A novel leakage_current_index_for_the_field_monitoring_of_overhead_insulators_under_harmonic_voltage

1568 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 65, NO. 2, FEBRUARY 2018
A Novel Leakage Current Index for the Field
Monitoring of Overhead Insulators Under
Harmonic Voltage
Riddhi Ghosh , Member, IEEE, Biswendu Chatterjee, Senior Member, IEEE,
and Sivaji Chakravorti , Senior Member, IEEE
Abstract—Leakage current measurement is the most
reliable and effective method for condition monitoring of
overhead insulators deployed in the field. However, a major
challenge in the leakage current based insulator monitoring
is to interpret the indices extracted from the leakage current
measurements under varying harmonic content in system
voltage. This paper reports the possibility of employing the
instantaneous value of time-integral of leakage current as a
low-sensitive parameter for the monitoring of leakage cur-
rent in overhead insulators in the presence of voltage har-
monics. It has been shown that any change in the harmonic
content of the system voltage has a significant influence
on the harmonic characteristics of the leakage current, but
has a comparatively less severe effect on the time-integral.
The monitoring technique has been validated through
laboratory recorded experimental data and incorporated in
an online measurement device that has been tested in the
laboratory.
Index Terms—Harmonic distortion, insulators, leakage
currents, measurements, monitoring, power system har-
monics, sensitivity, surface contamination.
NOMENCLATURE
s, s1, s3 Leakage current signal and its first and third
harmonics.
ω Fundamental frequency of leakage current.
T Time period of leakage current.
k Order of harmonic.
Ak Amplitude of kth-order harmonic of leakage current.
Qk Time-integral under kth-order harmonic.
Q Total time-integral of overall leakage current.
Pk Amplitude of kth harmonic in p.u. of fundamental.
θk Phase difference between fundamental and kth-order
harmonic of leakage current.
Manuscript received February 23, 2017; revised May 9, 2017 and May
31, 2017; accepted June 11, 2017. Date of publication July 28, 2017;
date of current version December 8, 2017. This work was supported
in part by the Technical Education Quality Improvement Programme-II,
Jadavpur University. (Corresponding author: Riddhi Ghosh.)
The authors are with the Department of Electrical Engineering,
Jadavpur University, Kolkata 700032, India (e-mail: riddhi.ju@gmail.com;
biswenduc@gmail.com; s_chakrav@yahoo.com).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIE.2017.2733490
SQ Sensitivity of time-integral of leakage current.
STHDi Sensitivity of total harmonic distortion.
SR3/5 Sensitivity of third-to-fifth harmonic ratio.
I. INTRODUCTION
OVERHEAD insulators are installed outdoors and are ex-
posed to a variety of environmental stresses such as con-
taminants, humidity, wind, and ice accumulation, making them
susceptible to failure. Insulator failure can significantly affect
the reliability of the power network, and may often lead to sys-
tem outages. Therefore, online applicable field monitoring tech-
niques for insulators are necessary to facilitate condition-based
maintenance at an early stage of degradation.
Different parameters such as surface conductivity, air pollu-
tion, equivalent salt deposit density (ESDD), and leakage current
measurement had been recommended by the CIGRE Task Force
33.04.03 for on-site field monitoring of insulators [1]. However,
over the years, leakage current measurement has emerged as
the most effective and widely employed technique for online
monitoring of overhead insulators [2], [3]. Leakage current on
insulators can be measured online using state-of-the-art leakage
current sensors [4], [5]. The measured leakage current is then
analyzed using suitable signal analysis techniques to extract
leakage current parameters that are well-correlated to insulator
surface condition.
The earliest leakage current parameters that have been re-
ported for insulator monitoring were the peak value [6], level
crossing [7], [8], and harmonic characteristics [2], [9]. Cumula-
tive charge of individual frequency bands were also reported as
indicators of surface condition by several researchers [10]–[12].
However, subsequent research has demonstrated that the con-
tamination on insulators can be well correlated to the nonlinear
characteristics of the leakage current flowing on the insulator
surface due to nonuniform current density and the formation of
dry-bands [12]. Hence, leakage current indices that are based on
the harmonic characteristics, such as the leakage current pattern
[12], [13], lower order harmonics [14], [15], phase angle [16],
[17], and third-to-fifth harmonic ratios [18], [19] have emerged
as more reliable indicators of insulator surface condition.
Most leakage current indices can reflect the true insulator
condition only if the applied voltage waveform remains
sinusoidal. However, due to the rapid increase in the number
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GHOSH et al.: NOVEL LEAKAGE CURRENT INDEX FOR THE FIELD MONITORING OF OVERHEAD INSULATORS UNDER HARMONIC VOLTAGE 1569
Fig. 1. Schematic arrangement of a typical online leakage current mon-
itoring system showing the effect of voltage harmonics on leakage cur-
rent pattern.
of distributed generating units, renewable energy sources and
associated power electronic components, injection of harmonics
into the system voltage has become a serious issue for the power
network [20], [21]. As a result of frequent variations in the
harmonic content of voltage waveform arising out of changing
nonlinear loads, the corresponding leakage current signal will
change. This is demonstrated in Fig. 1, which shows a schematic
arrangement of a typical online leakage current monitoring
system for overhead insulators [4], [23]. In the absence of
voltage information, the change in leakage current waveform
from LC1 to LC2 will be attributed to changes in surface
contamination, when in reality, the changes are emanating from
voltage harmonics. Therefore, the presence of harmonics in
the voltage can render most leakage current monitoring indices
ineffective, including third-to-fifth harmonic ratios, phase
angle or cumulative charge of individual frequency bands,
which are otherwise known as reliable indicators of insulator
condition.
Keeping this in mind, an alternative approach for condition
monitoring of insulators has been presented in this paper, based
on the instantaneous values of time-integral of leakage current.
Experiments have been carried out in the laboratory to under-
stand the changes in leakage current parameters from contam-
inated insulators exposed to different nonsinusoidal voltages
having varying harmonic content [23]. It has been shown that
the instantaneous value of time-integral, equivalent to the cu-
mulative charge, can exhibit low sensitivity to the presence of
voltage harmonics, an aspect that has not been explored pre-
viously in the context of leakage current measurement for in-
sulator monitoring. The contribution of a particular harmonic
towards the overall time-integral of the leakage current wave-
form has been shown to be inversely proportional to the order
of the harmonics. As a result, any change in the harmonic con-
tent of the system voltage has comparatively a smaller effect on
the time-integral of the leakage current as compared to other
traditional monitoring indices. Therefore, the proposed index
may be used in combination with other traditional monitoring
indices to improve the reliability of the monitoring system under
Fig. 2. Typical leakage current signal and its constituent fundamental
and third harmonic components.
field conditions. The method has been validated through offline
and online implementation of a measurement algorithm in the
laboratory.
II. TIME-INTEGRAL APPROACH OF ANALYZING
LEAKAGE CURRENT
A. Theoretical Background
The time-integral of the leakage current gives the absolute
area under the leakage current waveform. The time-integral Q
of a time-varying leakage current signal s(t) can be expressed as
Q =

s(t)|dt. (1)
Let us consider that the leakage current signal s(t) comprises
of the fundamental s1(t) along with a third harmonic component
s3(t), such that s(t) may be expressed as the sum of the individual
harmonics s1(t) and s3(t) as follows:
s(t) = s1(t) + s3(t). (2)
Let the fundamental and third harmonic components be rep-
resented as time-varying signals given by
s1 = A1 sin (ωt) (3)
s3 = A3 sin (3ωt + θ3) (4)
where A1 and A3 are the amplitudes of the fundamental and
third harmonic components, respectively, ω is the fundamental
frequency and θ3 is the phase difference between the fundamen-
tal and third harmonic. The signal s(t) along with its constituent
harmonics have been shown in Fig. 2.
The time-integral of the signal over one cycle, having time
period T, may also be expressed in terms of s(t) as in (5) or in
terms of s1(t) and s3(t) as in (6),
Q = 2
T /2
0
s(t)dt (5)
Q = 2
T /2
0
(s1(t) + s3(t))dt. (6)

The time-integral Q in (6) may be represented as the sum of
individual time-integrals under the fundamental and the third
harmonic, Q1 and Q3, respectively, given by
Q = Q1 + Q3 (7)
where Q1 and Q3 are expressed as
Q1 = 2
T /2
0
s1(t)dt (8)
Q3 = 2
T /2
0
s3(t)dt. (9)
Based on (9) and referring to Fig. 2, it may be observed that in
the positive half cycle of leakage current in the interval [0, T/2],
the shaded areas under the third harmonic component represent
sections that have the same area but of opposite polarity, and
thus will cancel each other. This is also true for the shaded areas
in the interval [T/2, T], and may be mathematically validated by
combining (3) and (4) with (8) and (9).The time-integrals Q1
and Q3 can therefore be written as
Q1 = 2
T /2
0
A1 sin (ωt)dt (10)
Q3 = 2
T /2
0
A3 sin (3ωt + θ3)dt. (11)
Simplifying Q1 and Q3 in (10) and (11) will give the individ-
ual time-integral values as
Q1 =
4A1
ω
(12)
Q3 =
4A3
3ω
cosθ3. (13)
Let P3 represent the peak value of the third harmonic com-
ponent expressed in per unit of the fundamental A1. Then, the
amplitude of the third harmonic component A3 in (13) may be
represented as P3 p.u. of A1. Therefore, Q3 may be rewritten as
a function of the fundamental amplitude A1 as follows:
Q3 =
4P3A1
3ω
cosθ3. (14)
Now, combining (12) and (14), Q3 may be expressed as
Q3 =
P3
3
Q1 cosθ3. (15)
In general, the expression for the contribution of the time-
integral for the kth-order harmonic Qk as a function of the
fundamental component time-integral may be expressed as
Qk =
Pk
k
Q1 cosθk (16)
where Pk represents the amplitude of the kth-order harmonic
expressed in per unit of the fundamental peak value and θk
represents the phase difference between the fundamental and
kth-order harmonic. θk may be determined from the harmonic
information extracted from the leakage current waveform us-
ing any harmonic extraction technique. In this work, the syn-
chronous detection or coherent detection technique has been
used to extract the individual harmonics [24], and θk has been
determined from the extracted harmonic information.
It may be observed from (16) that for a particular value of
Q1, if the fundamental current component is in phase with the
kth-order harmonic component, then the contribution of Qk to-
wards the overall time-integral is the maximum, and is equal to
one cycle of the kth-order harmonic component. This is because
in each interval [0, T/2] and [T/2, T], the time-integral of the
successive half cycles of kth harmonic in the interval will yield
equal areas of opposite polarity and the overall time-integral
for the first (k–1) cycles will be zero. As θk increases, the con-
tribution of Qk as a percentage of Q1 starts reducing due to
the factor cos θk . It needs to be emphasized here that θk is an
essential parameter that can be affected by external factors such
as contamination and humidity [16], [17] as well as voltage
waveforms. However, the advantage of the proposed monitor-
ing index is that irrespective of influence of external factors, the
contribution of the kth-order harmonic towards the time-integral
is limited to a maximum of one cycle of the harmonic. Also, Qk
reduces as the value of k (order of harmonics) increases, further
minimizing the influence of θk for higher order harmonics.
In the case of a practical leakage current waveform, there
will be multiple harmonics in the waveform as against only a
particular harmonic as has been discussed so far. In such cases,
the effect of the time-integral of the individual harmonics will
be additive and may be expressed as
Q =
N

k=1
Qk . (17)
B. Time-Integral Approach as an Index for Identifying
Voltage Distortion-Induced Leakage Current Changes
Leakage current can flow over an insulator surface when the
surface is exposed to contamination and is sufficiently humid.
When the insulator surface is dry, leakage current on the insu-
lator surface will be insignificant, irrespective of the degree of
contamination [25]. On the other hand, under wet conditions
and in the presence of contaminants, a significant amount of
leakage current can flow on the insulator surface. The contami-
nants, which include salt deposits from the environment, tend to
form a conducting layer on the insulator surface in the presence
of moisture [11], [14]. As the degree of contamination increases
with time, the electrolytic dissociation of the salt increases,
thereby increasing the conductivity and raising the magnitude
of the leakage current. Higher magnitude leakage current gives
rise to the possibility of nonuniform heating and formation of
dry-bands, which induces nonlinearity on the insulator surface
[16]. Therefore, a change in the contamination affects the funda-
mental leakage current component due to changes in the surface
conductivity and a change in the harmonics due to surface non-
linearity.
On the other hand, any change in the voltage harmonics at a
given contamination level will change only the corresponding
order of harmonics in the leakage current. This is because the
injection of kth-order harmonic in the system voltage will in-
duce a corresponding change in the kth harmonic in the leakage

TABLE I
INSULATOR SAMPLES TESTED
Insulator No. Service History Degree of Aging
Insulator 1 20 Years Severe Corrosion
Insulator 2 10 Years Mild Corrosion
Insulator 3 5 Years Light Corrosion
current, and will not affect the fundamental or any harmonic
other than the kth order. Therefore, a small deviation of the
harmonics in the voltage under a specific contamination level
and humidity should produce a small change in the time inte-
gral of the leakage current as expressed in (16), while a change
in environmental conditions such as contamination or humidity
should induce a comparatively larger change due to changes
in the surface conductivity. This property of the time-integral
can be effective in identifying distortion-induced changes from
contamination-induced changes in leakage current when used
along with traditional monitoring indices.
III. EXPERIMENTAL SETUP
A. Test Samples
The test objects used for the experiments consisted of three
naturally aged 11 kV single-disc cap and pin porcelain insu-
lators collected from the local power transmission company.
The degree of aging and service history of the insulators has
been elaborated in Table I. The insulators were contaminated
using the solid layer method to produce a uniform layer of con-
tamination according to IEC 60507. The contamination slurry
was prepared by mixing different proportions of NaCl with
40 g of Kaolin in 1 L of distilled water to give contamination
layers having ESDD in the range of 0.03–0.05 mg/cm2
and
0.07–0.09 mg/cm2
. The two contamination levels are hence-
forth denoted as contamination level 1 (light) and contamination
level 2 (moderate).
B. Experimental Setup
The experimental setup consists of a programmable high volt-
age harmonic waveform generator capable of supplying a peak
voltage of 20 kV. Different voltage waveforms with different
harmonic contents are applied to the samples under test. The
root-mean-square value of the fundamental component of the
applied voltage waveforms has been maintained at 11 kVrms,
and different harmonics have been injected into the applied
voltage. The applied voltage waveforms are measured with the
help of a digital storage oscilloscope across a resistive voltage
divider via a protective unit. The leakage current is made to
flow to earth via a 10-kΩ noninductive shunt resistor. The volt-
age drop across the shunt resistor was measured by the digital
storage oscilloscope via a protective unit. The data were sam-
pled at a sampling frequency of 50 kHz. The voltage and current
waveforms were stored for offline analysis. The schematic of the
experimental arrangement in the laboratory has been shown in
Fig. 3.
Fig. 3. Schematic of experimental setup in the laboratory.
TABLE II
VOLTAGE WAVEFORMS EMPLOYED FOR STUDYING CHANGES IN LEAKAGE
CURRENT PATTERN
Voltage Waveform Fundamental Harmonic Content
Third Fifth Seventh Ninth
V0 100% – – – –
V1 100% 3% – – –
V2 100% 5% – – –
V3 100% 8% – – –
V4 100% – 3% – –
V5 100% – 5% – –
V6 100% – 8% – –
V7 100% – – 3% –
V8 100% – – 5% –
V9 100% – – 8% –
V10 100% – – – 3%
V11 100% – – – 5%
V12 100% – – – 8%
V13 100% 3% 3% – –
V14 100% 3% – 3% –
V15 100% – 3% 3% –
C. Voltage Waveforms
For testing the insulators under different contamination lev-
els, a set of 16 different voltage waveforms having different
degrees of harmonic distortion have been used, as shown in
Table II. Voltage waveform V0 denotes a purely sinusoidal volt-
age while V1 through V12 contain a single harmonic component
each of varying harmonic percentages. Voltage waveforms V13,
V14, and V15 are composite waveforms having two different
harmonics.
IV. APPLICATION TO EXPERIMENTAL DATA FROM
CONTAMINATED INSULATORS
A. Leakage Current Waveforms and Harmonic Content
The 16 different voltage waveforms tabulated in Table II have
been applied to each contaminated insulator, and the leakage
currents were recorded in the laboratory. Some typical applied
voltage waveforms along with the corresponding leakage cur-
rent waveforms have been shown in Fig. 4 for insulator 2 and
a constant contamination level 2. It may be observed that there
are significant variations in the leakage current pattern and har-
monic content due to changes in voltage harmonics. Fig. 5 shows

Fig. 4. Different voltage waveforms (a) V3, (b) V6, (c) V9, (d) V12, and
(e) V15 applied to insulator 2 at contamination level 2, and (f)–(j) the
corresponding leakage currents recorded.
Fig. 5. Changes in leakage current harmonic content for different volt-
age waveforms for insulator 2, contamination level 2.
the changes in the harmonic content of leakage current on insu-
lator 2 at contamination level 2, for the different applied voltage
waveforms for insulator 2, contamination level 2. Such varia-
tions in harmonics are entirely on account of changes in applied
voltage waveforms and not due to changes in surface contam-
ination, making it difficult to monitor the insulators based on
harmonic characteristics.
B. Effect of Voltage Waveform on θk
The influence of voltage waveform on θk has been shown in
Fig. 6 for the third-, fifth-, seventh-, and ninth-order harmonics.
For applied voltage V0, the θk represents the phase difference
between the fundamental and kth harmonic of leakage current
in the absence of harmonics in applied voltage. However, when
a kth-order harmonic is present in the voltage, the θk will be sig-
Fig. 6. Influence of voltage waveform on θk for different order of
harmonics.
Fig. 7. Time-integral of leakage current under different voltage wave-
forms for the three insulators and two contamination levels.
nificantly affected as has been shown in Fig. 6. Typically, V1,
V2, and V3 contain 3%, 5%, and 8% of third harmonic, respec-
tively, and therefore θ3 will deviate from its value corresponding
to voltage waveform V0. In general, significant changes in θk are
observed when the voltage waveforms consist of the kth-order
voltage harmonics, as shown in Fig. 6.
C. Time-Integral of Leakage Current Waveforms
The time-integral of the leakage current was determined for
100 ms sections of waveforms under the 16 applied voltages
for the three insulators, each contaminated to the two levels.
The time-integral values obtained have been shown in Fig. 7
in logarithmic scale. It may be observed from Fig. 7 that the
time-integral of leakage current for any of the insulators at any
contamination level shows little variation with changes in the
harmonic distortion of applied voltage. It is also evident that as
the contamination level changes, there is a marked change in
the value of the time-integral of leakage current, which happens
as a result of the change in surface conductivity of insulators
arising from higher level of contamination.
The time-integral computed from the recorded leakage cur-
rent waveform can also be compared with the time-integral com-
puted from the individual harmonics of leakage current using
the amplitudes and phases of the individual harmonics extracted
from the leakage current waveform. The error between the

Fig. 8. Error between time-integral determined from recorded signal
and time-integral obtained from individual harmonics under different
voltages.
time-integral obtained from the individual harmonic compo-
nents and the time-integral obtained directly from the recorded
leakage current has been shown for the different insulators in
Fig. 8. The error between the time-integrals is observed to fall
within a range of approximately ± 2%. This helps in validating
that the practical values of time-integral obtained is in agree-
ment with the theoretical values obtained from (16) discussed
earlier in Section II-A.
D. Sensitivity Analysis of Time-Integral of Leakage
Current With Respect to Voltage Distortions
It has been highlighted previously that the sensitivity of a
monitoring index towards harmonic distortions in system volt-
age is an important criterion for insulator monitoring. Therefore,
the sensitivity of the time-integral towards changes in the total
harmonic distortion (THD) of voltage waveforms needs to be
evaluated against commonly used monitoring indices. In this
section, the sensitivity of leakage current time-integral with re-
spect to voltage distortion has been compared with indices such
as the THD and third-to-fifth harmonic ratio of leakage current
[18], [19]. The sensitivity parameters SQ , STHDi, and SR3/5
have been defined as changes in time-integral, THD, and ratio
of third-to-fifth harmonic ratios of leakage current for a unit
change in THD of voltage and have been depicted in (18)–(20).
The change in parameters used to compute the sensitivities is
determined with respect to the parameter values for purely si-
nusoidal voltage waveform V0 as base
SQ =
ΔQ/Q
ΔTHDv /THDv
(18)
STHDi
=
ΔTHDi/THDi
ΔTHDv /THDv
(19)
SR3 / 5
=
ΔR3/5/R3/5
ΔTHDv /THDv
. (20)
Fig. 9 shows the sensitivity of the three parameters for
different applied voltage waveforms for insulator no. 1 at
Fig. 9. Sensitivity of the different monitoring parameters at different ap-
plied voltage waveforms with respect to their values for a pure sinusoidal
voltage waveform for insulator 1 contamination level 1.
Fig. 10. Histograms showing the occurrences of absolute sensitivity
values for all acquired waveforms (a) SQ , (b) STHDi
, and (c) SR3 / 5
.
contamination level 1. As may be observed, SR3 / 5
, which is
a widely reported parameter for insulator monitoring shows a
high sensitivity to the changes in voltage harmonics. The har-
monic distortion of leakage current is also highly sensitive to
voltage harmonics. However, the time-integral exhibits signifi-
cantly low sensitivity compared to the other parameters.
The sensitivities of the three parameters have been deter-
mined under the different applied voltage waveforms for all
the three insulators at both contamination levels. A total of 90
sensitivity values are obtained for each parameter (3 insulators,
2 contamination levels, and 15 voltage waveforms). In order to
have a better insight into the typical sensitivity of the parameters
irrespective of contamination level or insulator aging, the sen-
sitivity for each parameter has been represented in the form of
histograms in Fig. 10. The histogram represents the number of
occurrences of absolute sensitivity values obtained for different
cases, after rounding off the sensitivity to the nearest multiple
of 0.1. The percentage occurrences along the y-axis, therefore,
represent the number of cases out of the 90 recorded wave-
forms, which have sensitivity values close to the corresponding

Fig 11. (a) Typical setup for implementing the measurement algorithm. (b) Schematic representation of the implemented measurement algorithm.
absolute sensitivity depicted along the x-axis. The difference in
sensitivity values for the three parameters is readily available
from a visual inspection of the histograms. Fig. 10(a) shows
that approximately 75% of the signals have sensitivity close
to 0.1 and over 95% of the sensitivity values for time-integral
are under 0.3. In comparison, Fig. 10(b) and (c) shows that a
much larger percentage of the sensitivity parameter has values
above 0.5.
V. ONLINE IMPLEMENTATION OF PROPOSED TECHNIQUE
The proposed time-integral based monitoring index was im-
plemented in an online measurement unit in the laboratory. The
algorithm deployed in the unit computes the time-integral of
the leakage current as well as the third-to-fifth harmonic ra-
tios within a given window, to enable us to compare between
the two indices. The test setup shown in Fig. 11(a) consists
of a contaminated porcelain insulator placed inside a humidity
chamber and connected to the programmable harmonic voltage
generator. Fig. 11(b) shows the schematic of the implemented
measurement algorithm. While testing the system in the labora-
tory, the field conditions were simulated in the following way:
the applied voltage waveforms were programmed to change ran-
domly every 15 min [26]. The data were stored every 15 min to
track the changes in leakage current with voltage waveform.
Fig. 12 demonstrates the results obtained over a 3-h window,
where both the time-integral and third-to-fifth harmonic ratio
recorded every 15 min have been shown, along with the applied
voltages. The relative humidity values have been changed after
every 1 h. It may be observed that when the humidity is in
the range of 50%–55%, the time-integral is close to 12.5 μC
irrespective of the voltage waveforms, while the third-to-fifth-
harmonic ratio varies over a much wider range. As the humidity
increases, the time-integral increases to approximately 16 μC at
a relative humidity of 65% and 20 μC at relative humidity of
80%–90%.
It needs to be emphasized here that the online implementation
done at a constant contamination with varying humidity serves
as a good validation technique for the measurement unit since
changes in contamination and humidity represent two differ-
ent field conditions. Also, during the experiments, although the
Fig. 12. Time-integral and third-to-fifth harmonic ratios of leakage cur-
rent obtained from hardware device over a period of 3 h in the laboratory,
under constant contamination and changing humidity.
TABLE III
COMPARISON OF THIRD-TO-FIFTH-HARMONIC RATIOS AND TIME-INTEGRAL
OF LEAKAGE CURRENT UNDER DIFFERENT ESDD AND CONSTANT HUMIDITY
ESDD Voltage Waveform Third/Fifth Time-
(mg/cm2
) Harmonic Ratio Integral
0.05 V0 (Sinusoidal) 4.12 71.1
V2 (5% of third harmonic) 4.47 70.8
V5 (5% of fifth Harmonic) 0.26 70.1
V8 (5% of seventh Harmonic) 3.46 72.3
0.12 V0 (Sinusoidal) 5.28 123.9
0.16 V0 (Sinusoidal) 7.31 172.0
leakage current magnitudes were observed to increase with an
increase in humidity, but the overall leakage current was stable,
making it possible to accurately study the effect of environmen-
tal factors on the time-integral of leakage current.

Table III presents a comparison between the time-integral
and third-to-fifth harmonic ratios at three different ESDD lev-
els and constant humidity under different voltage waveforms.
It may be observed that the third-to-fifth harmonic ratio is sig-
nificantly affected by the harmonics in voltage waveform at a
given ESDD and becomes inaccurate as a monitoring index. In
comparison, while the time-integral remains fairly stable under
constant ESDD irrespective of harmonics in voltage waveforms,
an increase in the ESDD is accompanied by an increase in the
time-integral of leakage current, making it a reliable index for
insulator monitoring.
VI. CONCLUSION
In this paper, a novel online monitoring index based on the in-
stantaneous time-integral of leakage current has been proposed
for monitoring and diagnosis of overhead insulators. The major
contribution of the proposed method is that the time-integral
based index, which is equivalent to the cumulative charge, ex-
hibits a significantly lower sensitivity to changes in voltage
harmonics as compared to previously reported popular leakage
current indices. It has been mathematically demonstrated that
the contribution of the time-integral of any harmonic compo-
nent towards the overall time-integral is directly proportional
to the peak magnitude of the harmonic expressed as per unit
of the magnitude of fundamental and the cosine of the phase
angle between the harmonic and the fundamental, while it is
inversely proportional to the order of the harmonics. Since the
time-integral is inversely proportional to the order of harmonics,
the maximum contribution of the harmonic component towards
the time-integral of the overall leakage current is limited to a
maximum of one cycle of the harmonic, which makes the pro-
posed index less sensitive to harmonic changes as compared
to other indices. It needs to be emphasized here that the exact
value of the time-integral will be dependent on the phase angle
θk , which is influenced by external factors such as contamina-
tion, humidity, and voltage harmonics. Therefore, it is further
possible to improve the efficiency of the proposed method by
investigating in detail the nature in which θk is influenced by the
external factors under field conditions. This could be a potential
research area for further development and future applications of
the proposed technique.
It has been highlighted that while the time-integral exhibits
low-sensitivity to leakage current changes on account of volt-
age distortions, it is sensitive to change in the degree of surface
contamination. The results have been validated using both lab-
oratory recorded offline data as well as online implementation.
The results obtained demonstrate that the proposed index may
be effectively employed along with other traditional monitor-
ing indices to discriminate between voltage distortion-induced
changes from contamination-induced changes in leakage cur-
rent, thereby making the technique suitable for possible on-field
implementation.
ACKNOWLEDGMENT
The authors would like to thank Dr. S. Dalai, Assistant Profes-
sor, Department of Electrical Engineering, Jadavpur University,
and A. Kumar, Jadavpur University, for their active interest and
support in carrying out this research work.
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Riddhi Ghosh (M’16) received the B.E. degree
in electrical engineering and the M.E.E. degree
in high-voltage engineering from Jadavpur Uni-
versity, Kolkata, India, in 2007 and 2012, respec-
tively, where he is currently working toward the
Ph.D. degree in electrical engineering.
He is currently a Research Fellow with the
High Tension Laboratory, Department of Elec-
trical Engineering, Jadavpur University. His re-
search interests include advanced techniques
for data acquisition and signal analysis for re-
mote condition monitoring of high-voltage systems.
Biswendu Chatterjee (M’12–SM’17) received
the M.E.E. and Ph.D. degrees in engineering
from Jadavpur University, Kolkata, India, in 2004
and 2009, respectively.
He is currently an Assistant Professor
with the Department of Electrical Engineering,
Jadavpur University. He has published more
than 40 research papers of which 21 are in re-
puted international journals. He has also au-
thored one book and has one U.S. patent in
his name. His current research interests in-
clude data acquisition and condition monitoring related to high voltage
systems.
Sivaji Chakravorti (M’90–SM’00) received the
Ph.D. degree in electrical engineering from Ja-
davpur University, Kolkata, India, in 1993.
Since 2003, he has been serving as a Pro-
fessor with the Department of Electrical Engi-
neering, Jadavpur University. He worked at the
Technical University Munich as a Humboldt Re-
search Fellow during 1995–1996, 1999, and
2007. He served as a Development Engineer
with Siemens AG, Berlin, Germany, in 1998.
He was a US-NSF Guest Scientist with Virginia
Tech, in 2003. He is currently a Director of the National Institute of Tech-
nology, Calicut, India. He has published more than 160 research papers,
has authored two books, and developed three online courses. His cur-
rent research interests include numerical field computation, condition
monitoring of transformers, signal conditioning in high-voltage systems,
application of artificial intelligence in high-voltage systems, and life-long
learning techniques.
Dr. Chakravorti is a Fellow of the Indian National Academy of En-
gineering and a Distinguished Lecturer of the IEEE Power and Energy
Society.

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