Measurement xxx (xxxx) xxx
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Measurement
journal homepage: www.elsevier.com/locate/measurement
Resistive component extraction of leakage current in metal oxide surge
arrester: A hybrid method
Abdullah Munir a, b, Zulkurnain Abdul-Malek a, *, Rai Naveed Arshad a
a
Institute of High Voltage and High Current, School of Electrical Engineering, Faculty of Engineering, Universiti Teknologi Malaysia (UTM), 81310 Johor Bahru,
Malaysia
b
Department of Electrical Engineering, NED University of Engineering and Technology, Karachi, Pakistan
A R T I C L E I N F O
A B S T R A C T
Keywords:
Leakage current
Resistive component of leakage current
Condition monitoring of surge arresters
Leakage current based condition monitoring is the most widely used method to ascertain the ageing of on-site
Metal Oxide Surge Arrester (MOSA). The extraction of resistive component of leakage current is necessary for
the exact health diagnostic of arrester. In particular, the third harmonic component of resistive current is known
to be directly correlated with the ageing of arrester. Although, some existing methods are still used to extract the
resistive leakage current but their computational procedures and accuracies have some limitations. This paper is
aimed to propose a newly developed technique, referred as hybrid method for the extraction of resistive leakage
current without acquiring the grid’s voltage. This method was developed on SIMULINK software and then
validated experimentally on 120 kV rated MOSA manufactured by ABB. Results have shown that the proposed
method is 3.2% more accurate than the modified shifted current method. It can be implemented to develop a
highly precise condition monitoring module for online monitoring of MOSAs.
1. Introduction
Surge Arresters act as overvoltage limiting devices to protect the
transmission and distribution system from high voltage surges caused by
severe lightning and switching operations [1,2]. Therefore, their con­
dition monitoring is vital to ensure the reliability of the power system
[3,4]. The most popular type of gapless MOSA contains zinc oxide
element due to its highly nonlinear voltage-current characteristics and
faster conduction response for high voltage surges [5,6].
Fig. 1 shows a typical voltage-current ‘V-I’ characteristic curve of
zinc oxide surge arrester. This V-I curve is divided into three regions
based on the applied voltage, as shown in Fig. 1. The region I is referred
as low current or steady state region due to the steady state operation of
MOSA. Four different voltage levels are defined in the low current re­
gion. The first point ‘Vc’ is the initial voltage, at which the total leakage
current of MOSA is mainly capacitive. while other points are the phase
to earth voltage ‘VP-N’, continuous operating voltage ‘VCOV’ and rated
voltage ‘Vrated’. The region II is known as the flat region, because a small
increase in the voltage increases the leakage current significantly. The
temporary over voltage ‘VTOV’ occurs in this region. On the other hand,
region III is called the high current region due to the discharging of
lightning current by MOSA. In this region, the residual or discharge
voltage is represented as ‘V10′ .
As the zinc oxide impedance cannot be designed infinity; therefore, it
draws leakage current at the standard operating voltage [7,8]. The
leakage current is acquired in two ways; offline and online. The offline
method requires the disconnection of arrester from the grid, while the
online technique monitors the leakage current of on-site arrester [9,10].
In most of the grid stations, it is challenging to acquire the high voltage
signal; therefore, it is preferable to measure online arrester’s leakage
current [9,11,12].
The total leakage current is decomposed into its resistive and
capacitive components [13]. The capacitive component depends on the
applied voltage. At the same time, the resistive current also depends
upon zinc oxide characteristics, ambient temperature, and other envi­
ronmental factors [14–16]. Any deterioration of the insulating proper­
ties of MOSA causes an increase in the resistive leakage current [17,18].
Therefore, it is used as the most reliable indicator of MOSA deterioration
[10,15,19,20].
Several techniques have been proposed for the extraction of resistive
component of leakage current such as conventional method [21],
capacitive current compensation method [23], modified shifted current
method (MSCM) [24,27], least square method [25], linear regression
method [26], and circuit-based method [7]. A comparative analysis of
* Corresponding author.
E-mail addresses: abdullah.munir@neduet.edu.pk (A. Munir), zulkurnain@utm.my (Z. Abdul-Malek).
https://doi.org/10.1016/j.measurement.2020.108588
Received 11 August 2020; Received in revised form 29 September 2020; Accepted 5 October 2020
Available online 12 October 2020
0263-2241/© 2020 Elsevier Ltd. All rights reserved.
Please cite this article as: Abdullah Munir, Measurement, https://doi.org/10.1016/j.measurement.2020.108588
A. Munir et al.
Measurement xxx (xxxx) xxx
these techniques is presented in table 1. In the conventional method, the
resistive current is measured at the instant when the voltage signal
reaches its maximum value. Although, this method is considered as the
benchmark procedure to acquire the resistive current with maximum
accuracy but it is not feasible for on-site measurement [10]. In the
capacitive current compensation method, the capacitive current is
compensated by adjusting the amplitude and phase angle of the refer­
ence signal. However, the presence of harmonics in the capacitive cur­
rent may interfere with the measurement of the nonlinear resistive
current [28].
MSCM is based on the waveform analysis of total leakage current
using the orthogonal relation between its resistive and capacitive com­
ponents [27,29]. Only the fundamental component of capacitive current
gets compensated in this procedure [30]. The algorithm is initiated by
reproducing a leakage current waveform with a phase shift of π/2 rad.
Actual leakage current is added with the reproduced leakage current to
produce a total current waveform. The time at which the peak value of
total current occurs is noted. The magnitude of capacitive current is
approximated at a time delay of π/2 rad to the peak time of total current
waveform. The generated capacitive current waveform is subtracted
from the actual leakage current to acquire its resistive component. In
this method it is assumed that no phase shift exists between the total
leakage current and its capacitive part. In actual the leakage current is
lagged by its capacitive component by some angle at rated voltage due to
the harmonics. The results of this technique are more accurate as
compared to the compensation technique. However the accuracy of re­
sults is affected by the approximation of capacitive current magnitude
and ignorance of phase angle between the total and capacitive leakage
currents at the rated voltage
In least square method, time-domain equations of the resistive and
capacitive currents are derived, followed by the least squares applica­
tion to estimate the capacitance and resistance of MOSA [25]. The ac­
curacy of the proposed method is decreased with the rise of resistive
leakage current at the rated voltage condition. To reduce the error of
least square method, the authors in [26] have proposed linear regression
method. Initially, linear and differential mathematical equations of the
resistive and capacitive leakage currents are derived in time domain,
which are then converted into linear regression model to determine the
resistance and capacitance of MOSA. Although, the results of this
method are better than the capacitive current compensation method but,
the accuracy is limited to noiseless voltage only. Similarly, the circuitbased analytical method estimates the resistive and capacitive currents
based on the dimensions of surge arrester [7]. However, the algorithms
of least square, linear regression, and circuit-based methods are not
validated for online measurement of resistive leakage current. Based on
the above discussion, it is concluded that reference signal and complex
implementation steps are required to extract the resistive current in
these methods and the results are not accurate enough [31]. Therefore, it
Table 1
Comparative analysis of the resistive current extraction techniques.
Conventional
Method
Capacitive
Current
Compensation
Method
Modified Shifted
Current Method
Least Square
Method
Linear Regression
Method
Circuit-based
Method
Principle of
Measurement
Limitation
Reference
IR is measured at the
peak instant of the
voltage
IR is determined by
adjusting the
magnitude and phase
of a reference signal to
compensate IC
The theoretical basis
of this technique
resides on 180 degrees
phase-shifted
capacitive current
injection to the
measured leakage
current in order to
extract IR
Time domain
equations are
formulated to
determine IR and IC
linear and differential
mathematical
equations of IR and IC
are derived in time
domain
IR and IC are
determined by using
the circuit element
values of MOSA
It is not applicable for
online measurement
[21]
The presence of
harmonics in voltage
disrupts the accuracy
[22,23]
Consideration of a
constant phase
between IC and IT at all
voltage levels
decreases the accuracy
of measurement
[5,14,24]
Complicated steps are
required to implement
this technique for
online monitoring
Accuracy is affected
by neglecting the
distortion from the
applied voltage
[25]
The performance of
method is not tested
for online
measurement
[26]
[7]
is highly desirable to propose a new method with simple steps and better
accuracy.
This paper intends to introduce a new ‘Hybrid Method’ to extract the
resistive leakage current without measuring the arrester’s voltage. It is
simulated in SIMULINK software and then tested experimentally on 120
kV rated MOSA. The obtained results are compared with the conven­
tional and modified shifted current methods. This comparison has
revealed that the proposed method is more accurate than the existing
method. More straightforward computational steps and high accuracy of
this technique can lead to design an effective online condition moni­
toring module of MOSA.
2. Hybrid method to extract the resistive current
The simplified equivalent circuit of MOSA consists of the parallel
combination of capacitance ‘C’ and nonlinear resistance ‘R’ as shown in
Fig. 2 [32,33]. The total leakage current ‘IT’ can be represented as the
Fig. 1. V-I characteristic curve of a typical MOSA.
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A. Munir et al.
Measurement xxx (xxxx) xxx
IR = IT − IC
The algorithm to extract the resistive component from the total
leakage current is illustrated as; (a) Filter the total leakage current signal
to suppress the high frequency noise and distortion above 1 kHz. (b)
Determine the peak value of the total leakage current. (c) Get the zero
crossing time reference of the filtered signal. (d) Determine the funda­
mental frequency ‘f’ of the leakage current. (e) Determine the magnitude
of IC using Eq. (4) and the phase angle between IT and IC using Eq. (3). (f)
Generate the capacitive leakage current waveform having the magni­
tude and phase angle obtained in (e). (g) Subtract the capacitive current
waveform from the total leakage current to obtain the resistive current
waveform.
Fig. 4 illustrates the block diagram of the proposed method to extract
the resistive leakage current of on-site MOSA. Initially the leakage
current is measured using a highly precise current sensor ALCL-40D.
Low pass filter is used to eliminate the high frequency noise and
distortion from the acquired current signal above 1 kHz. A simple 1st
order passive low pass filter is designed in Simulink with a resistor (160
kΩ) and capacitor (1nF). After eliminating the noise, peak value detector
is applied to detect the peak value of the filtered leakage current. Zero
crossing detector is used to determine the zero crossing time reference of
the filtered leakage current signal. Frequency detector is aimed to
determine the fundamental frequency of the leakage current signal.
Fig. 2. Simplified equivalent circuit of MOSA.
phasor sum of the nonlinear resistive ‘IR’ and capacitive components ‘IC’
as shown in Eq. (1). The capacitive component is subtracted from the
total leakage current to determine its resistive component.
(1)
IT = I R + I C
θ = sin−
1 IC
3. Methodology
(2)
IT
The algorithm of proposed method is developed in Simulink software
to determine the resistive leakage current, as shown in Fig. 5.
This technique is proposed for monitoring the online surge arresters.
However, experiments are carried out offline in high voltage laboratory.
To investigate the performance of proposed technique at different
voltage levels, the leakage current of a 120 kV rated MOSA manufac­
tured by ABB is measured at voltages from 10 kV to 120 kV. Table 2
shows the technical characteristics of the studied surge arrester
including different voltage levels of the low current region. The block
diagram of the experimental set up is shown in Fig. 6. A step-up trans­
former (240 V/250 kV) is used to apply the voltage to the tested MOSA.
The applied voltage is measured by a capacitive voltage divider with a
ratio of 686:1. A digital Picoscope kit is used to display and export the
measured signals to MATLAB. Both leakage current and voltage across
the arrester are measured in this experiment. Voltage measurement is
required to execute the conventional technique to extract the resistive
leakage current. A highly sensitive current sensor ALCL-40D is used to
measure the total leakage current of MOSA. Its technical specifications
are illustrated in table 3. Current sensor is specifically designed for the
measurement of arrester’s leakage current at power frequency of 45–65
Hz only with least effects of electromagnetic interference. Eq. (6) is used
to determine the leakage current ‘IT’ from the output voltage ‘VS’ of
sensor. The output characteristic curve of the sensor is shown in Fig. 7.
(3)
φ = 90 − θ
(5)
Fig. 3 shows the phasor diagram of IT with phase angles ‘θ’ and ‘φ’
between the peak values of ‘IT’ and ‘IR’ and ‘IT’ and ‘IC’ respectively. IT
leads IR by angle ‘θ’ and lags IC by angle φ. The resistive component of
leakage current exceeds from its capacitive component with the rise in
applied voltage. Therefore, the decrease in capacitive leakage current
decreases the angle ‘θ’ and consequently increases the angle ‘φ’ at the
rated voltage, as seen in Eqs. (2) and (3).
As the approximation of the capacitive component of leakage current
produces error in the extraction of resistive current from the modified
shifted current method. Therefore, in hybrid method, the capacitive
current magnitude is determined by calculating its equivalent capaci­
tance, which is directly dependent on the dimensions such as area ‘A’,
height ’d’ and permittivity ’∊’ of the metal oxide element. After finding
the magnitude, phase angle φ is calculated to lead the capacitive current
by total leakage current. This method is known as hybrid, because it
combines the circuit based method with the waveform analysis of shifted
current method. The peak values of capacitive and nonlinear resistive
currents are determined using Eqs. (4) and (5) respectively.
√̅̅̅
√̅̅̅
( 2)(2πf )(∊A)Vrms
Ic = 2ωCVrms =
(4)
d
IT = (2.6)(Vs )
(6)
4. Results and discussion
4.1. Simulation results
The proposed method is initially tested on the simulated leakage
current waveforms to extract its resistive component. Leakage current
waveforms of 120 kV rated MOSA are simulated in MATLAB at voltage
levels 10 kV, 93 kV, 98 kV, and 120 kV respectively. The simulated
leakage current waveform along with its extracted resistive component
are shown in Fig. 8(i)–(iv). It is observed that resistive leakage current is
increased with the rise in voltage from 12.36 µA at 10 kV to 2150.42µA
at 120 kV as shown in 8(i) and 8(iv) respectively. The simulation results
have revealed that the proposed method works well for the extraction of
Fig. 3. Phasor diagram of total leakage current.
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A. Munir et al.
Measurement xxx (xxxx) xxx
Fig. 4. Block diagram of the proposed method.
Fig. 5. Simulink model of the proposed method.
Table 2
Technical characteristics of the tested 120 kV rated MOSA.
Initial voltage (rms)
VC
10 kV
Phase-to-Earth Voltage (rms)
Continuous Operating Voltage (rms)
Rated Voltage (rms)
Temporary Over Voltage (rms)
Radius of MO disc
Height of MO column
VP-N
VCOV
Vrated
VTOV
r
d
93 kV
98 kV
120 kV
130 kV
0.03 m
1m
resistive leakage current at all voltage levels.
4.2. Experimental results
The proposed method is then applied to extract the resistive
component from the total leakage current of 120 kV rated MOSA
experimentally. Fig. 9(i)–(iv) show the experimental results of total
leakage, capacitive and resistive currents waveforms at 10 kV, 93 kV,98
kV and 120 kV respectively. At the initial voltage ‘VC’, the total leakage
current is mainly capacitive in nature having minimum contribution of
Fig. 6. Experimental set up for the measurement of leakage current.
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A. Munir et al.
Measurement xxx (xxxx) xxx
The variation of the calculated capacitive component of leakage
current with the applied voltage is shown in Fig. 10. It is observed that
the capacitive current changes linearly with the applied voltage unlike
the resistive component, which changes in non-linear manner. A linear
increase in the capacitive leakage current from 108.90 µA at 10 kV to
1296 µA at 120 kV is plotted in Fig. 10. It is due to the fact that
capacitance of MOSA is independent of the applied voltage, as depicted
in Eq. (4). Using the technical specifications of MOSA as mentioned in
Table 2, its capacitance is found to be 0.0245nF.
Although, IC is observed to increase linearly with the rise in applied
voltage. But, to validate the dominance level of IR at the rated voltage,
ration of IC/IT and IR/IT are plotted in Figs. 11 and 12 respectively.
Fig. 11 shows the decreasing trend of the ratio (IC/IT) and theta ‘θ’ with
the applied voltage. It is evident that the contribution of capacitive
component in total leakage current is high at the initial voltage. But this
contribution is decreased with the increase of nonlinear resistive current
at higher voltage levels. It is noticed that the ratio IC/IT is decreased from
99.36% at 10 kV to 51.6% at the rated voltage condition. Due to
decrease in the capacitive current, the phase angle ‘θ’ is also decreased
from 83.52 degree at 10 kV to 31.06 degree at the rated voltage.
Likewise, the variation of the ratio (IR/IT) and phi ‘φ’ with the
applied voltage is shown in Fig. 12. It is noticed that the ratio IR/IT is
increased from 11.27% at 10 kV to 85.65% at 120 kV. It is due to the fact
that resistive leakage current exhibits a nonlinear increase with the rise
in voltage level. Consequently, the angle ‘φ’ is also increased from 6.48
degree at 10 kV to 58.94 degree at the rated voltage. Due to the
capacitive nature of total leakage current, the lagging angle φ between IT
and IC is small at the initial voltage. However, the increase of IR also
increases the angle φ considerably at the rated voltage as shown in
Fig. 12.
Table 3
Technical specifications of current sensor.
Measuring Range
AC 1µA–50A
Inside Diameter
Turns
Frequency
Dimensions
37 mm
2400
45–65 Hz
134.5(W) × 165.5(H) × 61(D) mm
Leakage Current (μA)
3000
2500
2000
1500
1000
500
0
0
100
200
300
400
500
600
700
800
900
1000
Output Voltage (μV)
Fig. 7. Output characteristic curve of current sensor.
the resistive current as shown in 9(i). With the increase in voltage, the
dominance of capacitive component gradually decreases and total
leakage current becomes highly resistive at the rated voltage as shown in
9(iv). It is due to the fact that the resistive component of leakage current
increases considerably with the rise in applied voltage. The variation in
resistive current is noted from 12.36µA at 10 kV to 2151µA at 120 kV in
9(i) and 9(iv) respectively. It is also observed that the distortion in
leakage current signal is more pronounced at the higher voltage level
due to the rise in nonlinear current. On the basis of findings, it is evident
that the simulation and experimental results are closely related with
each other.
4.3. Comparison of experimental results
Table 4 shows the acquired values of the capacitive and resistive
components of total leakage current using the hybrid, conventional and
modified shifted current methods at voltages from 10 kV to 120 kV. The
Fig. 8. Simulation results of the proposed method (i) Leakage, capacitive, and resistive currents at 10 kV rms; (ii) Leakage, capacitive, and resistive currents at 93 kV
rms; (iii) Leakage, capacitive, and resistive currents at 98 kV rms; (iv) Leakage, capacitive, and resistive currents at 120 kV rms.
5
A. Munir et al.
Measurement xxx (xxxx) xxx
Fig. 9. Experimental results of the proposed method (i) Leakage, capacitive, and resistive currents at 10 kV rms; (ii) Leakage, capacitive, and resistive currents at 93
kV rms; (iii) Leakage, capacitive, and resistive currents at 98 kV rms; (iv) Leakage, capacitive, and resistive currents at 120 kV rms.
Fig. 12. Increasing trend of the ratio IR/IT and φ with the applied voltage.
Fig. 10. Variation of capacitive leakage current with the applied voltage.
(IC/IT) %,θ(degrees)
120
methods is observed. At VC, the resistive currents determined from the
proposed and modified shifted current methods are 0.8% and 1.2%
higher than the conventional method’s value. Similarly, at Vrated, the
difference in the parameter IR acquired from the proposed and shifted
current method is 5% and 8.2% with the conventional method.
The obtained values of the resistive current in Table 4 are used to plot
V-IR characteristic curves of MOSA as shown in Fig. 13. A significant rise
in resistive leakage current is observed beyond VCOV. It is noted from
Fig. 13 that the V-IR curves produced by the proposed and conventional
methods are closely related with each other. It is due to the fact that
almost similar results are obtained from both methods. On the other
hand, characteristic curve by the modified shifted current method is
deviated from the conventional curve as shown in Fig. 13.
To determine the actual difference in the results of modified current
method w.r.t the conventional technique, percentage errors are evalu­
ated, which are plotted in Fig. 14.
The curves as shown in Fig. 14 can be divided into three regions.
Region I ranging from 10 kV to 30 kV shows linear increase in the %
error for both methods. Region II starting from 30 kV to 90 kV displays
(Ic/IT)*100
Theta
100
80
60
40
20
0
10
20
30
40
50
60
70
80
90
93
Applied Voltage (kV) rms
98
100 110 120
Fig. 11. Decreasing trend of the ratio IC/IT and θ with the applied voltage.
calculated values of the phase angles θ and φ at voltage level from 10 kV
to 120 kV are also provided in the Table 4. A close coordination between
the resistive current obtained from the proposed and conventional
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Table 4
Computed values of the capacitive and resistive leakage currents using proposed, conventional and modified shifted current methods.
Vrms
(kV)
IT
(µA)
Proposed Method
IC
(µA)
IR
(µA)
θ
(Degree)
10
20
30
40
50
60
70
80
90
93
98
100
110
120
109.60
219.30
336.20
458.00
579.10
704.20
828.10
955.10
1126.30
1185.60
1253.00
1298.10
1510.00
2511.25
108.90
217.80
326.70
435.60
544.50
653.40
762.30
864.01
972.00
1012.70
1067.20
1089.20
1188.00
1296.00
12.36
25.60
79.35
141.48
197.17
262.61
323.50
406.80
569.00
616.50
656.57
706.31
932.07
2151.00
83.52
83.30
76.35
72.00
70.09
68.10
67.00
64.80
59.65
58.67
58.40
57.03
51.90
31.06
Conventional Method
Modified Shifted Current Method
φ
(Degree)
IC
(µA)
IR
(µA)
IC
(µA)
IR
(µA)
6.48
6.70
13.65
18.00
19.91
21.90
23.00
25.20
30.35
31.33
31.60
32.97
38.10
58.94
108.91
218.12
327.10
436.55
542.80
656.17
765.98
869.91
984.16
1027.56
1086.10
1110.20
1220.35
1455.58
12.25
22.65
77.65
138.50
201.80
255.60
314.70
394.30
547.70
591.40
624.80
672.70
889.30
2047.30
108.89
218.06
326.42
434.93
545.53
652.31
770.75
876.85
996.24
1009.77
1060.34
1029.10
1171.11
1185.00
12.40
23.20
80.50
143.50
194.30
265.30
302.80
378.60
525.40
621.30
667.60
719.20
953.20
2215.00
proposed method is 3.2% more accurate than the modified current
method in extracting the resistive leakage current.
Moreover, the proposed method is also applied to determine the most
sensitive indicator of arrester ageing, i.e., the third harmonic component
of resistive current. The variation of third harmonic current with the
applied voltage from 70 kV to 120 kV based on proposed and modified
current method is shown in Fig. 15. It is found that the proposed method
can extract the resistive third harmonic current more efficiently as
compared to modified shifted current method. At the rated voltage, the
third harmonic component extracted from the proposed and modified
current method are found to be 861.5µA and 827.9µA respectively.
Therefore, a difference of 33.60 µA is computed in the value of third
harmonic current extracted from both methods. Based on the difference,
it is established that the proposed method is 4% more accurate than the
modified current method to determine the third harmonic resistive
current at the rated voltage.
5. Conclusion
Fig. 13. V-IR Characteristic Curve of 120 kV Rated MOSA.
Third Harmonic Current (μA)
Existing methods to determine the resistive leakage current are less
accurate and require complex computational procedures. In this paper, a
hybrid method for the extraction of the resistive leakage current is
proposed. The algorithm of proposed method is simulated on Simulink
and its accuracy is validated experimentally on 120 kV rated MOSA.
Experimental results have established that the new method works well
for the extraction of resistive component from the metal oxide surge
arrester’s total leakage current without measuring the voltage signal. It
minimizes the errors in generating the capacitive current waveform by
calculating the actual capacitance of metal oxide element. The accuracy
of extracted resistance by proposed method is improved by introducing
the exact angle between the total leakage current and its capacitive
component, which is not considered in the previous technique. At the
Fig. 14. Relative error of the resistive leakage current using the proposed and
modified shifted current methods.
approximately a constant error in the values of IR at all voltage levels
obtained from both methods. Region III ranging from 93 kV to 120 kV
shows a significant rise in the error for the modified current method. On
the other hand, the proposed method exhibits a constant error in the
region III after VCOV. It is observed that the % error produced by the
proposed method at high voltage region is significantly less than the
modified current method. Moreover, the relative errors produced by the
modified shifted current and proposed methods at the rated voltage are
8.2% and 5% respectively. Based on the findings, it is inferred that the
Proposed Method
1000
900
Conventional Method
800
Modified Shifted Current Method
700
600
500
400
300
200
100
0
70
80
90
93
98
100
Applied Voltage (kV) rms
110
120
Fig. 15. Variation of third harmonic resistive current with the applied voltage.
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A. Munir et al.
Measurement xxx (xxxx) xxx
rated voltage, the results of proposed method are determined to 3.2%
more accurate than the modified shifted current method. Simpler and
easier computational steps make this technique more efficient than the
existing methods. The proposed method is also applied to extract the
third harmonic resistive current with accuracy of 4% higher than the
modified shifted current method. It is aimed to fabricate an online
condition monitoring module of MOSA by processing the output of
current sensor using this proposed algorithm.
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CRediT authorship contribution statement
Abdullah Munir: Conceptualization, Methodology, Software, Vali­
dation, Formal analysis, Writing - original draft. Zulkurnain AbdulMalek: Investigation, Resources, Supervision. Rai Naveed Arshad:
Writing - review & editing, Visualization.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Acknowledgements
Authors wish to thank Universiti Teknologi Malaysia (4B482,
01M44, 02M18, 05G88) and Higher Education Commission Pakistan
(HRDI) for their financial support.
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