A Partial Discharge Localization Method for AC XLPE Cable Based on Improved GCC Algorithm

Due to the influence of electromagnetic noise and other factors, existing cable partial discharge location methods cannot accurately locate discharge faults. To handle it, this paper proposes an online localization method for cable partial discharge signals that is suitable for practical engineering applications, based on the double-end localization method. The proposed method uses an improved generalized correlation algorithm to estimate the signal time delay, and takes into account the wave speed uncertainty of the local discharge signal. To improve local localizing accuracy under multiple localizing samples, a trimmed-mean data filtering speed algorithm is employed. Simulation and experimental results demonstrate that the proposed method effectively enhances time delay estimation accuracy and reduces localization error, even under complex electromagnetic noise environment and restricted sampling rates of detection equipment, when compared to traditional time delay estimation localization methods. The positioning accuracy of partial discharge in field experiments reached 97.43%-99.89%, which meets actual engineering requirements.


I. INTRODUCTION
C ROSS-LINKED polyethylene (XLPE) cables have been widely used in transmission and distribution systems for their commendable electrical and mechanical properties [1], [2].Due to the limited manufacturing process and subpar installation techniques, XLPE cable insulation may contain minor defects such as voids, contaminants, and bubbles during the initial operation process.Therefore, the presence of high electric fields may expose high-voltage partial discharges, heightening the risk of damage.Consequently, it is of great importance to propose a method for monitoring the partial discharge in XLPE cables in order to promptly locate and repair local defects [3], [4], [5].
In recent years, extensive research on the localization of cable partial discharge has been conducted [6], [7].The location of cable partial discharge was determined in [8] using the single-ended time-domain reflection (TDR) method, which entails calculating the time delay between incident and reflected waves.However, the approach can only be applied to short distance cable lines due to the significant attenuation of high frequency signals during propagation.The segmentation correlation-based multi-terminal partial discharge localization algorithm introduced in [9] is demonstrated to be more effective and precise at rapidly localising partial discharges than previous approaches based on the use of multiple terminals.Instead of relying on the detection and processing of reflected waves, which can degrade localization precision, time-of-arrival analysis has an advantage over single-ended TDR and phase difference techniques.In addition, it was suggested to estimate the defect location in the signal frequency domain by em-ploying the cross Fourier spectral density function of incident and reflected wave signals for localization in [10], which reduces the impact of localization pulse waveform distortion.Due to the overlapping phenomenon of incident and reflected waves, pulse separation becomes difficult and localization accuracy is diminished when the defect is close to the far end of the cable line.Despite the fact that many localization methods for cable partial discharge sources have been proposed by researchers, it is clear that these methods have implementation limitations that would lead to inaccurate results in the practical localization of partial discharge in cables [11], [12].Timedelay estimation localization [13] is still widely used to locate the origin of Partial discharge of cables today.Due to electromagnetic noise and the neglect of the frequency characteristics of the partial discharge pulse wave velocity, localization results are prone to considerable discrepancies from the actual ones in the field [14], [15], [16].Therefore, it is crucial to propose a novel cable online location approach based on the conventional time delay estimation location method to improve the accuracy of partial discharge location of distribution cables.
In this paper, we propose a method for localising partial discharges that is based on the double-end localization technique for AC cables, but accounts for the wave speed uncertainty of the partial discharge signal by employing an enhanced generalized correlation algorithm to estimate the signal time delay.In addition, a trimmed-mean data filtering speed algorithm is employed to improve local localizing accuracy under multiple localizing samples.Finally, simulation and experimental testing are used to confirm the reliability of the method proposed in this paper.

II. GENARALIZED CROSS-CORRELATION TIME DELAY ESTIMATION
Generalised cross-correlation (GCC) algorithm estimates the delay based on the maximum value of the cross-correlation function of the local discharge signals at both endpoints.The local discharge signals received at both ends of a cable in a localisation system originate from the same source [17].Consequently, there is a significant relationship between the signals at both extremities of the cable.Ideally, the time delay between the observed signals at both endpoints can be determined by calculating the correlation function between these two signals.
As illustrated in Fig. 1, the local discharge signals received at both cable ends A and B through the high frequency current transducer can be expressed as (1), If the noise signals n 1 (t) and n 2 (t) are uncorrelated, the final correlation function can be presented by (3), In the actual model of cable localization, the presence of reverberation and noise result in insignificant R x1 x2 (τ ) peaks, which decreases the precision of time delay estimation.In order to intensify the peak of R x1x2 (τ ), the mutual power spectrum can be weighted in the frequency domain based on a priori knowledge of the signal and noise [18], thereby suppressing noise and reverberation interference to improve the accuracy of the two signal delays, as depicted in Fig. 2.
The mutual spectral density function between the outputs y 1 (t) and y 2 (t) can be presented by (4), Then the mutual correlation function can be expressed as (5): (5) where: . By weighting the power spectrum of the two timedelayed signals, the GCC method minimises the impact of exogenous signals on the mutual correlation function [19].The weighting function W (f ) raises the spectral amplitude where signal interference is minimal, emphasising the relative position of the mutual correlation function's peaks.

III. A CABLE PARTIAL DISCHARGE LOCALIZATION METHOD BASED ON AN IMPROVED GCC ALGORITHM
Currently, the GCC algorithm is increasingly used for the localization of cable partial discharge.Despite its pervasive application, the algorithm still possesses limitations that limit its practical utility.Notable concerns include decreased localization accuracy in the presence of low signal-to-noise ratios, the impact of wave speed frequency characteristics on localization accuracy, and the impact of specific interference signals on online localization accuracy.
To address these issues, this paper proposes an improved GCC algorithm for the detection of local discharge signals in cables to increase localization accuracy, as depicted in Fig. 3.

A. OPTIMIZED PULSE TIME WINDOW TECHNOLOGY
① After preprocessing the received sampled signal with data derived from the enhanced empirical wavelet transform, the residual noise is estimated as a power spectrum and the separation threshold is calculated.To precisely identify the local discharge pulse in the sampled signal, equation ( 6) is used to determine U thr of the noise signal from the pulse signal.A rough estimate of the start and end time for the amplitude of the two local discharge signals to just exceed the threshold is t as , t ae and t bs , t be .
U thr = k P noise (6) where P noise is the residual noise power, k is the proportional coefficient.
② Determine the start and end times for the optimal time window, t ws and t we , using (7) and (8).t r , t f represent the time differences between the ascending and falling edges.t r and t f can be determined experimentally because the GCC method does not rely on accurately identifying the initial instants of two signals.t r is typically smaller than t f when modifying the settings because the rising edge of the partial discharge pulse signal is typically smaller than the falling edge.t ws = min(t as , t bs ) − t r (7) t we = max(t bs , t be ) + t f (8) ③ The optimized time window width Tw is calculated by (9), T w = t we − t ws (9) According to (9), the partial discharge pulse signals x 1 (t) and x 2 (t) are extracted from the two sampled signals at both ends, followed by conducting PHT-GCC time delay estimation of the two signals within the optimized time window.Fig. 4 depicts the schematic diagram of the optimised pulse window technology.

B. COUNTERMEASURES FOR SOLVING WAVE VELOCITY AND FREQUENCY VARIATION CHARACTERISTICS.
Time delay estimation-based online localization systems for cable partial discharge pulses commonly rely on artificially set reference wave velocities at present.Nevertheless, the actual electromagnetic wave velocity is a complex parameter that is affected by a number of variables, including cable structural parameters, operating environments, and electromagnetic wave frequency [20].This paper investigates the frequency characteristic function of electromagnetic wave phase velocity, beginning with the cable equivalent model.In normal cable operation, the leakage current caused by improper connection of the insulation between the inner diameter inductor and the outer diameter inductor is negligible, so the propagation constant of the coaxial cable can be presented by (10), Ideally, the unit equivalent inductance L 0 ' can be presented by (11), where: µ 0 is the magnetic permeability of the insulation layer between the inner and outer diameters of the cable; D A is the outer diameter of the cable and D C is the inner diameter of the cable.The equivalent inductance corresponding to the outer and inner semiconducting layers of the actual cable can be presented by ( 12) and ( 13), where: δ A is the skin depth of the outer semi-conducting layer of the cable, δ C is the skin depth of the inner semi-conducting layer of the cable.They can be expressed by( 14), where: σ is the conductivity.Therefore, the actual equivalent cable unit inductance can be presented by ( 15)-( 16), Substituting equations ( 15) and ( 12) into (10) yields: Expand (17) Taylor and keep the first two terms to obtain: where the phase shift constant is β, which can be presented by (20), From the relationship between wave speed and β, v can be expressed by (21), Using ( 21), the frequency-wave speed characteristic curve of electromagnetic waves traveling through a wire can be constructed.This enables the pace of electromagnetic waves to be determined by monitoring their centre frequency.By employing this approach, the typical problem of obtaining imprecise results as a result of arbitrarily determining the reference wave speed can be avoided.

C. TRIMMED MEAN DATA FILTERING ALGORITHM
In the field, electromagnetic interference from highfrequency communications is a common occurrence, making accurate cable localization problematic [21].This paper addresses this issue by proposing a novel out-trimmed mean data filtering method to efficiently eliminate identified poor data and improve the precision of localization results.This procedure achieves the desired results by employing three distinct data filters: a trimming filter, a grouping filter, and an averaging filter.
First, the samples from the localization outcome are sorted ascendingly by PD localization using the pruning filter, and then between 25 and 75 percent of the localization samples are filtered for use as input for the next filter.The pruning filter eliminates anomalies from location sample data as the initial filtering phase.
The Maximum Density Clustering Application (MDCA) algorithm is employed as the second layer of clustering filters.The MDCA algorithm is based on the concept of density and employs density instead of initial points to examine cluster affiliation, automatically determining the number of clusters and locating clusters of arbitrary shape.The specific steps of MDCA are as follows: ① Calculate the local density ρ i for the i th data point in the sample set by (22), with d c as the truncation distance, where : χ(x) can be presented by ( 23) ② Calculate the distance δ i from each data point to the high local density point by (24), ③ In the ρ-δ map, the data points with larger local density ρ and larger high local density point distance δ are selected as cluster class centers, and the data points with smaller local density ρ and larger high local density point distance δ are selected as data anomalies.
Finally, the cable localization result is obtained by averaging the cluster class localization samples using an average filter.

IV. SIMULATION A. SCENARIO DESIGN AND PARAMETERS
To assess the efficacy of the localizing methodology advanced in this study, a simulation test for partial discharge localization was conducted via the Matlab Simulink platform.A cable model spanning a distance of 2000 meters was constructed, with a single-core 8.7/10kV 50mm 2 YJV medium-voltage distribution cable serving as the subject of inquiry.
This section uses the Distributed Parameters Line equivalent circuit in MATLAB to simulate the cable distribution parameter model.The Distributed Parameters Line model is a cable simulation model based on the Bergeron Model, and the distributed resistance R, distributed inductance L, distributed capacitance C and wave impedance Z can be converted by formula, and the specific conversion process is as follows: Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply. 1) The equivalent resistor R is where: ρ is the resistivity of the conductor layer at 20 degrees Celsius; α is the temperature coefficient of the resistance of the conductor layer; k is the coefficient of change of resistivity due to processing, generally 1; D c is the inner diameter of the cable.
2) The equivalent capacitor C is where: ε is the relative permittivity of the insulation layer; ε 0 is the vacuum permittivity; D A is the outer diameter of the cable and D C is the inner diameter of the cable.
3) The equivalent inductance L is where: µ 0 is the permeability of the insulation layer between the inner diameter of the cable and the outer diameter of the cable.
4) The wave impedance Z is The simulation diagram is presented in Fig. 5, and the simulation parameters are detailed in Table 1.
The equivalent resistance, equivalent inductance, equivalent capacitance and wave impedance of the simulated cable can be obtained from the equation ( 25)∼(28), as shown in Table 2 below.
In the simulation, it is assumed that partial discharge occurs at endpoint B, into which the partial discharge simulation signal is injected, and the partial discharge signal waveform   is measured at endpoint A through an oscilloscope, endpoint A is grounded through wave impedance, cable length L ac = 1200m, L bc = 800m, signal amplitude A is taken as 6mV, attenuation coefficient τ is 1.25µs, oscillation frequency f c is 5MHz, sampling frequency is 100MHz, and duration is 20µs.The duration is 20µs, as shown in Fig. 6.

B. SIMULATION RESULTS
Assume that a partial discharge occurs at the defective end C of the cable, i.e., that a signal for a partial discharge is introduced at end C.At endpoints A and B, the delayed partial discharge signal is collected.In order to simulate electromagnetic noise interference in the field environment, −5 dB of Gaussian white noise is applied.The waveforms of the signals collected at the A and B ends are depicted in Fig. 7.
Fig. 8 depicts the frequency-wave speed characteristic curve that has been derived from the simulated cable parameters.The curve clearly indicates that at low frequencies the wave speed increases significantly with increasing frequency; at fre-quencies above 3MHz the wave speed varies slowly with frequency and approaches a constant indefinitely.Notably, the electromagnetic wave produced by a partial discharge has a significantly broad bandwidth, and its centre frequency can be significantly impacted by environmental interference noise.To address this issue, the present study employs an adaptive approach that utilizes sequential statistical filtering to divide the signal spectrum and applies a cliff criterion to select the corresponding frequency band of the partial discharge signal, as demonstrated in Fig. 9.By measuring the center frequency of the simulated signal, the wave speed of the partial discharge pulse signal is determined as v = 1.6593 × 10 8 m/s.
The empirical wavelet transform was used to remove noise interference in order to obtain the pre-processed double-ended local discharge signal pulse pairs, and the optimised pulse time window technique was used to obtain a time window T w covering the entire twin signal waveform, as shown in Fig. 10, with T w = 6.69 µs.The PHAT-GCC method was used to estimate the signal time delay within the optimised time window in combination with the local discharge signal wave speed v in order to estimate the sample  localisation results of the local discharge [22].As shown in Fig. 11, the peaks of the correlation function of the direct correlation delay estimation method are not prominent enough and are prone to false peaks under low signal-tonoise conditions, which affects the accuracy of the delay estimation.The improved GCC algorithm proposed in this paper can reduce the effect of out-of-band interference on the peak value of the correlation function, and the obtained delay estimate is −2.4µs.Combined with the wave speed estimate, the final localisation estimate is 1199.054mwith a relative error of 0.0473%.

C. DISCUSSION OF SIMULATION RESULTS
This study investigates the localization of partial discharge signals under various scenarios, including distinct defect point locations, signal-to-noise ratios, and sampling rates, in order to evaluate the accuracy and robustness of the proposed method.The localization results are compared with those obtained using the peak method, energy method, and cross-correlation method.Notably, the above three methods utilize the empirical wave speed v 0 = 1.67×10 8 m/s, whereas the proposed method estimates the wave speed based on the frequency characteristics of the wave speed, which yields a value of v = 1.6593 × 10 8 m/s.

1) INFLUENCE OF PARTIAL DISCHARGE SOURCE LOCATION ON LOCALIZATGION ACCURACY
To investigate the effect of local discharge source positioning D on localisation accuracy, the current study conducted 610 VOLUME 10, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.experiments by varying the position of the initial local discharge signal injection point C while maintaining a constant sampling rate of 100MHz and a signal-to-noise ratio of −5dB.The time window width T ′ w is preset at 20µs.Due to the fact that point C displays relatively symmetric localization results at cable distances of 0-1000m and 1000-2000m, this study only analyses the simulation of the partial discharge source within the range of 0-1000m.The obtained localization results are shown in Fig. 12.
The proposed method provides more precise localization than the conventional time-delay estimation method.The localization error curve of partial discharge source can be divided into two phases, as shown in Fig. 12.In stage 1, the localization error increases considerably the defective point nears the cable's end, whereas in stage 2, the localization error decreases as the defective point nears the cable's centre.As shown in Fig. 13, when the localization source is near the near end of the cable at point A, the first localization signal x b1 (t) received at the far end of the cable at point B overlaps with the second localization signal x b2 (t) reflected by point A, resulting in varying degrees of time delay estimation errors for the peak method, the energy method, and the cross-correlation method.

Comparison of error of localizing with different signal-to-noise ratios.
This paper proposes a pulse time window technique that accurately identifies the wave x b1 (t) and the reflected wave x b2 (t).This technique improves the precision of time delay estimation by excluding the reflected the correlation function operation.In addition, the proposed localization method utilises trimmed-mean filtering to reduce the localization error induced by the partial discharge source close to the cable end.In this method, a sample set of localization results undergoes a three-layer data filtration procedure.At a distance of 25 metres from the cable endpoint, it is possible to accomplish a relative localization error of 5.26 percent.This method improves the algorithm's performance and efficiency while diminishing the influence of residual noise interference on localization precision.

2) INFLUENCE OF SIGNAL-TO-NOISE RATIO ON LOCALIZATION ACCURACY
A constant distance of 1200 metres is maintained in this investigation between the regional discharge source and the cable termination.Then, the effects of signal-to-noise ratios of −10 dB, −5 dB, 0 dB, 5 dB, and 10 dB on the localization results of four partial discharge location techniques are investigated.The comparative analysis of these results is shown in Fig. 14.
As previously demonstrated, when the signal-to-noise ratio is low, the peak-based localization method performs inadequately in terms of both precision and robustness (−10 dB).This is because the initial wave peak of the peak method is less noticeable in low SNR environments, and the significant waveform distortion makes it difficult to identify the beginning of the partial discharge pulse's rising edge [23].Moreover, noise interference hinders threshold selection, resulting in wave peak selection errors.In contrast, the energy-based technique has suboptimal localization accuracy due to the requirement of less noise interference in selecting the energy inflection point.In situations where the partial discharge pulse signal has a low energy level or signalto-noise ratio, residual noise interference becomes more pronounced, thereby making the selection process more difficult.Moreover, the peak of the correlation function of the sampled signal may not correspond to the peak of the correlation function of the partial discharge pulse, but instead represent the peak of residual noise.This decreases the precision estimations of time delay.
This paper describes an optimised pulse time window technique that enhances the accuracy of localization by minimising the impact of random error.The proposed method generates a relative localization error of no more than 0.06% at a signal-to-noise ratio as low as −10 dB.These results indicate that the algorithm is stable and robust, as well as meeting the stringent requirements for precise localization in harsh environments with a low signal-to-noise ratio.

3) INFLUENCE OF SAMPLING RATE ON LOCATION ACCURACY
The effect of sampling rate on localization precision is investigated here.Specifically, Fig. 15 display the localization results of four distinct methods, where the localization source location and signal-to-noise ratio remain unaltered, and where the signal sampling rate is changed to 25, 50, 100, and 200 MHz, respectively.Fig. 15 illustrates that when the sampling rate is modest (25 MHz), each of the four localization techniques exhibits varying degrees of error.Notably, the peak method exhibits a relatively large localising error due to the distortion and drift of the initial wave crest of the signal caused by the low sampling rate, which impedes the determination of the exact instant that the initial wave crest occurred.Similarly, under low sampling rate conditions, the cumulative energy  curve of the energy method is distorted, resulting in a shift in the initial signal moment.In contrast, the localization results obtained using the cross-correlation method and the approach described in this study are superior.The correlation method does not require the estimation of wavefront arrival time and wave peak occurrence moment of the sampled signals at both ends, instead relying on the time delay of the estimated signal occurrence under the influence of the correlation function in order to maintain high localization accuracy even with a low sampling rate.In terms of accuracy, the proposed technique is superior to the cross-correlation method.The frequency features of wave speed are taken into account, leading to a more accurate calculation of wave speed during a partial discharge.To further mitigate the relative localization inaccuracy brought on by the low sampling rate, the trimmed-mean filtering technique averages the results of several localization samples.

V. TEST VERIFICATION A. TEST PLATFORM
In order to validate the efficacy of the partial discharge online location method proposed in this paper, a cable partial discharge location test was conducted at a cable plant, as depicted in Fig. 16.The cable utilized in the test had a length of 90m, and was of the ZR-YJV26/35kV model, with specific parameters detailed in Table 3.A scratch defect measuring 30mm in length, 2mm in width, and 1mm in depth was in-tentionally introduced along the surface at a distance of 27m from the A end of the cable.The high-frequency current transformer (HFCT) was employed to clamp the ground lead of the cable shield, with the partial discharge signal emanating from the cable defect being detected by the HFCT and transmitted to the dual port of the partial discharge detector for processing via RG316 coaxial line.

B. TEST RESULTS AND ANALYSIS
Fig. 17 and Fig. 18 depict the time domain waveform and frequency spectrum of the processed local discharge signal.Initially, the sampled data is by the enhanced empirical wavelet transform.Fig. demonstrates that the frequency coverage of the measured local discharge signal is more dispersed, making its central frequency difficult to determine.Consequently, wavelet decomposition is considered for decomposing the local discharge signal into individual frequency bands, reading the center frequency of each frequency band, and determining the final signal's center frequency via a weighted average operation.
By analysing the characteristics of commonly used wavelet bases and the characteristics of localised discharge signals from cables, along with the calculated Signal-to-Noise Ratio (SNR), Root-mean-square error (RMSE), and Normalised Correlation Coefficient (NCC), the employed wavelet basis function is symlet, and the number of decomposition layers is seven.Fig. 19 depicts the waveform and spectrum plots of the decomposed local discharge signal at the A-end.Table 4 displays the spectral amplitudes of the center frequencies at each scale, and it is apparent that the amplitudes of  the center frequencies at scale d5 are the greatest.The centre frequency of the measured partial discharge signal at end A is 4.375 MHz based on the weighted average of the centre frequencies at each scale, whereas the centre frequency of partial discharge signal at end B is 4.335 MHz.Based on the measured local discharge center frequency, the frequency-dependent wave speed of the local discharge signal is estimated to be v A = 1.7791 × 10 8 m/s and v B = 1.7795 × 10 8 m/s.
Using PHAT-GCC and the optimised pulse time window technique, the time delay for the double-ended local discharge pulse pair was estimated, as depicted in Fig. 20.To reduce the discriminative effect of the sampling rate on the maximum time delay estimate of the correlation function, five sampling sites near the peak of the correlation function were chosen for fitting the peak curve in order to obtain the most precise estimate of the time delay.The  final single-sample localisation results for the localisation experiments are displayed in Table 5.
According to the data presented in the preceding table, it is evident that the disparity between the localized results of a single sample and the actual discharge source location is relatively small, thus satisfying the requirements of online localization in engineering practice.Comparing the relative localization error to the simulation results, a discrepancy persists.This divergence can be explained by the fact that the propagation speed of the genuine partial discharge signal differs from the wave speed estimated from the wave speedfrequency curve.In addition, the manufactured cable's actual dimensions may not be identical to those calibrated, resulting in cable frequency variation parameters that are inconsistent with the theoretical value.
It is important to note that the centre frequency of the pulse signal is initially higher when it is emitted from the partial discharge source due to dispersion that occurs during the propagation of partial discharge pulses through cables.Yet, when the signal travels further, the core frequency drops and the rising and falling edges of the pulse signal flatten.Its lower centre frequency has a negative effect on the calculation of wave speed due to signal propagation.The actual partial discharge signal, which is a high-frequency electromagnetic wave, is fundamentally different from the simulated partial discharge mathematical model, and its amplitude uncertainty and steepness variability must be taken into account.However, the signal is easily oscillated and deformed, which leads to ''distortion peaks'' in the correlation function and hampers time delay estimates.
The trimmed-mean data filtering method is used to address aforementioned problem in the context of data analysis.The localization evaluation that considerably departs from the partial discharge is removed by applying the first filter of the trimmed-mean data filtering approach to a normalised set of 100 localization outcomes.The localization result typical amplitude characteristic map of the partial discharge signal is derived from the results between the lower and upper quartiles of sampling distribution, as shown Fig. 21.Finally, we divide the data into three groups and single out four outliers using the density maximum clustering technique.The largest sample cluster is the gold standard for source localisation in partial discharge.With relative inaccuracy of 0.45%, the final result of 26.54m satisfies engineering standards.

C. COMPARISON OF EXPERIMENTAL RESULTS
We employed the peak method, the energy method, and the cross-correlation method to localize the sampled partial discharge signal in order to facilitate comparisons with other time-delay estimation localization techniques.Based on the initial experiment, we utilised six additional 90-meter cables with identically sized defects positioned 5m, 10m, 20m, 30m, 40m, and 45m from end A. Simultaneously, 100 partial discharge experiments were conducted on each cable, four distinct localisation techniques were used to analyse the data.Notably, four methods implemented in this study all employ the trimmed-mean data filtering algorithm proposed in this paper for data processing.Due to symmetry of point C's localisation results at 0-45m and 45-90m of the cable, only the actual test circumstance of the local emission source at 0-45m is considered.The localization outcomes are detailed in Table 6.
According to the results presented in Table 6, the experimental localizing outcomes obtained by the four tested methods are in line with the simulation analysis results.However, the peak method, energy method, and crosscorrelation method neglect the frequency characteristics of the partial discharge wave speed, leading to inaccuracies in the localizing outcomes [24].Conversely, the method proposed in this study achieves accurate estimation of the partial discharge wave speed by plotting the corresponding frequency-wave speed characteristic curve of the experimental cable.Furthermore, the proposed technique of optimizing the pulse time window enables adaptive adjustment of the 614 VOLUME 10, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.correlation function's window size, considering the signal-tonoise ratio and sampling rate of the equipment.This approach minimizes the likelihood of ''distortion peak'' and ''false peak'' occurrences in the correlation function and enhances the precision of time delay estimation.In the field experiment, the accuracy of partial discharge localisation using this paper's method ranges between 97.43% and 99.89%, which meets actual engineering requirements.

VI. CONCLUSION
This paper proposes a double-end partial discharge localization method for AC cables, in which an enhanced generalised correlation algorithm is used to estimate the signal propagation delay, taking into account the uncertainty of the partial discharge signal transmission speed.In addition, a trimmed-mean data filtering speed algorithm is used to enhance location accuracy when multiple samples are present.Simulation and experiment evaluations are then used to validate the accuracy of the proposed method.The key findings are as follows: (1) The proposed optimised pulse time window technique enhances computational efficiency and noise resistance in time delay estimation for online partial discharge localization.This method is more adaptable to engineering requirements than traditional fixed time window methods and mitigates the impact of electromagnetic interference on accuracy.
(2) To address challenges of abnormal data and large location errors in practical engineering applications, a trimmedmean data filtering algorithm is introduced, which employs a three-layer filter to effectively remove noises, obtaining reliable location results.
(3) To accurately determine the pulse wavespeed of partial discharge signals in the cable propagation process, a frequency-wave speed characteristic curve of electromagnetic waves is constructed, and the pulse wave speed is precisely determined by identifying the center frequency of the spectrum.This approach eliminates the need for arbitrary reference of wave speed values, improving locating accuracy.
(4) Simulation and experiment analysis demonstrates that the proposed method yields superior accuracy in timedelay estimation and reduces locating errors in challenging environments of severe electromagnetic interference with a restricted sampling rate.As the relative errors of experimental results range from 0.11% to 2.57%, actual engineering requirements are satisfied, which indicates that the proposed method is viable to locatel partial discharge positions accurately.

FIGURE 1 .
FIGURE 1. Double-end arrival time analysis method.

FIGURE 3 .
FIGURE 3. Flow chart of cable localization based on improved GCC method.

FIGURE 4 .
FIGURE 4. Principle diagram of optimized pulse time window technique.

FIGURE 5 .
FIGURE 5. Principle diagram of optimized pulse time window technique.

FIGURE 9 .
FIGURE 9. Measurement of the center frequency of the partial discharge signal.

FIGURE 12 .
FIGURE 12.Comparison of relative localization error at different partial discharge source locations.

FIGURE 13 .
FIGURE 13.Incident wave and reflected wave propagation of partial discharge signal.

FIGURE 15 .
FIGURE 15.Comparison of localization results at different sampling rates.

FIGURE 19 .
FIGURE 19.Wavelet decomposition time and frequency spectrum of the measured A-side signal at different scale.