Fault localization on power cables using time delay estimation of partial discharge signals

ABSTRACT


INTRODUCTION
The reliability of power systems is of utmost importance, and the timely detection of faults in electrical equipment and cables is crucial for maintaining this reliability.According to IEC-60270, partial discharge (PD) refers to a local dielectric breakdown that occurs in a small part of an insulation system when the local electric field exceeds the local dielectric strength at a specific location in or near an energized object [1].The occurrence of PD can be attributed to factors such as contamination, aging, or damage to the insulating material between different voltage potentials, which can lead to gradual damage and eventual failures.Hence, reliable and nonintrusive PD localization methods are necessary for detecting and locating PD signals.These methods can be performed online during routine servicing or offline by energizing each successive phase with a high-voltage source [2].Table 1 illustrates some of the available methods for PD detection [3].
The process of PD location comprises three sub-processes that are critical to its success, as illustrated in Figure 1.The first sub-process is the detection of the PD at the sensor, which is extensively discussed [4].The second sub-process involves the application of de-noising techniques to eliminate electromagnetic noise, as described in [5].Finally, the time difference of arrival (TDoA) method is used to locate the PD [6].

ISSN: 2088-8708 
Fault localization on power cables using time delay estimation of … (Chin Kui Fern) 6001 Table 1.PD detection methods with their advantages, disadvantages, and applications

Description Advantages Disadvantages Application
Ultra-high frequency (UHF) measurement [7], [8] -Measuring the UHF electromagnetic signals emitted by PD events in the UHF frequency range (300 MHz to 3 GHz).-Example of sensors used: Antennas, coaxial cables, and resonant circuits.
-High sensitivity -Capability to detect PD events in real time.-Ability to detect PDs in the early stage of insulation deterioration.-Can be performed remotely.
-Measurement ranges are restricted -The requirement for specialized equipment.-The potential for interference from other sources -The potential for measurement errors due to reflections and multi-path effects.
-High-voltage electrical equipment, such as power transformers, gasinsulated switchgear, and cables.
Acoustic measurement [9]- [11] -  [16] have been developed to accomplish this goal, including the UHF method [17], optical acoustic technology [18], acoustic analysis [19], high-frequency current transformers (HFCTs) [20]- [22], Rogowski Coils [23], [24], and capacitive sensors [25].Each of these methods has its own strengths and weaknesses.The selection of a sensor depends on several factors such as the type of partial discharge being analyzed, the ambient conditions, and the desired measurement accuracy and sensitivity.
Detecting and extracting PD signals amidst noisy environments during on-site PD measurements poses a significant challenge.The presence of noise sources, such as thermal or resistive noise from measuring circuits and high-frequency sinusoidal signals that are electromagnetically coupled, make the task even more difficult.Precise and reliable detection of PD signals requires the implementation of advanced deep learning techniques [26], [27].To accurately detect PD signals, the TDoA of an UHF signal emitted by a partial discharge source can be calculated and detected.The first peak and cumulative energy methods, presented in [28], provide effective means for calculating and detecting TDoA.With the use of these techniques, the TDoA of the UHF signal can be precisely determined, thereby enabling the accurate detection of PD signals.
PD localization algorithms can improve power system reliability by detecting insulation problems in cables and power equipment in a substation.Numerous PD localization algorithms have been developed in recent years, including "UHF partial discharge localization algorithm" [29], [30], "partial discharge localization in high voltage systems" [31] "partial discharge localization method in transformers" [32], multiend correlation-based PD location technique (MEC) [33], segmented correlation and trimmed mean data filtering techniques for medium-voltage (MV) underground cable segmented correlation trimmed mean (SCTM) [34] and others.According to recent research, SCTM [34] outperforms the MEC algorithm in terms of PD location accuracy.The careful selection of a PD localization algorithm is crucial for improving the accuracy of the diagnosis of insulation problems in cables and power equipment, and thus enhancing the reliability of the power system.
This research aims to improve the accuracy and reliability of PD localization algorithms for power cables by investigating the best time delay estimation method.Some of their characteristics are lost during the denoising process when PD signals are in a high-noise environment.The aim of this study is to compare the performance of four-time delay estimation methods [35], [36], apart from the commonly used approaches maximum peak detection (MPD) and cross-correlation (CC), two new methods are also introduced by the authors, namely interpolation cross-correlation (ICC) and envelope cross-correlation (ECC) to determine the most effective approach.The results of this research have the potential to enhance the reliability of power systems.

METHOD
The proposed research study entails the utilization of MATLAB scripting to perform simulations aimed at evaluating the effects of four distinct time delay estimation methods on the online PD monitoring system under scrutiny.Figure 2 shows the proposed online PD monitoring system that utilizes a double-end PD sensor measuring method to estimate the PD location.This system may employ Rogowski coil (RC) or

De-noising
• Suppress the excessive noise detected by the PD sensor.• Depending on the noise condition, fast fourier transform (FFT), artificial neural network (ANN), discrete wavelet transform (DWT), and deep learning techniques will be used as de-nosing tools.• The signal-to-noise ratio of the PD signal will be high after the de-noising process, and it will be ready for the PD location process.

6003
HFCT as high-precision and non-intrusive sensors to capture the PD signal.However, due to the limitations of HFCT in saturation, size, weight, and cost [37], coreless inductive sensors in the form of Rogowski coils are preferred due to their ease of construction and maintenance, light design, compact size, low cost, and fast response [38].The RC sensor captures a 100 microseconds length signal window and has a 10 MHz sampling frequency that generates 10,000 data samples per window.Measured signals from PD Sensor A and PD Sensor B are transmitted to the substation's receiver for PD monitoring and estimation.The substation's data acquisition unit estimates the PD location on the power cable using the double-end PD location algorithm, which involves signal de-noising, time delay estimation, and PD location estimation.
The PD location algorithm's process flow is illustrated in Figure 3. Initially, the PD monitoring system imports the measured signal windows from PD sensor A (Window A) and PD sensor B (Window B).To ensure the accuracy and reliability of the PD location estimation process, the proposed methodology involves a comprehensive approach shown in Figure 3 verifies the presence of the PD signal, selects the most effective method for estimating the time delay, and uses the TDoA to estimate the PD location.These steps are critical for ensuring the accuracy and reliability of the PD location estimation process.The de-noising process is carried out using the DWT Daubechies 3 (db 3) mother wavelet and decomposition filter value of 4 to eliminate the effect of DWT de-noising on time delay estimation accuracy.The decision to utilize db 3 as a mother wavelet for DWT de-noising is supported by its favorable attributes, which include a well-balanced combination of time and frequency localization, as well as a relatively smooth and compact support.Additionally, the use of a decomposition filter value of 4 in DWT de-noising enables efficient multi-resolution analysis of the signal, resulting in enhanced noise reduction while still preserving important signal characteristics.The de-noising process is illustrated in Figure 4, which shows Figure 4 where  is the total cable length,  is the velocity of PD signal propagating along the cable, and   is the estimated time difference between two PD signals from Window A and Window B. The velocity of a PD signal as it travels through an underground cable is influenced by the cable's semiconducting and dielectric screen layers.As shown in (2) [39], [40] defines the propagation velocity of the PD signal along the cable  as (2).
where   is propagation velocity in free space (300 m/μs), and  is effective relative permittivity of the cable's dielectric and semiconducting screen layers.

Noise modeling
In practical scenarios, PD sensors can be susceptible to two types of interference: WGN and DSI.WGN is a stochastic signal characterized by a Gaussian probability distribution and flat power spectral density across all frequencies, it is identified by its amplitude which conforms to a normal or Gaussian probability density function [41].WGN is commonly used as a reference signal in signal processing and communication systems and can be generated synthetically through the use of a random number generator.Notably, WGN can be generated using the 'awgn' function in MATLAB.DSI is periodic interference with a specific frequency ISSN: 2088-8708  Fault localization on power cables using time delay estimation of … (Chin Kui Fern) 6005 introduced into a signal by external sources, such as electrical or electromagnetic interference.It is characterized by a sinusoidal waveform and can cause distortions or disruptions in the signal, affecting the accuracy and reliability of signal processing or communication systems.DSI signals, on the other hand, can be generated using the sinusoidal equation presented in (3) [33].In this case, four different frequencies of DSI signals are generated, which are f1 = 600 kHz, f2 = 800 kHz, f3 = 1.5 MHz, and f4 = 5 MHz.
where Amax is amplitude of the DSI range from 0.05 to 0.5 mV in intervals of 0.05 mV, and fi is frequencies used to generate the DSI signal.

MPD method
In estimating the time delay using the MPD method, the denoised signal obtained from Window A and Window B is subjected to an absolute operation to convert the negative portion of the signal to the positive side.Subsequently, the MATLAB function "max" is then utilized to determine the maximum point in the time series measured signal for both Window A and Window B, denoted as  , and  , , respectively.The time delay between two identical PD signals,   can be determined using (4).Based on the estimated time delay, the approximate location of the PD on the power cable can be calculated using (1).
where  , is the time at which the measured signal A reaches its maximum point,  , and  , is the time at which the measured signal B reaches its maximum point,  , .

CC method
The CC method is a widely used signal processing method for determining the similarity of two sets of time-domain PD signals, and is often employed in estimating time delay.The general CC function for a continuous signal is defined as (5) [42].
However, the signal output from measuring devices is often discrete, and the corresponding discrete CC equation is defined as (6).

𝑅 𝐴𝐵 = ∑ 𝐴[𝑛] × 𝐵[𝑛]
0 (6) where [] and [] are two signals from Window A and Window B,  is the number of samples in a window, and   is the CC coefficient.
To estimate the time delay of discrete PD signals from Window A and Window B using the CC method, the absolute denoised signals from Window A are multiplied, added, and circularly shifted with the denoised signals from Window B until the Window A sample is circularly shifted in a full cycle.Window B will remain unshifted because it is selected as the reference for Window A. This process generates a CC coefficient profile.The number of CC coefficient profile samples is the same as the number of Window A or Window B samples.If the number of samples that produce the maximum point from the CC coefficient profile,   is less than half of the CC coefficient profile samples, , then ( 7) is used to compute the sample delay between PD signals at Window A and PD signals at Window B,   .Otherwise, (8) will be used to compute   .The time delay between the PD signals in Window A and those at Window B, denoted as   , can be calculated using (9).The estimated location of PD on the power cable can be computed using (1).
=  −   (8) where  is the time interval between two samples and  =

ICC method
The ICC method is a novel approach proposed by the authors to enhance the accuracy of time delay estimation, and consequently improve the accuracy of PD location estimation.The primary concept of the ICC method is to increase the area of the PD signal for the CC process.This method comprises three distinct stages, namely peak finding, linear interpolation, and the CC process.
In the first stage, as depicted in Figure 5(a), the absolute denoised signals from Windows A and B undergo a peak finding process.To identify the peaks in the absolute denoised signals, the 'findpeaks' function of MATLAB is utilized, as shown in Figure 5(b).After the peak finding process, Window A and B will retain the peak samples, while the remaining samples will be discarded.Thus, a linear interpolation process is required to linearly interpolate the eliminated samples based on the peak samples.
Figure 5(c) displays the results of the linear interpolation process.During the second stage, the linear interpolation process is carried out using the 'fillmissing' function in MATLAB.The 'fillmissing' function uses linear interpolation to fill in the gaps between the peaks.A linear equation is required between two adjacent peak samples A and B, as shown in Figure 6.The linear interpolation equation can be defined as (10), where  is the voltage of the PD signal in the y-axis,  is the sample number in the x-axis,  is the slope of the linear line, and  is the value of  when the linear line intersects at the origin.
The linear equation can be easily determined by substituting the coordinate of two adjacent peaks A(x1, y1) and B(xn, yn).After the linear equation is determined, the gaps between peaks can be filled by substituting the sample's value, x into (10).The interpolation process is repeated for all of the gaps between peaks.
In the third stage, the CC process is applied to the interpolated signals from Windows A and B, as described in subsection 2.2.This stage utilizes the CC function defined in (6) to estimate the time delay between the PD signals from Window A and Window B. The estimated location of PD on the power cable can be computed using ( 1).

ECC method
The authors also proposed another new approach, the ECC method, comprising two distinct processes: the envelope and the CC process.Initially, the absolute denoised signals obtained from Window A and Window B are subjected to the envelope process using the 'envelope' function available in MATLAB.The envelope of a signal is a smooth curve outlining the upper and lower bounds of the signal's amplitude, as illustrated in Figure 7.The envelope process allows for the identification of the peaks in the signals, which are then utilized in the subsequent CC process.Figure 7(a) displays the absolute denoised PD signal utilized as input for the envelope process.Figure 7(b), on the other hand, presents the result of the post-processing absolute denoised PD signal after the envelope process.
As described in subsection 2.2, the CC process involves calculating the CC coefficient profile by multiplying, adding, and circularly shifting the signals from Windows A and B. In the ECC method, the CC process is applied to the enveloped signals rather than the raw signals.This allows for the identification of the peaks in the signals, which are then utilized in the CC process to increase the accuracy of time delay estimation and PD location estimation.

RESULTS AND DISCUSSION
In this section, the simulation results for DWT de-noising and percentage error of the PD location algorithm using MPD, CC, ICC, or ECC as time delay estimation methods for PD signals at Window A and Window B are presented.The most accurate method for PD location estimation is identified by analyzing and discussing the results.In subsection 3.1, the impact of DWT de-noising using Daubechies 3 mother wavelet and decomposition filter value of 4 is compared.Subsection 3.2 compares the average percentage error of the PD location algorithm using different time delay estimation methods.Similarly, subsection 3.3 compares the maximum percentage error of the PD location algorithm across the different methods.

DWT De-noising
To evaluate the effectiveness of DWT de-nosing technique in suppressing noise, WGN and DSI were added into Window A and Window B with signal-to-noise ratios (SNRs) ranging from 10.6 to -7.02 dB. Figure 8 depicts signals with varying levels of noise, and it is observed that the PD signal is still visible when the noise level is low, as demonstrated in Figure 8(a) and 8(b).However, when the noise level is high, as shown in Figure 8(c) to 8(f), the efficacy of the DWT denoising technique becomes significant in suppressing the noise.As depicted in Figure 9(a) to 9(d), DWT can effectively suppress noise, whereas in Figure 9(e) to 9(f), it is noticeable that DWT's noise suppression performance decreases.Therefore, a reliable time delay estimation method is essential in determining the time delay between two PD signals in Window A and Window B even if the noise in the PD signal cannot be entirely suppressed.

Comparison of average percentage error
The simulation results presented are based on a pre-determined PD location occurring 1.5 km away from the front end of the monitored cable.The simulation was conducted on a specific medium-voltage threecore monitored cable (50 mm 2 Cu/XLPE/PVC, 8.7/15 kV) with PD sensors sampling at a frequency of 100 MHz, a PD signal propagation velocity,  of 156.07 m/us as established in [40].The PD locations algorithm that employs MPD, CC, ICC, and ECC as time delay estimation methods, was executed 100 times for SNRs ranging from 10.6 dB to -7.02 dB to generate average PD location samples.The mean of these 100 samples is shown in Table 2, which indicates the SNR and average PD location obtained using MPD, CC, ICC, and ECC algorithms for 10 different noise amplitudes.The amplitude of DSI noise was incrementally raised from 0.05 to 0.50 mV in 0.05 mV intervals, while the amplitude of WGN was decreased in intervals of -2 dB, ranging from 0 to -18 dB.The SNR was then computed by adding the noise to the PD signals using (11) and ( 12) [43]: where   is the amplitude of the PD signal, and   is the amplitude of the noise.The results in Table 2 demonstrate that the average percentage error of PD location using MPD, CC, ICC, and ECC increases as the SNR in the dB unit decreased.This is due to the increased noise in Window A and Window B obscuring the PD signals, thereby reducing the accuracy of time delay estimation and increasing the percentage error of PD location.As a result, the accuracy of time delay estimation will be reduced, while the percentage error of PD location will increase.A reliable time delay estimation method can, therefore, reduce the percentage of PD location error.
To demonstrate the effectiveness of four different time delay estimation methods in reducing the percentage error of PD location, a comparison graph was drawn based on Table 2, shown in Figure 10.The results in Figure 10 demonstrate that the ECC method has the highest error percentage due to the enveloping process used in ECC, reducing the similarity between the PD signals from Window A and Window B and leading to inaccurate time delay computation.The MPD method has the second-highest error percentage, as it can accurately calculate the time delay between PD signals when the SNR is high and the PD signals retain their perfect shape.However, when the SNR decreases to 0.573 dB or lower, the PD shape is attenuated, making the MPD method unreliable.In contrast, the CC and ICC methods perform well in the time delay estimation process, as evidenced by the average percentage error of PD location remaining under 0.02% even as the SNR value decreases up to -0.764 dB.Specifically, the CC and ICC methods show an average percentage error reduction of at least 98.65% and 97.54%, respectively, compared to the MPD and ECC methods for the SNR equal to -0.764 dB.
Figure 11 presents a zoomed-in comparison graph of the CC and ICC methods.As shown in Figure 10, the CC and ICC methods perform similarly well when the SNR is higher than 0 dB.However, when the SNR decreases to -2 dB and below, the average PD location percentage error using the ICC method increases slightly more than when using the CC method.Nevertheless, both methods are able to maintain the average PD location percentage error below 0.02% when the SNR is -0.764 dB.In conclusion, the results indicate that the CC and ICC methods perform well in the time delay estimation process, and can reduce the percentage of PD location error.These findings may have practical implications for PD location systems in the field of power systems engineering.

Comparison of maximum percentage error
The maximum percentage error of PD location is another important criterion to consider when evaluating the effectiveness of time delay estimation methods in the PD location algorithm.In this section, the effectiveness of the PD location algorithm was evaluated using four different time delay estimation methods, namely MPD, CC, ICC, and ECC, under various SNR conditions ranging from 10.6 to -7.02 dB.The algorithm was run 100 times to find the maximum percentage error of PD location among the 100 estimated samples.Table 3 summarizes the results obtained from this analysis, indicating that the maximum percentage error of PD location follows a similar trend to the average percentage error, where both errors increase as the SNR decreases in the dB unit.
A comparison graph was drawn based on the results presented in Table 3, and Figure 12 illustrates the effectiveness of the different time delay estimation methods under varying SNR conditions.The ECC method was found to be inaccurate for SNR values less than -0.764 dB, while the MPD method was inaccurate for SNR values less than -0.573 dB.The zoomed-in graph shown in Figure 13 further reveals that the CC and ICC methods have the same maximum percentage error (0.05%) until the SNR reaches 2.62 dB.To further reduce the percentage error, a trimmed mean data filtering technique, as described in [35], can be used.However, conducting field experiments is necessary to validate the effectiveness of the CC and ICC methods in time delay estimation.

CONCLUSION
In summary, our research compared four different time delay estimation methods (the MPD, CC, ICC, and ECC methods).The simulations were used to quantify the performance of the proposed methods.The statistical results demonstrate that increasing noise level reduced the accuracy of time delay estimation, resulting in higher PD location estimation errors.Furthermore, when PD signals were heavily polluted with WGN and DSI, both the CC and ICC methods were more efficient than the MPD and ECC methods, with more than 90% average percentage error reduction.Our research provides valuable insights into the performance of different time delay estimation methods under varying levels of noise.These findings have important implications for applications such as PD location detectors and could inform the development of more accurate and efficient methods in the future.While our research sheds light on the performance of the CC and ICC methods in time delay estimation, further experimental work is needed to fully evaluate their efficacy.Future research could also look into how these methods perform under different operating conditions or with different types of signals.

Figure 2 .Figure 3 .
Figure2.Diagram of the online PD localization estimation system using double-end PD sensor measuring method[39]

Figure 4 .
Figure 4. DWT de-nosing and absolute process, (a) pre-processing measured PD signals that have been corrupted by white gaussian noise (WGN) and discrete sinusoidal interference (DSI), (b) post-processing denoised PD signal after DWT noise suppression, and (c) post-processing absolutely denoised PD signal after absolute processing

Figure 5 .Figure 6 .
Figure 5. Linear interpolation of peaks process: (a) absolute denoised PD signal as input to linear interpolation process, (b) absolute denoised PD signals local peak identification in (c) post-processing linear interpolation of absolute denoised pd signal local peak

Figure 7 .
Figure 7. Envelope process (a) absolute denoised PD signal as input to envelope process and (b) post-processing of absolute denoised PD signal after envelope process

Figure 8 .Figure 9 .
Figure 8. Varies level of WGN and DSI noises: (a) measured PD signal with 10.6 dB noises from Window A, (b) measured PD signal with 10.6 dB noises from Window B, (c) measured PD signal with 0.573 dB noises from Window A, (d) measured PD signal with 0.573 dB noises from Window B, (e) measured PD signal with -7.02 dB noises from Window A, and (f) measured PD signal with -7.02 dB noises from Window B

Figure 10 .Figure 11 .
Figure 10.Comparison of the average percentage error in PD location estimation methods MPD, CC, ICC, and ECC

Figure 12 .Figure 13 .
Figure 12.Comparison of PD location maximum percentage error estimation methods using MPD, CC, ICC, and ECC

Table 2 .
The average percentage error of PD location using MPD, CC, ICC, and ECC as time delay estimation methods, respectively

Table 3 .
The maximum percentage error of PD location using MPD, CC, ICC, and ECC as time delay estimation methods, respectively