Part B of this paper proposes a method for assessing the performance of spacer-dampers on a quad-bundled conductor using an existing system identification algorithm and experimental modal data obtained from Aeolian vibration measurements. To generate the frequency response function (FRF) as a force input, a shaker was used and attached at a certain distance via a rigid link, and acceleration was measured at the free span. To ensure that the data was not compromised, the excitation technique used was first evaluated in different configuration scenarios in part A of this paper. Three different commercial spacer-dampers were used in this investigation. One was placed at the mid-span and the other two placed at different locations. The damping performance was evaluated in terms of the main fatigue indicator, i.e. the bending stress envelope of both clamp edges at the spacer-damper and at the termination clamp. A better performance configuration of bundled conductors is the one that generates a bending stress

1. ฀ ฀ ฀ ฀ ฀ ฀ ฀
100
Abstract:
Part B of this paper proposes a method for assessing
the performance of spacer-dampers on a quad-bundled
conductor using an existing system identification
algorithm and experimental modal data obtained from
Aeolian vibration measurements. To generate the
frequency response function (FRF) as a force input, a
shaker was used and attached at a certain distance via
a rigid link, and acceleration was measured at the free
span. To ensure that the data was not compromised, the
excitation technique used was first evaluated in different
configuration scenarios in part A of this paper. Three
different commercial spacer-dampers were used in this
investigation. One was placed at the mid-span and the
other two placed at different locations. The damping
performance was evaluated in terms of the main fatigue
indicator, i.e. the bending stress envelope of both clamp
edges at the spacer-damper and at the termination
clamp. A better performance configuration of bundled
conductors is the one that generates a bending stress
envelope below that prescribed by existing standards.
Several identification algorithms were used to extract
the modal parameters, e.g. natural frequency, damping
ratio and mode shape. A high-order auto-regressive
exogenous (ARX) system identification algorithm
gave a better fit with insignificant standard errors. In
general, the analysis shows that a significant magnitude
with a negative sign of the frequency response function
(FRF) corresponds to the most efficient configuration.
Its skeleton geometry varies from a mass dominated
to a stiffness dominated characteristic with frequency.
However, the inclusion of one spacer-damper in the span
improved the vibration performance in one case only.
From various FRF skeleton analyses thus obtained, it
was possible, with respect to the frequency ranges, to
identify whether the mass or stiffness characteristics
were dominated for each bundled configuration. A
compromise between fatigue performance and dynamic
stability of the bundled conductors is discussed. In
most cases the best performance configuration shows a
vibration mode with negative damping factors.
, Part B: Assessment
of atigue and amping erformances
Y. D. KUBELWA1
*, A. G. SWANSON1
, D. G. DORRELL2
1
Vibration Research and Testing Centre, School of Engineering,
University of KwaZulu-Natal, South Africa
2
School of Electrical and Information Engineering,
University of the Witwatersrand, South Africa
KEYWORDS
Aeolian vibrations,ARX system identification, overhead lines, bundled conductors, frequency response function FRF
* danielkubelwa2010@gmail.com
Nomenclature
ARX Auto-regressive exogenous
Ri
Rigid clamp at the position i (i = 1 to 8)
SDi Spacer-damper i
ADij Accelerometer i at the arm j
STi Strain measured at the rigid clamp i
Ci Bundled conductor configuration i (with 0 as a configuration without any spacer-damper and nine
different configurations)
kt
Radial stiffness (Nm/rad)
Ht
Horizontal stiffness (Nm2
)
AEi Accelerometer at the excitation (i = 1 or 2)
AFij Accelerometer at sub-conductor i of the free-span placed at the position j

2. ฀ ฀ ฀ ฀ ฀ ฀ ฀
101
their dampers, there are relevant standards [3] and
recommendations [4] that have been established. The
main issues are the assessment of their performance, such
as fatigue, bending stress-bending amplitude relationship,
power dissipation, and self-damping evaluation [5]. Many
indoor facilities have been developed worldwide for
quality assessment and research investigations. These aid
OHTL manufacturers as well as electricity utilities and
independent research institutions. These facilities have
often been built using international standards [3, 4] and
described as having a span bench rigidly attached on two
concrete blocks and excited using a shaker connected at a
location where vibrations may not be severe.
For bundled conductors, some reservations were raised
by researchers [6] about conducting similar indoor
experiments, since it is not possible to reproduce the
natural motion of bundles. This motion is characterised by
breathing, swinging, and rotational modes. For instance, a
single conductor has two global modes in the vertical and
horizontal directions, while four normal modes occur in
twin-bundled conductors. Generally, Aeolian vibrations
are considered only as having vertical motion since it is
1 Introduction
Assessment of the vibration performance of overhead
transmissionlines(OHTLs)isimportantinordertoprevent
fatigue failure of the conductor. The lines are the most
important and most expensive component of an overhead
line system. It is pertinent to take account of the vibration
performance during the engineering design process.
OHTLs affected by wind-induced Aeolian vibrations
have been thoroughly investigated. These vibrations are
quite common and can lead to accelerated conductor
ageing, and ultimately to failure if not suppressed [1]. The
investigation of the vibration performance of bundled
conductors appears more complicated because of the sub-
conductors and the spacer-dampers [2]. In this case, an
experimentalmodalapproachcanbecomparedtoasystem
identification algorithm to extract local parameters such
as natural frequency, damping ratio, and mode shape. An
efficient protection scheme to mitigate Aeolian vibrations
on an OHTL conductor depends on the detection and
better understanding of the resonance frequency and
mode shape phenomena. For single conductors and
ADij Accelerometer at spacer-damper i of the sub-conductor j
ACij Accelerometer at the sub-conductor i of the control span j
MIMO Multi-inputs and multi-outputs
DAQ i Data acquisition i (i = 1 to 4)
CMIF Complex mode indicator function
SDijk and SDijk Strain-gauge bounded at arm of the spacer-damper i and at the subconductor j of the bundled
conductor with k the side of the strain-gage( a=left side and b=right side)
hij
(Hi
) Frequency response function (dB) and Hi
is the matrix of FRF responses
Angular velocity (rad/s)
U (t), e(t) and y(t) Respectively, input, error and output signal i
A and B Numerator and denominator polynomials o the identified system, respectively (of the idpoly
object in Mat
t, T and z Time, period, and discrete time of a sample interval (s)
OHTL Overhead transmission line
na
, nb
and nk
. Denominator coefficient, numerator coefficient and the input delay , respectively
rijk
and r*ij
Residual and its conjugate, respectively
k
and k
* Pole and its conjugate, respectively
Lr and ur Lower and upper value between response DOFi
fi
and fn
Frequency i and resonance frequency n (Hz)
DOFi Degree of freedom i
Ø Diameter (mm)
n Modal damping ratio (%) corresponding at the resonance frequency n

3. ฀ ฀ ฀ ฀ ฀ ฀ ฀
102
20]. The curve-fit estimation is an important step. If
this is weak, the residues of the modal parameters give
inaccurate values and their errors are often significantly
greater [21]. An efficient prediction model is necessary
for an accurate estimation of the modal parameters. There
are many existing prediction models using the modal
approach [22], but the most useful is the auto-regressive
exogenous (ARX) model [23-29] due to its simplicity.
This approach allows linearization of non-linear FRF in
a flexible structure [30] using high polynomial orders that
increase the variance of the estimation model at the same
time [31]. However, the weakness pointed out by many
researchers is that theARX models are allowed, with their
disturbance models, to be part of the parameterization
process [23-28, 31, 32].
System identification techniques are widely used to
extract modal and spatial structural parameters such as
mass, stiffness, resonance frequency, damping ratio, and
mode shape from an experimental modal analysis [33].
The main concern of the modal parameter estimation was
to assess, for instance, new structure design performance
[34], real-time health monitoring [34-38], damage
control of existing structures [39-43], and performance
of damped structures [44-47]. The principle of a classical
identification technique is often to establish a prior
relationship between the input excitation force and the
outputamplitude.Thisisdisplacementorvelocity,oragain
acceleration, or sometimes only the output data. These
were described in some recent papers [48-50]. Unlike the
force-response of a rigid structure, the implementation
of system identification techniques for a flexible or a
damped structure such as overhead line conductors, is
not a trivial task, since it would include the influence of
damping factors (viscous or hysteresis) [51]. Furthermore,
the performance assessment of an OHTL with bundled
conductors using a system identification approach has
become more complicated in terms of flexibility and
complex structure; therefore, a consistent selection of the
input-output system is necessary. In this case, single input-
multi-output(SIMO)ormulti-input-multi-output(MIMO)
configurations had to be considered for a more effective
vibration performance evaluation [52]. On the other hand,
a vibration mode of any excitation system should not
interfere with the output response. However, if there is
any interference that modifies the response, it has to have
quantifiable parameters, so that they may be assessed in
large compared with the horizontal motion. This is not the
caseforconductorbundles,becauseevenaslightdifference
of tension in each sub-conductor may become a source of
additional vibration modes [7]. Some of these modes in
the sub-conductors may create a rotational motion with
respect to the centre of mass of the bundled conductors.
In addition, vibration severity and wind velocity ranges
are important contributing factors in generating modes
since they are influencing the wavelength of the vibration.
As described in [8], the concepts of in-phase and out-of-
phase oscillations characterise the effectiveness of spacer-
dampers on twin-bundled conductors.
The theory of a bending-strain envelope was introduced in
[8] and has been used by many other researchers [9, 10].
Ideally, for efficient spacer-dampers, the bending stress
envelope measured by the sub-conductors should not
exceed 150 micro-strain and 200 micro-strain respectively
on both the edge of the spacer-damper clamps and the
termination clamp [11-13]. The first indoor experimental
work on bundled conductors is reported in [14], whereby
twin-bundled conductors with one spacer-damper in a
tandem configuration were subjected toAeolian vibration.
Ashaker was attached by means of a rigid connection and
the free span considered was located between the shaker
and the spacer-damper. Some years later, [15] compared
analytical models that they had developed in conjunction
with experimental work on twin-bundled conductors in
a vertical configuration. In this indoor work, the shaker
was located on the mid-span and attached at only one
sub-conductor (bottom). A performance study based on
a fatigue indicator, i.e., the bending strain envelope, was
reported in [16]. This study used both twin- and quad-
bundled conductors using various commercial spacer-
dampers. It can be noted that fatigue performance of an
OHTL may be related to the corresponding damping
capability, as this is relevant to the energy dissipated by
the system, along with other relevant parameters, such
as resonance frequency and mode shape. This approach
may be relevant to understanding the system or evaluating
the efficiency of the damping devices and for improving
design or expediting optimization. Extraction of such
modal parameters requires: (i) a curve-fit estimation of
measured data (experimental); and (ii) the determination
of modal parameters by using the function as established
in (i) for the curve-fitting of the force response in the
time domain [17, 18] or the frequency domain [19,

4. ฀ ฀ ฀ ฀ ฀ ฀ ฀
103
2 Methodology
2.1 Experimental set-up and instrumentation
The experimental system is shown in Figure 1.
Measurements and evaluation of the Aeolian vibration
performance of rigidly clamped quad-bundled
conductors with a 0.45 m spacing were conducted using
a 84.5 m indoor laboratory span. The arrangement is
illustrated in Figure 2 in which the blue dot represents the
locations of accelerometers. The tension in the various
sub-conductors was adjusted, making them slightly
different from one another and from the standard one,
this being 20 % of the ultimate tensile strength (UTS)
of the bundled. The shaker was connected using a rigid
connection via two force transducers in points 1 and 2
as shown in Figure 2. As such, the rigid connection was
fabricated using a light square steel tube so that its own
mode does not compromise the conductor. The velocity
was recorded and controlled at one location of each sub-
conductor, i.e., points 3, 4, 5, and 6 (Figure 2). These are
on the free span where the vibration performances were
assessed at about 20.125 m from the shaker. The bending
strain was measured and compared with the results in
[56, 57]. The type of cable used is shown in Figure 3 for
information.
the final analysis of interest. As such, the impedance or
mobility analysis of the excitation system used for the
structure under investigation may be particularly relevant
for identification from the interference point of view.
In this work, Aeolian vibration performances of
quad-bundled conductors in various configurations
were assessed using the ARX system identification
implemented in the MATLAB toolbox. First, the span
of bundled conductors was vibrated without any SD
attached; then, with one SD at the middle; and then
again, with two SDs attached at various inter-distances
between them. Three different commercial SDs were
employed in this experiment whose characteristics were
assessed in previous papers [53, 54]. Modal parameters
of various configurations were matched to the bending
stress envelope performance in order to determine which
SD or configuration was the most efficient. In part B of
this paper the excitation technique used is assessed and
the discussions of its validation is put forward in part A
of this paper [55]. Following the introduction (Section 1),
this paper includes 4 more sections: Section 2 gives the
methodology, Section 3 puts forward the experimental
results and discussions, Section 4 gives parameter
estimations, and finally, Section 5 draws conclusions of
the study.
Figure 1 Quad-conductor bundled bench with a spacer-damper
Figure 2 Idealised illustration of quad-bundled conductors with two spacer-dampers attached where the blue dot from 1 to 30
characterises the position of the accelerometers. R1 to R8 are indicating the rigid clamps where R5 to R8 are the termination clamps.

5. ฀ ฀ ฀ ฀ ฀ ฀ ฀
104
SD: AD21, AD22, AD23, AD24, AD25, and AD26; iv)
four on the mid-sub-span between the first and second
SD: AC21, AC22, AC23, andAC24; v) six on the second
SD : AD11, AD12, AD13, AD14, AD15 and AD16; vi)
four at each mid-sub-span between the second SD and the
termination rigid clamp:AC11,AC12,AC13, andAC14;
and vii) four at 89 mm measured from the termination
clamp edge: AT1, AT2, AT3, and AT4. However, for
configurations C0 (Figure 3-A) and C1 (Figure 3-B), the
number of accelerometers was reduced, respectively, to
twenty-six and twenty-eight. As where there are no SDs,
or only one SD attached, accelerometers were attached
on the sub-conductor where an SD was supposed to be.
To measure the bending strain at locations susceptible
to fatigue failure, strain gauges were glued on the
uppermost wire of the sub-conductor at the clamp edge
of the SD and termination clamp. This was a limitation
of the channels so two strain-gauges mounted in half-
bridge with a dummy (temperature compensation) were
used at each location and on both sides of the clamps.
In total, forty strain gauges (twenty active and twenty
dummies) were mounted at the locations indicated in
Table I.
Figure 4 describes various commercial SDs labelled
SD1, SD2, and SD3 that were used in this investigation
and for which the suppliers gave some of their physical
characteristics. This was in addition to their horizontal
and radial stiffnesses which were evaluated in [53, 54].
These SDs have the same sub-conductor spacing of
about 0.45 m, but significantly, different values of their
physical characteristics. All these SDs were fitted to a
Tern aluminium conductor steel reinforced (ACSR)
with a diameter of 27 mm as described in Figure 3.
Importantly, the ratio between the mass of the arm and
the frame of the various SDs plays a significant role in
the force transmission from the sub-conductor to the
frame via the rubber, and vice versa.
2.2 Instrumentation
For the indoor vibration testing of quad-bundled
conductors it is advantageous to move sensors along the
span bench and it is also convenient to collect as much
data as possible. This depends on the available number of
sensors and channels. Thirty accelerometers were used at
different locations as per Figure 5: i) two at shaker AE1
and AE2 (accelerometers at excitation); ii) four on the
free-span AF1, AF2, AF3 and AF4; iii) six on the first
Figure 3 Physical parameters of ACSR Tern conductor uses here as sub-conductor and illustration of ACSR Tern conductor
showing the steel and the Aluminium Wire
Figure 4 Physical parameters of different commercial spacer-dampers SD1, SD2 and SD3 and illustration of a spacer-damper
on the OHTL bundled conductors
Table I Location and annotation of strain-gauges on various sub-conductors related to Figure 2

6. ฀ ฀ ฀ ฀ ฀ ฀ ฀
105
was chosen based on the quad-bundled span set-up and
specific expected results of interest such as sample
rates, filtering system, and input and output signal
configurations. Since the frequency domain was selected
as the domain in which to conduct this investigation, all
experimental work was performed at in the frequency
range between 5 and 60 Hz, and in the velocity range of
about 0.1 to 0.3 m/s. Other relevant test parameters were
the sample rate NS
and sample size which was set at 2600
samples per second for 2600 samples. Virtual low-band
filtering was incorporated in the data-acquisition scheme
to suppress unnecessary noise. To ensure consistent
filtering, an automated condition was set up in such
way that each time the frequency fi
is tuned, the cut-off
frequency was automatically adjusted. The data was
acquired when the average velocity of 0.1 m/s at given a
frequency was reached at the control points (free span).
Figures 6-A and 6-B show the excitation system and
the suspension clamps. Figures 6-C and 6-D show the
instrumentation (force transducers and accelerometers)
located at the excitation. Figure 6-E illustrates where the
accelerometer and two strain-gauges are in relation to a
SD (clamp). Three different configurations of bundled
conductors are described in part A of this paper ranging
from C0 to C9. These were used in this work.
2.4 Automated approach: ARX And CMIF methods
An automated approach for estimation of modal
parameters requires two steps: first, detailing of the
transfer function and second, determination of the
modal parameters. Several algorithms and methods
need to be developed for these two steps. The transfer
function developed therefore allows for extracting of
modal parameters by analysing the poles and zeros.
An understanding of the system may save time in the
Figure 5 shows the architecture of the instrumentation
and the data-acquisition systems as well as the control
and the storage system. Four data-acquisition systems,
DAQ1, DAQ2, DAQ3, and DAQ4 were used including
the main system that also served as a central processing
unit (CPU). Besides the CPU (DAQ 1), the others
were located as near as possible to the measurement
points, particularly the strain gauges. This was in order
to minimise the additional resistance due to the cable
length. To overcome this additional resistance and to
suppress errors that may affect the measurement signal
in general, DAQs were interconnected to each other via
a local area network (LAN) by means of Router 1. This
is illustrated in Figure 5. DAQ1 was limited in terms of
random-access memory (RAM) and read-only memory
(ROM), another computer was used and linked to DAQ1
using Router 2. Hence, using LabVIEW, a virtual control
and storage filing system was designed through a second
computer.
2.3 Experimental method
Themainobjectiveofthisexperimentalinvestigationwas
to assess the performance of quad-bundled conductors,
with various commercial spacer-dampers, subjected
to Aeolian vibrations. For this, the performance of the
different SDs was correlated with the fatigue failure
indicators, especially the bending stress/strain and the
number of times the bending strain at both SD and
termination clamps crossed the upper limits. These
were set at 150 micro-strains and 200 micro-strains,
respectively. The bending strain envelope could be
obtainedbyadirectmeasurement.Thiswasanalternative
to an assessment of the modal parameters that required
more than raw data, i.e. mathematical prediction and
parameterization.As such, an experimental methodology
Figure 5 Schematic illustration of the instrumentations and the data-acquisition system used in the effective set-up
of quad-bundled conductors with two spacer-dampers attached

7. ฀ ฀ ฀ ฀ ฀ ฀ ฀
106
where
(2)
with
(3)
and
(4)
As such, the model structure parameterization depends
on the selection nth
-order of the ARX, which is given by
the number of denominator coefficients na
, number of
numerator coefficients nb
and the input delay nk
. Thus, for
causality purposes, it is always so that na
>nb
. However,
these parameters of the ARX order are important since
the best selection leads to an accurate prediction model
with consistent residual parameters (fit to estimation)
and an insignificant standard deviation SSE.
The expression in (1), after manipulation using a Laplace
transformation in the frequency domain, gives the FRF
application of existing algorithms. Based on current
knowledge and a literature review [17, 18, 22-47, 51,
52] of the non-linearity nature of the system under
investigation (Figure 2), an auto-regression exogenous
(ARX) and a complex mode indicator function (CMIF)
were identified and then employed in this study. The
practical implementation of ARX and CMIF requires a
betterunderstandingoftheanalyticaltheoryandtheactual
structure in order to estimate correctly the parameters
of interest. As described in Sections 2.1 and 2.2, the
system of shaker and quad-bundled conductors can be
modelled as a MIMO with two excitation points with
force transducers as inputs, and four outputs measured
using accelerometers. Figure 7 is an illustration of the
system that the ARX fits well. The disturbances are only
located at the two force transducers (inputs) and not at
the outputs. This is because a low-pass virtual filter was
incorporated during the signal conditioning from each
accelerometer.
In general, the multivariable ARX model structure
considering p-output and m-input can be expressed as
(1)
Figure 6 A) Excitation of bundled conductors using a rigid connection attached at 1 m from the clamps;
B) Dead end and rigid clamp; C ) and D) Force transducers and accelerometers at the excitation (rigid connection);
and E) Accelerometer and strain-gauges at SDs clamp
Figure 7 ARX modelling of MIMO system with two inputs and four outputs (TIFO)

8. ฀ ฀ ฀ ฀ ฀ ฀ ฀
107
three. This because of the various tensions observed in
the sub-conductors, where SC1 had the highest tension.
This could be justified by the difference in the vibration
severities compared to other SCs. However, because
to the channel limitation, only one strain-gauge was
used. This was used on the uppermost wire in the sub-
conductor. This could be another reason for the extreme
difference in the strain measured. To minimise other
additional strains in the measurement, the temperature
around the bench was maintained at almost 20°C to
control the creep of ACSR Tern conductor. Figure
8-B gives the tension against temperature of the sub-
conductor SC-2 between 11am and 1pm with an outdoor
temperature of about 26.5°C. Figure 8-C shows the
efficiency of various ACs evaluated as temperature
against position.
Three different commercial SDs were attached on the
sub-conductors. Their physical characteristics are given
in Figure 4 (Section 2). The measured bending strain
at the T-C shows that ST1 still has the highest value,
as shown in Figures 9-A, 9-B, and 9-C, respectively.
These were measured using C1 (SD1), C2 (SD2) and C3
(SD3). Apart from ST1, the measured strain points are
generally concentrated between 7 micro-strains and 100
micro-strains.
Figures 10-A, 10-B and 10-C display the bending strain
against frequency measured at the clamp edge (KE) of
hij
. This is
(5)
where rijk
and r*ij
are the residual and its conjugate,
respectively; k
and k
* are the pole and its conjugate,
respectively; Lr and ur are the lower and upper value
between the response DOFi and all reference response
DOFs, and N is the number of the vibration mode.
Equation (5) is an ARX polynomial algorithm from
the system identification toolbox of MATLAB. During
the implementation of the regenerated model, some
experimental parameters must be imported from
workspace to the dialogue box. This includes the inverse
of the sampling rate fs
(1/sec), frequency f (1/sec), input
forces u1
and u2
in N, and output acceleration (m/s2
): y3
,
y4
, y5
, and y6
.
3 Experimental Results
3.1 Bending strain results
A) Bundled conductors without any SD
Figure 8-A illustrates the bending strain against
frequency at the four termination clamps (TCs) denoted
by STi, as well as the safe strain design limit (SSD = 200
microstrains). The results showed that the bending strain
measured at ST1 was highest compared with the other
Figure 8 A) Bending strain vs frequency measured at the termination clamp of configuration C0 without any SD;
B) Illustration of tension stabilization vs time of the far end top sub-conductor (Sc-2) prior to beginning tests; and
C) Efficiency of AC disseminated in the lab given initial and final temperature vs AC position
Figure 9 Bending strain vs frequency measured at the termination clamp of configuration: A) C1; and B) C2; and C) C3

9. ฀ ฀ ฀ ฀ ฀ ฀ ฀
108
B) Bending strain results SD-A at 31.5 m and SD-B at
42.5 m
Two SDs were mounted using one of each SD type i.e.,
SD1, SD2 and SD3 that was added to configurations
C1, C2, and C3, respectively, with an SD at the mid-
span of the bundled conductors, as per Figure 3-C.
With the additional SD weight, there was an increase
in tension of the sub-conductor that had the highest
tension in the bundle. This serves as a leverage for
the other sub-conductors. This was attributed to the
vibration severity observed in the variations of bending
strain against frequency measured at their TCs for the
different configurations C4, C5, and C6. This is shown
in Figures 11, 12 and 13 if compared with C1, C2, and
various SDs in C1, C2, and C3, respectively. The SSD
line (SSD = 150 microstrains) was plotted against the
frequency in Figure 10-A. This allowed the evaluation
of the performance of the SDs in terms of conductor
wear. Hence, the observation of various bending strains
plotted showed that SD12a and SD12b are above the
SSD line for the configurations C1 (SD1) and C2 (SD2).
For the C3 configuration (SD3), in addition to SD12a
and SD12b, the highest bending strain values were
recorded in SD13a and SD14a. This variation in bending
strain may be justified by several factors such as the
additional weight and the clamp design of the SD, and
the torque of its clamps. Hagedorn et al. [2] established
the relationship mechanism of the bending strain at the
SD clamp edge.
Figure 10 Bending strain vs. bending frequency measured at SD clamp of A) SD1; B) SD2; and C) SD3
Figure 12 Bending strain vs frequency measured in configuration C5 at A) the termination clamp and at both clamps of the SDS placed at
B) 31.5 m and C) 42.5 m
Figure 11 Bending strain vs frequency measured in configuration C4 at A) the termination clamp and at both clamps of the SDS placed at
B) 31.5 m and C) 42.5 m

10. ฀ ฀ ฀ ฀ ฀ ฀ ฀
109
In general, the bending strains in all the configurations
C7, C8, and C9, were higher than those observed in
C4, C5, and C6, respectively especially at the SD-B
damper. Figures 14-A, 14-B and 14-C give the bending
strain against frequency measured in configuration C7
at the clamps of TC, SD-A, and SD-B. Figures 15-A,
15-B and 15-C give the bending strain against frequency
measured in configuration C8 at the clamps of TC, SD-
A, and SD-B. Finally, Figures 16-A, 16-B and 16-C
give the bending strain against frequency measured in
configuration C9 at the clamps of TC, SD-A, and SD-B.
C6, respectively. In general, at the TC, the bending strain
recorded in the configurations C0, C1, C2, and C3 at
ST1 were the highest and characterised the bending
strain envelope.
C) Bending strain results SD-A at 31.5 m and SD-B at
56.5 m
To evaluate the influence of the SD position on the
bundled conductors, the SD-B damper was moved from
42.5 m to 56.5 m while the SDA was kept at the same
position 31.5 m from clamp. This is shown in Figure 3-D.
Figure 13 Bending strain against frequency measured in Configuration C6 at A) the termination clamp and at both clamps of the
SDS placed at B) 31.5 m and C) 42.5 m
Figure 14 Bending strain against frequency measured in configuration C7 at A) the termination clamp and at both clamps of the
SDS placed at B) 31.5 m and C) 56.5 m
Figure 15 Bending strain against frequency measured in configuration C8 at A) the termination clamp and at both clamps of the
SDS placed at B) 31.5 m and C) 56.5m

11. ฀ ฀ ฀ ฀ ฀ ฀ ฀
110
3.2 Evaluation of performance based on bending
strain envelope on both spacer-damper (s) location
and rigid clamp
To evaluate the fatigue performance of the bundled
conductors, the bending strain at both clamp edges of the
SD and termination clamp were measured at different
frequencies from 5 to 60 Hz and constant velocity. The
results plotted as bending strain against frequency were
shown in Section 3.1. The measurements were counted
only for those points above the bending strain limit
defined as 150 micro-strains and 200 micro-strains at
the SD clamps (SD_A and SD_B) and termination (TC),
respectively. The global performance was obtained by
summing the number of points counted. It was observed
that configuration C6 was more effective in terms of
fatigue performance compared with other configurations,
with a total constraints count of about nine. C0, without
All the strain-envelope data results were plotted in
scatter graphs as strain against frequency, so that curve-
fitting techniques can be applied in order to generate
corresponding columns of strain points. The non-linear
regression technique was used to assess the relationship
of the scattered data. All complied and matched well to
the power curve:
(6)
Tables II, III, and IV give the various function
parameters for the simulation of all the configurations.
The significance of statistical simulation (predictions) is
expressed by the standard deviation S.E. This comprised
of all configurations between 1.714 and 2.886,
respectively, corresponding to the R-squared factors
0.9997 and 0.9983.
Figure 16 Bending strain against frequency measured in configuration C9 at A) the termination clamp and at both clamps of the
SDS placed at B) 31.5 m and C) 56.5m
Table II Parameters a and b of strain envelope vs. frequency curve fittings for
various configurations of bundled conductors without SD; and with one SD
installed at the mid-span C0, C1, C2, and C3
Table III Parameters a and b of strain envelope vs. frequency curve fittings for various configurations of
bundled conductors with two SDs installed at the mid-span from configurations C4, C5, and C6
Table IV Parameters a and b of strain envelope vs. frequency curve fittings for various configurations of
bundled conductors with two SDs installed at the mid-span from configuration C7, C8 and C9

12. ฀ ฀ ฀ ฀ ฀ ฀ ฀
111
corresponding frequency and sampling rates using the
MATLAB system identification toolbox. Since the
system was considered as MIMO (TIFO), each node
generated two sub-FRFs that were merged using the
MATLAB function (function: merge experiments).
Various merged FRFs are denoted as H3
, H4
, H5
, and H6
.
These correspond to the response of different nodes in
the free span of the bundle span as shown in Figure 2.
The ARX prediction was utilised. With a different model
order, firstly between 5 and 18, the harmonization for all
FRFs was to the highest order of 18 and characterized
by its parameters na
=9, nb
=8, nk
=10. In this condition
and in general, the estimation fit varied between 99 and
100 % with a standard deviation in the insignificant
ranges between 10-1 -6
. Overall, various FRFs
configurationsshowedfourresonanceandanti-resonance
frequencies associated with the 4-DOF system. For
instance, natural frequencies were easily determined by
inspection of the FRF curves; furthermore, their skeleton
geometries were analysed. In Figure 18 the skeleton
geometry was mainly stiffness dominated rather than the
mass dominated for 80 % of the frequency range.
any SD attached, had only four counted constraints at
the termination clamps. Figure 17 presents the number
of constraints that were violated using various bundle
configurations. C5 had two SD2 SDs of attached at 31.5
m and 42.5 m from the clamp (tension side). The violated
constraints were low at TC, SD_A, and SD_B clamps
compared with C8 which had a similar SD configuration.
By changing the distances between the SD2s from C5
to C8 (keeping SD_A and moving SD_B from 42.5 m
to 56.5 m from clamp) the drop-off fatigue performance
increased from 12 violated constraints to 62. With the
SDs in the same locations, SD3 in C9 has given better
fatigue performance with 32 counted violated constraints
compared to C7, and C8 with 86 and 62 constraints.
3.3 Frequency response function model
The FRFs for the known excitation conditions under the
various configurations C0 to C9 were investigated and
are given in Figures 18 to 21. Apart from C0, with no
SD and given in Figure 18, other configurations were
categorised into sub-groups of bundled conductors with
the same type of SD. FRFs (in dB) were obtained after
processing of the input and output data along with their
Figure 17 Bending strain chart of counted number above the safety strain design
measured at both clamp edges of termination clamp and SD clamp. Different
configurations are presented: i) C0 is without spacer-damper; ii) C1, C2, and C3
are with different SDs at the centre: they are SD1, SD2 and SD3; iii) C4, C5 and
C6 are with two identical SDs, one at 31.5m and one at 42.5 m: they are again SD1,
SD2 and SD3; and iv) C7, C8 and C9 also have two identical SDs, as in (iii), but
placed at 31.5 m and 56.5 m
Figure 18 Measured Force Response Frequency plots determined at the free span zone of various
sub-conductors of the bundled conductors in configuration C0 (without any SD attached) using
the MATLAB System identification toolbox

13. ฀ ฀ ฀ ฀ ฀ ฀ ฀
112
sensitivity check of the impact of excitation on the FRFs.
The condition of dynamic stability or instability that
usually leads the system to static stability or instability
was observed in some modes of vibration. A system
with a positive damping factor is called a dynamically
stable system, when it has a negative damping factor, it
is known as dynamical unstable [60, 61] as observed in
some modes of the vibrations.
Table V presents the values of modal parameters of
C0 (Figure 18). This was considered as a reference,
compared with other configurations with SDs. Tables
VI, VII, and VIII give the modal factors for the various
configurations categorized into SD1, SD2, and SD3
categories. In general, the configurations C1, C2, and
C3 with one SD attached present a system that was
dynamically stable, unlike the configurations of C0 and
those with 2 SDs attached.
3.4 Estimation of modal parameters
At first glance, diverse natural frequencies were
determined by inspection of the various FRFs curves
against frequency plots in Figures 18 to 21. To evaluate
the damping factor, the half power method [59] was
used as a first approach. It has often been difficult to use
this in cases of low frequency resolution and where the
mode peaks are often between two spectral lines. This
is the source of inaccuracy in the estimation of the FRF
damping ratios, mainly for frequencies above 30 Hz.
Alternatively, the CMIF approach was used to extract
automatically by means of a poles and zeros (I/O)
map in the MATLAB system identification toolbox™.
Parameters such as natural frequency, damping ratio,
poles, zeros, overshoot, and mode shapes were extracted.
Only the first two were explored thoroughly since they
are the measurables of the vibration performance. The
zeros of each transfer function were examined as a
Figure19 Measured Force Response Frequency plots determined at the free-span
zone of various sub-conductors of the bundled conductors in configuration C1
(one SD1 at mid-span), C4 (two SD1s: at 31.5 m and 42.5 m), and C7 (two SD1s:
at 31.5m and 56.5 m), using MATLAB System identification toolbox
Figure 20 Measured Force Response Frequency plots determined at the free-span
zone of various sub-conductors of the bundled conductors in configurations C2
(one SD2 at mid-span), C5 (two SD2s: at 31.5 m and 42.5 m), and C8 (two SD2s:
at 31.15 m and 56.5 m), using the MATLAB System identification toolbox

14. ฀ ฀ ฀ ฀ ฀ ฀ ฀
113
C2 has one SD2 and is the best fatigue performer
among the configurations with one SD. The associated
FRFs presented response magnitudes of the resonance
frequency between -30 and 0 dB. All damping factors
thus extracted were positive. In the category of
bundled conductors with two SDs attached, and with
configurations C7, C8, and C9, the last configuration
has given a better performance than the two others in
terms of a fatigue indicator. It is worth looking closely at
its FRF curves and modal parameters of other different
locations of bundled conductors.
4 Performance Analysis of
Bundled Conductors
Based on the fatigue performance, which was
derived from the bending strain against frequency,
the configuration C6 (two SD3s) showed the best
performance apart from configuration C0. Inspecting
the C6 FRFs, the response magnitudes were below -10
dB with the exception of node 4 of the third vibration
mode. However, C6 did present some cases of dynamic
instability as characterised by negative damping or an
overshoot greater than 100% (a non-stability zone).
Figure 21 Measured Force Response Frequency plots determined at the free-span
zone of various sub-conductors of the bundled conductors in configurations C3
(with one SD3 at mid-span), C6 (two SD3s: at 31.5 m and 42.5 m), and C9 (two
SD3s: at 31.5 m and 42.5 m), using the MATLAB System identification toolbox
Table V: Frequency fn
(Hz) and damping ratio (%) per vibration mode in configuration C0

15. ฀ ฀ ฀ ฀ ฀ ฀ ฀
114
Table VI: Frequency fn
(Hz) and damping n
(%) per vibration mode of configurations C1, C4, and C7
Table VII: Frequency fn
(Hz) and damping n
(%) mode in configurations C2, C5, and C8
Table VIII: Frequency fn
(Hz) and damping n
(%) mode in configuration C3, C6, and C9

16. ฀ ฀ ฀ ฀ ฀ ฀ ฀
115
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5. Conclusion
The vibration performance assessment approach of
spacer-dampers attached to an indoor short span of quad-
bundled conductors was developed based on the force
response frequency linked to its fatigue performance.
A bundled conductor with spacer-dampers can offer a
good performance in terms of fatigue failure, while
being dynamically unstable because of an excessive
additional number of spacer-dampers. Furthermore,
this investigation gives insight into some existing
optimization theories of spacer-dampers in bundled
conductors which experience Aeolian vibrations. This
topic has been subjected to additional and extensive
research, covering: (i) modal and stiffness participation,
(ii) poles-zeros cancellation, and (iii) the finite element
model updating (FEMU) approach. These are in order to
have a better understanding of the complex mechanisms
occurring on a bundled conductor. Therefore, using a
force response method and the anti-resonance frequency
sensitivities, consideration of the issues raised can
be beneficial for further understanding of bundled
conductor mechanisms. These address in frequency
ranges of Aeolian vibrations and there would be key
factors in developing the finite element method updating
6. Acknowledgments
The authors would like to acknowledge the support
of Prof Konstantin O. Papailiou, the Electrical Power
Research Institute (EPRI-USA), the Eskom Power Plant
Engineering Institute (EPPEI) Specialisation Centre
for HVDC and FACTS, Pfisterer (South Africa), and
African Cable (South Africa).
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transmission lines and power systems. He has industrial
work experiences such as in hydropower station and in
design of transmission lines.
Andrew Swanson was born in Johannesburg, South
Africa. He obtained his electrical engineering degrees
of BSc, MSc and PhD from the University of the
Witwatersrand in 2004, 2007 and 2015 respectively. He is
currently a senior lecturer at the University of KwaZulu-
Natal and a professionally registered engineer. He has
worked in industry as an engineering consultant on
traction power on railways. He is currently responsible
for research in the field of high voltage engineering
and is interested in insulation for transformers, gaseous
insulation, and electromagnetic interference. He has a
number of industrial collaborations.
David Dorrell was born in St Helens, UK. He has a
BEng (Hons) from The University of Leeds (1988), MSc
from The University of Bradford (1989) and PhD from
The University of Cambridge (1993). He is currently
a Distinguished Professor with The University of the
Witwatersrand. He was Professor of Electrical Machines
with The University of KwaZulu-Natal in Durban,
South Africa (2015-2020) and Director of the EPPEI
Specialization Centre in HVDC and FACTS at UKZN
(2016-2020). He has held positions with The Robert
Gordon University, UK, The University of Reading,
UK, The University of Glasgow, UK, and the University
of Technology Sydney, Australia. His research interests
cover electrical machines, renewable energy and
power systems. He has worked in industry and carried
out several industrial consultancies. He is a Chartered
Engineer in the UK and a Fellow of the IET. He is also a
Fellow of the IEEE, USA.
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8. Biographies
Yatshamba Daniel Kubelwa: was born in Democratic
Republic of Congo (DRC) where he graduated with the
Diplom-Ingenieur civil in Electrical and mechanical
Engineering at the Polytechnic Faculty of the University
of Lubumbashi in 2009. Four years later, He obtained
his Master of Science in mechanical Engineer at the
University of KwaZulu-Natal of South Africa. He is
currently awaiting for his Ph.D graduation in engineering
(electrical) at the same university this year 2020.
Kubelwa has received numerous prizes and awards
out of his studies and research. His research interests
include High voltage engineering, Aeolian Vibrations of