are respectively:
(x) =
ax
-ax , m
A„e~"' + B„e
l*
+ Z ‘f
(6-7)
g
„ z v
R
A
ax
VX) = N “V
R
_
-ax
(6-8)
where the subscript i is used to designate the left terminal. The A and B constants are
determined from the boundary conditions, i.e.:
At the Faulted structure (x = d)
(6-9)
Vx * d> - RIe
At the Left Terminal (x = 0)
It is assumed that the ground resistance of the left terminal is negligibly small. Therefore:
(6-10)
V (x = 0) = 0
i
The solution of the boundary conditions 6-9 and 6-10 yields:
NI
A£ ~ B£ ~
2a sinh(ad)
Thus
sinh(ax)
Vn = RI
£
e
(6-11)
sinh(ad)
NI
Vx) * —
a
cosh(ax)
sinh(ad)
*
m T
^!f
(6-12)
g
6-5
The last three equations are related to the left terminal. Similar expressions can be obtained
for the right terminal (replace x by y, d by v - d and If by If ), i.e.s
A
NI
= ---------------------------
= B
r
r
2a
sinh[a(v-d)]
sinh(ay)
V (y) = RI -------------------r
e sinh[a(v-d)]
NI
ir(y) ■ —
cosh(ay)
-
(6-13)
Z
.
^ r ‘f
(6-14)
At the faulted structure (x = d ; y = v-d), the total line to ground fault current If is:
If = If + If = Ij, + Ir + Ie
From this equation and Equations 6-12 and 6-14, the structure fault current is determined:
(1-Zm/Zg)lf
I
e
=
1 ^
(6-15)
1
tanh(ad)
tanh[a(v-d)]
The current I in the ground wire and the structure potential rise V (or structure current i
= V/R) at any point along the line are determined from Equations 6-11 to 6-14 by substituting
Ie by its value as given from Equation 6-15.
Equation 6-15 shows that the current Ie which flows in the faulted structure is a fraction
of the total fault current If. This current decreases when:
•
The mutual impedance between the phase conductor and the ground wire increases.
•
The ground wire impedance decreases.
•
The structure resistance increases.
From Equation 6-15, it is clear that the value of this structure current Ie can not exceed
(1 - //) times the total fault current. ^ is the coupling factor and is equal to the ratio of
the mutual impedance Zm to the ground wire impedance Zg. Depending on the material used
and number of ground wires installed, the value of pt generally varies between 0.1 and 0.5.
It is also apparent from Equations 6-12 and 6-14 that, in the presence of coupling between
the phase and metallic return conductors, a portion of the current (julf or jttlf) will stay in
the metallic return circuits ("trapped" current).
6.3.2 LONG AND SHORT TRANSMISSION LINES
The preceding method can not be applied for short lines, i.e., lines consisting of few spans
between the feeding station and the faulted structure. In this case the method of lumped
parameters should be used.
6-6
When it is assumed that the transmission line conductor characteristics and the structure
ground resistance are constant, then the lumped parameter method becomes very similar to
the distributed parameter method. That is, instead of the differential equations,
difference equations are used to derive the fundamental relations.
To investigate this case, the transmission line of Figure 6.4 is considered. The fault occurs
at structure number 0. There are n - 1 structures between this structure and the left terminal
and m - 1 structures between structure 0 and the right terminal. All structures have a
ground resistance R except for structure 0 whose resistance is Re. The left and right terminal
ground resistance values are R^ and Rr respectively. The impedance of the section of ground
wire between the terminal and the first structure (structures n-1 or m-1) is Z£ for the left
terminal and zr for the right terminal. The self and mutual impedances of a section of
ground wire between two consecutive structures are Zg and Zm respectively (expressed in
ohms).
i
if
f
n-1 . . . j +2 j+1 . .2
Figure 6.4
Lumped Parameters Method
The current ij+^ in a transmission structure j+1 is:
(6-16)
'j+1 " Vi “ Ij+2
where Ij+^ is the current in the section of ground wire between structures j and j+1. According
to Ohm's law, Equation 6-16 can be rewritten as:
V.
V.
J+1
J +2
R
where Vj is the potential rise of structure j and Zg is the ground wire impedance between
two consecutive structures. Rearranging this equation yields:
V.
J +2
<2
* h Vi * V
0
(6-17)
6-7
According to Kirchoff's law, the total voltage drop in a loop is zero. Therefore:
I . ,R + Z I, =0
j+1
m f
j+i g
which, based on Equation 6-16, can be rewritten as:
I.R -
I.^Z
j
V ' <2
^ = -t1)
(6-18)
(6-19)
Equations 6-17 and 6-19 are second order difference equations which hold for j = 2, 3,------,n-2.
That is, they apply at all but nodes 1 and n-1, where the following boundary equations are
applicable:
At the faulted structure
(6-20)
-V2 ♦ <2 ♦ -f) V, - V0 - I.R
e e
At the Left Terminal
Z
Z
11
(1 + -2- + -!■) v
-V . = -2- V = -2- i R„
z^
R
n-1
n-2
z^ n
z^ n £
(6-21)
Finally, at the left terminal, node n, the following relation must be verified:
(6-22)
I
+ i = I£
n
n
f
but since
I
=
n
V
.+ V
Z
-iTJ---D. + JE
z£
Z£
, V ,
R„
Z
,
' = _niL + _A ; + JE x
f Zl
ZSL n
ZZ
f
Equation 6-22 yields
z„-Z
i
n
=
1r f
VR£
z£+R£
(6-23)
From Equations 6-21 and 6-23, the following equation is obtained after elimination of in;
(1
r
-i
+ f )Vn- - V
- 1 'n"2
■■
V Ri
R,I,(I - A
2 f
n
(6-24)
The complete solution of the second order homogeneous difference Equation 6-17 is:
\
VS,(k)
Ag,e
ak , „
-ak
+ B£e
(6-25)
where
a = 2sinh~1(
)
(6-26)
and the subscript £ is used to designate the left terminal. The A and B constants are
determined from the boundary Equations 6-20 and 6-24. The following equations are obtained
after some simple algebraic transformations:
6-8
,D T
w - (n-1 )cx,, a,
AR£Xf " V0e
(6-e )
AA“
(6-27)
e(n-l)a(b.e-a) _ e-(n-1)a(b_eaj
(6-28)
B£ = Vo " A£
where
A =
)
-£
0
~ f-)
;
a = ~ + 2 ;
b =
i
1
+ ^ + J—
£
£
The ground wire current Ij and the structure potential rise are related according to the
following equation:
I. = (V
- V )/Z + zil/zn
J
J 1
J
9
m f g
Therefore, the complete solution of the nonhomogeneous difference Equation 6-19 is:
*f [
Vk>
a
DA^ ♦ (ea-1 )B^e-ka + ZJ
L
;]
(6-29)
A similar equation is also obtained for the right terminal:
Lr{k)
[<«-“- l)Arak“ + (eC,-l)Bre’k“
-ka - 2^,]
j ve
-
i;Mre
f
-1)Or(
(6-30)
'g
The Ar and Br coefficients are also given by Equations 6-27 and 6-28 in which R^, I £ and
n are replaced by Rr, Ir and m respectively and A is defined as:
Zn
A = (----- 2__)
Z
d _ _D1)
r
r
r
At the faulted structure the total line to ground fault If is:
If
= If + If = I£(1) + Ir(D + Ie
This last equation and Equations 6-29 and 6-30 yield:
Z
(1 - j1) If + (U£ + Ur)S
I
e
JL
=
(6-31)
1 + “ (2 " W£ - Wr)
where
.
S
_
a
= e
- e
-a
ui = x
Wj = ra<n-2)“(b-e‘a) - a-(n-2)a(b-e“)
/T,
= e(n“l)a(b-«'“) - e'(n'1)“(b-e“)
6-9
and Ur? Wr and Tr are defined based on relations similar to those used to define U£,
and l£ .
It should be noted that while Ie can easily be determined from Equation 6-15 using hand
calculations or conventional hand-held calculators, the faulted structure current I@ based on
equation 6-31 can only be reasonably calculated using a sophisticated programmable calculator
or a computer.
If the terminal ground impedances are assumed to be negligible (R^ ~ Rr ~ 0), the preceding
equations simplify considerably. In this case a is equal to b and Equations 6-25, 6-29 and
6-31 reduce to the following:
s i nh[(n-k)al
V (k) = I R ---------------------6 e sinh(na)
R
Vk) = ^
I
Z
9
+
(6-32)
,
731
9
(6-33)
If
(6-34)
e
[<}>(1 ,n) + (p(l ,m) ]
where
sinh[(n+1-k)a] - sinhC(n-k)a]
(6-35)
<j>(k,n)
sinh(na)
Since Equation 6-34 is very similar to Equation 6-15, a comparison between the results of
the computations using these equations yields interesting information concerning their
capabilities and limitations.
Figure 6.5(b) shows in graphical form the computation results based on Equation 6-34 (solid
lines) and Equation 6-15 (broken lines). The transmission line which was analyzed is shown
in Figure 6.5(a). This figure provides all the data used to perform the calculations. Similar
curves are also shown in Volume 2 of this report.
Firstly it should be noted that the lumped method results coincide with those obtained using
other exact methods such as the generalized double-sided method described later in this
chapter.
The distributed method yields a faulted structure current value lower than the value predicted
by the lumped method. This is true regardless of the fault location. However, the difference
between the distributed and lumped method results decreases as the distance from the
terminal to the faulted structure increases. At a distance of 3 to 5 km (2-3 mi) from the
terminal, this difference remains constant and independent of the fault location (about 10%).
The improvement of the accuracy is logical since the distributed method is valid only when
the distance between the faulted structure and the terminal is sufficiently long (5 km or
more) so that the discrete structure resistances can be replaced by distributed
resistances. When the fault is at the second structure from the terminal, the section of line
is too short and the computations yield an error of about 33%.
6-10
The 10% minimum error which remains regardless of the fault location, is inherent to the
equations applicable to the distributed and lumped methods, as shown overleaf.
f
Z =2.28+j0.77 tt/km
d
Terminal
LT
variable
v = 30 km
(a)
REFERENCE TRANSMISSION LINE
Terminal
RT
Based on
the Lumped Parameters
Concept
Based on
the Distributed Parameter
Concept
Terminal
(LT)
FAULTED STRUCTURE NUMBER (^2)
(b) DISTRIBUTED VERSUS LUMPED CONCEPTS
Figure 6.5
Distributed and Lumped Method - Constant Structure Resistance
6-11
When the fault occurs at large distances from both terminals, Equations 6-15 and 6-34 reduce
to the following similar equations. These new equations were obtained by replacing d, (v-d),
n and m with f and taking the limit of the original expressions as f increases to infinity:
- Distributed
:
I
e
- Lumped
:
i
e
= (l-Z /Z )l,/(l + 2 JrN/Z )
mgr
9
= (l-Z /Z )lf/coth(~)
mgr
2
;
a = Zsinh'1 (Q.5\!z /RN
^ 9
)
where Zm and Zg are expressed in ohms/unit length.
Except for faults at short distances from a terminal, it can be concluded that the distributed
method yields results which, for all practical purposes, are comparable to the lumped method.
As indicated by the preceding equations, the discrepancy between the two methods will
depend on the ratio of the structure grounding resistance to the impedance of the section
of ground wire between two structures. In most cases this discrepancy will be in the order
of 10%.
Figure 6.6 shows the current in the transmission line ground wire for a phase-to-ground fault
at various distances from the left (source) terminal. The solid-line curves correspond to the
results as computed by the lumped method, while the broken lines are for the distributed
method results.
This figure clearly illustrates the very good agreement between results from both methods.
Except for a fault at a very short distance from the terminal, the differences in the results,
already very small for a fault at the sixth structure from the terminal, are barely noticeable
when the fault occurs beyond structure 14.
Finally, it should be noted that because of the electromagnetic coupling between the phase
and ground wire, the ground wire current on the left side of the faulted structure does not
drop to zero when the fault occurs at a remote structure, but remains at a value equal to
the product of the fault current by the coupling factor (Zm/Zg). Similar curves are also
given in Volume 2. These curves are based on the distributed parameter method.
6.4 VARYING LINE PARAMETERS
Although the overhead conductor impedances are practically constant along a transmission
line, the ground resistance varies from one structure to the other, making it unrealistic to
assume a constant structure ground resistance along most transmission lines.
The methods presented in Section 6.3 are based on this assumption and, although the uniform
structure ground resistance value used is a mean value, the results are generally inaccurate
when the faulted structure or an adjacent structure has a ground resistance significantly
different from this average value. To improve the accuracy of the calculations it is important
to represent the faulted structure and its adjacent structures with resistances close to
the real values. The remaining structures are then represented by actual values or a
mean value. In this case, the previous methods can not be used and new approaches must
be developed to satisfy the modified requirements. In this section, a new calculation method
will be described. This method lends itself to digital computer processing and therefore was
used as the basis for the development of the computer program PATHS described in Appendix
D.
6-12
The loop and node equations can be used to solve for the unknown voltages and currents of
the equivalent circuit. In solving the equations, a stage is arrived at, where the equations
contain the terminal voltages of the span, the branch currents and the circuit
impedances. These equations can be written in matrix form as follows:
[Uk+1] = [Sk][Uk]
; k = 1
,
n-2
(6-36)
where
a, k
/g j k
I
a
I
[Uk]
(6-37)
g5k „
and
1
0
z
0
1
Z
0
0
0
1/Rk
[sk]
-Z
oa
-z
om
1
Z
om
om
og
(6-38)
0
/R. - (1+Z /R.)
k
og k
If there are n spans between the feeding terminal and the faulted structure, Equation 6-36
represents a series of n-2 equations which permits the computation of the currents and
voltages in span k+1 from the corresponding values in span k and vice-versa. The equations
for span 1 and n-1 are determined from the boundary conditions at the fault location and
at span n-1. Based on Figure 6.8, the following can be written:
R (I -I J
e a g, 1
Vi
[U
I
,)
R e (I a -I g, 1
3
I
a
I g, ,1
(6-39)
a
I,
1
and
_
V
V
I
I
—
a, n
g>n
a
g,n
.
V
R
I
a, n
.(I
.-I
)
n-1 g ,n-1 g,n
a
I
_ g»n
6-14
J
(6-40)
FauIt at
Tower #2
Lumped Parameter
Method
Distributed Parameter
Method
Fault at
Tower #6
Fault at
Tower #12
Pault at
Tower #32
"Trapped1
Current
STRUCTURE NUMBER
Figure 6.6
Currents in Ground Wire
Other methods have been developed and are also used. The method described by Sebo in
1969 [6] is an accurate approach which permits varying structure resistances along a
transmission line. More recent works have proposed alternative methods using different
computation techniques [7-10]. Essentially, all methods are based on the same initial equations.
The differences are caused by the methodology and algorithm used to perform the necessary
calculations. A brief description of Sebo's method follows.
6.4.1 SEBO'S METHOD
In Sebo's method, the section of transmission line between two consecutive structures is
represented as a six-terminal network. This six-terminal network is shown in Figure 6.7(b).
It consists exclusively of zero sequence self-impedances and is equivalent to the real circuit
of Figure 6.7(a).
This last circuit was originally proposed by Clarke [11] in order to retain the identity of
the earth return path. It is a zero sequence equivalent circuit, constructed on a per
phase basis for a three phase transmission line between two grounded structures solidly
bonded to the overhead ground wire.
6-13
Equations 6-36, 6-39 and 6-40 result in a chain multiplication of matrices of the type shown
by relation 6-38. This chain multiplication can be written as follows:
[U ] = [S
] [S ,]
n
n-1
n-2
[S33 [S23 [S^ [U^
(6-41)
Matrix Equation 6-41 results in three linear equations with five unknown quantities, i.e.,
^a,ns Ia> *g,l> ^g,n-l anc* ^g,n*
One additional equation is obtained from the terminal span loop, that is:
(6-42)
I a (Z a,n + Rj
x, - I g,n (Z
' g,n + R n-1 + Rn)
x, + I g ,n-1. R n-1. = 0
-x.
Ol >
DEFINITION OF SYMBOLS
Zoa: Self Impedance of Phase a, Span k
Zog: Self Impedance of Ground Wire, Span k
: Variable Related to Span k
Zoe: Earth Return Impedance, Span k
Vxk: Voltage of Conductor x at Span k
Zom: Mutual Impedance, Span k
Ixk: Current in Conductor x of Span k
Zx = Zox-Zoe, Span k (Conductor x)
: Tower Ground Resistance, Span k
(b) EQUIVALENT CIRCUIT
(a) REAL CIRCUIT
Figure 6.7
Circuit of One Span of a Line
The last equation needed to determine all the unknown quantities is obtained by noting that
the sum of the currents in the terminal and transmission structure grounding systems must
be equal to zero.
In some cases, the total fault current Ia is estimated from previous short-circuit studies or
has already been measured. Therefore, no additional equation is required and the
unknowns are determined with respect to Ia assumed as a reference 1.0 p.u. value.
It should be noted that the chain multiplication shown in Equation 6-41 may lead to serious
round-off errors during the computations, when the number of spans is large and/or where
the elements of the matrices vary between wide limits. This is similar to what can happen
to the single-sided elimination method described in the section following.
6-15
I
Figure 6.8
I
a
a
Ground Fault at Span n from the Source Terminal
6.4.2 THE SINGLE AND DOUBLE-SIDED ELIMINATION METHODS
The analyses presented in this section are an extension of the work originally published in
[9]. Essentially the equations are updated to cover the case of a three phase circuit with
mutual coupling between phase conductors. Two methods are described; the single-sided
elimination and the double-side elimination methods. The first method leads to equations
which express the current in a span as a function of the currents in the preceding (or
following) span. This procedure is particularly vulnerable to round-off errors. In contrast,
the double-sided method although not immune to round-off errors, is significantly less prone
to such errors. This is because the current in a span is determined as a function of the
currents on both sides of that span, leading to major differences in the structure of the
final equations and computational algorithms used to find the solutions.
The problem being analyzed is shown in Figure 6.9. A fault occurs on structure 0 of a
transmission line. The fault is either single, double or three phase to ground and the
transmission line is a single or double-circuit line.
The phase conductors may be transposed or untransposed. There are n and m spans between
the faulted structure and the left and right terminals respectively. There is one overhead
ground wire (or equivalent neutral conductor) in the transmission line.
The parameters of the network shown in Figure 6.9 are defined as follows. In order to
improve the readability of the equations, the superscripts used to designate the circuit
number (1 and 2 for a double-circuit) and the terminal side (l for left side and r for right
side) are dropped except when necessary.
Self impedance of phase conductors of the circuit in span k (ohms).
Zpk
ZXyk
Mutual impedance between conductors x and y in span k (ohms).
Structure ground impedance at extremity of span (ohms).
6-16
Zfx
Impedance of fault path for conductor x (ohms).
Zp
Equivalent source impedance at terminal (ohms).
Zg
Equivalent ground wire impedance at terminal (ohms)
Rt = rn
Ground impedance of terminal (ohms).
Re = r0
Ground impedance of faulted structure (ohms).
U
Transmission Line voltage (volts, phase-to-phase).
fi
Number of phase conductors (3 for a single circuit, 6 for a double circuit).
Equivalent Source
impedance
Left Terminal
Figure 6.9
Phase Conductors
Fau1 ted
Structure
No. 0
Right Terminal
Equivalent Network - General Case
The data given above are used to determine the currents in the loops shown in Figure 6.10.
Loop 0-x is defined by phase conductor x, the ground wire and the fault impedance. Loops
1 to n (or m) are defined by the ground wire and the structure impedance at the extremities
of each span. Loops 1 (left and right) have impedance Re in common, while loop n (or m)
has the terminal ground impedance as one of its branches.
For simplicity, it is assumed that the mutual impedances between phase conductors are all
equal and that the mutual impedances between the ground wire and any phase conductor
are also equal, i.e.:
= ZXyk ; where x or y represent the ground wire.
Zuk = ZXyk 5 where x and y represent a phase conductor.
This simplification will be removed in the next section.
6-17
Phase J + 1
Phase J
j+1>n
/
“pk
MMa-y-y/------ |-AAA/W|------ ---|-AA/WV------- AAAAAry--
■/(j+i>iCL
ej+1
(rv)Zf.
X/
X^-i X
------- ^SAA/Wj-------- -jAAAA/V—AAAr-|--------
zgnX "kX'ij
^X^-1 X
i-
n-1
Ground wire
Figure 6.10
zgl
fg
k-i
Fundamental Loops of the Network
The following equations govern the current in loops 1, k = 2, n-1 and n:
V
SF.
+ T.I. - r. I
11
j = 1 J-J
1 Z
+ R (I
c
s
- Ij = 0
1
■ y
Er
rk-1Ik-1 + TkIk " rkIk+1
Lj=l JJ
H
nSr
Lj = 1
r
,1
(6-43)
= 0
, + T I
n-1 n-1
0
n n
where
S,
k
= Z .
gk
k
mk
k-1
There are
m
pk
(6-44)
k
additional equations for each loop of type 0:
y
H
- Z .
n
Ef: - E sk\ + GF. + Zf;l! = E. ;
j=1 J
"f i i
k=1
i
for i = 1 ,y
(6-45)
where
n
^pk
G =
^mk
^uk^
(6-46)
n
H =
E
k=l
(zgk " Zmk + Zuk^
a
6-18
and Ej is the source voltage of phase i. The module of Ej is U and its angle will be 0°,
120° or 240° depending on whether conductor i represents phase a, b or c respectively. The
currents Ie and 1; are defined as follows:
I
e
= i£ + ir
1
1
If = F? ♦
I
!
Fr.
!
(6-47)
;
(6-48)
for i = 1, y
The Single-Sided Elimination Method
The form of Equations 6-43 suggests that the loop currents 1^ (k = 2, n) can be expressed
as a function of the total left terminal fault contribution
, the faulted structure current
Ie and the preceding loop current Ij.^. This is easily proved as follows:
First the equation related to loop k-1 is rewritten as:
(6-49)
Xk = Vk-2 + Vk-I + CkF*
where
Fil =
M
ZFj
j=l 1
Ak ' ' rk-2/rk-1
(6-50)
Bk = Tk-l/rk-l
Ck ' ‘ Sk-1/rk-l
Then, from the equation related to loop 1 the current I2 is written as:
I2
(6-5T
a2I£ + a2I1 + 62Ie
where
“2 = C2 = -Sl/r1
°2 = B2 + A2 = (TrRe)/rl = (Zpl + rl)/rl
(6-52)
62 = -A2 = Vrl
At this point, it can be proved by induction that Equation 6-51 is also valid for k = 3,
4,—,n. Based on the initial values given below, this general relation is:
Ik =
(6-53)
+ Vk-I + 6kIe
where
“k ' Akak-2 * Bkak-1 + C
0k ' Vk-2 + Bk0k-I
(6-54)
Sk = Vk-2 * Bk6k-1
6-19
The initial values of
cr^,
and
being:
a0 = al = o
= a1 = 1
(6-55)
6q = -1 and 6^
=
1
Assuming that the values of I^, Ie and
are known, all loop currents can be determined
using Equation 6-53. In this equation the current in loop k is computed following the
calculation of the preceding loop current (k-1). It should be noted here that the value of
oq , <rj and <5j can vary, at least theoretically, between wide limits (small to large values).
For that reason, the single-sided method is not suitable for computations involving large
numbers of spans and/or impedance values differing from each other by several orders of
magnitude. A detailed analysis on the sensitivity of the method to variations in the number
of spans and impedance values is not of interest to this study. However, the following
example will clearly illustrate the round-off errors which can be caused during the computations.
When it is assumed that there is no electromagnetic coupling between the phase conductors
and the ground wire (Z^ = 0), the sum of a [<+
becomes equal to 1. This is proved as
follows. From Equation 6-34, this sum is found to be:
“k * °k =
Since <*1+
Vv2
anc]
+ 0k-2> + Ek (V, * Vi’ + Ck
are equal to 1 (Equation 6-55) and since:
aQ+
Ak + Bk + Ck = ^"rk-2 + Tk-1 " Sk-1^/rk-1 = 1
Then the value of
+.
will remain constant and equal to 1 for all spans k.
Assuming that Zg^ = 1 f], r^ = 0.1 Q and Re = r0 ^ 0 Q, then Table 6.1 gives the computed
values of
ana
as performed by a 32 bit computer (^ 7 digits) and a 10 digit hand
calculator.
COMPUTER
CALCULATOR
K
ak
°k
V°k
0
1
2
3
4
5
6
7
8
0.
0.
-10.
-130.
-1560.
-18600.
-221650.
-2641210.
-31472880.
1 .
1 .
11 .
131 •
1561 .
18601.
221651.
2641210.
31472848.
1.
1.
1.
1.
1.
1.
1.
0.
-32.
Table 6.1
ak
0.
0.
-10.
-130.
-1560.
-18600.
-221650.
-2641210.
-31472880.
ak
1 .
1 .
11 .
131 .
1561.
18601.
221651.
2641211.
31472881.
Vak
1.
1.
1.
1.
1.
1.
1.
1.
1.
Round-Off Errors In Computations
The round-off errors are clearly illustrated in this table. Although it is possible to eliminate
this type of problem using suitable techniques, it is preferable to use a different
approach which is not subject to such complications. The double-si ded method is one possible
approach to this problem.
6-20
The Double-Sided Elimination Method
This method follows the same steps as for the single-sided method up to Equation 6-48.
However, instead of using Equation 6-49, Equation 6-43 is rewritten to produce the following
equation (k = 2, n-1):
(6-56)
= Vk-1 + BkIk+1 * v*
where
Ak
rk-1/Tk
(6-57)
Bk = rk-1/Tk
Ck = Sk/Tk
The
and
defined by (6-57) are always less than or equal to 1. This is a significant
computational advantage which drastically reduces round-off error problems.
Equation 6-56 becomes valid for k = 1 and n when the following definitions are made:
A] = -Re/(TrRe>
(6-58)
B1 =
C1 =
and
An “
(6-59)
Bn " -Rt/(Tn-Rt>
Cn = Sn/(T„-Rt>
Through easy but lengthy algebraic transformations it can be shown (see [9] for calculation
details) that the currents in loops 2 to n can be expressed by the following equation:
(6-60)
Ik = V* + VkIn + Ve
and the currents in loops 1, n-1 by:
(6-61)
Ik = ukI£ + vkIn + wkIe
where
Uk = (ak + 6k\-1)/Ak
Vk = ak/Ak
(6-62)
Wk = 6k6k-l/Ak
Ak = 1 " 6kek-1
uk = (nk + ek ak+1)/Ak
(6-63)
vk = ekak+1/Ak
wk = 0k/Ak
6-21
and for k = 2, n:
5k'
(6-64)
0k = °k*i5kBk/Ak
“k ' ^kV, * Ck)sk/Ak
and for k = 1, n-1:
£k = Bk/(l"Ak£k-1)
9k = ek-iekAk/Bk
(6-65)
^ = (W-,+ Ck)ek/Bk
Equations 6-64 and 6-65 are based on the initial values given in Table 6.2.
6.
i
ai
a.
i
£.
1
0.
I
ni
0
1
0
0
i
0
n
B1
A1
ci
i=n+1
A
i =n
Table 6.2
B
n
n
c
i=0
i =1
Initial Values
Detailed calculation shows that the 8, <r, e and tj coefficients are positive values which
can not exceed 1. The <r and 6 coefficients are also positive and are bounded as follows:
a. <
i
0. <
i
R
.+Z
n-1 gn
V
"gi
This is also another major reason why the method is less subject to round-off errors.
Equations 6-60 and 6-61 allow the calculation of the loop currents as a function of the total
fault contribution from the terminal (F^), the terminal ground system current (In) and the
current in the faulted structure (Ie).
These currents must be determined before one can proceed with the loop current calculations.
Replacing 1^ in Equation 6-45 by its expression on the right-hand side of Equations 6-60 and
6-61, yields:
j=1
IF* - fcl
(SjV,A
I
n
E
S. v. )I
k k
n
(6-66(a))
- (SjWj
6-22
?Bk«k)
p-r _ _£
Zj-.r . - E.
fI
I
i
where i = 1, m (m is the number of phase conductors) and Fjr
conductor i of the right terminal.
is the current in phase
A similar equation (6-66(b)) is applicable for the right terminal:
lur
cr r
(H -S,U|
PK) E
2
+
- (S^ +
j=1
^
(6-66(b))
eT
z^.F. =
(sW + EsX1*
fi i
1
Therefore, Equations 6-66(a) and 6-66(b) represent 2m equations with 2m + 3 unknowns. Three
more equations are needed. Two equations are obtained from Equation 6-43 applied to the
terminal loops (k = n for left terminal and k = m for right terminal):
(S* + r
v n
U
P
J E F • + (T
^ j
n
j=1
n-1 n-1
H
£
..5,
£ F1; + (Tr - rr 1Vr Jir - / 1Wr
m-1 m-1
*—1
j=1
j
m
n
T
_
I
= 0
(6-6?(a))
,V .) I - r , W ,1 - 0
n~1 n-1 n
n-1 n-1 e
y
(Sr + rr 1Ur .)
m
r
m-1 m-1
m
(6-67(b))
m-1 m-1 e
and the last equation is obtained from Equations 6-47 and 6-61:
£
u,
1
Equations
n
„
r£ .
F. +
f—1.
j
>y
j=1
r
u.
1
6-66, 6-67
m
cr .
X F- +
- , J
J=1
and
6-68
£T£ , r r
v.I + v,I +
1 n
1 n
,..£
. .r
(W. + W,
1
1
-
1)1
e
=
(6-68)
0
provide the solutions for the unknowns
Fj,
ln and
Ie.
The double-si ded elimination method is well suited for computer-based solutions. It provides
fast and accurate results without a large problem with undesirable effects, such as round-off
errors.
The computer program PATHS developed within the scope of this study is not based on this
method but rather on the following more general form of the method. This choice gave the
program increased capabilities and more flexibility to implement future extensions and
enhancements. In addition, because the equations developed are more general, they can be
used, after minor modifications, in a variety of other but still related problems such as
electromagnetic induction and substation grounding analyses.
6.4.3 THE GENERALIZED DOUBLE-SIDED ELIMINATION METHOD
The power system network being analyzed is shown in Figure 6.9. The parameters shown in
this figure are as described in the preceding section.
The phase conductors of the network may be considered as a number of elementary loops
consisting of short conductor segments between pairs of nodes, each grounded via a fictitious
very high impedance ground. When this concept is adopted, the fundamental loops of the
network may be selected as shown in Figure 6.11. In this figure, the loops related to the
phase conductors correspond to the transmission line spans. Hence, the nodes will be located
at each transmission line chain of insulators.
The concept introduced in the preceding paragraph is not unreasonable. The high impedances
to ground of the nodes are equivalent to the per span capacitances of the phase conductors.
These capacitances have not been neglected in the derivation of the final solution. However,
as can be observed from Equation 6-7Q(b), the effect of neglecting the capacitances can
easily be accounted for in the final equations.
6-23
Loop 0-y
r =R
Loop k
Figure 6.11
Fundamental Loops of the Network
The equations which follow are established using the left side of the network (left terminal).
Except when necessary to avoid ambiguity, the superscript l (for left) has been omitted
from the variables. It is obvious that similar equations can be written for the right-side
loops of the network.
The following equations apply for loops k = 2 to n-1 of each phase conductor i (i = 1,
M):
y+i
,
1
1
Xk " aikIk-1
T
T
“ik^l = 0
(6-69)
j=i
where
sijk ■ <2ijk * Rt>/Tik
;
for
I - 1,y
and
j = 1 ,y
sijk ' <2igk * Rt>/T,k
;
for
i = 1 ,1J
and
j = p + 1 = g
a.,
ik
= ck-,/Tlk
bik
= c.k /T..
ik
T.,
ik
= c, . + Z., + c
k-1
^ik
Lk
(6-70(a))
When the line capacitance is neglected, i.e •> ck is assumed to be a very high impedance (c(<
= oo), (6-70(a)) becomes:
a.k
=0.5
bfk
=0.5
(6-70(b))
6-Zk
An equation similar to 6-69 applies for the ground wire i = /* + 1 = g
Y'
A-!
j=1
s .. i/ + i g _ a..Ir, .
gjk k
i k k-1
bikIk+1
= 0
(6-71)
where
s_.i = Z ../I .
gjk
gjk gk
;
for
j = 1 ,p
J
’M
aik = a9k " rk-1/Tgk
(6-72)
^ik
kgk
rk'/^gk
T . = r, . + Z . + r,
gk
k-1
gk
k
Equations 6-69 and 6-71 can be condensed into the following matrix equation:
(6-73)
csk]CFk] = CAk]CFk-i] * [VCW
where the matrices are diagonal, column or square and are defined as follows:
Span Current Matrices (unknowns)
1
Ci
H
1
k-1
k
[Fk]
"
;
'
[Fk-i] =
ipk
CFk+1]
"
C,
1
. i9k.
I9
k-1_
Coefficient Matrices
'12k
s
K
21k
«
" v
v
[Sk]
N
ylk
’gi k-
gyk
6-25
0--
0
0
a2k
0
0
\
c/y
\
-0 a
0
0
0
Vik
agk
b.. 0ik
0 vb
2k
N
[Bk]
-0
o
-0
I
I
o
\
1
n0
-0 b
o
yk
b
gk
Matrix Equation 6-73, when applied to the left and right sides of the network, provides (m
+ 1) (n + m - 4) simultaneous linear equations to determine the (m + 1) (n + m) unknown
span currents.
The 4(m + 1) equations still required to completely solve the system are obtained from the
boundary conditions at the left and right terminals and on both sides of the faulted structure.
In the following, only the left side boundary equations are established.
Left Terminal
The following matrix equation holds at the last loops (terminal loop) of the transmission
line:
[S ] [F ] = [A ] [F ,] + [£]
n
n
n
n-i
(6-74)
where
Ign
12n21n
i
CS 3
n
i
i
8
v
\
X
\
X
S
5g1n-
V
• gyn
6-26
1
a,
1n
0?2
2n
[An]
EE]
\
i
x
0
—0 a
gn
for i = 1, y:
s. . = (Z.. + RJ/T.
i jn
j in
t
in
for j = 1,
s . = (Z . + R )/T
gm
gin
t'
gn
=
a.
cn~1,/T.in
in
= r ,/T
a
n-1 gn
gn
e.
= E./T.
i in
T.
in
= c
T
= r
gn
y + 1,
j * i
(6-75)
, + Z. + R.
n-l
in
t
, + Z
+ R
n-1
gn
t
Side of Fault Location
The following matrix equation can be written for the first loop of the transmission line:
CF1 ] = [B.|] [I2] - CH]
(6-76)
[F0]
where
1
s
121-
S211
x
igi
\
\
[S^
s
gi 1
ygi
’gyn
b11h °b21
[B1 ]
0
0---------------------- o bg1
6-27
‘11
12-
ig
22
21
[H]
■hgy
gi-
and, for
i = 1,
n:
for j = 1, y + 1,
surzrn/T-n
SgI1
99
j
i
i
Zgi1^Tg1
bi1 = C1/Ti1
b . = r./T
gi
1
gi
Hn = <zh + V/Tn
(6-77)
hgg - Re/Tg1
h.. = R /!.,
iJ
e 11
H . = R /T ,
gj
e gi
T., = Z.,+ c,
11
i1
1
T
1
gi
= z , + r,
gi
i
The fault path current matrix [F0] has been introduced in Equation 6-76. This matrix is
defined as follows:
■1£
-1
.21
'1
[F0] =
Matrix [F0] introduces
equations.
y£
1
gj>
m
+
+
I1r
I1
I2r
I1
>
1
=
o
[Fp
[pP
(6-78)
1?"
+ 1 unknowns and matrix Equation 6-78 generates
m
+ 1 linear
There are now as many equations as there are unknowns. Therefore, a solution can be
obtained by inversion of the complete matrix system or using other algorithms suitable for
solving a set a simultaneous linear equations. Obviously, this approach is reasonable only
when the number of spans in the network is relatively small. In practice, this is seldom the
case. Therefore, it is necessary to reduce the size of the system to a smaller number of
simultaneous equations.
6-28
The following double-sided matrix elimination method will allow each loop current to be
expressed as a function of the fault path current [F0].
Elimination Procedure Starting at the Terminal
Equation (6-74) can be written as:
[F n ] = [an ] [I n
,] + [A n ]
(6-79)
-1
where
[a ] = [S ]“1 [A ]
n
n
n
(6-80)
[V = [V~' [E]
Rewriting Equation 6-73 and taking into account Equations 6-79 and 6-80 results in the
following recursive formula valid for k = 2, n:
[Fk] = Cak]
[Fk_1] + [Ak]
(6-81)
where
Ca^
= [N,]-' [A,]
:xk:
= cn,]-' CBk: nk+1:
[V
- tsk] - [Bk] [tW
(6-82)
Elimination Procedure Starting at the Fault Location
Similarly Equation 6-76 is written as:
[F^ =
[F2] +
[F0]
(6“83)
where
Ir}^
= [S^-1
[B1 ]
[a1 ] = -[S^-1
(6-84)
CH]
By taking into account Equations 6-83 and 6-84, Equation 6-73 can be rewritten as a recursive
formula valid for k = 1, n-1:
CFk]" [V [,W + Cak] ^
(6‘85)
where
“k3
Cak] = [Mk]"1
CHk] = [Sk]
[Ak] [ak_1]
(6-86)
- [Ak] [Vl]
6-29
Double-Sided Elimination.
At a given loop i = 1, n-1 , matrix Equations 6-81 and 6-86 become:
] tr.] . [A.+1:
[f.:
-
cn,: [Fi+|: + [a.] [f0:
Multiplying the first of these two equations by r?j and adding both equations yields:
[F.] = [U.] + [V.] [Fq]
;
for i = 1,
n-1
(6-8?)
where
[U.] = [W.r1
Cn.]
[V.] = CW.]'1
[c.]
[W.] = [u ]
- En.]
[A.+1]
(6-88)
[a.+1]
;
[u] is the unit matrix
Matrix Equation 6-87 gives the currents in span i based on the currents [F0] circulating
in the fault paths. These currents are determined from Equations 6-78 and 6-87 applied
to span 1 on the left and right sides of the fault.
The following expression is obtained:
[Fq] = [F^] + [Fj] = cuj] + [uf] + { [V^] + [vj] 1 tFo]
which reduces to:
CF0] = | [u] - [V^] - [v!|] I"1 | cu|] + [u!|] |
(6-89)
where
[u] is the unit matrix
[VJ and [UJ are determined from Equation 6-88.
6.4.4 PRACTICAL CONSIDERATIONS
Ideally, transmission line ground fault computations should be made using the actual conductor
and structure ground impedance values. The conductor self and mutual impedances have been
discussed in Chapter 2. Although soil characteristics influence these impedances, the use of
an average soil resistivity yields impedance values only a few percent different from those
which could be measured directly.
Structure Resistance Values
Generally there are large variations in soil structure along the route of a transmission line,
and hundreds of transmission line structures. Often, the ground resistances of a large number
of these structures are not known. Sometimes, an average ground resistance value can be
assigned to a group of structures based on the shape of their footings, their installed grounding
system and earth geological characteristics common to the sites where these structures are
6-30
located. As can be seen from the example shown later, two situations can develop depending
on which structures are the ones for which there is no data or only an average ground
resistance value.
When these structures are located at some distance from the faulted structure, even
large variations in the average resistance values have little effect on the magnitude or
distribution of the fault current. This is clearly illustrated by the results of Figure 6.13.
These results are related to the transmission line of Figure 6.12 where a fault occurs at
structure 72 from the left terminal.
BASE
10
10
10
10
A
1
19
10
10
B
10
10
100
100
c
10
10
10
10
D
10
10
10
10
CASE
Figure 6.12
T0WE * RESISTANCE
10
10
10
10
10
10
10
—
—
10
10
10
10
10
10
1
10
10
10
10
10
10
10
10
19
1
10
10
10
10
19
1
10
10
10
1
10
(IN OHMS)
A Phase-to-Ground Fault on a Transmission Line
For example, a factor of 10 change in the resistances of four structures located midway
between the left terminal and the faulted structure (R37 = R38 = 100 ^ and R39 = R40 =
1 fi), does not change the currents at or near the faulted structures by more than a fraction
of one percent. The same conclusion applies when the resistances of structures 1 and 2 (the
structures which are the closest to the left terminal) are changed from 10
to 1 Q and
19 Q, respectively. In this last case however, the current in structure 1 rises from 2.9 A
(10
case) to 22.3 A (1
case). In both cases the total fault current remains constant.
However, when the faulted structure and/or one of its adjacent structure resistance
values are not well known, significant differences are obtained between computed results
based on the various assumed values. This situation is also illustrated in Figure 6.13.
The preceding discussion indicates that it is important to use accurate ground resistance
values for those structures which are closest to the point of fault. Utilities which measure
the resistance (or the soil resistivity) of all their transmission structures need only decide
whether to use the actual resistances of the remote structures or an average value. When
not all the required data are on file, a decision must be made as to whether ground resistance
(or resistivity) measurements should be conducted at the site of interest.
Fortunately, such predicaments are scarce in practice. When a fault current distribution
analysis at a given structure is necessary, that structure is usually either special or in a
special area. In either case, the structure may have already been the subject of
particular attention and suitable data about the structure and the soil conditions where it
is erected will typically be available.
6-31
For example, the structure may be located in a densely populated area and require a specially
designed grounding system. Alternately, an incident caused by a ground fault at a structure
may require a detailed investigation into the cause of the incident. In such cases,
detailed measurements are generally required.
Mutual Coupling
The mutual impedances between the ground wire and the phase conductors reduce the apparent
impedance of the circuit seen from the feeding terminals. Therefore, the value of the total
fault current calculated is larger than the value computed neglecting these mutual impedances.
The mutual coupling has also another effect which is to force the circulation of "trapped"
current in the ground wire which returns directly to the source. This current plays a major
role in reducing electromagnetic induction on neighbouring circuits. This effect is commonly
designated as the ground wire screening effect.
Terminal Structures
When the transmission line is relatively short, all structures will carry the fault current to
ground in the same manner as for the faulted and adjacent structures. However, in the case
of long lines, the terminal structures start collecting currents from earth as if these structures
were part of the terminal grounding system.
1600-
aicc
cc
D
Q
D
<
LL
_)
<
oHhUO
Case
Base
Total Fault I^
(in Amperes)
2757-667
A
2757.673
B
2757-667
C
2811.870
D
2793-650
Case C
(R72 = U2 ; R71 = 19 it)
z
HIcc
h-OD
3
<0S
85
STRUCTURE NUMBER
Figure 6.13
Effects of Ground Resistance Values
6-32
90
148
Central Structures
For a long transmission line, the structures located in the central area between a terminal
and the faulted structure conduct at most, a negligible current to earth. Therefore, these
structures need not be modelled in the circuit.
This is an important effect, since it permits the analysis of long and short tramsmission
lines based on a limited number of structures represented in the circuit. For example, if a
maximum of 100 structures per terminal is permitted by a computer program, transmission
lines up to approximately 20 miles in length can have all structures included in the model.
For longer lines, it is necessary to reduce one or several sections of the transmission line
into equivalent Pi sections. For example, all structures can be included for 10 miles at each
extremity of the transmission line and the remaining central portion of the line can be
replaced by one equivalent single span of appropriate length.
REFERENCES
1 - Janos Endreyni, "Analysis of Transmission Tower Potential During Ground Faults", IEEE
Transactions on Power Apparatus and Systems, Vol. PAS-86, No. 10, October 1967.
2 - R. Rudemberg, "Transient Performance of Electric Power Systems", McGraw-Hill Book
Company, 1950 (book).
3 - F. Desieno, P. Marchenko, G. S. Vassel, "General Equations for Fault Currents in
Transmission Line Ground Wires", IEEE Transactions, Vol. PAS-89, No. 8, November/December
1970, pp. 1891-1900.
4 - R. Verma, D. Mukhedkar, "Ground Fault Current Distribution in Sub-Station Towers and
Ground Wire", IEEE Transactions, Vol. PAS-98, No. 3, May/June, 1979, pp. 724-730.
5 - A. J. Pesonen, "Effects of Shield Wires on the Potential Rise of HV Stations", Offprint
from SAHKO-Electricity in Finland, 53, 1980, No. 10, pp. 305-308.
6 - S. A. Sebo, "Zero Sequence Current Distribution Along Transmission Lines", IEEE
Transactions, Vol. PAS-88, No. 6, June 1969.
7 - C. Dubanton, G. Gramd, "Influence of the Location of the Fault on the Screening Effect
of Earth Wires", CIGRE Paper 36-01, August 1974.
8 - F. Dawalibi, D. Mukhedkar, "Ground Fault Current Distribution in Power Systems - The
Necessary Link", IEEE Paper AF77 754-5, Summer Meeting, Mexico 1977.
9 - F. Dawalibi, "Ground Fault Current Distribution Between Soil and Neutral Conductors",
IEEE Transactions, Vol. PAS-99, March/April 1980, No. 2, pp. 452-461.
10- F. Dawalibi, D. Bensted, D. Mukhedkar, "Soil Effects on Ground Fault Currents", IEEE
Transactions, Vol. PAS-100, No. 7, July 1981, pp. 3442-3450.
11 - E. Clarke, "Circuit Analysis of AC Power Systems", Wiley, New York 1956.
6-33
LIGHTNING PERFORIVIANCE
OF TRANSIVIISSION LINE STRUCTURES
7.1 GENERAL
Literature on lightning phenomena and related effects is voluminous. Even when limited
to the subject of power system engineering, the list of research work published in the last
50 years remains impressively extensive. A meaningful review of the important literature
which has contributed to a better understanding of transmission line performance during
lightning activities involves hundreds of papers and reports published by distinguished researchers
throughout the world. This formidable task is beyond the scope of this chapter which
concentrates on the response of transmission line structures to direct lightning strokes.
Furthermore, no attempt is made to examine the problem in a broad power system engineering
perspective which would necessarily involve a probabilistic approach in order to reflect the
statistical nature of lightning and its effects on power systems [1,4]. This chapter reviews
analytical methods and computation techniques presently available to determine the
performance of a transmission line structure struck by lightning.
7.2 EFFECTS OF LIGHTNING ON POWER LINES
Among the many events which can lead to a power system outage or equipment damage,
lightning is certainly the major identifiable cause [2]. This has been so since the earliest
days of the electric power industry. There are an estimated 1000 thunderstorms at any
moment in time throughout the world. The most visible manifestation of a thunderstorm is
the thundercloud, a strongly convective cumulo-nimbus cloud. The phenomena which take
place inside this cloud are not well known because of the extremely violent internal turbulence.
Moreover, the mechanism by which thunderclouds become electrified is still the subject of
controversy [1]. The lightning discharge mechanism has been the subject of extensive research
for many years however, and is now well understood. The following is a very brief summary
of the lightning discharge process. A comprehensive description of this process can be found
in [1].
7.2.1 THE LIGHTNING FLASH
The lower portion of a thundercloud is usually negatively charged while its upper part carries
positive charges. Thus, most cloud discharges to ground are negative discharges. Occasionally,
positive discharges are produced by clouds with a small positive charge at their base.
7-1
The leader stroke is always initiated at a point of maximum electric field strength. This
point is generally located at the base of the thundercloud, initiating a downward leader.
Less frequently, this point is located at the top of a tall building or structure or
elevated ground, resulting in an upward leader, often termed an upward streamer. Frequently,
this upward streamer develops as a downward leader approaches the earth.
In the initial stage of the formation of a negative lightning stroke, the downward leader
starts at the negatively charged base of the cloud and proceeds towards ground in successive
steps, separated by time intervals of 40 to 100 ms (stepped leader). Each step follows a
seemingly random path and is believed to be practically independent of the nature, configuration
and number of the various grounded objects below. However, as the electric charges in the
cloud follow the leader stroke at an average speed of 100 km/s, the electric field on the
surface of grounded structures increases rapidly until a critical electric field strength of
approximately 500 kV/m is reached, causing the initiation of upward streamers from the
most prominent structures.
The first discharge occurs when one of these streamers reaches the tip of the downward
leader. Following the first discharge or return stroke, there may be one or several successive
discharges of various magnitude and duration.
The distance from ground at which the upward streamer is initiated is called the "striking
distance" and plays a major role in the design of shield wires for the protection of transmission
lines against lightning outages.
The preceding discussion of the leader stroke mechanism suggests that ground resistance
may not be a factor in determining the probability of a lightning stroke to a particular
structure. This conclusion however, is challenged by recent statistical and laboratory
observations which confirm the common belief that lightning is attracted by low ground
resistance structures [3]. The attract!vennes of good grounds to lightning can be explained
by the process taking place during the last stage of the stepped leader progression towards
the earth. As the distance to earth decreases, several streamers are initiated from various
locations. However, the major portion of the discharge will occur along the path of lowest
impedance. This explains the occurence of simultaneous strokes at different locations. It is
important to note that the lightning susceptibility of low resistance grounds should not be
interpreted as a reason to seek high resistance transmission line structure designs in an
effort to reduce the number of strokes on the line. Regardless of structure resistance, the
transmission line remains the preferred target for a lightning discharge and the transmission
line structure will dissipate a direct lightning stroke more easily if it has a low resistance
value.
7.2.2 THE BACK FLASHOVER MECHANISM
Fifty years ago, it was generally believed that protection of transmission lines from direct
strokes was impossible. Now, all but a few transmission lines are designed to withstand a
large proportion of direct lightning discharges. Since the importance of service continuity is
constantly increasing, research efforts are being directed towards the development of improved
protection equipment and more accurate methods of predicting the lightning performance of
transmission lines, particularly with regard to the response of structures to direct lightning
strokes.
There are three mechanisms by which insulation flashover results from a lightning stroke:
a - Electromagnetic induction,
b - Direct stroke or shielding failure,
c - Back flashover.
7-2
Transient voltages are electromagnetically induced in power lines as a result of lightning
strokes occuring in the vicinity of the lines. These induced voltages are caused by the very
rapid collapse of the electric field due to the lightning current discharge. This type of
induced voltage, although the cause of numerous problems on distribution systems, is generally
harmless to tranmission lines rated 100 kV or more. This source of distribution line insulation
failure is not examined further in this study. The reader will find a wealth of useful
information on this subject and references in [1].
Even when a transmission line is equiped with shield wires optimally located to intercept
lightning strokes, the line may, occasionally, be subject to a direct stroke. This possibility
is explained by the previously defined "striking distance", which is the basis for various
electrogeometric theories developed to explain outages due to the shielding-failure flashover
mechanism. These concepts will not be developed here and reference is again made to [1]
as a comprehensive source of additional information. This chapter is devoted to the back
flashover mechanism, defined as the insulation failure due to excessive rise in potential
of the transmission line structure when struck directly by lightning. The case of a lightning
strike to the overhead shield wire at midspan can be analyzed by essentially the same
methodology.
Discharge of lightning current into earth via a transmission line structure may raise the
potential of the structure with respect to remote ground to several times the
transmission line voltage. If this value exceeds the dielectric strength of the transmission
line insulators, a back flashover occurs, soon followed by a power frequency arc fault along
the ionized air path created by the lightning arc. This mechanism is illustrated by Figure
7.1.
IDEALIZED
LIGHTNING SOURCE
GROUND
WIRE
stress
FOOTING
GROUNDING
REMOTE
GROUND
(a)
Figure
DIRECT LIGHTNING STROKE
7.1
(b)
EQUIVALENT SIMPLIFIED CIRCUIT
A Typical Transmission Line Back Flashover
The majority of lightning outages on shielded transmission lines are the result of back
fl as hovers, since only a small porti on of the strokes directly strike the phase conductors of
an effectively shielded line.
7-3
At the instant of impact of a lightning stroke on a transmission line structure, current waves
originate at the point of impact and travel along the various paths at velocities between
0.2 and 0.9 the speed of light. Current waves move along the overhead ground wires towards
other structures and a current wave flows to ground through the structure and its grounding
system, including the structure footing and counterpoises, if any. Upon arrival at a terminal
(local grounding system) or junction points, (adjacent structures) the waves are partially
reflected and return to the point of impact where they interfere with the continuing initial
current discharge. This process is depicted in Figure 7.2. Generally, successive reflections
up and down the affected structure and from adjacent structures reduce the voltage buildup
across the insulators well before the lightning discharge process is completed. Hence, the
time of maximum likelihood of an insulation breakdown is generally at the very beginning
of the lightning discharge for fast front waves, and a few microseconds after the initial
stroke for slower front waves.
LIGHTNING__
STROKE WAVE
CONCENTRATED
GROUNDING
SYSTEM
i
GROUND
WIRE
PHASE
CONDUCTOR
INDUCED.
WAVE
INSULATOR
STRING
Figure 7.2
ORIGINAL
/ WAVE
COUNTERPOISE
REFLECTED
WAVE
Travelling Waves After a Lightning Stroke to a Structure
The usual criterion for the occurence of a back flashover is that the calculated overvoltage
curve intersects the insulator volt-time curve. More sophisticated criteria could be used to
account for variations in the impulse strength with waveshape [4]. However, a reliable
and realistic flashover prediction is dependent on the accuracy of the computation of the
stress voltage applied across the insulators. This accuracy is essentially dependent on the
reference analytical model and assumptions used to simulate the back flashover mechanism.
It is also heavily influenced by the selected values of parameters which singnificantly affect
the physical process.
Over the past fifty years, several analytical models of varying degrees of complexity
have been proposed for back flashover computations [5,7,11-15]. As yet, none of these methods
have exhibited an obvious superiority over the others. The reasons for this will become
evident as we proceed through this chapter. Nevertheless, it should be noted that most of
the researchers working on these analytical models have reported reasonable agreement
between their computations and measurements. Furthermore, as will be illustrated, different
analytical models will usually lead to similar results if the initial values of the variables
are judiciously chosen [5]. Clearly, it is a situation where analytical and computational
difficulties impose too many simplifying assumptions which, although appropriate in some
cases, are not always justifiable. Furthermore, because field measurements are equally
complex and difficult to interpret, the experimental results have not only failed to
answer the controversial issues, but have in some cases, introduced additional confusion to
this intricate subject.
7.3 ANALYTICAL MODELS FOR BACK FLASHOVER COMPUTATIONS
Figure 7.2 shows the passive elements of the lightning current path which, if present, will
have a major influence on the lightning performance of the transmission line structure:
-
Overhead ground wires.
Phase conductors.
Phase insulators.
Transmission line structures.
Concentrated grounding systems.
Counterpoises.
In addition, characteristics of the current source, or lightning stroke channel, such as current
magnitude and wave shape can significantly affect the lightning performance of the structure.
The accuracy and complexity of the analytical model used in the computations will depend
not only on the elements and source parameters retained in the simulation, but also on their
representation in the model. This section describes several models used by design engineers.
7.3.1 SIMPLIFIED MODELS
The solution of electrical transient problems leads to differential equations which, unfortunately,
very quickly become untractable even with only moderate increases in the complexity of
the electrical circuit. This difficulty is somewhat alleviated by the use of the Laplace
transform which converts the differential equations into equivalent algebraic equations, similar
to the ones obtained by a steady state analysis of the problem [6]. However, the inverse
Laplace transformation, required to obtain the final solution in the time domain, generally
cannot be obtained analytically. Practically, however, there are several techniques, most of
them suitable for computerized applications, which provide the inverse transformation
with acceptable accuracy.
Various authors have proposed simple electric circuits consisting of lumped elements as a
model for determining the potential at the top of the structure [7-11]. The most widely used
circuit is based on the so-called AIEE method [12]. Three typical models are shown in Figure
7.3. Because of the symmetry of the problem, the transmission line is shown folded back
on itself at the structure that was struck by lightning. Hence all the original circuit
parameters, except those related to the structure which was struck, are halved.
7-5
GROUND
WIRE
(l-A)s(t)
PHASE
CONDUCTOR
(a)
Figure 7.3
(b) AIEE METHOD
(c)
Simplified Models
The Inductance/Resistance Method
The simplest approach is to neglect all parameters except the structure ground resistance,
R. If i(t) represents the portion of the stroke current flowing in the structure at time t,
then the structure top potential with respect to remote ground is simply:
e(t) = Ri(t)
For very high values
approximation gives
leads to increasingly
resistances of 10 to
(7-l(a))
of structure resistance (say about 100 ohms and more), this very rough
a reasonable order of magnitude approximation of the top potential. It
optimistic values as the resistance decreases to more typical structure
20 ohms.
The results are considerably improved if the transmission line structure is represented by
an additional lumped inductance L, as shown in Figure 7.3(a). In this case the structure top
potential is:
e(t) = Ri (t) + L -—^1
(7“ 1 (b))
The structure current i(t) is a function of the stroke current s(t), the lightning channel
circuit and other circuit paths. Solutions are provided in [7] when the stroke current is
represented by a double-ramp wave. For arbitrary current waves, the solution may be obtained
as follows.
First, a unit step stroke current u(t) (i.e., u=0 for t<0 and u=l for t>0) is assumed to strike
the structure top. Based on the parameters of the circuit model used, the current in the
structure is then determined. Let this current be g(t). Note that g(t) is often referred to
7-6
as the indicial response of a system to the unit step stimulus u(t). For example, in Figure
7.3(b), the fraction of the stroke current flowing in the overhead ground wires is estimated
as a constant fraction (1-A) of the total current. Therefore:
g(t) = Au(t)
(7-2(a))
Generally, A is a complex function of time and of several circuit parameters. From Figure
7.3(a), the following equation is obtained:
Z
g(t) =
T - [ 1-e'at ] u(t)
g
(7-2(b))
2r 7
where
2R+Z
a
g
~2T
Next, the superposition technique is used to derive the current i(t) of the structure following
an arbitrary stroke s(t). The stroke s(t) is approximated as the sum of a series of step
functions of appropriate magnitude suitably displaced in time (see Figure 7.4(a)). The total
structure current i(t) is then expressed as the sum of the individual currents computed using
Equation 7-2, for each previously defined step function:
i(t) = s (0)g(t) +
[A. g(t-t. )]
k=1
where
K
(7-3)
K
may be selected as:
xk.
k
■jViLLlilki flT
V, - tk
s (t)
CURRENT WAVE
s(t)
s(t)=at
(t)=[at+B]u(t-T)
0
tit
k
k+1
TIME
(a) ARBITRARY WAVE
Figure 7.4
(b) DOUBLE-RAMP WAVE
Approximation of a Current Surge
7-7
Alternatively, a closed analytical form solution may be obtained from Duhamel's integral:
i (t) = s (0)g(t)
+J~
-j- g(t-T)dx
(7_/*)
A close examination of Equation 7-4 reveals that it is the limit of Equation 7-3 when the
interval At between successive times, (t^, t^i) decreases to zero (see also the definition
of Xk).
For the double-ramp stroke current illustrated in Figure 7.4(a) and the circuit of Figure
7.3(c), K on cel [7] obtained relatively simple expressions for the current i(t) for times less
than twice the travel time of a reflected current wave returning from the adjacent transmission
line structure.
Further sophistication can be introduced by including the structure and grounding system
capacitances to ground. This is usually of no practical interest since the extremely low time
constant, RC, results in negligible capacitance effects for normal stroke current rise times.
The AIEE Method
The AIEE method illustrated in Figure 7.3(b) assumes that the structure top potential is
equal to the voltage drop across the structure ground resistance R plus the voltage determined
from the structure self-inductance, assumed to be a constant 20 mH.
The potential across the insulator strings is obtained from the structure top potential,
decreased by an amount equal to the electrostatic voltage induced in the phase conductor
by the overhead ground wires. This method was translated into charts and used extensively
for many years [12].
7.3.2 TRAVELLING WAVE MODELS
Although sometimes accurate, the simplified models often fail dramatically in predicting the
lightning tripout rates of some EHV lines. Apparently, the tall transmission line structures
and their relatively low ground resistances cause the voltage drop across the structure to
become a major fraction of the top potential. Thus, preference is given to the use of the
surge impedance of a structure rather than the lumped inductance. This approach is further
justified through better accuracy in the calculation of steep-front current wave effects. It
is also consistent with other traditional methods used in lightning performance
calculations which account for the surge impedance of various lightning path components,
such as phase conductors, ground wires and counterpoises. Finally, it is more suited for use
with travelling wave models and it is in reasonable agreement with advanced concepts of
electromagnetic field theories [5,13-15].
A Simple Equation
If the transmission line structure and lightning stroke path surge impedances are assumed
equal to Zg and all travelling wave reflections except the first one at the base of the
affected structure are neglected (see Figure 7.5), the potential of the top of the structure
becomes [16]:
e(t)
Zsi(t) [u(t) +
R -Z
,
irsr U<t-2T>]
7-8
(7-5)
where Rs is the structure ground resistance and T is the time of travel of the current i(t)
from the top to the bottom of the structure. If the transmission line structure is represented
as a lossless transmission line, the surge impedance Zs is:
Z
(7-6)
=yil/c'
where l and c are the per unit length values of distributed inductance and capacitance of
the structure. In practice, the surge impedance of transmission line structures varies between
60 to 180 ohms. The lightning path surge impedance, as estimated in the literature,
varies from 200 to 600 ohms. Hence, Equation 7.5, which is based on the assumption of
equal structure and stroke path surge impedances, must be used with caution.
An Improved Equation
If it is assumed that the structure and its connections have no effects upon the stroke
current, which is equivalent to saying that the lightning channel impedance is large compared
to the equivalent surge impedance Z as seen from the top of the structure, and, if it is
further assumed that a step (rectangular) wave Iu(t) is injected by the stroke into the
structure and ground wire, as shown in Figure 7.5, three equal voltages waves e(t) will travel
away from the structure top along the three paths identified previously.
GROUND
WIRE
3e(t-T
PHASE
CONDUCTOR
T= TRAVEL TIME = H/v
(a) LIGHTNING STROKE ON A
TRANSMISSION LINE STRUCTURE
Figure 7.5
(b) REFLECTION LATTICE DIAGRAM FOR
TRAVELLING WAVE CALCULATIONS
Lightning and Travelling Waves
In the initial stages, several reflections will occur at the top and base of the affected
structure before the reflected waves from the adjacent structures return to the observation
point, i.e., the arm of the structure. The following analysis is carried out for the time period
preceding the return of the reflected waves from the adjacent structures.
The voltage wave e(t) is equal to the product of the stroke current and the equivalent surge
impedance:
Z Z
e(t) = Zlu(t)
-2 s
1+21
(7-7)
lu(t)
As illustrated in the lattice diagram of Figure 7.5, the wave arrives at the structure arm
after a time interval, h/v, where v is the wave velocity in the structure (0.7 to 0.9 the
velocity of light). At the same instant, a voltage wave Me(t-h/v) proceeds along the
phase conductor as a result of the retarded electric coupling with the ground wire. M is
the coupling factor between the phase conductor and ground wire.
The voltage wave e(t) moves down toward the base and is subject to a first reflection from
the structure ground resistance. The reflected wave /3e(t) proceeds upwards and arrives at
the structure arm after a time (2H-h)/v. It is then partially reflected back towards the base
of the structure. This reflected wave causes a voltage a/3e(t-2H/v-h/v) at the structure arm,
while the refracted waves, moving along each side of the ground wire, induce a voltage
wave M(l- a)/Se(t-2H/v+h/v) on the phase conductor. The resultant voltage V(t) across the
insulator strings can be calculated with the help of a lattice diagram of the type shown by
Figure 7.5(a). This calculation leads to the following expression:
'l-M)u(t-T) +
V(t) = ZI
°o r
E °J
j=i L
r
eJ [u (t+x-jT) + [a - M(l-a)J u(t-r-jT)
L
(7-8)
where a and /3, the reflection factors at the top and base of the structure respectively,
are given by the following expressions:
1-21
9
s
a = -r2-----------
+
(7-9(a))
21.
R s - Zs
R s + Zs
(7-9(b))
where r is the wave travel time from the top to the arm of the structure (r=h/v) and T
is twice the wave travel time from the top to the base of the structure (T=2H/v).
Surge Impedances
Equation 7-8 can be expanded to include the wave
exercise will not be undertaken here since it is
offer additional insight into the travelling wave
applicability of the surge impedance concept will
to eliminate a major weakness of this approach.
reflections from adjacent structures. This
not essential to this study and does not
technique illustrated above. Instead, the
be discussed and an attempt will be made
Equation 7-8 requires calculation of the reflection coefficient and coupling factors, which
in turn, are derived from surge impedance values. Thus, the accuracy of Equation 7-8 in
predicting the voltage stress across the insulator strings is dependent on the degree to which
these factors accurately represent the fundamental parameters of the physical process and
on the accuracy of the expressions used to represent these parameters. Since the travelling
wave calculations have assumed constant surge impedances and lossless metallic conductors
and structures (real-valued surge impedance), neither of these requirements are adequately
satisfied. This subject will be expanded upon in Sections 7.4 and 7.5. It should be emphasized
7-10
that the constant surge impedance assumption is not necessarily valid in all problems, since
surge impedance generally varies with time and is dependent on the transmission line structure
configuration and shape of the stroke current wave. This dependency was shown by a number
of authors [5,13-15,17-19] who analyzed the response of simple structure configurations
(cylinder, cone) and various current waveshapes. For example, the surge impedance of a
cylindrical structure to a rectangular wave current was determined [15] as:
Zs = 60 ln[v^(ct/a)j
(7-10(a))
where
c
t
a
isthe velocity of light,
isthe time,
isthe cylinder radius.
If the rectangular wave is replaced by a ramp wave, the surge impedance becomes [17]:
Z
s
60 In
/let
a
a
2ct
+
a
(7-10(6))
2ct
If the transmission line structure is represented as a conical structure, then the surge
impedance, when energized by an arbitrary wave current, has been shown to be constant
[17]:
Z
s
60 1 n
r'
—r
(7-11)
Lsi n6j
where 8 is the half-angle of the cone. This constant surge impedance is in reasonable
agreement with experimental measurements using model structures with a conical shape
[17,20].
The foregoing discussion suggests that if time-dependent surge impedances (transient or
dynamic surge impedances) are used instead of the less exact constant surge impedances,
accurate solutions eguivalent to those obtained from field theories can be attained using the
travelling wave technigue. This is convincingly demonstrated in a discussion of the field
theory approach described in [5].
The travelling wave technigue was used to develop a simple lightning back flashover computer
program (STRIKE) for this EPRI project. The main feature of this program is that the stroke
current wave is assumed to be made of a succession of several curvilinear segments of three
basic types, suitably displaced in time. The rectangular, ramp, and exponential wave types
were used on a variety of structures represented by their equivalent cylindrical representation.
Typical results related to the problem illustrated in Figure 7.6, are shown in Figure 7.7.
Because of the extensive work required to improve the capability and flexibility of the
program in accounting for actual conditions such as variable structures, counterpoises, soil
breakdown, etc., as discussed in Sections 7.4 and 7.5, no significant effort was made to
enhance the program. Thus, the usefulness of the program is essentially academic.
7-11
IMPEDANCES (IN £})
EQUIVALENT
CYLINDER
GROUND
WIRES
H=30m
STRUCTURE
GROUNDING
SYSTEM
Figure 7.6
CASE
NO.
7" 12
R
CO
15
2
hOO
oo
15
3
400
550
15
h
100
550
15
0.<l
Typical Structure Top Potentials
g
00
TIME (jus)
Figure 7.7
Z
1
Illustration of a Typical Problem
0.2
Zt
s
7.3.3 ELECTROMAGNETIC FIELD MODELS
As long as the lightning performance predicted by approximate methods was satisfactory,
no need was seen for a more rigorous approach. Early in 1950, however, the lightning outage
rates of several transmission lines were found to be about 10 times those predicted by
design. This anomaly stimulated considerable research work and as a result, an advanced
electromagnetic field theory was proposed [5,13-15]. This theory validated the analytical
model based on the surge impedance concept, provided that the concept was extended to
include time varying and wave shape dependent surge impedances, as previously discussed.
Unfortunately, it failed to explain the high lightning outage rates. Nevertheless, the field
approach remains one of the most rigorous theoretical methods to describe the lightning
response of transmission line structures.
Two theories have been developed. The field-cancellation method, introduced by Wagner [13],
and the loop-voltage method, originally employed by Lundholm et al [5] and then by Wagner
and Hileman [14-15]. Both theories are based on the fundamental electromagnetic equations
of Maxwell. The loop-voltage method is simpler and lends itself to practical calculations at
the expense of slightly less accuracy than the field cancellation method. The loop-voltage
method is explained in detail in [5] and [14] and will only be described briefly. It is of
interest to note that the field cancellation method is based on the determination of a
distributi on of charges which produce a quasi steady-state electrostatic field (called
"cancellation field") opposite to the electromagnetic ("forcing") field produced by a set of
travelling waves. The loop-voltage method, on the other hand, ignores the effects of charges
because the line integral of an electric field (or voltage) about a closed loop is independent
of the electric charges.
Electric Field Produced by a Moving Uniform Distribution of Charges
If the uniform distribution of electric charges shown in Figure 7.8 is considered and if it is
assumed that these charges are moving along the cylindrical conductor at a velocity v equal
to or less than the velocity of light c, the following argument can be made.
Figure 7.8
Moving Wave of Electric Charges
Since electromagnetic waves in free space travel with the velocity of light, the effect of
an elementary charge, dq=qdx, located at point M(x,0) at the instant t would only reach the
observation point P(w,y) after a time delay r/c where r is the distance between M and P.
Hence, the electric field at P is retarded and the potential at point P is called the retarded
potential. The preceding observation suggests that it is possible to compute the retarded
potentials at any point and time if the distribution of electric charges as a function of time
is known.
7-13
From electromagnetic field theory, the retarded vector potential A is related to the current
I injected into a long cylindrical conductor as follows (see Figure 7.8):
I(x,t-r/c)
dx
r
A =
(7-12)
Where I represents the current vector flowing along the cylindrical conductor (|I|= I = qv)
and r is the distance between the conductor element dx and the observation point P. It has
been assumed that the current wave I is rectangular as illustrated in Figure 7.8. This
assumption will be used throughout unless indicated otherwise.
The vector potential at point P and time t is axial (no radial component) and is caused by
the charge distribution extending from the origin o (x = 0) to the point M (x = z)
reached by the current wave at the instant t-r/c. Therefore, the retardation effect can be
introduced as follows:
_ UoI /
% Jo
dx______
/(w-x) 2 + y2
(7-13)
where
Z =
c-v
U ± c
TO2 +
R2
+ w
(7-H)
and
U = ----- (vt-w)
c+v
-V
(7-15 (a))
c-v
c+v
(7-15 (b))
The integration
expression:
A
of
s i nh
Equation
7-13
is
straightforward
and
+ sinh"1 [^]
results
in
the
following
(7-16)
The vector potential A can be used advantageously to determine the electric potential
difference between two points. As stated, the sum of the electrostatically induced voltage
around a closed path is zero. Mathematically, this is equivalent to:
1
Folcv
Vpath
4tt(c + v)
dx
(7-17)
+ R2
Computation of the voltage stress developed across an insulator string consists of an evaluation
of Equation 7-17 along a closed integration path, including the insulator string as one portion
of the path. In the following, the integration will be carried out in steps involving various
portions of the closed path. This integration is necessary in the axial direction only, since
the vector potential is axial and thus, has no radial component. Hence, If PI and P2 are
two points located on a line parallel to the current carrying conductor (see Figure 7.8), the
potential difference between these two points is determined from Equation 7-17 as:
V
Pi
-V
P2
dolv
kn
s i nh
-1 Mi
R
7-14
s i nh
U
RJ
(7-18)
where Uj and U2 are defined by Equation 7-15(a). If v is equal to the velocity of light,
then Equation 7-18 should be expressed in logarithmic form. Thus for v = c:
V
Ct " W!
P
(7-19)
Ct - W2.
At this stage, it is of interest to note that any point outside the sphere of influence, i.e.,
the sphere centered at O with radius ct, is not influenced by an electromagnetic wave.
Consequently, the potential along a portion of the path lying outside the sphere is zero.
Thus, when PI , P2 or both are outside the sphere of influence, wj , W2 or both must be
substituted by the cutoff values, as illustrated in Figure 7.8:
w = ± t/c2t2 - y2
where the negative sign applies to a point P located to the left of the origin in Figure 7.8.
Determination of the Currents in the Ground Wire and Structure
Through repeated application of Equation 7-17 along a suitable closed path, it is possible to
determine the current Ig flowing on each side of the ground wire and the current Is moving
downward in the structure (see Figure 7.9). If it is assumed that the surface of the earth
is an equipotential surface (zero soil resistivity) and that the structure and ground wire are
perfect conductors, the value of Vpath in Equation 7-17 along the path JFK shown in Figure
7.9, must be zero since it only involves perfect metallic circuits and a segment outside the
sphere of influence (segment FK). Therefore:
#*‘-/$rdx'°
(7-20)
Noting that the currents shown in Figure 7.9 produce only tangential fields, Equation 7-20
is readily solved using Equation 7-18. For simplicity, it is assumed that the current wave
velocity in the structure and ground wire is the velocity of light. Equation 7-19 can then
be used instead of the more complex equation, 7-18. Integration along the JFK loop (see
Figure 7.9) leads to:
I
Poc
g
4tt
1 n
ct-a
ct-a
+ 1 n
ct+a
ct+a
■I
s
4u
1n
ct~b
ct-8
= 0
(7-21)
where
PocAtt = 30
(a+a)2 + b2 = c2t2
(3+b)2 + a2 = c2t2
after a time t such that a«ct, Equation 7-21 reduces to:
'g [6°'"T-J-A60(7-22)
The terms in brackets represent the transient surge impedances, introduced earlier (see
Equation 7-10(a)). The bracketed term on the left is defined as the transient surge impedance
of the ground wire, and the one on the right is the structure transient surge impedance.
7-15
Finally, the sum of the structure and ground wire currents must be equal to the total
lightning stroke current 1^, i.e.:
21
g
+ I
s
= T
(7-23)
t
Ig and Is are now determinable from Equations 7-22 and 7-23. It is interesting to note that
these two equations are the same as would be derived using the surge impedance concept.
GROUND
WIRE
STRUCTURE
Figure 7.9
Integration Path of Vector Potential
Voltage Across the Insulator String
With the currents in the structure
path must be selected to determine
shown in Figure 7.10 is selected to
induced in the phase conductor is
insulator voltage was estimated to
and ground wire determined, another closed integration
the voltage across the insulator string. The loop OGBDFO
perform this calculation. It is assumed that the current
negligible. The effect of this induced current on the
be about 8% on the conservative side [14].
GROUND
WIRE
GROUND
WIRE
PHASE
CONDUCTOR
(a)
VIEW ALONG TRANSMISSION LINE
Figure 7.10
PHASE
CONDUCTOR
(b)VIEW TRANSVERSE
LINE
Voltage Across Insulator String
7-16
TO TRANSMISSION
Because the path
field along GB is
is zero since all
voltage along the
string. Therefore,
V
s
GB is outside the sphere of influence, the line integral of the electric
zero. Similarly, the sum of the line integrals along paths OG, BD and FO
conducting elements are assumed to have zero resistivity. Thus, all the
closed loop OGBDFO appears across the path DF, i.e., across the insulator
If Vs designates the voltage stress across the insulator string, we have:
-Vpath
(7-24)
Since path DF is orthogonal to the direction of flow of all currents, the line integral along
this path is zero. Thus, only three integrals in Eguation 7-24 need to be calculated to
determine the insulator voltage. This calculation is straightforward and leads to the following
result:
V
s
= 60 I In f - 30 I In
g
b
s
(7-25)
~r
ct-h
This eguation is valid for t > h/c (wave travel time from O to F) and for t < (2H-h)/c (time
for the reflected wave to return to F). For t > (2H-h)/c, it is necessary to consider the
original and the reflected wave currents.
Reflected Wave Concept
Thus far, the field theory has been described without introducing the concept of reflected
and refracted waves. In principle, it is possible to continue the analysis without introducing
this mathematical technique. What is needed is a definition of the mathematical constraints
such as boundary conditions, which apply to the problem being investigated. In this analysis
for example, the earth is assumed to be a perfectly conducting and therefore equipotential
surface. This defines one boundary condition. Another constraint was developed when it was
tacitly assumed that no charge accumulation can occur in the system. Furthermore, the
stroke path is assumed to be of infinite impedance. Therefore no current originating from
the ground wire or structure can flow back through this path.
It is possible to develop the relations which account for all of these constraints and to solve
the set of equations thus developed to determine the insulator voltage as a function of time.
The reflected travelling wave technique leads to the same result however, in a very elegant
manner consisting of repeated application of the approach previously outlined (for the specified
first time interval) but including a suitable time lag to account for the finite velocity of
electromagnetic waves.
The principle of the reflected wave technique is depicted in Figure 7.11. A mirror image
of the system is created and identical but opposite waves are produced by the images. This
artificial arrangement satisfies the boundary conditions, since the earth's surface will always
remain at zero potential; initially because no wave has reached the surface and later because
both the positive (original) and negative (reflected) waves reach each point of the surface
simultaneously. However, a point close to the top of the structure will not have its potential
reduced by the negative or reflected wave before a time interval of about 2H/c, i.e., twice
the wave travel time along the structure. This is illustrated in Figure 7.11.
7-17
TRAVELLING WAVE
_____FIELD THEORY
CAUSED BY
ORIGINAL WAVES
DOWN IN
Structure
(2H-h)/c
time
CAUSED BY
FIRST REFLECTED
WAVE (FROM IMAGE STRUCTURE)
(a)
METHOD OF IMAGES
Figure 7.11
(b) TYPICAL STRUCTURE POTENTIAL
Wave Reflection and Refraction Technique
If the mirror image is hidden, the incident wave appears to be completely reflected when
it reaches the base of the structure. When this reflected wave reaches the top of the real
structure, it produces a set of new waves which will travel along the ground wire and down
the structure in the same manner as the primary current wave, but delayed in time.
Calculation of the magnitude of these new current waves uses a method similar to the
method used to determine Ig and Is. That is, application of the constraint that the line
integral of the electric field along a closed metallic path must be zero. In this case, however,
there are primary and reflected current waves to consider in the equations. This process
continues indefinitely because there can be no accumulation of charge in the system. Strictly
speaking, the division of an upward wave at the top of the structure, into a refracted wave
moving along the ground wire and a reflected wave proceeding to the base of the structure,
varies with time. However, after the first reflection at the top of the structure, this division
can be considered constant with good accuracy. In this case, the application of the field
theory equations becomes equivalent to the use of constant reflection and refraction
coefficients.
Insertion of a Finite Structure Ground Resistance
The field theory can readily be expanded to include the case where the structure has a
finite ground resistance which can be represented by a lumped element. An effective method
to account for the presence of the resistance Rs is to create a new system of current waves
at the junction point between the structure base and its grounding system of magnitude - trls.
cr is defined as:
2R
a =
-i—
(7-26)
s
s
where Zs is the structure transient surge impedance applicable at the time considered.
-
7-18
Other Enhancements
By application of a variety of semi-empirical formulas, it is possible to account for effects
which were not considered in the preceding field theory approach. For example, corona in
the ground wire can be simulated by increasing the radius of the ground wire by an appropriate
amount [5]. Also, the effects of induced currents in the phase conductor can be approximated
by the introduction of coupling factors [15]. Further refinements such as the inclusion of
upward streamers, have also been proposed [21].
7.4 UNCERTAINTIES DM THE ANALYTICAL MODELS OF A STRUCTURE
It is legitimate to question the usefulness of efforts aimed at developing new refinements
such as those described previously, particularly when the controversial nature of some of
the fundamental assumptions made to construct electromagnetic field theories are carefully
reviewed.
Some of these assumptions are:
a
b
c
d
e
f
-
Lightning stroke modelled as an ideal current generator
Lossless conducting elements
Zero resistivity earth
Concentrated or lumped structure ground resistance
Time-invariant ground resistance
Equivalent geometrical representation of a structure
Although important, the first assumption will not be discussed here since it involves the
formation mechanism of the lightning discharge, a very controversial subject which is well
outside the scope of this work [1]. Thus, the following discussion will concentrate on the
last five assumptions.
7.4.1 LOSSLESS CONDUCTING ELEMENTS
All of the previously described analytical models assume that the ground wire, the phase
conductors and the metallic elements of the transmission line structure are lossless conducting
elements. The practical consequence of this assumption is that waves travel in the conductors
at the same velocity and without shape distortion, i.e., a rectangular wave impressed at the
structure top remains rectangular when it reaches its base. This property also exists in lossy
conductors satisfying the "Heaviside condition" which implies that the ratio of the conductor
series resistance to series inductance (per unit length values) be equal to the ratio of the
leakage (or shunt) conductance to its shunt capacitance (distortionless conductors).
When applied to steel conductors such as the elements of a structure, ground wires, or
counterpoises, a lossless representation is difficult to accept because of the relatively high
conductor series impedance, particularly during transients. Thus, a lossy line satisfying the
Heaviside condition is a more appropriate assumption. Unfortunately, the conductor parameters
are frequency-dependent and consequently, it is impossible to select conductor characteristics
which satisfy the distortionless line condition throughout the frequency spectrum experienced
during a lightning stroke. Moreover, the theory of lossy transmission lines leads to a
surge impedance and propagation constant which are complex numbers, whereas real values
are obtained with the lossless line approach. Finally, another significant source of losses and
further computation difficulties may exist because of the nonlinear properties of steel
elements which are subject to hysterisis and magnetic saturation.
7-19
The difficulty of the problem may be further compounded by the presence of nonuniform
current carrying elements, i.e., elements having a position dependent surge impedance.
Although it is possible to analyze lossy conductors by field theory or by the distributed
circuit approach, the consideration of nonlinear effects and/or continuously nonuniform or
inhomogeneous lines leads to extremely complicated and extensive computations. Such efforts,
where possible, would be unproductive if the added accuracies provided by the analytical
refinements were only marginal.
Unfortunately, the effects of many of the preceding parameters are unknown or highly
uncertain. Thus, it is only possible to speculate about the effectiveness of the contemplated
enhancements. However, it is reasonably safe to state that the effects of electromagnetic
losses not accounted for in the present theory are at least an order of magnitude less than
the overall response and could be approximated by the inclusion of appropriate resistances
at specific locations of the system. This is because the response of a transmission line
structure is largely determined by the system components present within a span of the
faulted structure.
7.4.2 EARTH RESISTIVITY
The assumption of zero resistivity is often used in electrostatic and electromagnetic problems
and allows application of the widely known "method of images". Unfortunately, it is incompatible
with the previous statement concerning the localized effects of a lightning stroke on a
structure, and is in direct conflict with theoretical and experimental evidence that soil in
the vicinity of a buried conductor injecting current into the earth assumes a potential near
the conductor potential with respect to remote ground. This situation is depicted in Figure
7.12. Typically, if the structure base dimension is 15 m (50 feet), the earth potential is still
in the order of 5 to 10% of the structure potential rise at 100 m (328 feet) from the center
of the base.
REMOTE
GROUND
(0 VOLT)
POTENTIAL OF
BASE OF TOWER
X-—- EARTH SURFACE
^
POTENTIAL
EQUIPOTENTIAL SURFACE
AT ABOUT 0 VOLT.
DISTANCE
(b) EXTENDED MIRROR IMAGE CONCEPT
EARTH SURFACE POTENTIAL PROFILE
Figure 7.12
Earth Resistivity and Earth Potentials
7-20
Earth surface potentials will vary with time according to a function strongly related to the
current stroke. An immediate consequence of this is that it is not possible to apply the
convenient "flat mirror" technique, used to create images of the original system, including
travelling charges of opposite polarities.
There is a surprising absence of research work or discussion on this subject, in the literature
related to power engineering. This is particularly surprising in view of the extensive research
work conducted on analytical models based on less significant approximations. Definitive
conclusions on the effects of finite earth resistivity will have to await the development of
an appropriate analytical model to account for this effect.
In theory, it may be possible to use a technique similar to the method of images. However,
the mirror will not be fl at and the images will be distorted and time-varying in order to
keep the reference surface at zero potential at all times (see Figure 7.12). It could be more
appropriate to select a surface which, during steady-state conditions, is at a specified low
percentage of the structure potential and use it as the zero potential reference surface.
Another solution could be to solve the problem in the frequency domain as discussed in
greater detail in Section 7.5.
7.4.3 ANALYTICAL MODELS OF EXTENDED GROUNDING SYSTEMS
The discussions of the preceding section are even more applicable to long grounding systems
since earth surface potentials will remain at high values even at large distances from the
structure. However, since this aspect of the problem has already been discussed, the following
discussion will address the subject of the transient response or impedance of a long grounding
system, such as a counterpoise. The steady-state impedance of a counterpoise was discussed
in Chapter 5. Several useful design charts are presented in Volume 2 of this report.
It is evident that the lossless transmission line approach is not valid because of the conductor
shunt conductance, sometimes designated as leak ance, which plays a major role in the
dissipation of current into the earth. In addition, the internal series resistance of the
counterpoise can hardly be ignored. As explained, waves will travel at a fraction of the
velocity of light typically 0.2 to 0.8 and will be subject to distortion and exponential decay.
The transient response of counterpoises has been measured and analyzed [22,23,24]. In a
more recent work [18], an attempt was made to account for the frequency dependent nature
of counterpoise parameters. This work has been shown to be reasonably accurate through
good agreement between calculated and measured results [25]. A similar approach, described
in [26], neglects the effects of frequency on the counterpoise parameters. However, the
approach allows for soil ionization effects as will be discussed here and has been treated
in [27].
For comparison, the indicial transient impedances of a counterpoise as derived by Bewley
[23], Devgan, and Whitehead [18] and Annenkov [26] are given:
Bewley
Z(t) =
i-E
e
8
•at
k=1 (2K-1) 2rr2
cosYkt +
f a
L2Y.
7-21
^k
Yk
"
2a
1
JI s i nY,k t
1
(7-27)
where
a
= 1/2RC£
1
2
I
1
(2K-1) 27T2
LC£2
1
R2C2&2
(2K-1)tt
2£/LC
and
^
R
C
L
is
is
is
is
the
the
the
the
counterpoise length (meters)
dc ground (shunt) resistance (ohms)
counterpoise capacitance per unit length
counterpoise inductance per unit length.
Devgan and Whitehead
(assuming constant parameters)
Z(t) = ^ [o„74e_1-1at + 0.26e"0-07at]
+ R [l-e"2at]
(7-28)
where all variables are as defined previously. In addition the following expressions were used
to determine the counterpoise parameters:
,T
u
ohms
C = iTeo(er + l)^ln
-
1j
farads "meter
henrys/meter
d =
meters
/2ah
where a is the counterpoise radius, h its depth of burial, e0 the permittivity of free space,
er the relative permittivity of soil, m soil permeability and p soil resistivity.
Annenkov
(response to the ramp function i(t) = It)
■2gt
■et
-Jip-.
1
-e
(7-29)
where
(8
= l/2£0erP
r
= H
/2v
(v velocity of propagation in the soil)
Rc is the steady-state dc resistance of the counterpoise, including the effect of soil
breakdown (ionization). Its expression is given by:
Rc ■
'
4L 2r/h
7^=1
+ r J
-
2
2
where
-L- F 1-..l-.e"2et 1 +
£EC
L
28t
J
-8t
28t
t/T
1
-e
3
and Ec is the soil critical breakdown gradient.
7-22
Although there is room for further refinements by inclusion of the effects of frequency
dependent parameters and soil ionization, it is apparent that counterpoises have received
adequate attention with regard to transient response. However, we are not aware of any
work which uses this analytical work to examine actual lightning performance problems.
7.4.4 SOIL IONIZATION MECHANISM
When subjected to an impulse current with a high crest magnitude, soil may be subject to
localized electrical breakdowns at points of maximum potential gradient, i.e., near the edge
of ground conductor elements. This phenomenon was discussed in Chapter 5 in the context
of steady-state currents in concrete. The subject was also discussed in Chapter 10 where it
was concluded that soil breakdown is rather infrequent in high voltage transmission line
structure faults. Nevertheless, it is possible that for a long section of transmission line
passing through a zone of high resistivity and keraunic level, this phenomenon may need to
be taken into consideration if effective mitigation steps are to be found where dictated by
unsatisfactory outage rates.
The apparent resistivity of homogeneous isotropic soil is constant as long as the soil potential
gradient around the electrodes injecting current remains below a specific value Ec, the soil
critical breakdown potential gradient or soil ionization threshold gradient. As the surge
current increases with time, a value Ic is reached which causes breakdown, arc discharges
in the soil [27-31], and an apparent decrease in soil resistivity. The critical current Ic is
generally in the kA range and its relation to Ec or Jc, the critical current density in soil,
is largely dependent on the current electrode. A typical experimental resistivity-current
curve is illustrated in Figure 7.13(a). This figure clearly shows the nonlinear characteristics
of soil resistivity at high impulse currents.
CURRENT DENSITY IN SOIL
(a) HYSTERESIS IN RESISTIVITY-CURRENT
CURVE
Figure 7.13
(b) ANALYTICAL MODEL BASED
ON GROUNDING ROD
Dynamic Resistivity-Impulse Current Curve
7-23
Liew and Darveniza [27], after carefully examining various experimental test results from
several types of electrodes buried in different soils [28-30], have recently proposed an
analytical model to describe the time-variant (dynamic) nonlinear characteristics of some
basic forms of concentrated grounding electrodes. In the model proposed, the soil is
characterized by three parameters (see Figure 7.13 for illustration):
Fc Critical breakdown gradient of soil (V/m),which varies between 50 and 500 kV/m,
depending on soil type (zone 1).
X
Soil ionization coefficient (s_l). This is the coefficient which describes the rate
of exponential decay of the resistivity from its nominal value at time 0 to its value
at time t (zone 3). An empirical value of 0.5x106 s_l provides good correlation with
test results.
Soil deionization coefficient (s-1). This coefficient accounts for the soil resistivity
recovery from its value at time 0 to its nominal value (zone 2). A value of about
0.22x106 s-1 was found to give the best agreement with test results.
7
As the current injected into the ground electrode increases, the current density 3 in the
immediate vicinity of the electrode surface eventually exceeds the critical density Jc. Soil
breakdown occurs and, progressively, the radius of the zone where soil is ionized (zone 3)
increases until it reaches a maximum radius ac corresponding to the current crest.
Beyond zone 3, the resistivity of the soil remains at its nominal value PQ (zone 1). However,
as the current decreases from its peak value, a buffer region (zone 2) develops as the current
density is now below the critical value Jc and constantly decreasing. In the deionization
zone, the resistivity recovers to its nominal value. In each of the zones just described, the
soil resistivity, as a function of time, is given by the following expressions:
No Ionization Zone 1
(7-30)
p(t) = p0
Deionization Zone 2
p(t) = pm + (po-pj [(1-J/JC)2 (l-e"Yt)J
(7-3D
where P m is the value of resistivity at current 3C during the decay period.
Ionization Zone 3
P(t)
Poe
-At
(7-32)
The most significant result of these impulse current experiments and predictions for
concentrated electrodes is that the impulse coefficient, i.e., the ratio of the impulse resistance
to the low current steady-state resistance, is between 1 and some minimum value. This ratio
quickly decreases toward this minimum value (about 0.2) with an increase in the impulse
current peak and with increasing soil resistivity values. This clearly suggests that during a
lightning stroke with a current peak sufficient to initiate the soil ionization process, a
mitigating effect with respect to transmission line lightning performance is provided by the
7-24
soil breakdown. This mitigation is more effective than previously thought because of the
significant reduction in the impulse coefficient afforded by concentrated electrodes in the
10 to 100 kA current range. This possibly explains the good lightning performance of sections
of lines with concentrated grounding systems installed in unusually high resistivity soils. It
should be noted, however, that the minimum attainable impulse coefficient increases very
guickly with the number of interconnected concentrated electrodes such as ground rods. For
example, the minimum coefficient is about 0.6 with a hollow sguare of 4 rods.
Finally, it is important to note that the above analytical model fails to describe the
performance of concentrated electrodes with localized high current densities. In such cases,
breakdown will occur along discrete linear paths and the implicitly assumed diffuse
growth of soil ionization, becomes comparable to a mini-lightning stroke. This situation is
also likely to occur in nonuniform soils which may present one or several paths with low
critical breakdown gradient strength.
Despite the foregoing limitations, it does not appear that researchers or designers have taken
advantage of this useful and realistic analytical model to optimize or improve the grounding
systems of transmission lines.
7.5 FREQUENCY DOMAIN APPROACH
A review of the analytical methods which have been developed to predict the lightning
response of transmission line structures would not be complete without a discussion of the
freguency domain approach which, surprisingly, has not been widely used to predict the
lightning response of a structure. As evidenced in this chapter, all analytical methods discussed
in the literature have been developed based on the time-domain approach. Moreover, except
for a few cases, field and model measurements have been conducted with impulse or surge
generators.
This observation does not appear to be justified by facts, convincing evidence, or sound
judgment. Rather, our assessment of the state-of-the-art supports an opposite view which
will be explained. This view is also implied in [11] and is indirectly supported by many
successful applications of the freguency domain method of solving transient problems.
7.5.1 FREQUENCY EFFECTS ON ELECTRICAL CONSTANTS OF MATERIALS
In the preceding section, the freguency dependent nature of electric conductor parameters
was mentioned and its immediate implications were briefly outlined. An obvious conseguence
of this is the effect of surge wave shape on lightning performance, since any surge can also
be regarded as the superposition of many harmonic components. This effect may explain, at
least partially, noticeable differences in the indicial response of the individual legs of the
same transmission line structure [32].
Figure 7.14(a) depicts typical curves of the dielectric and conductivity constants of a
homogeneous medium. Figure 7.14(b) shows the approximate magnitude of these variations
for a common substance, pure ice, at a temperature slightly below the freezing point.
7-25
102
103
DIELECTRIC
CONSTANT
104
105
DIELECTRIC
CONSTANT
RESISTIVITY
CONDUCTIVITY
FREQUENCY
FREQUENCY
(a)
Figure 7.14
TYPICAL CHARACTERISTIC
_______ CURVES_________
(b)
(Hz)
CHARACTERISTIC CURVES OF PURE ICE
(APPROXIMATE VALUES AT ABOUT 0°C)
Frequency Dependence of Material Electrical Constants
This frequency dependence is briefly explained by the decrease in time for the polarizing
charges to separate and participate in the current conduction as the frequency is raised
from a low value to the MHz range.
These curves present a convincing argument in favor of the frequency domain approach,
since it is excessively difficult and time-consuming to include this frequency dependence in
a time simulation, while it is easily and readily adaptable to the frequency domain approach.
7.5.2 CLARITY AND PRECISION
An outstanding advantage of the frequency domain approach is provided in the clarity by
which the concept of impedance and surge impedance is defined, as opposed to the sometimes
ambiguous definitions given to terms such as "surge" impedance, "dynamic" (surge) impedance,
"transient" (surge) impedance and "impulse" (surge) impedance, when represented in the time
domain.
This ambiguity and the lack of wave shape definition has resulted in serious difficulties in
interpreting, comparing or repeating experimental work conducted by various researchers.
For theses reasons, researchers of Electricite de France [11] decided to analyze their
rocket-triggered lightning test results in the frequency domain. Some of their conclusions
are very perplexing indeed. For example, as discussed in Chapter 10 of this report, they
conclude that the test lattice structure response to lightning strokes was essentially that of
a pure inductance of about 3 to 5 mH throughout the surge frequency spectrum. This is
contrary to the surge impedance concept. However, we disagree with the conclusion reached
in [11] concerning the equivalent inductance representation of a transmission line structure.
7-26
This is because firstly, only one particular structure was tested, and secondly because the
variation in structure parameters with frequency was not accounted for in the
conclusions. It is argued here that differences in the rate by which the structure characteristics
vary with frequency could have been such that the surge impedance varied linearly with
frequency in the same manner an inductance normally varies with frequency. This would also
explain why the measured inductance is about half the theoretical value (see Chapter 10).
Nevertheless, we are in complete agreement with the view expressed in [11] concerning the
use of a "harmonic" (surge) impedance which is the ratio of the measured voltage to the
impressed sinusoidal current at a specific frequency. This definition, when used in conjunction
with the Fast Fourier Transform technique, allows an efficient and precise means of expressing
computation and measurement results conducted in the time domain to the frequency domain
and vice-versa.
7.5.3 HYBRID MODELS
A practical approach to the problem of representing the lightning performance of a structure
can be enhanced manyfold if the many possible refinements, which can be introduced to the
components of the system, lead to a final hybrid analytical model constructed from the
refined and accurate submodels. In the time domain for example, the field theory could be
applied to the soil ionization and the counterpoise models and the resultant hybrid model
could be solved linearly in small time steps. Obviously, such a model would raise considerable
difficulties. In contrast, the frequency domain method, because of its inherent linear
characteristics, is particularly adaptable to hybrid analytical models.
7.5.4 CONCLUSION
It is obvious, even to the nonspecialist, that the subject of analytical models for transmission
line structures hit by lightning strokes, is an exceedingly complex one. This review can only
briefly discuss the subject. Although original views and ideas have been expressed in this
chapter, these are essentially speculative and remain to be confirmed or rejected. Only
future extensive research work can help in clarifying these issues.
REFERENCES
1 - R. H. Golde (Editor), "Lightning", Volume 2, Academic Press Inc., US Edition, New York
1977.
2 - Report of joint IEEE-EEI Subject Committee on EHV Line Outages, IEEE Transactions
on PAS, Vol. PAS-86, 1967, p. 547.
3 - A. Cimador, R. Fieux, B. Hutzler, "Influence des Resistances des Prises de Terre sur le
Foudroiement des Pylones d'une Ligne 225 kV", E.D.F. Bulletin de la Direction des Etudes
et Recherches, Serie B, No. 4, 1974, pp. 29-42.
7-27
4 - M. Darveniza et Al, "Modelling for Lightning Performance Calculations", IEEE Transactions
on PAS, Vol. PAS-98, No. 6, November/December 1979, pp. 1900-1907.
5 - R. Lundholm, R. B. Finn, W. S. Price, "Calculation of Transmission Line Lightning
Voltages by Field Concepts", AIEE Transactions on PAS, Vol. 76, February 1958, pp. 1271-1283.
6 - A. Greenwood, "Electrical Transients in Power Systems", Wiley- Interscience, John Wiley
and Sons Inc., 1971.
7 - E. F. Koncel, "Potential of a Transmission Line Tower Top When Struck by Lightning",
AIEE Transactions on PAS, June 1956, pp. 457-462.
- S. B. Griscom, J. W. Skoogglund, A. R. Hileman, "The Influence of the Prestrike on
Transmission Line Lightning Performance", AIEE Transactions on PAS, Vo. 77, December
1958, pp. 933-941.
8
9 - J. G. Anderson, J. H. Hagenguth, "Magnetic Fields Around a Transmission Line Tower",
AIEE Transactions on PAS, Vol. 77, February 1959, pp. 1644-1649.
10- F. A. Fisher, J. G. Anderson, J. H. Hangenguth, "Determination of Lightning Response
of Transmission Lines by Means of Geometrical Models", AIEE Transactions on PAS, Vol. 78,
February 1960, pp. 1725-1735.
11- P. Kouteynikoff, "Modele pour le Calcul de 1'Impedance d'une Prise de Terre Longue aux
Basses et aux hautes Frequences", Electricite de France, Report HM/72-04670.
12- AIEE Committe Report, "A Method of Estimating Lightning Performance of Transmission
Lines", AIEE Transactions on PAS, Vol. 69, pt.II, 1950, pp. 1187-1196.
13- C. F. Wagner, "A New Approach to the Calculation of the Lightning Performance of
Transmission Lines", AIEE Transactions on PAS, Part III, Vol. 75, December 1956, pp.
1233-1256.
14- C. F. Wagner, A, R. Hileman, "A new Approach to Calculation of Lightning Performance
of Transmission Lines. II", AIEE Transactions on PAS, Part III, Vol. 78, December 1959, pp.
996-1021.
15- C. F. Wagner, " A New Approach to the Calculation of the Lightning Performance of
Transmission Lines - III; A Simplified Method: Stroke to Tower", AIEE Transactions on PAS,
Part III, Vol. 79, October 1960, pp. 589-603.
16- R. Davis, J. E. M. Johnston, "The Surge Characteristics of Tower and Tower Footing
Impedances", IEE Journal, 1941, Vol. 88, Part II, pp. 453-465.
17- M. A. Sargent, M. Darveniza, "Tower Surge Impedance", IEEE Transactions on PAS, Vol.
PAS-88, No. 5, May 1966, pp. 680-687.
18- S. S. Devgan, E. R. Whitehead, "Analytical Models for
Systems", IEEE Transactions, Part III, Vol. PAS-92, pp. 1763-1770.
Distributed
Grounding
19- J. A. Selvaggi, R. J. Nigbor, R. L. Kloecker, "The Green’s Function of a Cylindrical
Tower", IEEE Transaction paper No. C72-558-5, IEEE PES Summer Meeting, July 1972, San
Francisco, California.
20- P. C. Buchan, W. A Chisholm, "Surge Impedance of HV and EHV Transmission Towers",
Final Report No. 78-71, Canadian Electrical Association.
7-28
21- C. A Liew, M. Darveniza, "A Sensitivity Analysis of Lightning Performance Calculations
for Tranmssion Lines", IEEE Transactions on PAS, Vol. PAS-90, 1971, pp. 1443-1451.
22- E. D. Sunde, "Surge Characteristics of a Buried Bare Wire", AIEE Transactions, Vo. 59,
1940, pp. 987-991.
23- L. V. Bewley, "The Counterpoise", General Electric Review, Vol. 37, No. 2, February
1934, pp. 73.81.
24- L. V. Bewley, "Theory and Tests of the Counterpoise, "Electrical Engineering, (AIEE
Transactions), Vol. 53, August 1934, pp. 1163-1172.
25- M. Kawai, "Studies of Tower Footing Resistance on Transmission Lines", IEEE paper 31
CP 65-704, IEEE Summer Meeting, Detroit, Michigan, 1965.
26- V. Z. Annenkov, "Calculating the Impulse Impedance of Long Earthings in Poor Conducting
Ground", Electrichestvo, No. 11, 1974, pp. 62-79.
27- C. A. Liew, M. Darveniza, "Dynamic Model of Impulse Characteristics of Concentrated
Earths", Proceedings IEE, Vol. 121, No. 2, February 74, pp. 123-135.
28- P. L. Bellashi, "Impulse and 60 Cycle Characteristics of Driven Grounds", AIEE Transactions,
Vol. 60, March 1941, pp. 123-128.
29- P. L. Bellashi, R. E. Armington, A. E. Snowden, "Impulse Characteristics of Driven
Grounds", Vol. 61, 1942, pp. 349-363.
30- K. Berger, "The Behavior of Earth Connections Under High Intensity Impulse Currents",
CIGRE Publication No. 215.
31- E. Y. Ryabkova, V. M. Mishkin, "Impulse Characteristics of Earthings for Transmission
Line Towers", Electrichestvo, No. 7, 67-70, 1976.
32- E. J. Rogers, "Impedance Characteristics of Large Tower Footings to a 100 ns Wide
Square Wave of Current", IEEE Paper 80 SM 662-7, IEEE, PES Summer Meeting, Minneapolis,
Minnesota, July 1980.
7-29
8.1 GENERAL
Only a small proportion of the electric schock incidents reported each year involve high
voltage power eguipment or installations. Most electrocutions are caused by lightning or
involve low voltage circuitry and household electrical devices. A recent survey conducted
among North American utilities indicates that there have been no fatal accidents due to
excessive touch or step voltages in the vicinity of transmission line structures [1]. A summary
of the results of the survey is given in Chapter 11.
This by no means suggests that incidents involving high voltage installations have not occured.
We are aware of several electrocutions involving grazing cattle in the neighbourhood of high
voltage lines and one incident with a human fatality which occured in Europe and is described
in [2]. The victim, a camper, apparently was crawling out of his tent at the time a
phase-to-ground fault occured at a nearby transmission line structure.
It is apparent however, that only a very small number of fatalities can be attributed to
high earth surface voltages near faulted transmission line structures. A recent study in
Finland [29] estimates the probability of an accident to be in the order of 10-8 per year
per structure for 120 to 420 kV structures.
The measurements and theoretical analyses conducted during this EPRI project and elsewhere
[3,4] suggest that this extremely low accident rate is not a result of transmission line
structure grounding design but rather is a consequence of a very low probability of human
exposure to hazardous situations. More precisely, for an electrocution incident to occur, the
following events must occur simultaneously:
a- A ground fault at a transmission line structure sufficient in magnitude to
generate hazardous step and touch potentials.
b- A person must be in a dangerous position near this specific structure at the
time of the fault.
Because of the infrequent presence of people near high-voltage transmission line structures
and because a fault at any specific structure is very unlikely, the electrocution incident is
an extremely low probability event.
This favorable situation may not exist at some exposed locations along transmission lines or
may change in the future because of increased joint use of transmission line right of ways
in densely populated urban centers and progressively higher fault current magnitudes and
probabilities of fault occurence. It is the project engineer's responsibility to determine the
transmission line locations which present high human exposure risks and, if necessary, to
design a suitable grounding system to control hazardous earth surface voltages. While this
chapter is intended to help the engineer in assessing the nature and severity of a ground
potential rise hazard, it also describes a methodology for designing a suitable grounding
system for earth surface potential control based on the methods developed in Chapters 4,
5 and 6.
8- 1
8.2 THE ELECTROCUTION EQUATION
It is now well established that the duration and magnitude of the current traversing the
human body determines the severity of an injury. The well known Dalziel electrocution
equation, I5 = p/v^, where p is a constant proportional to body weight, t is the time
duration of the electric shock and Ij-, the rms value of the maximum permissible body current,
is the reference equation used by the majority of North American engineers to determine
the safety of power system grounding installations [5,6,7].
The electrocution equation, as applicable to humans, can only be determined empirically by
extrapolating experimental data obtained from tests on four-legged animals and primates.
The electrocution equation is also designated as the fibrillation threshold of current as a
function of duration.
Dalziel's equation [5,13,14] is based on the statistical analysis of published experimental data
and, since the minimal data which exist on electrocutions is subject to interpretation, it is
not surprising to note that there is major disagreement among researchers concerning the
exact nature of the electrocution equation and that different fibrillating threshold levels are
in use in other countries [7]. It appears from more recent research work [9,10,11,12] that
Dalziel's equation may not be sufficiently conservative in the 0.3 to 3 second fault duration
range and may be overly conservative for body weights in excess of 60 kg (133 lbs).
The electrocution equation is of prime importance in the design of safe grounding and
protective relaying systems. This equation describes the relationship between the fibrillating
threshold body current, shock duration, and body weight during exposures to voltage sources
of various magnitudes and frequencies. Although a literature search shows an urgent need
for further research work to establish more suitable electrocution equations, it is not within
the scope of this EPRI project to develop, recommend or criticize new or existing equations.
However, the various theories which have been developed concerning these equations are
summarized in the next section.
Thus, it is the role of the design engineer to select the most suitable equation, based on
the applicable standards, guides [8], existing rules and regulations. The information in this
section gives a brief summary of several research works aimed at determining the most
suitable form of the relation between the maximum permissible body current I^ (also designated
as the minimum fibrillating current) and the various influencing parameters. These parameters
are not all well-known and it is clear that further work is required to fully understand the
significant parameters. However, three variables, body path characteristics, current frequency,
and current duration have been shown by experimentation to be closely interrelated to
the safe body current magnitude. Therefore, the general form of the electrocution equation
can be written as:
Ib = <i>(p,f >t)
(8-1)
where
Ib is the maximum permissible body current in amperes rms (for a given body path p)
which will not cause death to more than x % of a sample population having similar
body path characteristics.
f
is the current frequency in Hz.
t
is the duration of the fault in seconds.
p
is one or several parameters characterizing the body path followed by the current.
8-2
Dalziel's equation was established for power frequency current (50 to 60 Hz) durations
between 8 ms and 5 s and a percentage x of 0.5 % of the population. The body path is
characterized by the constant p which is proportional to body weight.
8.2.1 THE ELECTROCUTION MECHANISM
The passage of electric current through living biological specimens can produce stimulation
of excitable tissue at low current intensities, or coagulation of protein and burning and
charring at high current intensities. Although in many cases, persons have survived high
currents despite severe injuries, most electrocution fatalities occur during low-intensity
current shocks because of asphyxia (respiratory arrest) or heart fibrillation (cardiac arrest).
Fibrillation, more common than asphyxia as a cause of death, is the random contraction and
relaxation of the heart muscle fibers in the ventricles resulting in a loss of the pumping
action of the heart chambers and cardiac arrest. Unless circulation is restored (for example,
by de fibrillation) no later than 3 to 4 minutes after the electric shock, irreversible brain
damage occurs. Respiratory arrest occurs during the passage of current because of the
contraction of the chest muscles. Generally, spontaneous resumption of respiration occurs
after the shock current has ceased. For shock durations of a few seconds or less, respiratory
arrest is unlikely. It is only when the arrest of respiration persists after the electric shock
that a serious risk of death exists, if the victim is not resuscitated by artificial respiration.
Lee [15] describes several electrocution incidents which suggest that this sustained respiratory
arrest occurs only when the current path is through the respiratory center located in the
lower part of the brain.
Since most power frequency electrocution incidents do not involve the head, fibrillation is
usually used as a reference in the design of safe power installations. Respiratory arrest is
probably of interest in the case of a direct lightning strike on standing persons, a subject
not within the scope of this project.
8.2.2 THRESHOLDS OF CURRENT
A current in the order of 5 mA can be sensed by the tongue while 0.5 to 1 mA is the
minimum current which can be perceived by the fingers. As the current increases, a tingling
sensation occurs followed quickly by a painful muscular contraction. At a current of 6 to 7
mA for women and 9 to 10 mA for men (at 50-60 Hz) a threshold is reached beyond which
it is no longer possible to release the energized conductor. This current is called the let-go
current. For still higher currents (20-50 mA) breathing difficulties, suffocation and even
asphyxia may occur if the electric shock duration lasts for minutes. Currents in the order
of 100 to 200 mA may cause death by heart fibrillation if the electric shock duration is in
the order of 0.5 second.
8.2.3 PARAMETERS INFLUENCING HEART FIBRILLATION
The fundamental variables which govern the electrocution Equation 8-1; the magnitude,
frequency and duration of the current, and its path through the human body; depend on a
number of other biological parameters which, unfortunately, are statistical rather than
constant in nature. Since there is only limited experimental data, it is understandable
that the exact values of some of these parameters are still uncertain.
The role played by these parameters is becoming somewhat clearer through research in the
medical and engineering fields. The significant parameters described in this section have a
direct effect on the magnitude of the current which traverses the body of a human or animal
8-3
subject to electric shocks. Other parameters have more subtle, unknown or sometimes
controversial effects. In order to fully understand the interaction between these variables,
it is important to describe the "strength -du rati on curve" of excitable living tissue. This is
well summarized in [16].
Experimental measurements show that there is an approximately hyperbolic relation between
the stimulus strength s (current density of the electric stimulus) and the duration t of this
stimulus:
s = f + r
(8-2)
Equation 8-2, which is a very well established relationship in physiology, was originally
proposed by Lapicque [17]. Figure 8.1 is a plot of Equation 8-2 and shows that the threshold
current density required for stimulation increases as the duration of the stimulus is decreased.
There is a minimum current r (designated as the rheobase) for an infinitely long duration
stimulus, below which no tissue excitation is possible. The constant a, depends on the type
of excitable tissue.
STIMULUS
STIMULUS DURATION (s)
Figure 8.1
Strength-Duration Stimulus Curve
There are other equivalent forms of the strength-duration equation. Referring to Figure 8.2,
the following develops an equation based on the equivalent electrical circuit of a cell. The
cell membrane excitable tissue can be represented as a capacitor C shunted by a resistance
R. The transmembrane potential difference is slightly less than 100 mV at rest. Following
an electric stimulus which reduces this potential by about one third or more, a regenerative
process takes place which depolarizes the cell and reverses the cell polarity slightly before
restoring the transmembrane resting potential. When the membrane is of a muscle cell (e.g.,
heart muscle), contraction follows depolarization.
The product RC is the membrane time constant r. A current stimulus s applied to this
parallel RC circuit is related to the time constant r and to the rheobase r as follows:
s
r
(8-3)
8-h
s
s
STIMULUS
STIMULUS
(a)
(b)
EXCITABLE TISSUE
Figure 8.2
EQUIVALENT CIRCUIT
Equivalent Circuit of a Typical Cell Membrane
Pearce and his colleagues [18] have shown that there is good agreement between the measured
strength-duration curve and the relation predicted by Equation 8-3. Therefore, Equation 8-3
can be used instead of Equation 8-2 to predict the response of excitable tissue to
electric stimulus. However, it is important to note that this response is based on the
application of a single electric pulse (stimulus). When repetitive stimuli are applied to the
tissue, only a sub-multiple of the pulses will stimulate the cells because of the refractory
period of the cell. The refractory period is the time interval following a stimulus where any
further stimuli applied to the cell will not be detected by the cell.
The above considerations explain why low frequency currents (50-60 Hz) produce ventricular
fibrillation more readily than higher frequency ac currents. If, at high frequencies, sinusoidal
alternating current peaks are considered as a succession of short duration pulses, only a
fraction of these pulses are effective in stimulating the tissue. Thus, as the frequency is
increased, the magnitude of the fibrillating threshold current is increased. This phenomenon
is well known by surgeons and is the basis for recently developed diathermy and electrosurgery
techniques.
Ventricular fibrillation can be produced by repetitive electric stimuli more readily than with
a single stimulus. Experiments show that at power frequencies, the magnitude of the current
required to initiate ventricular fibrillation is a minimum. A single stimulus (e.g., lightning
surge) can precipitate ventricular fibrillation only when it occurs during the time interval
of the ventricle pumping cycle (slightly less than 1/3 of the heart cycle) and when the
stimulus is approximately twenty times higher than the threshold of excitation when the
heart is at the end of the period of relaxation and filling of the ventricles (diastole).
This dangerous time interval is called the vulnerable period of the heart cycle and could
explain the observation that only about 1/3 of persons struck by lightning die.
In diastole, an electric stimulus of the heart causes a premature heart beat if the duration
of the stimulus is less than the duration of the premature beat. For a longer duration
stimulus or repetitive stimuli, several premature heart beats are initiated and the beats
follow each other with increasing frequency. After each premature beat, the fibrillation
threshold (initially 20 times the excitation threshold) is progressively lowered until it approaches
the normal threshold of excitation of the ventricle during the nonvulnerable period of the
heart (i.e., diastole).
8-5
The above discussions are in agreement with experimental results [19] which indicate that
there is a discontinuity of the 50 % ventricular fibrillation probability curves for electric
shock durations in the order of one third the heart cycle as shown in Figure 8.3.
THRESHOLD OF
FIBRILLATION
FOR 50%
FIBRILLATING
PROBABILITY
NON
FIBRILLATING
THRESHOLD
■=- OF HEART
3 CYCLE v
TIME (ms)
Figure 8.3
Threshold of Ventricular Fibrillation for a 50 Kg Man
The transition zone between short and long duration levels is of particular interest to power
system engineers because it corresponds to time durations in the order of the normal response
time of protective relays (0.2-2 s). In this zone, the relation is linear with a slope very
close to -1. This suggests that for the time range 0.2-2 s, the equation It=constant (Osypka
[12]) is more appropriate than the IvC=constant proposed by Dalziel [13]. In practice, however,
there is little difference in the results of the two equations for durations corresponding to
this transition zone.
In spite of the considerable progress since the beginning of this century, the data related
to electrocution are still very experimental in nature and cannot be accurately correlated
with actual electrocution cases. The major difficulty is in that most meaningful shock data
have been obtained under experimental conditions where the current stimulus was directed
toward the target, (i.e., the heart) generally through direct stimulations of the target. In
actual electrocution accidents, contact is generally made through the extremities (hands or
feet) and only an unknown fraction of the total current reaches the vulnerable tissues of
the body. Unfortunately, it appears that there has been no work directed at a determination
of the current paths through a human body and there is no indication that efforts have been
made to extrapolate any test data available from quadrupeds to humans.
The scarcity of experimental data relating human and animal response to electric shocks is
certainly one of the reasons for the existence of several forms of the electrocution equation
as developed by various researchers working with essentially the same experimental data.
8-6
8.2.4 THE ELECTROCUTION THEORIES
In the design of an electrical grounding system, one of the important aspects to be considered
is the safety of the installation during fault conditions when current enters the grounding
system and causes differences in potential between various accessible points of any grounded
metallic structure and the soil surface in the vicinity of the grounding system. In order to
assess the safety of an installation, the engineer must know the highest tolerable body
current (or voltage) which must be compared with the calculated or measured currents under
fault conditions. This important reference value is the current fibrillation threshold or
tolerable body current usually specified by national and international standards or guides and
is determined from the electrocution equation discussed previously. In Norh America, the
equation proposed by Dalziel [14] is recommended by the widely used IEEE Guide No. 80
[6,7]. In other continents and countries, different equations are in use [8]. However, all
equations lead to practically equivalent results and relate the magnitude of the body current
to its duration without distinguishing between the points of application of the electric stimulus
which is implicitly assumed to be sinusoidal and at power frequency (50 or 60 Hz). Despite
some lack of flexibility of the equations in coping with the wide variations in the values of
the variables encountered in practice, they are of vital importance in the design of suitable
mitigation steps for effective electrical shock prevention.
There are essentially four major time-dependent electrocution equations. These have been
developed by Dalziel [14], Osypka [12], Geddes [10] and Biegelmeier [19]. The equations were
derived empirically from a statistical analysis of the fibrillation current versus time data.
A recent paper by Bridges [20] provides a good summary of these four major concepts and
their related equations:
Dalziel's Equation
Dalziel concluded after examining results of experiments conducted by others, that the
fibrillating threshold of current is inversely proportional to the square root ot the electric
shock duration:
Ib = p//t
(8-4)
Osypka's Equation
Using essentially the same data as used by Dalziel, Osypka developed an equation where the
fibrillating threshold is inversely proportional to the electric shock duration (except for
durations exceeding 1 second where the current remains constant):
Ib = d/t
(8-5)
Geddes' Equation
Based on physiological considerations pertaining to the irritable tissue concept discussed
earlier in this section, Geddes proposed the following equation where the current is also
inversely proportional to the electric shock duration:
Ib = a/(t-b) + c
(8-6)
Biegelmeier's Equation
Bielgelmeier's work is also based on the irritable tissue concept. The equation proposed by
him is illustrated in Figure 8.3. Bielgelmeier considers that the fibrillating threshold current
is discontinuous with time:
^ = A
<
0.2
rb = B
>
2
<
t <
1 b = C/t
;
0.2
s
s
(8-7)
2
8-7
s
In the above electrocution equations a, b, c, d, A, B, C and p are statistical constants which
depend on the degree of safety to be achieved. Since absolute safety is economically
prohibitive and unpractical, the maximum safe body current is selected such that x % of
the population, consisting of "standard" persons of a defined body weight, will not be subject
to fibrillation (for example, IEEE Guide 80 [6] proposes 99.5 % of 50 Kg persons). Figure
8.4 shows the safe body current as a function of its duration according to Dalziel,
Osypka and Bielgelmeier.
BIELGELMEIER
OSYPKA
DALZIEL
i
i i i
TIME (mS)
Figure 8.4
Safe Body Current Versus Time
As previously stated, it is not within the scope ot this EPRI project to propose an electrocution
equation. Consequently, the general form of the equation as given by (8-1), will be used.
8.2.5 THE ELECTRIC SHOCK CIRCUIT
Electric shocks are possible only when current flows through the body of a human or animal.
This necessarily means the existence of a closed path, the electric shock circuit, which
includes at least a portion of the body of the victim.
8-8
Because of the numerous activities performed by human beings and the variety of electrical
apparatus used, the points of contact in an electric shock can be anywhere on the body.
However, in the case of potential transmission line grounding incidents, the most common
points of contact will be at the hand or foot extremities. Generally, two types of contacts
are considered: step contact and touch contact.
These are illustrated in Figure 8.5. This figure also shows the equivalent circuit which applies
in each case. The various parts of the circuit have been identified and can be grouped in
three categories:
1- Resistance due to man-made insulating materials (gloves, shoes, or soil surface
covering insulating materials).
2- Body surface resistance (skin resistance).
3- Resistance of internal body tissues (heart, hands, legs, etc.).
EQUIVALENT CIRCUIT
ACTUAL CIRCUIT
(b) STEP CONTACT TYPE
Figure 8.5
The Electric Shock Circuit
It has been shown previously that the fibrillation threshold depends on current passing through
the heart tissues. More precisely, the current density in the heart tissues appears to be the
primary factor in determining whether or not fibrillation occurs. The equivalent circuits of
Figure 8.5 show that the distribution of body current between the heart (unit 5) and
other parts of the body, depends on the path followed by the current and on the ratio of
the heart resistance (R5) to the neighbouring tissue resistances (Rg for touch contact, R4
and Rg for step contact). The magnitude of the total body current is dependent on the
voltage across the contact areas and on the various resistances of the electric shock circuit.
8-9
No literature has been found concerning research on the distribution of shock currents through
the human body or the resistance of current paths through the human body. Consequently,
the detailed equivalent circuits of Figure 8.5 are of academic interest only. In practice, the
body path is represented by one lumped equivalent resistance (see Figure 8.6) and total body
current, not heart current, is used to define tolerable current levels. For example, in Dalziel's
equation, only body weight is a factor. The safe body current is independent of the current
path. As can be concluded intuitively from Figure 8.5, this is not the case. Moreover,
according to Louchs [24], a man can withstand a foot-to-foot current about 25 times higher
than a hand-to-foot current. It is important to remember, however, that a nonfatal but
painful foot-to-foot current might result in a fall with possibly serious consequences. Thus,
more sophistication can not be justified without further research and great care must be
exercised in the selection of the biological constants. Simple, conservative equations appear
to provide the most reasonable approach to shock hazard determination.
Body Resistance
It is useful to qualitatively consider the effects of the various body resistances of Figure
8.5. Firstly, it is clear that the resistance of body current paths such as legs or hands, is
inversely proportional to the cross-section of the paths. This leads to the conclusion that
body resistances of a child are higher than those of an adult. This is an important fact
observed experimentally by Whitaker [21] and means that for the same voltage across the
contact areas, less current will flow through the body of a child. It should be noted that
for identical situations, the areas of contact for a child are usually less than for an adult
(hands or feet). Consequently, the contact resistances are also higher. Despite the lack of
conclusive data relating to children, it may be argued that although the fibrillating threshold
current for a child is less than for an adult, the same voltage limits might apply to both
the adult and the child, because of the inherently higher-child body resistance. The preceding
considerations raise an important but still unresolved question. What is the relationship
between body weight and fibrillation threshold? It is known that the minimum fibrillation
current increases with body weight.
According to Dalziel [5], this current is proportional to weight. In contrast, Geddes has
concluded that the fibrillation current varies with the square root of the body weight.
However, based on the elec trophy si ological concept described earlier, one can conclude that
for bodies of the same general proportions, the response of excitable tissue is identical
provided that the current density in the tissue is identical. The current density criterion
[20] appears more appropriate for extrapolation purposes and leads to a fibrillating
current proportional to the 2/3 power of body weight. The 2/3 power relationship is derived
from the observation that for a given shape of different weights, cross-sectional area varies
as the 2/3 power of the weight. Since most experiments were made on quadrupeds, extrapolation
of the results to bipeds based on the body weight criterion will introduce unknown errors.
The body current density factor also raises difficulties due to the unknown distribution of
current within the body of the victim. Again, uncertainties prevent us from selecting the
most appropriate assumption. Therefore, the more simple relations, although somewhat
inaccurate, remain a reasonable choice.
Figure 8.6 shows a simplified equivalent circuit of the electric shock path. In this circuit,
the whole body path is represented by a single resistance. Several experiments [20-23] show
that this resistance is a function of the voltage applied across the contacts and skin condition
at the contact areas.
Excluding skin contact resistance, the resistance of the internal body tissues and organs with
current flowing between hands and feet is in the order of 300 to 500 ohms. At relatively
low voltages (< 250 V) the contact resistance of dry intact skin is in the order of 100
kilohms/cm2. However, if the skin is wet or not intact, the contact resistance may be only
8-10
a fraction of a kilohm and will become considerably less effective in limiting body current.
Since skin resistance, dominant under normal conditions, can easily be reduced to a value
comparable to the body internal resistance, various researchers have suggested lower bound
values of combined skin and internal body resistance. Typical suggested "worst case" values
range between 500 and 1500 ohms.
gloves
r
^body
tower
shoes
covering
(a) TOUCH VOLTAGE
Figure 8.6
(b)
STEP VOLTAGE
Simplified Equivalent Electric Shock Circuit
It should be noted that touch or step voltages in excess of 100 volts are not uncommon in
the vicinity of faulted transmission line structures. At these higher voltages the body
resistance exhibits a negative, nonlinear characteristic as shown in Figure 8.7 from Freiberger
[25]. Body resistance has also been shown to decrease with time if the duration of contact
is in the order of a few seconds or more and the voltage is above 50 volts [22,26]. This is
a result of skin breakdown, often evidenced by the blisters, which is caused by the heat
generated from the current flow.
Since transmission line fault durations are generally less than 0.5 s, the IEEE Guide 80
recommended body resistance (i.e., 1000 ohms) is believed to be reasonably conservative in
this context of transmission line grounding systems.
Resistance of Gloves and Shoes
Relatively new dry shoes are probably the best protection against electric shock hazards. It
is probable that many theoretically dangerous situations for bare-footed persons go unnoticed
by persons wearing good insulating shoes. According to an extensive experimental survey
conducted by Electricite de France [27], the resistance of dry new shoes varies between 50
and 200 megohms. When wet, the resistance drops dramatically to the kilohm range, with
values as low as 800 ohms. If the shoes are not new and are wet, the resistance drops below
500 ohms in many cases. Thus, it may be prudent to ignore the effect of shoe resistance,
especially when safety precautions are considered at locations such as recreational or camping
areas where bare-footed persons, especially children, are very likely.
8-11
Since the use of gloves is very uncommon except when safety measures are clearly necessary,
the glove resistance shown in Figure 8.6 should generally be assumed to be zero.
AVERAGE WITH FINGERS
(10cm2 CONTACT)
___
AVERAGE WITH FULL HAND
(100cm2 CONTACT)
------ AVERAGE VALUES
•yr ZONE OF MEASURED
^ VALUES
VOLTAGE STRESS (volts, rms)
Figure 8.7
Body Resistance Versus Applied Voltage (Redrawn from [25])
Surface Soil Resistance of Feet
For the purpose of circuit analysis, the human foot is usually represented by a conducting
metallic disc or rectangular plate. The contact resistance of the foot with the soil is generally
neglected.
In some cases, a 5 to 15 cm (2 to 6") layer of crushed rock (or similar semi-insulating
material) is spread on the surface above the ground grid to provide a series resistance
between the natural soil and the feet of a person standing above the grid. This practice is
beneficial only when this surface layer resistivity is significantly higher than the natural top
soil resistivity (say 5 times or more). Otherwise, a significant grounding system current will
flow in this surface layer and the earth potentials will be significantly different from the
potentials computed assuming a uniform soil.
Assuming that the surface layer resistivity is Ps and the thickness of this layer is e, this
soil-to-foot series resistance Rf becomes:
Rf = ps f
(8-8)
8-12
where S represents the area of the metallic disc or plate representing the foot. With a 6
cm thick layer and a 0.02 m2 foot contact surface, Rf is 3 ps, a value commonly used in
substation grounding.
Ground Resistance of a Foot
If a person is standing well away from a grounded structure so that no mutual resistive
coupling exists between the grounding electrodes represented by the feet and the structure
ground system, the resistance to remote ground of the feet must be taken into consideration
in the electric shock path equivalent circuit. A typical situation where this factor must be
considered occurs in the case of transferred potentials, as illustrated in Figure 8.8.
In this case, the series resistance of the foot, not only includes the surface layer (when it
exists), but also the natural surrounding soil. This resistance is then more appropriately
designated as the foot resistance to remote ground. Volume 2 of this report provides charts
to determine the foot resistance when the soil consists of a surface layer and an equivalent
infinite deeper stratum.
TO
SOURCE
Figure 8.8
Ground Resistance of Feet
The Safety Criterion
It is now possible to define the condition which will warrant that the body current is not
a fribrillating threshold current for at least x % of the population.
If Vf is the calculated touch voltage (hand-to-feet), the body current i must be less than
the fibrillating threshold 1^:
Vt
' = Rb + iR‘- !b =
If Vs is the calculated step voltage (foot-to-foot) we similarly have:
V
i=---------------< i
= 4>(p,f,t)
(8-10)
Rb + 2Rf
8-13
For example, if Dalziel's equation is used, assuming a body resistance of 1000 ohms and no
surface gravel, Equation 8-9 becomes:
Vt
1000
p
/t
where p = 0.116 for 99.5 % of a population consisting of 50 kg adults.
8.2.6 SAFE IMPULSE OR SURGE CURRENTS
Essentially, everything said so far regarding safe current levels applies equally well to very
short (microseconds) or long duration currents (seconds) with few exceptions. That is, the
safety criteria of Equations 8-9 and 8-10 are valid regardless of the shape and duration of
the electrocution voltage. Unfortunately, the values of the biological constants which affect
the electrocution equation are not well known when impulse, lightning or power system surge
currents are involved.
Several direct and indirect lightning strike and power system surge electrocution incidents
indicate that a person can survive very short duration currents (1 to 1000 ms) of 20 to 100
A, as illustrated in Figure 8.9 which is based on capacitor discharge incidents reported by
Dalziel [28]. This indication is confirmed in Figure 8.10 which shows the effect of frequency
on perception current, also reported by Dalziel [5]. With increasing frequency, the perception
of current changes from tingling to the sensation of heat.
DANGEROUS ZONE
SAFE ZONE
TIME CONSTANT (microseconds)
Figure 8.9
Nonfatal Surge Capacitor Discharge Currents (Redrawn from [28])
8-14
___
PERCENTILE 0.5
___ PERCENTILE 50
------ PERCENTILE 99.5
FREQUENCY (Hz)
Figure 8.10
Perception Current as a Function of Frequency (Redrawn from [5])
From a limited number of electric shock incidents involving the discharge of high voltage
capacitors, Dalziel [28] concluded that the energy criterion, l2t=constant, is applicable for
impulse or surge currents.
An uncertainty exists concerning the appropriate value of body impedance when subject to
high magnitude surge currents. Not only is the body impedance reduced because of the high
voltage level, it is also shunted by a capacitance. The value of this capacitance is not well
known although suggested values range from 100 to 500 pF. This capacitance appears to
play a mitigating role by diverting a major portion of the current which would otherwise
flow through the body tissues. There is clearly an urgent need for extensive research
concerning electric shocks caused by surge or impulse currents. However, until better
information is available it seems prudent to adopt conservative low body resistance values,
i.e., about 300 ohms or less.
It is important to note that the transmission line structure grounding system provides much
better protection against electric shocks from lightning than a tree or any other poorly
grounded structure. Thus, the engineer need not be concerned about shock hazards from the
lightning incident itself but rather, should investigate the possible power system fl as hover
resulting from a lightning strike on the transmission line structure. If engineering analysis
indicates that mitigation measures must be applied, these should be based only on the power
frequency current effects.
8-15
8.3 PROBABILISTIC CONSIDERATIONS
Safety criteria, although derived from extensive experimental data, must recognize that
absolute safety remains an unachievable ideal and that some degree of risk is present in
many aspects of life. The concept of "relative safety" is already embedded in the electrocution
equation, 8-1, which prescribes the fibrillating threshold current for a certain percentage of
the population. In other words, it is recognized that there is always a very small percentage
of the population which, for various reasons; extreme fatigue, heart disease, etc., will be
vulnerable to currents harmless to the great majority of the population.
Although it is the function of engineers to indicate the practicality and economical cost of
achieving the different levels of safety, it is the role of governemental and standard
committees to establish the maximum acceptable level of risk. Consequently, the probabilistic
methodology presented in this section should not be used without prior knowledge of its
applicability, and conformance to the regulations, standards or company directives which are
in force.
8.3.1 THE PROBABILITY OF AN ELECTROCUTION INCIDENT
The occurence of an electric shock in a power system network, particularly at a transmission
line structure, requires the simultaneous occurence of two unfavourable and, generally,
unrelated events:
a- Occurence of a power system ground fault resulting in a circulation of all or
a fraction of the fault current into earth through a transmission line structure.
b- Presence of a human being in an exposed position near the structure.
It is important to note that such an occurence may be hazardous to life only if the fault
current magnitude and duration are such that the current generated in the body exceeds the
permissible value. In other words, the incident may be fatal only if the stress function (body
current) exceeds the strength function (threshold of fibrillating current).
Since high voltage transmission line faults are relatively infrequent and generally of very
short duration (<0.5 s), the two events, a and b, are rarely coincident. This is a significant
factor in the apparent absence of fatalities from electrocution due to transmission line
structure faults.
8.3.2 THE STATISTICAL PROBABILISTIC APPROACH
In Finland, where the average soil resistivity varies between 1000 and 10,000 ohm-meters
[29], most attempts to meet the grounding requirements of the Finnish electrical safety code
(1957) have been condemned to failure because of the difficulties in obtaining low power
system ground resistance at realistic costs. This unacceptable situation prompted an extensive
study which resulted in a new safety code [30] based on a systematic probabilistic analysis.
This technique permits the design of a grounding electrode with a predicted yearly maximum
number of electroction incidents. This approach could not have been implemented without
extensive statistical data related to power system outages and population exposure to
transmission line structures in Finland.
8-16
The large and increasing number of transmission line structures and the very low observed
electrocution accident probability associated with these structures would appear to justify a
similar probabilistic approach in North America. Because this approach appears to be applicable
to transmission line grounding system design, the methodology developed in [30] and presented
in [29] will be summarized in this section. However, it must be kept in mind that the
probabilistic concept presumes that:
a- Statistical data are available in order to determine the probability of the
various events leading to the accident.
b- A maximum acceptable number of yearly electrocution accidents at any
transmission line is defined.
There is sufficient data on power system outages to permit a realistic evaluation of the
probabilities associated with transmission line faults. However, as yet, there is no North
American guide which attempts to define an acceptable probability of an electric shock
accident at a transmission line structure.
Determination of Accident Probability
The probability that the fibrillation current threshold will be exceeded when the human body
conducts an arbitrary current i, is given as:
R =
F(i) f(i)di
(8-11)
where
F(i) represents the body strength function, i.e., the cumulative distribution of maximum
permissible body current for a given population sample.
f(i) represents the body stress function, i.e., the distribution of the possible body
currents at a fault current site.
The body strength function can be determined statistically from physiological tests on animals.
By analyzing and extrapolating these results to humans, it is possible to derive heart fibrillation
threshold values as a function of time for various probability percentages (0.5 %, 1 % etc.).
By assuming a Gaussian distribution and taking into account the noncritical heart-time
interval, Karkainnen and Palva [29] determined by an iterative method the current and
voltages corresponding to the different probabilities of heart fibrillation. Their results show
that the constant energy law (e.g., Dalziel's equation for a 0.5 % probability) agrees well
with their function in the time range of 0.2 to 5 seconds. For times less than 0.2 s or
greater than 5 s, the function is essentially constant. This function can be written as:
[oTtT ♦ °'25]4.(i)
; for t
<
0.56
s
; for t
>
0.56
s
F(i)
(8-12)
<Mi)
where t is the time in seconds and <t>(\) represents the cumulative distribution function of
a (0,1) normalized Gaussian distribution. This formula assumes that the Gaussian distribution
is valid for the whole current range.
8-17
The body strength function F(i) varies with the duration of the electric shock but is well
defined for each specific current duration. However, the body stress function f(i) varies
widely from one grounding installation to another and is dependent on the grounding system
arrangement, soil structure, power system configuration and characteristics at that location.
Thus, F(i) must be determined at each site where a grounding system is to be designed. This
task may be cumbersome since it requires the calculation of body current at various locations
(and in various positions) throughout the grounding system.
Furthermore, it is necessary to express the magnitude of these various calculated currents
as a probability function. In practice, this is feasible only through computer simulation.
Alternatively, it is possible to adopt a conservative approach which assumes that regardless
of location, a person will be subject to the maximum computed body current i0. In this case
the function f(i) reduces to the Dirac (or impulse) function 5(i0) of the current i0, and the
probability R of Equation 8-11 becomes equal to the body strength function F(i0).
Once F(i) and f(i) have been determined, the probability R that the fibrillating current will
be exceeded if a person is exposed to a shock voltage at the site under investigation is
obtained using Equation 8-11. However, the final probability P of an accident depends on
the probability H of a power system fault involving the grounding system at the site during
the observation period T (usually one year). This probability depends primarily on the average
frequency of ground faults X involving the site during the observation period T.
It is also necessary to consider the fact that a person is not always present in a possibly
hazardous area. This is accomplished by including in the analysis the probability W of a
person being located in a hazardous position during the period T.
The final probability of an accident is therefore:
P =
R H W
(8-13)
which expresses, in probabilistic form, the previously defined fundamental conditions required
to cause a potential hazard to life.
In practice, H is determined from the observed statistical distribution of ground faults and
W is derived from population density statistics and the average exposure of an individual to
the site under consideration.
Based on their statistical observations and using the fundamental concepts of the probabilistic
theory [31], Karkainnen and Palva [29] showed that the product H.W can be expressed as:
(8-14)
H W = Z P. (l-qnk)
k=1
K
where
n _ _-AT
Pk “ e
_ _ ,
(XT)k
kl-------
a+b/n
a2 + (b/n)2
q - i----- tT— +-------*——
2T2
8-18
and
a
is the duration of the fault,
b
is the time spent by the person at the site.
n
is the number of equal time intervals into which b has been divided.
X is the average frequency of ground faults at the site during the observation period
T.
In the above, q represents the probability that the hazardous voltage will not be observed
during one period of exposure, while
is the probability of having k ground faults
during the period T.
Equations 8-11, 8-13 and 8-14 can be used to accurately estimate the final probability of
an accident. It is apparent however, that computations of this probability will require the
determination of several difficult statistical distribution functions. It is also evident that if
a decision is taken to proceed with the probabilistic approach, careful examination of the
detailed approach (briefly described here) and statistical data as presented in [29,30] is
necessary.
However, it is genuinely difficult to assess the effectiveness and/or appropriateness of a
probabilistic approach to safety, based on sophisticated computations, particularly when our
limited knowledge of the physiological effects of electric currents is considered. Further
research work in this area is certainly justified. For the present, depending on the nature
and complexity of the problem being considered, it may be concluded that simplified
computations, based on conservative assumptions, are best used to determine the three
fundamental probabilties of Equation 8-13.
The simplest analysis is obtained when values of these probabilities are known from previous
work or assumed equal to known conservative values. For example, the probability W of
having someone at the site in an exposed position may be taken as 1. An interesting
alternative could also be provided through the use of empirical relations to determine R, H
and W. These relations would necessarily be based on extensive statistical data derived from
observations at actual installations of the type being considered; in this case, high voltage
transmission lines.
8.3.3 THE SELECTIVE DETERMINISTIC APPROACH
The major disadvantage of the probabilistic approach is that it can be used only if certain
statistical information related to the site under consideration is available. Moreover, even
if the necessary information is gathered, an acceptable probability limit is necessary to
achieve safe design objectives. Finally, since the statistical data related to faults on
transmission line structures do not usually make any distinction between individual structures,
the probabilistic approach may lead to situation where protective measures are taken at
structures remote from populated centers, while other structures located in densely populated
areas, may not be equipped with mitigation measures because of significantly lower fault
probabilities.
For the above reasons, it may be argued that it is preferable to use a selective deterministic
approach rather than a probabilistic approach, especially when safety around transmission
line structures is being investigated. The terms "deterministic" and "selective" are used to
emphasize the fact that electric shock hazard is considered as certain at only some particular
structures where the risk of exposure is estimated to be particularly high.
8-19
Structures located in densely populated centers or in areas such as schoolyards, parks or
recreational areas are obvious examples of vulnerable transmission line structures.
This approach has the advantage of permitting the analysis of any structure on an individual
basis. Consequently, it allows decisions to be based on the merits of each case. Another
advantage of the approach is the standardization which may be developed in identifying the
types of transmission line structures which must be thorougly investigated from a safety
point of view. For example, three classes of structures may be considered:
a- Structures located in areas where the density of the population is less than x
per square kilometer (low exposure).
b- Structures located in areas where this density is greater than or equal to y
per square kilometer (y>x) (moderate exposure).
c- Structures located in specific areas where the risk of exposure of humans
to the structure is unusually high (schoolyards, recreational parks, etc.).
An intermediate class may be added, recognizing that in moderate exposure areas, safety
investigation is only required at those structures which may rise to a potential above a
specific value. For example this new class is created by stating that:
d- Structures which are erected in areas where the density of the population is
between x and y per square kilometer (x<y) and which, during ground faults, may
be raised to a potential exceeding U kilovolts.
Many variations to the above illustrative rules could be proposed and could include some
aspects of the probabilistic approach described earlier. The final decision regarding the
optimum choice remains the responsibility of the design engineer who, based on the present
and future standards, will have to decide whether or not improvement and/or mitigation
measures are required for the grounding system of the structure being considered.
8.4 SAFE DESIGNS AND MITIGATION TECHNIQUES
As shown in Chapter 5, the earth potential in the vicinity of the grounding system of a
transmission line structure is directly proportional to earth resistivity p and to the current
I discharged to the soil by the grounding system. Hence, the touch or step voltages which
exist in the vicinity of a transmission line structure are also proportional to the resistivity
P and current I, since they are a function of the difference in earth potential between two
specific points. Consequently if U is used to designate a stress voltage (touch or step), then
the following relation is applicable:
U = A p I
(8-15)
Based on the same uniform soil conditions, the resistance R of the structure is also proportional
to P and can be written as:
R = B p
(8-16)
In the above two relations, A and B are constants which generally depend on the configuration
of the grounding system. A and B can be readily determined from the equations presented
in Chapter 5. Equations 8-15 and 8-16 will now be used to illustrate the characteristics of
the equation which is used to evaluate the level of safety at a transmission line structure.
8-20
8.4.1 EVALUATION OF THE SAFETY LEVEL
Equations 8-9 and 8-10 show that the body current i can be expressed in the general form:
i =
(8-17)
Rb +
where U is the stress voltage (step, touch, etc.), Rj-, is the body resistance between the
points of contact and Rp is the total resistance of all protective, semi-insulating materials
in the current path outside the body. As previously stated, this resistance may be zero in
the worst case or may include a relatively high skin resistance, shoe or glove resistance or
resistance of a thin layer of gravel on top of the natural low resistivity top soil.
In the following, the resistance R^ is assumed equal to 1000 ohms and Rp is selected as
1.5PS where ps is the resistivity of a thin layer of gravel. As discussed in Section 8.1, this
value of Rp corresponds to the parallel resistance of both feet of a person standing on the
gravel. Therefore, using Equation 8-15, Equation 8-17 can be rewritten as:
A p I
1000 + 1.5PS
(8-18)
The magnitude of the current I is dependent on many variables, as explained in Chapter 6.
However, it can be expressed to a good approximation as follows [32] (see also Figure 8.11):
V
|R(1+Zs/Zg)
I
(8-19)
where
V
is the magnitude of the phase to ground voltage.
Zs is the equivalent current source impedance as seen from the phase conductor at
the faulted structure (Zs=rs+jxs).
-g is the equivalent ground wire (and counterpoises, if any) return path impedance as
seen from the faulted structure (Zg = rg+jxg).
For the sake of simplicity in the following discussion, the impedances Zs and Zg are assumed
to be pure inductances, i.e., Zs ~ jxs and Zg ~ jxg.
According to Equation 8-16 and 8-19, Equation 8-18 becomes:
; = ______________ A p v
........................ .........
(1000 + 1.5PsK/b2 p2(l +
Xs/Xg)2+
(8-20)
xs2
The above body current is safe only if it does not exceed the value of Ij-, in Equation 8-1.
If Dalziel's Equation 8-4 (with p=0.116) is used to determine I^, this condition becomes:
_________ A
p
V_________ <
Vx 2 + (1 + x /x )2B2p2
s
s
g'
116 + 0. 174Ps
Vt
8-21
(8-21)
Although this inequality has been derived from certain specific conditions, it is of tremendous
importance since it incorporates the key paramaeters used to mitigate ground potential rise
hazards in the vicinity of the structure.
Z
Figure 8.11
s
Approximate Equivalent Transmission Line Circuit
Before proceeding with the next section, the reader is reminded that it is implicitly assumed
that Ps is several times larger than the top soil resistivity p such that the response of the
grounding system is essentially unaffected by this relatively thin, high resistivity surface
layer. Typically, Ps is assumed to be 5 times P or greater since, for lower values, its
effectiveness decreases drastically and its usefulness becomes questionable.
8.4.2 IMPROVING SAFETY AROUND TRANSMISSION LINE STRUCTURES
A close examination
V and the equivalent
as design constants.
Modern transmission
primary relays, and
of the variables which intervene in (8-21) reveals that the line voltage
source impedance xs can not be easily modified and should be considered
Also the fault clearing time is, for all practical purpose, a constant.
lines are usually designed to clear a fault in less than 0.1 s with the
0.5 s with the back-up protection.
However, careful attention should be paid to the possibility that the fault remains uncleared,
should the steady state fault current be less than the relay setting. This situation will
generally occur at structures not equipped with a ground wire or continuous counterpoise
and with high ground resistances. With long clearing times t, the right-hand side term of
(8-21) reduces substantially and the safety criterion will often not be satisfied. In this case,
the first corrective measure is to install sufficient ground conductors at the structure to
ensure its resistance drops to a sufficiently low value to cause a fast relay response.
8-22
At this stage, we are left with the following design parameters to control the safety around
the structure:
p
Average resistivity of local volume of soil
Ps
Resistivity of thin layer of covering gravel
Xg
Equivalent neutral current return path impedance
A, B
Configuration of the grounding system
The A and B functions are dependent on the extent and geometry of the grounding system.
It is important to note that normally the extent is more or less represented by B and the
geometry is essentially represented by A.
Because these parameters can be modified at the structure to varying degrees, they
the four fundamental techniques which can be economically used to control step
potentials at the structure. Depending on the circumstances, some techniques
effective than others. Often, however, a combination of two or more techniques are
to achieve optimum results.
designate
and touch
are more
necessary
In this section, techniques related to the first three parameters are discussed. The technique
concerning the extent and geometry of the grounding system is described in the next section,
because it usually represents the final mitigation measure when the other techniques fail to
achieve the required level of safety.
In order to better assess the effectiveness of the various hazard mitigation techniques, it
is essential to note that according to (8-21), the complexity of the mitigation task increases
with the line voltage V except when the extent of the grounding system increases (B decreases)
and the source impedance (Zs = jxs) decreases at the same or a higher rate. This situation
usually occurs when four-legged lattice towers are used. With tubular or single-shaft structures,
supplemental grounding conductors are required to provide a similar effect. In addition, it
should be noted that when the source impedance can be neglected in (8-21), the level of
safety (left-hand side of inequality) becomes independent of the average soil resistivity. This
remark is of fundamental importance as will be explained. Finally, when xs is not negligible,
the left-hand side of (8-21), which is proportional to body current, is a function of the
average soil resistivity and exhibits a maximum for some unfavourable soil resistivity, Pu.
This corresponds to the positive root of the first derivative of this function. In practice,
this means that there is a particular resistivity value which will cause a maximum hazard
for a given installation. Several of these curves have been presented in [33,34]. Figure 8.12
shows typical curves.
Chemical Treatment of Soils
Depending on the value of the source impedance Zs the body current curve will approximate
one of the typical shapes shown in Figure 8.12(a). Examination of these curves reveals that
chemical treatment of soils to decrease earth resistivity, is effective in reducing body
currents only if the final resistivity value achieved is to the left of the theoretical maximum
of the curve. In fact, as is illustrated in this figure, a resistivity decrease could increase
the body current. These observations underline the importance of exercizing caution in
requesting chemical treatment of the soil around a transmission line structure.
In summary, it can be said that the effectiveness of the treatment increases with the source
impedance, as seen from the structure. In practice, it is of little benefit to apply chemical
treatment at a structure with a ground resistance several orders of magnitudes larger than
the source impedance, as seen from the structure.
8-23
Except in simple cases, a final decision should be taken only after careful examination of
the computation results. It must be remembered that any chemical treatment remains
effective only for a certain time period and must be reapplied as required. For this reason
it is not recommended, except in exceptional cases.
(b) TYPICAL DESIGN RESULTS
(a) TYPICAL CURVE SHAPES
Figure 8.12
Body Current Versus Resistivity
Effects of a Thin Layer of Gravel
It is possible to improve the safety around a transmission line structure by adding a thin
layer of high resistivity gravel on top of the natural soil. This method is appropriate when
the resistivity of the gravel is several times larger than the top soil resistivity. Otherwise,
it may influence the response of the grounding system to a degree that it is no longer
accurate to compute the grounding system response without including the layer of gravel in
the soil model.
The use of gravel as a means of decreasing the hazard around a structure suffers two other
drawbacks, serious enough perhaps to limit its use to a small number of locations where
preventive maintenance is available. The first problem associated with the use of gravel
results from the wide variations in the resistivity of gravel, depending on the origin of the
material. According to the measurements described in [34], the resistivity of gravel varies
not only with moisture content but is also dependent on the location from which it was
originally extracted, as shown in Figure 8.13. This problem is alleviated if the type of gravel
is clearly indicated in the design specifications. The second difficulty associated with the
use of gravel is the likelihood of deterioration of the original insulating properties
through a progressive accumulation of soil and wind blown debris in the voids between
the gravel material. This should be of no concern if regular maintenance is provided at the
protected site or if other low maintenance materials, such as asphalt, are used.
Installation of Ground Wires or Counterpoises
Chapters 3, 6 and 10, recent publications [32,33], and a number of charts in Volume 2 of
this report clearly show that overhead ground wires or counterpoises can dissipate a significant
portion of the total fault at a structure.
8-24
Consequently, ground wires and counterpoises represent a very effective means of reducing
the electrical shock hazard at critical structures. The effect of installing such neutral
conductors is a reduction in the impedance Zg 0f the return current paths, as can be
concluded from (8-21).
If the transmission line is not equipped with overhead ground wires or if it has insulated
ground wires, a counterpoise connecting the structure to several adjacent structures offers
an effective hazard reduction technique, since it works as a stress equalizer among the
connected structures. In fact, safety is generally improved at all structures compared to the
case where each structure is isolated from the others. The only disadvantage is that any
ground fault at one structure will involve all other structures in the group so connected.
The equations of Chapter 6, computer program PATHS, and the charts of Volume 2 provide
several methods which can be used to accurately compute the effectiveness of a proposed
design. Furthermore, Chapter 3 provides a good illustrative example of the significant effects
of the overhead ground wires.
RESISTIVITY
OF GROUND WATER
# 57 CLEAN CRUSHED GRANITE
(GARNER, N.C.)
WASHED LIMESTONE
(GULLIVER, MICHIGAN)
WASHED LIMESTONE
iPRESQUE ISLES, MICHIGAN)
CRUSHER RUN (GRANITE
(GARNER, N.C.)
RESISTIVITY OF WATER (ohms-meter)
Figure 8.13
Resistivity of Gravel (Redrawn from [34])
8.4.3 GROUND POTENTIAL MITIGATING CONDUCTORS
If the usual grounding system of a transmission line and its overhead ground wires (if they
exist) are not sufficient to provide a safe environment at critically located transmission line
structures, the installation of some special additional ground conductors should be considered
to reduce step and touch voltages.
8-25
A practical and widely used arrangement [3,35] of such conductors consists of a ring or a
square loop buried at a shallow depth around the structure base. If necessary, several
concentric grading rings buried at progressively increasing depths can be installed in difficult
cases. These rings are usually designated as ground potential control rings or loops. Some
typical ring arrangements are shown in Figure 8.14.
PROFILE
PROFILE
RING
No. 2
(100
■2 RINGS
1
3 RINGS
RING
RING
RING
LATERAL DISTANCE
(a)
FOUR-LEG LATTICE TOWER
Figure 8.14
%)
LATERAL DISTANCE
(b)
SINGLE-SHAFT TOWER
Typical Ground Potential Mitigating Rings
The ring provides beneficial effects on the overall performance of the grounding system as
follows:
a- It reduces the ground resistance and, in most cases, the potential rise of the
structure.
b- It reduces the steep potential gradients which exist near the buried part of
the structure.
c- It reduces the earth surface potentials in the vicinity of the structures.
These effects result in touch and step voltage reductions as illustrated in Figure 8.14.
Examples of the mitigating effects are presented in Chapters 3 and 10 and in numerous
charts in Volume 2. Additional examples are shown in [3,35]. The example of Appendix B of
[35] displays the results of field measurements made on a single ground rod equipped with
a variable number of concentric grading rings, placed progressively deeper in the ground.
Field measurement and computation results related to actual installations are described and
discussed in [3] and in Chapter 10 of this report. The main conclusion drawn is that
touch and step potentials can be substantially reduced by a single ground potential mitigating
ring, optimally dimensioned. Further reductions are obtained by the installation of additional
rings at progressively increasing distance and depth. Theoretically, the touch and step
potentials can be reduced to an inconsequential value by the use of a sufficient number of
rings. However, it is important to note that the effectiveness of each additional ring decreases
very quickly after the installation of the first ring.
8-26
8.4.4 OTHER SAFETY MEASURES
Other means of improving safety in the vicinity of a critically located transmission structure
include the installation of an insulating fence and/or covering the soil surface around the
structrure with a thick layer of a good semi-insulating material such as asphalt. This layer
must be properly inclined as to avoid water accumulation.
These techniques may not always be practical or aesthetic in park or recreational areas.
The presence of a fence is not necessarily an obstacle to everybody and may attract children.
Thus, whenever possible, techniques such as the installation of ground wires, counterpoises
or ground potential rings should be used because they provide invisible and effective mitigation.
REFERENCES
1 - EPRI Project RP 1494-1 Interim Report, "Transmission Line Grounding - Survey of Utility
Practices" by Safe Engineering Services Ltd., Montreal.
2 - A. Goubet, "Sur les Risques pour les Personnes Resultant de la Montee en Potentiel du
Sol au Voisinage Immediat d'un Support de Ligne Electrique en Gas d'Ecoulement a la Terre
d'un Courant de Defaut", Internal Report ST/AL/MC, Direction du Gaz de 1'Electricite et
du Charbon, Paris, December 6, 1974.
3 - E. A. Cherney, K. G. Ringler, N. Kolcio and G. K. Bell, "Step and Touch Potentials at
Faulted Transmission Towers", IEEE Transactions on PAS, Vol. PAS-100, No. 7, July 1981,
pp. 3312-3321.
4 - F. Dawalibi, W. G. Finley, "Transmission Line Tower Grounding Performance in Nonuniform
Soil", IEEE Transactions on PAS. Vol. PAS-99, No. 2, March/April 1980, pp. 471-479.
5 - C. F. Dalziel, "Electric Shock Hazard", IEEE Spectrum, February 1972, pp. 41-30.
6 - IEEE Guide 80, "Guide for Safety in Substations Grounding", Institute of Electrical and
Electronics Engineers, New York, 1976.
7 - F. Dawalibi, M. Bouchard, D. Mukhedkar, "Survey on Power System Grounding Design
Practices", IEEE Transactions on PAS, Vol. PAS-99, No. 4, July/August 1980, pp. 1396-1405.
8 - V. Yablonski, B. Shatkovska-Karpa, "Allowable Touch Voltages in the COMECON Standard
Proposal", Electrichestvo, No. 7, 1980.
9 - J. E. Bridges, K. Rogler, J. Wingfield, R. Kaleckas, "Electric Shock Prevention Investigation",
Final Report HTRI Project E6373, Contract No. CPCS-76-0093, Oct. 1977.
10- L. A. Geddes, L. E. Becker, "Principles of Applied Biomedical Instrumentation", 2nd
Edition, John Wiley and Sons, 1975.
8-27
11- G. Biegelmeier, K. Rotter, "Electrische Widerstrade Und Strome in Menschliken Korper",
E Und M 99, 1971, pp. 104-109.
12- P. Osypka, "Quantitative Investigation of Current Strength, Duration and Routing in AC
Electrocuti on Accidents Involving Human Beings and Animals", Technical College of
Braunschweig, Brunswick, W. Germany, 1966/SLA Translation Center, TT-6611470.
13- C. F. Dalziel, "Threshold 60-Cycle Fibrillating Currents", AIEE Transactions, Vol. 79,
Part III, 1960, pp. 667-673.
14- C. F. Dalziel, W. R. Lee,"Reevaluation of Lethal Electric Currents", IEEE Transactions,
Vol. IGA-4, No. 5, September/October 1968, pp. 467-476.
15- R. H. Golde, "Lightning", Academic Press, New York, 1977, Chapter 16 of Vol. 2, by
W. R, Lee, pp. 521-543.
16- G. L. Ford, L. A. Geddes, "Transient Ground Potential Rise in Gas Insulated Substations;
Assessment of Shock Hazard", IEEE Paper 82 WM 010-7, IEEE PES Winter Meeting, New
York, January/February 1982.
17- L. Lapicque, "Definition Experimentale de 1'Excitabilite", Proc. Soc. Biol. 1909, 77:280:283.
18- J. A. Pearce et Al, "Stimulation With Ultrashort Duration Pulses", PACE 1981.
19- G. Bielgelmeier, W. R. Lee, "New Considerations on the Threshold of Ventricular
Fibrillation for AC Shocks at 50-60 Hz", IEE Proc. Vol. 127, No. 2, Pt. A, March 1980.
20- J. E. Bridges, "An Investigation of Low-Impedance Low-Voltage Shocks", IEEE Transactions
on PAS, Vol. PAS-100, No. 4, April 1981, pp. 1529-1537.
21- H. B. Whitaker, "Electric Shock as it Pertains to the Electric Fence", Underwriters
Laboratories, Bulletin of Research No. 14, pp. 3-56, 1939.
22- M. S. Hammam, R. S. Baishiki, "A Range of Body Impedance Values for Low Voltage,
Low Source Impedance Systems at 60 Hz", Paper 82 SM 476-0, IEEE PES Summer Meeting,
San Francisco, July 1982.
23- A. Sances, Jr., et Al, "Effects of Contacts in High Voltage Injuries", IEEE paper 81 WM
217-9, IEEE PES Winter Meeting, Atlanta, February 1981.
24- W. W. Loucks, "A New Approach to Substation Grounding", Electrical News and Engineering,
May 15, 1954.
25- J. Freiberger, "Der Electrische Widerstand Des Men Menschliche Korpers", Berlin, Springer,
1934.
26- W. B. Kouwenhoven, "Effects of Electricity on the Human Body", Electrical Engineering,
Vol. 68, pp. 199-203, March 1949.
27- "Recherche de 1'Influence des Chaussures sur les Dangers Presentes par les Tensions de
Pas", Certificat No. 162763, Electricite de France.
28- C. F. Dalziel, "A Study of the Hazards of Impulse Currents", AIEE Transactions on PAS,
October 1953, pp. 1032-1043.
8-28
29- S. Karkainnen, V. Palva, "Application of Probability Calculations to the Study of the
Earthing Voltage Requirements for Electrical Safety Codes", Reprint from SAKHO, Electricity
in Finland, No. 11, 1974.
30- Publication Al-74 of the Electrical Inspectorate, "The Electrical Safety Code", in Finnish
or Swedish, Helsinki, 1974.
31- A. Papoulis, "Probability, Random Variables and Stochastic Processes", London, 1965.
32- F. Dawalibi, D. Mukhedkar, "Ground Fault Current Distribution in Power Systems - The
Necessary Link", IEEE Paper A 77 754-5, IEEE PES Summer Meeting, Mexico City, July
1977.
33- F. Dawalibi, D. Bensted, D. Mukhedkar, "Soil Effects on Ground Fault Currents" IEEE
Transactions on PAS, Vol. PAS-100, No. 7, July 1981, pp. 3442-3450.
34- G. E. Smith, "Resistivity of Some Surface Coverings Used in Substation Yards as a
Function of Resistivity of the Wetting Agent and as a Function of Time After Wetting",
Internal Report, April 1978, Ref. KJ 1W18, Carolina Power and Light, N.C.
35- The Electricity Authority of New South Wales, "Earthing Handbook", Australia, June
1975.
8-29
FIELD MEASUREMENT TECHNIQUES
The design of optimum ground electrodes is critically dependent on soil resistivity at the
site. Thus, it is essential that resistivity be accurately determined to allow an accurate
prediction of grounding system performance. It is usually desirable to check the design
calculations by measuring the ground resistance of the electrode after construction.
For transmission lines, standard grounding systems are normally used all along the line except
at a limited number of critical locations which require special investigations. Consequently,
measurements at most sites are limited to verification that the resistance values are within
design limits and to determine if additional grounding is required.
Field resistance and resistivity measurements are therefore an integral part of the engineering
work related to transmission line grounding.
9.1 GROUND RESISTANCE MEASUREMENT
The principle of ground electrode resistance measurements is illustrated in Figure 9.1. This
figure shows, in schematic form, an earth electrode to be tested, a return electrode, which
can be any other ground electrode sufficiently distant from the test electrode, and a power
source which is used to pass current between the two electrodes. The measurement objective
is to determine the rise in potential of the test electrode with respect to remote ground
as a result of the test current I.
The principal difficulty encountered in ground resistance measurements is in locating a
suitable return electrode. To facilitate proper measurements, the electrode under test and
return electrode must be completely "isolated" as far as any metallic conduction paths or
mutual earth resistances are concerned. If an existing structure is to be used as a return
electrode, assurances must be obtained that there are no metallic connections, however
indirect, between the two grounds. In practical terms, this assurance is usually very difficult
to obtain. Consequently, a new return electrode is normally installed for the purpose of the
tests. The requirements for the return electrode are dictated, to a large extent, by the
characteristics of the grounding system being measured, and, to a lesser degree, by the soil
conditions. In general, the measurement problems become more difficult as the ground
impedance of the grounding system decreases, as the dimensions of the grounding system
increase, and as the level of ambient electrical noise and soil resistivity both increase.
The problems described are generally of minor concern in carrying out resistance measurements
on transmission line structure grounds. This is because of the small physical dimensions,
generally remote location, and relatively high resistance of structure grounds as compared
to substation or large building grounds. The connection of a continuous overhead ground wire
creates an additional set of problems that will be discussed later in this chapter.
9-1
If it were possible to readily locate an ideal remote ground reference point for any ground
electrode resistance measurement, and if the isolation of the test and return electrodes
could always be assured, resistance measurement would be a very simple process as illustrated
in Figure 9.1. One voltage measurement between the grounding system and remote ground
for a given test current would yield the desired result. In practice however, neither an ideal
remote reference point or an assurance of isolation is obtainable and a measurement technique
must be used which compensates for, or identifies deviations from the ideal arrangement so
meaningful results can be obtained. The fall-of-potential method is the most widely used
measurement technique in this regard and is the principal method discussed in this chapter.
I
STRUCTURE
BEING
MEASUREDX
REMOTE"
RETURN
CURRENT
ELECTRODE
C2
"REMOTE"
POTENTIAL
/PROBE
JL-P,
Figure 9.1
Principle of Ground Resistance Measurement
9.2 TEST METHODS
There are three principal methods used to measure the resistance of ground electrodes; the
two-point method, the three-point method, and the fall-of-potential method [1], The
fall-of-potential method is by far the most widely used in the electrical industry according
to a survey conducted in 1976 [2].
9.2.1 TWO-POINT METHOD
In this method the total loop resistance of the unknown and return ground electrodes is
measured. The resistance of the return electrode is assumed to be negligible in comparison
with the resistance of the unknown ground and the measured value in ohms is assumed to
be the resistance of the unknown ground. The technique is obviously limited to the measurement
of relatively high resistance grounds, such as a single ground rod, or small ground array,
provided that a low ground resistance system is readily available at the test site.
9.2.2 THREE-POINT METHOD
The three-point method involves the use of two auxiliary grounds (2 and 3) of resistances
designated T2 and rj. The unknown ground resistance r^ is determined by measuring the
resistance between each pair of grounds and solving for rj from the equation:
r
- r
12
i
+ r
23
(9-1)
13
2
9 -2
There are several limitations to this technique which restrict its use to the measurement
of small, high resistance grounds in areas where the three grounds can be located well out
of the zone of influence of each other.
Since neither this method nor the two-point method have any built-in checks to assure that
significant errors are not being introduced into the measurements, the fall-of-potential
technique has become the universally accepted test method. The two and three-point methods
should only be used to obtain rough estimates of ground resistance or to perform
repeated measurements for experimental purposes once the adequacy of the test configuration
has been independently verified.
9.2.3 FALL-OF-POTENTIAL METHOD
The fall-of-potential method of resistance determination involves the use of an auxiliary
return current electrode and a series of surface potential measurements taken at increasing
distances from the grounding system under test. Provided that the auxiliary electrode has
been located sufficiently remote from the grounding system and coupling effects between
voltage and current leads have not affected readings, the potential measurements will reach
(or become asymptotic) to a level which represents the rise in potential of the tested
electrode due to the test current. The general arrangement of electrodes is shown in Figure
9.2. Current electrode Cl and the fixed potential electrode PI are located on the grounding
system. The remote auxiliary current electrode is designated C2. The potential electrode P2
is sequentially located at regular intervals moving away from Cl and voltage and current
readings taken at each P2 location. An apparent resistance value is determined from each
set of voltage and current readings. If the apparent resistance is plotted against distance,
a levelling of the apparent resistance values will be observed as the potential probe P2
becomes remote from the grounding system.
In carrying out fall-of-potential measurements, the voltage lead may be extended in the
same direction as the current lead or at an angle, usually 900. Although less convenient,
keeping the voltage and current leads at right angles to each other minimizes the mutual
impedance between the leads; a very desirable situation when low impedance grounds are
being measured. For transmission line structure measurements or measurements involving
small substations, the unknown ground resistance is usually large enough and the zone of
influence around the tested electrode small enough that mutual impedance errors are
insignificant regardless of current and voltage lead orientation.
When measuring the resistance of transmission line structure grounds, it is highly
desirable to locate the remote current electrode in an orthogonal direction to the transmission
line right of way in order to minimize the induced voltages in the test leads and equipment.
This has safety as well as measurement implications because of the large unbalances which
can occur in the phase conductors during ground faults.
If the unknown resistance is approximately one ohm or larger and the return electrode has
been adequately located, a potential profile taken from the tested electrode to the return
current electrode will look similar to the curve of Figure 9.2. (see also Figures 9.5 and 9.6).
A distinct flat portion of the curve, indicating a zone under the influence of neither the
tested nor return electrodes, can readily be observed. The apparent resistance observed in
this portion of the curve is the resistance of the tested electrode. In many cases, however,
the curve obtained during fall-of-potential measurements does not resemble the curve of
Figure 9.2 and interpretation procedures must be applied to make use of the data or to
correct the test set-up.
9-3
FOUR TERMINAL
RESISTANCE
TEST SET
C,
V
o Pi O
POTENTIAL
PROBE IN
OPPOSITE
DlRECTION
STRUCTURE
BEING
TESTED
'.i
—0i i t LJ
POTENTIAL
PROBE
tnr
TRUE
RESISTANCE
VALUE
FALL OF POTENTIAL ^
CURVES
^
X
Figure 9.2
RETURN
CURRENT
ELECTRODE
C2
0 P*o
POTENTIAL PROBE DISTANCE
Fall-of-Potential Test Schematic Diagram and Typical Test Results
9.2.4 THEORY OF THE FALL-OF-POTENTIAL METHOD
Figure 9.3 shows an electrode E located at some distance from a second current carrying
electrode G. If no current is conducted through electrode E and if E is located at a vary
large distance from electrode G, or any other current carrying electrode, the self potential,
Vee, (ground potential rise) of E is zero.
If a current I
the electrode
potential rise
the electrode
enters electrode E, the potential rise of E, Veej is given as IRe where Re is
impedance. If I = 1 ampere, then Pe = Vee = lRe = Re. Pe designates the
of electrode E when 1 A flows in the electrode. Pe is numerically equal to
impedance in ohms.
Assume now that at some finite distance from E, a current I is passed into the soil through
electrode G (E does not conduct any current). Because of the local earth potential, electrode
E, initially at zero potential rise, will be at potential Veg as a result of the resistive coupling
between E and G. If I = 1 A, then Veg = Peg, which is numerically equal to the so called
"mutual resistance" between E and G. If electrode E also carries 1 A of current, the potential
rise of electrode E will be Pe + Peg.
The theoretical expressions from which Pe and Veg can be determined are complex and will
not be presented here except for simple earth and electrode configurations. The more general
expressions were determined in Chapter 5 for the grounding systems of transmission line
structures.
Derivation of the Fundamental Equations
The problem is illustrated in Figure 9.3. The potential probe location x0 which leads to an
apparent ground impedance (V/I) equal to the grounding system impedance Re, is required.
9-4
The current i flowing in
current I injected in the
return current electrode
presented in this section,
U
e
the potential probe F is neglected compared to I. At a time t,
grounding system E, is assumed positive and I, collected by the
G, is assumed negative. Based on the definitions and symbols
the following relations hold:
= Pfe 1 - P fg
(9-2)
= P I - P£ I
e
fg
(9-3)
Uf and Ue are the potentials, with respect to remote ground, of electrode F and E respectively.
The voltage V measured by the fall-of-potential method is:
V = u
- u£
e
f
therefore
I (P
V
- P
e
eg
pr +
fe
fg
(9-4)
)
Pe is the potential caused by electrode E on itself when carrying a current of 1 ampere.
This is by definition the impedance Re of electrode E. Therefore, Equation 9-4 can be
written as:
V
I
R
e
P
+
eg
(9-5)
" Pfe5
Pfg and Pfe are functions of the spacing between the electrode (E, G and F), the
configurations and the soil characteristics.
electrode
a- Uniform Soil
Let us define the following functions a,
shown in Figure 9.3, (it is assumed that
and x):
4> and
a, <f>
^ with respect to the coordinate system
and ^ are only functions of distances d
= ct(d)
(9-6)
Pfg = <j>(d “ x)
(9-7)
P
eg
Pfe =
(9-8)
^(x)
According to Equation 9-5 the measured impedance R = V/I will be equal to the true
impedance Re if:
F> fg - P eg - P£fe = 0
that is:
(j) (d - x) - a(d) - ip (x) = 0
Identical Electrodes and Large Spacinqs. If electrodes E and G are identical
d is large enough such that Peg = a(d) ~ 0, then Equation 9-9 becomes:
cj>(d - x) -
ifj(x)
=
0
(9“9)
4> = \(f
and if
(9-10)
Hemispherical Electrodes. If electrodes E and G are hemispheres, their radii are small
compared to x and d, and soil is uniform, the potential functions a, <f> and ^ are inversely
proportional to the distance from the center of the hemisphere. If the origin of the axis is
at the center of hemisphere E, Equation 9-9 becomes:
1/(d - x) - 1/d - 1/x = 0
(9-11)
The positive root of Equation 9-11 is the exact potential probe location x0:
x
= 0.618 d
o
This is the usual 61.8% rule [9]. If the potential probe F is at location F2 (E side, see
Figure 9.3) then d-x should be replaced by d+x in Equation 9-11. In this case the equation
has complex roots only. If F is at location F^ (G side, see Figure 9.3) then d-x should be
replaced by x-d in Equation 9-11. The positive root in this case is:
x
o
= 1.618 d
b- General Case
If the soil is not uniform and/or electrode E and G have complex configurations then, the
functions a, 4> and ^ are not easy to calculate. In such cases, computer solutions are
generally required [3].
TRANSMISSION
LINE STRUCTURE
BEING \
MEASURE[K X--------
POTENTIAL
PROBE
RETURN
CURRENT
ELECTRODE
Figure 9.3
Required Potential Probe Location in Fall of Potential Measurements
9.2.5 INTERPRETATION OF FALL-OF-POTENTIAL DATA
In order to carry out accurate resistance measurements using the fall-of-potential method,
it is very important that the theoretical limitations of the technique be understood. It is
also important that the engineer or technologist conducting the measurements appreciate
the effects that various deficiencies in a test set up will have on measurement data so that
the deficiencies can be corrected on site and useful measurement data obtained.
9-6
As stated previously, the difficulties encountered with fall-of-potential measurements increase
as the size of the ground electrode being measured increases and the resistance to be
measured decreases [3]. Although it is unlikely that serious difficulties of this nature will
be encountered in many transmission line ground measurements (assuming that the tests are
carried out before the overhead ground wire is installed), the reasons for these
difficulties will be discussed in detail.
Firstly, as the resistance of an unknown electrode decreases, the voltages to be measured
in the vicinity of the electrode become lower while the electrical interference usually
becomes greater. This is because of increased power distribution at the large sites, be they
HV transmission lines, substations or industrial facilities. For example, a large substation in
an area of low resistivity could have a resistance of 0.25 ohms or less. The typical test
current from a portable Megger type instrument is in the order of 40 ma. This combination
results in a total induced voltage of 10 millivolts or less in the electrode being tested. Since
it is not uncommon for residual voltages in the order of 1 to 10 volts to be present in a
large grounding system, accurate measurement or even detection of the test signal can be
a major problem. This situation also exists when the measurements are made on transmission
structures equipped with long counterpoises and/or overhead ground wires.
Secondly, as the size of a grounding system increases, the zone of influence of the grounding
system increases and it becomes more difficult to establish a return electrode that is
completely isolated from the electrode being tested. For any facility other than remote
substations or transmission line structures, the problem is usually compounded by connection
of numerous external grounds such as water mains, gas pipes, communication circuits and
low voltage distribution neutrals to the main ground. These connections can effectively extend
the zone of influence of the tested ground considerably and in an unpredictable pattern.
Another significant but less understood factor affecting fall-of-potential measurement is soil
structure. When the soil structure is not uniform, the shape of the fall-of-potential curve
can be noticeably affected, as can the correct potential probe location for determining the
true resistance of the unknown electrode when the traverse follows the same direction as
the remote current electrode. This soil structure dependence, originally described in [4], is
shown in Figure 9.4. The curves of this figure give the required potential probe location for
various two-layer soil structures.
The effects of soil structure on fall-of-potential measurements are discussed extensively in
[3,4]. Generally, the zone of influence around a ground electrode in two-layered soil
which has a higher resistivity lower layer is greater than one in soil with a lower resistivity
bottom layer. This effect can be best understood by considering the path of least resistance
for current leaving the ground electrode. When the surface layer is more conductive than
the bottom layer, ground currents will tend to flow out horizontally rather than penetrate
the higher resistivity layer below. This effect can make accurate resistance measurements
very difficult to obtain in areas where a ground electrode is buried in soil overlying bedrock
or other high resistivity sublayers.
When very low ground resistances are being measured, it is usually necessary to locate the
remote current electrode at significantly greater distances from the electrode under test
than with small, high resistance grounds. When the moveable potential probe is located along
the same direction as the current probe, inductive coupling between the current and voltage
leads may introduce a significant error in the measured apparent resistance of the electrode.
Simply separating the voltage and current leads may not be sufficient since the mutual
impedance is only affected to a small degree by separation distance. For example, increasing
the separation between two parallel conductors from 1.5 to 75 m (5 to 250 feet) may only
lower the mutual impedance between the two conductors by a factor of 0.5. The actual
mutual impedance between the current and voltage leads depends on soil resistivity, frequency,
and length of parallel exposure. For soil resistivities in the order of 100 ohm-meters and a
9-7
separation of 8 m (25 feet), the mutual impedance is in the order of 0.4 ohms per kilometer.
Thus, a test current of 2 amperes could introduce a 0.08 volt error in a 100 m (330 feet)
long potential lead. For an unknown resistance of 0.1 ohms, this would be 40% of the voltage
being induced in the measured electrode. The effect of coupling between voltage and current
leads is to slant the fall-of-potential curve upwards to the right, tending to obscure any
levelling off which may occur as the potential probe leaves the influence of the measured
electrode. Figure 9.5, derived from a computer study of an actual test illustrates the effect
of potential traverse direction and mutual coupling between voltage and current leads on
the fall-of-potential curve.
Figure 9.4
Required Potential Probe Location in a Two-Layer Structure
Figure 9.5 shows a potential profile (curve 1) taken orthogonally to the direction of the
return current electrode. The resistance of the grounding system being tested has been
determined analytically to be 0.42 ohms. This figure also shows the fall-of-potential curve
taken in the same direction as the return current electrode, (curve 2) and the related curve
modified to account for a mutual impedance of 0.4 ohms per kilometer between voltage and
current leads.
If a fall-of-potenti al curve is taken from a direction other than towards the return current
electrode, a "good" curve will always be obtained. That is, the curve will always level off
at some point. If, however, the return current electrode has not been located outside of the
zone of influence of the measured electrode, the result may be significantly lower than the
true resistance value. To ensure that this does not occur, the return current electrode must
be located well beyond the distance of the "knee" in the measured fall-of-potential curve.
One means of determining if the current electrode is sufficiently remote, is to relocate the
current electrode approximately 10% beyond the original location and observe if the measured
9-8
potential changes. If the potential does not change, the return current electrode is adequately
located. If an increase in potential is observed, the current electrode should be relocated
even further away.
There may be cases where it simply is not possible to obtain a return current electrode
that is outside the zone of influence of a very extensive grounding system. In these cases,
the use of computer techniques may be the only means of obtaining accurate results from
the measurement data. The use of a grounding computer program to interpret fall-of-potential
data is described in reference [3].
NEGLECTING EFFECTS
OF COUPLING BETWEEN LEADS
INCLUDING EFFECTS
OF MUTUAL IMPEDANCE
BETWEEN LEADS
----- ©
FALL OF POTENTIAL
CURVES IN SAME
DIRECTION AS C2
CURRENT ELECTRODE
FALL OF POTENTIAL
CURVE AT RIGHT
ANGLES TO C2
CURRENT ELECTRODE
DISTANCE ALONG PROFILE (meters)
Figure 9.5
Fall of potential Profile Results of an Actual Test
9.2.6 OVERHEAD GROUND WIRES
The presence of an overhead ground wire connected to a transmission line structure can
considerably complicate transmission line structure ground resistance measurements. Using
conventional instrumentation such as a Megger null-balance instrument, it is virtually impossible
to determine the resistance of the local ground compared to the much lower resistance
usually created by a large number of adjacent structures, interconnected by the overhead
ground wire.
The key to determining the resistance of a specific structure ground equipped with an
overhead ground wire lies in the impedance versus frequency characteristics of the ground.
A transmission line structure ground, by itself, will typically exhibit an almost constant
impedance over a wide frequency range. Adjacent grounds, interconnected by the overhead
ground wire, will exhibit an increasing impedance with frequency as the impedance of the
overhead ground wire becomes significant with respect to the parallel resistance of the
structure grounds. At high frequencies of say 20 kHz or above, the effects of adjacent
structures should be almost completely removed from the impedance measurement.
9-9
At least one manufacturer has developed an instrument specifically designed to take advantage
of this effect to measure the resistance of transmission line structure grounds [8]. Since
this instrument uses a fixed frequency to carry out the impedance measurement, it is not
possible to verify, by plotting an impedance versus frequency curve, that an asymptotic value
has been reached.
A voltmeter/ammeter test set up which employs a variable frequency power source along
with a frequency selective voltmeter can be used to carry out a similar measurement.
Although considerably less convenient than the single instrument referred to above, this
method does permit a meaningful impedance versus frequency plot to be obtained.
Since mutual impedance coupling effects will be very significant at high frequencies, great
care must be taken when carrying out these measurements using either of the described
methods. In general, both voltage and current leads should be kept as short as possible,
allowing for the usual probe location considerations of the fall-of-potential method. In
addition, the current and voltage leads should be oriented at 900 in order to allow the
minimum amount of coupling.
Tests carried out on a 138 kV transmission line equipped with an overhead ground wire using
the variable frequency voltmeter/ammeter technique are described in Chapter 10. For these
tests, the overhead ground wire was disconnected from several of the pole grounds in order
to measure the structure ground alone as well as with the overhead ground wire connected.
Similar tests on a 500 kV transmission line are also described in this same chapter.
9.3 GROUND RESISTANCE MEASUREMENT INSTRUMENTATION
The instrumentation required to carry out accurate ground resistance measurements depends
very significantly on the structure being measured, on soil conditions, and on ambient
electrical noise levels at the measurement site. For small, high resistance ground electrodes
such as ground rods, isolated transmission line structures or small substations, portable earth
testers such as the Megger null-balance, or direct reading earth testers such as the Vibroground,
are the most commonly used instruments [2]. As discussed in Section 9.2, the limitations of
these instruments become apparent as the resistance being measured drops below 1 ohm and
ambient electrical noise levels increase. Also, at low values of ground electrode impedance,
the reactive component of a ground electrode impedance may be significant and a test
instrument capable of measuring the reactive and resistive components may be desirable.
9.3.1 PORTABLE GROUND TESTERS
There are several models of portable ground testers on the market. Most employ either a
hand-cranked magneto or internal battery-powered inverter as a power source and some type
of bridge circuit to simultaneously detect voltage and current and give a readout in ohms
when the instrument is balanced. The most commonly used instruments of this type, the
Megger hand-cranked and battery-powered units, give a 3 digit readout in ohms via the three
decade dials used to null the instrument galvanometer. A range selector switch is used to
select a full scale reading of 9.99, 99.9, 999, or 9990 ohms. The hand-cranked version of
the Megger instrument, by generating a variable frequency ac signal, is somewhat less
sensitive to stray ground currents than the battery-powered models. As with all instruments
of these types, the resolution becomes very poor as the measured apparent impedance drops
to 1 ohm and below. In spite of some manufacturer's claims to the contrary, measurements
9-10
below 1 ohm with most portable instruments should be considered as approximate at best.
All instruments of this type can be used to carry out measurements by any one of the three
methods described in Section 9.2.
9.3.2 VOLTMETER/AMMETER METHOD
Measuring instruments employing a null-balance bridge have offered an advantage of drawing
no current through the voltage sensing leads in the balanced condition. However, the availability
of inexpensive, high impedance (greater than 1 megohm) direct reading digital voltmeters
has made the voltmeter/ammeter technique very practical for ground resistance measurements.
The main advantage this method offers over the use of portable ground testers is in the
increased current that can be passed between the two current probes. The disadvantage is
in the considerably increased cost, complexity and bulk of the measurement apparatus. A
typical voltmeter/ammeter test set-up for measuring earth resistance is shown in Figure 9.6.
The interface unit shown in Figure 9.6 contains a variable transformer as well as step-up
and step-down transformers for accomodating a wide range of loop impedances. Such equipment
is usually constructed by the user or purchased as a custom assembly to meet specific testing
requirements. The primary disadvantage of this arrangement is the inability to distinguish
between ambient power frequency signals and the test signal. The set-up is only suitable
when the voltages induced in the earth by the test current significantly exceed the stray
voltage levels. This may not always be possible, particularily with ground impedances in the
range of 0.5 ohms or less.
DIGITAL
VOLTMETER
AC POWER
SOURCE.
RETURN
- CURRENT
ELECTRODE
POTENTIAL
PROBE
INTERFACE
UNIT
ADJUSTABLE
AUTO TRANSFORMER
ISOLATING
TRANSFORMER
Figure 9.6
AMMETER
ELECTRODE
TO BE
MEASURED
Voltmeter/Ammeter Test Set-Up
A significant improvement in the usefulness of the circuit of Figure 9.6 can be obtained if
the frequency of the power source used can be adjusted to 5 Hz or more away from the
frequency of the ambient interference and a selective frequency voltmeter substituted for
the wide bandwidth digital meter shown. A meter such as the Hewlett Packard 3581C is
capable of resolving a 3 Hz bandwidth signal with excellent rejection of out-of-band signals.
Thus, test signal voltages well below the level of ambient interference can readily be
measured with an accuracy of typically 1%. A 60 Hz rejection filter can be used at the
voltmeter input if required [7].
9-11
A further refinement to the test configuration is introduced by the use of a variable frequency
power oscillator in order to measure the ground impedance over a wide range of frequencies.
This permits identification of the resistive and reactive components of ground impedance
and can be of considerable value when measuring transmission line structure grounds which
are connected to a continuous overhead ground wire. By increasing the frequency to a
sufficiently high value, usually 20 kHz or higher, it may be possible to observe only the
impedance of the ground to which the current lead is attached. Considerable care must be
taken when taking high frequency measurements however, since inductive and capacitive
coupling effects between current and voltage leads may be very significant. Figure 9.7
illustrates a complete test configuration for this type of measurement (see also Figures 10.4
and 10.5 of Chapter 10).
ADJUSTABLE FREQUENCY
POWER SOURCE
frequemcv
SELECTIVE
VOLTMETER
RETURN
JCURRENT
Electrode
POTENTIAL
PROBE
INTERFACE
UNIT
ADJUSTABLE
AUTOTRANSFORMER
ISOLATING
TRANSFORMER
Figure 9.7
WIDE FREQUENCY
BAND AMMETER
ELECTRODE
TO BE
MEASURED
Functional Schematic - High Current Frequency Selective
Ground Resistance Test Set-Up
9.3.3 HIGH FREQUENCY PORTABLE INSTRUMENTS
A portable instrument has been developed [8] specifically for measuring the ground resistance
of transmission line structures equipped with overhead ground conductors but not equipped
with continuous counterpoises. This instrument is fully electronic and generates a 25 kHz
test current from an internal Ni-Cad battery. The resulting structure ground potential rise
is measured by the instrument and an apparent resistance obtained which has eliminated the
effect of the overhead ground wire. Since this method uses the fall-of-potential
technique, the usual considerations of electrode spacing and lead coupling must be observed.
9.3.4 OTHER MEASUREMENT SYSTEMS
In an attempt to simplify the determination of resistance and reactive components of low
impedance grounds, a measurement technique has been developed [5] which utilizes a Fast
Fourrier Transform digital signal analyser and a white noise power source to measure the
impedance and phase angle over a wide frequency range. The technique is basically the same
9-12
as the voltmeter/ammeter technique described previously, except for the signal source and
metering devices. Figure 9.8 shows the general configuration of the instrumentation used in
the measurement procedure. The digital signal analyser is a Hewlett Packard Model 5420.
The primary advantage of this technique over a conventional voltmeter/ammeter technique
is in the ease with which a wide frequency range plot of impedances can be obtained,
eliminating the need to extrapolate measurements taken at a limited number of frequencies
to obtain a 60 Hz value. The main disadvantage is in the relatively high cost and complexity
of the measurement apparatus.
REMOTE
POTENTIAL PROBE
DUAL
CHANHEL
FFT
DIGITAL
SIGNAL ANALYZER
GROUNDING
Figure 9.8
General Instrumentation Arrangement for the Measurement
of Ground Impedances Using a FFT Digital Analyser
A portable instrument has been developed [6,15] for measurement of the resistive and reactive
components of ground impedances using a phase sensitive detector. The unit is described in
[6] and offers excellent immunity to high levels of ambient power frequency interference,
even when measuring ground resistances in the order of 0.1 to 0.2 ohms. Two versions of
the instrument are being offered: The DET1, a unit similar to the one described in the
reference paper and the DET2, a less sophisticated instrument, capable only of resistance
measurements.
For transmission line structure measurement, the DET2 instrument is more than adequate.
In some recent tests [16] carried out on 300 kV transmission line structures the DET2
instrument performed very well, measuring resistances as low as 1.5 ohms and as high as
200 ohms with excellent stability and resolution. A conventional Megger null balance instrument
was used to carry out duplicate measurement in several cases and yielded nearly identical
results for structure resistances above 20 ohms. For low structure resistances, in particular
measurements on structures to which an overhead ground wire was attached, it was not
possible to obtain a satisfactory reading with the null balance instrument due to high levels
of ambient interference. An additional advantage of the digital instrument was in the reduced
measurement time, being about 10% of the average time required to obtain a reading on
the null balance instrument.
9.4 MEASUREMENT TECHNIQUES
As with most field measurement requirements, ground resistance testing is subject to numerous
possibilities for the introduction of errors, detected or undetected, in the measurement
process. The development of a sufficient understanding of the measurement process, combined
with a carefully developed measurement technique is essential if reliable results are to be
obtained. Some of the most common sources of errors in fall-of-potential measurements are:
9-13
•
Inadequate separation of the unknown and auxiliary current electrodes.
m
Operation of instrumentation at inadequate sensitivity levels.
•
Location of auxiliary current electrodes or potential probes in the vicinity of buried
metallic structures.
•
Inductive coupling between voltage and current leads.
•
Excessively high current probe resistance which can lead to parasitic capacitance
and resistance errors [6].
•
Incorrect interpretation of fall-of-potential data.
•
Uncalibrated instrumentation.
As has been stressed previously, the susceptibility of a resistance measurement to errors
generally increases as the measured resistance decreases, particularly below one ohm. It
is recommended, however, that similar procedures be followed for all measurements and, as
experience is gained, short cuts or simplifications can be made where it is known that the
accuracy of the results will not be significantly affected.
Good preparation is essential to the accomplishment of a successful field measurement
program. A standard check list of items required is very helpful to ensure that no unpleasant
surprises occur at the test site. A typical list for a field measurement using the
voltmeter/ammeter technique is shown in Table 9.1. Prior to the commencement of
measurements, all available "as built" drawings relating to underground services should be
obtained in order to check for the location of buried pipes, counterpoise, cables, ducts or
other structures which could affect the resistance measurements. Proposed remote current
probe and potential traverse locations should be marked on the site plans to assure their
suitability.
ITEM
1
2
3
4
5
6
7
8
9
10
1
12
13
14
15
16
17
18
19
20
Note “
Table 9.1
DESCRIPTION
QUANTITY
PORTABLE TESTER
A.C. GENERATOR
TEST LEAD SPOOLS
THREE FOOT GROUND RODS
FOUR POUND HAMMERS
VICE GRIPS
TWO-WAY RADIOS
'-■HIGH CURRENT INTERFACE UNIT
*BATTERY POWERED FREQUENCY SELECTIVE VOLTMETER
*BATTERY POWERED DIGITAL VOLTMETERS
TEST LEADS FOR METERS
DATA SHEETS
FIBERGLASS SURVEY TAPES
BEARING COMPASS
SMALL TOOL KIT
RULER AND DIVIDERS
SITE PLANS
PROGRAMMABLE CALCULATOR
GRAPH PAD
CAMERA AMD FILMS
1
1
4
5
2
2
1
1
1
2
As required
As required
2
1
As required
As required
As required
t
1
As required
In the absence of high ambient noise levels, these units
may be replaced by portable ground testers such as Meggers
or the like.
Resistance Measurement Equipment Check List
9-14
Once a remote current probe location has been established, the resistance of the current
loop should be checked by a simple two terminal resistance measurement. There is no unique
loop resistance value above which the test configuration should be rejected, although loop
resistances in excess of 1,000 ohms are generaly quite difficult to work with. When the
voltmeter/ammeter method is being used with test currents in excess of 1 ampere, safety
and power source considerations will dictate that loop resistances not exceed one or two
hundred ohms. Values below 100 ohms would be preferable. When a suitably low auxiliary
electrode resistance is not attainable with a single ground rod, an array of ground rods can
be used. To be effective, the rods should be located at least 4.5 to 6 m (15 to 20 feet)
apart and driven as deeply as possible. Obviously, low lying areas with noticeable ground
water are ideal for locating a remote electrode and should be used where possible.
As mentioned in Section 9.2.4, mutual coupling between voltage and current leads may
introduce significant errors into measurements of low impedance ground electrodes. Table
9.2 shows the approximate amount of mutual impedance between two parallel conductors
laid on top of the soil for various soil resistivities, spacings and lengths of parallel exposure.
This table does not account for possible coupling between additional lengths of wire on reels,
a factor which can be very significant if adequate care is not exercised in the placement
of the current and voltage spools. If the expected value of resistance to be measured is in
the order of the mutual impedance given in Table 9.2, the potential measuring apparatus
should be located completely separate from the current source and, if possible, the potential
profile should be taken at right angles to the direction of the auxiliary current electrode.
It is worthwhile to note that
measurements using a reversing dc power source and a
synchronous detector
are not affected by mutual impedances between current and
voltage leads. In any case, transmission line structure resistance measurements are unlikely
to be significantly affected by mutual impedances between the test leads.
Leakage resistance and stray capacitance between test leads and ground are other effects
that can influence the results of low value ground impedance measurements [6]. These effects
are unlikely to be of significance in most transmission line structure ground measurements
although they could become significant in high frequency measurements of structure grounds
connected to overhead ground wires. In order to minimize these effects, it is essential that
test leads be kept dry, particularly if the leads contain any splices; current and voltage
probe resistances be kept low and the leads be separated as much as possible.
It is essential that the measured values of apparent resistance be plotted as a fall-of-potential
traverse is being conducted. Only in this way can anomalies in the measurement be detected
and accounted for, and an assesment made as to the adequacy of the remote current electrode
location. It is usually useful to take readings at relatively large potential probe intervals
initially and then to take intermediate readings where an apparent knee or "flat spot" in
the curve has been observed.
A primary requirement of the measurements is to determine whether or not the remote
current electrode has been located outsi de the zone of influence of the electrode being
tested. For small grounding systems, locating the return current electrode at a distance of
at least 10 times the largest dimension of the grounding system will usually assure this.
When this distance is unpractical, the remoteness of the current electrode must be determined
by verifying that a potential traverse in the direction of the current electrode produces a
distinct zone of nearly constant readings near the midpoint between the two electrodes.
Alternatively, a traverse in a direction opposite or at right angles to the direction of the
current electrode (C2) should produce constant apparent resistivity readings within the distance
at which C2 has been located. As a further test, if C2 is relocated somewhat beyond the
original location, the constant apparent resistivity values should be unchanged.
9-15
SOIL RESISTIVITY
(OHM-METERS)
CONDUCTOR
SEPARATION
(METERS)
Sz|
MUTUAL
IMPEDANCE
AT 60 Hz
OHMS/KM
0HMS/M1LE
i
1
i
100
500
2500
1
100
500
2500
10
10
10
0.311
0.1(0
0.46
100
500
2500
50
50
50
0.22
0.28
0.34
100
500
2500
250
250
250
0.11
0.16
0.22
1
1
0.51
0.57
0.63
“ ~~
Table 9.2
i
i
i
,
1
1
i
1
l
i
i
i
i
l
i
l
i
i
0.82
0.92
1.01
0.55
0.64
0.74
0.35
0.45
0.55
0.17
0.26
0.35
Mutual Impedance Between Two Parallel Conductors
on the Surface of the Earth
When the voltmeter/ammeter technique is used with test currents of a few hundred milliamperes
or more, hazardous voltages may be produced at the auxiliary current electrode and in the
soil immediately surrounding the current electrode. Consequently, considerable caution should
be exercised when tests are carried out under these circumstances. Two-way radios should
be used to maintain communication between the person working at the remote end of the
traverse and the operator of the power source. A "dead-man" switch should always be used
to energize the test apparatus so that there is no possibility of accidentally leaving the C2
electrode energized.
Measuring tapes used in resistance testing should always be nonmetallic for two reasons.
Firstly, the presence of a long metallic path along the line of the traverse could affect
potential readings. Secondly, a metal tape could transfer hazardous potentials from the
vicinity of the auxiliary current electrode to a person remote from the electrode.
Finally, the issue of instrument calibration must always be addressed. The environmental
extremes often encountered in field work may affect instrumentation accuracy. Direct sunlight
on a hot summer day or temperatures below 0 °C can easily submit test instruments to
temperatures outside their operational limits. It is a good practice to carry calibrated
resistances of 1 and 10 ohms that can be inserted in series with the Cl lead on the electrode
being measured. If the PI lead is placed above the shunt, the apparent resistance should
increase by exactly the value of shunt, provided that contact resistances between the current
lead and the ground electrode being tested are sufficiently low. This calibration procedure
is illustrated in Figure 9.9.
9.5 EARTH RESISTIVITY TESTS
The object of earth resistivity tests related to grounding system design is to assist in the
determination of an appropriate soil model which can be used to predict the effect of
the underlying soil characteristics on the performance of the grounding system during ground
faults.
9-16
An accurate determination of earth resistivity characteristics from test results can be a
complex task. Measurement results are often subject to different interpretation because
of the characteristically complex variations in earth composition and because surface electrical
test methods are remote from the structures influencing the test results.
CALIBRATED
SHUNT
UNKNOWN
RESISTANCE
TO BE
MEASURED
= (R +R)
NOTE
Figure 9.9
RETURN
CURRENT
ELECTRODE
This cheak does not identify measurement errors
due to mutual coupling between voltage and
current leads.
Field Calibration Check of Ground Resistance Measuring Equipment
Usually, the electrical characteristics of the earth are sufficiently uniform over horizontal
distances to permit the consideration of the soil beneath typical industrial sites or transmission
line structures to be uniform over horizontal dimensions. Similarly, vertical variations in
resistivity can often be described by one, or more frequently, two distinct layers of earth.
In the two layer case, the interface between the two layers of earth is often found within
a few meters of the surface. Although a two layer earth structure model can be a major
simplification of the real situation, it has been shown [11,12] to be an excellent representation
of complex earth structures for electrical grounding calculations.
In carrying out resistivity measurements for the design of transmission line structure grounds,
it should be kept in mind that the dimensions of structure grounds are generally small and,
as such, will not be influenced to a great degree by very deep soil resistivities. This should
be considered when resistivity tests are planned and measurement results interpreted [11].
Resistivity determination methods and the theory behind the most commonly used methods
are discussed in detail in Chapter 4. In this chapter only galvanic resistivity measurement
methods such as the Wenner array method or driven ground rod method will be discussed.
9.5.1 THE FOUR POINT METHOD
The most widely used measurement configuration is a four-probe method developed by Dr.
F. Wenner of the U. S. Bureau of Standards [13]. As shown in Figure 9.10(a), four uniformly
spaced earth probes are inserted into the earth surface in a straight line. The outer pair of
probes are used as current input probes and the inner pair as potential references. Using
the Wenner geometry, the apparent measured resistivity is:
4713 R
P
1 +
2a
'
(9-12)
2a
----
/a2 + 4b2
/4a2 + 4b2
9-17
where
P = apparent soil resistivity in ohm-meters.
R = ratio of measured voltage to test current in ohms,
a = uniform probe spacing, in meters,
b = uniform probe penetration depth, in meters.
Considering probe penetration depth to be a constant, Equation 9-12 effectively describes
the variation in measured resistivity as a funtion of probe separation, a. Physically, the
greater the probe spacing, the greater the volume of earth encompassed by the test current
in its traverse from Cl to C2 and hence, the greater depth of earth involved in the
measurement. The task of accurately relating the apparent resistivity measured by this
procedure and the true resistivity at specific depths is complex but to a first approximation,
the apparent resistivity which is measured at probe spacing a may be considered indicative
of the average resistivity to a depth a.
For probe spacings where a»b, the above formula can be simplified by neglecting b. The
relationship then becomes:
p = 2TraR
3)
For probe spacings of approximately 10 times the electrode depth, the error introduced
by the simplified formula is less than 1%. For a probe spacing equal to the electrode depth,
the apparent resistance value obtained from the 'simplified formula is 40% lower than the
correct result. Thus, probe depth must be accounted for if the measurement is made for
short spacings.
If the measured values of apparent resistivity vary significantly with probe spacing, a
nonuniform soil structure is indicated. The development of an appropriate two-layer soil
model from measured resistivity data is discussed in detail in Chapter 4. The computer
program RESIST has been developed for this purpose.
An important variation of the four probe method is the unequally spaced or Schlumberger-Palmer
arrangement shown in Figure 9.10(b). This method overcomes a shortcoming of the Wenner
method often encountered at large probe spacings where the magnitude of the potential
between the potential probes is too small to give reliable measurements. By moving the
potential leads closer to the outer current electrodes, the potential value is increased and
the sensitivity limitations encountered using the Wenner method may be overcome. For large
probe spacings, the apparent resistivity according to the Schlumberger-Palmer method is
given as:
p = TTRc(c+d)/d
(S-'lk)
where
c = Spacing between voltage and current probes,
d = Spacing between inner voltage probes.
R = Measured apparent resistance.
9.5.2 DRIVEN GROUND ROD METHOD
The driven ground rod method [9,14] may, in some cases, be preferred to the Wenner method
because of the type of ground electrode to be installed. If the electrode resistance is heavily
dependent on the resistance of an array of ground rods, then this method may be considered
to be most representative of the actual design situation. It has been shown, however, that
the driven ground rod method produces results that are consistent with the Wenner method
9-18
only in reasonably uniform soils [14]. In nonuniform soils, the appropriate interpretation of
the driven ground rod method results may become an exceedingly complex task.
FOUR TERMINAL
TEST
SET
O
Q
D.lL
CURRENT
PROBE
POTENTIAL
PROBES
(a)
Figure 9.10
CURRENT
PROBE
c, it—la
s'
X
/
CURRENT
PROBE
POTENTIAL
PROBES
(b)
WENNER
C2
CURRENT
PROBE
SCHLUMBERGER
Four Point Method of Earth Resistivity Measurement
In using the driven ground rod method, the fall-of-potential method is applied to measure
the resistance of a single driven rod. The apparent resistivity is then determined from
the relation:
2'irLR
(9-15)
P
l1 n —j—
8L
i1
d
where
= Apparent soil resistivity to depth L (ohm-meters).
L = Length of driven rod in contact with earth (meters),
d = Diameter of rod (meters).
R = Measured value of resistance (ohms).
p
Because of the shallow penetration that can be achieved in practical situations, the very
localized measurement area and the inaccuracies encountered in two layer soil conditions
[14], the driven ground rod method is only normally suitable for use in limited circumstances
such as small transmission line structure grounds. In areas of difficult terrain, the driven
ground rod method may be the only practical means of determining soil resistivity.
9.5.3 RESISTIVITY MEASUREMENT INSTRUMENTATION
In order to carry out resistivity measurements by the Wenner or similar methods, it is
necessary to provide a source of test current and a means of measuring the voltage between
the voltage sensing probes in the test electrode array, or a means of determining the ratio
of this voltage to the test current.
Numerous instrumentation packages have been developed to carry out either of the above
determinations. These packages vary considerably in portability, sensitivity, operating
convenience and cost. According to a recent survey [2] of electrial utilities throughout the
9-19
world, the Megger null-balance and direct-ohm reading type instruments are by far the most
widely used instruments for measuring earth resistivity. These instruments are both very
well suited for field work, being small in size and weight and relatively easy to operate.
The test current supplied by these and most portable instruments is relatively small however,
typically in the order of 40 milliamperes. In areas of high ambient noise, very high or very
low resistivity, and particularly at large probe spacings, sensitivity can be a problem and
these instruments may not be suitable if accurate measurements are required.
In order to overcome the sensitivity limitations of portable instrumentation, a direct
measurement technique using a voltmeter, ammeter and an ac current source, rated at
several hundred watts or more can be used. In order to avoid interference problems with
ambient 60 Hz fields or ground currents, it is usually necessary to use a power source which
operates 5 Hz or more away from 60 Hz, and to use a frequency selective voltmeter to
measure the voltage between the voltage sensing points. The power source for such
measurements may be a portable ac generator which has been adjusted to a suitable frequency
and transformed to an appropriate source voltage.
It is somewhat more convenient to use a variable frequency power oscillator, although this
adds considerably to the cost and source power requirements of the system because of the
low efficiency of the power amplifier. As well, there is normally no interest in carrying out
resistivity measurements over a range of frequencies. Thus, the ease of frequency adjustment
is of less value than in ground electrode impedance measurements where the full capabilities
of the power oscillator can be utilized.
The DET2 digital earth tester described in Section 9.3.4 is very convenient in carrying out
resistivity measurements because of the speed with which readings can be obtained and the
excellent resolution of the instrument at low apparent resistance readings. The primary
limitation of the unit is in the maximum current probe resistance which cannot exceed 7300
ohms for both electrodes in series. This can present considerable difficulties if the surface
resistivity is greater than 2000 to 2500 ohm-meters.
9.5.4 MEASUREMENT TECHNIQUES
The measurement of earth resistivity using any of the instrumentation systems described
previously is a relatively straightforward procedure. Obvious examples of good measurement
practice such as ensuring good probe to soil contact, avoiding traverses adjacent to or across
large buried metallic structures and maximum separation of current and voltage leads should
always be observed.
As probe spacing increases, the susceptibility of the measurements to errors increases.
Portable instruments of the Megger category with range scales should always be operated
at the maximum available sensitivity setting, and should not be relied on when the most
significant digit is down to zero, ie. with two digit accuracy. When using Megger type
instruments, it can be helpful to insert a milliammeter in series with the current leads, to
monitor the applied test current. A drop in test current to 10% or less with the hand-cranked
type of instrument can often indicate a poor current probe contact and a possibly suspect
reading. If a low test current is observed, the probes should be checked and driven
deeper or moistened in order to improve the probe contact resistance. At very close probe
spacings however, the probe should be kept as short as possible and the soil left undisturbed
if representative readings are to be obtained. Instrument sensitivity is less of a problem at
close probe spacings however, so that low test currents may produce satisfactory results.
9-20
One of the most common faults in resistivity measurements is a failure to take measurements
out to sufficiently large probe spacings. As a minimum, the total traverse should cover the
dimensions of the grounding electrode under consideration. Ideally, the maximum probe spacing
should exceed the dimensions of the electrode under consideration by extending the traverse
to three times the electrode dimensions.
At very large probe spacings, coupling between voltage and current leads and interference
in the voltage sensing leads can introduce measurement errors. Voltage and current leads
should be separated as much as possible and probe resistances kept as low as possible. Mutual
coupling between voltage and current leads will not normally be a problem if the apparent
resistance is greater than 0.5 ohms. Below this, caution must be exercised.
A source of coupling between voltage and current leads that is often overlooked is the close
proximity of test lead spools. Significant coupling can result when two spools are located
close to each other with their centers on a common axis. The spools should always be
separated as much as possible and oriented with the spool axes at right angles.
The reliability of field measurements can be improved considerably if the apparent resistivity
for each probe spacing is calculated and plotted as the measurements are being taken. In
this way, discontinuities in the measurements can be observed immediately and the source
of the discontinuity identified. Buried pipes, tanks, recently excavated and filled areas, and
rock outcroppings are all examples of sources of discontinuities in resistivity data. Such
anomalies should be identified and logged and a determination made as to whether or not
the disturbance is entirely localized and can be ignored or should be taken into account in
the developement of an appropriate soil model.
An orthogonal traverse should always be taken to check the results of any resistivity traverse.
If the same traverse center is used the results of the two traverses should track fairly
closely. Large differences, of say 30% or more, between apparent resistivity values at the
same probe spacing could indicate a measurement anomaly. Plotting both traverses on the
same graph is extremely helpful in locating these.
A standard data sheet should be prepared and used for all resistivity measurement data
recording. The sheet should contain spaces to record details of the test site, test equiment,
and weather conditions as well as all of the measurement data. It is also very advisable to
accurately locate the traverse location on a detailed site plan at the time the measurements
are made. Photographs can also be very helpful. The objective of data recording should
be to ensure that a third party not having participated in the measurements, can carry out
a detailed and accurate interpretation of the measurement results.
9.6 SAFETY PRECAUTIONS
It should be strongly impressed on all test personnel that a lethal potential can exist between
a station or transmission structure ground if a power system fault involving the grounding
system under test occurs while the ground tests are being made.
Since one of the objectives of tests on a grounding system is to establish the location of
remote ground for both current and potential electrodes, the leads to these electrodes must
be treated as though a potential could exist between test leads and any point on a station
ground grid or transmission line structure ground. It is also possible that long test leads run
parallel to a transmission line could become energized by mutual impedance coupling between
a faulted phase conductor and the test leads. The magnitude of potentials transferred by
test leads during power system fault conditions can be considerable, particularly in the case
of a faulted transmission line structure where ground potential rises in excess of 10 kV
would not be uncommon.
9-21
Obviously, the preceding discussion points to the necessity of caution when handling the test
leads, and under no circumstances should the two hands or other parts of the body be allowed
to complete the circuit between points of possible high potential difference. It is true that
the chances are extremely remote that a fault will occur while test leads are being handled,
but this possibility should not be discounted. Therefore, the use of insulating shoes, gloves,
blankets and other protection devices are advised whenever measurements are carried out
at an energized power station or transmission line.
In all cases, safety procedures and practices adopted by the particular organization involved
should be followed.
REFERENCES
1 - IEEE Recommended Guide for Measuring Ground Resistance and Potential Gradients in
the Earth. IEEE Standard 81-1962.
2 - M. Bouchard, F. Dawalibi, D. Mukhedkar, "Survey on Ground Resistance and Earth
Resistivity Measurements". IEEE transactions on PAS, Vol. PAS-96, July/August 1977, pp.
1076 (Paper A 77 204-1).
3 - F. Dawalibi, D. Mukhedkar, "Resistance Measurement of Large Grounding Systems". IEEE
Transactions on PAS, Vol, PAS-98, November/December 1979, pp. 2348-2354.
4 - F. Dawalibi, D. Mukhedkar, "Ground Electrode Resistance Measurements
Nonuniform Soils". IEEE Transactions on PAS, Vol. PAS-93, January 1974, pp. 109-115.
in
5 - I. D. Lu, R. M. Shier, "Application of a Digital Signal Analyzer to the Measurement of
Power System Ground Impedances". IEEE Transactions on PAS, Vol. PAS-100, April 1981, pp.
1918-1922.
6 - P. H. Reynolds, D. S. Ironside, A. H. Silcocks, J. B. Williams, "A New Instrument for
Measuring Ground Impedances", IEEE PES, Paper A79 080-3, IEEE PES Winter Meeting, New
York, 1979.
7 - F. P. Zupa, J. F. Laidig, "A Practical Ground Potential Rise Technique for Power
Stations". IEEE Transactions on PAS, Vol. PAS-99, January/February 1980, pp. 207-216.
8 - J. Ufermann, K. Jahn, "High Frequency Earth Resistance Measuring Instrument". Brown
and Boveri Journal No. 3/67, pp. 132-135.
9 - IEEE Standard No. 81, "Recommended Guide for Measuring Earth Resistivity Ground
Impedance and Earth Surface Potentials of a Grounding System". New Edition, to be published
in 1982.
9-22
10- E. B. Curdts, "Some of the Fundamental Aspects of Ground Resistance Measurements"
AIEE Transactions on PAS, Vol. 77, part I, 1958, p. 760.
11- F. Dawalibi, D. Mukhedkar, "Influence of Ground Rods on Grounding Grids", IEEE
Transactions on PAS, Vol. PAS-98, November/December 1979, pp. 2089-2098.
12- G. F. Tagg, "Earth Resistances". George Newnes Ltd., London, 1964.
13- F. Wenner, "A Method of Measuring Resistivity", National Bureau of Standards, Scientific
paper 12, No. S-258, 1916, p. 499.
14- C. J. Blattner, "Study of Driven Ground Rods and Four Point Soil Resistivity Tests",
IEEE Transactions, Vol. PAS-101, No. 8, August 1982, pp. 2837-2850.
15- D, S. Ironside, "Some Recent Developments in Portable Ground Resistance Test Instruments",
paper presented at the High-Voltage Power System Grounding Workshop Sponsored by EPRI,
May 12-14, 1982, Atlanta, Georgia.
16- I. Simpson, "Alcan Smelters and Chemicals Kitimat Works Grounding Study", David Bensted
and Associates Ltd., Final report, June 1982.
9-23
COMPARISON BETWEEN
MEASUREMENTS AND COMPUTATIONS
10.1
GENERAL
Excellent agreement has been obtained between experimental results measured using
power system grounding models and calculated results based on recently developed analytical
equations. [1,2,3]. Good agreement has also been obtained between the computed surge
response of transmission line towers and the measured values on experimental scale models
of transmission line structures [4,5,6].
There is however, little published information giving comparisons between calculated and
measured results of tests carried out on actual transmission line installations. One reason
for this is the difficulty in obtaining accurate soil resistivity information at a particular
site, since this often involves a determination of resistivity variations with depth as well as
over lateral distances. In addition, tests involving high frequency or impulse currents are
difficult to implement and require careful interpretation.
Despite the above difficulties, successful measurement programs for both power and surge
frequencies have been reported in the literature [7,8,9,10]. The key to successful completion
of such tests is in the careful planning of the test program and in the selection of the most
suitable test equipment.
In this chapter, two of these test programs will be described in detail. These test programs
are:
®
The Ontario-Hydro/American Electric Power (OH-AEP) 500 kV 765 kV transmission
line tests [7].
•
The Electricit§ de France (EDF) rocket-triggered lightning test program at St.
Privat d'Allier [9,10].
The main subject of this chapter however, consists of two recently completed measurement
programs conducted within the scope of this EPRI project. These tests will be described in
detail and the measurements will be compared with the analytical results obtained from the
computer programs developed under this EPRI project. These measurement programs are:
•
The Rochester Gas and Electric Corporation (RGE) 115 kV H-frame wood pole
transmission line tests.•
•
The Tennessee Valley Authority (TVA) 500 kV transmission line staged-fault tests.
10-1
There are several objectives in describing these tests. One is a validation of the analytical
derivations (and therefore, the corresponding computer programs) presented in this report.
It is believed however, that this goal has been reached in the excellent agreement obtained
between scale models and analytical models [2,3]. The next objective is to show that a
"practical" agreement can also be obtained when the predictions are compared with actual
installation results where the variables are not all rigidly controllable and/or arbitrarily
selectable.
Included in this chapter is a detailed description of the test activities, test equipment,
measurement problems, and solutions. The
preparation of the test data for the various
computer programs and the interpretation of the computed results is also described. Hence,
when used in conjunction with the previous Chapter 9 on field measurements, this chapter
should serve as a guide to the successful
implementation of transmission line grounding
measurements and subsequent test data interpretation.
10.2 THE RGE 115 kV TRANSMISSION LINE MEASUREMENTS
A section of a Rochester Gas and Electric 115 kV transmission line near Fillmore, New
York, on Route 19A was selected as a site to carry out a series of measurements on H-frame
wood poles which are representative of a large portion of the 115-230 kV transmission lines
in existence in North America.
One objective of the measurements was to observe and describe the conditions which are
likely to exist during routine field tests on energized transmission line poles and further, to
interpret and discuss the field results with respect to the calculations carried out using the
computer programs RESIST and GTOWER (see Appendices B and C).
The measurements involved earth resistivity tests and fall-of-potential impedance/resistance
measurements on the pole grounding electrodes. The ground impedance measurements were
carried out with and without the double overhead ground wires connected to the pole ground
being measured.
10.2.1 TEST SITE
The site of the measurements, near Fillmore
New York, was an area of relatively flat
terrain. The transmission line was located on an old railway right of way. The elevated road
bed was readily identifiable, although it was heavily overgrown with blackberry bushes. A
footpath down the center of the right of way provided the only access to some of the
transmission line structures. The surface soil layer of the elevated roadbed consisted of a
cinder or coke material. This was the only place in the area where this material was found
and was assumed to have been used as fill for the railroad bed.
The area on each side of the right of way was farmland. Route 19A ran parallel with the
transmission line, approximately 35 m (115 ft) west. The site of the remote current electrode,
300 m (984 ft) north of structure 161, was at the side of a small pond (see Figure 10.1).
The soil at that location was a very heavy wet clay.
The area between the transmission line right of way and Route 19A where three of the
resistivity traverses were taken, is a RGE pole yard. It was apparent that some minor
excavation had taken place at some time which involved filling in the ditch alongside the
former railway line and cutting into the elevated roadbed. Poles A and B of transmission
line structure 161 were located on the edge of the pole yard where the roadbed appeared
to have been cut away.
10-2
Route 19 A
Pole Yard
115 kV
H-Frame Wood
Route 19 A
RaiIway
Structure
No.------------
Figure
10.1
(a)
Rochester Gas aid Electric Test Site
3-POLE STRUCTURE (str.163)
Figure 10.2
115
(b) 2-POLE STRUCTURE
kV Wood Structures
10-3
(str.
I6l)
Two types of structures were investigated. Structure 163 was a 3-pole structure with a steel
guy wire and anchor connected to the overhead ground wire (Figure 10.2(a)). Structures 159,
160, 161 and 162 were H-frame (2 pole) structures as shown in Figure 10.2(b). In all
cases except structure 163, the test lead was connected to a bared portion of the copper
wire which ran up the pole from the ground rod buried adjacent to the pole, to the overhead
ground wire (see Figure 10.3(a)). In the case of structure 163, this connection was made to
the guy wire (Figure 10.3(b)) which was connected to the overhead ground wires via a cable,
presumably under considerable tension, across the top of the two outer poles (see Figure
10.2(a)).
(a) TEST LEADS CONNECTED TO VERTICAL
GROUND VI RE
Figure 10.3
(b) TEST LEADS CONNECTED TO GUY WIRE
Current (Cl) and Potential (PI) Test Lead Connections
At the time the measurements were taken, the soil surface was very wet from heavy rains
of the previous day.
10-4
10.2.2 TEST EQUIPMENT
Two types of instrumentation were used in the measurements carried out at the RGE test
site:
•
A hand-cranked Megger (null balance instrument model ET3) was used to carry
out the earth resistivity measurements and resistance measurements on one of
the structures (structure 161) with the connection to the overhead ground wires
open-circuited.
®
A voltmeter/ammeter test system consisting of a California Instruments model
501T power source, a Hewlett-Packard 3581C frequency-selective voltmeter and
a Fluke model 8050A digital multimeter, was used to measure the ground impedances
with the overhead ground wires attached and the ground resistances of several
transmission line poles when the pole grounds were isolated from the overhead
ground wires. These instruments, shown in Figure 10.4, were also used to measure
the ground impedances for various frequencies up to a value of 5000 Hz. The
test power source was a porTable 2.5 kW generator which powered the 501T
variable frequency power unit. The 501T provided the test current via an interface
unit designed to provide test voltage control, circuit isolation and a convenient
interface with the voltage and current measuring apparatus. A functional schematic
of the test setup is shown in Figure 10.5.
Figure 10.4
Test
Equipment
The wire used for the current and voltage test leads was No. 16 AWG type TEW. Four 1000
foot spools of wire were used in these tests. The portable wire reels used were specially
designed to ease the frequent winding and unwinding operations necessary during the
measurements.
10-5
Portab le
Generator
Selective
Vo 1tmete r
Return
Current
E ?ect rode
Potential
Probe
Variable
Frequency
Generator
Interface Unit
Figure 10.5
Elect rode
to be
'Measured
Functional Schematic of the Test Set Up
10.2.3 EARTH RESISTIVITY TESTS
A total of four resistivity traverses were carried out at the location shown in Figure 10.6.
The measurement results are given in Appendix F, Tables F-l to F-4, and are also
plotted in Figures 10.7 to 10.11. The selection of a good location to carry out a traverse
was restricted considerably by the heavy undergrowth beneath the transmission line. One
traverse (RGE 04) was carried out directly underneath the line between structures 160 and
161 where a footpath existed. It was not possible to carry out an orthogonal traverse at
this location. Three other traverses were carried out in the pole yard. Two of these traverses
(RGE 01-1 and RGE 03) gave inconsistent and erratic readings as probe spacings increased
beyond 3 meters. The apparent resistivity values obtained in the two questionable traverses
dropped very rapidly beyond the 3 m probe spacing. It was suggested by the RGE personnel
present at the test site that the fill used when the pole yard was built could have contained
discarded scrap metal. This would explain the results obtained.
Traverses RGE 01-1 and RGE 01-2 were centered approximately 70 m (230 ft) north and 20
m (67 ft) west of structure 161. The first traverse, taken parallel to the transmission line,
gave reasonable results for probe spacings of 0.5, 1 and 2 m but showed a sharp drop in
apparent resistivity at spacings of 3 and 5 m. The results of the orthogonal traverse (RGE
01-2) were very similar to those of the first traverse at spacings of 2 m or less but, showed
slightly increasing resistivity values at the probe spacings up to 10 m, rather than the sharp
drop in apparent resistivity observed in the first traverse. It was concluded that buried metal
structures extending along the orthogonal traverse line were responsible for the sharp decrease
in the apparent resistivity of traverse RGE 01-1. Other effects, such as interference from
the transmission line, could not possibly account for such large measurement differences.
Traverse RGE 04-4 was located immediately underneath the transmission line and was centered
between structures 160 and 161. A footpath along the right of way facilitated the measurements
in this location. The results of this traverse differed from those of the previous pole yard
traverse by a factor of approximately 1 to 2 for short spacings (except for a spacing of 0.5
m). This difference is attributed to the different surface covering described earlier and to
the fact that the entire traverse was along an elevated path approximately 1.5 m above the
level of the surrounding terrain. The values measured at close probe spacings indicate that
the fill material constituting the elevated path has a low resistivity value. The apparent
resistivity values approached the results of traverse RGE 02-1 as the probe spacing increased.
10-6
Return
Current Electrode
Fa t1-of-Poten tia
Profiles
T rave rse
Traverse 03
01 ,2
I ravers'
Traverse
W? re
Ok
Route 19 A
Route 19 A
Pole A
Structure
Figure 10.6
St ructure
St ructure
St ructure
St ructu re"
Rochester Gas & Electric Measurement Site 115 kV Transmission Line
10.2.4 ANALYSIS OF THE RESISTIVITY TESTS
The preceding qualitative analysis of the field results can not provide all the necessary
information required to develop a suitable equivalent soil model for grounding studies.
Computer program RESIST (Appendix B) was used to determine the equivalent soil models
related to each resistivity traverse. Other methods described in Chapter 4 could be used
also. In particular, the graphical chart provided in Volume 2 of this report will lead to
similar results and is very convenient for a quick estimate or in the absence of computer
facilities.
RESIST determines a two-layer soil which is defined by three parameters; top-layer resistivity
Pi, top layer thickness h and bottom layer resistivity P2. These are later used as input
data to grounding computer programs such as GTOWER (Appendix C). When the measured
apparent resistivity traverse exhibits a shape which indicates that the soil is too complex
to be modelled by a two-layer structure, the resistivity traverse can be subdivided into
appropriate segments which are then analyzed separately. Each traverse segment is then
identified with a two-layer soil and the final equivalent two-layer soil model is constructed
from engineering considerations, such as the extent and burial depth of the grounding system
at the measurement site. This approach was used to analyze traverse RGE 04 which exhibits
a three-layer earth structure with clearly different resistivity values for each layer.
The analysis of traverses RGE 01-1, RGE 01-2 and RGE 03 using RESIST program was
straightforward since the measured apparent resistivity curves in all three cases indicated
a two-layer earth structure. The equivalent models derived by RESIST are given in Table
10.1. These models lead to an excellent curve match with the field results as shown in
Figures 10.7, 10.8 and 10.9 respectively.
10-7
TRAVERSE
EQUIVALENT SOIL MODEL
h
P2
Pi
(m)
(ft-m)
(n-m)
DESCRIPTION/COMMENTS
RGE 01-1
Parallel to transmission line
207.6
14.4
1.41
0.75
RGE 01-2
Perpendicular to transmission line
209.9
110.3
RGE 01-3
Parallel to transmission line
165.1
38.3
2A
RGE 04
Between structures 160 and 161
(0.5 m spacing ignored)
54.2
149.2
1.5
58.3
337.9
2.8
156.6
30.6
25.9
First section of curve (up to a
RGE 04 (a) spacing of 16 m and 0.5 m spacing
ignored).
Second section of curve (with first
RGE 04 (b) two-layers replaced by an
equivalent sing1e-1ayer)
Table
10.1
Equivalent Two-layer Soils
APPARENT RESISTIVITY (ohm-meters)
Traverse:
rge
01-1
Computed Apparent Res Istivlty
Measured Apparent Resistivity
160
-
PROBE SPACING (meters)
Figure 10.7
Earth Resistivity Traverse RGE 01-1
10-8
2k0 .
Computed Apparent Resistivity
.®~- Measured Apparent Resistivity
Traverse:««
01-2
PROBE SPACING (meters)
Figure 10.8
Earth Resistivity Traverse RGE 01-2
Traverse: RGE
03
Computed Apparent Resistivity
Measured Apparent Resistivity
PROBE SPACING (meters)
Figure 10.9
Earth Resistivity Traverse RGE 03
10-9
Traverse RGE 04 was first analyzed with all the measurement data except for the very
short spacing value of 0.5 m. This spacing was discarded because it reflects the higher
surface layer resistivity of the footpath and therefore, will not influence the resistance
calculations of the pole ground rods. As can be seen from Figure 10.10, the equivalent
two-layer soil determined by RESIST (see Table 10.1) does not match the measurement results
well, except for the short probe-spacing zone of the curve.
A second RESIST run was carried out using the data from traverse RGE 04 but without the
20 and 30 m probe spacing values. The equivalent soil model computed by RESIST is given
in Table 10.1. This soil model leads to excellent agreement between the measured and
calculated values for all probe spacings below 20 m (see Figure 10.10). However, it also
suggests a 340 Q -m infinitely deep bottom layer. This of course does not agree with the
data which show decreasing soil resistivity with depth. Hence, the 340 ft-m resistivity layer
must have a finite thickness, and a third layer with a lower resistivity value is indicated.
Traverse:
rge
_ _ _ _ _ _ RGE 0i(
_____ RGE OMa)
Computed Apparent Resistivity
_ _ _ _ _ _ RGE 04(b)
—©---Measured Apparent Resistivity
160 .
PROBE SPACING (meters)
Figure 10.10
Earth
Resistivity Traverse RGE 04
10-10
04
In order to determine this third layer resistivity and the thickness of the 340 fi-m second layer,
a third RESIST run was completed with the 20 and 30 m probe-spacing data and a soil
resistivity value at 1 m spacing, of 150 £2-m. The 1 m, 150 £2-m values represent an equivalent
uniform soil which replaces the original 58.3 fl-m / 337.9 fi-m / 2.8 m two-layer model
determined in the second RESIST run. This equivalent single - layer can be determined
empirically using the partial curve matching technique referred to in Chapter 4. However,
since our final goal is to derive an equivalent two-layer soil from the more exact three-layer
model, engineering judgment and visual interpolation was used to determine the equivalent
single-layer resistivity. One of these considerations was that all previous traverses had an
average apparent resistivity value in the order of 100 to 200 fi-m. The results of this third
RESIST run are summarized in Table 10.1.
Thus, the soil structure at this location can be described by the following parameters:
Top Layer
Resistivity Px
Thickness hj
:
ft-m
2.8 m
53
;
Mid-layer
Resistivity P2
Thickness h£
: 338 Q-m
: 23 m
Bottom Layer
Resistivity P3
:
30 Q-m
Since the pole ground rods are less than 2.5 m long (8 foot ground rods), the bottom layer
resistivity will have little effect on the resistance of the rods. Therefore, it is concluded
that for the purpose of ground rod resistance calculations, the equivalent two-layer soil
to be selected for traverse RGE 04 is the one obtained when the measurements at 20
and 30 m are ignored (RGE 04(a)).
10.2.5 GROUND IMPEDANCE MEASUREMENTS
Impedance measurements were carried out on the grounds of five consecutive transmission
line structures of the Rochester Gas and Electric 115 kV line (structures 159 to 163).
Measurements were taken at all 5 structures with the overhead ground wires solidly connected
to all pole grounds. The vertical wire connecting the local pole ground to the overhead
ground wires was cut at each pole of structure 160 and 161 (see Figure 10.3(a)) and the
pole ground resistances were measured individually.
The return current electrode C2 was located 300 m (984 ft) north of structure 161 (Figure
10.6). Three one meter ground rods were driven into very wet soil at the side of a small
pond and connected via short jumper wires. The resistance of the return electrode was
subsequently estimated from the measurement results to be about 21 ohms (see Appendix F,
Table F-5).
Initially, fall-of-potential measurements were attempted using the Megger instrument. It was
found however that a satisfactory null could not be obtained. The instrument galvanometer
swung randomly from extreme left to right as the instrument was cranked and the selector
dials adjusted to obtain a null. This type of instrument behaviour is normally exhibited when
the level of stray voltage appearing across the voltage terminals of the instrument exceeds
the test signal by a large factor of approximately 25 to 1. Thus for an apparent impedance
of 2 ohms, a stray voltage of 2 volts or more is likely to cause measurement difficulties.
10- 11
Actual experience could vary considerably according to the resistance of the return electrode,
interfering frequency and type of null-balance instrument used.
The above difficulty is quite common when the transmission line is energized and low
impedances are being measured. There are techniques which can be used to overcome this
problem. The selective voltmeter/ammeter technique used at the site is one suitable technique
which also permits frequency sweeps during the impedance measurements. The functional
schematic of the test setup is shown in Figure 10.5.
The results of the fall-of-potential profiles taken to determine the transmission line pole
ground impedances are given in Appendix F (Tables F-5 to F-14).
The first fall-of-potential profile was taken from structure 161 with the Cl and PI electrodes
clamped to the ground conductor at pole A of structure 161. As can be seen from the results
(Table F-5), the potential readings rose very quickly to a stable value, indicating a very
small zone of influence around the local ground rod of pole A. Once the fall-of-potential
profile has been established, the potential probe was relocated at the 240 m location where
apparent impedance readings were taken over a range of frequencies from 50 Hz to 5000
Hz (Table F-7). The impedance increased noticeably with frequency, indicating the presence
of a significant inductive component in the apparent ground impedance. A discrepancy in
the value measured at 1000 Hz for current levels of 1.0 and 2.0 amperes was attributed to
overloading and distortion of the power amplifier output at the higher current value.
Without relocating either of the remote probes, C2 or P2, the Cl and PI electrodes were
located on the ground at poles 160 B and 159 B. It was assumed at this point that nearly
identical readings would have been obtained if the other pole ground (for a given structure)
was used as the ground tie point. Similarly, it was anticipated that readings at successive
structures would be very similar since the local ground would be expected to contribute
little to the overall measured ground impedance, except at very high frequencies. The results
were somewhat different than expected, however. The 50 Hz readings taken at the first
three structures ranged from 1.68 ohms to 2.35 ohms. Structures 162 and 163 (measured
later) gave values of 3.85 ohms and 1.15 ohms. At 1000 Hz, the impedance readings ranged
from 5.5 ohms (163) to 7.15 ohms (162 B), a considerably narrower range (Tables F-5 to
F-12).
It was noted during some of the tests that the test current did not remain constant, even
though the source voltage did not appear to be unstable. After discussions with RGE personnel
concerning the anomalies in the measurement results and an examination of the inconsistencies,
it was concluded that the connection between the overhead ground wires and the vertical
wire to the local ground was the most likely source of the problem. A resistance reading,
taken with a digital multimeter, between the two-ground wires on poles 161 A and 161 B
measured 89 ohms. Since the two overhead ground wires were almost certainly tied together
at adjacent structures by the horizontal steel cross member or cable (at guyed structures),
the problem is most probably caused by a poor connection to the local ground, as originally
suspected.
The lowest values of impedance were obtained at structure 163, a three pole guyed tower.
The ground connection in this instance was made to the guy wire since no local grounds,
other than the guy wire anchor, were installed. Being under considerable tension and connected
directly to both overhead ground wires, this ground was believed to be very well tied
electrically to the overhead ground wires (Figure 10.3(a)). The readings taken at structure
163 were consistently the lowest of all readings at all frequencies. Thus, at all other
structures, it was assumed that a contact resistance of from 0.5 to almost 3 ohms existed
between the overhead ground wires and the pole ground wires at structures 159 through 162.
An approximate equivalent circuit of the ground connections at the base of each
10-12
structure is shown in Figure 10.11. This contact resistance, which may lead to significant
error in ground impedance measurements, is typical when low voltages are used during
the measurements [11].
Connections to
Adjacent Towers
Overhead Ground Wire to
Vertical Wire Contact Resistance
local
/
Ground
Resistance
Pole A
Figure 10.11
Pole B
Equivalent Circuit of Grounding Connections at Double-Pole Structures
The connection from the overhead ground wire to the local ground was cut at poles 161 A,
161 B, 160 A and 160 B in order to measure the local ground resistance at each pole. Pole
161 A and 161 B grounds were measured with the Megger instrument which was not affected
by stray fields while measuring the relatively high resistance local grounds at poles 161 A
and 161 B. The grounds at poles 160 A and 160 B were measured using the voltmeter/ammeter
test system. Measurements were taken at frequencies ranging from 50 Hz to 2000 Hz with
a test current of 1.0 ampere. A slight drop in apparent impedance was observed. Mutual
impedance effects between test leads accounts for this apparent decrease in electrode
resistance. The test results are shown in Tables F-13 and F-14 of Appendix F.
10.2.6 ANALYSIS OF THE GROUND IMPEDANCE MEASUREMENTS
Since no resistivity measurements could be conducted in the immediate vicinity of the
transmission line structures and because of the large variations in the resistivity values
observed from one site to the other, no attempt was made to assign to each structure any
specific two-layer soil from the models derived in Section 10.2.4 and summarized in Table
10.1. Instead, the resistance of a typical pole ground rod buried in the soils described in
Table 10.1, was calculated using the computer program GTOWER.
The results obtained from GTOWER are summarized in Table 10.2. RGE practice is to equip
each pole of the two-pole structure with a 8 foot, 5/8" diameter ground rod buried at an
average depth of 1 foot. The ground rods at each pole of the structure are connected to
the overhead ground wires via a vertical wire stapled to the pole. The one rod and two rod
results shown in Table 10.2 simulate the measurements made with the vertical wire cut at
each pole of the structure and with the two structure pole grounds connected via a jumper
wire.
10-13
No
RESISTIVITY
TRAVERSE
ID
SOIL STRUCTURE
Pi
(ft-m)
GROUND RESISTANCE
(ohms)
P2
ONE-ROD
Q-m)
TWO-RODS
Un i form
100.0
-
2
RGE 01-1
207.6
14.4
1.41
8.9
4.8
3
RGE 01-2
200.9
110.3
0.75
45.9
25.3
h
RGE 03
165.0
38.3
2.4
36.7
19-5
5
RGE 04
54.2
149.2
1.5
32.7
18.8
6
RGE 04 (a)
58.3
337.9
2.8
27.2
16.8
Table 10.2
-
38.3
21.3
Pole and Structure Ground Resistances
When the computed ground resistances are compared with the measured values at structure
160 (33 and 40 £2 for pole resistances and 20 £2 for structure resistance; see Appendix F,
Table F-13), reasonable agreement is obtained for both pole and structure ground resistances
when the reference traverses used to perform the calculations are RGE 01-2, RGE 03 and
RGE 04.
There is poor agreement however between the pole ground resistances computed using the
same resistivity models and the measured results for structure 161 given in Table F-14 of
Appendix F (average measured ground rod resistance is 85 £2). Assuming the ground electrode
was intact, this difference can only be explained by the presence of a relatively small volume
of soil material (surrounding structure 161) with a resistivity value 2.5 to 3 times the average
local soil resistivity. This illustrates well the effects of local soil resistivity anomalies on
small grounding systems such as short ground rods.
The apparent ground impedance of a structure, when equipped with a continuously grounded
overhead ground wire, is frequency dependent and will vary from a low resistance value at
very low frequencies, to a higher, predominantly resistive value at intermediate frequencies
(25 to 50 kHz) as the resistance of the local ground become dominant it will exhibit a high
reactive impedance at lightning or surge frequencies (200 to 1000 kHz). This behaviour is
depicted in Figure 10.12.
Zs = Rs+ja)X
(a) Frequency = 0Hz
Figure 10.12
(b) Frequency = 25 kHz
(c) Frequency = 500kHz
Frequency Dependence of Transmission Line Grounds
10-14
Figure 10.12 shows a ladder network where R represents the transmission line structure
ground impedance (all assumed equal to an average value); Rs is the ground resistance of
the structure at the point of observation; Z is the self impedance per span of the overhead
ground wires and X is the inductance of the structure or vertical ground wires along the
poles. At low and intermediate frequencies, the structure inductance is negligible and can
be ignored. At 0 Hz, the per span impedance Z reduces to the per span dc resistance of
the ground wires (r0).
The impedance of the ladder network, as seen from the fault or test location (without the
resistance of the local structure) is [11,12]:
Z
= (Z + /z2 + kRZ)/b
(10-1)
e
Therefore the total impedance measured at the structure, including the structure ground
resistance, is:
Z
Z (Z + /z2 + 4RZ)
= —----------------------------t
4Z + Z + /z2 + 4RZ
s
(10-2)
Table 10.3 gives the calculated results from Equation 10-2, based on the measured structures
of the RGE 115 kV transmission line. The average structure ground resistance R is assumed
to be approximately 30 ohms, while the tested structure ground resistance Rs is assumed to
be 20, 30 or 50 ohms (according to the measurements R(160) = 20 Q and R(161) = 46 fi).
The per span impedance Z of the two 7 No. 7 alumoweld ground wires were calculated using
the computer program LIN PA described in Appendix A (span length = 125 m). Finally the
downlead inductance X is estimated to be approximately 15 mH.
Frequency
(Hz)
R
(ohms)
s
(ohms)
per Span Impedance
(ohms)
r
jail
20
50
400
2000
30
30
30
(ohms)
jt)Lt
rt
Measured
Note
0.510
1.543
1.67
1
1.487
0.536
1.581
1.15
2
50
1.513
0.558
1.613
2.35
3
20
2.660
1.946
3-296
3.85
1
2.7H
2.128
3.447
3.12
2
50
2.745
2.289
3.574
4.25
3
20
5.391
3.937
6.676
9-3
1
5.584
4.728
7.317
8.15
2
7.808
30
30
30
0.257
0.213
0.358
1.548
0.769
7.155
5.660
50
30
1 Zt 1
Equivalent impedance Calculated
(ohms)
(ohms)
1.456
20
1000000
1 Zt I
Zt
z
R
30
19.66
73.6
2285.
50
(1) According to measurements, Rg - 20
Q,
5.494
5.673
9.6
3
21.91
-
-
29.46
10.09
31.14
-
-
49.01
11.42
50.32
-
-
corresponds to structure 160. Value measured from pole B.
(2) Value measured at structure 163.
(3) According to measurements, Rs = 50 ^corresponds to structure 161. Value measured from pole A.
Table 10.3
Frequency Response of Transmission Line Structures
The calculated and measured values of the apparent impedance Zj- are shown in Figure 10.13.
Examination of this figure indicates that the agreement between measured and calculated
values is reasonable, particularly when the effect of the contact resistance is considered. If
this contact resistance (estimated at .5 to 2 ohms) is eliminated by shifting down all the
measured values by, say 0.8 $1, the average measured values track the average computed
curve very well.
10-15
0
Figure 10.13
Measured and Computed Apparent Impedance
10.3 THE TVA 500 kV TRANSMISSION LINE MEASUREMENTS
The Tennessee Valley Authority conducted a series of staged fault tests on their 52 km (32.2
miles) long 500 kV transmission line between Johnsonville and Cumberland steam generating
stations. The faults were all single phase-to-ground and were made at tower 130, a few
meters away from the special fault structure, shown in Figure 10.14, which was used to
initiate them. The fault structure, shown again in Figure 10.15 while an arc was developing,
is located about 10 km (6.2 miles) from Cumberland.
Although the tests were carried out by TVA to achieve several goals, one of the main
objectives of the tests was to determine the distribution of the fault current between the
overhead ground wires and the transmission line towers and the earth potential around the
faulted tower so that comparisons could be made with values calculated using computer
programs PATHS and GTOWER.
A program of resistivity and ground resistance measurements was undertaken at the test
site as part of the 500 kV staged fault tests, to accurately determine the parameters required
for calculating the fault currents and earth potentials.
Since the two overhead alumoweld ground wires of the 500 kV transmission line are normally
insulated from the supporting towers to provide a circuit for carrier communication [13],
the initial staged fault tests were made while the ground wire insulators at tower 130 and
at 20 other adjacent towers (10 on each side of tower 130) were short-circuited to simulate
a transmission line with ground wires solidly connected to the towers. The final test was
conducted with the transmission line operating under normal conditions, i.e., with the ground
wires insulated from the towers. The ground wire insulators provided a 2.2 cm (0.87") air
gap. Under dry conditions, this air gap will flash over for an average voltage of 15 kV.
10-16
PHASE C
Figure 10.14
Test Site; Tower 130 and Fault Structure
Figure 10.15
Arc Initiated at Fault Structure
10-17
The complete measurements conducted by Tennessee Valley Authority (TVA) and Safe
Engineering Services (SES) were as follows:
Resistivity Measurements (October 1981)
•
4 traverses around tower 130 (by TVA).
•
3 traverses around tower 130 (by SES).
Resistance Measurement
•
Tower 1 to tower
•
Tower 125 to tower 135 (carried out by TVA, October 1981).
•
Tower 130 (several measurements by SES, October 1981).
166
(carried out by TVA between May and July 1970).
Impedance Measurements (SES, October 1981)
•
At tower 130 with ground wire insulators short-circuited at tower 130 and 20
other adjacent towers (10 on each side of tower 130).
Earth Surface Potential Profiles (SES, October 1981)
•
Around tower 130 with ground wires insulated from tower.
•
Around tower 130 with ground wire insulators short-circuited attower 130 and
20 other adjacent towers.
Staged Fault Tests (TVA, October 1981)
The following measurements were made three times with the ground wires electrically
connected to tower 130 and 20 other adjacent towers, and once with the ground wires
insulated from the towers.
•
Total fault current at the fault location (Ij-).
•
Total fault current in ground wires at the fault location (Ig).
•
Current in ground wires arriving at towers 125 to 129 and 131 to
•
Current in ground wires leaving tower 125 and tower 135.
•
Current in ground wires arriving at Johnsonville and Cumberlandstations.
•
Current in neutral of transformers at Johnsonville and Cumberland stations.
•
135.
Total fault current contribution from Johnsonville and Cumberland stations (I;
Ic).
•
Ground potential rise of Johnsonville and Cumberland Station grounding grids.
•
Tower 130 ground potential rise measured with respect to two different remote
points 90° apart (with respect to transmission line right of way.
10- 18
The staged fault test measurements are illustrated in Figure 10.16.
The results of the staged fault current measurements which were carried out between October
27 and October 30, 1981 are presented in Section 10.3.10 where they are compared with
the calculated values.
The results of the resistivity, ground resistance/impedance and potential profile tests carried
out on October 27 and October 28, 1981 are given in detail in Appendix G. They are analysed
and discussed in Sections 10.3.5 and 10.3.6. All the measurements taken by SES were made
using the selective voltmeter and ammeter method described in Section 10.2.2. No portable
power generator was required for these tests since 120 volts ac power was available at the
site.
Tower
Ground Potential
Rise
-'etc
--etc
Phase A
Remote
Soi 1
Grid
Grid
T owe r
Fault
Structure
Tower
129
Remote
Soi 1
CUMBERLAND
J0HNS0NV1 LIE
Figure 10.16
'
Ground
Tower
Wire
131
Staged Fault Tests Measurements
10.3.1 TEST SITE
The fault site, near 500 kV tower 130, is a wooded area of irregular terrain as illustrated
by Figure 10.17. The topography is characterized by numerous small gulleys with a small
stream or ground water at the bottom of each. The transmission line right of way was
traversed by three such gulleys between towers 130 and 129. Although not evident at the
test site, it was apparent at nearby locations that the area is underlain by old, stratified
bedrock which has been thrust up into innumerable small ridges and domes. The soil overburden
appears to vary in thickness from a few feet to a hundred feet or more. No exposed bedrock
was visible in the vicinity of the test site. Thus, it was not possible to estimate the
overburden height in that area other than by interpretation of resistivity measurement data.
At the time of the measurements, the ground was very wet as a result of heavy rains in
the preceding few days. Vehicle traffic on the right of way created a considerable disturbance
to the terrain near the test site, as deep ruts in the ground were created by the spinning
wheels of the numerous TVA and other vehicles at the site. The weather was sunny for most
of the tests however, with an ambient temperature in the range of 10 to 15 °c.
10- 19
The areas on each side of the 500 kV right of way were heavily wooded. Vegetation on the
right of way itself had recently been cut down to about 15 cm (61'). Portions of the right
of way close to the fault location traversed open fields.
Right-of-way
6.9 kV
Tower
(b)
Gravel Road
Top View of the Test Site
Soi] Profile
Center Profile
50 Ft Left
------ 50 Ft Right
G rave 3
Road
Second
Gulley
Fi rst
Gu1 ley
Profile View of the Test Site
Figure 10.17
Topography ot the Test Site
10.3.2 500 kV STAGED FAULT TEST DESCRIPTION
To create a fault on the 500 kV line, a drop wire from one phase of the 500 kV line was
connected to a conductor strung between two wooden poles on opposite sides of the transmission
line right of way. This cross conductor was placed approximately 15 meters (50 feet) above
the ground as shown in Figure 10.14. A second conductor was strung approximately 5 meters
(16.4 feet) below the 500 kV cross-conductor. This conductor was connected solidly to the
metal structure of tower 130.
10-20
The fault was created by the vertical firing of an arrow, the end of which was attached to
a long nylon wire terminated by a short length of a metallic wire which initiated the arc
when passing by the cross-conductors. The arrow was shot from a specially modified crossbow
which was mounted vertically in a wooden support stand (Figure 10.18). The crossbow was
fired remotely via a solenoid-inverter arrangement which allowed the person activating the
device to be standing well away from the faulted tower.
TOWER 130
POTENTIAL
TRANSFORMERS
CROSSBOW
Figure 10.18
Potential Transformers and Crossbow Near Tower 130
Once initiated, the arc developed into a large fireball between the parallel phase and ground
cross-conductors and generated a loud thunder-like bang. Although very difficult to estimate,
the duration of the fireball appeared to be approximately 1/4 to 1/2 second. The actual
fault clearing time was apparently 3 to 4 cycles.
The phase and ground wire currents were measured using suitably rated conventional current
transformers. The secondary winding currents were locally coded, then transmitted to the
measuring equipment trailer via fiber optic cables. There, the received signal was amplified,
decoded and sent to the recording apparatus. This technique electrically isolated interference
picked up from the energized transmission line.
All the fiber optic cables and associated circuitry were tested and calibrated by TVA personnel
a few days before the initiation of the first staged fault tests.
Immediately after the first staged fault test on Tuesday October 27, it was apparent that
something was wrong. Smoke was observed rising from the measuring equipment installed in
a trailer at the test site.
10-21
Smoke was also observed at one of the two high-voltage potential transformers mounted on
a small open trailer located immediately adjacent to the faulted tower (Figure 10.18). An
inspection revealed that the faulted tower structure had been inadvertently tied to the
potential transformer casings. This resulted in a flashover from the PT casings to the low
voltage secondary windings which lead into the equipment trailer. Thus, the full potential
rise of the tower (more than 10 kV) was transferred into the equipment trailer on low
voltage leads. As a result, several circuit cards in the recording amplifiers were damaged.
This test was partially successful in that some data were obtained prior to the equipment
damage and measurements at the two stations at each end of the faulted line were successful.
On the same day, a second test was carried out with the potential transformer ground lead
problem rectified. Unfortunately, it was then learned that several of the optical fiber cables
used to transmit the fault current data from adjacent towers had been deliberately cut
by vandals. Out of a possible 14 overhead conductor current readings, only 6 were recorded.
Specially trained personnel with the appropriate splicing kits were required to repair the
damaged fiber optic cables. This resulted in a two day delay in completion of the tests.
The final tests were carried out onFriday with no improvement over test No. 2 because,
not only the repaired fiber optic cables did not perform correctly, but also the current
readings from two additional towers (127 and 128) were lost, presumably because of new
damaged sections of the corresponding fiber optic cables.
Fortunately however, the most important readings related to transmission line grounding
analysis were successfully recorded. These readings included the total fault current in the
ground wires and the potential rise of the faulted tower 130.
10.3.3 LOW CURRENT TESTS
Soil resistivity tower footing resistance and earth potential gradients were measured at the
TVA staged fault test site to provide the best possible input data to the transmission line
grounding programs used to analyze the faulted power system. All measurements carried out
by SES used the voltmeter/ammeter method with test currents of up to 2 amperes. A 250
VA variable frequency power source (California Instruments model 251T) was used to supply
the test current and a Hewlett Packard model 3581C selective frequency voltmeter was used
to measure voltage. The test current was measured by a Fluke true rms digital voltmeter
model 8010A. A schematic of the test instrumentation arrangement is shown in Figure 10.5.
TVA personnel duplicated the resistivity and the ground resistance measurements (ground
wires insulated) at tower 130 to compare measurements conducted using relatively sophisticated
equipment against the more expedient type of measurement usually conducted by utilities
using conventional equipment. In addition, TVA personnel repeated the ground resistance
measurements at towers 125 to 135 (towers 1 to 168 were measured in 1970). These results
are contained in Appendix G (Tables G-17 to G-19).
The resistivity measurements were carried out along four orthogonal directions as shown in
Figure 10.19(a). Four sets of test probes extending in these four directions from tower 130
were installed by TVA personnel prior to the SES tests. Each test probe consisted of a 1.2
m (4 foot) ground rod driven to a depth of 0.9 m (3 feet). These probes were used for
resistivity and fall-of-potential measurements. Additional temporary probes were used to
measure potential gradients and resistivity for close probe spacings underneath and immediately
adjacent to tower 130. The resistivity measurements for close probe spacings were repeated
using the short, temporary probes instead of the 0.9 m (3 foot) probes. Six days prior to
the SES tests, TVA personnel had carried out resistivity measurements with a Biddle Megger
10-22
model 597 instrument using the probe locations identified on the site plan. The results of
these measurements are contained in Appendix G (Tables G-l to G-7). All resistivity
measurements were based on the Wenner array configuration shown in Figure 10.19(b).
The potential profile measurements, which were also used to determine fall-of-potential
ground impedance measurements, were labelled as indicated in Figure 10.25 and Figure 10.26.
The measurements were made with the ground wires insulated and short-circuited as already
explained. The potential results of the profile measurements are given in Appendix G (Tables
G-8 to G-16).
Traverse 03
and
Traverse 2-
Buried
Leg Anchor
Traverse 10
and
Traverse f-2\
Traverse
Traverse 04
Traverse 2-2
b
a
JOHNSONVILLE
CUMBERLAND
(a) Location of Trave
Figure 10.19
(b)
Wenner Method
Resistivity Measurements
10.3.4 SES TEST PROCEDURE
The same basic procedure was applied in all of the measurements carried out by SES. Once
the four test leads (two current and two voltage leads) had been located, an ac voltage of
up to 160 volts was applied between the current electrodes from the power oscillator. The
multimeter was located in series with the low voltage side of the power oscillator output.
In all tests, the output current was set to as high a value as could be obtained without
exceeding the 250 VA power output or voltage limits on the power oscillator. Since the
rating of the oscillator was limited at very low or very high frequencies, some low frequency
measurements had to be carried out at reduced power levels. The primary factor determining
output current, however, was the resistance of the current electrodes. For the resistance
and potential profile tests, test currents in the order of 1.5 amperes were used. In order to
achieve this current level, it was necessary to drive multiple ground rods interconnected via
a horizontally buried bare copper wire. The test currents used for resistivity measurements
were considerably lower because of the high resistance of a single rod and the 160 volt
limit on the power source. Test currents for resistivity ranged from as low as 0.01 amperes
to 0.20 amperes.
10-23
The nominal test frequency used in all tests was 70 Hz. When a test at a different frequency
was required, the test probe locations were left fixed while test currents of different
frequencies were applied and the appropriate voltage readings taken.
Once a stable test current was obtained, the voltage between the two potential leads was
measured using the selective voltmeter. This instrument was used at the 3 Hz bandwidth
switch position to ensure rejection of all 60 Hz ambient noise and the AFC feature was
used to ensure that the receiver remained tuned precisely on the power source frequency.
As a calibration check, a Beckman 3020 digital multimeter was periodically connected in
parallel with the selective voltmeter. Although the Beckman is a wideband meter, for many
of the measurements the out of band signal voltages were a factor of 10 or more below
the measured test voltage and thus had negligible influence on the measured wideband voltage.
The selective voltmeter was also calibrated frequently using the instrument's internal calibration
feature.
10.3.5 EARTH RESISTIVITY TESTS
The resistivity traverses which were carried out by TVA and SES are illustrated in Figure
10.19(a). The measured results for these traverses are given in Appendix G and plotted in
Figures 10.20 to 10.24. Two SES traverses, TVA 03 and TVA 10, utilized the same installed
ground rods as used by TVA in tests carried out the week before. All resistivity measurements
were based on the Wenner array configuration shown in Figure 10.19(b).
Traverse:
....
TVA 1-
Computed by RESIST
Measured by TVA (Megger)
240 _
This measurement
point was discarded
during the
computations
160
_
Equivalent Soil
1.1m (3.6 feet)
PROBE SPACING
Figure 10.20
Resistivity Traverse TVA 1-1
10-24
(feet)
360
Traverse:
tva 2-2
200-
Computed by RESIST
Measured by TVA (Meggi
Equivalent Sol
Pi = 31^
97
h
.
20
■
i
b0
■
1
60
■
= 3.1?m (10.A feet
r---------- *---------- 1-----------'---------- j-----------'---------- r
100
80
PROBE SPACING
Figure 10.21
120
140
(feet)
Resistivity Traverse TVA 2-2
Because of the major effects that probe depth can have on resistivity measurements with
close probe spacings, the measurement data for 0.45 m (1.5 foot) probe spacing were analyzed
using an accurate form of the apparent resistivity formula (see Appendices F or G). This
formula gives the "average" surface layer resistivity to a depth approximately equal to the
probe spacing. During the field resistivity tests the temporary probes were driven a few
centimeters into the soil for 0.45 m (1.5 foot) probe spacing. Resistivities in the order of
600 to 1000 ohm-meters were recorded. This is about two to five times the values measured
using the 0.9 meter (3 foot) preinstalled ground rods.
The high surface soil resistivity is caused by the presence of small trees and the considerable
quantity of other vegetation which had been recently cut a few centimeters from the ground
(Figure 10.27). Because the surface soil resistivity has a negligible effect on the ground
resistance and the surface potentials (at an average depth exceeding 8 centimeters), the
calculations should be performed based on the "average" surface resistivity measured with
the deeper preinstalled ground rods.
10-25
360 .
Traverse:. TVA
280 .
1-2
200 .
Computed by RESIST
TVA 1-2
Measured by TVA (Megger)
-------
Computed by RESIST
(partial Curve Matching Technique)
TVA 10
•
Measured by SES (voltmeter/ammeter)
®
Not included in computations
(both sections of curve)
E
Not included in computations
(first section of curve)
EQUIVALENT SOIL (TVA 10)
First section of curve
EQUIVALENT SOIL
Last section of curve
Pi - 352 fi-m
P2 - 162.5 ^“m
hi = l.kl m (8.1')
PROBE SPACING
Figure 10.22
(TVA 1-2)
Pi = 309 ft-m
P2 = 209 ft-m
h = 1.35 m (4. A
(feet)
Resistivity Traverses TVA 1-2 and TVA 10
The measurement results show noticeable differences between the various traverses. However,
there are several similarities and a general trend of the apparent resistivity curves. All
curves indicate a complex earth structure, which, considering the nature of the terrain, is
to be expected.
Examination of Figures 10.20 to 10.24 and the following analysis indicates that the soil
structure around tower 130 should be treated with a three to four layer model, with a thin
moderate resistivity top-layer (P} = 250 to 350 P-m, hi = 1.5 m) underlain by a relatively
thick low resistivity layer (P2 = 70 to 90 P-m, h2 = 4 m). These two upper-layers rest on
one or more soil layers with an average resistivity in the order of 400 P-m (a typical value
for ancient layered-rock formations).
Since it is not yet practical to analyze grounding problems in soils with more than two
layers, it is necessary to find a suitable equivalent two-layer soil model for the real soil
conditions observed at the test site. Unfortunately, the problem is further complicated
because, even within a small radius from the tower, the earth structure appears to vary
with the direction of the traverse being examined. Therefore, to arrive at a "practical"
equivalent soil model which will represent the tower grounding system with reasonable
accuracy, averaging techniques must be employed on all traverses as well as sound engineering
judgment.
10-26
Fortunately, in most power grounding problems, significant variations in the soil characteristics
can be tolerated at moderate or large distances from the ground electrode, without noticeable
effects on its grounding performance. By moderate distances it is meant about two to three
times the largest dimension of the grounding system. It is therefore permissible and quite
accurate to replace the "distant" soil layers by an equivalent one. In many instances this
equivalencing (or averaging) technique can even be performed at relatively short distances
from the ground conductors without significantly changing the essential aspects of the
grounding system response to fault currents. Such transformation techniques are often applied
in geological prospecting and use the concept of transversal and longitudinal earth resistivity
[14]. This concept however can not always be applied in power grounding because of the
fundamental difference between a point source ground electrode which is in contact with
one single soil layer at a time, and an extensive grounding system which may be in contact
with more than one layer and hence, be poorly modelled if two of these layers are replaced
with one single equivalent layer.
320 -|
. TVA 203
Traverse: TVA
--------- Computed by RESIST
....... Measured by TVA (Megger)
_ ____ Computed by RESIST
TVA 03
...4.-.- Measured by SES (vol tmeter/ammeter)
200 .
160
-
120
_
EQUIVALENT SOIL
TVA 03
Pi = 3^
h
= 0.8Am (2.75 feet) h
= 0.8m (2.6 feet)
PROBE SPACING
Figure 10.23
(feet)
Resistivity Traverses TVA 2-1 and TVA 03
10-27
320 _
Traverse:
tva oa
__ Computed by RESIST
(Partial Curve Matching Technique)
Measured by SES
(vol tmeter/ammeter)
Equivalent
EQUIVALENT SOIL
FIRST SECTION
OF CURVE
LAST SECTION
OF CURVE
Pi = 280.5
P 3 = 321.
• 93 rn (29.3 feet
PROBE SPACING
Figure 10.24
(feet)
Resistivity Traverse TVA 04
Consequently, the following principle must always guide the power engineer during the
development of an equivalent or average soil structure:
•
Always combine layers which are not in direct contact with major parts of a
grounding system. Try to maintain the integrity of the real earth structure where
soil is in contact with the ground conductors.
This principle has been followed below. However, in other situations it may be impossible
to apply. In such cases, several different two-layer soil models encompassing the real model
should be constructed and analyzed as the limiting cases.
10.3.6 ANALYSIS OF THE RESISTIVITY TESTS
All resistivity traverses were analyzed using computer program RESIST to derive an equivalent
two-layer soil model from the apparent resistivity measurements, for use in the tower
grounding analysis. The results of this analysis are plotted in Figures 10.20 to 10.24 and are
summarized in Table 10.4.
In four cases (TVA 1-1, 2-1, 03 and 2-2) a reasonable equivalent two-layer soil was obtained
for probe spacing of 25 m (80 ft) and more. In three other cases however (TVA 1-2, 10 and
04) the presence of the deeper layers was noticeable at shorter probe spacings and therefore,
a partial curve matching technique was necessary to distinguish the predominant soil layers.
10-28
The results of the analyses are displayed in Figures 10.22 and 10.24. The two-layer equivalent
soil models which were derived in each case by keeping the first layer resistivity (pj) and
height (hj) unchanged and replacing the mid and bottom layers with an equivalent one, are
given in Table 10.4. This derivation, which is not unique, is largely empirical and based on
experience and judgment. It will be shown later that other values (in the same order of
magnitude) would lead to small but noticeable changes in the actual computed values. During
a design stage, such parameter variations should be used to determine worst case situations.
In a comparative study such as this, the uncertainties involved in the proper choice of the
parameter value suggest that a perfect match with the measured data will be purely
coincidental. The closeness of the agreement will therefore be limited by the computed
difference between the two probable, but reasonable extreme values of the uncertain
parameters.
RESISTIVITY
TRAVERSE
EQUIVALENT SOIL MODEL
DESCR1PT1 ON/COMMENTS
Pi
(a-m)
h
(m)
P2
(Q-m)
MEASURED
BY
TVA 1-1
Along transmission line
(toward Cumberland)
250
130
1.1
TVA
TVA 2-2
Perpendicular to transmission
1ine
(south East)
vk
197
3.2
TVA
309
203
1.35
TVA
352
162.5*
2.47
SES
TVA 1-2
TVA 10
TVA 2-1
TVA 03
TVA Qi)
Along transmission line
(toward Johnsonvi1le)
Perpendicular to transmission
1 i ne
(north-wes t)
Along transmission line
(centered at tower 130)
310
118
0.8
TVA
ikh
113
0.84
SES
280
120
2.56
Note
* Equivalent single layer
Table 10.4
Equivalent Two-layer Soils
The SES resistivity curves (measured using the selective voltmeter/ammeter method) and the
TVA resistivity curves (measured using a Megger) agree quite well although the SES
measurements give consistently slightly higher values.
Resistivity traverse 04 was centered underneath tower 130 and extended outwards uniformly
in each direction underneath and parallel to the 500 kV line. This traverse utilized the
installed 0.9 m (3 foot) ground rods on both sides of the tower. At close probe spacings,
temporary short rods were driven at appropriate locations. This arrangement permitted a
traverse with 46 m (150 foot) maximum probe spacing.
Test currents of 0.025 amperes were used for close probe spacings while tests currents of
up to 0.2 amperes were used at large probe spacings. Note that the use of very low test
currents (such as those generated by a Megger) might not have been practical had the
transmission line been in service. However this would have depended on the degree of
line imbalance, test lead arrangement with respect to the line, soil resistivity, ground rod
depth, and other factors.
10-29
The resistivity tests and subsequent interpretation analyses suggest several equivalent two-layer
soil models characterized by the following ranges of values (see Table 10.4):
P1 = 250 to 350 tt-m
P 2 = 110 to 210 Q -m
h
=
1 to 3 m
These variations are not due to measurement uncertainties, and represent the real situation
at the tower site. Despite the variations, the various models remain equivalent. For example,
when comparing two models, pj increases from 250 to 344 fi-m, P2 decreases from 130 to
113 SI -m and h drops from 1.1 to 0.84 m. These variations have opposite actions and tend
to cancel so that the various models will produce comparable results.
Therefore, the potential profile and ground resistance analysis of Section 10.3.6 could be
based on all the equivalent soils derived from the traverses (Table 10.4). However, to simulate
a normal test program and to establish a fair basis for the comparisons, only one of the
duplicate measurements (made by SES and TVA) for the same traverse should be considered.
It was therefore decided to analyze both measurements separately and to use the SES based
computation results as the reference for comparison with the measured earth potential and
ground resistance values, since these were obtained using the same test equipment.
Finally the sensitivity of tower grounding performance to small variations in the soil
characteristics was established by considering additional soil models, qualitatively (logically)
and quantitatively compatible with the measurement results. A total of ten different soil
models are examined in the next section. Table 10.5 describes these models and provides a
brief explanation of the methodology used to construct them.
CHARACTERISTICS OF MODEL
h
Model
No.
(fi-m)
(^-m)
i
250
130
1.1
3.6
2
31^
197
3.2
10.5
3
3^4
113
0.84
h
352
162.5
5
280
6
(m)
DESCRIPTION OF
MODEL CONSTRUCTION METHODOLOGY
REFERENCE
(feet)
Derived from RESIST computations
(traverse TVA 1-1)
TVA
measured
Derived from RESIST computations
(traverse TVA 2-2)
TVA
measured
2.75
Derived from RESIST computations
(traverse TVA 03)
TVA
measured
2.47
8.1
Derived from RESIST computations
(traverse TVA 10)
SES
measured
120
2.56
8.4
Derived from RESIST computations
(traverse TVA 04)
SES
measured
308
ISO
1.76
5.8
Averaqe of all values in table
10-4
TVA + SES
averaged
7
296
163.5
1.61
5.3
Averaqe of TVA values in table
10-4
TVA
averaged
8*
325
132
1.95
6.4
Averaqe of SES values in table
10-4
SES
averaged
9
300
143
1.4
4.6
Compatible Model (could have been
compatible
selected by other investigators)
10
341
132
1.52
5.0
Compatible Model (could have been
compatible
selected by other investigators)
Note
* Reference Soil Model for Grounding Computations.
Table 10.5
Origin of Soil Models Analysed
10-30
10.3.7 EARTH POTENTIAL AND GROUND IMPEDANCE TESTS
The potential measurements at 500 kV tower 130 were taken in two stages. First, measurements
were carried out with the overhead ground wires connected to the test tower 130. The C2
return current electrode consisted of three vertical rods interconnected by a length of bare
copper wire which was buried 5 to 8 cm (2-3 in) below the mud at the bottom of a
small gully, 95 m (315 feet) west of the test tower, along the transmission line right of
way (Figure 10.25). This electrode was determined to have a resistance of 95.5 ohms.
The first fall-of-potential profile TVA 01 was taken at right angles to the transmission line
(north-west) and utilized the ground rods previously installed by TVA personnel. Potential
readings were taken out to a distance of 65 m (215 feet). With the potential probe at
the 65 m location, the tower current electrode Cl was located on all four corner legs of
tower 130. There was no measurable difference in readings. The test frequency was then
varied from 20 Hz to 20 kHz and the apparent tower impedance determined for each
frequency.
The second fall-of-potential profile, TVA 02, was in the same direction as the return current
electrode and again used the previously installed ground rods as potential measurement probes.
In this profile, as well as the previous one, the first measured point (0 m) was at the center
of the tower. Thus, the 0 m reading is not zero volts because the tower is in contact with
the earth at the corners only.
Immediately following profile TVA 02, a detailed potential profile (TVA 11) was measured
between the south and west tower legs.
The results of all these potential profiles are given in Appendix G (Tables G-8 to G-ll).
Measuring
Equipment
Profile 01
95 m (315
Potentia 1
Current
Lead (Cl)
Current
Profile 02
Return
Current
E1ect rode
(In first Gu1 ley)
Potentia 1
Probe P
Tower Leg
JOHNSONVILLE
Figure
10.25
Buried Leg
Anchor
Profi1e 11
CUMBERLAND
Potential Profile Measurements
(Ground Wires Connected to Tower 130 and 10
Adjacent Towers on Each Side of Tower 130)
10-31
For the next series of potential measurements taken the following day, the overhead ground
wire was insulated from the tower. This was the normal operating condition for this line.
The first traverse (TVA 05), shown in Figure 10.26, was in the opposite direction to the
current electrode. The current electrode (C2b) was initially the same electrode as used for
TVA 01 and TVA 02 but was then relocated 180 m (600 feet) further down the transmission
line right of way. The potential reading at 96 m (315 feet) changed by 1.2% when the
current electrode was relocated. The new C2b electrode was higher in resistance than the
first, therefore a lower test current had to be used. Potential profile TVA 05 used the
installed ground rods as potential probe locations.
Potential profile TVA 06 used the same C2b electrode as TVA 05 and was taken towards
this electrode. Thus, TVA 06 was a repeat of TVA 02 but with the overhead ground wires
insulated from the tower. Similarly, TVA 07 was a repeat of TVA 01 with the overhead
ground wires isolated.
Return
Current Electrode
n Second
Gulley
• C2b
Profile 07
Prof lie 09
In First
Gulley
Potential
Probe /
Profile 08
Leg to Leg)
# C2a
Profile 06
Profile 05
Buried Anchor
Tower Leg
1 80 m
CUMBERLAND
JOHNSONVILLE
Figure 10.26
Potential Profile Measurements
(Ground Wires Disconnected From Tower 130)
Profile TVA 08 was a very detailed potential profile between the north and west tower legs
of tower 130 (see Figure 10.27).
The final potential profile TVA 09, was taken in a south-east direction from tower 130,
once again using the ground rods installed by TVA as potential probes. At the 46 m (150
foot) probe location, potential readings were taken for test frequencies from 40 to 5000 Hz.
The results of the measurements made while the overhead ground wires were insulated from
the tower, are given in Appendix G, Tables G-12 to G-16. The last tables of this appendix
(G-17 to G-19) give the ground resistances of all the 500 kV transmission towers between
Johnsonville and Cumberland. These towers were measured by TVA personnel a few years
after the construction of the line and towers 125 to 135 were remeasured in October 1981
during the staged fault tests.
10-32
The measurements were made using a direct-reading Megger Instrument with the return
current and potential electrodes in opposite directions (along the line) at 60 to 70 m
from the measured tower. As will be shown later in this section, during such measurement
conditions, the measured resistance is generally lower than the real value by approximately
5% (assuming a problem-free measurement).
Tower
Leg
Profile to
Adjacent Leg
Figure 10.27
500 kV Tower Leg
10.3.8 ANALYSIS OF THE HIGH FREQUENCY TESTS
The measurements contained in Appendix G, Table G-16, made while the ground wires were
insulated, established that there is no significant inductive component in the ground impedance
of tower 130. In fact, a slight decrease in the apparent ground impedance was observed as
the freguency was increased from 40 Hz to 5000 Hz. This effect is attributed to some
waveform distortion in the signal of the variable frequency power unit due to the relatively
high load current.
The effect of connecting the ground wires to tower 130 and to 20 other adjacent towers
(10 on each side of tower 130), appeared very clearly in the measurement results (see Table
G-9). The apparent ground impedance, as measured from tower 130, increased regularly as
the frequency was swept from 40 Hz to 20,000 Hz, indicating the presence of a significant
inductive component. A simple calculation reveals that none of the resistive and inductive
components of this impedance could have been constant while the frequency varied. This is
to be expected if one examines Figure 10.28 which is an equivalent circuit of the electrical
network which was measured.
With dc or extremely low frequency currents, the equivalent combined ground impedance
reduces to a pure resistance. As frequency increases, the ground wires introduce an inductance
which is greatly influenced by the tower resistance values. However, when the frequency
reaches a value which makes the first span impedance significantly larger than tower 130
ground resistance, the measured impedance is determined mainly by the resistance of tower
130, and becomes therefore almost a pure resistance.
10-33
a
139
Tower
No.
Average Span = 320 m
Zg=r+jtoJl = Per Span
Figure 10.28
FREQUENCY
(Hz)
IMPEDANCE (J]/Kra)
r
0.433
0.889
1.931
1.961
1.992
2.006
1.248
2.051
2.009
1.364
2.414
1.538
4.666
2.196
2.476
7.510
9.016
3.011
1.200
0.269
1.218
0.521
60
1.238
0.767
70
1.246
100
1.274
200
400
800
1.871
1000
2.031
11.14
2000
2.792
21.54
8.289
10000
13.17
20000
20.91
30000
Table 10.6
Impedance of Ground Wires
IMPEDANCE (fi/mile)
r
ko
50000
(10501)
Equivalent Circuit with Ground Wires Connected
20
5000
UO
27.34
38.13
45.89
85-93
162.3
236.7
381.9
3.269
4.494
13.34
21.19
33.65
44.00
61.36
0.839
1.235
1.431
3-885
14.51
17.93
34.67
73.85
138.3
261.3
380.9
614.7
Ground Wire Impedance
The measurement results have been plotted in Figure 10.29 and can be compared with the
calculations made using the equivalent circuit of Figure 10.28 and the ground wires equivalent
impedances as determined by computer program LINPA (see Appendix A). These impedance
values, calculated for various frequencies and assuming a 300 fi-m average soil resistivity,
are given in Table 10.6.
lO-S1*
10
Computed Ground Impedance
Z apparent
—
129 Tower 131
132'
Measured Ground Impedance
38 139 1^0
FREQUENCY (Hz)
Figure 10.29
Measured and Computed Ground Impedances
Good agreement exists between the measured and computed values for frequencies between
200 and 400 Hz. Outside this frequency range the agreement is in the order of ± 20% which
is acceptable for this kind of measurement. It should be noted that the measured values
exceed the calculated ones for frequencies less than 300 Hz and are constantly lower above
that frequency. There are several factors which can explain the differences observed between
the measured and computed values. Of these, it is believed that the calculated ground wires
impedance value is the major factor, mainly because the impedance calculations are based
on Carson's equations [20] which assume an infinite line with a uniform soil for the earth
return, while the actual ground wires are finite in length (21 spans) and are grounded at
intermediate points.
10.3.9 ANALYSIS OF THE LOW-FREQUENCY TESTS
The low-frequency tests consisted essentially of earth potential profile measurements along
parallel and orthogonal directions to the transmission line at tower 130.
These potential measurements may easily be converted into fall-of-potential curves which
can be used to determine the tower ground impedance (see the fall-of-potential measurement
technique described in Chapter 9). This step was not necessary in this case, because the
actual grounding systems were first analyzed using computer program GTOWER. It was then
simple to establish, from the earth potential computations, that the measured ground impedance
value at a distance of approximately 63 m (215 feet) from the tower center, is about 5%
lower than the true value. Therefore, the ground impedance value of tower 130 was estimated
to be about 7.1 fi when the ground wires are insulated from the tower and 1.38 fi when
they are connected to tower 130 and to 20 other adjacent towers.
10-35
These ground impedance values were then used to determine the potential as a
percentage of the total ground potential rise (GPR) of the tower (see Appendix G, Tables
G-8 to G-16).
Modelling of Tower 130 Grounding System
The transmission line structures of the 500 kV line between Johnsonville and Cumberland
are four-legged lattice towers with a square base. A typical TVA 500 kV tower is shown in
Figure 10.30(a). The tested tower 130 is 31 m (102 ft) to the cross-arm and has a 9.3 m
(30 ft) square base (Figure 10.30(b)). Each tower leg is supported by an off-center, pyramid-like,
earth anchor (Figure 10.31).
The earth anchor is a square base made of U-shaped steel beams resting on four triangular
plates. Figure 10.31 shows the earth anchor details and dimensions.
I nsu1ated
Ground Wire
(a) 500 kV lover
Figure 10.30
(b) Tower No.
130 Base
A typical TVA 500 kV Tower
The four earth anchors are the only metallic elements of tower 130 which are in contact
with the soil. Therefore, these earth anchors were also the transmission tower grounding
system.
Computer program GTOWER accepts horizontal and vertical cylindrical ground conductors
only. Thus, it was necessary to develop an equivalent grounding model of the earth anchor.
This is relatively easy if the following rules are observed:
•
The equivalent model should occupy about the same soil volume as the original
system.
•
Grounding elements which are close to points where potential computations are
desired should be replaced with modeled elements which are as similar as possible
to the originals.
•
Closely spaced conductors should be replaced by an equivalent conductor based
on the GMR technique.•
•
Conductor diameter has a small effect on the grounding performance.
10-36
It is possible to derive several equivalent models of any given system which will produce
practically identical results.
Tower
Ground Line
SIDE VIEW
TOP VIEW
Figure 10.31
300 kV Tower Leg Earth Anchor
The model selected for this study is depicted in Figure 10.32. As shown later, the computation
results obtained using this equivalent model were only a few percent different from those
calculated using the original earth anchor (as computed by computer program MALT [15]
which accepts inclined ground conductors).
0.5'
—
SIDE VIEW
5- 5 1
y
Tower
Figure 10.32
Equivalent Earth Anchor Grounding Model
10-37
Computer program GTOWER was used to analyze this equivalent grounding system when
embedded in one of the ten soil models determined in Table 10.5. In addition to the tower
ground resistance, two earth surface potential profiles taken along the directions shown in
Figure 10.30, were calculated by GTOWER. Soil models numbered 6, 7 and 8 represent the
average soil at the tower site with model 8 being the reference for the comparisons with
the measured results.
Ground Wires Connected to the Towers
As explained in Section 10.3.8,
ground impedance measured at
120 to 140. The computations
with a phase angle of 16.80 at
there is a significant inductive component in the apparent
tower 130 when the ground wires are connected to towers
made to develop Figure 10.29 yielded a ground impedance
a frequency of 70 Hz (used during measurements).
The potential profile measurement results are shown in Figure 10.33 in percent of the tower
ground potential rise (GPR), i.e., the tower ground impedance times tower current. The
measurements can be compared to the computation results from GTOWER based on soil
model 8. Note however that the results from GTOWER were converted to percent taking
into consideration the inductive component of the ground impedance. The procedure used to
carry out this conversion is as follows.
COMPUTED RESULTS
(with Inductance of transmission line)
ground taken into consideration
Center Profile (soil model 8)
Leg Profile (soil model 8)
MEASURED RESULTS
Center Prof Ile TVA 01
Right-Side Leg Profile TVA
Left-Side Leg Profile TVA 1
Mode 1
DISTANCE FROM ORIGIN OF PROFILE (feet)
Figure 10.33
Measured and Computed Potential Profiles
(Ground Wires Connected to Tower)
10-38
The tower ground impedance Z was first determined from the tower ground resistance R
computed by GTOWER using the relation Z = R/cos(16.8°). The converted earth surface
potential values in percent of the GPR were then calculated by dividing the computed
potential values by 100 ZI where I is the tower fault current. The difference between the
values based on the ground impedance and those based on the ground resistance is in the
order of 2 to 3% only.
Figure 10.33 shows that there is very good agreement between measurements and computations
for both potential profiles.
SOIL
MODEL
CALCULATED (tt)
Pi
(£2-m)
P 2 (fl-m)
h(m)
GTOWER
MALT
1
250
130
1.10
6.5
-
2
311!
197
3.20
13.8
-
3
3*1 ft
113
0.8ft
5.7
U
352
162.5
2.1)7
11.5
-
5
280
120
2.56
9.0
-
6
308
150
1.76
8.35
-
7
296
163.5
1.61
8.6
-
5.4
8*
325
132
1.95
8.3
7.9
9
300
1 ^3
1.40
7.5
7-1
10
3ft 1
132
1.52
7.3
6.9
Note
* Used as reference
Table 10.7
Computed Ground Resistances
Ground Wires Insulated From the Towers
The resistivity analysis has shown that the test site soil structure was complex. That is,
a multi-layer type, probably with sloping layers. It also developed three average soil models
from the five base soil models constructed from the resistivity traverse measurements.
It is interesting to note that despite the differences between the base soil models, the
potential profile computations show essentially two types of performance as illustrated in
Figure 10.34.
Soil models 2, 4 and 5 gave
identical to those of model 3,
of 35% (with respect to the
and 3 are comparable with a
very similar results (model 2 results, which are practically
are not shown) and are characterized by an earth potential
GPR) at the center of the tower. The results from models 1
tower center potential in the order of 47%.
The computed tower ground resistances however, show larger differences between the
base models than those observed in the case of the potentials expressed in percent of the
GPR. These resistance values are shown in Table 10.7.
Note that the ground resistances based on the detailed representation of the earth anchor
(use of computer program MALT), are about 5% lower than those obtained with the equivalent
earth anchor model. The average difference between the potential profiles computed using
both earth models is also in the order of 5%, as shown in Figure 10.36.
The tower ground resistance as determined by GTOWER is practically the same (8.4
ohms) for all three average soil models (6, 7 and 8). For the reference soil model 8, which
represents the average of SE5 resistivity measurements, the calculated resistance is 8.3
ohms, i.e., about 17% higher than the measured 7.1 ohms. The detailed representation of
the earth anchor leads to 7.9 ohms, about 11% higher than the measured resistance. Therefore,
the agreement between measured and computed ground resistances is considered satisfactory.
10-39
100
100
COMPUTED RESULTS
so.
Model 8
90
Mode 1 6
Model 7
cr
SOIL MODEL
cr
a.
Ijll
70
h
CL
0
**»
O
---------------------- n
Pi
o
o
C
60
Mode 1
1
2
3
6
o
<
u.
CL
5
60
Pi(ft-m)
250
316
3V6
352
2So
h(feet)
P? Ul-m)
130
197
113
162.5
120
3.6
10.5
2.75
8.1
Leg Profi1e
MEASURED RESULTS
70_
«
*
Center Profile TVA 07
Center Profile TVA 05
+ Center Profile TVA 06
60-
o
50
111
HO
Model 7
Leg ProfiIe
(model 8)
$
c
o
4^
Model 8
Model 6
80-
80
Center Profi1e
Leg P rof 1 1 e
(model 6)
50_
Center Profile TVA 09
O Right-side Leg Profile TVA 08
4 Left-side Leg Profile TVA 08
Leg Profi1e
(model 7)
LU
H
o
a.
8.6
40“.
'6.6325il3m
r5- 3' | 296i1-'m
163.5n-m
Model 7
cr
<
30
LU
cr
<
Hi
20
20’
-
->---- '---- 1---- 1---- 1---- 1---- 1---- 1---- 1
20
60
60
80
100
'----
1---- ■
120
I
1
160
T-
I
160
0
DISTANCE FROM ORIGIN OF PROFILE (feet)
Figure 10.34
Computed Potential Profiles (Soil Models 1 to 5)
(Insulated Ground Wires)
I
|
20
I
j
60
I
J
60
i--------------- 1---------1---------------1------------<—-------T--------- ,-------------- 1--------1--------------- 1—
80
100
120
160
160
DISTANCE FROM ORIGIN OF PROFILE (feet)
Figure 10.35
Measured and Computed Potential Profiles
(Insulated Ground Wires)
COMPUTED RESULTS
(based on model 9)
Center ProfiIe
GTOWER Program
Leg Profi1e
Center Prof!le
MALT Program
Leg P rofi1e
MEASURED RESULTS
Profiles (TVA 05 to TVA 09)
SOIL MODELS
Profi1es
based on
Mode! 10.
Mode 1 9
Model
10
DISTANCE FROM ORIGIN OF PROFILE (feet)
Figure 10.36
Measured and Computed Potential Profiles Compatible Soil Models
(Insulated Ground Wires)
The measured and computed earth potential profiles are shown in Figure 10.35. Good agreement
exists between test and calculated results for the leg potential profile and for the portion
of the center profile which is close to the tower (1 to 10%). This agreeement decreases as
the distance from the tower increases.
Similar conclusions can be made regarding Figure 10.36, which shows the results of soil
models 9 and 10 (labelled as "compatible models" in Table 10.5). Note that the potential
values calculated which are based on models 9 and 10 are practically identical to those
obtained from soil model 6'. This result confirms that several equivalent soil models can be
used to suitably represent a grounding system buried in a complex soil structure. These
models however, can not be constructed arbitrarily and must be based on a sound analysis
of the resistivity measurements.
10-41
10.3.10 ANALYSIS OF THE TVA STAGED FAULT CURRENT MEASUREMENTS
At the time of the 500 kV staged fault tests near tower 130, the equivalent positive and
zero-sequence networks of the power system were as shown in Figure 10.37.
Z^^I+jJS.S
Z0=0.20+j0.61
TEST
SITE
1o=0.03+j1.19
LEGEND
----- Equivalent Circuit
____ Actual Circuit
Positive Sequence Impedance
Zg~ Zero Sequence Impedance
Z| > 950
NOTE: ALL IMPEDANCES ARE IN % ON TOO MVA
BASE VOLTAGE = 500 kV
Figure 10.37
Equivalent Positive and Zero-Sequence Network
A simple calculation predicts a fault current of approximately 14,000 A for a phase-to-ground
short-circuit near the test site. The fault contributions from Johnsonville and Cumberland
are 4,300 A and 9,700 A respectively. However, this useful calculation does not reveal the
distribution of fault current between the faulted tower and the overhead ground wires. In
many cases, this can be approximated using the simplified equations of Chapter 6. These
equations assume that the contribution to the fault from both sides of the faulted phase is
known. If this approximation leads to significant errors, computer programs such as PATHS
(see Appendix D) can be used to accurately determine the fault current distribution between
towers and overhead ground wires. In all cases however, it is necessary to determine the
self and mutual impedances of the transmission line conductors (faulted phase and ground
wires).
The analysis of the staged fault tests was carried out using the computer program PATHS
developed within the scope of this EPRI project. A description of the analytical basis of
this program is presented in Chapter 6.
Construction of the Equivalent Transmission Line Circuit
In order to analyze a faulted transmission tower using the computer program PATHS, it
is necessary to represent each of the faulted transmission line terminals by an equivalent
single power source or load. The transmission line may be single or double-circuit and may
10-42
carry a load current prior to the fault. The load current and its direction of flow are
described by the magnitudes and angles of the vectors representing the driving source voltages
at each terminal.
The equivalent circuit of the TVA 500 kV power network used for the staged fault tests is
shown in Figure 10.38. The impedances of the transmission line equivalent terminals were
determined from the data given in Figure 10.37. The positive, negative and zero-sequence
impedances were converted into phase quantities using the relation Zphase = (1/3)(Z1+Z2+Z0).
The transmission line conductor impedances were calculated by the computer program LINPA
described in Appendix A. The line parameter calculations were made assuming a 300 f2-m
average soil resistivity and the line geometry shown in Figure 10.39. This figure also gives
the computed line impedances for the equivalent 4-wire transmission line (obtained as a
result of phase bundle and ground wire reductions into equivalent single conductors). The
terminal ground resistances were selected as 0.1
in accordance with the test results which
show that the Johns onville and Cumberland station ground impedances are very low (below
0.1 Q). These resistances have negligible effects on the calculations of this study.
Figure 10.38
Equivalent Faulted Transmission Line Circuit
The analyses were initially carried out assuming that the source voltage at each end of the
transmission line was 500 kV (phase to phase). In fact, the transmission line was carrying
about 480 A from Cumberland to Johnsonville prior to the staged fault tests. Thus, other
PATHS runs were made, this time with the magnitude of the driving voltage at the terminals
equal to the measured values during the tests. The computed net current in the phase
conductors was 500 A, flowing from Cumberland to Johnsonville. Only small differences were
observed between the computed results obtained based on the equal and unequal voltage
assumptions, as shown by the values given in Table 10.8
The computations were made for the bonded ground wire condition, i.e., with the ground
wires solidly connected to tower 130 and to 20 other adjacent towers. The condition with
the ground wires insulated from the towers except at the towers where the ground wire
insulators flashed over was not analyzed because the flashovers occured randomly on each
side of tower 130. Consequently, it was not possible to determine from the test results
10-43
which towers were conducting current into ground. However, the test results indicated that
several towers outside the zone which was monitored (i.e., the zone defined by towers 125
to 135) did flash over. It is believed that the random nature of the location of the ground
wire insulator flashover is due to the wide variations in dielectric strength of the insulator
assembly. This strength is estimated to be 10 to 20 kV depending on the air gap distance
provided by the two clipped washers of the insulator [13].
10.1m
10.1m
Ground W1re
7 No.9 A1umowe1d
Phase Conductors
954 kC mi]
(1.5')
12.2 m
45/7 Strands
ACSR (RAIL)
B1 @ i ® B2
Phase B
Phase A
Phase C
MATRIX OF CONDUCTOR IMPEDANCES
(fl/mi le)
A
(A1 + A2 + A3)
B
(B1 + B2 + B3)
C
(Cl + C2 + C3)
A
0.131 + jl.136
B
0.093 + j0.584
0.129 + j1.136
c
0.091 + jO.501
0.093 + jO.584
0.131 + j1.136
D
0.092 + jO.558
0.092 +
j 0.570
0.092 + jO.558
Figure 10.39
0
(G1 + 02)
1.992 + j1.235
Transmission Line Conductor Impedances
The measurement results and the related computation results are summarized in Table 10.8
for the bonded ground wire condition, and in Table 10.9 for the insulated ground wire
condition. The measurement results were determined from the oscillograms which were
recorded at both station sites and at the test site during the four staged fault tests carried
out during the last week of the month of October 1981. These oscillograms are shown in
Figure 10.40, 10.41 and 10.42.
Figure 10.40 shows the oscillograms recorded at the test site near tower 130. As mentioned,
no meaningful oscillograph traces were obtained during test No. 1. Tests No. 2 and No. 3
were made when the overhead ground wires were solidly connected to the 20 towers adjacent
to tower 130 and during almost identical power system conditions. Therefore, one would
expect similar values of current in the same tower for each test. This is not the case, as
shown in Table 10.8. This table shows considerable difference between the measured and
calculated results at towers 134, 135, 133 and 131. Since the fiber optic cables used to
trasnmit the measurement signals from these towers to the recording site were repaired
after being cut and because good agreement exists between measured and calculated results
at all locations which did not experience fiber optic cable damage, it is concluded that the
measured currents at towers 132 to 135 for tests No. 3 and 4 are inaccurate, due to
equipment failure or calibration error.
10- 44
Table 10.8 gives a summary of the measured and calculated results assuming:
a- Equal source voltage magnitudes at Johnsonville and Cumberland (500 kV phase
to phase) and ignoring the 11.5 mH coils in series with the ground wires at these
stations.
b- Equal source voltage magnitudes with the 11.5 mH coils in place.
c- Unequal source voltage magnitudes at the terminals with the 11.5 mH coils
in place.
TEST
1
TEST
2
RES U L T S
COM P U T E D
MEASURED RESULTS
TEST THREE PHASE CIRCUIT
3
a**
I 135
(A)
-
-
-
i n1*
(A)
-
375
112*
301
I 133
(A)
-
-
225*
539
I 132
(A)
-
-
300*
I 131
(A)
750
T 129
(A)
128
423
b**
412
c**
SINGLE PHASE CIRCUIT
a**
435
315
-
569
-
-
b*
415
299
539
629
c**
438
316
571
665
893
627
297
537
627
664
-
750
840
842
892
-
843
-
-
913
915
969
-
916
969
(A)
825
-
1110
1113
1179
-
1114
1179
1 127
(A)
450
-
628
-
630
667
(A)
-
-
800
849
-
802
849
T 125
(A)
-
-
712
630
802
711
667
I 126
753
-
711
753
12410
12421
13150
-
12407
13139
10960
10973
11616
-
10959
11605
10274
10304
10968
10307
10916
I
TTotal Fault (a;
12375
12300
I PHGW
(a:
-
f
V Orthoqonal
tv;
-
*
10800
9125
t
V Parallei
(v;
-
*
10000
i no
(Ai
10800
1500
2380
1447
1451
1536
-
1452
1537
2400
2176
1973
2188
-
1893
2097
9264
8930
9240
9327
9340
10865
-
9329
10806
9000
8880
8880
9307
9320
10375
-
9309
10306
(A
6048
6050
6240
7920
7755
8216
7762
8595
(A
85
95
90
V Phase A“N (kV
308
-
IReturn 0HGW (a;
2A80
I Residua1;31 □ (A
1 Phase A
(A'
IN 500 kV
IN 161 kV
IReturn OHGVj
(A
-
1575
308
308
288
288
319
-
288
319
1100
900
725
690
731
-
705
643
IResIdual 3Io(A
3180
3200
3120
3085
3082
2278
-
3079
2335
I Phase A
(A
3720
3720
3600
3105
3102
2778
-
3099
2835
IN 500 kV
(A)
2200
2300
2300
2603
2601
2747
2628
2402
IN 161 kV
(A)
288
288
264
288
264
V Phase A-N (kV)
-
264
264
1200
264
-
Notes
■' Inaccurate (or unusable) test results
** Assumption a = equal terminal voltage /no 11.5
coils
Assumption b = equal terminal voltage/and 11.5 mH coils
Assumption c * unequal terminal voltages/and 11.5 mH coils
f This is the GPR of tower No. 130.
Table 10.8
Banded Ground Wires Test Results and Computations
The above three conditions were analyzed using computer program PATHS based on the
actual three-phase circuit and assuming a single-phase circuit (phases B and C ignored).
Minor modifications to the input data routines of PATHS were necessary to run some of
these cases. Detailed examination of Table 10.8 shows good agreement between measured
and calculated results. From an engineering point of view, computations based on the three
assumptions, a, b, and c are equivalent. The computed values of current returning from earth
to the transformer neutrals at both stations are consistantly higher than the measured values
while the reverse is true for the current returning through the ground wires. Therefore, it
is suspected that the mutual impedances between the phase conductors and the ground wires
are slightly higher than those used in the computations.
10-45
Particularly good agreement was obtained between measured and calculated ground potential
rise (GPR) of the faulted tower which is the reference value in the transmission line grounding
analysis. The measured potential rise values (shown in Table 10.8) were obtained with respect
to a reference point some 60 m (200 ft) away from tower 130. As already discussed in this
chapter, this situation leads to a measured GPR approximately 5% lower than the true value.
Therefore, the comparison should be made using a GPR 1.05 times the measured value.
MEASURED RESULTS
TEST
4
t
t
Notes
Table 10.9
I 135
(A)
I 13^
(A)
I 133
(A)
I 132
(A)
-
I 131
(A)
-
I 129
(A)
-
I 128
(A)
-
I 127
(A)
I 126
(A)
T 126
(A)
I Total Fault
(A)
13100
T 0HGW
(A)
11000
V Orthoaonal
(V)
13125
V Parallel
I 130
(V)
(A)
13750
2100
I Return 0HGW
(A)
2360
I Residual ; 3Io
(A)
9240
I Phase A
(A)
8928
IN 500 kV
(A)
5856
IN 161 kV
(A)
V(J) A-N
(kV)
I Return 0HGW
(A)
785
I Residual ; 31o
(A)
3240
I Phase A
(A)
3680
IN 500 kV
(A)
2250
IN 161 kV
(A)
1200
V4> A-N
(kV)
375*
-
750*
-
488**
_
90
308
264
* Inaccurate test results
** In previous tests no osciHogram traces were
obtained for tower 126. Therefore, this value
is questionable.
This is the GPR of tower No. 130.
Insulated Ground Wires Test Results
The measured results of test No. 4 corresponding to the insulated ground wire case, are
summarized in Table 10.9. Because the towers which conducted fault current to earth were
not identified, it was not possible to simulate the test using program GTOWER. However,
the measurement results indicate that the major difference between this and other tests is
in the increase in the proportion of fault current flowing through tower 130 (about 2000 A
compared to 1500 A in the other tests). Computer simulations show that as the number of
towers available to conduct current to earth decreases on each side of the faulted tower,
the magnitude of the faulted tower current increases (assuming that the equivalent source
impedance is several times higher than the tower impedance). This suggests that the number
of towers which conducted fault current into the earth during test No. 4 was less than
10 out of 20 towers.
10- 46
Consequently, it is necessary to apply safety factors to the computed current (assuming
continuously bonded ground wires) of a tower in a transmission line equipped with insulated
ground wires. Based on the above data, a safety factor of 1.5 is suggested. An alternate,
and perhaps more rigorous, method consists of computing the tower fault currents initially
assuming that flashovers only occurred at the two towers immediately adjacent to the faulted
tower. The calculations are then repeated, each time adding a new pair of towers, until the
computed voltage accross the ground wire insulation of the closest noncurrent-carrying
neighbouring towers becomes less than the minimum dielectric strength of the ground
wire insulators.
TOWER 135 CURRENT
1 p.u. = 2400 A
SPAN
GW CURRENT (135)
1 p.u. = k80Q A
TOWER 134 CURRENT
1 p.u. = 2400 A
TOWER 133 CURRENT
1 p.u. = 2400 A
TOWER 132 CURRENT
1 p.u. = 2400 A
TOWER 131 CURRENT
1 p.u. = 2400 A
TOTAL
TOTAL FAULT (lt)
1 p.u. = 2400 A
0HGW
CURRENT IN 0HGW
1 p.u. = 14400 A
TOWER 128 CURRENT
1 p.u. = 2400 A
TOWER 127 CURRENT
1 p.u. = 2400 A
TOWER 126 CURRENT
Ortho.
TOWER 130 GPR
1 p.u. = 40 kV
TOWER 130 GPR
Paral.
1 p.u. = 40 kV
SCALE:
1 p.u.
Figure 10.40
TEST No. 2
TEST No.
3
TEST No.4
(Ground Wires
Current and Voltage Oscillograms Measured at Tower Site
10- h7
Insulated)
TOWER
130
SITE
OHGW
p.u. = 800 A
Residual
1 p.u. = 2A00 A
500 kV Neutra
1 p.u.= 2400 A
161 kV Neutral
p.u. = 320 A
Phase A
1 p.u. = 2400 A
Phase A-Neutral
1 p.u. = 176 kV
1 p. u. 1 p. u.
TEST No.
1
TEST No. 2
SCALE
Figure 10.41
TEST No. 3
TEST No. 4
{Ground Wires Insulated)
Current and Voltage Oscillograms Measured at Cumberland Station
10- 48
OHGW
Residua
1920 A
500 kV Neutral
1 p.u. = 960 A
161 kV Neutral
NOT RECORDED
NOT RECORDED
1 p.u. = 960 A
Phase A
1 p.u.
1200 A
Phase A-Neutral
p.u.= 132
kV
TEST No.
p.u.
1 p.u.
SCALE
Figure 10.42
TEST No. 2
TEST No. 3
TEST No. k
(Ground Wires Insulated)
Current and Voltage Oscillograms Measured at Johnsonville Station
10- bS
10.4 THE OH/AEP 500/765 kV TRANSMISSION LINE MEASUREMENTS
I
In April and May 1979, the American Electrical Power (AEP) conducted a series of staged
fault tests on the Kammer-Marysville 765 kV line. A total of four towers were faulted. At
each of the four towers, two guyed-vee and two lattice structures, measurements were made
of fault currents, earth components of fault currents and earth potential profiles. Ontario
Hydro (OH) participated with AEP in the earth potential profile measurements. Later, a
series of tests was also performed on an isolated 500 kV lattice tower adjacent to Ontario
Hydro's outdoor high voltage test facility at Kleinburg, Ontario.
These measurements have been described and discussed in detail in a recent comprehensive
paper [7]. Only the key aspects of the measurements, including a comparison of the test
results with analytical computations, are presented in this section. An interesting feature of
the measurements is a study of the effectiveness of a special ground potential control ring
(GPC) installed as part of the tower grounding, to reduce step and touch voltages.
10.4.1 THE AEP MEASUREMENTS
Figure 10.43 shows the AEP Kammer-Marysville 765 kV transmission line and the
locations of the four test sites. Two single phase to ground faults were staged at each tower
while the Kammer station was open-ended during the tests. The fault current fed from
Marysville station during each fault is given in Figure 10.43.
Lattice Towers
Guyed-Vee Towers
>
4860 A
6330 A
2645 A
2650 A
u~\
SO
4920 A
6424 A
2645 A
2400 A
_l
Tower
>
I
515
T t
^0
I
LU
_J
486
36
1
13
s
24 Km :
' (15 mi}':
,
56
Km
(22 mi )
230 Km
“(143 mi )
237 Km
(147 mi
244 Km
(151
Figure 10.43
mi)
The AEP 765 kV Test Sites (Redrawn from [7])
Figure 10.44 shows a plan view of the guyed-vee towers and the cross section of the GPC
ring installation around guy anchor D of tower 13. This figure also shows the directions of
the earth potential profiles B, D and E measured at tower 13. Only the D potential profile
was measured for tower 36 which was not equipped with the GPC ring.
10-50
ORIGIN
OF PROFILE
Profile B
^ Profile E
Kammer
Marysvi11e
5-5 m
ORIGIN
OF PROFILE
Tower
Base
TOP VIEW
Tower
Guy
Anchor
Wi re
Profile D
SIDE VIEW
Connecting Spoke
1.8m Diameter
Guy Anchor
Diameter No. k
Copper Ring
Figure 10.44
Plan View of Guyed-Vee Towers (Redrawn from [7])
Several resistivity measurements were taken at various locations near the towers prior to
and following the tests. Significant variations in the measured values along various traverses
were observed. These variations are probably a result of the hilly terrain at the towers.
Therefore, the average apparent soil resistivities of Figure 10.45 were used to determine an
equivalent two-layer soil model at each tower site.
Computer program RESAP [16] was used to perform the resistivity computations. RESAP is
the more general SES computer program from which RESIST was derived. The computed
characteristics of the equivalent soil models, also given in Figure 10.45 were used by the
computer program MALT [15] to calculate the tower resistance and the earth potential
profiles. MALT is a general SES grounding program used as a reference to develop the
program GTOWER. The results of the measurements and MALT computations are shown in
Table 10.10 and in Figures 10.46 and 10.47. Because the tower grounding system consists
essentially of horizontal and vertical elements, the computation results of MALT and GTOWER
are practically identical.
10-51
Pi = 60 Q-m
P2 = 250 Q-m
h
= 3 ni
Towe r 1 3 ____
Tower 36
PROBE SPACING
Retire 10.45
(m)
Average Apparent Soil Resistivities Around Guyed-Vee Towers
(Redrawn from [7])
TOWER
No.
RESISTANCE (fi)
Measured
Computed
13
2.3
2.34
36
2.0
2.08
Table 10.10
Guyed-Vee Tower Resistances
Very good agreement between computed and measured resistances was obtained for both
towers. Good agreement between the computed and measured potential profiles is evident
except in profile B of tower 13. The differences between measured and computed values
are in the order of 10% and are probably a result of the soil structure at the profile B
location which was significantly different from the average soil structure assumed in the
computations.
The four staged fault tests at towers 13 and 36 indicated that only 20 to 30% of the total
fault current entered the tower ground. Most of the fault current flowed in the ground wires
which were connected to the faulted tower.
The measurements conducted at the four-legged lattice towers 486 and 515 lead to similar
observations as at the guyed-vee towers. However, the agreement between computed and
measured values, rated between good and acceptable for most results, is poor for 2 of the
8 potential profiles measured (discrepancy of 20 to 50%) and for the tower resistance values
when the GPC ring is not connected to the tower.
10-52
Measurements
C£
o
a.
Measurements
.MALT Computations
L.
<D
§
Profile D
o
d-P
Profile E
<
O
Q.
Profile B
X
Iq;
<
UJ
LATERAL DISTANCE (m)
Figure 10.46
100 .
Earth Potential Profiles for Tower 13 (Redrawn from [7])
MALT Computations
Measurements
Profile D
LATERAL DISTANCE
Figure 10.47
(m
Earth Potential Profile for Tower 36 (Redrawn from [7])
In all cases however, the measurements and computations show that when the GPC ring (see
Figure 10.48) is connected to the latttice tower, the reduction in touch voltage (compared
to the unconnected case) is substantial.
10-53
GPC Ring
(actual
Tower
Foot 1ng
No.
GPC
4 Copper
Ring
omputer Mode 1}
GPC Ring
TOP VIEW
— Ground Rod
Potential
Profile B
Potentia 1
Profile C
\ Potentia
Potent I a 1
Profile A
SIDE VIEW
Figure 10.48
Plan View of 765 kV Lattice Tower Footing (Redrawn from [7])
10.4.2 THE OH MEASUREMENTS
The AEP measurements clearly indicate that to achieve good agreement between measured
and computed values, the soil structure at the test site must be accurately determined and
the measurements must be performed under controlled conditions insensitive to or isolated
from interference from energized transmission line conductors and other sources of electrical
noise.
This objective was met by performing a series of tests on an isolated 500 kV lattice tower
situated approximately 300 m from Ontario Hydro's outdoor high-voltage test facility at
Kleinburg. The legs of this tower are insulated from the tower grounding and the concrete
reinforcing bars by insulating plates, as shown in Figure 10.49. The GPC ring of No. 4
copperweid wire and the ground rods were bonded to the steel.
INSULATOR
WINDOW
TYPE CT
Figure 10.49
500 kV Tower Leg at Kleinburg (Courtesy of Ontario Hydro)
10- 5k
The GPC ring and the four ground rods were electrically connected to the steel at each leg
by removable bonding straps. This grounding scheme, illustrated in Figure 10.50, permitted
measurement of the tower resistance and earth surface potentials for various grounding
arrangements. Thus, it was possible to examine the contributions from the concrete pier
rebars, ground rods and GPC ring either alone or in combination.
Earth surface potential measurements were made using earth contact pads weighted down
by 15 kg (33 lb) concrete cylinders as shown in Figure 10.51.
GPC Ring
(Actual)
Potential
Prof!le
TOP VIEW
GPC Ring
(Computer Model
Tower Footing
------
3m Ground Rod
Connecting
St rap
SIDE VIEW
Figure 10.50
Plan and Cross Sectional Views of the 500 kV Tower Footing
(Redrawn from [7])
Figure 10.51
Earth Surface Potential Measurement Pads
(Courtesy of Ontario Hydro)
10-55
Core drillings in the vicinity of the test tower revealed that the soil is clay to 30 m (98
ft) depth. Computer analysis of the apparent resistivity data, shown in Figure 10.52, yielded
a two-layer soil model consisting of a 30 Q-m resistivity top layer, 15 m (49 ft) deep, and
a 100 . fi-m resistivity bottom layer. This two-layer soil model was used to conduct the
analyses with the computer program MALT.
100
.
Computations
(RESAP)
Measurements
PROBE SPACING (m)
Figure 10.52
Resistivity Measurements at Kleinburg Test Site (Redrawn from [7])
The measurement and computation results for the six different grounding arrangements are
summarized in Table 10.11 (tower ground resistances), and in Figures 10.53 to 10.55 (normalized
earth surface potentials along the profile shown in Figure 10.50).
GROUNDING
ARRANGEMENT
RODS
ONLY
Measured
Resistance
(A)
2.77
1.06
1.41
0.966
1.33
0.97
Computed
Resistance
(A)
2.78
1.07
1.61
1.03
1.56
1.00
Table 10.11
RODS AND FOOTING REBAR FOOTING REBAR RODS AND
RODS, REBAR
GPC RING CAGES ONLY
AND GPC RING FOOT 1NG REBAR AND RING
Kleinburg Tower Ground Resistance
10 -56
Ground
Rod
Location
Ring
Location
Rods Only
Rods + GPC Ring
Measurements
STANCE FROM ORIGIN OF PROFILE
Figure 10.53
(m)
Earth Surface Potential Profiles for Ground Rods
and GPC Ring (Redrawn from [7])
Ground
Location
Location
___ Rebar Only
------ Rebar + GPC Ring
.
Measurements
DISTANCE FROM ORIGIN OF PROFILE (m)
Figure 10.54
Earth Surface Potential Profiles for Rebar Cages
and GPC Ring (Redrawn from [7])
The computations take into account the entire grounding configuration as illustrated in Figure
10.50. In computing the tower grounding performance for the ground rods alone, the rebar
cages and the GPC ring are consi dered as in situ metallic elements not bonded electrically
to the ground rods. This was necessary because these elements, especially the rebar cages,
act as a current path to the ground rods and noticeably influence the measured results (see
the discussions and conclusion at the end of [7]).
10-57
Although not shown in the figures, the potential profiles were measured and computed over
a lateral distance of 24 m (79 ft). Agreement between measurements and computations is
remarkably good over the entire profile. Similar excellent agreement also exists between
measured and computed ground resistances of all grounding configurations.
Ground
cc
CL.
Location
o
4-
O
<3^
Location
---------•
Rods + Rebar
Rods + Rebar + GPC Ring
Measurements
<
O
Q_
<
UJ
DISTANCE FROM ORIGIN OF PROFILE (m)
Figure 10.55
Earth Surface Potential Profiles for Ground Rods With Rebar Cages
and GPC Ring (Redrawn from [7])
The success of this measurement/computation program is due to:
•
Accurate measurement of the apparent soil resistivity at the test site and derivation
of a suitable equivalent two-layer soil model.
•
Absence of electrical interference and noise.
•
Good test procedures and appropriate measuring equipment.
•
Detailed knowledge and representation of the metallic elements forming the tower
grounding system.
In bonding the GPC ring to the tower, the touch voltage for a person standing 1 m (3 ft)
away from the tower leg decreases from approximately 60% of the tower potential rise
in the "rods only" case to about 20%. However, since the tower potential rise, assuming
constant current, also decreases when the GPC ring is bonded to the tower (because the
ground resistance has decreased), the actual reduction of the touch voltage is even greater.
The authors of the OH-AEP test program also conducted a sensitivity analysis using the
computer program MALT, to determine the influence of the fundamental parameters on the
grounding performance of a 500 kV lattice tower equipped with one or two GPC rings. Their
main conlclusion was that it is possible to reduce the touch voltages to less than 5% percent
of the value which exists in the absence of the GPC rings.
10- 58
10.5 THE EDF ROCXET-TRIGGEERED LIGHTNING MEASUREMENTS
Electricite de France (EDF) has recently completed an extensive lightning measurement
program. This program started in 1973 and was still active in 1981 [8,9,10]. During this eight
year program at the Saint Privat d'Allier test site in France, 94 lightning flashes were
triggered by means of the rocket-wire method described by Newman [17]. The program
included a wide variety of measurements intended to gain further understanding of the
lightning process and its effect on the environment, including power transmission lines. In
particular, a series of measurements were conducted to determine the response of a
transmission line tower and its grounding system to direct lightning strokes.
The principal facilities at the experimental station are a transmission line tower supporting
a rocket-launching platform at the top (see Figure 10.56) and a ground level launching area
(see Figure 10.57).
Figure 10.56
Tower Structure at St. Privat d'Allier
(Courtesy of Electricite de France)
10-59
I
Figure 10.57
Ground Level Rocket-Launching Area
(Courtesy of Electricite de France)
The tower structure is 26 m (85 ft) high and is mounted on insulators (see Figure 10.58).
This tower is equipped with appropriate measuring equipment to monitor the potential rise
of the structure and the grounding system potential rise during direct lightning strokes.
During 1977 and 1979, it was possible to measure the lightning performance of three different
tower grounding electrode configurations (see Figure 10.59):
•
A 1 m (3 ft) radius hemisphere
•
A 1 m x 1.5 (3 ft x 4.5 ft) double loop electrode.
•
A 6 m (20 ft) long vertical ground rod.
A surge generator was used at another test location, to measure the surge characteristics
of three additional electrode configurations, in order to supplement the rocket triggered
lightning measurements [9] (see Figure 10.59).
The measurement results (current and voltage magnitudes as a function of time) were
translated into the frequency domain using a Fast Fourier Transform algorithm adapted to
lightning surges. This approach has the advantage of showing the response of the tower and
its grounding system as a function of frequency and can be used to predict the lightning
performance of the tower for any current waveform once the current is broken down into
its harmonic components.
<
10 -60
Figure 10.58
Tower Base and Insulator Supports
(Courtesy of Electricite de France)
HORIZONTAL CONDUCTOR
GROUND ROD
HEMISPHERE
Xi
F
f;
"7
J
F
1m
X (3.3')
,1
w
0.6m
(2')
i
15m
(50')
TWO-BRANCH STAR
Figure 10.59
!l1l|]
TTFTT
IfP
—T"
1 .Sm X
----------------^a.
... . ...=3:
(5') y
11m
*
nn
/ (3.3')
DOUBLE-LOOP
GRID (Depth = 0.4m)
Electrode Configuration Subjected to Surge Tests
(Redrawn from [10])
10 -61
10.5.1 EQUIVALENT CIRCUIT OF THE TOWER STRUCTURE
At low frequencies, the impedance of a tower structure can easily be neglected with respect
to its footing ground resistance. At very high frequencies or for surge and lightning currents,
the structure may represent a significant portion of the overall impedance.
There is extensive literature on the lightning response of transmission line towers.
Unfortunately, no consensus has been reached concerning the optimum representation of a
tower structure. There are two basic concepts; the first one, often used to establish the
rate of failure of a transmission line, considers the tower structure as a surge impedance;
the second approach lumps the tower structure into a localized self-inductance.
The EDF lightning measurements support the localized self-inductance concept as can be
seen from Figure 10.60, which gives the tower structure impedance as a function of frequency.
This figure shows that the tower structure inductance is in the order of 3.5 mH, a value
about half the theoretical value calculated using the formula [18]:
L = ^
(10-3)
where
L is the inductance (mH)
h is the tower height (m)
r is the equivalent radius of the tower base (m)
for h = 26 m, r = 2 m, the tower inductance L is 7.6
mH.
Measured
(26 m Tower)
FREQUENCY (Hz)
Figure 10.60
Tower Structure Impedance (Redrawn from [10])
The EDF measurements were obtained during actual lightning strokes and were measured
with sophisticated equipment and great care. Thus, solid evidence in favor of the localized
inductance concept has been obtained. However, more measurements must be conducted for
other tower structure configurations and heights, in order to eliminate any doubt concerning
the validity of this concept.
10-62
10.5.2 EQUIVALENT CIRCUIT OF THE GROUNDING ELECTRODES
No soil ionization phenomena (soil breakdown due to excessive potential gradients) were
recorded during rocket-triggered lightning tests at the tower site for current peaks in the
order of 20 kA. Since the tower structure is not equipped with ground wires as in most
transmission lines and is therefore isolated, it can be concluded that the ionization effect
can be ignored in most cases involving high voltage lines and lightning currents in the order
of 20 kA crest or less.
Horizonta1 Conductor
Double Loop
Hemisphere
FREQUENCY (Hz)
Figure 10.61
Ground Impedance of Hemispherical, Double Loop
and Horizontal Electrodes (Redrawn from [10])
Ground Rod
Two-Branch Star
FREQUENCY (Hz)
Figure 10.62
Ground Impedance of a Ground Rod and a Two Branch Star
(Redrawn from [10])
10-63
The measurement results, shown in Figures 10.61 and 10.62, indicate that except for the
hemispherical electrode, the grounding electrodes exhibit an inductive component which
become noticeable at very high frequencies, generally above 100 kHz.
The EDF results also show that the impedance of the ground electrodes is a rising function
of frequency and there is no indication that an asymptotic value is reached as the surge
impedance concept suggests.
From the ground rod measurement results it is concluded that concentrated electrodes
can be represented by a resistance in series with an inductance. This representation is valid
for electrode dimensions of less than 5 to 8 m (16 to 26 ft). For a 6 m (20 ft) ground rod
the measured inductance was in the order of 5 txH.
For ground conductors 10 m (30 ft) and more, in length, the ground impedance increases as
the square root of the frequency at high frequencies. This indicates that the ground electrode
can be modelled by a line with distributed constants [10]. The ground impedance can be
approximated from:
Z = /R(R + jZTrfl)
(i°-4)
where
Z is the ground impedance (ohms).
R is the low frequency resistance of the electrode (ohms).
L is the self inductance of the electrode (Henrys).
f is the frequency (Hertz).
The measurements indicated that the self inductance of a linear ground electrode conductor
is in the order of 1.2 mH per meter.
REFERENCES
1 - F. Dawalibi, D. Mukhedkar, "Optimum Design of Substation Grounding in Two-Layer
Earth Structure - Part I, Analytical Study". IEEE Transactions, Vol. PAS-94, No. 2, March/April
1975, pp. 252-261.
2 - F. Dawalibi, D. Mukhedkar, "Transferred Earth Potentials in Power Systems", IEEE
Transactions, Vol. PAS-97, No. 1, January/February 1978, pp. 90-101.
3 - F. Dawalibi, D. Mukhedkar, D. Bensted, "Measured and Computed Current Densities in
Buried Ground Conductors". IEEE Transactions, Vol. PAS-100, No. 8, August 1981, pp.
4083-4092.
4 - Michael A. Sargent, Mat Darveniza, "Tower Surge Impedance", IEEE Transactions on
Power Apparatus and Systems, Vol. PAS-88, No. 5, pp. 680-687.
10-64
5 - F. A. Fisher, J. G. Anderson, J. H. Hagenguth, "Determination of Lightning Response
of Transmission Lines by Means of Geometrical Models", AIEE Transactions on PAS, February
1960, pp. 1725-1735.
6 - P. C. Buchon, W. A. Chisholm, "Surge Impedance of HV and EHV Transmission Towers",
Report No. 78-71, Canadian Electrical Association.
7 - E. A. Cherney, K. G. Ringler, N. Kolcio, G. K. Bell, "Step and Touch Potentials at
Faulted Transmission Towers", IEEE Transactions on PAS, July 1981, Vol. PAS-100, No. 7,
pp. 3312-3321.
8 - R. Fieux, P. Portal, "La Station Experimentale de St. Privat d'Allier Resultats Generaux,
Caractbristiques des Coups de foudre Declenchbs". E. D. F. Bulletin de la Direction des
Etudes et Recherches - serie B, Reseaux Electriques, Matiriels Electriques, No. 4, 1979, pp.
39-63.
9 - R. Fieux, P. Kouteynikoff, F. Villefranque, "Measurement of the Impulse Response of
Grounding to Lightning Currents", Electricite de France, Proc. of the 15th Europeen Conf.
on Lightning Protection, Vol. 2, pp. K440-K450, Uppsala, Sweden.
10- P. Kouteynikoff, "Reponse Impulsionnelle des Prises de Terre aux Courants de Foudre"
CIGRE paper 121-03, 1981.
11- A. J. Pesonen, "Effects of Shields Wires on the Potential Rise of HV Stations" Offprint
from SAKHO - Electricity in Finland, 1980, No. 10, pp. 305-308.
12- Janos Endrenyi, "Analysis of Transmission Tower Potentials During Ground Faults", IEEE
Transactions on PAS, Vol. PAS-86, No. 10, October 1967.
13- A. C. Pfitzer, G. M. Wilhoite, "Tennessee Valley Authority's 500 kV System - Transmission
Line Design", IEEE Transactions on PAS, Vol. PAS-85, No. 1, January 1966, pp. 28-35.
14- G. V. Keller, F. C. Frischknecht, "Electrical Methods in Geophysical Prospecting" Pergamon
Press 1977, (Book).
15- F. Dawalibi, "User Manual for Program MALT", Safe Engineering Services Ltd., Montreal,
1979.
16- F. Dawalibi, "User Manual for Computer Program RESAP", Safe Engineering Services
Ltd., Montreal, 1979.
17- M. N. Newman, "Use of Triggered Lightning to Study the Discharge Channel" Problems
of Atmospheric and Space Electricity, Elsevier, New York, 1965.
18- R. Fieux, "RQle des cables de Garde sur les lignes 63/90 kV", Note HM/72-4404,
1980, Electricite de France.
19- R. H. Golde, "Lightning", Vol. 2, Academic Press 1977 (Book edited by R. H. Golde).
20- John R. Cars on," Wave Propagation in Overhead Wires With Ground Return", Bell System
Technical Journal, October 1926.
10-65
I
CHAPTER 11
SURVEY OP NORTH AMERICAN
TRANSMISSION LINE GROUNDING PRACTICES
11.1 OBJECTIVES OF SURVEY
As a very important part of a comprehensive examination of transmission line grounding
methods, a survey was undertaken to determine the practices and attitudes of North American
power utility companies regarding the grounding of high voltage transmission lines. The
questionnaire was designed to investigate specific quantitative standards used in the
design of transmission line grounding systems as well as to examine the general attitudes
and concerns of power utilities on the subject. These inputs were solicited to assure that
the results of the work being carried out would adequately reflect the concerns, objectives
and experience of the utilities for whom the work is being undertaken through EPRI.
The questionnaire addressed problems related to lightning and 60 Hz fault conditions and
examined safety and operating reliability considerations in the design of grounding systems.
Questions were asked which would permit grounding system design practices to be related
to system voltages, keraunic levels, failure rates, and perceived hazard levels associated
with ground faults.
Specific details regarding measurement, construction and maintenance procedures were
surveyed with the objective of providing useful feedback to utilities on how their practices
compare with others and to guide in the adoption of recommended standards in these areas.
11.2 SURVEY DISTRIBUTION
The survey questionnaire was distributed to a total of 162 power utilities in the United
States and Canada. The utilities were selected from the Electrical World Directory of Electric
Utilities and from lists of utilities provided by EPRI.
Only those utilities identified as having high voltage transmission lines rated 115 kV or higher
were selected for participation in the survey.
A total of 88 completed or partially completed questionnaires were received. In some cases,
one response was identified as representing several companies under common ownership. Thus,
the results represent the input of somewhat more than 88 utilities. The distribution of
utilities responding to the questionnaire according to total number of employees is shown in
Figure 11.1. It can be seen that the greatest portion of respondents (25%) were utilities
with between one and two thousand employees and that only 6% of the responding utilities
had fewer than one thousand employees.
11-1
30
.
30
25 -
25
<y>
20
15
o
O'
10
5
0
FROM:
TO:
0
0.5
0.5
1
1
2
2
3
3
5
5
7
7
10
10
15
15
30
TOTAL NUMBER OF EMPLOYEES (IN THOUSANDS)
Figure 11.1
Size of Utilities which Answered the Questionnaire
In most cases, the questionnaire was sent to the manager of Transmission Engineering or
the equivalent position within the utility. A list of participating organizations is contained
in Appendix E.
11.3 RESPONSE TO THE SURVEY
As indicated, a total of 88 questionnaires, representing approximately 95 utilities were
received. In many cases, the questionnaire was only partially completed, presumably because
the respondent did not understand the question or had no involvement with the specific topic
being questioned. Additional comments were provided on at least one subject by 77 utilities,
and 36 utilities provided reference documentation such as internal standards, reports, design
guides, or drawings.
Occasionally, the response to a particular question by a respondent was ambiguous or in
obvious conflict with the response to another question. In these cases, an attempt was made
to resolve the ambiguity by analyzing the data further or seeking clarification from other
sources.
The comments received provide an excellent source of background information on most topics
covered in the survey, and several additional topics or points of view not specifically addressed
in the questionnaire.
11.4 QUESTIONNAIRE FORMAT
The questionnaire was divided into six sections, covering various aspects of transmission line
grounding practices. Section I covered general aspects including design standards, performance
objectives, costs and perceptions of the relative importance of grounding. The second section
dealt with pre-cons true ti on measurements and was intended to determine the extent to which
utilities carry out field measurements related to transmission line grounding and the techniques
used in such measurements.
11-2
I
Section III dealt with engineering design aspects and questioned the extent of calculations
performed relating to grounding variables used in the design equations, basic hypotheses, and
the degree of satisfaction with calculation techniques. This section was subdivided to consider
both lightning and 60 Hz fault conditions.
Section IV addressed safety considerations and the extent to which calculations and/or
measurements are carried out to evaluate the safety of grounding systems. The variables
used in design calculations for safety were surveyed, as were the attitudes of utilities
regarding hazard levels associated with transmission line grounding systems.
Section V covered construction, measurements and maintenance and surveyed specific details
of ground electrode construction materials and techniques, and subsequent testing and
maintenance of installed grounding systems.
The final section dealt with current practice and design standards of utilities for transmission
line grounding systems. Skywire usage, structure ground impedances and the important question
of failure rates due to lightning were surveyed.
Most questions were of the multiple choice or single word (or number) answer type. Comments
and reference documentation were requested in most sections.
11.5 ANALYSIS OF THE RESPONSES
The responses to the questionnaire were initially tabulated by question number and the
percentage of respondents in each reply category determined. Since most questions were not
answered by all respondents, each percentage was determined as a percent of those answering
the question, as well as a percentage of total respondents.
In order to gain insight into the significance of grounding practices and transmission line
performance, an attempt was made to correlate transmission line failure rate data with
various design practices and standards. This is discussed in Section 11.5.6.
The important results of the six sections of the questionnaire are summarized below.
11.5.1 GENERAL (SECTION I OF SURVEY QUESTIONNAIRE)
From the responses to the questions in this section, it is apparent that power system
performance under the influence of lightning disturbances is the overiding concern of utilities
when transmission line grounding systems are designed. Most utilities (94%) considered
grounding to be important and 62% of those considered it to be of fundamental importance
with respect to the overall performance and reliability of transmission systems.
Grounding represents less than 5% of the design and construction budgets of most utilities
although 13% reported that construction costs directly related to grounding accounted for 5
to 10% of the total construction budget. Only one utility reported engineering costs related
to grounding in the 10% to 15% range, the majority put engineering costs at less than 5%.
The understanding of transmission line grounding problems was considered to be satisfactory
by 47% of the utilities surveyed and less than satisfactory by 10%. The remainder considered
their understanding to be either good or very good.
11-3
11.5.2 MEASUREMENTS (SECTION II)
The survey investigated field measurement practices of utilities in two areas; pre-design and
post-construction. This section covered pre-design activities although some inconsistencies in
the answers to this section suggest that this may not have been understood by most
respondents. For example, only 36% answered "yes" to question 1, which asked whether or
not field measurements were conducted prior to construction while the remaining questions
in this section dealing with measurement techniques were answered by most respondents.
Thus, these responses were interpreted in the context of all transmission line related
measurements and not measurements related only to transmission line structure grounding
design.
Approximately one half of the responding utilities conduct soil resistivity measurements,
primarily for the purpose of estimating the resistance of structure grounds or to categorize
the soil structure in order to apply appropriate standard grounding arrangements. By far the
most common technique used for resistivity measurement is the Wenner method using a
Megger type instrument (null balance or direct reading). The problem of interpretation of
earth resistivity measurements is handled using engineering judgment or design charts by all
but two of the responding utilities who used more elaborate theoretical methods employing
computers. Only 18% of the respondents used field data from geological surveys to assist
in the interpretation of resistivity data.
All but two of the utilities conducting earth resistivity measurements develop a uniform soil
model from resistivity data. One utility uses a two-layer soil model and one uses an
expotentially varying soil model.
Eighty nine percent of the utilities responding to this section consider their field measurement
procedures and interpretation techniques to be satisfactory or better, 11% consider them
less than satisfactory. 17 utilities provided comments on the type of improvements required
to make field measurements more useful and reliable. These comments are summarized in
Section 11.6.
11.5.3 ENGINEERING (SECTION III)
Seventy five percent of the responding utilities indicated that they carry out conceptual
design calculations related to transmission line grounding, including lightning and 60 Hz fault
conditions. Fourty eight percent of all utilities indicated that 60 Hz fault calculations were
carried out. Computers or programmable calculators are used by 33% of those who carry
out design calculation for transmission structure grounds. As suggested in the section dealing
with measurements, most utilities use an equivalent uniform soil resistivity model in these
calculations. Ground rods are the most common grounding electrode assumed in the calculations.
The distribution of fault current between a transmission structure and skywires assumed by
utilities in their 60 Hz fault calculations varied considerably. While 32% of those carrying
out calculations assumed all 60 Hz current to flow in the structure, the remaining utilities
assumed distributions as shown in Figure 11.2.
Sixty four percent of all responding utilities indicated that design calculations were carried
out related to lightning conditions on transmission lines. Most calculations include the soil
resistivity and structure grounding leakage (dc) resistance in the calculations, while parameters
such as soil permittivity, permeability and impulse breakdown gradient are seldom used.
11-4
5
5
4
(/l
3
hu.
o
cc
LU
CQ
2
2
1
. 1
X
z 0
0
0
10
20
30
40
50
60
FAULT CURRENT IN TOWER (IN
Figure 11.2
70
%.
80
90
100
)
Distribution of Fault Current Between Structure and skywires
Keraunic levels are used by 95% of those utilities involved in lightning condition calculations,
while the detailed electrical parameters of structures and structure footings are used by
a relatively small number of utilities. As expected, all of the utilities who carry out
engineering calculations for lightning conditions do so in order to estimate transmission line
rates of failure. Estimating charts and empirical formulas are the principal tools used to
carry out these calculations.
The basic hypotheses used in rate of failure calculations for lightning conditions vary
considerably except for soil structure, which is considered uniform by more than 90%.
The structure impedance is ignored by 40% of these utilities; reflections and refractions at
neighbouring structures are ignored by 47%; mutual coupling effects between phase and
ground wires are ignored by 42%, while the increased mutual coupling effects of corona are
ignored by 56% of the utilities in their lightning condition calculations.
Most utilities who carry out 60 Hz and lightning calculations consider their methods to be
satisfactory or better. Only two utilities considered these to be unsatisfactory. Fifteen
utilities provided comments regarding improvements that could be made to make their
calculation methods more accurate. These comments are summarized in Section 11.6.
11.5.4 SAFETY CONSIDERATIONS (SECTION IV)
From the responses to this section, it is apparent that most utilities do not consider safety
around transmission line structures to be a serious problem. About 75% of all utilities
indicated that no investigations were conducted to determine public or personnel safety
around transmission line structures for 60 Hz fault or lightning conditions. Hazard levels
were calculated according to the IEEE Guide 80 standard in most cases.
Sixteen percent of the respondents investigate the safety of structure grounding at all
transmission structures, while another 13% conduct investigations in high exposure areas.
Fourty six percent do not conduct any safety investigations related to structure
grounding.
In comparing the hazard levels within substations to those due to 60 Hz faults on transmission
structures, out of the 68 utilities responding to this question, 73% believed the hazard level
associated with transmission structure to be lower or significantly lower. Seven percent
considered the hazard due to transmission structure faults to be greater, with the remainder
considering the two hazard levels comparable.
Seventy five percent of the responding utilities considered their approach to safety at
transmission line structure to be acceptable and 15% considered it unacceptable. Ten percent
did not reply to this question.
11-5
No utilities indicated that they were aware of any accident (fatal or otherwise) caused by
60 Hz faults on transmission structures. The consensus was that hazards associated with
transmission structure grounding would remain constant or increase somewhat over the next
ten years. The primary reasons given for increases in the hazard level were, higher voltage
and fault capacity systems and increased exposure.
Twenty utilities provided comments on corrections or improvements they believed necessary
to increase safety around transmission structures. These comments are summarized in Section
11.6.
11.5.5 CONSTRUCTION / MEASUREMENTS / MAINTENANCE
This section contained several questions relating to types and sizes of materials used in the
construction of structure grounding electrodes. These results can be examined in the detailed
response tabulation.
Sixty four percent of the utilities indicated that field measurements are conducted at all
structures after installation, to check the footing resistance. These measurements are, in
almost all cases, used to initiate grounding system modifications if the resistance is inadequate.
Thirty nine utilities provided estimates of the additional costs typically incurred by such
modifications. These data are summarized in Figure 11.3.
ADDITIONAL COST
Figure 11.3
Additional Cost of Grounding
One utility out of the 88 respondents indicated that staged fault tests were always conducted
after line construction, while 85% indicated that staged fault tests are never conducted.
Structure grounds are checked at some time by 75% of the utilities. Mechanical failures due
to vandalism, accidental damage and corrosion were identified as the primary reasons for
periodic or occasional grounding checks.
Figure 11.4 illustrates the distribution of the estimated lifespan of ground rods and counterpoises
provided by 53 utilities. The average of the estimate for each is around 30 years.
11-6
0
10
20
30
<t0
50
70
80
USEFUL LIFE (IN YEARS)
Figure 11.4
Average Useful Life of Ground Conductors
Most utilities keep records of the type and location of tripouts or protection system
malfunctions. The principal cause of transmission line failure is identified as mechanical
damage.
As to the quality of their construction procedures, measurement techniques
programs, most utilities considered these to be satisfactory or good. There
noticeable shift downwards in perceived quality from construction to
maintenance. From this and subsequent comments summarized in Section
that maintenance is considered to be the most neglected area.
and maintenance
was, however, a
measurement to
11.6, it is clear
11.5.6 TYPICAL DESIGN AND DATA (SECTION VI)
This section surveyed the application of ground wires, grounding electrode configurations,
desired ground resistances and failure rates. Ground wires, grounded at each structure and
connected to the substation ground are employed by a large majority of utilities on all 100
kV class and higher systems. Two utilities, only partially install ground wires on 500 kV and
700 kV systems, and one utility makes no use of ground wires on 300 kV class systems.
Twenty percent of the utilities partially install ground wires on 100 kV class systems.
The results of the questions concerning structure grounding arrangements, desired ground
resistance, and failure rates are summarized in the accompanying Figures 11.5, 11.6 and
11.7. The final question concerned the lightning failure rates of single versus double circuit
lines and showed that a slight majority (58%) of those who answered this question did not
consider double circuit line to be more failure prone.
The utilities were grouped into those reporting maximum structure resistances of less
than 30 ohms and greater than or equal to 30 ohms. The mean failure rates for each group
in each voltage class were then determined with the results shown in Table 11.2.
11-7
VOLTAGE
CLASS
UTILITIES WITH MAX. TOWER
RESISTANCE < 30 ^
No. of
Failure
Rate
(Mean)
Utilities
Std. Dev.
100 kV
18
1.732
1.39
200 kV
17
1.37
300 kV
11
1.26
500 kV
6
Table 11.1
.404
UTILITIES WITH MAX. TOWER
RESISTANCE > 30 £3
No. of
Failure
Rate
(Mean)
Utilities
Std. Dev.
13
2.39
1.58
1.68
9
2.27
1.418
1.0
6
■ 98
1.03
2
.27
.04
.38
Maximum Structure Ground Resistances
The results of the comparisons for the 100 and 200 kV classes could be significant, suggesting
that lower footing resistances will result in lower failure rates due to lightning. The values
are close enough however, that other factors, not considered in this comparison, could distort
the results. Keraunic levels, for example, have not been considered and a correlation between
keraunic levels and average soil resistivities could affect the above results in either direction.
In order to obtain additional information from the responses to the survey questionnaire,
attempts were made to derive relationships between various transmission line grounding
performance criteria and design criteria. Since no utilities were able to identify any safety
problems related to transmission line grounding, only transmission line performance data were
considered in the analysis.
Initially, the utilities were grouped into high and low failure rate groups. A failure rate of
one failure per 100 miles per year was used as the separation point. The responses to various
engineering design related questions were then compared between the two failure rate groups
but no meaningful relationships were observed. A detailed analysis was then undertaken of
the relationship between structure resistances and lightning failure rates. This was investigated
for each voltage class of transmission line. The mean values of maximum structure resistance
for each class were compared between high and low failure rate companies.
The results of this are shown in Table 11.2.
VOLTAGE
CLASS
HIGH FAILURE RATE UTILITIES
( > FAILURE
/100 MILES /YEAR)
Max. Tower Footing
No. of
Res i stance £2
Utilities
Mean
Std. Dev.
LOW FAILURE RATE UTILITIES
( < FAILURE /100 MILES /YEAR)
No. of
Utilities
Max. Tower Footing
Res i stance £2
Mean
Std. Dev.
100 kV
6
107
194
8
26
31
200 kV
2
260
340
8
27
28
300 kV
6
23
24
3
15
10
500 kV
2
15
7
4
28
30
700 kV
1
10
0
1
25
0
Table 11.2
Transmission Line Lightning Failure Rates
11-8
Although 100 kV and 200 kV class mean values are significantly higher, the distribution is
skewed considerably by one utility reporting a maximum value of 500 ohms. If these data
are not considered, the values are very similar. However, it was difficult to draw any firm
conclusions from this result.
CONTINUOUS
COUNTERPOISE
RADIAL
COUNTERPOISE
nn n
GROUND
ROD ONLY
TOWER
FOUNDATION ONLY
TT
r~i-,
a
fl n-
■
n
J□nD
r—i czi
J1
£=□D=l
300 kV
^ rTI
500 k\I
700 kV
»
0
^
■____ '
40
80
«
0
■
40
TYPE
Figure 11.5
11'
OF
80
-L-
I
«
0
GROUNDING
t
40
I
i
80
t
..g..,,!
I
0
40
(IN % OF TOTAL)
Grounding Arrangement
11-9
I
i
80
DESIRED
VALUE
MINIMUM
MEASURED
MAX I MUM
MEASURED
i—i—1
0
1
100 kV
o
a
LU
m
s:
=>
■z.
20 ’
—i
10-
Tl
n
r-1
n
.
200 kV
UTILITIES
»
__i__i__i____i_
—
o
cc
s
s
Z5
Z
i
“1
r-n—
20 *
10 '
0
r
jTh
L
ri
- rffci
0
20
i+O
0
n&
-T—T-T"..
.<----
lAi M
4
ip
RESISTANCE
Figure 11.6
——■cL-..-,------inLr* infa.......
I 0
0
40
(IN OHMS)
Transmission Structure Resistance
AVERAGE
MAXIMUM
AVERAGE
100 kV
NUMBER
RATE
MAX I MUM
200 kV
300 kV
Figure 11.7
100
OF
FAILURES
Lightning Rate of Failures
11-10
11.6 SUMMARY OF COMMENTS RECEIVED
NOTE : (n) gives the number of respondents who provided the comment.
SECTION I - GENERAL
1-1 Which
(7)
(5)
(4)
(2)
(2)
Guide is Followed ?
IEEE Guide No. 80
National Electric Safety Code
Westinghouse Electrical T&D Reference Book
EPRI Transmission Reference Book
IEEE Practice for Grounding of Industry and Commercial Power Systems
1-2 Why Install Grounding Systems ?
(5) To prevent lightning failures
(4) To keep ground resistance below 10 ohms
(4) To prevent structure damage
(3) To minimize induced voltages on pipelines, telephone lines, etc.
(2) To follow state regulation, overhead line general order 95
SECTION II - MEASUREMENTS
II-4
Objectives of Taking Field Data ?
(3) To help to decide the type & size of the grounding system
(3) To verify the adequacy of the installed system
(2) To assist in the design of the structure
(1) To determine the necessity of putting in more grounding
(1) To perform calculations to minimize the effect of transmission line on adjacent
pipelines
II-5
Methods Used to Measure Resistivity ?
(3) Megger (3-point, 4-point) terminal test
(2) Direct ohm-meter method of 2-terminal test
II-6
Types of Instrument Used ?
(3) Vibroground meter model 293
II-7
Interpretation of Measurements ?
(2) To develop a two-layer model
(1) Use "Tagg's" method to derive formula for ground resistivity determination
11-10 Improvements to Make Measurements & Interpretation More Reliable ?
(4) A comprehensive set of standards on measurement techniques and interpretations
(2) A better method to measure structure resistance
(2) A better model for multi-layer nonuniform resistivities
(1) Better equipment, more measurement
(1) A formula of resistance as a function of seasonal soil moisture content
11-11
SECTION III - ENGINEERING
III-l 60 Hz Fault Calculations Variables ?
(2) Grounding conductor resistance
HI-5 Distribution of Fault Current Between Tower Ground Electrode and Ground Wire ?
(2) Percentage varies with line arrangements, structure spacing & ground conditions
III-6 Lightning Calculation Variables ?
(3) Shield angle
(2) Air gap with steel
(1) Flashover characteristics
III-7 Methods of Determining Transmission Line Rate of Failure Due to Lightning ?
(4) Methods referred to in EPRI Transmission Line Reference Book 345 kV & Above
(3) Historic records
(1) IEEE methods
III-ll Improvements ?
(4) Better guidelines
(1) Better statistical data to indicate which design variables are more valuable than
others
(2) More related computer programs to be written
SECTION IV - SAFETY CONSIDERATIONS
IV-2
Source of Maximum Value of Tolerable Body Surge Current ?
(3) IEEE Guide 80
(3) Dalziel's electrocution formula 1= 0.116/ VU
(2) 5 mA, rule of thumb
IV-6
Investigations of Safety of Structure Grounding ?
(5) No investigations are conducted
(3) Thorough & frequent checkings
(2) Thorough checking plus special grounding in highly exposed areas
(1) Only investigations where there are parallel pipeline exposures
IV-8
Analyze Hazards During 60 Hz Fault or Not ?
(2) Do not because it is believed that as long as ground resistance is held below 10
ohms, it is safe
IV-9
Ever Analyze Special Structure Grounding Electrodes ?
(3) Study variable counterpoise patterns
(2) Study ring-shaped electrode
IV-11 Improvements For Safety ?
(2) Increase the engineering staff
(2) Verification of formula & maximum current values that can be tolerated during
faults
(1) Some structure grounding should be designed specifically for public safety
(1) Inform & educate the public about safety
(1) Develop step & touch potential criteria
11-12
IV-13 Future Hazards Associated With Transmission Line Structure Grounding for Next
Ten Years ?
(21)Believe will go up because of:
1/ more line construction
2/ more intense land use which cause more exposures
(3) Believe no real problem
(1) Believe will go down due to better transmission grounding design and installations
SECTION V - CONSTRUCTION / MEASUREMENT / MAINTENANCE
V-2
Approximate Diameter of Conductor Used ?
(2) AWG # 4 copper
(1) Size depends on fault current
V-4
Equipment Used to Install Structure Grounding ?
(2) Rock drills & grout mixers
(1) Compressor & air hammer
V-6
Field Measurements Taken ?
(4) Resistance of ground rod
(1) Soil resistance
V-9
Methods to Measure Structure Footing Leakage Resistance ?
(3) 3-point method
V-10
Equipment Used ?
(1) BBC high frequency ground resistance tester
(1) 3-probe null balance resistance testing instrument
V-ll
Purposes for Staged-Fault Tests ?
(4) Relay coordination
(1) Potential rise of gas pipeline under lines
(1) Research purposes
V-13
Reasons for Checking Transmission Structure Grounds ?
(5) Better safety and line performance during lightning
(4) To look for any damage caused by vandalism, agricultural activities, corrosion, etc.
V-13
Methods Used for Checking Ground System ?
(4) Visual inspections
(2) Resistance measurements
(1) Sample excavation
V-17
Cause of Transmission Line Permanent Failure ?
(5) Lightning storms
(4) Trees
(3) Vandalism
(3) Accidents
(2) Misoperations
(2) Equipment failures
V-19
Modification to Improve Grounding Performance ?
(12) Better maintenance such as more inspection, better measurement techniques, better
equipment, better trained .staff
11-13
SECTION VI - TYPICAL DESIGN AND DATA
VI-1
Equipped With Overhead Ground Wire ?
(1) Only apply to lines that perform poorly.
11.7 CONCLUSION
The survey results overwhelmingly confirmed what was already suspected; North American
power utilities do not follow any common, generally accepted transmission line grounding
standards nor do they apply similar practices in measurement, design or construction procedures.
The practices, needs and understanding of transmission line grounding by utilities varies
widely. Conflicting concepts and opinions exist in almost every significant aspect of this
important subject.
It is hoped that this report will provide the framework for a coordinated and more unified
approach to transmission line grounding problems.
11-14
APPENDIXES
APPENDIX
A
COMPUTER PROGRAM LINPA
FUNCTION
LINPA computes the self and mutual impedances of phase and ground conductors of transmission
lines. The program uses the equations developed by Carson, assuming a uniform soil structure.
LINPA first calculates and prints the complete impedance matrix. Then, if requested, it
performs bundle reductions and prints a reduced impedance matrix where the original group
of conductors of the bundle are represented by a single equivalent conductor.
REFERENCES
Information on this program is given in Chapter 2. Carson's equations are described in
references 1 and 3 of Chapter 2 and in several power engineering textbooks. A typical
application of LINPA is described in Chapter 3.
GENERAL
LINPA was developed for use in an interactive mode. In this mode, the user is prompted to
provide the required input data and answers in free-format. A typical interactive session is
shown in Page A-5.
The program can also be readily operated in batch mode. In this mode, the user must organize
the data in a file prior to running the program. The batch mode is particularly advantageous
when running several cases with small differences in the input data. The following guidelines
and the interactive session shown in Page A-5 provide the necessary instructions to build
an input data file for the program LINPA.
GUIDELINES
All values entered on a data line must be separated by a comma. Blanks are interpreted as
a YES, zero or default answer, depending on the data expected by the program.
LINPA accepts up to 8 different types of data lines. Occasionally, several data lines of the
same type are accepted by the program. In this case, the user must enter a line consisting
of the world END as the last entry to instruct the program that the series of data lines of
the current type has ended.
A typical input data file is shown in Page A-4. This file can be prepared based on the
following guidelines:
A-1
Data Line 1 : Start
This line must necessarily be a YES to initiate execution of the program. A NO will stop
the program.
Data Line 2 : Comment
Enter any alphanumeric character to provide comments and general references. These lines
are not processed by the program but simply reprinted at the top of the output printout.
Up to four lines of comments may be entered. If less than four comment lines are entered,
the comments must be terminated with a line consisting of the word END.
If the character
is among the characters entered in a comment line, all the information
to the right of this character is ignored. This is a useful feature (for both interactive
and batch modes) which allows the user to include additional comments in the input data
which will not appear in the printout.
Data Line 3 : Run Identification
Enter a four digit identification code which will be printed at the top right-hand side of
each page of printout.
Data Line 4 : System of Units
If the metric system is to be used, provide a data line beginning with a YES. If the British
system of units is requested, two data lines are needed; line 1 is a NO and line 2 is a YES.
Data Line 5 : Bundle Reduction
Enter YES if the program is to reduce all the conductors of a bundle into an equivalent
single conductor. Enter NO if bundle reduction is not required. The conductors in a
bundle have the same phase number.
Data Line 6 : System Frequency
Enter the frequency (Hz) at which the impedance matrix is to be calculated. A zero frequency
is interpreted by the program as direct current.
Data Line 7 : Earth Resistivity
This is the average resistivity value of the soil along the length of the transmission line
consi dered. This value should always be expressed in ohm-meters regardless of the system
of units selected.
A-2
Data Line 8 : Conductor Data
Provide, in one line, the characteristic values of each conductor. The characteristic values,
separated by commas, are illustrated in the following line:
PHA, CODE, X, Y, RADIUS, XXX, RAC, NO, ORAD, RCOR
where
PHA is the phase number of the conductor. Note that this phase number does not play
any role other than grouping the conductors into a number of bundles to be replaced
by eguivalent single conductors. For example, the two ground wires of a
transmission line can be assigned the phase number 4 (or 7 for a double circuit line)
in order to reduce them to the eguivalent ground wire needed for the program PATHS.
CODE represent, the digits 0 and 1. If 0 is selected, LINPA interprets the following
XXX entry as being the GMR of the conductor. If 1 is used, XXX is interpreted as
being the conductor inductive reactance at one foot spacing.
X is the horizontal distance of the conductor as measured from an arbitrary origin on
the surface of earth. This distance is in m or ft depending on the units selected.
Y is the average height above ground of the conductor expressed in m or ft.
RADIUS is the conductor radius in m or ft.
XXX is the geometric mean radius (GMR) of the conductor (in m or ft) or its inductive
reactance at one foot spacing (in ohms/km or ohms/mi), depending on the value of
code.
RAC is the 60 Hz ac internal resistance of the conductor in ohms/km or ohms/mi.
NO is the number of outer strands of the conductor. This value
system frequency (data line 6) is greater or equal to 2,000 Hz.
is needed only if the
ORAD is the radius of the outer strands (m or ft). This value
frequency is greater than or equal to 2,000 Hz.
is needed only if the
RCORE is the overall radius of the conductor core (m or ft). If all the strands are of
the same material, then RCORE = ORAD. If the conductor is a solid conductor then
RCORE = RADIUS. This value is needed only if the frequency is greater or equal to
2,000 Hz.
The user should provide as many data lines of type 8 as there are transmission line conductors,
up to a maximum of 25 which is the limit of the released version of LINPA. A data line
with END in the first columns must be the last line entered.
A-3
INPUT DATA FILE FOR BATCH MODE PROCESSING
BABE TEST FILE (APPENDIX A)
EXAMPLE FOR CHAPTER 3
TYPICAL LINE 345 KV
DETROIT EDISON CACSR 54/7 #954
EX1
N
Y
Y
60
150
l,Or-19.33333,48.*.04983,.0404*.0998
1*0*-20.83333*48.*.04983 *.0404 *.0998
2*0,-26.83333*69.5*.04983*.0404*.0998
2*0*-28 * 33333 *69.5*.04983 *.0404 *.0998
3,0*-20.33333,94.*.04983*.0404*.0998
3.0, -21.83333,94.,.04983*.0404,.0998
4.0, -12*0,109.,.02121,0.00276,1.437
4.0. 12.0.109...02121.0.00276.1.437
5.0. 19.33333.48...04983..0404..0998
5.0. 20.83333.48...04983..0404..0998
6.0. 26.83333.69.5..04983..0404..0998
6.0. 28.33333.69.5*.04983,.0404,.0993
7.0. 20.33333.94...04983..0404..0998
7.0. 21.83333.94...04983..0404..0998
END
A-4
*2
19*10)
TYPICAL INTERACTIVE DIALOGUE AND COMPUTER PROGRAM PRINTOUT
PR06RM LINPA
THIS PROSRAH CALCULATES THE IHPEBAHCES OF TRANSMISSION LM CONBUCTORS
(PHASE LINE PARAMETERS)
NOTES
1- RESPONO TO OJESTIONS BY YES OR NO
OR* INCH APPRIMIATEt BY TYPING THE REQUIRED DATA.
2- Y* YE* YES* BLANK CHARACTERS AND RETURN CARRIAGE ARE
INTERPRETED AS YES, OTHER CHARACTERS ARE INTERPRETED AS NO,
3- 0* 0,* BLANK CHARACTERS OR A RETURN CARRIAGE ARE INTERPRETED AS A ZERO VALUE
OR* HHEN APPLICABLE* ARE REPLACED BY DEFAULT VALUES,
START
? yes
ALL CONDUCTORS BELONGING TO THE SAME BUNDLE ARE* BY CONVENTION, CONSIDERED AS FORMING ONE IPHASE*.
THEREFORE* IF THE BUNDLE REDUCTION OPTION IS ENABLED, THE PROGRAM HILL REDUCE THE BUNDLE INTO
ONE EQUIVALENT SINGLE CONDUCTOR. FOR EXAMPLE ,*
- IF SEVERAL OVERHEAD GROUND-HIRES ARE TO BE REDUCED INTO ONE EQUIVALENT CONDUCTOR
DECLARE EACH GROUND-HIRE AS PART OF THE SAME PHASE* I.E,* PHASE #4 FOR A
SINGLE-CIRCUIT 3-PHASE LINE OR PHASE * 7 FOR A DOUBLE CIRCUIT 3-PHASE LINE
- IF YOU DISH TO COMBINE PHASE A1 AND PHASE A2 OF A DOUBLE CIRCUIT LINE
DECLARE THE CONDUCTORS OF BOTH BUNDLES AS PART OF THE SAME FICTITIOUS PHASE * N
ENTER COMMENT LINES. (MAXIMUM OF 4)
TERMINATE HITH END AT THE BEGINNING OF A NEU LINE,
file (appendix A)
for chapter 3
typical line 345 KV
Detroit Edison (ACSR 54/7 #954,2 19*10)
??
?
bsse
exaepletest
?
ENTER RUN IDENTIFICATION (4 DIGITS),
? exl
SYSTEM OF UNITS
- METRIC ?
? no
- BRITISH ?
? yes
DO YOU HANT TO REDUCE THE CONDUCTOR BUNDLES INTO EQUIVALENT SINGLE CONDUCTORS ?
? yes
ENTER THE POMER SYSTEM FREQUENCY (HERTZ)
?
m
ENTER EARTH RESISTIVITY (OHMS-HETER)
? 150
A-5
CONDUCTOR'S DATA (MAX. OF 25 CONDUCTORS)
YOU CAN ENTER THE GHR OR THE INDUCTIVE REACTANCE
AT ONE FOOT SPACING (60 HERTZ),
GMR IS USED WHEN THE CODE (SEE BELOW) IS 0 OR BLANK*
OTHERWISE THE REACTANCE XI AT ONE FOOT SPACING (60 HERTZ) IS USED,
ENTER THE PHASE NUMBER* THE CODE* THE X AND T COORDINATES (FT)
THE RADIUS (FT)* THE GMR (FT) (OR XI(OHMS/MILE))
AND THE AC RESISTANCE (OHHS/HILE) OF THE CONDUCTORS,
TERMINATE WITH END AT THE BEGINNING OF A NEW LINE,
EXAMPLE : PHA*CGDE*X*Y*RADIUS*GMR*RAC
? 1*0*-19.33333*48.*,04983*,0404*.0993
? l»6*-20,83333*48,*,04983*.0404*,0998
? 2*0*-26,83333 *69♦5 * *04983 *,0404*,0998
? 2*0*-28,33333*69,5.,04983.,0404.,0998
? 3.0*-20,33333*94,*.04983*,0404*.0998
? 3*0*-21.83333.94,.,04983*.0404.,0998
? 4*0*-12.0*109,.,02121.0,00276.1.43?
? 4.0.12,0.109,.,02121.0,00276.1,437
? 5.0*19,33333*48,*.04983?,0404.,0998
5.0.20,83333.48,.,04983.,0404.,0998
6*0.26,83333*69,5.,04983.,0404*,0993
6*0*28,33333.69,5.,04983.,0404.,0998
7.0.20,33333.94,.,04983.,0404.,0998
7.0.21,83333.94..,04983.,0404..0998
? END
?
?
?
?
?
A-6
LINPA PAGE
RUN J EX1
comments
XBASE TEST FILE (APPENDIX A)
mt &wb 3
IDETSOIT EDISON (ACSR 54/7 #954
RUN IDENTIFICATION
UNITS SYSTEM
1
mmmmmttnmmmtmm
t
i
t
19110)
COMMENTS
*
5 EX1
1 BRITISH
BUNDLE REDUCTION
: YES
CALCULATION METHOD
: CARSON
SYSTEM FREQUENCY
:
60,00 HERTZ
SOIL RESISTIVITY
l
150.00 OHMS-METER
NUMBER OF CONDUCTORS S 14
LINPA PAGE 1 2
RUN : EX1
CONDUCTORS DATA AS ENTERED BY USER
t-------------------------------------- 1
CONDUCTOR PHASE
NUMBER NUMBER
1
2
3
4
5
h
1
8
9
10
11
12
13
14
1
1
2
2
3
3
4
4
5
5
6
6
7
7
X
FEET
Y
FEET
-19.33
-20.83
-26,83
-28.33
-20.33
-21.83
-12,00
12,00
19,33
48,00
48,00
69,50
69,50
94.00
94,00
109,00
109,00
48,00
48,00
69,50
69,50
94,00
94,00
3A
28.33
20,33
21.83
RADIUS
FEET
GMR
FEET
.4983E-01
,4983E-01
.4983E-01
,4983E-0i
.4983E-01
.4983E-01
.2121E-01
.2121E-01
.4983E-01
.4983E-01
.4983E-01
.4983E-01
.4983E-01
,4983E-01
.4040E-01
.4040E-01
.4040E-01
.4040E-01
.4040E-01
.4040E-01
.2760E-02
.2760E-02
.4040E-01
.4040E-01
,4040E-01
.4040E-01
.4040E-01
.4040E-01
END OF INPUT DATA
A-7
RAC
OHHS/HILE
.9980E-01
•9980E-01
.9980E-01
,9980E-0i
.9980E-01
.9980E-01
.1437EI01
.1437E+01
,9980E-01
.9980E-01
.9980E-01
.9980E-01
.9980E-01
.9980E-01
LINPA PAGE I 3
RUN S EX1
CONDUCTORS DATA AS STORED BY PROGRAM
--- ¥
<—-—
CONDUCTOR PHASE
NUMBER NUMBER
1
2
3
4
5
6
7
1
1
2
2
3
3
8
4
4
9
5
10
5
11
12
13
14
6
&
7
7
X
METERS
-5,89
-6,35
-8,18
-8,64
-6,20
-6.65
-3,66
3.66
5,89
6.35
8.18
8.64
6.20
6.65
Y
METERS
14.63
14.63
21,18
21,18
28,65
28,65
33.22
33.22
14,63
14.63
21.18
21.18
28.65
28,65
RADIUS
METERS
PERMEABILITY
RELATIVE
RAC
OHMS/KM
,1519£-01
.1519E-01
.1519E-01
.1519E-01
.1519E-01
.1519E-01
.6465E-02
.6465E-02
.839IETOO
.6203E-01
.6203E-01
.6203E-01
.6203E-01
.6203E-01
•6203E-01
,8931ET00
.8931EW0
.6203E-01
.6203E-01
.6203E-01
.6203E-01
.6203E-01
.6203E-01
,15191-01
,1519E-01
.1519E-01
,1519E-01
.1519E-01
.1519E-01
.8391E+00
.8391E+00
.8391ET00
.8391E+00
•8391E+00
.8157E+01
.8157E+01
,8391EW
.8391E+00
.8391E+00
.8391E+00
.8391ET00
.8391E+00
END OF INPUT DATA
A-8
LINPA PAGE 5
RUN I EX1
DETAILED LINE PARAHETERS AT
IHPEDANCES
FIRST
4
60,00 HZ
- OHHS/HILE
VALUE IS RESISTANCE. SECOND VALUE IS REACTANCE
COND, NUHB,
4
COND.
NUHB,
i
.192
1.395
2
.092
,941
.192
1.395
3
,092
.612
,092
,614
.191
1.396
4
,092
.609
.092
.612
.091
.942
.191
1,396
5
.091
.527
.091
.527
,091
,600
.091
,598
6
.091
,527
,091
,527
,091
,602
,091
,600
7
.091
,492
.091
.492
.090
,539
,090
,537
8
,091
,479
,091
,478
.090
.506
.090
,503
9
,092
.547
.092
,542
,092
,514
,092
,511
10
.092
.542
.092
,538
.092
,511
.092
.508
11
.092
,514
,092
.511
.091
.508
,091
,505
12
.092
.511
.092
.508
,091
.505
,091
.502
13
.091
.493
.091
.491
,091
.510
,091
.507
14
,091
,491
.091
,489
.091
.507
,091
,504
COND. NUHB.
6
5
8
7
MB.
MB.
5
,190
1.398
6
,090
.944
.190
1,398
7
,090
.649
.090
,643
1.526
1,859
8
.090
.560
.090
,555
,089
.608
1.526
1.859
9
.091
.493
.091
,491
,091
.479
.091
,492
10
.091
.491
.091
,489
.091
,478
,091
.492
11
,091
,510
.091
.507
.090
,506
.090
.539
12
,091
,507
.091
,504
,090
,503
,090
,537
13
.090
,543
.090
,539
.090
,560
,090
,649
14
.090
,539
.090
.535
.090
,555
.090
,643
A-9
CON!),
COND,
NUHB
NUHB,
11
10
9
12
COND.
NUHB.
9
.192
1.395
10
.092
.941
.192
1.395
11
.092
.012
.092
.614
,191
1.396
12
.092
,609
.092
.612
,091
,942
,191
1,396
13
.091
.527
,091
.527
,091
.600
.091
.598
14
.091
.527
.091
.527
.091
,602
,091
,600
COND.
14
13
NUHB,
1§ggg
1
13
,190
1.398
14
.090
,944
.190
1,398
LINPA
RUN
PHASE
LINE
PAGE ! 5
l EX1
PARAHETERS
IHPEDANCES - OHHS/HILE
FIRST VALUE IS RESISTANCE) SECOND VALUE
COND. NUHB.
IS
REACTANCE
4
3
1
COND.
NUHB.
1
,142
1,168
2
.092
.611
,141
1.169
3
,091
,527
.091
,599
.141
1.169
4
.091
,485
,090
.521
,090
.602
,808
1.234
5
,092
,542
,092
,511
,091
.492
.091
.485
6
.092
.511
,091
,505
,090
,508
,090
.521
7
,091
,492
.090
,508
.088
,540
.090
,602
COND. NUHB.
6
5
7
COND.
NUHB.
5
,142
1.168
6
,092
.611
,141
1,169
7
.091
,527
.091
,599
END OF PRGGRAH
LINPA
tmtunnnntnn
A-l o
.141
1.169
APPENDIX
B
COMPUTER PROGRAM RESIST
FUNCTION
This program determines an equivalent two-layer earth model from the measured apparent
resistivity data. The resistivity values must have been measured using the equally-spaced
four probe or Wenner method. The equivalent earth model is characterized by the thickness
of the first layer and by the resistivity values of the upper and lower layers of soil.
REFERENCES
Information on this program is given in Chapter 2. The analytical theories on which RESIST
is based are described in Chapter 4. A typical application of this program is given in Chapter
3. Additional examples are included in Chapter 10.
GENERAL
RESIST was developed for use in an interactive mode. In this mode, the user is prompted
to provide the required input data and answers in free-format. A typical interactive session
is shown in Page B-5.
The program can also be readily operated in batch mode. In this mode, the user must organize
the data in a file prior to running the program. The batch mode is particularly advantageous
when running several cases with small differences in the input data. The following guidelines
and the interactive session shown in Page B-5 provide the necessary instructions to build an
input data file for the program RESIST.
GUIDELINES
All values entered on a data line must be separated by a comma. Blanks are interpreted as
a YES, zero or default answer, depending on the data expected by the program.
RESIST accepts up to 9 different types of data lines. Occasionally, several data lines of the
same type are accepted by the program. In this case, the user must enter a line consisting
of the world END as the last entry to instruct the program that the series of data lines of
the current type has ended.
A typical input data file is shown in Page B-4. This file can be prepared based on the
following guidelines:
B-l
Data Line 1 : Start
This line must necessarily be a YES to initiate execution of the program. A NO will stop
the program.
Data Line 2 : Comment
Enter any alphanumeric character to provide comments and general references. These lines
are not processed by the program but simply reprinted at the top of the output printout.
Up to four lines of comments may be entered. If less than four comment lines are entered,
the comments must be terminated with a line consisting of the word END.
If the character
is among the characters entered in a comment line, all the information
to the right of this character is ignored. This is a useful feature (for both interactive
and batch modes) which allows the user to include additional comments in the input data
which will not appear in the printout.
Data Line 3 : Run Identification
Enter a four digit identification code which will be printed at the top right-hand side of
each page of printout.
Data Line 4 : System of Units
If the metric system is to be used, provide a data line beginning with a YES. If the British
system of units is requested, two data lines are needed; line I is a NO and line 2 is a YES.
Data Line 5 : Type of Terminal Used
Plots of measured and computed earth resistivities are automatically produced by the program
for display on a terminal. If the terminal is a video screen, only one character at a time
can be displayed in a specific location. This is not the case of printers and hard-copy
terminals which allow overprinting.
The program uses two different routines to produce plots, depending on the type of terminal.
The hard-copy terminal routine produce the most accurate plots. However, the other routine
can be used on a video or hard-copy terminal.
This line should be a YES for a video terminal and a NO for a hard-copy terminal.
Data line 6 : Maximum Probe Spacing
Once the equivalent two-layer earth model has been determined, RESIST computes the
apparent resistivity values which would have been obtained along the resistivity traverse if
the earth structure was identical to the computed model.
A total of 50 points are computed along the traverse. The maximum probe spacing of the
array (in m or ft) must be defined by the user in this data line.
B-2
If zeroes or blanks are entered in this line, RESIST assumes that the maximum probe spacing
is 1.5 times the largest probe spacing used in the field measurements. This choice leads to
a balanced appearance of the measured and computed curves of the plot produced by RESIST.
Data Line 7 : Measured Apparent Values
The measured results may be entered as apparent resistances or as apparent resistivities. A
NO in this data line means apparent resistivities have been entered. A YES instructs the
program that apparent resistances have been entered. RESIST will then calculate apparent
resistivity values according to the equation:
p = 27TaR
where
P
is the resistivity, R the resistance and a the spacing.
The above equation is only valid when the probe depth is approximately 1/10 or less of the
probe spacing. In cases where this is not so or other influencing factors are known to be
present, the user should determine apparent resistivity values using a more appropriate
equation.
Data Line 8 : Measured Values
In this line, the user enters the probe spacing (in m or ft) and measured apparent resistance
(in ohms) or apparent resistivity (in ohm-meters). The two values should be separated by
a comma.
The user must enter one data line for each pair of measured values. As explained, a line
beginning with END instructs the program that all measured points have been entered.
Date Line 9 : Accuracy Values
Two accuracy values (in p.u.) are expected by the program in this data line. If the user
does not specify, RESIST selects two default values.
The first value represents the optimization accuracy of the earth model search algorithm.
A value of 0.001 is often a very good choice. However, two runs may sometimes be necessary
to achieve an optimum fit. In the first run, a large value such as 0.01 or the default value
should be selected to speed-up the computation. The computed and measured curves should
then be examined. If the fit is reasonable or if a better match is doubtful because the real
soil is a very distinct three or four layer model, then a second run should not be made. It
is recommended however, that the user try different accuracy values to obtain a good feel
for the sensitivity of the program to changes in specified optimization accuracy.
The second accuracy value is used to determine the end of the computation of the series
terms in the development of two-layer models. The default value of 0.01 (1%) is an appropriate
choice.
B-3
INPUT DATA FILE FOR BATCH MODE PROCESSING
YES
BASE TEST FILE <APPENDIX B>
EXAMPLE FOR CHAPTER 3
END
EX1
YES
YES
O.
NO
2.5*320
5.0*245.
7.5*182.
lO.*162
12.5*168.
15.* 152.
END
0.00001*0.001
TYPICAL INTERACTIVE DIALOGUE AND COMPUTER PROGRAM PRINTOUT
PMHUft RESIST
ttttutttutt
AHALYSIS ASD INTERPRETATION OF APPARENT RESISTIVITY HEASURENENT AROUND
TRANSMISSION LINE STRUCTURES
NOTES I
1-RESP0ND TO SUESTIONS BY YES m NO
OR? WHEN APPROPRIATE! BY TYPING THE REQUIRED DATA,
2-Y» YE? YES? BLANK CHARACTERS AND RETURN CARRIAGE ARE
INTERPRETED AS YES, OTHER CHARACTERS ARE INTERPRETED AS NO,
3-0? 0,? BLANK CHARACTERS OR A RETURN CARRIAGE ARE INTERPRETED AS A ZERO VALUE
OR? HHEN APPLICABLE? ARE REPLACED BY DEFAULT VALUES,
START ?
? aes
-“3
ENTER COMMENT LINES (MAX, OF 4)
TERMINATE HITH END AT THE BEGINNING OF A NEW LINE,
*
—
base test file (appendix B)
exatple for chapter 3
ENTER RUN IDENTIFICATION (FOUR
DIGITS)
? exl
UNITS USED
-METRIC SYSTEM ?
? yes
VIDEO TERMINAL OR HARD-COPY TERMINAL (PRINTER) FOR OUTPUT ?
VIDEO ?
t yes
ENTER MAXIMUM PROBE SPACING (METERS OR FEET)
FOR THE CALCULATED APPARENT RESISTIVITY PROFILE*
DEFAULTS 1,5 TIMES MAXIMUM SPACING OF THE MEASURED PROFILE,
YOU MAY ENTER
1- THE APPARENT MEASURED RESISTANCE (V/D?
2- THE APPARENT RESISTIVITY VALUES
OR
APPARENT RESISTANCE T
? no
ENTER YOUR FIELD DATA RESULTS IN SEQUENCE,
ONE LINE FOR EACH MEASUREMENT AT A GIVEN SPACING,
TERMINATE HITH END AT THE BEGINNING OF A NEW LINE,
EXAMPLE S SPACING (M OR FT)? MEASURED VALUE (OHMS OR OHMS-METER)
? 2,5?320
?
?
?
?
?
5,0?433,0
5*0?245.
7,5?182,
10.?162
12.5?168.
15*?152*
? END
ENTER *
OPTIMIZATION ACCURACY? AND
SUM OF SERIES TERMS ACCURACY. (2 LAYER SOIL)
(PER UNIT VALUES, DEFAULT VALUES ARE 0,01 AND 0.01)
EXAMPLE l 0,005?0,001
0,00001?0,001
B-5
RESIST PAGE t 1
RUN : EX1
mmmmmmmmn
comhents
nmnmmmmtmn
BASE TEST FILE (APPENDIX B)
EXAMPLE FOR CHAPTER 3
ttWtttttttttttttttMtttt
COMMENTS tttttttMtttttttttttttttt
RUN IDENTIFICATION t EX1
SPACING IN METERS
OPTIMIZATION ACCURACY
! .000010 (P.U.)
SUM OF SERIES TERMS ACCURACY 5 .001000 (P.U.)
BEST POSSIBLE FIT OCCUREO BEFORE REQUIRED ACCURACY HAS OBTAINED
TRYING TO CONTINUE FIT PROCESS MAY LEAD TO DIVERGENCE
ACTUAL ACCURACY = .009148
BEST ACCURACY = .001140
REACHED ON ITERATION 188
RESIST PAGE I 2
RUN 1 EX1
MEASURED APPARENT VALUES
SPACING
(M OR FT)
2.5000
5.0000
7.5000
10.0000
12,5000
15,0000
RESISTANCE RESISTIVITY
OHMS-METER
OHMS
320,0000
20,3718
245.0000
7,7986
182.0000
3,8622
162.0000
2,5783
168.0000
2.1390
152,0000
1,6128
RESIST PAGE ! 3
RUN ! EX1
OPTIMIZATION STATUS
NUMBER OF ITERATIONS ?
AVERAGE UMBER OF SERIES TERMS USED
FOR TWO LAYER SOIL i
OPTIMIZATION ACCURACY 1
319
45
,1140 %
B-6
RESIST PAGE J 4
RW I EX1
RESULTS
COHPUTATIOH
TOP LAYER RESISTIVITY
383,4982 OHMS-METER
BOTTOM LAYER RESISTIVITY 147.6571 OHMS-METER
REFLECTION FACTOR
-.4440 (P.U.)
TOP LAYER THICKNESS
2.5626 METERS
RESIST PAGE I 5
RUN ! EX1
COMPUTED APPARENT RESISTIVITY
PROBE SPACING
(METERS)
,0100
,9000
1.8000
2,7000
3,6000
4.5000
5,4000
fcSR
8,1000
9,0000
9.9000
10,8000
11,7000
12,6000
13,5000
14,4000
15,3000
16,2000
17,1000
18.0000
18,9000
19,8000
20.7000
21,6000
APPARENT RESISTIVITY
(OHMS-METER)
383,4982
378,8418
355,4416
318,8212
280.9366
248,6495
223,5756
204,8539
191.1726
181,1541
173,8834
168,5325
164,5478
161.6009
159.3079
157.5274
156,1245
155.0033
154,0953
153,3506
152,7327
152,2147
151,7761
151.4015
151,0791
PROBE SPACING
(METERS)
,4500
1,3500
2,2500
3.1500
4.0500
4,9500
5,3500
8,5500
9,4500
10.3500
11,2500
12,1500
13.0500
13.9500
14,8500
15,7500
16,6500
17,5500
18,4500
19.3500
20,2500
21,1500
22,0500
APPARENT RESISTIVITY
(OHMS-METER)
382.8643
369,5771
337,9856
299.4948
263,9175
235,2636
213,4963
197,4698
185.7408
177,2362
171,0070
166,3970
162,9967
160.3800
158,3631
156 97855
155*5335
154,5262
153.7051
153,0277
152,4626
151,9865
151.5816
151,2344
150,9345
RESIST PAGE 1 6
RUN : EX1
COMPARISONS
SPACING CALCULATED APPARENT MEASURED APPARENT DISCREPANCY
(METERS) RESISTIVITY(OHMS-M) RESISTIVITY(OHMS-M) (PERCENT)
2.500
5,000
7.500
10,000
12,500
15,000
327,4372
233.8807
187,4388
168,0307
159,5344
155,3505
320,0000
245,0000
182,0000
162,0000
168.0000
152,0000
2,32
-4,54
2,99
3.72
-5,04
2.20
AVERAGE DISCREPANCY BETWEEN
MEASURED AND CALCULATED RESISTIVITIES
.28 PERCENT
B-7
RESIST PAGE I 8
RUN 5 EX1
APPARENT RESISTIVITY OHHS-HETER
0<
39*
78*
0*0000-1................................. .
I
I
I
117,
156.
195,
.1______I______ I—
4,6000-1
I
I
I
I
I
I
I
I
I
9,2000-1
I
I
I
I
I
I
I
I
I
13.8000-1
I
I
I
I
I
I
I
I
I
18,4000-1
I
I
I
I
I
I
I
I
I
, KEASURED RESISTIVITY
f CONFUTED RESISTIVITY
APPARENT RESISTIVITY
END OF RESIST
234,
273.
312,
351,
...I______I______ I______ I—
APPENDIX
C
COMPUTER PROGRAM GTOWER
FUNCTION
GTOWER computes the ground resistance of a transmission line structure and the earth
surface potential profiles at any point around the base of the tower.
The program can be used to analyze any structure grounding system made of cylindrical
horizontal and vertical conductors buried in a uniform or two-layer earth.
REFERENCES
Information on this program is given in Chapter 2. The theoretical basis of GTOWER is
described in Chapter 5. A typical application of GTOWER is shown in Chapter 3. Other
examples are examined in Chapter 10.
GENERAL
GTOWER was developed for use in an interactive mode. In this mode, the user is prompted
to provide the required input data and answers in free-format. A typical interactive session
is shown in Page C-6.
The program can also be readily operated in batch mode. In this mode, the user must organize
the data in a file prior to running the program. The batch mode is particularly advantageous
when running several cases with small differences in the input data. The following guidelines
and the interactive session shown in Page C-6 provide the necessary instructions to build
an input data file for the program GTOWER.
GUIDELINES
All values entered on a data line must be separated by a comma. Blanks are interpreted as
a YES, zero or default answer, depending on the data expected by the program.
GTOWER accepts up to 10 different types of data lines. Occasionally, several data lines of
the same type are accepted by the program. In this case, the user must enter a line consisting
of the world END as the last entry to instruct the program that the series of data lines of
the current type has ended.
A typical input data file is shown in Page C-5. This file can be prepared based on the
following guidelines:
C-1
Data Line 1 : Start
This line must necessarily be a YES to initiate execution of the program. A NO will stop
the program.
Data Line 2 : Comment
Enter any alphanumeric character to provide comments and general references. These lines
are not processed by the program but simply reprinted at the top of the output printout.
Up to four lines of comments may be entered. If less than four comment lines are entered,
the comments must be terminated with a line consisting of the word END.
If the character
is among the characters entered in a comment line, all the information
to the right of this character is ignored. This is a useful feature (for both interactive
and batch modes) which allows the user to include additional comments in the input data
which will not appear in the printout.
Data Line 3 : Run Identification
Enter a four digit identification code which will be printed at the top right-hand side of
each page of printout.
Data Line 4 : System of Units
If the metric system is to be used, provide a data line beginning with a YES. If the British
system of units is requested, two data lines are needed; line 1 is a NO and line 2 is a YES.
Data Line 5 : Symmetry
Generally, a transmission line structure is symmetrical. If so, only ground conductors in the
positive quadrant need be inputted if the coordinate system is centered at the base of the
structure.
Program GTOWER does not accept as input, ground conductors located outside of the positive
quadrant of the coordinate system which has its xoy plane on the surface with the oz axis
directed toward the center of earth. This is in no way a limitation of the program, since
the user can always locate the coordinate system far enough from the grounding system so
as to include the entire grounding system in the positive quadrant.
A line beginning with YES instructs the program that the grounding system is
symmetrical and that the ox and oy axes are the symmetrical lines. The origin of the
coordinate system is also a point of symmetry.
A NO entry simply means that the grounding system is in the positive quadrant of the
coordinate system.
C-2
Data Line 6 : Type of Terminal Used
Plots of the earth surface potential profiles are automatically produced by the program on
a terminal. If the terminal is a video screen, only one character at a time can be displayed
in a specific location. This is not the case of printers and hard-copy terminals which allow
overprinting.
The program uses two different routines to produce plots, depending on the type of terminal.
The hard-copy terminal routine produce the most accurate plots. However, the other routine
can be used on a video or a hard-copy terminal.
Enter a YES to select video terminal and a NO to select the hard-copy terminal.
Data Line 7 : Soil Data
This line may contain up to three values, separated by commas. The first two values are
the upper and lower layer earth resistivities of the earth respectively (in ohm-meters). The
third value is the upper layer height (in m or ft).
If the earth is uniform, only the first resistivity value need be entered. If either the lower
layer resistivity or upper layer height is zero, then uniform earth is assumed.
Data Line 8 : Fault Current
This line provides the fault current flowing to earth through the grounding system (in
amperes).
Data Line 9 : Ground Conductors
The user must enter one line per grounding system conductor or one line per positive quadrant
conductor if the system is symmetrical. If a ground conductor is curvilinear, it must first
be broken down into appropriate linear segments.
The ground conductors are entered in two steps. In the first step, all horizontal conductors
are entered. The last entry must be followed by an END line. If no horizontal conductors
exist, the END line must still be entered. In the next step, the vertical ground elements
are entered. An END line must be the last entry whether or not there are vertical elements.
At least one, and no more than 67 conductors can be specified. The radius of a vertical
conductor can not exceed 2 m (6.5 ft) and that of a horizontal conductor must be equal or
less to 0.5 m ( 1.6 ft). Horizontal conductors must be completely buried in earth.
Horizontal Conductors
The values in the following line are expected by GTOWER, separated by commas:
XO, YO, XE, YE, RAD, DEP
C-3
where
XO and YO are the X and Y coordinates of one end (origin) of the conductor (m or
ft).
XE and YE are the X and Y coordinates of the other end (extremity) of the conductor
(m or ft).
RAD is the radius of the conductor (m or ft).
DEP is the depth of the conductor (m or ft).
Vertical Conductors
The following data line must be entered to identify vertical conductors:
X, Y, RAD, LEN, TED
where
Xand Y are the coordinates of the vertical conductor (m or ft).
RAD is the radius of the conductor (m or ft)
LEN is the
length of the conductor (m or ft)
TED is the depth of the upper end of the conductor (m or ft).
Data Line 10 : Potential Profiles
The user may select up to ten profiles along which earth surface potentials will be computed
at specific intervals. Each profile is defined as follows:
XO, YO, XE, YE, SPA
where
XO and YO are the X and Y coordinates of the origin
of the profile
(m or
XE and YE are the X and Y coordinates of the extremity of theprofile
ft).
(m or ft).
SPA is the distance between two consecutive points of the profile (m or ft).
A line beginning with END instructs GTOWER that no more profiles are to be calculated.
Note that the profile points may be in any quadrant of the coordinate system.
C-k
INPUT DATA FILE FOR BATCH MODE PROCESSING
Y
BASE TEST FILE < APPENDIX C)
EXAMPLE FOR CHAPTER 3
TOWER GROUNDING PLUS ONE RING
END
EX2
N
Y
Y
Y
383.5*147.&6»8*405
lOOO
13.5*12.3*12.3*13.5*0.04 » 5 * 4
13.7*12.5*12.5*13.7*0.04*5.4
13.9*12.7*12.7*13.9*0.04*5.4
14.1*12.9*12.9*14.1*0.04*5.4
14.3*13.1*13.1*14.3*0.04*5.4
14.5*13.3*13.3*14.5*0.04*5.4
0.0*18.5*18.5*18.5*0.04*0.75
18.5*0.0*18.5*18.5*0.04*0.75
END
14.* 14.*0.04*5.36*0.04
END
14.0*0.0*14.0*30.0*0.5
END
C-5
TYPICAL INTERACTIVE DIALOGUE AND COMPUTER PROGRAM PRINTOUT
PROGRAM GTOWER
tttttttttttttt
THIS PROGRAM CALCULATES THE PERFORMANCE OF TRANSMISSION
LINE GROUNDING SYSTEMS DURING POWER FREQUENCY FAULTS!
- RESISTANCE OF GROWING SYSTEM
- EARTH SURFACE POTENTIALS (STEP AND TOUCH VOLTAGES)
NOTES !
1-RESPOND TO QUESTIONS BY YES OR NO
ORf WHEN APPROPRIATEf BY TYPING THE REQUIRED DATA,
2-Yf YEf YESf BLANK CHARACTERS AND RETURN CARRIAGE ARE
INTERPRETED AS YES. OTHER CHARACTERS ARE INTERPRETED AS NO,
3-0f 0,f BLANK CHARACTERS OR A RETURN CARRIAGE ARE INTERPRETED AS A ZERO VALUE
ORf WHEN APPLICABLEf ARE REPLACED BY DEFAULT VALUES.
START ?
? yes
••d-'d-o-'O
ENTER COMMENTS LINES, (MAXIMUM OF
TERMINATE WITH END AT BEGINNING OF A NEW LINE,
base test file (appendix C)
exasple for chapter 3
toner Sroundind plus one dround potential control rind
ENTER RUN IDENTIFICATION, (4 DIGITS)
? ex2
SYSTEM OF UNITS
-METRIC SYSTEM ?
? no
-BRITISH SYSTEM ?
? ses
? yes
IS YOUR TOWER (OR POLE) GROUNDING SYSTEM SYMMETRICAL ?
VIDEO TERMINAL OR HARD-COPY TERMINAL (PRINTER) FOR OUTPUT ?
VIDEO ?
? yes
ENTER SOIL DATA
ENTER TOP AND BOTTOM LAYER RESISTIVITIES (OHMS-METER)
AND TOP LAYER HEIGTH, (METERS OR FEET)
IF UNIFORM SOILf ENTER TOP LAYER RESISTIVITY ONLY,
EXAMPLE !R01fR02fH OR RO
? 383»5f147»66f8,405
?
ENTER FAULT CURRENT IN TOWER GROUNDING,
1000
C-6
COHFIIMATION OF TOWER GROUNDING
••'d —d**3'*«9
A- HORIZONTAL CONDUCTORS, <HAX. OF
16)
- ENTER THE (X»Y) COORDINATES OF CONDUCTOR EXTREMITIES (ORIGIN AND END)
THEN THE RADIUS FOLLOWED BY THE BURIAL DEPTH OF THE CONDUCTOR,
- ENTER EACH NEW CONDUCTOR ON A SEPARATE LINE,
- EXAMPLE i XOfYOfXEfYEiRABfDEPTH,
- ALL VALUES ARE IN METERS OR FEET,
- TERMINATE BY TYPING END AT THE BEGINNING OF ft NEW LINE
IS.SjlZ.SflZarO.SfO.OAfS.A
14.1>12,9,12,9,14,1,0,04*5.4
14.3.13.1.13.1.14.3.0. 04.5.4
14.5.13.3.13.3.14.5.0. 04.5.4
i 0.0,18,5,18.5,18.5,0.04,0.75
0.18.5.18.5.0.04.0.75
? 18.5.0.
? end
B- VERTICAL CONDUCTORS, (MAX, OF
8)
- ENTER THE (X,Y> COORDINATE OF THE CONDUCTOR,
THEN THE RADIUS, THE LENGTH AND TOP END DEPTH OF THE CONDUCTOR.
- ENTER EACH NEW CONDUCTOR ON A SEPARATE LINE,
- EXAMPLE I X,Y,RAD,LENGTH,DEPTH
- ALL VALUES ARE IN METERS OR FEET
- TERMINATE BY TYPING END AT THE BEGINNING OF A NEW LINE,
? 14.,14,,0,04,5.36,0,04
? end
POTENTIAL PROFILES AT THE SURFACE OF SOIL,(MAX,OF 10)
- ENTER THE <X,Y> COORDINATES OF PROFILE EXTREMITIES (ORIGIN AND END)
FOLLOWED BY THE SPACING BETWEEN TWO CONSECUTIVE POINTS.
- EXAMPLE I XO,YO,XE,YE,SPACING
- START EACH PROFILE SPECIFICATION ON A NEW LINE.
- ALL VALUES ARE IN METERS OR FEET
- TERMINATE BY TYPING END AT BEGINNING OF A NEW LINE,
? 14.0,0.0,14.0,30.0,0.5
? end
END OF INPUT DATA FOR PROGRAM GTOWER,
C-7
GTOWER PAGE 5 1
RUN ! EX2
tttmmtmmmmmtmmm
IBASE TEST FILE (APPENDIX C)
LE_F0R_CHAPTER_3£we
cohhents
mtmmmmmnnmtmum
%
POTENTIAL CONTROL RING
cohhents
!
ntmmmmmntnnmmtm
RUN IDENTIFICATION ( EX2
UNITS SYSTEH 5 BRITISH
SYHHETRICAL CODE 5 YES
POTENTIAL OPTION 5 YES
GTOWER PAGE { 2
RUN 5 EX2
SOIL DATA
I--------*
-
TOP LAYER RESISTIVITY
BOTTOH LAYER RESISTIVITY
TOP LAYER HEIGTH
REFLECTION FACTOR
t
5
J
t
383,500 OHHS-HETER
147.660 OHHS-HETER
8.405 FEET
-.444
FAULT CURRENT
I------------ *
- IF i 1000,000 AHPERES
GTOWER PAGE i 3
RUN : EX2
CONDUCTORS DATA
- HORIZONTAL CONDUCTORS
t---------- 1
YO
FEET
*- - - - - $
XE
FEET
---- S
—
YE
FEET
*- - - s
13.5000
12.3000
12,3000
!?:»
12.9000
13.1000
13,3000
18,5000
18,5000
13,5000
i!:W
14,1000
14,3000
14.5000
18.5000
18,5000
XO
FEET
14.1000
14.3000
14.5000
0.0000
18.5000
KRB
12,9000
13,1000
13.3000
18.5000
0.0000
RADIUS
FEET
DEPTH
FEET
t---------- 1
*---------- ?
0400
5.4000
m
5,4000
5.4000
5.4000
,7500
.7500
a
0400
0400
0400
0400
0400
C-8
- VERTICAL CONDUCTORS
1------ 1
Y
FEET
*---------- «
RADIUS
FEET
*---------- 1
LENGTH
FEET
*---------- S
DEPTH
FEET
1---------- 1
14.0000
14.0000
,0400
5.3600
,0400
X
FEET
GTOWER PAGE I 4
RUN \ EX2
PROFILES DATA
*-------------- $
--------END OF PROFILES------YE
XE
FEET
FEET
t---------- $
t---------- 1
------ ORIGIN OF PROFILES----YO
XO
FEET
FEET
1---------- 1
t---------- 1
14.0000
14,0000
0,0000
30,0000
SPACING
BETWEEN
POINTS IF)
t---------- 1
,5000
END OF INPUT DATA
AVERAGE NUMBER OF SERIES TERMS USEB=
5
GTOWER PAGE i
RUN t EX2
*
*
I COMPUTER RESULT %
t
*
GROUND POTENTIAL RISE
GPR i
1216243 VOLTS
RESISTANCE OF TOWER GROUNDING
*---------------------------------------- —$
RESISTANCE X 124621 OHMS
AVERAGE NUMBER OF SERIES TERMS USED=
5
C-9
5
BTQHEK PAGE J 6
RUN I EX2
POTENTIAL PROFILE 1 1
t----------- — -------------1
POINT
NUMBER
1
2
3
4
5
6
?
8
9
10
11
12
13
14
15
U
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
#
38
39
40
41
42
43
44
45
46
47
48
49
50
51
X
FEET
14.000
14.000
14.000
14.000
14.000
14,000
14,000
14,000
14,000
14.000
14,000
14.000
14,000
14.000
14.000
14,000
14.000
14.000
14,000
14,000
Y
FEET
-- *
0.000
.500
1,000
1.500
2,000
2.500
3.000
3.500
4,000
4.500
5.000
5,500
6,000
6.500
7,000
7.500
8.000
8.500
9.000
9.500
14,000
14.000
14,000
14.000
14.000
14,000
14.000
14.000
14,000
14.000
14,000
14,000
14,000
14,000
14,000
11*
10.000
14.000
14,000
14,000
14,000
14,000
14.000
14.000
14.000
14.000
14,000
14,000
14,000
14,000
14.000
18.500
19.000
19,500
20,000
20.500
21.000
21,500
22.000
22,500
23.000
23,500
24,000
24.500
25,000
10.500
11.000
11.500
12.000
12,500
13.000
13,500
14.000
14.500
15.000
15.500
16,000
16,500
17,000
11*
POTENTIAL
VOLTS
PERCENT
OF GPR
--- ------ 4
4
6189,711
6191,512
6196.936
6206.052
6218,978
6235.941
6257.046
6282.640
6313.074
6348.772
6390.232
6438.031
6492,832
6555.393
6626.771
6707.566
6798.145
6901.764
7019.012
7150,655
7301,250
7472.154
7668,011
7896,352
8169.292
8510,670
8959,655
9673.174
11620,592
9865.886
9356,276
9131,764
9055.782
9105,393
9275,290
50.893
50,908
50.953
51.028
51,134
51.273
51,447
51.657
51.908
52,201
52,542
52.935
53.386
53.900
54.487
55,151
55,896
56,748
57,712
58,794
60.033
61,438
63.048
64,926
67.170
69,977
73.668
79,535
95.547
81,120
76.930
75,084
74,459
74.867
76.264
Ml
m
10119,229
9556.326
8721,292
7981,065
83,203
78,574
71.709
65.622
60,532
56.256
52,590
49,414
46,630
44.167
41,969
39,996
38,240
36,622
7362,027
6841,881
6396.065
6009.817
5671.253
5371.629
5104.349
4864,312
4650.855
4454,009
C-10
GTOWER PAGE 5
RUN { EX2
POINT
NUMBER
--------- *
X
FEET
t---------- $
Y
FEET
*----- -—|
POTENTIAL
MOLTS
1---------- *
I--------- 1
14.000
14.000
14.000
25.500
26,000
26.500
i«
2:IH
14.000
14.000
14.000
14.000
14.000
23.000
28.500
29,000
29.500
30,000
4274,499
4110,144
3959.120
3819,890
3691.145
3571.763
3460.775
3357,342
3260.730
3170,295
35,146
33,795
32,553
31,408
30.350
29,368
28.455
27,605
26.811
26,067
C-11
PERCENT
OF GPR
7
GTOUER PAGE
RUN 5 EX2
,
0,
I__
1300.
3900,
2600.
5200,
6500.
7800.
.J______ i______ I______ I______ I______ I___
t
8
POTENTIAL (MOLTS)
9100.
10400,
11700,
13000.
..I______ I______ I__-
_I
+
0 0000-1
I
I
I
I
+
+
*
+
+
+
I
1
I
t
+
6.0000-1
+
i
s :o a 3 T i m o a e ^ —««««-* es
I
I
*
*
f
1
I
I
I
1
+
4
4
12,0000-1
+
I
I
I
I
I
I
1
I
I
4
«
rs ir-fr-t-n o s s -o
18,0000-1
1
I
1
1
I
I
4
4
+
I
24,0000-1
(
F
)
I
I
1
I
I
I
I
1
I
4
4
4
4
4
4
4
4
4
4
*
4
4
4
, GRID POTENTIAL RISE
4 EARTH SURFACE PROFILE # 1
EX2
PROFILE BASED ON
1000,00 AHPERES TONER CURRENT
C-12
«
GTfflO PAGE 5
RUN I EX2
L
0,
,
10
,
20
30.
40,
50.
T
0,0000-1
I
I
I
I
I
I
I
I
I
6.0000-1
I
I
■T
+
*
t
+
i
1
1
I
I
I
I
I
I
I
I
I
I
I
I
I
I
18.0000-1
I
I
I
I
I
I
I
I
I
12.0000-1
24,0000-1
1
I
I
I
I
I
I
I
I
, GRID POTENTIAL RISE
+ EARTH SURFACE PROFILE # 1
EX2
NQRHALIZED PROFILE BASED ON 100 VOLTS GPR
END OF GTtttER
mmmtm
C-13
60.
POTENTIAL (VOLTS)
^70,
^80,
^90,
9
100,
(
APPENDIX
D
COMPUTER PROGRAM PATHS
FUNCTION
PATHS is used to compute currents in the ground wire and in the structures of a single or
double circuit transmission line when a fault occurs at any structure on the line. Each line
extremity is connected to a terminal representing the equivalent network at the end of the
line.
Single, double and three phase-to-ground faults are permitted.
REFERENCES
Information on this program is given in Chapter 2. PATHS is based on the generalized
double-elimination method described in Chapter 6. A typical application of PATHS is described
in Chapter 3. Another example is analysed in Chapter 10.
GENERAL
PATHS was developed for use in an interactive mode. In this mode, the user is prompted
to provide the required input data and answers in free-format. A typical interactive session
is shown in Page D-10.
The program can also be readily operated in batch mode. In this mode, the user must organize
the data in a file prior to running the program. The batch mode is particularly advantageous
when running several cases with small differences in the input data. The following guidelines
and the interactive session shown in Page D-10 provide the necessary instructions to build
an input data file for the program PATHS.
GUIDELINES
All values entered on a data line must be separated by a comma. Blanks are interpreted as
a YES, zero or default answer, depending on the data expected by the program.
PATHS accepts up to 28 different types of data lines. Occasionally, several data lines of
the same type are accepted by the program. In this case, the user must enter a line consisting
of the world END as the last entry to instruct the program that the series of data lines of
the current type has ended.
A typical input data file is shown in Page D-9. This file can be prepared based on the
following guidelines:
D-l
Data Line 1(a) : Start
This line must necessarily be a YES to initiate execution of the program. A NO will stop
the program.
Data Line 1(b) : Detailed Explanations
Enter YES if you need detailed explanations (during interactive sessions) and NO otherwise.
Data Line 2 : Comment
Enter any alphanumeric character to provide comments and general references. These lines
are not processed by the program but simply reprinted at the top of the output printout.
Up to four lines of comments may be entered. If less than four comment lines are entered,
the comments must be terminated with a line consisting of the word END.
If the character
is among the characters entered in a comment line, all the information
to the right of this character is ignored. This is a useful feature (for both interactive
and batch modes) which allows the user to include additional comments in the input data
which will not appear in the printout.
Data Line 3 : Run Identification
Enter a four digit identification code which will be printed at the top right-hand side of
each page of printout.
Data Line 4 : System of Units
If the metric system is to be used, provide a data line beginning with a YES. If the British
system of units is requested, two data lines are needed; line 1 is a NO and line 2 is a YES.
Data line 5 : Detailed Printout
A YES in this line is a request for computation of the currents in every structure and ground
wire span of the transmission line.
If a NO is entered in this line, data lines 6 to 8 should be skipped because the optional
plots produced by PATHS only display the detailed computation results in graphical form.
Data Line 6 : Plots of Structure Currents
Enter a YES if plots of the currentin a structure, as a function of the structure (tower)
number, are required. A NO must be entered if the plots are not required.
Data Line 7 : Plots of Span Currents
Enter a YES if a plot of ground wire span currents on each side of the faulted structure
as a function of the span number, is required. Enter a NO if this is not required.
D-2
Data Line 8 : Type of Terminal Used
Skip this line if a NO was entered in lines 6 and 7. If the terminal is a video screen, only
one character at a time can be displayed in a specific location. This is not the case of
printers and hard-copy terminals which allow overprinting.
The program uses two different routines to produce plots, depending on the type of terminal.
The hard-copy terminal routine produce the most accurate plots. However, the other routine
can be used on a video or a hard-copy terminal.
This line should be a YES for a hard-copy terminal. Two lines, a NO followed by a YES,
are needed to select the video terminal.
Data Line 9 : Zero Impedances
True zero impedance values cannot exist in reality. In order to avoid computation errors
due to zero impedance loops, PATHS modifies zero resistance and inductance values to 0.001
ohms. This does not apply to mutual impedances.
If zero impedance values are required, this line should be a YES, otherwise NO.
Data Line 10 : Line Transposition
Enter YES if transmission line conductors are transposed, otherwise NO.
When the transposed transmission line is so specified, PATHS assumes that all mutual
impedances between the phase conductors of a circuit are equal and that the mutual
impedances between the equivalent ground wire and the phase conductors of a circuit are
also equal.
Data Line 11 : Single or Double Circuit
Enter a YES for a single circuit transmission line. Enter NO and then YES in the next line
if the problem involves a double circuit transmission line.
Data Line 12 : Line Voltage
This is a pair of values separated by a comma. The first value represents the real part of
the line voltage of phase A of circuit 1 (in kV). The second value is the imaginary part of
this voltage (in kV). Generally, it is easier to take this voltage vector as the reference
vector (zero imaginary part). The voltages of the other phases are automatically generated
by PATHS.
Data Line 13(a) : Nature of Left Terminal
Enter a YES if the left terminal is a power source (contributes a current into the fault)
with respect to circuit No. 1, otherwise NO.
D-3
Data Line 14(a) : Left Terminal Data
Enter the following data:
NAME, RG, IG, REQ1, IEQ1, REQ2, IEQ2
where
NAME is the name of the terminal.
RG+jIG is the ground impedance of the grounding system of the terminal (in ohms).
REQl+jlEQl is the equivalent system impedance of the terminal for circuit No. 1
(in ohms).
REQ2+jIEQ2 is the equivalent system impedance of the terminal for circuit No. 2
(in ohms).
Data Line 15(a) : Number of Structures on Left Side
Enter the number of structures between the faulted structure, No. 0, and the left terminal.
This value must be greater than zero.
Data Line 13(b) : Nature of Right Terminal
Similar to 13(a)
Data Line 14(b) : Right Terminal Data
Similar to 14(a)
Data Line 15(b) : Number of Structures on Right Side
Similar to 15(a)
Data Line 16(1) : Phase Impedance of Circuit 1
Enter the resistance and reactance of the phase conductors of circuit No. 1 (in ohms/km or
in ohms/mile). This is the average value of the phase impedances computed by a line
parameter program.
If the transmission line is not transposed, skip the following data lines 17, 18 and 19.
D-4
Data Line 17(1) s Phase-to-Phase Mutual Impedance
This is the average value of mutual impedance between phase conductors of circuit No. 1
(resistance and reactance in ohms/km or ohms/mile).
Data Line 18(1) : Ground Wire-to-Phase Mutual Impedance
This is the average value of mutual impedance between the ground wire and the phase
conductors of circuit No. 1 (in ohms/km or ohms/mile).
Data Line 16(2) : Phase Impedance of Circuit 2
Similar to 16(1) but for circuit No. 2 (if any).
Data Line 17(2) : Phase-to-Phase Mutual Impedance
Similar to 17(1).
Data Line 18(2) : Ground Wire-to-Phase Mutual Impedance
Similar to 18(1)
Data Line 19 : Circuit-to-Circuit Mutual Impedance
This is the average value of the mutual impedance between the phase conductors of circuit
No. 1 and circuit No. 2 (in ohms/km or ohms/mile). This. data line must be entered only in
the case of a double circuit line.
Skip the following data line (20) if the transmission line was specified to be transposed.
Data Line 20 : Mutual Impedances of Untransposed Lines
Because the transmission line is untransposed, the mutual impedance between each pair of
conductors must be specified. The unspecified values are assumed to be zero. The mutual
impedance value between two conductors is specified as follows:
ID1, ID2, RMU, IMU
where
ID1 and ID2 identify the first and the second conductor respectively. Al, B1 and Cl
designate phases A, B and C of circuit No. 1 and GW designates the ground wire.
RMU+jXMU is the mutual impedance (in ohms/km or ohms/mile).
When the mutual impedance of all conductor pairs have been specified, an END line must
be entered to instruct the program to move to the next type of data.
Data Line 21 : Ground Wire Self Impedance
Enter the resistance and inductance of the impedance of the ground wires or lumped equivalent
ground wire in ohms/km or ohms/mile.
D-5
Data Line 22 : Faulted Structure Impedance
Enter the resistive
structure (in ohms).
and
inductive
components
of
ground
impedance
of
the
faulted
Data Line 23 : Fault PATH Impedances
The program PATHS assumes that there is a connection between the phase conductors, ground
wire and the "faulted" tower structure. These connections define the fault paths. By default,
PATHS assumes an infinite impedance path (open connection) between the phase conductors
and the structure and a zero impedance path (solid metallic connection) between the ground
wire and the structure. This corresponds to a no fault condition.
The user may simulate any type of fault by specifying impedance values other than the
default values. It is only necessary to define those values which are different from the
default values. For example a ground fault on phase A of circuit 1 is created by entering
the following data line:
Al, 0.0, 0.0
This implies that the fault impedance path between phase conductor Al and the structure
is O.O+jO.O ohms. The general format of the data line is:
ID, RCON, ICON
where
ID is the conductor identification as defined in data line 20.
RCON+jICON is the fault path impedance (in ohms).
A line beginning with END must be entered after all fault path impedances have been
defined.
Data Line 24(a) : Distances Between Left Side Structures
Enter a YES if the structures on the left side of the faulted structure are to be considered
egually spaced. In this case, the average spacing between two consecutive structures is
specified in the next data line (type 25) and the ground impedances of the structures are
specified by data lines of the type 26.
If a NO is entered, specifying that the distance between two adjacent structures is variable
along the left section of the line, then the distance between a structure and the adjacent
structure to the left and the structure ground impedance must be defined by data lines
of the type 27.
Consequently, in the case of a YES, data line 27 must be skipped and for a NO, both data
lines 25 and 26 must be ignored.
Data Line 25(a) : Average Left Side Structures Spacing
Enter the average spacing between two adjacent structures on the left portion of the
transmission line (in m or ft).
D-6
Data Line 26(a) : Left Side Structures Ground Impedances
The general format of this line is:
I, 3, RTOWER, ITOWER
where
I and 3 represent the group of structures bearing the numbers I and 3, all having the
following ground impedance:
RTOWER+jITOWER is the ground impedance of structures No. I to 3 (in ohms).
An END line must be entered once all structures have been specified.
Only one structure is specified when 1=3. It is possible to overwrite the specification of a
structure by entering a new data line followed by a data line beginning with a NO to confirm
that overwriting is not accidental. For example, if 1=5 and 3=21 in one data line and later
a line with 1=17 and 3=18 is entered, then structures 17 and 18 will have the last specified
values only if a data line with NO is entered immediately after the new structure specification.
Data Line 27(a) : Left Side Structures Data
This data line is used when the distances between structures are not equal. The general
format of this line is:
I, 3, SPA, RTOWER, ITOWER
where
I and 3 represent the group of structures bearing the numbers I and 3. These structures
are all separated by the following distance and have the following ground
impedance.
SPA is the distance between two consecutive structures (in m or ft).
RTOWER+jITOWER is the ground impedance of structures No. I to 3 (in ohms).
A line beginning with END must be entered to instruct the program that all structures have
been specified.
The procedure for overwriting previously specified values is also applicable (see data line
26).
Data Line 28(a) : Left Side last Structure Spacing
This is the distance between the left terminal and the closest transmission line structure
(in m or ft). This structure is the highest numbered structure of those on the left of the
faulted structure (structure No. 0).
D-7
Data Line 24(b) ; Distances Between Right Side Structures
Similar to data line 24(a).
Data Line 25(b) : Average Right Side Structure Spacing
Similar to data line 25(a).
Data Line 26(b) : Right Side Structure Ground Impedances
Similar to data line 26(a).
Data Line 27(b) : Right Side Structure Data
Similar to data line 27(a).
Data Line 28(b) : Right Side Last Structure Spacing
Similar to data line 28(a). This is the last data entry of the program PATHS.
D-8
INPUT DATA FILE FOR BATCH MODE PROCESSING
Y
Y
BASE TEST FILE <APPENDIX D>
EXAMPLE FOR CHAPTER 3
SINGLE CIRCUIT
NO RING
EX I
N
Y
Y
Y
Y
N
Y
Y
Y
Y
345
Y
TlrO.01*0.0**99*14.85
14
Y
T2»0.01*0.0*2.64*39.59
85
0.141*1.169
0.091*0.579
0.090*0.536
0.808*1.234
31.67
A1*0.0*0.0
END
Y
800.
1*1*27*O
2*3*24 *O
4*5? 22 * O
6*14*20*0
END
800 ♦
Y
800.
1*1*28*0
2*3*27*0
4*7*24*0
8*10*22*0
11*85*20*0
END
800 .
D-9
TYPICAL INTERACTIVE DIALOGUE AND COMPUTER PROGRAM PRINTOUT
PR08RAH PATHS
%%%%%%%%%%%%%
THIS PROGRAM CALCULATES THE DISTRIBUTION OF FAULT CURRENT IN A
TRANSMISSION LINE SUBJECT TO A FAULT ON A TOWER.
NOTES :
1-RESPOND TO QUESTIONS BY YES OR NO
OR. WHEN APPROPRIATE. BY TYPING THE REQUIRED DATA,
2-Yf YE. YES. BLANK CHARACTERS AND RETURN CARRIAGE ARE
INTERPRETED AS YES. OTHER CHARACTERS ARE INTERPRETED AS NO,
3-0. 0., BLANK CHARACTERS OR A RETURN CARRIAGE ARE INTERPRETED AS A ZERO VALUE
OR. WHEN APPLICABLE. ARE REPLACED BY DEFAULT VALUES,
START
? yes
DO YOU WANT A PRINTOUT OF THE GUIDELINES BEFORE STARTING THE CONVERSATIONAL SESSION ?
? yes
GENERAL GUIDELINES
tttttttttttttttttt
1- YOU CAN MODEL A SINGLE OR DOUBLE CIRCUIT TRANSMISSION
LINE WITH NO OR ONE OVERHEAD GROUND-WIRE, IF THERE ARE
SEVERAL GROUND-WIRES, FIND AN EQUIVALENT FICTITIOUS 0H6W CONDUCTOR
(YOU CAN USE BUNDLE REDUCTION TECHNIQUES OR EQUIVALENT
(SEE COMPUTER PROGRAM LINPA),
2- ALL IMPEDANCES AND VOLTAGES MUST BE ENTERED IN CARTESIAN FORM,
I.E., FIRST ENTER REAL PART THEN IMAGINARY PART OF NUMBER.
EXAMPLE ’, RNUMBER, INUMBER
3- IF THE PHASE CONDUCTORS OF ONE CIRCUIT ARE NOT TRANSPOSED
YOU MUST ENTER THE MUTUAL IMPEDANCE BETWEEN ALL PHASE AND
GROUND WIRE CONDUCTORS OF ALL CIRCUITS (EXCEPT WHEN ZERO),
HOWEVER WHEN THE PHASE CONDUCTORS OF ALL CIRCUITS ARE DECLARED
TRANSPOSED, YOU MUST ENTER ONE AVERAGE VALUE FOR THE
MUTUAL IMPEDANCE BETWEEN i
A- ALL
B- THE
C~ THE
(*> TOTAL
PHASES OF A CIRCUIT*, AND
PHASES OF CIRCUITS 1 I 2 (DOUBLE CIRCUIT), AND
PHASE CONDUCTORS AND THE GROUND-WIRE FOR EACH CIRCUIT*
OF TWO VALUES FOR A DOUBLE CIRCUIT LINE
TO ENABLE THE TRANSPOSITION OPTION, ANSWER IYESI TO THE
APPROPRIATE QUESTION (SEE BELOW)
4- WHEN THE PHASE CONDUCTORS ARE NOT TRANSPOSED THE MUTUAL
IMPEDANCES ARE SPECIFIED USING THE FOLLOWING CONDUCTOR
IDENTIFICATION CODE !
Al- PHASE A OF CIRCUIT
LINE VOLTAGE ANGLE
Bl- PHASE B OF CIRCUIT
LINE VOLTAGE ANGLE
Cl- PHASE C OF CIRCUIT
LINE VOLTAGE ANGLE
A2- PHASE A OF CIRCUIT
VOLTAGE ANGLE
jo_ LINE
t
1
=
1
=
1
=
2
=
0
+120 SHIFT
+240 SHIFT
0
GW- EQUIVALENT SINGLE OVERHEAD GROUND-WIRE
D-10
5- ft SECTION. IS DEFINED AS THE PORTION OF TRANSMISSION LINE BETUEEN
TWO GROUNDED POINTS OF THE GROUND-WIRE AND THE GROUNDING SYSTEM
(USUALLY A TOWER GROUND) AT THE SECTION'S EXTREMITY WHICH IS OPPOSITE
TO THE FAULT LOCATION.
NORMALLY THESE POINTS CORRESPOND TO A TRANSMISSION LINE TOWER
WICH IS CONNECTED TO THE GROUND WIRE.
6- YOU CAN SPECIFY IN ONE DATA LINE ONE OR SEVERAL CONSECUTIVE
SECTIONS WITH IDENTICAL CHARACTERISTICS. YOU ARE ALLOWED
TO ENTER A MAXIMUM OF 200 SECTION DATA LINES.
NO LIMITS ARE ASSIGNED TO THE NUMBER OF SECTIONS PROVIDED HOWEVER
THAT THE NUMBER OF SECTION DATA LINES IS NOT EXCEEDED
7- ALL UNSPECIFIED MUTUAL IMPEDANCE VALUES ARE ASSUMED ZERO
ALL UNSPECIFIED SECTION DISTANCES ARE ASSUMED EQUAL TO
THE LAST SPECIFIED SECTION DISTANCE,
ALL UNSPECIFIED TOWER IMPEDANCES ARE ASSUMED AS 99999.+J0.
UNLESS THE ZERO IMPEDANCE ACCEPTANCE OPTION IS ACTIVATED
ANY ZERO RESISTANCE OR INDUCTANCE SPECIFIED BY THE USER
WILL BE TAKEN AS 0.001
8- TO SIMULATE PHASE TO TOWER FAULT» SPECIFY AN APPROPRIATE
LOW IMPEDANCE CONNECTION BETWEEN THE FAULTED PHASE(S)
AND THE TOWER STRUCTURE,
IF NOTHING IS SPECIFIED FOR A GIVEN PHASE CONDUCTOR THEN THE PROGRAM
ASSUMES NO CONNECTION BETWEEN THIS PHASE AND TOWER STRUCTURE
BY DEFAULT THE EQUIVALENT GROUND WIRE IS ASSUMED TO HAVE A
PERFECT CONNECTION TO THE TOWER STRUCTURE, HOWEVER YOU CAN
SIMULATE A BAD OR OPEN CONNECTION (GW-TOWER) BY ENTERING A
SUITABLE IMPEDANCE VALUE FOR THIS GROUND WIRE TO TOWER CONNECTION
ENTER COMMENT LINES. (MAXIMUM OF 4)
TERMINATE WITH iENDt AT BEGINNING OF A NEW LINE,
base test file (appendix D)
example for chapter 3
single circuit
no around potential control rind
ENTER RUN IDENTIFICATION. (4 DIGITS)
? exl
SYSTEM OF UNITS
- METRIC ?
? no
- BRITISH ?
? yes
DETAILED PRINTOUT OPTION.
CURRENT IN EACH TOWER WILL BE CALCULATED MS PRINTED ?
? yes
DO YOU WANT PLOTS OF I
1- FAULT CURRENT DISTRIBUTION IN TOWERS ?
? yes
2- FAULT CURRENT DISTRIBUTION IN OVERHEAD GROUND WIRE ?
? yes
PRINTOUT ROUTED TOt
- A PRINTER OR A HARD-COPY TERMINAL?
? no
D-11
- ft VIDEO TERHINftl <NO OVERWRITE CAPABILITY) ?
? aes
ARE YOU PLAHHIHG TO ENTER ZERO IHPEDANCE VALUES ?
? aes
ARE YOUR PHASE CONDUCTTOS TRANSPOSED ?
? aes
SINGLE OR DOUBLE CIRCUIT
-SINGLE ?
? aes.
ENTER THE LINE VOLTAGE IN KV (PHASE TO PHASE).
EXAKPLE S RVOLTfIVQLT.
? 345
DATA FOR LEFT-SIDE OF FAULTED TOWER
EACH CIRCUIT OF THE TERMINAL REPRESENTS
A SOURCE OR A LOAD.
IS THE TERMINAL A SOURCE WITH RESPECT TO CIRCUIT NUMBER ONE ?
? aes
TERMINAL DATA
ENTER THE NAME, THE GROUNDING SYSTEM IMPEDANCE (OHMS)
AND THE EQUIVALENT TERMINAL IMPEDANCE (OHMS) OF CIRCUIT NUMBER ONE
FOLLOWED (WHEN APPLICABLE) BY THE TERMINAL IMPEDANCE (OHMS) OF CIRCUIT NUMBER TWO.
EXAMPLE! NAME'RGROUNDjIGRQUNDjREQII>IEQtliREQf2rIEQ*2
? TliO.OlfO.Oi.99*14,85
? 14
ENTER THE NUMBER OF GROUNDED TOWERS ON THIS SIDE OF FAULTED TOWER,
NOTE ! TERMINAL IS NOT CONSIDERED AS A TOWER
DATA FOR RIGHT-SIDE OF FAULTED TOWER
EACH CIRCUIT OF THE TERMINAL REPRESENTS
A SOURCE OR A LOAD,
IS THE TERMINAL A SOURCE WITH RESPECT TO CIRCUIT NUMBER ONE ?
? aes
TERMINAL DATA
ENTER THE NAME. THE GROUNDING SYSTEM IMPEDANCE (OHMS)
AND THE EQUIVALENT TERMINAL IMPEDANCE (OHMS) OF CIRCUIT NUMBER ONE
FOLLOWED (WHEN APPLICABLE) BY THE TERMINAL IMPEBANCE (OHMS) OF CIRCUIT NUMBER TWO,
EXAMPLEt NAME»RGRQUNB»IGROUND.REQHrIEQtl.REQ*2»IEQI2
? T2.0,01,0,0»2.64.39.5?
ENTER THE NUMBER OF GROUNDED TOWERS ON THIS SIDE OF FAULTED TOWER.
NOTE 1 TERMINAL IS NOT CONSIDERED AS A TOWER
CONDUCTOR IMPEDANCES
ENTER THE PHASE IMPEDANCE OF CIRCUIT 1 IN OHMS/MILE
EXAMPLE* RPHASE.IPHASE
? 0,141.1,169
ENTER PHASE TO PHASE MUTUAL IMPEDANCE FOR CIRCUIT 1 OHHS/HILE
EXAMPLE! RMUTUPHASE.IMUTUPHASE
? 0,091.0.57?
0-12
ENTER PHASE TO GROUND HIRE HUTUAL IKPEDANCE Fffi CIRCUIT 1 OHHS/HILE
EXAHPLE? RMUTU6R0UND»IMUTUGROIWD
? 0.090»0.536
ENTER GROUND HIRE IHPEDANCE IN OHHS/HILE
EXAHPLE: RGHfIGU.
f
0.808)1.234
ENTER THE FAULTED TWER GROUNDING IHPEDANCE (OHHS)
EXAHPLE 1 RFAULT) FAULT
? 31.67
PROVIDE CONDUCTOR TO TOMER STRUCTURE CONNECTION (FAULT PATH) IHPEDANCE (WHS)
UHEN DIFFERENT FROH DEFALT VAUES
I.E.)
PHASE CONNECTION ! OPEN
GROUND HIRE CONNECTION ! SOLID
EXAMPLE *, B2fRCON» ICON
TERMINATE WITH IENDt AT THE BEGINNING OF A NEH LINE.
AlfO.OfO.O
? end
TOMER IHPEDANCE
LEFT SIDE OF FAULTED TOMER
ARE ALL SPACIN6S BETWEEN TOWERS EQUAL ?
? yes
ENTER THIS SPACING.(METERS OR FEET)
? 800
?
?
?
?
?
ENTER THE TOMER IMPEDANCE (OHMS)
EXAHPLE1 IrJ)RTOHER)ITOUER
TERMINATE WITH END AT THE BEGINNING OF A NEH LINE
lri)27)0
2)3)24)0
4)5)22)0
6)14)20)0
end
WHAT IS THE DISTANCE BETWEEN THE LAST TWER AND TERMINAL STATION ? (H OR FT)
? 800
RIGHT SIDE OF FAULTED TOMER
ARE ALL SPACINGS BETWEEN TOWERS EQUAL ?
? ses
ENTER THIS SPACING.(METERS OR FEET)
? 800
ENTER THE TWER IMPEDANCE (OHMS)
example: I)J)RtoheR)Itower
TERMINATE WITH END AT THE BEGINNING OF A NEH LINE
? 1)1)28)0
? 2)3)27)0
? 4)7)24)0
?
8)10)22.0
? 11)85.20)0
? end
WHAT IS THE DISTANCE BETWEEN THE LAST TOMER AND TERMINAL STATION ? (M OR FT)
? 800
D-13
PATHS PAGE *. 1
RUN 5 EX1
INPUT DATA
mmmt
t
*
t
t
t
BASE TEST FILE (APPENDIX D)
EXAMPLE FOR CHAPTER 3
SINGLE CIRCUIT
m RING
%
RUN IDENTIFICATION ! EX1
UNITS SYSTEM
t BRITISH
TYPE OF CIRCUIT
5 SINGLE
PRINTOUT ON TERMINAL
OPTIONS SELECTED
ZERO IMPEDANCE ACCEPTANCE
t YES
TRANSPOSED PHASE CONDUCTORS
5 YES
DETAILED OUTPUT
I YES
PLOT OF CURRENT DISTRIBUTION IN TOWERS
S YES
PLOT OF CURRENT DISTRIBUTION IN GROUND WIRE I YES
PATHS PAGE 1 2
RUN S EX1
CIRCUIT DESCRIPTION
LEFT TERMINAL (NO.l) DATA
GROUNDING SYSTEM IMPEDANCE 5
CIRCUIT NUMBER ONE
EQUIVALENT SOURCE IMPEDANCE 1
SOURCE TERMINAL. VOLTAGE I
.990 +J
345.000 +J
.010 +J
0.000 OHMS
14.850 OHMS
0.000 KILOVOLTS
RIGHT TERMINAL (N0.2) DATA
NAME S T2
GROUNDING SYSTEM IMPEDANCE
5
.010 «
CIRCUIT NUMBER ONE
EQUIVALENT SOURCE IMPEDANCE 5
SOURCE TERMINAL. VOLTAGE !
2.640 +J
345.000 +J
0.000 OHMS
39.590 OHMS
0.000 KILOVOLTS
D-14
SELF 1HPEMNCE
CIRCUIT 1 {PHASE CONDUCTORS)
S
OVERHEAD EQUIVALENT GROUND HIRE l
,141 +J
,808 +J
1,16? OHHS/HILE
1,234 OHHS/HILE
CONDUCTOR TO FAULTED STUCTURE CONNECTION IMPEDANCE
PHASE Al TO TONER STRUCTURE
PHASE Bl TO TONER STRUCTURE
PHASE Cl TO TOWER STRUCTURE
GROUND WIRE TO TOWER STRUCTURE
!
5
0,000 +J
------- OPEN
------- OPEN
0.000 +J
l
1
0*000
—
0*000
PATHS PAGE I 3
RUN : EX1
HUTUAL IMPEDANCES
CONDUCTOR OF CIRCUIT <T0> CONDUCTOR OF CIRCUIT
Bl
Bl
1
1
1
Al
1
GN
Bl
1
Cl
1
Al
Al
IMPEDANCE OHHS/HILE
.091 «
.579
,091 +J
.579
.091 +J
,579
.090 FJ
,536
GW
1
1
1
0
0
.090 4J
.536
GN
0
,090 +J
.536
Cl
Cl
PATHS PAGE I 4
RUN i EX1
GROUND IMPEDANCE OF TONERS
FWILTED TONER *,
31,670 +J
0.000 OHHS
LEFT SIDE OF FAULTED TONER
NUMBER OF GROUNDED TONERS S
TOWER TO TONER
NO.
NO.
1
2
4
6
1
3
5
14
14
TOWER GROUND
IHPEDANCE
OHHS
27,000
24,000
22,000
20,000
DISTANCE FROM LAST TONER (NO.
+J
tJ
+J
W
DISTANCE FROM
PRECEDING TOWER
FEET
0,000
0.000
0,000
0.000
800.000
800.000
800,000
800,000
14 ) TO TERMINAL T1
D-1 5
\
800.000 FEET
RIGHT SIDE OF
FAULTED TWER
NUNBER OF GROUNDED TOUERS
1
3
7
10
85
4
8
11
DISTANCE
85
TOWER GROUND
IMPEDANCE
OHMS
TOWER TO TOWER
NO.
*N°'
1
2
i
28.000
27.000
24.000
22.000
20.000
+J
«
«
+J
+J
DISTANCE FROM
PRECEDING TOWER
FEET
^
0.000
0.000
0.000
0.000
0.000
800.000
800.000
800,000
800.000
800.000
FROH LAST TtSiER (NO. 85 ) TO TERMINAL T2
I
800.000 FEET
END OF INPUT DATA
PATHS PAGE i 5
RUN 5 EX1
COMPUTATION RESULTS
mmmtmmm
CURRENT DISTRIBUTION AT FAULTED TOWER
NATURE OF CURRENT
MODULE
AMPERES
ANGLE
RADIANS
______ ____________
*
* TOTAL FAULT
t TOTAL EARTH
t
15272.103
376.073
t
t LEFT SIDE GROUND WIRE
* RIGHT SIDE GROUND WIRE
%
% LEFT SIDE PHASE Al
8936,025
5993,235
RIGHT SIDE PHASE Al
11499,338
3773,411
% LEFT SIDE PHASE Bl
114.460
116.113
t
-1.45 t
-1,07 t
$
1,71 *
1.65 $
*
-1,45 *
-1,44 1
Jr
* RIGHT SIDE PHASE Bl
t
I
III ME 11
1
t------------- -------- --- ------ *
FWILTED TOWER POTENTIAL RISE t
-1.72 *
1.43 t
*
1:8 f
t
----------------------------------------- 1
11910.243 V.» < -1.07> RADIANS
D-16
PATHS PAGE 5 6
RUN ! EX1
DETAILED PRINTOUT
%%%%%%%%%%%%%%%%%
CURRENT IN EACH SECTION AND TOWER
LEFT
SECTION
NO.
t-
SIDE OF FAULTED TOWER
SECTION CURRENT
RODULE
ANGLE
AMPERES RADIANS
TOWER
NO.
TOWER CURRENT
MODULE
ANGLE
AMPERES RADIANS
t
t
*
%
t
t
t
t
t
t
1
2
3
4
5
6
7
8
9
t iO
* 11
* 12
13
t 14
t
%
*
15
8936.025
8557,254
8169,789
7819.224
7475.273
7168.133
6869.129
6607.428
6381.656
6190.642
6033.404
5909.143
5817.228
5757.196
5728.742
1.71
1.70
1.68
1.67
1.66
1.65
1.63
1.63
1.62
1.61
1.61
1.60
1.60
1.60
1.60
1
2
3
4
5
6
7
8
9
10
11
12
13
14
400.390
407.153
366.369
357.612
317.858
308.139
268.733
t
1
2.04 t
2,00 t
1.97 t
1,94 *
1.91 t
1.88 *
1,86 *
l.'HJ
160.195
126.380
93,359
60,919
28.856
1,80
1.79
1,78
1.77
1.76
t
t
t
*
*
t
- - - - -t
t-
D-17
PATHS PAGE 5 7
RUN I EX1
RIGHT SIDE OF FAULTED TOUER
SECTION
NO.
*1
t
t
%
t
%
t
t
%
t
t
t
t
TOUER
NO.
TOUER CURRENT
MODULE
ANGLE
AMPERES RADIANS
----- 1
—
i
2
3
4
5
6
7
8
9
10
11
12
i 13
t 14
* 15
t 16
l 17
* 18
* 19
t 20
* 21
t 22
$
1
$
*
*
l
l
1
SECTION CURRENT
ANGLE
MODULE
AMPERES RADIANS
23
24
25
26
27
28
29
30
5993.235
5631.547
5284.852
4964.605
4632.166
4325.692
4043.322
3783.372
3522.627
3283.152
3063.499
2842.257
2640.000
2455.466
2287,520
2135,140
1997.398
1873,443
1762,487
1663.783
1576.612
1500.267
1434.040
1377.217
1329.069
1288,853
1255,821
1229,226
1208,332
1192.428
1.65
1,62
1,60
1.58
1,55
1.53
1.51
1,50
1,48
1.47
1,46
1.45
1.45
1.45
1,45
1,46
1.47
1.49
1,50
1.53
1.55
1,58
1.61
1,64
1.68
1.71
1.74
1.78
1,81
1,84
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
390,626
371.612
340.549
350,699
320,815
293.265
267.864
266.670
243,242
221.759
222,268
202.525
184,535
168.143
153,206
139,595
127,193
115.892
105,594
96,211
87,661
79.870
72,771
66,302
60.408
55,037
50.143
45.683
41.620
D-18
2.03
1,98
1.94
1,89
1,84
1,80
1.75
1,70
1.65
1,60
t
%
»
*
t
*
*
t
*
t
»
t
1,55 *
1,50
1,45
1.40
1.35
1.30
1.25
1,20
1.15
1.10
1,05
1.00
.95
.90
,85
*
t
t
t
«
*
$
*
*
t
*
t
*
t
.80 «
,75 1
,70 *
,65 *
PATHS PAGE t 8
RUN t EXi
RIGHT SIDE OF FAULTED TOWER (CONTINUED)
SECTION
NO*
i
%
t
%
t
t
31
32
33
34
35
35
37
38
39
40
% 41
t
t
*
%
t
t
42
43
44
45
46
47
t 48
t
49
* 50
t
% 51
l 52
i
%
t
*
53
54
55
56
t 57
t
58
59
60
61
* 62
t
63
t
t
t
t 64
t #55
1180,839
1172,598
1167,758
1165,501
1165,379
1166,985
1169,960
1173,998
1178.837
1184.256
1190,072
1196.133
1202,313
1208.512
1214.648
1220,659
1226.494
1232.116
1237,498
1242.620
1247.472
1252.045
1256,340
1260,357
1264,101
1267.580
1270,802
1273,779
1276,521
1279,041
1281.351
1283.464
1285,393
1286,624
1288,224
1.87
1,90
1.93
1.95
1.98
2.00
2.01
2.03
2.05
2.06
2.07
2.08
2,09
2,10
2.11
2,11
2.12
2.12
2,12
2.13
2.13
2.13
2.13
2.14
2.14
2.14
2.14
2,14
2,14
2,14
2.14
2.14
2.14
2,14
2.14
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
58
59
60
61
62
63
64
37,917
33.776
31.591
28.812
26,254
23.916
21.785
19,844
18,075
16,463
14.995
13.656
12.437
11.325
10.313
9.390
8,549
7.783
7.085
6.449
5.870
5.343
4.863
4.426
4.029
3,668
3,340
23$5
.60
.56
,50
.45
,40
.35
.30
.25
,20
,15
.10
.05
-.01
-.06
-.11
-.16
-.21
-.26
-.31
-.36
-.41
-.47
-.52
-.57
-.63
-.68
-.74
2.531
2.311
2.114
1,937
1.597
1.617
-.91
-.97
-1.03
-1.09
-1.69
-1.15
D-19
t f
t
TOWER CURRENT
MODULE
ANGLE
AMPERES RADIANS
t
*
%
%
1
*
t
t
t
*
t
t
*
*
t
%
t
*
*
t
*
*
t
t
t
$
t
CJT-O
t
t
TOUER
NO,
03
t
t
*
SECTION CURRENT
ANGLE
AMPERES RADIANS
MODULE
*
*
*
t
t
*
PATHS PAGE J f
RUN 5 EXI
RIGHT SIDE OF FAULTED TONER (CONTINUED)
SECTION
NO.
if
t
t M
67
68
% 69
* 70
t
t
* 71
t
t
72
73
* 74
t 75
76
% 77
% 78
t
t
t
%
%
79
80
81
82
83
% 84
t 85
* 86
*
%
SECTION CURRENT
MODULE
ANGLE
AMPERES RADIANS
1289.672
1290.993
1292.199
1293.301
1294.310
1295.235
1296.088
1296.878
1297.615
1298.310
1298.972
1299.611
1300.237
1300.859
1301.488
1302,133
1302,805
1303,515
1304,272
1305,087
1305,973
2,14
2.14
2.14
2,14
2,14
2,14
2.14
2,14
2,13
2,13
2,13
2.13
2.13
2,13
2,13
2.13
2.13
2.13
2.13
2.13
2.13
TOUER CURRENT
MODULE
ANGLE
AMPERES RADIANS
TONER
NO,
65
1.474
1.366
1.274
1.195
1.128
1.074
1.029
.994
,968
.950
,938
,932
,933
,938
.949
.965
.986
1.013
1.047
1.088
1.137
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
—------- -------------------------- ----------------------- —---------- -- ------------------------
-1,19
-1,26
-1.33
-1,40
-1.47
-1.54
-1.60
-1,66
-1,71
-1.76
-1,79
-1.82
-1.84
-1.85
-1.86
-1.85
-1.83
-1.81
-1,77
-1,74
-1.69
St
%
*
t
St
t
t
*
*
t
»
t
t
St
t
t
t
«
St
t
$
t
t
---------------------
PATHS PAGE 5 10
RUN S EXI
RETURN EARTH CURRENT IN TERMINAL GROUND SYSTEMS
NAME
t------t
% T1
* T2
*
t-------
TERMINAL
POSITION
LEFT
RIGHT
MODULE
AMPERES
6058.651
2390,222
ANGLE
RADIANS
----------1
X
-1.37 X
-1.64 X
X
----------i
D-20
PATHS PAGE I 11
RUN I EXI
0,
I__
900,
1800,
2700,
3600,
4500.
3!?rn w s s c s a s
:s:
o » -s —io m c n
0,0000-1
I
I
I
1
1
I
I
I
I
7,5000-1
I
I
I
I
I
I
I
1
I
. CURRENT IN EACH SECTION
LEFT SIDE OF FAULTED TONER
D-21
5400.
CURRENT (HOMLE) AHPERES
6300.
7200.
8100.
9000,
PATHS PAGE
RUN t EXI
l
12
CURRENT (NODULE) AHPERES
1200.
1800.
2400,
3000.
3600,
4200,
4800.
5400.
6000,
0.
600.
I______ I_ _ _ _ __ J_____ „I_ _ _ _ _ _ _ I_ _ _ _ _ _ _ I_ _ _ _ _ _ _ I......... .... I_______ I_ _ _ _ _ _ _ I_______ I
0.-I
4
I
«
I
»
I
I
1
I
»
I
I
»
I
*
10,-I
t
I
I
t
1
4
i
i
i
4
i
«
4
i
i
4
i
4
20,-1
4
I
4
I
4
I
4
I
4
1
4
I
4
I
4
I
4
I
4
30.-I
4
I
4
I
4
I
4
I
4
4
I
I
4
4
I
I
4
4
I
40,-1
4
4
I
T
l
S
E
C
T
1
0
N
N
U
H
B
E
R
I
70,-1
I
I
I
I
1
I
I
I
I
80,-1
I
I
I
I
I
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
. CURRENT IN EACH SECTION
RIGHT SIDE OF FAULTED TOUER
D-22
PATHS PA6E *. 13
RUN 1 EXI
O,
41,
I__
I__
O.OOOO-I
CURRENT (HOWIE) AHPERES
82.
123.
164.
205.
246.
287,
328,
369.
410,
.1______ I______ I_______ I_______I_______I_______ I______ I_______I
I
I
T
0
y
E
R
1
I
I
I
I
I
I
7.0000-1
I
N
U
H
B
E
R
I
I
I
I
I
I
I
I
»
CURRENT IN EACH TOUER
LEFT
SIDE OF FAULTED TWER
D-23
PATHS PA6E I 14
RUN 1 EX1
CURRENT (HOWIE) AMPERES
0,
40,
80,
120.
160.
200,
240,
280.
320,
360,
400.
I___ ___ I_ _ _ _ _ _ _ I_ _ _ _ _ _ _ I_ _ _ _ _ _ _ I______ I______ I_______ I______ I_______ I_ _ _ _ _ _ _ I
0,-1
4
I
6
I
4
I
♦
I
»
I
4
I
4
I
4
I
4
I
4
10,-1
4
I
4
I
4
I
4
I
4
I
4
I
4
I
4
I
4
I
4
20,-1
4
I
4
I
4
1
4
I
4
I
4
I
4
I
4
I
4
I
4
30,-1
4
1
4
I
4
I
4
4
I
l
T
0
U
E
R
I
I
I
I
?0.-I
I
I
I
I
I
I
I
N
U
M
6
E
R
I
I
80,-1
I
I
I
I
. CURRENT IN EACH TOWER
RIGHT SIDE OF FAULTED TOWER
END OF PROGRAM PATHS
mmmtmmmt
D-Zk
APPENDIX
E
LIST OF SURVEY RESPONDENTS
1 - Alabama Power Company
2 - Alcan Smelter & Chemicals Ltd.
3 - Allegheny Power Service Corporation
4 - Atlantic City Electric Company
3 - Arkansas Power & Light Company
6 - Arizona Public Service Company
7 - American Electric Power Service Corporation
8 - Bonneville Power Administration
9 - Boston Edison Company
10 - Baltimore Gas & Electric Company
11 - British Columbia Hydro Power Authority
12 - Calgary Power Ltd.
13 - Consumers Power Company
14 - Cincinnati Gas & Electric Company
15 - Columbus & Southern Ohio Electric Company
16 - Central Hudson Gas & Electric Corporation
17 - Commonwealth Edison Company
18 - Central Illinois Public Service Company
19 - Central Louisiana Electric Company Inc.
20 - Delmarva Power & Light Company
21 - Duke Power Company
22 - Dallas Power & Light Company
23 - Florida Power Corporation
24 - Gulf States Utilities Company
25 - Georgia Power Company
26 - Hawaian Electric Company Inc.
27 - Hydro-Quebec
28 - Houston Lighting & Power Company
29 - Illinois Power Company
30 - Iowa Public Service Company
31 - Indianopolis Power & Light Company
32 - Iowa Electric Light & Power Company
33 - Idaho Power Company
34 - Kansas Gas & Electric Company
35 - Kansas City Power & Light Company
36 - Kentucky Utilities Company
37 - Los Angeles Department of Water & Power
38 - Lake Superior District Power Company
39 - Long Island Lightning Company
40 - Missouri Utilities Company
41 - Metropolitain Edison Company
42 - Minnesota Power & Light Company
43 - Mississippi Power & Light Company
44 - Nevada Power Company
E-1
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
-
New Brunswick Electric Power Commission
New Orleans Public Service Inc.
Northwestern Public Service Company
Nebraska Public Power District
Northeast Utilities Service Company
Niagara Mohawk Power Corporation
New York State Electric & Gas Corporation
Nova Scotia Power Corporation
Ontario Hydro
Ohio Edison Company
Otter Tail Power Company
Omaha Public Power District
Orange & Rockland Utilities Incorporation
Public Service Company of Oklahoma
Pensylvania Power Company
Puget Sound Power & Light Company
Public Service Electric & Gas Company
Pensylvania Power & Light Company
Puerto Rico Water Ressources Authority
Philadelphia Electric Company
Portland General Electric Company
Pacific Gas & Electric Company
Pacific Power & Light Company
Potomac Electric Power Company
Rochester Gas & Electric Corporation
Southwestern Public Service Company
Southern California Edison Company
Saskatchewan Power Corporation
St. Joseph Light & Power Company
San Diego Gas & Electric Company
Salt River Project Agricultural Improvement & Power District
Sierra Pacific Power Company
Seattle City Light Department
Tampa Electric Company
Texas Electric Service Company
The Dayton Power & Light Company
Toledo Edison Company
Tennessee Valley Authority
Utah Power & Light Company
Virginia Electric & Power Company
Wisconsin Electric Power Corporation
Wisconsin Public Service Corporation
Wisconsin Power & Light Company
Washington Water Power Company.
E-2
APPENDIX
F
ROCHESTER GAS AND ELECTRIC CORPORATION (RGE)
115 KV TRANSMISSION LINE GROUNDING
\*
At ics.
j
TEST
Figure F.1
TEST RESULTS
RGE1s 115 kV Transmission Line Test Site
F- 1
Kysorvi
RESISTIVITY MEASUREMENTS
TRAVERSE
i
^
01-1
TRAVERSE
Traverse parallel to transmission line. Center of traverse
about 60 meters (200 feet) north of structure 161.
I
Wenner method
i
Equipment used: Megger
RESISTIVITY MEASUREMENTS
TABLE f-
I
METER
READING
c
Traverse perpendicular to transmission line. Center of traverse
about 60 meters (200 feet) north of structure 161.
9
Wenner method
i
Equipment used: Megger
MEASURED VALUES
SCALE
FACTOR
s
APPARENT
RESISTANCE
R = c. s
(f!)
55.6
APPARENT
RESISTIVITY
P
(Q-m)
igST?
0.5
0.25
556
0.1
1.0
0.25
274
0.1
2.0
0.25
850
0.01
8.5
0.25
306
0.01
3-06
57-9
0.25
69
0.01
0.69
21.7
0.25
-
3.0
5.0
10.0
*
178.2
107.8
27.4
-
NOTE
-
-
**
METER
PROBE
PROBE
READING
SPACING DEPTH
c
a
b
(Meters (Meters)
E = 4 + aVb1
b
/F
;
APPARENT
RESISTANCE
R - c.s
APPARENT
RESISTIVITY
P
(ft-m)
(a)
NOTE
1.0
0.25
266
0.1
173.0
*
2.0
0.25
981
0.01
9-81
124.4
*
0.25
595
0.01
5.95
112.6
0.25
367
0.01
3.67
115.5
0.25
196
0.01
1.96
123.2
3.0
5.0
10.0
16.6
* For short spacings and relatively long buried probes, the following
formula must be used to determine the apparent resistivity.
2trbR
P = -----------------------------—--------—------2 In (2 *
+ 2/F - /t - £
1 +
SCALE
FACTOR
s
**
* For short spacings and relatively long buried probes, the following
formula must be used to determine the apparent resistivity.
where
01-2
9
MEASURED VALUES
PROBE
PROBE
SPACING DEPTH
a
b
(Meters) (Meters)
rge
TABLE
F = 1 + a2/bJ
** Questionable readings due (very probably) to buried metal structures.
2*rbR
p = ------------ -- ----------------------- ------------21n(-.-...—) + 2/F - /E - f
where
1 .
£ - k + az/bz
b
;
F - 1 + a2/b2
f-2
RESISTIVITY MEASUREMENTS
TRAVERSE
rge
RESISTIVITY MEASUREMENTS
TABLE
TRAVERSE
03
i
Traverse parallel to transmission line and adjacent to pole 162.
Center of traverse about 6 meters.
1
Wenner Method
i
Equipment used : Megger
o<,
I
Traverse parallel to transmission line and along path between poles
161 and 160. Center of traverse about halfway between poles.
I
Wenner method
8
Equipment used : Megger
MEASURED VALUES
MEASURED VALUES
METER
PROBE
PROBE
READING
SPACING DEPTH
c
a
b
(Meters (Meters)
TABLE
SCALE
FACTOR
s
APPARENT
RESISTANCE
R * c.s
(0)
APPARENT
RESISTIVITY
P
METER
PROBE
DEPTH
READING
b
c
(Meters)
NOTE
PROBE
SPACING
a
(Meters)
*
0.5
0.1
635
1.0
0.1
106
(Q-m)
APPARENT
RESISTANCE
R = c.s
(n)
APPARENT
RESISTIVITY
0.1
63.5
204.0
0.1
10.6
67.0
SCALE
FACTOR
s
P
(Q-m)
1.0
0.25
236
0.1
23-6
153-5
2.0
0.1
117
0.1
11.7
147.2
3.0
0.1
606
0.01
6.06
114.3
2.0
0.1
481
0.01
4.81
60.5
5.0
0.1
236
0.01
2.36
74.2
**
3.0
0.1
436
0.01
4.36
82.2
10.0
0.1
70
0.01
0.70
44.0
**
4.0
0.1
392
0.01
3.92
98.5
30.0
0.1
-
**
5.0
0.1
335
0.01
3.35
105.3
145.8
-
-
-
* For short spacings and relatively long buried probes, the following
formula must be used to determine the apparent resistivity.
8.0
0.1
290
0.01
2.90
12.0
0.1
249
0.01
2.49
187.7
16.0
0.1
214
0.01
2.14
215.1
20.0
0.1
118
0.01
1.18
148.3
30.0
0.1
57
0.01
0.57
107.4
2irbR
27TbR
p *
E *= A + a 2/b*
b
/f
;
f - 1 + a 2/b2
** Unreliable readings due (very probably) to buried metal structures.
------------------------------------------------------------------------
2 1n(2 * ■£) . 2/F - /I - £
2ln(IjLj!) ♦ 2/F - /E - £
1 +
*
For short spacings and relatively long buried probes, the following
formula must be used to determine the apparent resistivity.
p * --------- -------------------where
NOTE
where
1 ♦ /F
E => It + aJ/b2
b
;
F = 1 + a2/b2
POTENTIAL MEASUREMENTS
PROFILE
I
8
i
I
rge
TABLE
f-5
POTENTIAL MEASUREMENTS
PROFILE
02-1
Structure 161, pole A. Low Frequency Test
Return current electrode about 300 meters
feet) north of
transmission line right of way
Overhead ground wires connected to transmission line grounds
Equipment used:
- Selective voltmeter + ammeter
- Power Frequency generator.
B
l
(985
I
I
CURRENT
I
(Amperes)
2.0
20.0
40.0
60.0
2.0
80.0
100.0
2.0
2.0
120.0
llto.o
2.0
2.0
160.0
180.0
2.0
2.0
200.0
220.0
2.0
2.0
2140.0
260.0
276.0
Return
Current Probe
2.0
2.0
2.0
2.0
RGE 02"2
MEASURED VALUES
VOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
Z = /r2 -4- (J|2L2
<fi)
20.0
f-6
Structure 161, pole B, Low Frequency Test
Return current electrode about 300 meters (985 feet) north of
transmission line right of way
Overhead ground wires connected to transmission line grounds
Equipment used:
- Selective voltmeter + ammeter
- Power frequency generator
MEASURED VALUES
POTENTIAL
PROBE
LOCATION
(Meters)
TABLE
4.5
4.9
4.5
4.5
4.5
4.7
4.7
4.7
4.6
4.5
4.8
4.6
4.7
5.1
2.0
5.3
2.0
46.6
MEASURED
POTENTIAL
CURRENT
(in %
NOTE
FREQUENCY
of GPR )
(Hertz)
2.25
50
2.49
2.25
2.25
100
2.25
2.35
50
50
2.35
2.35
50
50
2.3
2.25
50
50
2.4
2.3
50
50
2.35
2.55
50
50
2.65
50
23.3
50
50
POTENTIAL
PROBE
LOCATION
(Meters)
3.35
0.
1.0
2.5
5.0
10.0
20.0
60.0
150.0
210.0
240.0
CURRENT
I
(Ampe res)
VOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
Z = /r2 + w2l2
(n)
2.0
2.0
1.7
0.85
0.0
0.0
2.0
2.0
5.5
5-6
2.75
2.8
2.0
5.0
2.0
2.0
5.6
5.7
2.0
2.0
2.0
2.0
6.2
5.9
5.9
2.5
2.85
0!
3.1
2.95
2.95
6.2
3.1
.
MEASURED
POTENTIAL
CURRENT
(in %
FREQUENCY
of GPR )
(Hertz)
50
50
50
50
50
50
so
50
50
50
50
50
* Measurement made at pole A of structure 161
** Measurement made at pole B of structure 161 (origin of profile)
NOTE
*
**
POTENTIAL MEASUREMENTS
PROFILE RGE
1
I
I
I
POTENTIAL MEASUREMENTS
TABLE F
PROFILE
°2-3
I
I
Structure 161 pole A, Frequency Sweep Test
Return Current electrode about 300 meters
feet) north of
transmission line right of way
Overhead ground wires connected to transmission line ground
Equipment used:
- Selective voltmeter + ammeter
“ Power frequency generator
(985
I
I
IhO.O
CURRENT
I
(Amperes)
(985
240.0
240.0
240.0
2.0
2.0
240.0
2.0
2.0
2.0
240.0
240.0
24o.o
240.0
240.0
240.0
--------- 241770-----
MEASURED VALUES
VOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
Z = /r* + w2L2
(!5)
2.0
2.0
2.0
2.0
1.0
1.0
. s
0 47
RGE 02-4
Structure 161 pole B,Frequency Sweep Test
Return current electrode about 300 meters
feet) north of
transmission line right of way
Overhead ground wires connected to transmission line grounds
Equipment used:
- Selective voltmeter + ammeter
- Fewer frequency generator
MEASURED VALUES
POTENTIAL
PROBE
LOCATION
(Meters)
TABLE
4.7
5.1
5.3
5.8
6.3
7.0
8.5
10.2
12.5
7.1
9.6
MEASURED
POTENTIAL
CURRENT
(in %
FREQUENCY
of GPR )
(Hertz)
2.35
so
2.55
2.65
7R
100
2.9
3.15
3.5
4.25
5.1
6.25
7.1
9.6
12.0
NOTE
240.0
240.0
240.0
240.0
150
200
250
400
600
1000
1000
POTENTIAL
PROBE
L0CAT1 ON
(Meters)
*
*
2000
4971
* Difference between the reading is probably caused by the sine wave distorsion
of the power frequency generator at 2 amperes and frequencies above 1 KHz.
CURRENT
I
(Amperes)
VOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
Z = /r2 + oj2L2
(12)
240.0
240.0
2.0
2.0
2.0
2.0
2.0
1.0
240.0
0.496
6.2
6.7
7.7
8.6
13-0
9.2
4.6
3-1
3.35
3.85
4.3
MEASURED
POTENTIAL
CURRENT
(i n %
NOTE
FREQUENCY
of GPR )
(Hertz)
50
6.5
9.2
100
200
400
1000
2000
9-274
5000
POTENTIAL MEASUREMENTS
PROFILE
i
fi
B
B
TABLE
f-9
POTENTIAL MEASUREMENTS
PROFILE
RGE 02-4
Structure 159 pole B, Frequency Sweep Test
Return current electrode about 300 meters ($85 feet) north of
transmission line right of way
Overhead ground wires connected to transmission line grounds
Equipment used:
- Selective voltmeter + ammeter
- Power frequency generator
8
1
B
I
2i(0.0
2*40.0
CURRENT
I
(Amperes)
MEASURED VALU ES
VOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
Z = /r2 + u)2L2
(a)
240.0
2.0
2.0
2.0
240.0
240.0
2.0
2.0
240.0
2.0
02-5
Structure 160 pole B, Frequency Sweep Test
Return current electrode about 300 meters (985 feet) north of
transmission line right of way
Overhead ground wires connected to transmission line grounds
Equipment used:
- Selective voltmeter + ammeter
- Power frequency generator
MEASURED VALUES
POTENTIAL
PROBE
LOCATION
(Meters)
rge
TABLE
4.6
5.15
6.45
8.60
13.0
20.6
2.3
2.575
3-225
4.3
6.5
10.3
MEASURED
POTENTIAL
CURRENT
(in %
NOTE
FREQUENCY
of GPR)
(Hertz)
POTENTIAL
PROBE
LOCATION
(Meters)
CURRENT
I
(Amperes)
50
100
200
240.0
240.0
240.0
400
1000
240.0
240.0
2.0
2.0
2.0
2.0
2000
240.0
VOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
Z = /r2 + ai2L2
(17)
MEASURED
POTENTIAL
CURRENT
(i n %
FREQUENCY
of GPR)
(Hertz)
2.0
3.35
3.95
5.25
7.70
13.2
1.675
1.975
2.625
3.85
6.6
50
100
200
400
1000
2.0
18.6
9-3
2000
NOTE
POTENTIAL MEASUREMENTS
PROFILE RGE
g
i
I
1
POTENTIAL MEASUREMENTS
TABLE p-n
PROFILE
°2-7
Structure 162 poles A and B, Frequency Sweep Test
Return current electrode about 300 meters (985 feet) north of
transmission line right of way
Overhead ground wires connected to transmission line grounds
Equipment used;
- Selective voltmeter + ammeter
- Power frequency generator
I
I
I
I
I
MEASURED VALUES
VOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
z = A2 * u>2l2
(fi)
A.9
MEASURED
POTENTIAL
CURRENT
(in *
FREQUENCY
of GPR)
(Hertz)
NOTE
2.45
2.65
3.2
4.05
50
100
200
400
A
A
A
A
210.0
2.0
2.0
2.0
210.0
2.0
5-3
6.4
8.1
210.0
210.0
2.0
2.0
17.7
6.35
8.85
1000
2000
A
A
210.0
210.0
2.0
2.0
7.7
7.6
3-85
3.8
50
100
B
B
210.0
2.0
14.3
7.15
1000
B
210.0
210.0
■n
CURRENT
1
(Amperes)
12.7
CO
A = pole A
B = pole B
02-8
Structure 163» Frequency Sweep Test
Return current electrode about 300 meters (985 feet) north of
transmission line right of way
Overhead ground wires connected to transmission line grounds
Equipment used;
- Selective voltmeter + ammeter
- Power frequency generator
MEASURED VALUES
POTENTIAL
PROBE
LOCATION
(Meters)
rge
TABLE F-'2
POTENTIAL
PROBE
LOCATION
(Meters)
CURRENT
1
(Amperes)
VOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
Z = /r2 + iu2L2
(n)
210.0
210.0
2.0
2.0
2.3
2.8
1.15
1.4
210.0
2.0
4.05
2.025
210.0
210.0
2.0
2.0
6.25
11.0
210.0
210.0
2.0
2.0
16.3
25.6
3.125
5.5
8.15
12.8
MEASURED
POTENTIAL
CURRENT
NOTE
(in %
FREQUENCY
of GPR )
(Hertz)
50
100
200
400
1000
2000
5000
POTENTIAL MEASUREMENTS
PROFILE
I
i
1
I
RGE
TABLE
f->3
POTENTIAL MEASUREMENTS
02-9
PROFILE
Structure 160 poles A and B, Frequency Sweep Test
Return current electrode about 300 meters
feet) north of
transmission line right of way
Downleads disconnected from pole ground rods
Equipment used:
- Selective voltmeter + ammeter
- Power frequency generator
i
i
(985
I
i
CURRENT
1
(Ampe res)
02-10
Structure 161 poles A and B, Low Frequency Test
Return current electrode about 300 meters (985 feet) north of
transmission line right of way
Downleads disconnected from pole ground rods
Equipment used : Megger
MEASURED VALUES
POTENTIAL
PROBE
LOCATION
(Meters)
rge
TABLE
MEASURED VALUES
VOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
2 = /r2 . gj2 L2
(a)
ho
MEASURED
POTENTIAL
CURRENT
(i n %
FREQUENCY
of GPR )
(Hertz)
50
NOTE
200.0
20370
1.0
1.0
')0.0
5071
50.1
1000
A
A
200.0
200.0
1.0
1.0
33.7
33-7
33.7
33.7
50
100
B
B
200.0
200.0
200.0
1.0
1.0
1.0
33.5
33.1
32.7
33.5
33.1
32.7
200
500
1000
B
B
B
200.0
1.0
32.6
32.6
2000
B
200.0
200.0
1.0
1 .0
20.3
20.3
19.8
SO
1000
AB
AB
19.8
POTENTIAL
PROBE
LOCATION
(Meters)
200.0
200.0
METER
READING
SCALE
FACTOR
828
0.1
1.0
APPARENT
IMPEDANCE
2
Z = /r
22
. g L
POLE
ID
{a)
107
82.8
107.0
MEASURED
CURRENT
FREQUENCY
NOTE
(Hertz)
A
B
i
Notes:
A = pole A ground rod
;
b = pole B ground rod
AB = pole A ground rod in parallel with pole B ground rod.
(
I
APPENDIX
TENNESSEE VALLEY AUTHORITY (TVA)
500 KV STAGED FAULT AND TOWER GROUNDING TEST RESULTS
,Portlano
ClARKSVIi
Gallatu
iGoodlelis
'
Xil
TEST
SITE
500 kV
kj0'®.
TRANSHISS IOli
I I MC
kflid Hii
•
i'3
\
Figure G.1
TVA1s 500 kV Johnsonvi11e-Cumber1 and Transmission Line
G-1
(
I
RESISTIVITY MEASUREMENTS
RESISTIVITY MEASUREMENTS
TABLE G-i
TRAVERSE
TRAVERSE
(Measured by TVA)
3
S
I
8
i
Traverse parallel to transmission line and directed toward
Johnsonvi11e
Wenner method with one current electrode kept in same location
(at tower 130)
Equipment used: Megger
MEASURED VALUES
£T>
l
MEASURED VALUES
APPARENT
RESISTIVITY
P
(ft-m)
APPARENT
RESISTANCE
(n)
NOTE
PROBE
SPACING
a
(feet)
1.5
3.0
ItO.O
235.3
*
1.5
3.0
3.0
31.0
2it8.4
*
5.0
3.0
17-5
196.5
*
3.0
5.0
10.0
3.0
7.5
150.7
*
10.0
15.0
3.0
4.9
143.9
*
15-0
20.0
3.0
4.2
162.9
*
20.0
30.0
3.0
2.6
150.2
30.0
ko.o
3.0
1.55
119.1
40.0
50.0
3.0
1.3
124.7
50.0
60.0
3.0
1.1
126.6
60.0
70.0
3.0
0.9
120.8
70.0
100.0
3.0
1.1
191.6
100.0
* For short spacings and relatively long buried probes, the following
formula must be used to determine the apparent resistivity.
PROBE
DEPTH
b
APPARENT
RES I STANCE
(n)
APPARENT
RESISTIVITY
P
(ft-m)
(feet)
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
264.7
*
41.0
328.6
*
30.0
337.0
*
13.8
277.3
*
8.0
235.0
*
4.9
190.1
*
3-3
190.7
2.49
191.4
2.1
201.5
2.3
2.35
264.7
315.4
1.1
210.8
For short spacings and relatively long buried probes, the following
formula must be used to determine the apparent resistivity.
ZtrbR
-----------------------—-------------------------------------
2 in
where
p =
E = i, + a2/b2
b
;
F " 1 + a2/b2
--------------------------------------------- ------------ —-
2 In(2 * l/t) + 2/F - /E - £
+ 2/F - /E - £
1 ♦ /F
NOTE
45.0
2nbR
p =
1-2
tva
(Measured by TVA)
i
Traverse parallel to transmission line and directed toward
Cumberland
Wenner method with one current electrode kept in same location
(at tower 130)
Equipment used : Megger
PROBE
PROBE
SPACING DEPTH
a
b
(feet)
(feet)
TABLE
where
1 + /F
E 3 A + a2/b2
b
;
F = 1 * a2/b!
g-2
RESISTIVITY MEASUREMENTS
TRAVERSE
tva
RESISTIVITY MEASUREMENTS
TABLE
2-1
TRAVERSE
(Measured by TVA)
Traverse perpendicular to transmission line in south-east direction
i
Wenner method with one current electrode kept in same location
(at tower 130)
Equipment used : Megger
S
Traverse perpendicular to transmission line in north-west direction
B
Wenner method with one current electrode kept in same location
(at tower 130)
I
Equipment used: Megger
MEASURED VALUES
PROBE
PROBE
SPACING DEPTH
a
b
(feet)
(feet)
1.5
3.0
5.0
10.0
15.0
20.0
30.0
40.0
50.0
60.0
70.0
100.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
MEASURED VALUES
APPARENT
RESISTIVITY
P
(ft-m)
APPARENT
RESISTANCE
(0)
NOTE
PROBE
SPACING
a
(feet)
49.0
36.2
19.8
288.2
290.1
*
224.4
a
6.0
120.6
*
10.0
3.1
91.1
*
15.0
2.7
104.7
*
20.0
1.77
102.3
30.0
1.38.
106.0
40.0
1.2
115.1
50.0
120.1
60.0
124.8
70.0
153.3
100.0
1.05
0.93
0.8
*
* For short spacings and relatively long buried probes, the following
formula must be used to determine the apparent resistivity.
1.5
3.0
5.0
PROBE
DEPTH
b
(feet)
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
APPARENT
RESISTIVITY
P
(fi-m)
APPARENT
RESISTANCE
(fi)
45.0
39.0
31.0
*
312.5
*
348.2
*
16.1
323.6
*
10.0
293.8
*
6.9
3.2
2.56
267.7
*
2.09
200.5
184.9
196.7
1.85
1.52
212.9
204.0
210.8
1.1
* For short spacings and relatively long buried probes, the following
formula must be used to determine the apparent resistivity.
2TbR
------ -----------------------------------------------------------
P
2 In (— ■*) + 2/F - /E - £
2 1n(2-—-) * 2/F - /E - £
where
1 ♦ /F
£ = 4 + a2/b2
b
;
F = 1 + a2/b2
NOTE
264.7
27TbR
p *
2-2
(Measured by TVA)
i
I
™
TABLE ^
where
1 + /F
E = 4 ♦ a2/b2
b
;
F
RESISTIVITY MEASUREMENTS
TRAVERSE
TABLE
g-5
RESISTIVITY MEASUREMENTS
TRAVERSE
TVA 03
(Measured by SES)
TABLE
tva oa
(Measured by SES)
B
Traverse orthogonal to transmission line in north-west direction
9
Traverse parallel to transmission line and centered at tower 130
I
Wenner method with one current electrode kept in same location
(at tower 130)
i
Wenner method with center of traverse kept at center of tower
9
Equipment used:
9
Current frequency kept constant at 70 Hz
9
Equipment used:
- Selective voltmeter + ammeter
- Power frequency generator
- Selective voltmeter + ammeter
- Power frequency generator
MEASURED VALUES
PROBE
SPACING
a
(feet)
O
I
U1
PROBE
DEPTH
b
(feet)
MEASURED VALUES
APPARENT
CURRENT
VOLTAGE
RESISTANCE
V (P -P ) I(C1-C2)
(fi)
(amperes)
(volts)
1 2
APPARENT
RESISTIVITY
P
(fi-m)
NOTE
PROBE
SPACING
a
(feet)
733.
682.
954.
297.
*
2.0
*
*
5.0
8.0
*
10.0
3.80
0.100
0.100
254.0
234.0
327.0
50.5
38.0
304.5
*
16.6
3-0
2.03
0.100
20.3
228.
*
23-3
10.0
3-0
0.617
0.100
6.17
12**.
*
30.0
*
1.5
0.15
2.54
0.010
1.5
0.25
2.34
0.010
1.5
0.25
3.27
0.010
1.5
3.0
5-05
3.0
3.0
5.0
15.0
3.0
0.657
0.200
3.285
20.0
3.0
0.558
0.200
2.79
96.5
108.2
30.0
3.0
0.390
0.200
1.95
112.7
90.0
1(0.0
3-0
0.286
0.200
1.43
109.9
110.0
1.26
120.9
150.0
130.6
160.9
50.0
3.0
0.252
0.200
60.0
3.0
0.193
0.170
70.0
3.0
0.168
0.180
1.13
0.933
100.0
3.0
0.126
0.150
0.84
40.0
70.0
PROBE
DEPTH
b
(feet)
0.33
0.33
0.33
0.33
3.0
3.0
3.0
3.0
3.0
3.0
3.0
3.0
VOLTAGE
CURRENT
APPARENT
V (P -P ) I (C1-C2) RESISTANCE
(volts)
(amperes)
(fi)
1 2
1.780
0.650
0.443
0.025
71.2
26.0
17.72
0.200
10.25
0.200
5.30
1.06
0.395
0.308
0.150
2.63
277.0
249.6
276.8
206.0
171.6
118.6
0.150
2.05
118.6
0.242
0.150
1.61
124.0
0.164
0.130
1.26
169.3
0.140
0.130
1.077
185.7
0.151
0.150
1.01
212.2
0.169
0.200
0.845
242.8
0.025
0.025
2.05
formula must be used to determine the apparent resistivity.
27TbR
------------------------------- —------------------- ----------
p =
2 in (i?--!-*!) + 2/F - /E - £
1 W?
E « <l ♦ a2/b2
b
;
*
*
*
*
*
A
* For short spacings and relatively long buried probes, the following
formula must be used to determine the apparent resistivity.
2TTbR
whe re
NOTE
125.2
* For short spacings and relatively long buried probes, the following
p =
APPARENT
RESISTIVITY
P
(fi-m)
F = 1 ♦ a2/b2
------------------------------------------------------------- —
2 In
♦ 2/F - /E - £•
b
t + /F
where
E = A ♦ a2/b2
;
F » 1 + a2/b2
G-6
RESISTIVITY MEASUREMENTS
TRAVERSE
TABLE
TVA 10
{Measured by SES)
i
Traverse parallel to transmission line and directed toward
Johnsonvi1 le
i
Wenner method with one current electrode kept in same location
(at tower 130)
I
Equipment used:
- Selective voltmeter ♦ ammeter
- Power frequency generator
MEASURED VALUES
PROBE
PROBE
SPACING DEPTH
b
(feet)
(feet)
1.5
0.25
CURRENT
VOLTAGE
APPARENT
V (pi-p2) I (C1-C2) RESISTANCE
(amperes)
(«)
(volts)
APPARENT
RESISTIVITY
P
(fi-m)
NOTE
2.86
0.02
11(3.0
417.3
*
45.0
265-0
*
1.5
3.0
9.01
0.20
3.0
3.0
8.1(2
0.20
42.1
337.4
*
5.0
3.0
1(.59
0.15
30.6
343-7
*
10.0
3-0
2.17
0.15
14.46
290.7
A
15-0
3.0
1.272
0.15
8.48
249.1
*
*
20.0
3.0
0.7i(it
o.u
5.31
206.1
30.0
3.0
0.510
0.11|
3.64
210.5
1(0.0
3-0
0.1(20
0.15
2.80
215-2
50.0
3.0
0.396
0.15
2.64
253.3
60.0
3.0
0.520
0.20
2.60
299.2
70.0
3.0
0.539
0.20
2.695
361.7
100.0
3-0
0.269
0.20
1.345
257.7
* For short spacings and relatively long buried probes, the following
formula must be used to determine the apparent resistivity.
2trbR
p =
-------------------------------------------------------------------
2 In
where
+ 2/f - /E - £
1 ♦ /F
£ * A + a2/b2
G“6
b
;
F = 1 ♦ a2/b2
G-7
POTENTIAL MEASUREMENTS
PROFILE
tva
TABLE
g-8
POTENTIAL MEASUREMENTS
01
(continued)
Return current electrode in first gulley (- 315')
I
Profile orthogonal to transmission line in north-west direction
i
Overhead ground wires connected to tower 130 and to adjacent towers
on each side of tower 130
I
Equivalent tower impedance - 1.382 Q
MEASURED VALUES
CURRENT
I
(Ampe res)
MEASURED VALUES
VOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
Z * /r2 + w2L2
(n)
MEASURED
POTENTIAL
CURRENT
(in %
NOTE
FREQUENCY
of GPR)
(Hertz)
POTENTIAL
PROBE
LOCATION
(feet)
CURRENT VOLTAGE
i
V
(Ampe res) (Volts)
70
70
70
215.0
215-0
215.0
35.5
35.1
70
70
215.0
215-0
1.516
1.50
1.50
0.910
36.1
31.2
70
70
215-0
1.50
3-65
0.963
1 .015
1.056
30.3
26.5
1.20
6.35
5-85
5.60
1.527
1 . 107
23.7
19.9
70
70
70
719.0
215-0
215.0
1.50
1.67
1.55
1.61
1.69
0.195
0.185
0.96
0.965
SO
55.0
1-527
1.527
1.76
Oo
5570
1.527
1.825“
1.153
1.179
1.195
16.6
16.7
~TT3------
75.0
85.0
1.527
1.527
11.4
95.0
105.0
1.527
1-527
1.225
1.251
1.266
135.0
155.0
165.0
195.0
1.527
1.527
0.851
0.866
0.878
0.891
0.897
21.0
26.0
1.527
1.527
.... 1-39
1.65
25.0
30.0
35.0
5573
1.527
1.527
1.527
’•527
1.527
19.5
20.0
1.527
1.87
0.950
70
70
1.303
1.310
70
70
1.316
1.316
6.8
6.8
70
70
2.01
1.316
6.8
70
2,01
1.316
1.297
6.8
6.1
70
70
1.250
-
20
1.250
-
40
65
1.527
1.277
1.286
... 1,527
1.527
1-99
2.00
1.527
1.527
2.01
2.01
215-0
1.527
225.0
315.0
1.527
1.527
215.0
0-500
215.0
215-0
1.00
0.625
1.25
1.50
70
70
70--------
9.5
8.5
7.6
7.1
5.7
5.2
1-91
1.93
1.95
1.96
115.0
70
1.98
1.92
1.280
-
70
70
70
215.0
215.0
APPARENT
IMPEDANCE
Z = /r2 + iii2L2
(n)
38.6
37.5
36.6
1.30.
1.32
1.36
1.36
1.37
15-0
16.5
18.0
g-9
PROFILE TVA01
1
POTENTIAL
PROBE
LOCATION
(feet)
TABLE
1.50
1.50
1.50
1-92
1.97
2.23
2.65
3-20
MEASURED
POTENTIAL
CURRENT
(in %
FREQUENCY
of GPR )
(Hertz)
1.280
-
70
1.313
-
100
1.671
1.767
-
200
-
600
2.133
2.30
-
1000
2.90
3.90
6.66
6.82
-
2000
5000
10000
-
10000
20000
5.216
_
800
NOTE
TABLE
POTENTIAL MEASUREMENTS
PROFILE
tva
POTENTIAL MEASUREMENTS
2-10
02
PROFILE
I
9
Return current electrode in first gulley (- 315')
I
Profile along transmission line toward Johnsonvilie
B
Overhead ground wires connected to tower 130 and to 10 adjacent
towers on each side of tower 130
I
Equivalent tower impedance =* 1.382 Si
Return current electrode in first gulley (- 3151)
Leg to leg profile
I
Overhead ground wires connected to tower 130 and to 10 adjacent
towers on each side of tower 130.
B
Equivalent tower impedance - 1.382
MEASURED VALUES
CURRENT VOLTAGE
V
I
(Amperes) (Volts)
APPARENT
IMPEDANCE
Z = /r2 + oj2 L2
to)
MEASURED
POTENTIAL
CURRENT
(in %
frequency
of GPR )
(Hertz)
30.0
1.527
1.52
1.00
27.6
35.0
1)5.0
1.527
1.527
1.61
1.76
1.05
1.15
2l*.0
55.0
1-527
1.88
1.23
11.0
60.0
65.0
75-0
1.527
1.527
1.527
1.91*
2.00
2.10
1.27
1.31
1.38
8.1
5.2
85.0
1.527
1.527
2.17
2.20
1.1*2
1.1*1*
-2.7
95-0
115.0
135.0
1.527
1.527
2.1*0
2.65
1.57
1.71*
-
155.0
165.0
1.527
1.527
3.00
3-00
1.96
1.96
-1*1.8
-1*1.8
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
195.0
215.0
1.527
1.527
A.62
5-90
3.03
3.86
-119.2
-
179.3
70
70
225.0
C2
1.527
-229.2
70
15.0
1-527
1.26
0.83
16.5
1.527
1-527
1.527
1.28
1.30
0.81*
0.85
0.87
1.33
25.0
1.527
1.527
1.527
1.527
18.0
19.5
20.0
21.0
21).0
1.527
G-11
n
i
MEASURED VALUES
POTENTIAL
PROBE
LOCATION
(feet)
tva
TABLE
1.33
1.35
1.1*1
1.1*3
6.95
11*7.9
39-9
39.2
38.5
37.0
37.0
36.3
33.1*
32.0
0.87
0.88
0.92
0,91*
1*. 55
96.85
16.8
\.k
-h.2
13.6
25.9
6908.
NOTE
(feet)
POTENTIAL
PROBE TO
LEFT
LEG
RIGHT
LEG
1.0
1.5
3.0
CURRENT
I
(Amperes)
VOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
Z = /R2 ■*■ U)2L2
to)
MEASURED
POTENTIAL
CURRENT
(in %
FREQUENCY
of GPR)
(Hertz)
29
28.5
1.50
1.50
0.200
0.301*
0.13
0.20
90.6
85.5
27.0
0.480
0.32
76.8
26.0
1.50
Jt.O
6.0
25.0
21*.0
1.50
1.50
1.50
0.570
0.675
0.761
0.1*5
0.51
72.5
67.1*
63.1
1.50
1.50
1.50
0.970
1.10
1.18
0.65
0.73
0.79
53.0
1*7.2
1^78
1.50
1.23
1.26
. *
1.22
0.82
1*0.7
1.50
1.50
1.50
0.81*
0.83
0.81
39-2
1.50
1.50
1.16
1.10
1*1*. 3
1*7.2
1.50
1.50
1.50
1.50
0.980
0.77
0.73
0.65
0.51
0.1*0
0.320
0.265
0.31
0.21
77-6
81*.8
0.175
0.117
91.5
5.0
22.0
20.0
8.0
10.0
TSTo
12.0
16.0
15.0
11*.0
*.0
15.0
ii
16.0
17.0
19.0
13-0
11.0
20.5
9.5
22.5
21*.5
7.5
5.5
l*.5
25.5
26.5
27.5
28.0
3.5
2.5
2.0
1.50
1.50
28.5
1.5
1 Rh
-
1
1 21
0.765
0.605
0.1*65
0.38
0.177
39.9
1*1.1*
53.0
63.1
71.1
87.2
70
70
70
70
70
70
70
70
75
70
70
70
70
70
70
70
70
70
70
70
70
70
NOTE
POTENTIAL MEASUREMENTS
PROFILE
tva
TABLE G-'2
POTENTIAL MEASUREMENTS
05
PROFILE
TABLE
™
I
Profile parallel to transmission line,toward Cumberland
B
Along direction parallel to transmission line, toward Johnsonville
1
Return current electrode in second gulley (* 600 feet)
i
Return current electrode in second gulley (- 600 feet)
8
Overhead ground wires disconnected from tower 130
B
Overhead ground wires disconnected from tower 130
i
Tower resistance - 7*1 ohms
I
Tower resistance - 7*1 ohms
MEASURED VALU ES
POTENTIAL
PROBE
LOCATION
(feet)
MEASURED VALUES
yOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
2 = /R^, oj2L2
(fl)
MEASURED
potential
CURRENT
(in %
NOTE
FREQUENCY
of GPR)
(Hertz)
POTENTIAL
PROBE
LOCATION
(feet)
-15.0
0.7
2.8
4.0
43.66
0.0
15.0
0-7
0.7
2.82
2.74
4.03
3-91
43.26
44.87
18.0
0.7
0.7
2.76
2.80
3.94
4.0
44.47
43.66
19-5
20.0
OJI
0.7
2.85
2.86
4.07
4.08
42.65
42.45
70
70
70
70
70
70
70
21.0
2A.0
25.0
30.0
35.0
0,-7.............. 2.89
3.00
0.7
3.03
0.7
3.20
0.7
3.30
41.85
39.64
39.03
35.61
33.60
70
70
70
70
70
25.0
0.7
4.13
4.28
4.33
4.57
4.71
45.0
0.7
3.56
5.08
28.37
70
51.0
60.0
65.0
75.0
85.0
na
....0-7
0.7
0.7
0.7
5.83
3.96
4.01
4.15
4.22
5.47
5.66
22.94
20.32
70
70
70
70
60.0
65.0
75.0
95.0
0.7
4.26
6.08
14.28
7o
70
105-0
115.6
105.0
115.0
0-7
0.7
4.30
4.35
6.14
6.21
13.48
12.47
70
70
135-0
155.0
135.0
155.0
0.7
0.7
4.45
4.50
6.36
6.43
10.46
9.46
70
70
165.0
0.7
4.55
6.50
8.45
0.7
0.7
4.65
4.70
6.64
6.71
0.7
0.7
1.4
4.70
___
-
CURRENT
I
(Amperes)
195.0
215.0
225.0
31.5..0
315..0
...
G-13
5.73
5.93
6.03
19.31
16.50
15.09
'
15.0
nrs
18.0
19.5
20.0
21.0
24.0
30.0
35.0
45.0
55.0
85.0
95-0
CURRENT
I
(Amperes)
APPARENT
IMPEDANCE
VOLTAGE
V
(Volts)
Z = /ft2 + oj2Lz
(n)
2.40
2.42
4.0
43.66
43.19
0.6
0.6
2.45
2.49
2.50
4.08
4.15
4.17
42.49
41.55
0.6
2.55
4.25
40.14
0.6
0.6
0.6
2.64
2.66
4.40
4.43
4.70
38.03
37.56
33.80
4.93
30.52
25.82
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
4.03
os
2.96
3.16
3-30
5.27
5.50
3.36
3.42
5.60
5.70
3.55
5.92
3.60
3-66
6.0
0.6
3.70
—5T7E
0.6
6.10
6.17
15.49
14.08
70
70
13.14
70
70
... -3.fe2.....
6.68
0.697
4.79
6.87
70
215.0
0.698
4.83
6.44
5.43
70
70
225.0
OgT- ----- Ol
6.92
315.0
0.7
6.71
5.43
70
4.75
6.78
4.43
70
9-39
6.71
5.53
70
* Return electrode located in first Gulley (- 315 feet)
70
70
70
7.357
4.66
195-0
5.15
21.13
19.72
16.67
05B
165.0
.29
70
22.53
8.45
6.57
5.97
3.21
2.54
2.00
6.50
6.63
70
70
70
70
70
70
70
70
70
70
rr774
3.90
"
liTTTi
07
0.6
0.698
*
MEASURED
POTENTIAL
CURRENT
(in 1
FREQUENCY
of GPR)
(Hertz)
70
70
70
70
70
70
70
NOTE
POTENTIAL MEASUREMENTS
TABLE G-1'*
POTENTIAL MEASUREMENTS
PROFILE
PROFILE TVA°7
I
Profile perpendicular to transmission line, along north-west
direction
I
Return current electrode in second gulley (- 600 feet)
I
Overhead ground wires disconnected from tower 130
I
Tower resistance - 7*1 ohms.
I
Profile across tower and between legs
Return current in second gulley (- 600 feet)
l
Overhead ground wires disconnected from tower 130
B
Tower resistance ~ 7*1 ohms
MEASURED VALU ES
(Amperes)
VOLTAGE
V
(Volts)
CURRENT
l
TVA 08
i
MEASURED VALUES
POTENTIAL
PROBE
LOCATION
(feet)
APPARENT
IMPEDANCE
Z = /r2 + u>2 L2
(£2)
MEASURED
POTENTIAL
CURRENT
(in %
FREQUENCY
of GPR )
(Hertz)
(feet)
NOTE
POTENTIAL
PROBE TO
LEFT RIGHT
LEG
LEG
CURRENT
1
(Amperes)
VOLTAGE
V
(Volts)
APPARENT
IMPEDANCE
2
2
-10
0.0
0.6
2.40
4.0
43-66
70
2.0 28,0
0.6
0.6
0.6
2.44
2.48
4.07
4.13
42.72
41.78
70
70
3-0
27.0
-
18.0
0.6
2.52
4.20
40.84
70
4.0
5.0
26.0
25.0
0.6
0.6
1.356
1.590
2.26
2.65
iq.q
20.0
0.6
0.6
2.56
2.58
4.27
39-90
39.44
70
70
24.0
23-0
0.6
0.6
1.800
1.940
3.0
21.0
0.6
2.62
4.37
38.50
70
n
n.6
70
70
2.09
2.18
10.0
20.0
0.6
—J7S1
STTH
36.62
35.45
31.92
23717
0.6
0.6
0.6
0.6
0.6
4.50
4.58
4.83
22.0
21.0
25.0
30.0
35.0
2.70
2.75
2.90
6.0
7.0
8.0
9-0
70
70
70
70
45.0
0.6
3.16
5.27
25752
55.0
60.0
65.0
0.6
0.6
0.6
3.30
3.39
3.41
5.5
5.65
5.68
22.5
20.4
75.0
85.0
0.6
0.6
3-50
3.60
5-83
6.0
05.0
105.0
0.6
6.02
0.6
3.61
3.66
115.0
0.6
3.72
6.1
6.2
135.0
155.0
165.0
195-0
0.6
0.6
0.6
0.6
3.80
3.81
3-85
3.90
6.33
6.35
6.42
6.5
215.0
0.6
3.93
6.55
225.0
315.0
0.6
0.6
3.95 ...
4.06
6.58
6.77
19.95
17.84
15.49
70
yu
19.0
12.0 18.0
13.0 17.0
11.0!
1.44
**
3.23
3-48
3.63
2.25
2.32
3.75
0.6
0.6
2.36
3.93
2.38
2.40
3.97
4.0
3.97
3.87
44.6o
44.13
43.66
70
70
70
70
70
70
70
70
70
70
70
70
70
43.66
44.13
70
70
70
70
70
70
n-i
-
68.17
62.67
57.75
54.46
50.94
48.82
57rTg~
45-54
14.0
16.0
70
16.0
17.0
14.0
13.0
0.6
0.6
2.40
2.38
12.0
11.0
10.0
9.0
0.6
0.6
2.35
2.30
3.92
0.6
0.6
2.25
2.19
3.75
3.65
44.83
46.01
47.18
48.59
0.6
0.6
2.10
3.5
3-3
3-07
50.70
53-52
56.8l
75
18.0
70
70
12.67
8755
70
70
70
70
7S
19-0
20.0
21.0
7.75
70
25.0
26.0
7.28
4.69
70
70
10.56
9.62
-
MEASURED
POTENTIAL
CURRENT
NOTE
(in %
FREQUENCY
of GPR )
(Hertz)
0.6
0.6
15.26
14.08
10.80
0.865
22
Z = /r + U) L
(£ )
15.0
16.5
■>U
TABLE g-15
22.0
23.0
24.0
8.0
7.0
6.0
5.0
0.6
1.98
1.84
4.0
3.83
.
70
70
70
0.6
1.67
1.45
2.78
02
60.80
65.96
70
70
27.0 --3,0.
2.0
0.6
0.6
1.26
1 .02
2.10
1.70
70.42
76.06
70
70
29.0
0.6
0.675
1.125
84.15
70
4.0
28.0
Note
1.0
0.6
Presence of roots at surface of soil
*
POTENTIAL MEASUREMENTS
PROFILE
g
TABLE g-i 6
TVA 09
Profile perpendicular to transmission line along south-east direction
i
Return current electrode in second gulley
I
Overhead ground wires disconnected from tower 130
600 feet)
I
Tower resistance - 7*1 ohms
HEASURED VALUES
POTENTIAL
PROSE
LOCATION
CURRENT
1
VOLTAGE
V
(Amperes)
(Volts)
(feet)
APPARENT
POTENTIAL
IMPEDANCE
Z = A2 + a)2 L2
to)
of GPR )
MEASURED
CURRENT
NOTE
FREQUENCY
(Hertz)
0.600
0.600
2.22
2.23
3.7
3.72
67.88
67.65
19-5
0.600
0.600
2.25
2.27
3-75
3.78
67.18
66.71
70
70
20.0
21.0
0.600
0.600
2.28
2.31
3.8
3-85
66.68
65.77
70
70
.0
25-0
30.0
0.600
0.600
0.600
2.1(0
2.1(5
2.66
6.
6.08
—6.63
63.66
62.69
373E
70
-------70--------
15.0
16.5
18.0
2k
70
70
70
35.0
0.600
2.81
6.68
103
70
1(5.0
55.0
0.600
o.6oo
3.05
3.20
5.08
5-33
28.60
70
70
60.0
0.600
65.0
75-0
0.600
0.600
85.0
3.30
5-5
22.53
70
3.1(0
3.50
5-67
5-83
20.19
17.86
70
70
3.63
6.05
6.17
6.32
6.37
6.50
6.63
16.79
13.16
11.03
10.33
8.65
6.57
70
70
70
70
70
70
6.67
6.7
6.72
6.10
5-63
5.60
70
70
70
6.93
70
6.22
“TTS7
8765
-TOOT
95.0
105.0
115.0
135.0
155-0
0.600
0.600
0.600
0.600
0.600
3.70
3-79
165.0
195.0
215-0
0.600
0.600
k.00
0.600
6.02
6.03
225.0
0.600
6.05
6.75
315.0
165.0
iSSTo
0.600
0.600
0.600
6.08
6.01
J79S
6.8
165.0
165.0
0.600
0.600
3-80
3-70
6.33
6.17
Note *
3.82
3.90
3.98
6.6b
5750
Potential probe driven partially in a root
G-11
10.80
fJTT?
70
1989
5000
*
i
i
GROUND RESISTANCE MEASUREMENTS
i
Measurements made by TVA on October
(during the staged fault test period) at 10 towers
adjacent to tower 130 (5 on each side)
I
Tower number increases from JohnsonvHle to Cumberland
I
TABLE
GROUND RESISTANCE MEASUREMENTS
Equipment used: Megger
TOWER
NUMBER
126
(Q.)
4.0
53---------
127
7.5
5-5
130
131
132
6.0
10.0
11.0
133
1311
10.5
15.5
135
q.o
128
129
TOWER
NUMBER
GROUND
RESISTANCE
(G)
TOWER
NUMBER
GROUND
RESISTANCE
(Q)
I
Measurements made by TVA from May to July 1970 on the
Johnsonvi11e-Cumberland 500 kV transmission line section
■
Tower number increases from Johnsonvi1le to Cumberland
B
Equipment used: Megger
TOWER
NUMBER
GROUND
RESISTANCE
(G)
6
9
TOWER
NUMBER
GROUND
RESISTANCE
(Gl
10
h
5
20
29
6
22.5
12
36
37
9
15
9
67
68
17
69
16
9
13
12
70
71
11
6
72
73
21
2
3
7
8
9
10
11
12
13
14
15
16
17
4
20
14
5
14
16
40
16
39
40
41
42
43
44
45
66
22
10
20
18
2475
4
77
78
8
79
2
50
3
80
5
3
7
20
81
10
82
3
20
15
83
84
85
14
10
2
16
86
87
12
8
51
22
40
52
53
54
21)
63
64
65
15
21
13
7
23
9
9
3
6
4
48
49
46
47
19
20
23
6!
62
7
15
5
20
11
21
6
8
5
18
.
TOWER
NUMBER
31
32
33
34
35
1
2
i.75
GROUND
RESISTANCE
(.01
6
10
5
CO
125
GROUND
RESISTANCE
TABLE G-18
10
5
20
74
75
76
55
56
27
6
19
3
57
8
28
4
7
58
59
16
10
88
29
89
4
3
3.Q
5
60
8
90
is
25
26
5
TABLE
GROUND RESISTANCE MEASUREMENTS
(continued)
I
Measurements made by TVA from May to Juiy 1970 on the
Johnsonville-Cumberland 500 kV transmission line section
I
Twer number increases from Johnsonvi lie to Cumberland
i
Equipment used: Megger
TOWER
NUMBER
GROUND
RESISTANCE
(Q)
GROUND
RESISTANCE
(ft)
5
15
151
152
GROUND
RESISTANCE
(ft)
3
1
153
154
3
5
6
155
156
127
9
157
7
3
9
128
7
8
6
158
159
160
12
161
162
11
21
14
163
16
164
165
166
15
23
1
TOWER
NUMBER
91
92
6
5
121
122
93
95
96
22
20
123
124
125
10
91*
10
4
126
97
13
98
99
21
3
100
101
n
13
102
103
16
17
104
105
10
4
129
130
131
132
13
2k
133
134
12
20
8
135
7
106
4
136
6
107
108
7
5
137
138
9
12
109
3
12
110
111
3
19
139
140
112
113
m
20
6
12
141
142
143
3
15
7
115
12
116
117
118
6
18
119
5
11
120
6
13
144
8
145
146
147
8
148
149
13
11
L£2
6
7
1
G-14
TOWER
NUMBER
4
4
g-,9