Application of Probabilistic Neural Networks Using High-Frequency Components’ Differential Current for Transformer Protection Schemes to Discriminate between External Faults and Internal Winding Faults in Power Transformers

Citation: Chiradeja, P.; Pothisarn, C.; Phannil, N.; Ananwattananporn, S.; Leelajindakrairerk, M.; Ngaopitakkul, A.; Thongsuk, S.; Pornpojratanakul, V.; Bunjongjit, S.; Yoomak, S. Application of Probabilistic Neural Networks Using High-Frequency Components’ Differential Current for Transformer Protection Schemes to Discriminate between External Faults and Internal Winding Faults in Power Transformers. Appl. Sci. 2021, 11, 10619. https://doi.org/10.3390/ app112210619


Introduction
Nowadays, the Electricity Generating Authority of Thailand (EGAT) uses conventional methods (such as over-current, voltage, and differential relays) to diagnose power transformer faults. However, there are some events that cause unnecessary operation of the differential protection. At the same time, the cause of the differential signal is larger, even though there is no internal fault. In addition, there are several decision algorithms that have been developed for relay protection to prevent mistake tripping. Thus, the unnecessary operation of the protective equipment under different non-fault conditions is solved by several methods, including magnetizing inrush current, ratio mismatch, through-fault current line, etc.
This research presents a new decision algorithm of protective relay development to discriminate between external and internal faults. The simulation system is modeled

•
Design a new decision algorithm for protective relay to discriminate between internal and external faults. • Study the simulation model in the ATP program to understand and consider the issues in the study.

•
Analyze the decision algorithm's performance to determine the most suitable faultdetection methods.
This study is organized as follows: in Section 2, relevant research has been described in order to broaden the perspective of understanding and consider the issues in the study more clearly. In Section 3, the wavelet transforms are explained to understand the analysis process. In Section 4, the simulation model is made in the ATP program and generates the resulting signal for wavelet analysis. The fault-detection algorithm is explained in Section 5, and the decision algorithm is presented in Section 6. The results are compared between three fault detection methods in two cases to find the most suitable method. Finally, the conclusions are presented in Section 7.
For transformer defect diagnostics, a novel multi-input and multi-output polynomial neural network (PNN) is proposed [10]. The five types of characteristic gas that match the four fault categories of sample data are used to train and produce a single-output PNN I classification model. Then, there is a model for detecting transformer faults based on multiple outputs, PNN II, which is designed to target high-energy discharge, low-energy discharge, and thermal heating fault types. The results of simulations and tests demonstrate that accuracy can reach 100%. The frequency response traces of the tested winding were analyzed using convolutional neural networks (CNN) [11]. The proposed method has been shown to be capable of accurately locating faults. To detect DSV location in transformer winding, convolutional neural networks were used to extract key information from frequency response traces. The location of all applied DSV faults in the transformer winding was pinpointed with 100% accuracy. In paper [13], the discrete time-series convolution neural network (DTCNN) is constructed. HDCNN's performance has been verified. The conditions of a suitable source dataset for TRU fault diagnosis, as well as the transfer layers from the pre-trained HDCNN, are discussed on this foundation. The comparison of transfer learning to other algorithms under various noise conditions shows that it is an effective technique to build a diagnosis network for similar equipment and can often lead to higher performance.
Finite element analysis of internal winding faults in a distribution transformer is presented in the study [17]. The transformer's terminal behaviors are investigated using an indirect coupling of the finite element approach and circuit modeling. The circuit model was exported and used in a circuit analysis program to investigate the transformer's terminal characteristics. For comparison, previous experimental data were employed. We can observe that the FEA transformer model can accurately predict the terminal values of a distribution transformer's internal winding defect. Soft computing models such as fuzzy logic and adaptive neuro-fuzzy inference system (ANFIS) have been used to implement dissolved gas analysis (DGA) [23]. For diagnostic capability, the models were tested using a reported fault database. The ANFIS model is a dependable system with a high degree of precision. Because the ANFIS model is so simple to create, it can overcome the constraints of traditional DGA-based transformer fault diagnosis approaches.
The hyperbolic S-transform-based approach in [29] was used to distinguish between internal faults, external faults, incipient faults, and inrush currents. This method was operated in two stages. External faults were first distinguished from other disturbances while an internal disturbance was being detected. The system was then subjected to the absolute deviation of the S-transform matrix. Analyzing diverse industry standards of dis-solved gas analysis [36] yields new defect features. To improve diagnosis accuracy, two effective data pre-processing methods are used. As fault classifiers, a least-square support vector machine, a support vector machine, and a support vector data description are constructed in experiments, and the best parameters of the three classifiers are found via particle-swarm optimization. A detailed comparison of the performance of threesupport vector machine-based classifiers is made for the first time in the field of dissolved gas analysis.
Through electromagnetic transient program (EMTP) simulations, a transient-based protection system is presented and evaluated [39]. The angle between the zero-sequence voltage and current phasors is estimated by the fault-detection technique. The estimation is performed at the dominating transient frequency of the network response within the initial milliseconds after the failure. The protection system's performance is assessed for a distribution network in both unearthed and compensated neutral scenarios using a Monte Carlo method in which fault resistance, incidence angle, and fault location variations are treated as random variables in EMTP simulations. The application of IEC 61850-9-2 LE-sampled values in transients-based protection by implementing a line-protection intelligent electronic device (IED) that can distinguish between internal and external faults by comparing the polarities of wavelet coefficients of the line currents at either end of the line is discussed in [43]. A real-time digital simulator is used to implement the power system portion. In IED implementations, special attention is paid to simulating the restrictions experienced by a real relay. The findings show that IEC 61850-sampled data can be employed effectively in a transients-based protection mechanism that can withstand extreme conditions. Fault diagnosis by a wavelet transform has been investigated in many research papers [47][48][49][50][51][52][53]. Adel Aktaibi et al. [30,38] introduce an implementation of d-q axis components and wavelet-packet-transform-based hybrid technique. It is based on high-frequency sub-band contents in the d-q axis components. Then, it required one level of the wavelet packet transform (WPT) for the synchronously rotating of frame components to discriminate inrush currents from all types of internal fault currents. The WPT based on the differential protective relay in paper [49] used Butterworth passive (BP) filters to distinguish the magnetizing inrush current and restrain the relay from the operation. The BP filters are designed to extract the second-level details consisting of high-frequency components of the three-phase differential current. In previous studies [50][51][52][53], the coefficients of the first scale from the discrete wavelet transform were compared to distinguish between external and internal defects in power transformers (DWT). To give comparison indicators to discern between external and internal faults, the maximum coefficient of distinct current phases (A, B, C) was divided by the zero-sequence differential current. The decision algorithm suggested in this paper can help distinguish between internal and exterior errors and provide better outcomes. DWT, on the other hand, may not be sufficient for a thorough characterization. To improve its effectiveness in power transformer protection, DWT's performance should be improved. Furthermore, to increase power transformer protection, artificial neural network techniques have been proposed in several of the approaches in the literature [7][8][9]. The comparison between different methodology and application that has been previously research can be summarize as shown in the literature survey in Table 1. Transient-stationary current model [44] DWT [54][55][56] Transformer Inrush current reduction Control switching strategies [1,4] Internal fault and inrush current discrimination Auto-correlation function based technique [6] Hyperbolic S-transform-based method [29] Internal fault detection Finite element [17,19] Internal and external faults detection Winding mechanical defects [47] DWT [50][51][52][53] Fault detection ANN [8,9,15,16,34] PNN [10] CNN [11,13,14] WT and PNN [12,18] DWT and BPNN [57] FRA diagnostics [20] Fuzzy logic [24][25][26]28,30] Fuzzy logic and ANFIS models [23] Fuzzy logic and BPNN [27] Hybrid support vector machine [31,36] Transient-stationary current model [37][38][39][40][41][42][43] Hybrid Grey Wolf Optimizer and LS-SVM [33,35] Deep learning [5] Machine learning [32] 3. Theory

Wavelet Transforms
A wavelet waveform has a short duration, a tiny waveform, and a specific shape (near zero). A wavelet transform is a tool that divides data, functions, or operators into frequency components and examines a resolution adjusted scale in each component. The analytical band can be fine-tuned with the wavelet transform to achieve precise measurements of lowand high-frequency components. The results of the wavelet transform are displayed in the time and frequency domains to expand signals using either time compression or dilation of a fixed wavelet function known as the mother wavelet. The signals are created by the mother wavelet stretching (scaling: a) or shrinking (shifting: k) of the wavelet itself as it moves along the time axis. A DWT signal analysis can choose from a variety of scales (m) and positions (k) for integrated wavelets, resulting in a signal at the scale of interest. The actual input signal is received when integrating the signal at all resolutions. As shown in Equation (1) [58,59], the wavelet transform scales the analytical results by a factor of two. where: n is the number of data points (integer); m is the scaling (integer); k is the shifting (integer); is the mother wavelet.
The mother wavelets, i.e., Daubechies (db), Symlets (sym), Biorthogonal (bior), and Coiflets (coif), were employed in the previous study paper [56] to examine the coefficient values and behaviors for fault classification in transmission line systems and transformers. As a result, Daubechies appears to be suitable for use in fault analysis, so Daubechies was chosen as the mother wavelet in this study.

Probabilistic Neural Network (PNN)
When the PNN was created in the 1960s, computing power and memory were both limited. The PNN is a neural network for pattern classification that is built using classical probability theory. It is a direct development of prior work with Bayesian classifiers. As shown in Figure 1, the PNN is made up of three layers of neurons (input, radial basis layer, and competitive layer) that are connected by weights. wavelet itself as it moves along the time axis. A DWT signal analysis can choose from a variety of scales (m) and positions (k) for integrated wavelets, resulting in a signal at the scale of interest. The actual input signal is received when integrating the signal at all resolutions. As shown in Equation (1) [58,59], the wavelet transform scales the analytical results by a factor of two.
where: n is the number of data points (integer); m is the scaling (integer); k is the shifting (integer); is the mother wavelet.
The mother wavelets, i.e., Daubechies (db), Symlets (sym), Biorthogonal (bior), and Coiflets (coif), were employed in the previous study paper [56] to examine the coefficient values and behaviors for fault classification in transmission line systems and transformers. As a result, Daubechies appears to be suitable for use in fault analysis, so Daubechies was chosen as the mother wavelet in this study.

Probabilistic Neural Network (PNN)
When the PNN was created in the 1960s, computing power and memory were both limited. The PNN is a neural network for pattern classification that is built using classical probability theory. It is a direct development of prior work with Bayesian classifiers. As shown in Figure 1, the PNN is made up of three layers of neurons (input, radial basis layer, and competitive layer) that are connected by weights. The PNN is trained in two stages: 1. Data are fed into the input layer, which is subsequently passed on to the radial basis layer. The distances between the input and weight vectors are calculated. Equation (2) [60] is used to generate the output values in the radial basis layer.
where: ϕ(p) is the output of the radial basis layer; p is the input pattern vector; IW1,1 is the center vector of the radial basis layer; is the spread constant for the radial basis layer (smoothing parameter). The PNN is trained in two stages: 1. Data are fed into the input layer, which is subsequently passed on to the radial basis layer. The distances between the input and weight vectors are calculated. Equation (2) [60] is used to generate the output values in the radial basis layer.
where: ϕ(p) is the output of the radial basis layer; p is the input pattern vector; IW 1,1 is the center vector of the radial basis layer; σ is the spread constant for the radial basis layer (smoothing parameter).
2. The radial basis layer's output values are transferred to the competitive layer, which associates a specific class with the net output value, which is a vector of probabilities. Finally, as shown in Equation (3) [60], a competitive activation function is applied to the net output of the competitive layer to calculate the maximum value of these probabilities, yielding a value of 1 for this class and 0 for the other classes.
where: f 2 is the function of competitive activation; LW 2,1 is the weight vector between radial basis and competitive layers.

Simulations
BCTRAN is a well-known ATP/EMTP subroutine for computing the primary and secondary windings in each phase of a two-winding, three-phase transformer. Bastard et al. [61] proposed modifying the BCTRAN subroutine to look at the transformer's inherent problems. In general, the BCTRAN represents a transformer with a 6 × 6 matrix of inductances, but under internal fault circumstances, the matrix is changed to 7 × 7 dimensions to incorporate winding to ground failures.
The following is a summary of the internal fault simulation procedure using the BCTRAN subroutine: First step: create 6 × 6 matrices (R) and (L) to depict the transformer based on the manufacturer's test data without taking into account internal faults.
Third step: by adding lumped capacitances to the transformer's terminals, the interwinding and earth capacitances of the HV and LV windings can be replicated [61].
After, at a sampling rate of 200 kHz, the ATP/EMTP program is used to replicate the fault's transient signal. Figure 2 [62] depicts the examined architecture as part of Thailand's power transmission and distribution infrastructure. To simulate all characteristics by a manufacturer setup, a 50 MVA, 115/23 kV, two-winding, three-phase transformer is utilized as a model as shown in Figure 3. The primary and secondary current waveforms are simulated using ATP/EMTP and interfaced to the MATLAB/Simulink program to construct the fault-diagnosis process. In Figures 4 and 5, the fault signals of the transformer primary and secondary currents are shown and correspond to the two protection zones. In the case of an internal fault condition, the primary and secondary current waveforms obtained for a winding to ground fault are shown in Figure 4, whereas cases of external faults are shown in Figure 5.   Figure 2, is a step-down transformer that connects two sub-transmission sections. The transformer simulation is carried out by altering the system parameter condition as follows: the angles of the voltage waveform in phase A at the instants of fault inception were 0-330° (in 30° steps). The fault positions of the internal winding faults in (a) are designated on any phase of the transformer windings (both primary and secondary) at lengths of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90%, measured from the line end of the windings. For the inter-turn faults, the position of point a on the transformer winding, as shown in (b), was varied at the length of 10%, 20%, 30%, 40%, 50%, 60%, 70%, and 80%, measured from the line end of the windings. For the inter-turn faults, the position of point b on the transformer winding, as shown in (b), was varied at the length of 10%, 20%, 30%, 40%, 50%, 60%, 70%, and 80% measured from the line end of the windings. The phase winding of the transformer with internal faults is separated into two portions in the event of winding to ground faults and three parts in the case of inter-turn faults, as shown in (b). (c) The capacitances are as follows: the stray capacitance between the high voltage winding and ground is Chg, the stray capacitance between the low voltage winding and ground is Clg, and the stray capacitance between the high voltage and low voltage winding is Chl.
In addition, external faults of the transformer (on transmission lines) are simulated with varied conditions as follows: The primary and secondary current waveforms are simulated using ATP/EMTP and interfaced to the MATLAB/Simulink program to construct the fault-diagnosis process. In Figures 4 and 5, the fault signals of the transformer primary and secondary currents are  Figure 2, is a step-down transformer that connects two sub-transmission sections. The transformer simulation is carried out by altering the system parameter condition as follows: the angles of the voltage waveform in phase A at the instants of fault inception were 0-330 • (in 30 • steps). The fault positions of the internal winding faults in (a) are designated on any phase of the transformer windings (both primary and secondary) at lengths of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90%, measured from the line end of the windings. For the inter-turn faults, the position of point a on the transformer winding, as shown in (b), was varied at the length of 10%, 20%, 30%, 40%, 50%, 60%, 70%, and 80%, measured from the line end of the windings. For the inter-turn faults, the position of point b on the transformer winding, as shown in (b), was varied at the length of 10%, 20%, 30%, 40%, 50%, 60%, 70%, and 80% measured from the line end of the windings. The phase winding of the transformer with internal faults is separated into two portions in the event of winding to ground faults and three parts in the case of inter-turn faults, as shown in (b). (c) The capacitances are as follows: the stray capacitance between the high voltage winding and ground is C hg , the stray capacitance between the low voltage winding and ground is C lg , and the stray capacitance between the high voltage and low voltage winding is C hl .
The primary and secondary current waveforms are simulated using ATP/EMTP and interfaced to the MATLAB/Simulink program to construct the fault-diagnosis process. In Figures 4 and 5, the fault signals of the transformer primary and secondary currents are shown and correspond to the two protection zones. In the case of an internal fault condition, the primary and secondary current waveforms obtained for a winding to ground fault are shown in Figure 4, whereas cases of external faults are shown in Figure 5.

Fault-Detection Algorithm
The differential currents are calculated from the simulated signals, and the resulting current signals are retrieved using the DWT, which is a subtraction of the primary current and the secondary current in all three phases and the zero sequence. The coefficients from each scale of DWT can be considered and used in fault detection through numerous trialand-error processes based on the differential current of all three phases.
The DWT is applied to the 1/4 cycle of current waveforms after the fault initiation, based on a trial-and-error procedure. To decompose the high-frequency components from the current signals, the Daubechies 4 (db4) mother wavelet [54][55][56][57] is used. The coefficients of the signals obtained from the DWT are squared and studied in each scale. As shown in Figures 6-8, when a fault develops, the coefficients of high-frequency components change abruptly compared to those before the fault occurs. This abrupt change is employed as a predictor of fault occurrence. Figure 6 depicts an internal fault at 20% of the winding length, while Figure 8 depicts an exterior fault at 20% of the transmission line length. The input signal is represented in Figure 6a on the top trace of the figure. As shown in Figure 6a, the input signal is a multisignal trace from each high-pass filter that corresponds to a certain scale parameter. Figures 6 and 7 indicate that the coefficients of high-frequency components change abruptly when a fault occurs compared to those before the fault occurs; yet, as shown in Figure 8, the coefficient in each scale of the DWT does not change.

Fault-Detection Algorithm
The differential currents are calculated from the simulated signals, and the resulting current signals are retrieved using the DWT, which is a subtraction of the primary current and the secondary current in all three phases and the zero sequence. The coefficients from each scale of DWT can be considered and used in fault detection through numerous trial-and-error processes based on the differential current of all three phases.
The DWT is applied to the 1/4 cycle of current waveforms after the fault initiation, based on a trial-and-error procedure. To decompose the high-frequency components from the current signals, the Daubechies 4 (db4) mother wavelet [54][55][56][57] is used. The coefficients of the signals obtained from the DWT are squared and studied in each scale. As shown in Figures 6-8, when a fault develops, the coefficients of high-frequency components change abruptly compared to those before the fault occurs. This abrupt change is employed as a predictor of fault occurrence. Figure 6 depicts an internal fault at 20% of the winding length, while Figure 8 depicts an exterior fault at 20% of the transmission line length. The input signal is represented in Figure 6a on the top trace of the figure. As shown in Figure 6a, the input signal is a multi-signal trace from each high-pass filter that corresponds to a certain scale parameter. Figures 6 and 7 indicate that the coefficients of high-frequency components change abruptly when a fault occurs compared to those before the fault occurs; yet, as shown in Figure 8, the coefficient in each scale of the DWT does not change.
employed as a predictor of fault occurrence. Figure 6 depicts an internal fault at 20% of the winding length, while Figure 8 depicts an exterior fault at 20% of the transmission line length. The input signal is represented in Figure 6a on the top trace of the figure. As shown in Figure 6a, the input signal is a multisignal trace from each high-pass filter that corresponds to a certain scale parameter. Figures 6 and 7 indicate that the coefficients of high-frequency components change abruptly when a fault occurs compared to those before the fault occurs; yet, as shown in Figure 8, the coefficient in each scale of the DWT does not change.  The similarity between the fault signals' waveforms from Figures 6 and 7 can be seen. The result obtained from the fault-detection algorithm presumes that these signals are in their fault condition. Figure 8 shows that the coefficient at each scale of the DWT does not change. Therefore, the result obtained from the fault-detection algorithm presumes that these signals are in their normal condition. Fault detection is necessary for the decision algorithm to detect and discriminate between the power transformer's internal and external faults. Thus, the classification of fault detection is considered. The coefficient in scale 1 from the DWT appears to be enough to indicate the fault inception, according to numerous simulations [50,51]. The coefficient in scale 1 from the DWT is utilized in many simulations [50,51] and appears to be sufficient to identify the occurrence of a fault; therefore, the coefficient in scale 1 is sufficient to train and test processes for the probabilistic neural network (PNN) without the higher-scale coefficients.

Decision Algorithm
The neural network toolboxes in MATLAB [60] are used to accomplish the training process. Table 2 shows how input datasets are standardized and separated into 162 sets for training and 90 sets for validation before the training process begins. The PNN's behavior can be significantly influenced by the input pattern. As a result, the goal of this study is to use an algorithm's input pattern to detect and distinguish between external  The similarity between the fault signals' waveforms from Figures 6 and 7 can be seen. The result obtained from the fault-detection algorithm presumes that these signals are in their fault condition. Figure 8 shows that the coefficient at each scale of the DWT does not change. Therefore, the result obtained from the fault-detection algorithm presumes that these signals are in their normal condition. Fault detection is necessary for the decision algorithm to detect and discriminate between the power transformer's internal and external faults. Thus, the classification of fault detection is considered. The coefficient in scale 1 from the DWT appears to be enough to indicate the fault inception, according to numerous simulations [50,51]. The coefficient in scale 1 from the DWT is utilized in many simulations [50,51] and appears to be sufficient to identify the occurrence of a fault; therefore, the coefficient in scale 1 is sufficient to train and test processes for the probabilistic neural network (PNN) without the higher-scale coefficients.

Decision Algorithm
The neural network toolboxes in MATLAB [60] are used to accomplish the training process. Table 2 shows how input datasets are standardized and separated into 162 sets The similarity between the fault signals' waveforms from Figures 6 and 7 can be seen. The result obtained from the fault-detection algorithm presumes that these signals are in their fault condition. Figure 8 shows that the coefficient at each scale of the DWT does not change. Therefore, the result obtained from the fault-detection algorithm presumes that these signals are in their normal condition. Fault detection is necessary for the decision algorithm to detect and discriminate between the power transformer's internal and external faults. Thus, the classification of fault detection is considered. The coefficient in scale 1 from the DWT appears to be enough to indicate the fault inception, according to numerous simulations [50,51]. The coefficient in scale 1 from the DWT is utilized in many simulations [50,51] and appears to be sufficient to identify the occurrence of a fault; therefore, the coefficient in scale 1 is sufficient to train and test processes for the probabilistic neural network (PNN) without the higher-scale coefficients.

Decision Algorithm
The neural network toolboxes in MATLAB [60] are used to accomplish the training process. Table 2 shows how input datasets are standardized and separated into 162 sets for training and 90 sets for validation before the training process begins. The PNN's behavior can be significantly influenced by the input pattern. As a result, the goal of this study is to use an algorithm's input pattern to detect and distinguish between external and internal power transformer failures. The maximal coefficients of the 1/4 cycle DWT are used as training input patterns. The PNN's output variables are labeled 1 or 2, referring to external and internal defects, respectively. The internal fault will occur if the PNN's output value is 1. If this output value is 2, on the other hand, an external error will occur. Case 1: The maximum DWT coefficients capable of detecting a fault. A PNN structure comprises four input neurons and one output neuron, while the radial basis layer has 162 neurons (the number of neurons is always equal to the number of training sets). The input patterns for post-fault differential current waveforms are the maximum coefficients details (cD1) from DWT in the first scale at the 1/4 cycle of phase A, B, C, and zero sequence, as illustrated in Figure 9.  A PNN structure comprises four input neurons and one output neuron, while the radial basis layer has 162 neurons (the number of neurons is always equal to the number of training sets). The input patterns for post-fault differential current waveforms are the maximum coefficients details (cD1) from DWT in the first scale at the 1/4 cycle of phase A, B, C, and zero sequence, as illustrated in Figure 9. Case 2: The maximum ratio attained using the DWT division method As illustrated in Figure 10a, the input patterns are the maximum ratio obtained from a division algorithm between the differential current coefficient from DWT and the zero sequence for post-fault differential current waveforms. In Figure 10b,c, a PNN structure consists of three neurons inputs and one neuron output, while the number of neurons in Case 2: The maximum ratio attained using the DWT division method As illustrated in Figure 10a, the input patterns are the maximum ratio obtained from a division algorithm between the differential current coefficient from DWT and the zero sequence for post-fault differential current waveforms. In Figure 10b,c, a PNN structure consists of three neurons inputs and one neuron output, while the number of neurons in the radial basis layer is 162 (owing to the fact that the number of neurons is always equal to the number of training sets).

Input
Radial Basis Layer Competitive Layer (c)  During the training process [8], a normalization method uses a z-score method that has a mean of 0 and a standard deviation of 1. The z-score measures the distance of a data point from the mean in terms of the standard deviation. The standardized dataset has a mean of 0 and a standard deviation of 1, and retains the shape properties of the original dataset (same skewness and kurtosis). The z-score of a value x is z = (x−µ) σ . The PNN begins with the random initial weight and increasing spread in the radial basis layer, Appl. Sci. 2021, 11, 10619 13 of 20 which corresponds to bias value (b = 0.8326 Spread ) from 0.0001 to 0.1. The increase step of 0.0001 is used to compute the number of minimum errors. This technique is repeated until the maximum number of spreads is reached or until the number of minimal errors equals zero, at which point the training is terminated. The training procedure is depicted in Figure 11 as a flowchart, and the training outcomes are shown in Table 3.
During the training process [8], a normalization method uses a z-score method that has a mean of 0 and a standard deviation of 1. The z-score measures the distance of a data point from the mean in terms of the standard deviation. The standardized dataset has a mean of 0 and a standard deviation of 1, and retains the shape properties of the original dataset (same skewness and kurtosis). The z-score of a value x is = ( ) . The PNN begins with the random initial weight and increasing spread in the radial basis layer, which corresponds to bias value ( = . ) from 0.0001 to 0.1. The increase step of 0.0001 is used to compute the number of minimum errors. This technique is repeated until the maximum number of spreads is reached or until the number of minimal errors equals zero, at which point the training is terminated. The training procedure is depicted in Figure 11 as a flowchart, and the training outcomes are shown in Table 3. Figure 11. Flowchart for the training process. Table 3. Results of the training procedure in comparison.

Comparison Information
Case 1 Case 2 Input neurons 4 3 Figure 11. Flowchart for the training process.  60 60 Following the training procedure, the decision algorithm is used to distinguish between the different types of power transformer faults. As demonstrated in Tables 4 and 5, case studies are modified in order to verify the decision algorithm's capabilities. The results have two studied cases. Each studied case has 84 sets. There are 54 sets for the internal winding fault (there are 27 sets for low-voltage winding and 27 sets for high-voltage winding) and 30 sets for the external short circuit (there are 15 sets for low-voltage winding and 15 sets for high-voltage winding). The average accuracy of defect detection from the decision method suggested in this research is highly satisfactory, according to the results. The fault-detection methods are compared between BPNN, PNN, and RBF, the latter of which are the currently used methods of fault detection. Each method is studied in two cases in the same set. The results in Tables 4 and 5 show the percentage of fault detection accuracy in each phase and coil distance. The average accuracies of internal winding faults in Table 4 are very close in value. Every method in every case has an accuracy of over 92.59%, most of which are up to 100%. When considering the accuracy of each method of detecting internal winding faults, it was found that PNN, BPNN, and RBF methods gave an accuracy of up to 98.15%, 98.15%, and 97.22%, respectively. The accuracy of the three methods was very similar. This supports that all three methods can be used to detect internal winding faults. For the external winding fault detection in Table 5, the results show that the RBF method has very little accuracy compared to the other methods, with an accuracy of 21.67%. In contrast, the BPNN and PNN methods have an accuracy of 91.67% and 95%, respectively. In this study, the results of external faults showed that the PNN method gave the greatest accuracy. Therefore, it is most suitable for use in detecting external faults compared to the above methods.
Finally, when analyzing the overall test results, including internal and external faults, it was found that the PNN method provided the most accurate fault detection. As shown in Figure 12, the detection accuracy result of the PNN method is up to 193.15% from 200%, while the BPNN and RBF methods have an overall accuracy of only 189.82% and 118.89%, respectively. Finally, when analyzing the overall test results, including internal and external faults, it was found that the PNN method provided the most accurate fault detection. As shown in Figure 12, the detection accuracy result of the PNN method is up to 193.15% from 200%, while the BPNN and RBF methods have an overall accuracy of only 189.82% and 118.89%, respectively. In a comparison of the detection methods in Figure 13, the sum of detection accuracy between internal and external faults in each detection method is compared. The results show the percentage of accuracy in detecting internal and external faults and the sum of those percentage values for each detection method. The PNN method is the most accurate in both internal and external fault detection, providing an internal fault accuracy of 98.15% and an external fault accuracy of 95%. The sum of percentage accuracy is 193.15% of 200%.
Subsequently, the accuracy of the PNN method was determined in each case of the fault-detection methods consisting of the maximum coefficient algorithm (Case 1) and the maximum ratio algorithm (Case 2), as shown in Figure 13. The maximum coefficients algorithm of the PNN method provides the highest accuracy, providing an overall accuracy of 196.67% of 200%, divided into the internal fault detection accuracy within 100% and the external fault detection accuracy within 96.67%. While the maximum ratio algorithm provides an accurate analysis of the PNN and BPNN methods that are closely related, the BPNN method is slightly greater. The overall accuracy of the BPNN method is 191.49%, and the PNN method is 189.63%. The external fault detection accuracy of the PNN and BPNN methods are the same, 93.34%, while the internal fault detection accuracy of the BPNN method is 98.15%, and the PNN method is 96.30%. Therefore, from the analysis of all the test results, the PNN method is most suitable for detecting internal and external faults, and the maximum coefficient algorithm is the most effective in detecting faults. In a comparison of the detection methods in Figure 13

Conclusions
This study investigates a new technique for detecting and distinguishing external and internal power transformer defects. This method, which uses a mix of DWT and PNN, has been presented. The DWT has been used to deconstruct high-frequency fault signal components. To compare the DWT maximum coefficient and the maximum ratio of the division algorithm, the PNN was divided into two training cases. In various circumstances, different fault kinds and locations on both the main and secondary sides of the power transformer are considered. The average accuracy of the DWT maximum coefficient cases is more than 96.67 percent, which is more satisfactory. The simulation results demonstrated that the PNN and BPNN are effectively implemented and perform fault detection with satisfactory accuracy. The PNN method's maximum coefficients algorithm has the highest accuracy, with an internal fault detection accuracy of 100 percent and external fault detection accuracy of 96.67 percent. The maximum ratio technique gives an accurate analysis of the nearly comparable PNN and BPNN approaches; the BPNN method is significantly greater. The BPNN method has a 191.49 percent overall accuracy, while the PNN approach has a 189.63 percent overall accuracy. External fault detection accuracy is 93.34 percent for both the PNN and BPNN approaches, while internal fault detection accuracy is 98.15 percent for the BPNN method and 96.30 percent for the PNN method. However, the PNN method is most suitable for detecting internal and external faults, and the maximum coefficient algorithm is the most effective at detecting the fault. Although the suggested approach produces satisfactory results, the overall accuracy indi- Subsequently, the accuracy of the PNN method was determined in each case of the fault-detection methods consisting of the maximum coefficient algorithm (Case 1) and the maximum ratio algorithm (Case 2), as shown in Figure 13. The maximum coefficients algorithm of the PNN method provides the highest accuracy, providing an overall accuracy of 196.67% of 200%, divided into the internal fault detection accuracy within 100% and the external fault detection accuracy within 96.67%. While the maximum ratio algorithm provides an accurate analysis of the PNN and BPNN methods that are closely related, the BPNN method is slightly greater. The overall accuracy of the BPNN method is 191.49%, and the PNN method is 189.63%. The external fault detection accuracy of the PNN and BPNN methods are the same, 93.34%, while the internal fault detection accuracy of the BPNN method is 98.15%, and the PNN method is 96.30%. Therefore, from the analysis of all the test results, the PNN method is most suitable for detecting internal and external faults, and the maximum coefficient algorithm is the most effective in detecting faults.

Conclusions
This study investigates a new technique for detecting and distinguishing external and internal power transformer defects. This method, which uses a mix of DWT and PNN, has been presented. The DWT has been used to deconstruct high-frequency fault signal components. To compare the DWT maximum coefficient and the maximum ratio of the division algorithm, the PNN was divided into two training cases. In various circumstances, different fault kinds and locations on both the main and secondary sides of the power transformer are considered. The average accuracy of the DWT maximum coefficient cases is more than 96.67 percent, which is more satisfactory. The simulation results demonstrated that the PNN and BPNN are effectively implemented and perform fault detection with satisfactory accuracy. The PNN method's maximum coefficients algorithm has the highest accuracy, with an internal fault detection accuracy of 100 percent and external fault detection accuracy of 96.67 percent. The maximum ratio technique gives an accurate analysis of the nearly comparable PNN and BPNN approaches; the BPNN method is significantly greater. The BPNN method has a 191.49 percent overall accuracy, while the PNN approach has a 189.63 percent overall accuracy. External fault detection accuracy is 93.34 percent for both the PNN and BPNN approaches, while internal fault detection accuracy is 98.15 percent for the BPNN method and 96.30 percent for the PNN method. However, the PNN method is most suitable for detecting internal and external faults, and the maximum coefficient algorithm is the most effective at detecting the fault. Although the suggested approach produces satisfactory results, the overall accuracy indicates that it has to be improved in order to attain higher precision. This strategy, on the other hand, will be useful in the power transformer's differential protection scheme. The method will be improved in the future so that the transformer's magnetizing inrush current can be determined.