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ELECTRICAL TRANSMISSION AND SUBSTATION STRUCTURES 2012 © ASCE 2013
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Aeolian Vibration of Conductors:
Theory, Laboratory Simulation & Field Measurement
Robert Whapham
P.E., SM.IEEE
Global Market Manager - Transmission, Preformed Line Products (PLP),
660 Beta Drive, Mayfield Village, Ohio 44143, Phone: (440) 473-9202,
email: [email protected]
ABSTRACT
The conductors of transmission lines are subjected to a variety of motions caused by
the wind. The most common motions are aeolian vibration, sub-conductor oscillation
(bundled conductors), galloping (generally associated with a light ice coating) and
wind sway.
Unless controlled, motions of conductors can produce damage to the conductor and
other elements of the transmission system that will negatively affect the reliability
and serviceability of the system.
Sub-conductor oscillations, galloping and wind sway are associated with higher wind
velocities, and in the case of galloping a light to moderate ice coating is required to
initiate the motion. These motions are generally characterized as low frequency, high
amplitude.
Aeolian vibration, which is the subject of this paper, is associated with smooth (nonturbulent) winds in the range of 2 MPH to 15 MPH, and can occur on a daily basis.
In contrast to galloping and sub-conductor oscillations, aeolian vibration is
characterized as high frequency, low amplitude motion.
This paper describes the theory of aeolian vibration, simulation of aeolian vibration in
the laboratory to test the performance of conductor and conductor hardware, with a
focus on how vibration damper performance is measured and finally the methods
used to monitor aeolian vibration in the field on operating transmission lines.
THEORY OF AEOLIAN VIBRATION
When a smooth stream of air passes over a cylindrical shape, such as a conductor,
vortices (eddies) are formed on the leeward (back) side as depicted in Figure 1.
These vortices alternate from the top and bottom surfaces, which create alternate
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pressures that tend to push the conductor up and down. This is mechanism that
causes aeolian vibration.
Figure 1 – Formation of Vortices
The term “smooth winds” is important because unsmooth air (i.e. air with turbulence)
will not generate the vortices and the associated alternating pressures. The degree of
turbulence in the wind is affected by the surrounding terrain and the wind velocity.
Winds higher than 15 MPH usually contain a considerable amount of turbulence.
The frequency at which the vortices alternate from the top to bottom surfaces of a
conductor can be closely approximated by the following relationship develop by V.
Strouhal in 1878:
Vortex Frequency (Hertz) = 3.26V/d
where: V is the wind velocity normal to the conductor in MPH
d is the conductor diameter in inches
3.26 is an empirical aerodynamic constant
One thing that is clear from the above equation is that the frequency at which the
vortices alternate is inversely proportional to the diameter of the conductor. For
example, the vortex frequency for a 795 kcmil 26/7 ACSR (Drake) conductor under
the influence of an 8 MPH wind is about 24 Hertz. A 3/8” overhead shield wire
under the same 8 MPH wind will have the vortices alternating at about 72 Hertz.
Field vibration measurements will be discussed later in this paper, but to illustrate the
difference in frequencies between a conductor and the overhead shield wire above it,
Figure 2 and Figure 3 show a one second analog recording of a 1272 kcmil 45/7
ACSR conductor and the 3/8” EHS overhead shield wire captured in the same span at
the same time.
Figure 2 – 1272 Kcmil 45/7 ACSR
(11 Hertz)
Figure 3 – 3/8” Overhead Shield Wire
( 41 Hertz)
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Sustained aeolian vibration activity occurs when the vortex frequency closely
corresponds to one of the natural vibration frequencies of the span of conductor. This
sustained vibration activity “locks in” and takes the form of discrete standing waves
with forced nodes at the support structures and intermediate nodes spaced along the
span at intervals that depend on the particular natural frequency (Figure 4). The
vibration activity will continue until the wind speed changes.
Anti-Node
Loop Length
Node
Figure 4 – Standing Wave Vibration
The natural frequencies at which a wire under tension will vibrate in a series of
standing waves are approximated by:
F = (Tg/w)1/2 x N/2S
where:
F is the natural frequency in hertz
T is the tension in pounds
g is the gravitational constant of 32.2 ft/sec2
w is the conductor weight per foot
N is the number of standing wave loops
S is the span length in feet
For example, the natural frequencies for an 800 ft. span of 795 kcmil 26/7 ACSR
(“Drake”) conductor at a tension of 4,725 lb are given by:
F = 0.233 x N
For a wind velocity of about 8 MPH, the span in this example would have 100
standing waves (N=100), each about 8 ft in length (loop length). At a higher wind
speed near 12 MPH the loop length will decrease to 5.3 ft (N=150). The loop length,
especially at the higher wind velocity plays an important role in the placement of
vibration dampers.
In most cases the maximum peak-to-peak amplitude (at the anti-node) of a conductor
vibrating in the field will not exceed the conductor diameter.
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ELECTRICAL TRANSMISSION AND SUBSTATION STRUCTURES 2012 © ASCE 2013
The expected level of aeolian vibration on a line is influenced by the conductor
tension, the surrounding terrain and the prevailing wind conditions; however
conductor tension has the greatest influence. Conductor tension limits are included in
Rule 261H1b. of the National Electrical Safety Code, but using these limits does not
prevent adverse effects from aeolian vibration over time. Safe working tensions
(without vibration dampers) are the subject of CIGRE Publication #273, 2005, but
these limits may be too conservative for practical line design purposes. The use of
“moderate” tensions and vibration dampers is common practice.
EFFECTS OF AEOLIAN VIBRATION
It should be understood that the existence of aeolian vibration on a transmission or
distribution line doesn’t necessarily constitute a problem. However, if the magnitude
of the vibration is high enough, damage in the form of abrasion or fatigue failures
will generally occur over a period of time.
Abrasion is the wearing away of the surface of a conductor and is generally
associated with loose connections between the conductor and attachment hardware or
other conductor fittings. The looseness that allows the abrasion to occur is often the
result of excessive aeolian vibration.
Abrasion damage can occur within the span itself at spacers (Figure 5a), spacer
dampers and marker spheres, or at supporting structures (Figure 5b).
Figure 5a – Abrasion Damage at Spacer
Figure 5b – Abrasion at Loose Hand Tie
Fatigue failures are the direct result of bending a material back and forth a sufficient
amount over a sufficient number of cycles. Removing the pull tab from a can of soda
is a good example.
All materials have a certain “endurance limit” related to fatigue. The endurance limit
is the value of bending stress above which a fatigue failure will occur after a certain
number of bending cycles, and below which fatigue failures will not occur, regardless
of the number of bending cycles.
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In the case of a conductor being subjected to aeolian vibration, the maximum bending
stresses occur at locations where the conductor is being restrained from movement.
Such restraint can occur in the span at the edge of clamps of spacers, spacer dampers
and vibration dampers. However, the level of restraint, and therefore the level of the
bending stresses, is generally highest at the suspension hardware at the supporting
structures.
When the bending stresses in a conductor due to aeolian vibration exceed the
endurance limit, fatigue failures will occur (Figures 6a & 6b). The time to failure
will depend on the magnitude of the bending stresses and the number of bending
cycles accumulated.
Figure 6a – Fatigue of Outer Strands
Figure 6b – Fatigue of Inner Strands at
Bolted Suspension (Clamp Moved for Photo)
Fatigue failures such as shown in Figures 6a and 6b affect the integrity and
serviceability of a transmission line and must be repaired immediately when
discovered.
THE ENERGY BALANCE PRINCIPLE
It is important to be familiar with the Energy Balance Principal to understand the
phenomenon of aeolian vibration and how it affects the conductor and related
hardware. Some analytical computer programs have been written using this
approach, but because of the complexity of the system, to date these programs can not
be relied on to predict the level of vibration on a line or the performance of dampers.
The Energy Balance Principal simply states that the amount of energy entering a
system must be equivalent to the amount of energy leaving the same system. For the
system of a vibrating conductor, the energy entering the system is the energy
imparted from the wind (aka, Wind Power Input). The energy leaving this system is
the energy dissipated by any conductor self-damping, plus the energy absorbed by
vibration dampers, and finally the energy that reaches the conductor hardware at the
structures.
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Wind Power Input
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Extensive wind tunnel studies have been used to estimate the energy imparted by the
wind to a vibrating conductor. Collectively this research has shown that wind energy
may be expressed in the general (non-linear) form:
P = L x d4 x f3 x fnc(Y/d)
where:
P is the wind energy in watts
L is the span length
d is the conductor diameter
f is the vibration frequency in hertz
Y is the anti-node vibration (peak-to-peak)
fnc(Y/d) is a function derived from the wind tunnel experimentation
Conductor Self-Damping
The self damping characteristics of a conductor are basically related to the freedom of
movement or “looseness” between the individual strands or layers of the overall
construction. In standard conductors the freedom of movement (self damping) will
be reduced as the tension is increased. It is for this reason that vibration activity is
most severe in the coldest months of the year when the tensions are the highest.
Some conductors designed with higher self damping performance use trapezoidal
shaped outer strands that “lock” together to create gaps between layers. Other
conductors, such as ACSS (formerly SSAC), utilize fully annealed aluminum strands
that become inherently looser when the conductor progresses naturally from initial to
final operating tension., or if the conductor is pre-tensioned to 50% of the rated
strength before installing.
The IEEE established a standard (IEEE 563-1978) for the measurement of conductor
self-damping in the laboratory, however because of the difficultly of the testing and
the time required, there is only a limited amount of this data available to apply to the
Energy Balance Principle with any confidence.
Energy Absorbed by Vibration Dampers
Dampers of many different types have been used since the early 1900s to reduce the
level of aeolian vibration within the span and, more importantly, at the supporting
structures.
The damper most commonly used for conductors is the Stockbridge type damper,
named after the original invention by G.H. Stockbridge about 1924. The original
design has evolved over the years but the basic principle remains: weights are
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suspended from the ends of specially designed and manufactured steel strand, which
is secured to the conductor with a clamp (Figure 7).
When the damper is placed on a vibrating conductor, movement of the weights will
produce bending of the steel strand. The bending of the strand causes the individual
wires of the strand to rub together, thus dissipating energy. The size and shape of the
weights and the overall geometry of the damper influence the amount of energy that
will be dissipated for specific vibration frequencies. Since, as presented earlier, a
span of tensioned conductor will vibrate at a number of different resonant frequencies
under the influence of a range of wind velocities, an effective damper design must
have the proper response over the range of frequencies expected for a specific
conductor and span parameters.
Figure 7 – Vibration Damper
An effective damper is capable of dissipating most of the energy imparted to a
conductor by the wind (ranging from 2 to 15 MPH) for the specified “protectable”
span length. The same applies to longer spans where multiple dampers are required
to dissipate the energy from the wind.
Placement programs developed by damper suppliers take into account span and
terrain conditions, suspension types, conductor self-damping, and other factors to
provide a specific location in the span where the damper or dampers will be most
effective. The placement of the damper or dampers is also highly influenced by the
standing wave loop length at a higher wind velocity such as 15 MPH.
The most common way to estimate the amount of energy dissipated by a vibration
damper is to conduct laboratory damper efficiency tests in accordance with IEEE
Standard 664-1193 “IEEE Guide for Laboratory Measurement of the Power
Dissipation Characteristics of Aeolian Vibration Dampers for Single Conductors”, or
with IEC 61897.
The in-span damper performance testing in the laboratory gives a clear indication of
the anticipated performance of the damper in the field. For this test the damper is
attached to a 90 ft to 100 ft length of tensioned conductor and positioned where it
would be on a span in the field. Blocks of steel plates with grooves specific for the
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conductor size being tested are used to eliminate any effects from the dead-end
hardware (Figure 8). Even though the test span is short compared to the span in the
field, the test method assures that the power dissipated by the damper can be
determined for the appropriate frequency range. The power dissipated by the damper
is not a function of span length, so the results can be used to determine the damper’s
effectiveness on a field span as discussed below.
Figure 8 – Damper Efficiency Test Setup
The time consuming test requires that the power dissipated by the damper be
measured over the range of frequencies that the conductor will vibrate in the field.
One method that is defined in the standards and commonly used is the Inverse
Standing Wave method. With the damper in the span the nodes are no longer pure
nodes; there is a small amount of vertical amplitude based on the effectiveness of the
damper. Using sensitive accelerometers and carefully positioning them at one
apparent node and anti-node in the test span away from the damper, the ratio of the
node to anti-node can be calculated and this ratio can be used to determine the power
dissipated by the damper for each of the specific frequencies being tested. To test the
full range of frequencies that a damper is expected to provide protection for may take
3 to 4 days because of tuning each test frequency and positioning the accelerometers.
The results of the testing is presented as a graph of power dissipated (vertical axis)
versus the frequency (horizontal axis). This is shown in the upper curve of Figure 9.
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Damper Efficiency - VSD40B @ 150 micro-strain level Damper Placement = 39"
from Rigid Clamp
16
14
Power (W)
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12
10
8
6
4
2
0
0
10
20
30
40
50
60
Frequency (Hz)
Dissipated Pow er (Damper B)
Wind Pow er input (275m Span)
Figure 9 – Damper Efficiency Test Results
The lower curve in Figure 9 is the estimated wind power for a 900 ft (275m) span of
the conductor size being tested, based on the formula presented earlier in this paper.
Based on the measured damper efficiency (power dissipation) the damper tested at
the placement used is capable of dissipating the estimated wind energy input for the
900 ft span (i.e., all of the data test values fall above the wind power curve for the
complete frequency range).
This is also how damper suppliers determine the maximum span for which one
damper can be used. If the wind power curve in Figure 9 were plotted for a longer
span, it would shift upward and some of the damper test values would fall below the
wind power curve, which is not desirable. For this example the damper as tested
would protect a 900 ft span in an area with open terrain. For longer spans two or
more dampers would be recommended, based on the total span length and the
surrounding terrain.
Placement programs developed by damper suppliers use terrain factors to adjust the
maximum span protected by a single damper. In areas with trees adjacent to the line,
for example, the span protected by a single damper may increase due to the
anticipated increase in the turbulence in the wind. The placement program may also
factor in some level of conductor self-damping for specific conductors in determining
the maximum span.
FIELD TESTING
Beginning in the late 1950s considerable work was completed on the development of
rugged equipment for the field measurement of aeolian vibration and on the
interpretation and presentation of the results.
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In 1966 the IEEE Committee on Overhead Line Conductors published a
“standardized” method for measurement and presentation of results that is still used
today, and has been included in IEEE 1368, “Guide for Vibration Field
Measurements of Overhead Conductors”.
The field vibration recorder developed by Ontario Hydro in the early 1960s (Figure
10) is an analog device that is still being utilized today. Recorders more recently
developed use digital technology to record and store the data, however unlike the
analog device these digital recorders do not currently capture the time when each
record occurred.
Figure 10 – Ontario Hydro Vibration Recorder
The best way to understand the process of recording and interpreting field vibration
data is to follow the process that is used with the Ontario Hydro Recorder (analog).
In this way you will understand the steps that are done automatically in the newer
(digital) recorders.
As shown in Figure 10 special mounting hardware is used to establish a very rigid
attachment between the recorder and the suspension hardware. The recorder
measures the differential displacement (vertical movement) between the suspension
and the conductor during vibration activity. The input arm of the recorder is secured
to the conductor at a specified distance from the suspension hardware. The IEEE
recommended distance is 3.5 in from the edge of a keeper on a bolted suspension
clamp.
Field vibration recorders take a one second measurement of the vibration amplitude
and frequency once every 15 minutes during the study period, usually two weeks.
The assumption is made that the vibration activity recorded during the one second
will remain the same (“locked in”) for the entire 15 minute period.
Figure 11 shows a sample analog trace taken with the Ontario Hydro recorder.
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Figure 11 – One Second Trace for 1272 45/7 ACSR (11 Hertz)
The frequency and amplitude of each trace can be determined using a calibrated
magnified viewer for the analog recorder, and these records are accumulated and
summarized by the number of traces for each amplitude/frequency combination.
The newer digital recorders determine the frequency and amplitude for each record
(one per 15-minute period) automatically and add them to a built-in histogram that
can be downloaded into a computer when the recorder is removed from the line.
Rather than presenting vibration data in vibration amplitude, it was established by the
IEEE to convert the differential movement at the 3-1/2” distance to a bending strain
on the conductor. Extensive laboratory testing conducted by Poffenberger and Swart
of PLP starting in the late 1950s established an equation that is used to convert the
differential displacement measured in the field to the bending stress on the aluminum
strands of the conductor. Furthermore, the standard representation for field test data
established by the IEEE plots the bending stress (in micro-strain) on the horizontal
axis and the number of million cycles per day (MC/day), based on frequencies of the
measured records on the vertical axis (Figure 12).
1.2
Megacycles/Day Exceeding Stra
Shown
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ELECTRICAL TRANSMISSION AND SUBSTATION STRUCTURES 2012 © ASCE 2013
0.8
0.4
0.0
0
100
200
300
400
Microstrain p-p
R1 - Undamped
R2 - Damped
R3 - Undamped
Figure 12 – Results of Field Vibration Study – IEEE Format
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It is common during field vibration studies to remove dampers from some of the
phases in the test spans in order to determine the background vibration level of the
conductors without dampers. These results can then be compared to results in the
same span and same test period on a phase or phases on which the dampers were
installed, as in Figure 12.
There is no exact safe micro-strain level established for different sizes and types of
conductors, but levels above 150 to 200 micro-strain have been know to cause
conductor fatigue over a period of time.
You can see in Figure 12 that there is activity on the phases without dampers above
150 micro-strain, based on the test period, and that the dampers reduced the measured
vibration levels below that level. Therefore, field vibration measurements can be
used to verify the damper efficiency information that was determined in the
laboratory testing. However field testing is expensive and should be done during the
coldest period of the year to be conclusive.
CONCLUSIONS
The theory and causes of aeolian vibration of overhead lines is well understood and
documented.
Uncontrolled aeolian vibration can lead to fatigue damage of the aluminum strands of
conductors.
Proven methods exist to evaluate the effectiveness of vibration dampers both in the
laboratory and in the field.
REFERENCES
IEEE (2012). “National Electrical Safety Code”, 2012 Edition
CICGE Task Force B2.11.04 (2005). Report #273, “Overhead Conductor Safe Design
Tension with Respect to Aeolian Vibrations”
IEEE (1991). Std. 563-1978, “IEEE Guide on Conductor Self Damping
Measurements”
IEEE (1993). Std. 664-1193, “IEEE Guide for Laboratory Measurements of the
Power Dissipation Characteristics of Aeolian Vibration Dampers for Single
Conductors”
IEC 61897 (1998). “Overhaed Lines – Requirements and Tests for Stockbridge Type
Aeolian Vibration Dampers”
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IEEE. Std 1368, “Guide for Vibration Field Measurements of Overhead Conductors”
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