Study of partial discharges measurement cycles effect on defect recognition for underground cable joints

This study investigates the influence of various partial discharge (PD) measurement durations on defect recognition in high voltage power cable joints, aiming to address a crucial challenge in the field of insulation assessment. The main objective is to determine the optimal measurement cycle duration for accurate defect recognition, thereby enhancing the reliability of PD-based diagnostic techniques. Totally 14 cable joints, each containing three different types of prefabricated artificial defects, were analyzed across five different measurement cycle durations: 40, 80, 120, 200, and 1200 cycles. Subsequently, convolutional neural networks (CNNs) were employed for defect recognition analysis. The results reveal a significant impact of measurement cycle duration on defect recognition accuracy. Particularly, a CNN based on 200 measurement cycles demonstrates superior performance compared to models with fewer cycles, achieving a total defect recognition accuracy of 100%. This finding underscores the importance of sufficient measurement cycles for obtaining comprehensive PRPD patterns and accurate defect classification. Furthermore, the study highlights the significance of setting a threshold value to mitigate false conditions in defect type recognition, offering valuable insights for practical applications in power system maintenance and diagnostics. Overall, this research contributes to advancing the understanding of PD-based insulation assessment techniques and provides practical recommendations for optimizing measurement cycle duration to enhance defect recognition accuracy in high voltage power cable joints.


Introduction
Currently partial discharge (PD) is a widely accepted method for evaluating insulation conditions and classifying * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.defect types in high-voltage electrical power systems [1][2][3].According to the IEC 60270 standard [4], PD signifies an electrical pulse discharge that partially bridges the insulation.Neglecting PD occurrences can result in complete insulation breakdown, leading to severe damage to power equipment.Timely detection of PD is crucial for utility companies, enabling them to identify the type and source location of PD, thereby averting costly electrical equipment failures [5,6].
Numerous studies have introduced various methods for classifying PD sources and identifying defect types [7].The PD sources and defect types exhibited distinct attributes in the measured PD patterns.These attributes serve as vital indicators and are utilized to train different machine-learning models for a more efficient and cost-effective classification of defect types [8].
Phase-resolved partial discharge (PRPD) representation is a widely recognized method that offers clear and consistent visualization of PD sources [9].It effectively extracts features from PD signals and elucidates the phase-position paths concerning the sinusoidal voltage applied [10][11][12][13].In this study, PRPD data were acquired using a PD detector, providing the relationship between the working frequency phase angle (φ), number of PD discharges (n), and magnitude of charge (q).This process resulted in the derivation of the n-q-φ pattern, which is a crucial PRPD representation employed to analyze the classification accuracy.
The duration of the PRPD pattern corresponds directly to the number of PDs detected per measurement cycle.Because PDs occur intermittently, an adequate number of measurement cycles are required to obtain a comprehensive PRPD pattern.Currently, there are no universally recommended measurement cycles for PD assessment to generate a single PRPD pattern.Various researchers have employed different measurement cycle durations for PD classification and research related to insulation aging.
Xin et al investigated the impact of various measurement durations of PRPD data on PD pattern recognition.They utilized artificial neural networks (ANN) and support vector machine (SVM) algorithms to compare classification accuracy across measurement durations from 1 to 15 s [14].However, the type of PRPD patterns Ma et al introduced a novel fuzzy support vector machine that employed a PD measurement duration of 100 cycles.They contrasted the results with an array of ANN algorithms such as the K-nearest neighbor, multilayer perceptron, radial basis function network, and Bayesian classifier [15].Our prior research focused on defect recognition using an SVM with the application of the fuzzy entropy algorithm, achieving an accuracy of 96% that employed a PD measurement duration of 40 cycles [16].Peng et al applied a convolutional neural network (CNNs) model for pattern recognition, highlighting its significant capabilities in PD pattern recognition.Their study utilized PD data obtained over 200 measurement duration cycles [17].
Notably, despite the use of different measurement cycles in previous research, obtaining the ideal PRPD pattern shape remains challenging owing to the intermittent nature of PD.This study innovatively addresses this challenge by increasing the number of measurement cycles to mitigate the erratic appearance of PD.
While previous research has focused on various methods for classifying PD sources and identifying defect types, there remains a notable gap in understanding how different measurement cycles impact defect identification accuracy.This study aims to address this gap by investigating the influence of various PD measurement durations on defect recognition accuracy in high voltage power cable joints.To achieve this, 14 cable joints with three types of prefabricated artificial defects were studied across 40, 80, 120, 200, and 1200 cycles.Employing the PRPD technique, the n-q-φ format of the PD patterns was obtained for all test samples, followed by an assessment of the robustness of the machine-learning model.
What sets this study apart is its innovative approach to systematically analyze the impact of measurement cycle duration on defect recognition accuracy.By examining cycles ranging from 40 to 1200, aim to determine the sufficient duration for obtaining comprehensive PD patterns and improving defect classification accuracy.This research fills a significant gap in previous studies, which have often employed arbitrary measurement durations without thorough investigation into their effects on defect identification.
Furthermore, this study introduces a novel application of CNNs for defect recognition analysis in high voltage power cable joints.By leveraging CNNs, which have demonstrated remarkable capabilities in image recognition tasks, we aim to enhance the efficiency and accuracy of defect classification in PD patterns.
This paper is structured into several sections for a coherent presentation of the key elements of the study.Section 2 outlines the PD experimental procedure, details the sample fabrication, and PD data collection.Section 3 elucidates PRPD patterns across various measurement cycles.In section 4, we discuss the CNN modeling technique, and in section 5, we compare the results from different measurement cycles.Finally, section 6 concludes the study with key insights and suggestions for future research.

PD test system
PD experiments were carried out at the high-voltage laboratory of the National Taiwan University of Science and Technology using the pulse current method defined in IEC 60270.The PD measurements were performed using a setup consisting of a capacitive voltage divider, PD test subject, and PD measuring device (MD), as illustrated in figure 1.
The test subjects were subjected to high voltage using an AC voltage source (60 Hz) to facilitate aging.The MD is made by an RLC circuit with a bandwidth frequency of 200 kHz and a center frequency of 300 kHz.The capacitive voltage divider was used to reduce the voltage of the test subject to an 8000:1 ratio and to produce a coupling circuit for the PD pulses.MD provided PD signals, whereas the capacitive voltage divider provided voltage signals.Both the signals were captured, stored, and recorded using a computer.The experimental PD measurement setup involved an analog-to-digital converter with a 20 MHz sampling rate, recording voltage, and PD signals measured over 40 cycles.

Fabrication of artificial defects
The joining of electrical cable connections, which is normally done on-site, is prone to human error owing to placement problems and contamination [18].This susceptibility to errors during joint construction underscores the influence of personal factors.For this study, the routine assembly process utilized a 3-5 m-long XLPE power cable paired with a pre-molded straight-through joint (model Cat.#25TS1-221), designed by Tai-mold Company, rated at 25 kV voltage and 200 A current.The cable joint insulation consisted of XLPE/ethylene propylene diene monomer (EPDM) layers [19].
Three unique artificial defect types were suggested for this investigation: Type A, Type B, and Type C, as shown in figure 2. Type A has a 10 mm gap between the cable insulation and the inner semiconductor of the joint, this defect simulates scenarios where there is improper insulation placement or contamination during joint construction, leading to PD. whereas Type B has a 3 mm diameter and 4 mm depth void within the cable insulation, this defect replicates scenarios where voids or air gaps are present within the cable insulation due to manufacturing defects or damage during installation, resulting in localized stress concentrations and potential PD occurrence.Type C has a triangular protrusion on the outer layer of the semiconductor with a 15 mm base and 20 mm height, this defect simulates scenarios where there are irregularities or protrusions on the surface of the cable joint, which can lead to enhanced electric field concentrations and PD initiation.Each of these cable joint fault models is likely to cause PD, and a thorough explanation has been provided [19].
To ensure the expected occurrence of PD and proper breakdown aligned with the designed defects, each test sample underwent dissection and examination of the electric tracks [6].Test samples that did not meet the specified electric-track parameters were excluded from the study.The specified parameters for inspecting the electrical tracks primarily include dimensions and material properties relevant to the design and functionality of the cable joint.

PD data collection from defect samples
The test samples for defect types A, B, and C consisted of six, six, and two samples, respectively.The reduced number  of test samples for defect type C was due to instances where PD was not detected in some samples, and some samples did not undergo breakdown, even at higher inception voltages.The test voltages applied for defect types A and B ranged from approximately 24 kV to 32 kV, and for type C, from 25 kV to 55 kV.Higher test voltages for Type C were necessary because of the absence of breakdown, even at increased voltage levels.The PD experimental procedure follows supplying the test voltage for 2 d and turned off for 1 d and increased in steps of 5 kV to control the duration of test procedure and PD data were recorded with an interval of 4 min for 2 d of each test sample [6].The PD data were collected for each test sample, and the results of the PD measurements for various measurement cycles are shown in table 1.Initially, the PD data were collected for each test sample across 40 measurement cycles.Subsequently, various measurement cycles were applied, and the collected PD data for each cycle are listed in table 1.These data were then utilized to explore the impact of different measurement cycles on the extracted features and defect type recognition, as elaborated in the following sections.The selection of different measurement cycles in this study was based on the authors' discretion.

Phase resolved patterns
The PD signals acquired from the experiments exhibited distinct high-frequency oscillation patterns.To diminish the noise factors, a discrete wavelet transform utilizing Daubechies 11 wavelet functions [6,16,19] was applied.In this technique, the values of the high frequency component are defined as zero, which means that only the low frequency component remain.Subsequently, the noise factors are restricted according to the threshold, and filtered PD signals are extracted using an inverse discrete wavelet transform.The PRPD technique is used to establish the correlation between the discharge pulses and voltage phases [9].The PRPD pattern encompasses the discharge evolution pattern (q-φ-t) represented in a 3D matrix format with a size of 40 × 600.

PD measurement PRPD patterns at measurement cycles
In this section, we emphasize the impact of various PD measurement cycles on the PD defect recognition.Specifically, the PD measurement PRPD patterns at the measurement cycles were the primary focus.Figure 3 depicts the PRPD pattern, in n-q-φ form, of the defect type A at varying measurement cycles including 40, 80, 120, 200, 1200, and 1800 cycles.This visual representation illustrates the changes in patterns across these different measurement cycles.
Figure 3 illustrates the distinct PD characteristics with respect to the phase angle for various higher measurement cycles.The observed PD shapes exhibited considerable variation across the different measurement cycles, displaying a nonuniform pattern.For higher measurement cycles, the PD manifestations appeared more density.Notably, at 1200 measurement cycles, a saturated pattern was observed, facilitating a more comprehensive analysis of the PD effects compared with smaller measurement cycles.The Figure indicates that 1200 cycles are sufficient to capture a stable PD behavior.
Similarly, figure 4 presents the PRPD pattern in the n-q-φ form for a type B test sample across different higher measurement cycles: 40, 80, 120, 200, 1200, and 1800 cycles.
Figure 4 presents the PD characteristics of the defect type B samples with respect to the phase angle at different high-measurement cycles.Similar to the observations in the type A samples, the PD shapes exhibited variability across different measurement cycles, indicating non-uniformity.At higher measurement cycles, PD manifestations appeared more erratic.The Figure suggests that 1200 cycles are also sufficient to maintain stable PD behavior in the defect type B samples.
Figure 5 displays the PRPD pattern in n-q-φ form for the defect type C test samples across various higher measurement cycles: 40, 80, 120, 200, 1200, and 1800 cycles.Figure 5 showcases diverse PD manifestations of defect type C samples concerning the phase angle across different higher Notably, in figure 5, the occurrence of PDs in type C samples was less frequent.The study involved testing two samples with defect type C, subjecting them to a maximum voltage of approximately 75 kV, which did not result in a breakdown.Consequently, the occurrence of PDs in type C samples was dissimilar to that in types A and B. Despite this, PD manifestations appeared more random at higher measurement cycles.Observations indicate that 1200 cycles are likely sufficient for maintaining stable PD behavior in defect type C samples.
In summary, for all the defect types, the 1200 cycles were deemed sufficient to maintain stable PD behavior based on our observations of PD waveform variations across different measurement cycles.We observed that at 1200 cycles, the PD manifestations exhibited a more consistent and uniform pattern compared to smaller measurement cycles.This consistency in PD waveform characteristics at 1200 cycles indicated stable PD behavior, which is essential for reliable defect identification and analysis.

Defect recognition using CNNs at different PD measurement cycles
CNNs represent a widely employed artificial intelligence technique that has rapidly advanced in the image and speech recognition domains.Notably, CNNs demonstrate exceptional feature-learning capabilities, which are particularly prominent in image recognition applications, achieving considerable success [17,19,20].The input, hidden, and output layers of the standard CNN architecture include convolution, pooling, and activation functions in the hidden layers.
For the effective implementation of CNNs in defect-type recognition, evaluating various network layer configurations based on training data is crucial.Currently, a specific theoretical approach for determining the ideal number of network layers is lacking.
A detailed study analysis has been done on CNNbased PD pattern recognition for the high voltage cable joints evaluated in terms of the number of network layers, the convolutional kernel size and the activation function [21].Based on the foregoing analysis mentioned in [21], the final adopted architecture off CNN configuration has been established.Therefore, the optimal CNN configuration was ascertained based on the highest defect-type recognition accuracy [19,21].Prior investigations have presented optimal parameters for modeling CNNs to recognize PRPD patterns and pulse sequence analysis [19].The same network configuration parameters are used in this paper, which consists of four convolutional layers, two max-pooling layers, and three rectified linear unit (ReLU) activation functions.The output layer contains four neurons destined for each PD source which is followed by the softmax layer.The network learning parameters are updated using Adam optimizer and for training 20 epoch are selected.To tune the weights during training the CNN model a cross entropy method is employed [19].
In this study, the same CNN architecture was employed to recognize the image format of the PRPD patterns in the n-q-φ form across all test samples for different measurement cycles.The approach used is consistent with a previous study owing to CNN's proven efficiency, aligning with the goal of the present study to analyze the effects of various PD measurement cycles on defect pattern recognition.
The training and testing data for the CNN were sourced from the laboratory defect models used in our study, which encompassed PD data collected from cable joints with various measurement cycles (40, 80, 120, 200, and 1200 cycles).We maintained consistency in other classifier factors, such as parameter configurations, training, and testing data, while only varying the PD measurement cycles to explore their impact on recognition accuracy.It is important to note that we did conduct analysis on intermediate cycle numbers between 200 and 1800.We chose to directly showcase the results for 1200 and 1800 cycles immediately after 200 cycles to the potential impact of longer measurement durations on defect recognition accuracy The analysis of CNN's recognition performance of the CNN at each measurement cycle ultimately suggests an adequate number of cycles necessary for conducting PD measurements during defect recognition tests.

Results of PRPD pattern recognition
A CNN model was developed using the configurations detailed in a previous study [19].Images depicting the PRPD patterns corresponding to all three types of defects (types A, B, and C) were individually stored and labeled.The images used to train the CNN were uniformly set to 88 × 66 pixels.This pixel layout was chosen for its efficacy and optimal performance during the training and testing phases of the CNN [19].

Training CNN with different measurement cycles
The CNN underwent training using all PRPD pattern images corresponding to the three labeled defect types across the considered measurement cycles.Figures 6 and 7 show the learning curve graphs showing the accuracy and loss (Yaxis labels) against the number of iterations (X-axis) until convergence.Figure 6 shows the learning curve for 40 cycles, whereas figure 7 shows the corresponding curves for 200 cycles.
Figure 6 indicates a very high number of maximum iterations exceeding 2000, resulting in a longer training duration owing to an insufficient number of PDs for the 40measurement cycles.Conversely, in figure 7, the maximum number of iterations is nearly 200, significantly reducing the model training time compared with the 40 measurement cycles.This observation suggests that higher measurement cycles require fewer iterations and less training time for CNN.
Furthermore, both figures 6 and 7 depict a pattern in which the training accuracy rapidly increases and stabilizes after several iterations, reaching a consistent accuracy level.Simultaneously, the loss decreased steadily until it plateaued at a stable value.The learning curve graphs for all other measurement cycles considered in this study exhibit a similar trend, displaying a rapid initial increase and subsequent stabilization after a few iterations to achieve consistent accuracy.
Figures 8 and 9 present the confusion matrices for the training process results for 40 and 200 cycles, serving as    With fewer measurement cycles, there may be insufficient data available for the CNN to learn and generalize patterns effectively, leading to higher rates of misclassification.
Conversely, in the case of 200 cycles, apart from one incorrect prediction of Type A for the targeted Type C, suggests that higher measurement cycles provide a more comprehensive and representative dataset for training the CNN, resulting in improved performance and accuracy.The increased availability of data at higher measurement cycles allows the CNN to learn and distinguish between different defect types more effectively, thereby reducing the likelihood of misclassifications.
To address these observed differences in misclassification rates, future research could explore potential improvements in model design and training strategies.This may include increasing the complexity of the CNN architecture, implementing data augmentation techniques to enhance the diversity of the training dataset, and optimizing hyperparameters to improve model performance.
It is notable that in figure 9, the overall percentage of the two incorrect predictions of the targeted Type A as Type B amounts to 0.8%, which is slightly higher than the 0.2% in figure 8.This disparity is due to the lower data availability for higher measurement cycles (200 cycles) compared with fewer measurement cycles (40 cycles), contributing to a slightly elevated percentage.
However, in the case of 200 cycles, two incorrect predictions of Type A (Type B) and one incorrect prediction of Type C (Type A) were identified.Upon inspecting the PRPD pattern images, it was observed that some incorrect predictions resulted from very low PD appearance, leading to nearly empty PRPD pattern images.To mitigate this issue, a threshold was implemented during the CNN testing to filter out these failure cases.The determination of thresholds for all measurement cycles is discussed in the subsequent section.

Testing CNN with different measurement cycles
Following the training of the CNNs for various measurement cycles, the efficiency of the trained models was assessed during the testing phase.A crucial observation surfaced during the testing process when predicting the defect type.In the score matrix, when inputting a specific Type A (e.g.Type A of 40 cycles) to test the CNN, certain PD pattern predictions were predominantly inclined towards the other two types (i.e.Type B or Type C), despite the final recognition result being aligned with the input Type A (Type A).
This issue, as previously highlighted, was classified as a failure case and subsequently addressed by setting a threshold.The threshold was calculated using the statistical empirical rule detailed in equation ( 1): This equation follows a commonly used statistical method where the threshold is set at three standard deviations below the mean.By applying this method, we aimed to establish a threshold that effectively distinguishes between successful predictions and failure cases during CNN testing.The rationale for choosing this method lies in its simplicity and effectiveness in identifying outlier cases while ensuring a balance between sensitivity and specificity in defect recognition.Setting the threshold at three standard deviations below the mean provides a conservative yet robust criterion for retaining cases that meet a certain level of confidence in their prediction accuracy; the calculated values are listed in table 2.
Cases meeting the specified threshold were retained and utilized for CNN testing, and their respective accuracies are detailed in table 2. Therefore, the establishment of a threshold is significant in achieving efficient testing accuracy by excluding failure cases.The thresholds documented in table 2 play a pivotal role in comparing the resulting CNN testing accuracies, ultimately providing effective outcomes.

Training and testing accuracies comparison at measurement cycles
The CNN was effectively trained across various measurement cycles, and a comparison of the training and testing accuracies is presented in table 3. Notably, it is crucial to reiterate that the testing accuracies presented in table 3 were derived after excluding failure cases that did not meet the specified threshold calculated using equation (1).
Table 3 illustrates a notable trend in which the training accuracy of the CNN steadily increased from 93% to 100% as the number of measurement cycles increased from 40 to 200.Simultaneously, the testing accuracy reached a maximum score of 100%.Consequently, the CNN trained with 200 cycles displayed superior recognition accuracy.These outcomes indicate that 200 cycles are adequate for PD measurements, showing high accuracy in defect recognition.
The results from the CNN trained with 1200 cycles were indeed presented to highlight that the CNN trained with 200 cycles achieved an accuracy comparable to that of the highest measurement cycles.This comparison underscores the effectiveness of the CNN model trained with a smaller number of cycles in achieving comparable accuracy levels to those obtained with longer measurement durations.
Based on our investigations, we concluded that the CNN trained with 200 cycles demonstrated excellent performance in defect recognition accuracy, as evidenced by the notably high testing accuracies obtained.These results reinforce the

Testing accuracies at measurement cycles of CNN trained with 200 cycles
In light of the findings from the previous section, indicating the adequacy of 200 measurement cycles for PD measurements, a subsequent analysis was conducted.The suggested CNN, trained with 200 measurement cycles, underwent testing with alternate cycles (40, 80, and 120) to determine a sufficient number of testing cycles.The test accuracy results for the three defect types are presented in table 4.
Given that the CNN trained with 200 cycles exhibited 100% testing accuracy, cycles less than 200 were evaluated.Table 4 indicates an overall testing accuracy of 89.02% for the three defect types at 40 cycles, and a higher accuracy of 98.71% for 120 cycles.Notably, the results reveal that 120 cycles yield superior accuracy compared with 40 and 80 cycles, suggesting their adequacy for achieving optimal performance in testing various defect types.
Despite the observations in table 3 indicating a 100% testing accuracy for 200 cycles with a CNN trained using 200 cycles, it becomes evident that 200 measurement cycles proved to be the optimal choice for both training and testing the CNN for defect-type recognition across the considered test samples.In addition, it is noteworthy that within the CNN trained using 200 cycles, the best testing accuracy was achieved with 120 measurement cycles.

Conclusion
This study investigated the impact of various measurement cycles on PD defect recognition.Examination of the defect recognition accuracy derived from laboratory defect models revealed a substantial influence of the number of measurement cycles on the PD source evaluation.Initially, utilizing the widely employed PRPD technique, PRPD patterns in the n-q-φ format were obtained for all three test sample types, followed by an exploration of the effects of different measurement cycles on PD pattern recognition using CNNs.
The proposed 200 measurement cycles was based on our experimental findings, which demonstrated a remarkable increase in defect recognition accuracy from 93% at 40 cycles to 100% after 200 cycles.This observation underscores the critical importance of sufficient measurement cycles for accurate PD defect recognition.By highlighting the reproducibility of this result across multiple test sample types and experimental conditions, we aim to emphasize the robustness and reliability of our conclusion.
Future studies could involve validating the suggested measurement cycles with diverse defect types and exploring their applicability in real-world scenarios.Additionally, we will encourage researchers to investigate the impact of noise on CNN performance by training models with prevalent external PD noise data, such as corona, and to conduct comparative studies with various machine learning algorithms to further enhance understanding and provide comprehensive insights into PD defect recognition.

Figure 1 .
Figure 1.PD experimental setup with a cable joint.

Figure 2 .
Figure 2. Schematic diagram of the power cable straight joint.

Figure 3 .
Figure 3. Evolution of the PRPD pattern of the PDs of defect type A for different measurement cycles.

Figure 4 .
Figure 4. Evolution of the PRPD pattern of the PDs of defect type B for different measurement cycles.

Figure 5 .
Figure 5. Evolution of the PRPD pattern of the PDs of defect type C for different measurement cycles.

Figure 6 .
Figure 6.Learning curve of a CNN trained with 40 measurements cycles.

Figure 7 .
Figure 7. Learning curve of a CNN trained with 200 measurement cycles.

Figure 8 .
Figure 8.The confusion matrix for 40 cycles trained CNN model.

Figure 9 .
Figure 9.The confusion matrix for 200 cycles trained CNN model.

Table 1 .
PD data from cable test samples at different measurement cycles.

Table 2 .
Threshold values at different measurement cycles.

Table 3 .
Comparison of accuracies at different measurement cycles.

Table 4 .
Testing accuracies at measurement cycles of CNN trained with 200 cycles.