Support Vector Machine Parameters Optimization for 500 kV Long OHTL Fault Diagnosis

Faults can seriously damage high-voltage (HV) power systems, particularly if they occur on the long overhead transmission line (OHTL) that connects the nuclear power plant (NPP) to the electrical grid. Finding OHTL problems quickly and accurately is essential for the economy, safety, and dependability of the HV power systems. It is essential to pinpoint the problematic phase to avoid unneeded power outages. Thus, one of the most crucial research challenges is now how to identify, classify, and locate OHTL faults. In this study, transient current with high frequency oscillations that arise immediately after a defect at the sending end is investigated in a single-circuit, single-side fed Egyptian 500-kV HV long OHTL. Asymmetric and symmetric faults and locations are also represented in the Alternative Transients Program-Electro Magnetic Transients Program (ATP/EMTP) simulation model under varying fault resistance and inception angles. The proposed solution in this paper is an Optimized Support Vector Machine (OSVM), whose characteristics are optimized via a mutant particle swarm optimization (MPSO) method to detect 500 kV long OHTL faults. The localizer model is also built for practical applications, including power system noise contaminating fault signals. The findings prove that the suggested approach locates the fault in 0.012 seconds from the start of the event, with a 0.0098 percent average percentage error, and without being impacted by differences in fault distance, fault resistance, noise, or fault inception angle. Additionally, the optimised classifier reaches a 99.85% accuracy rate, enhancing line system dependability and advancing nuclear system development.


I. INTRODUCTION
The transmission network, which carries power over great distances from generators to load sites, is a high voltage network [1]. Long transmission systems cover many kilometres and are frequently vulnerable to various failures. Short circuits between the lines and with the ground frequently result from environmental restrictions like storms, snow, etc. as well as other tiny but natural concerns like animals, birds, The associate editor coordinating the review of this manuscript and approving it for publication was Tariq Masood . and even increasing vegetation problems [2]. These result in transmission lines having minor to major failures. According to statistics, line failures are the most typical fault in electrical systems [3]. Therefore, it is crucial to identify it and pinpoint its position in order to implement the appropriate corrective measures and quickly restore electricity. Numerous studies on the various methods for precise fault location identification have been done over time. Numerous approaches that employ line data from one or more terminals to pinpoint the site of faults fall into the categories of analytical methods, methods based on artificial intelligence (AI), methods using magnetic VOLUME 11, 2023 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ sensors, methods using travelling waves, and methods based on software [4], [5], [6], [7]. The writers of Reference [8] give an in-depth analysis of the various fault location techniques, along with the advantages and disadvantages associated with each of them. The classification of a fault is essential for locating the defective line and isolating it to prevent harm to the linked equipment as well as avoidable power draining. Removing faults is essential to restoring system stability early and avoiding prolonged power outages [9]. Relays and other faultfinding devices feed real-time fault data, such as voltage, current, frequency, and power factor, to various protection [9].
Short circuits often occur in transmission lines between other lines or between other lines and land as they cross a variety of terrains. These flaws frequently have a permanent character and need to be fixed manually. To help workers identify the root of a problem and quickly locate it, an accurate prediction of the fault location is crucial. This facilitates the speedy elimination of the fault-causing component and the return of normal power flow. Additionally, the presence of OHTL noise complicates the operation by injecting harmonics into the system [10].
Numerous scholars have investigated various approaches for fault analysis [8]. The proposed study uses an optimized support vector machine to find transmission line defects (OSVM). The use of OSVM makes it possible to compute fault features more easily, quickly, and accurately by reducing the dimension of these electrical parameters. Additionally, OSVM is incredibly helpful in handling noisy data. A vast and distributed dataset's principal direction of variation are the only ones that OSVM can pinpoint. As a result, it decreases the effect of noise's randomness, making MPSO-SVM more acceptable for use in a noisy medium like the OHTL.
Using recorded data from the line and digital signal processing, a new, extremely accurate method for fault location is presented in this work. The ATP/EMTP is used to simulate a real 200 km 500 kV OHTL one circuit in Egypt. These signals are then analysed using SVD in fraction domain to create SVD-based fault signals. To make the process more useful, OHTL noise is also added into the current signals. First, the faults are categorised, then they are located.
Using the three-phase SVD, each fault feature is extracted, that has been gathered at 19 intermediate geometric sites along the 200 km transmission line for various fault classes. One of the 19 sites serve as the training set for the localizer algorithm, and the remaining 18 serve as the basis for the test set. The support vector machine's penalty parameter c and δ kernel parameter are crucial for the accuracy of the diagnosis and must be properly predetermined. As a result, the mutant particle swarm optimization-support vector machine model (MPSO-SVM) is created, in which the particle swarm method determines the best values for the support vector machine's parameters c and δ. As a result, the OSVM with mutant particle swarm optimization is a wonderful opportunity for applications involving defect identification and localization.

A. RELATED WORK
The defective phase or phases in a power transmission network must be removed in order to restore system stability. Researchers have developed numerous computational techniques for fault diagnosis [11], [12].
Well-known methods have been used to diagnose faults such as impedance-based methods, traveling wave-based algorithms, and state estimation-based approaches. The authors surveyed different fault detection methods, including their pros. and cons. The transient patterns of voltage and current are used to determine the fault distance in transient-based fault location methods. Moreover, in comparison to prior impedance-based approaches, a fault location methodology was proposed that uses both the peak time and amplitude of the fault current at the local place with reasonable accuracy and speed [11], [12].
The use of extreme learning machines (ELMs)-powered neural networks for analysis is one of the most recent advancements in this field [13], [14]. Wavelet Transform (WT) has played a significant role in many studies of fault analysis as a traditional method for fault signal analysis, even when incorporating modern compensating devices [15]. The fuzzy inference system [16] as well as the (ANFIS) model, a hybrid model combining wavelet analysis [17], and neural networks, which are widely used as a primary analytical technique alone, is another helpful tool for fault analysis. This hybrid model has frequently been supplemented by WT analysis in order to develop wavelet-based ANFIS models and as a helpful method of thorough examination [18]. (SVM) has also been used in various studies relevant to power system protection algorithms as a key standalone method of research [19].
Even though SVM-based algorithms are very popular for fault analysis as well, noise contamination might cause them to require extensive training [11], [12].
While [26] authors offer a method for fault diagnosis intended for busbar zone protection, [27] authors also study faults in OHTL with multiple sources connected to the system. As shown by the authors of [28], who supplied polynomial and Gaussian radial basis function (RBF), or [29], who used dyadic WT-based SVM for fault classification, wavelet and SVM are widely used to develop potent hybrid models.
The development of fault analysis strategies can also be aided by a number of additional techniques. In view of this, a precise method created using MPSO-SVM for locating and identifying OHTL faults. This technology was regarded as a low cost, high precision solution because it only sending side transient current for fault detection and classification. Due to its directed sensitivity toward the higher as well as significant fluctuations of data and low sensitivity toward noise, the MPSO-SVM statistical technique has been proven to be quite useful in various fault studies, and more so in the field of OHTL analysis.
The previous techniques are quite successful, but they suffer from being caught in local optima and also have a very long time requirement. A better approach is proposed to address these difficulties. The mutant particle swarm optimization (MPSO) approach has been devised, which removes the worst particle by randomly generating a mutant particle and utilizing the best components of traditional PSO. The mutant particle attempts to avoid the other particle at the local optima. Moreover, the MPSO has easy implementation, high precision, and fast convergence.

B. MOTIVATION AND CONTRIBUTIONS
Recently, SVM has made outstanding progress in a variety of study fields, including face recognition, signal processing, and fault diagnosis. Additionally, because SVM-based classifiers' effectiveness is independent of the number of features, they offer higher generalisation qualities than ANN-based classifiers. Since there are an infinite number of features in our situation, this characteristic is excellent for fault diagnosis because it enables computation using the original data without first processing it to extract the features. The support vector machine's penalty parameter c and γ kernel parameter are critical for the accuracy of the diagnosis and must be properly specified. As a result, MPSO-SVM is created, in which the particle swarm method determines the ideal parameters for the support vector machine. Therefore, the SVM with MPSO is a viable choice for fault detection and tracking. The significant contributions of this study are as follows: • This paper proposes an improved support vector machine (SVM) for 500 kV long OHTL fault diagnosis with parameters optimized by a mutant particle swarm optimization (MPSO). A MPSO-based approach is proposed in order to improve the classification accuracy and training time of the SVM classifier.
• The ATP/EMTP is used to simulate an Egyptian 500kV OHTL that is fed to our proposed method.
• The DFRFT (Discrete Fractional Fourier Transform) retrieves characteristics from an ATP/EMTP current waveform. The DFRFT transforms the processed current signal's spatial and frequency domains. To improve classification performance, it is important to manage the varied fractional power characteristics of the current signal across the spatial-frequency domain.
• Singular Vector Decomposition (SVD) recovers the key features by extracting the most significant singular value from each phase. This feature reduction aids in decreasing the classifier's processing time, which is appropriate for real-time applications.
• The SVM's kernel function is chosen to be the Gaussian radial basis function. The MPSO utilised to determine the kernel parameter and penalty parameter because they are closely related to the accuracy of the fault diagnosis model.
• After that, based on the output current signal training patterns created in the previous phases, faults are identified, categorised, and traced using the OSVM approach.
• The performance of the OSVM is examined under different fault situations (noise, fault resistances (R) and inception angles (⊖)). The structure of paper is as follows: Section II describes the system model, namely, Egyptian 500kV OHTL, load, and faults. Section III. Presents the analysis of 500 kV OHTL fault signals. Section IV highlights the concepts of DFRFT, SVD and SVM schemes. The proposed fault diagnosis algorithm for the system under study is discussed in Section V. The simulated results are illustrated in Section VI. Finally, Section VII summarizes the paper. Figure 1 shows the nuclear power unit connected to the power grid via 200 km 500 kV transmission line single circuit. The system capacity is 1250 MVA, and the load of the plant is 425 MVA [30], [31].

II. 500-kV OHTL SINGLE CIRCUIT DESCRIPTION AND COMPONENTS MODELING
A three-phase set of 50 Hz sinusoids with maximum values of 500 A, and 289 kV defines the phase current and voltage Eq. (2).
Due to the enormous impact on transmission line components under various faults, it is necessary to either correctly measured the behaviour or dependably predict it using simulations. These performances depend for precise system component modelling. As a result, a single circuit for a 200 km long 500 kV OHTL in Egypt is implemented in this part employing high frequency model components using ATP-EMTP.

B. 500 kV OHTL MODELING
The OHTL used in this work is shown in Fig. 2. LCC JMarti model was used to simulate the OHTL under identification of diameter and sag of 500kV Transmission Line shown in Table 1 [7], [34]. Figure 3 depicts a typical grounding scheme for a tower with four parallel legs. Each leg has a vertical rod with a length of (1.5 m) and radius of (1.25 cm), and the mutual impedance between the vertical rods and horizontal grounding conductors is not considered because of the large spacing between them. The soil parameters such as ρ are taken as 100 .m, εr and µr are taken as 10 and 1, respectively [7]. To obtain an accurate performance from the grounding rod, the nonlinear behaviour of the rod's ground resistance is taken into consideration.   The ground resistance is calculated based on Eq. (2) [7], [35], [36]. Where R(t) is in and given by:

C. TOWER GROUND SYSTEM MODELING
where, i is the current through the rod (kA), E 0 is the critical soil ionization gradient (in this study is taken as 350 kV/m as a case study). The constant resistance R o ( ) of the model is based on the rod dimensions and the soil parameters [37].

D. RECEIVING END SYSTEM MODELING
The load can be easily modelled by a standard component RLCY3 as a Three-Phase Grounded-Wye with R, L parameters R = 800 and L = 5 mH.

E. ASYMMETRIC, SYMMETRIC FAULTS MODELING
Asymmetric and symmetric faults are subdivided into two categories based on the types shown in Fig. 4 [11]. Asymmetric faults include single phase to ground faults (LG), two phase faults (LL), and two-phase faults to ground (LL-G). On the other side, symmetric faults also include three-phase faults such three-phase short circuit (LLL) and three-phase short circuit to ground (LLL-G). Short-circuit conditions are recreated as a time-controlled switch with resistance in ATPDraw to examine the effects of different fault inception angles and fault resistances.     Fig. 6 shows the three-phase current waveforms at that location. For the system phases and a 10 fault resistance, these faults are applied at a 90 • angle. Figure 7 shows the sending side signals under different location (with fault resistance=10 , Inception Angle =90 • and fault location= (10 km, 100 km, 190 km) for the onephase (a) to ground fault. It is obvious that the faulted phase current signal peak reduced from 14 kA to 650 A to 500 A by about 96%. Figure 8 shows the sending end signals under different R (with R = (1 , 25 , 50 ), Inception Angle = 0 • and fault location = 10 km for the one-phase (a) to ground fault. It is clear that the faulted phase current amplitude reduced from 7500 A to 4380 A by about 42%. Figure 9 show the sending end signals under different inception angle (with fault resistance = 20 , Inception

IV. FRFT, SVD, AND SVM OVERVIEW
Since they are used in our suggested fault diagnosis technique, FRFT, SVD, and SVM schemes will be briefly covered in this section.

A. FRACTIONAL FOURIER TRANSFORM (FRFT)
N. Victor [38] proposed the FRFT, which generalises the Fourier Transform (FT). FT determines the spectral content of a signal, not the timing of the spectral components [39]. Signals in the time-frequency domain are rotated by the FRFT method. As a result, the FRFT can convert a signal x (t) to X α (u), which is represented in a intermediate domain between time and frequency. Let x (t) be a sampled periodic signal with a period 0 . The αth order DFRFT of x(t) can be mathematically expressed as follows [39].
where, where N is the number of points and k = 0,1, 2, . . ...N of DFRFT matrix as diagonal elements. The coefficients of the DFRFT are determined by a fractional factor (α) ranging from 0 to 1 [22]. Therefore, in the suggested method, we choose eigenvector DFRFT as a feature extractor because of its superior advantages (with a factor between 0 and 1).

B. SINGULAR VALUE DECOMPOSITION (SVD)
A matrix factorization method known as singular value decomposition (SVD) is extremely helpful for a variety of tasks such as pattern recognition, data dimension reduction, matrix approximation, pseudo inverse computation, and solving linear equations. SVD has been successfully applied to signal processing as a data processing method and has been shown to be successful in preventing modal aliasing. Any matrix may be divided into three matrices as follows: where UU' = 1 and VV' = 1, which are referred to as the left and right singular vectors, respectively, and U and V are unitary matrices. The singular values of A, which are determined by determining the eigenvalues of AA', are represented by the diagonal matrix S. It has the following representation: where ρ is the rank of the matrix A. Note that s 1 >s 2 >. . . >s ρ , i.e., s 1 is the largest singular value. SVD has a dimension-reduction method since it may characterise the feature matrix as a collection of values (singular values). High stability is also present for the single values. In other words, as the feature matrix element changes, the single values do not significantly vary.

C. SUPPORT VECTOR MACHINE (SVM)
As a hypothesis space for linear functions, SVM systems use a high dimensional feature space. Statistical learning theoryderived learning biases are incorporated into the learning algorithm used to train the SVM [41], [42], [43]. The training set's class boundary must be maximised to obtain the ideal separation hyperplane. This hyperplane deceit at the boundary's midway and must subject to the constrains: Minimze : Subject to the constrains: y i (w.
The dual form solution is used to computationally solve the optimization issue.
where the kernel function is K (x i , x j ). The radial basis function (RBF) employed in this study is where γ and C are, respectively, the kernel and penalty parameters.

V. THE PROPOSED OPTIMIZATION TECHNIQUE
It is obvious that local minima present challenges for the conventional PSO [43], [44], [45]. A new modification to the traditional PSO is proposed as a solution to the fault diagnostic issues raised in this study. At the outset of this subsection, a PSO overview is provided. In order to fulfil its needs in the search space, PSO draws its inspiration from social and cooperative behaviors that many species display [46]. This algorithm determines the next spots in the search based on the current movement of the particles, Personal Experience (PE), Aggregate Experience (AG), and other factors. The initial population (swarm) of size N and dimension D is denoted where T denotes the transpose operator. Each individual particle Y P (p = 1,2, . . ., N ) is given as Y P = [Y p , 1 , Y p , 2 , . . ., Y p , M ] T . Also, the initial velocity of the population is denoted as S = [S 1 , S 2 , S 3 ] T . Thus, the velocity of each particle Y P (p = 1,2, . . ., N ) is given as S p = [S p , 1 , S p , 2 , . . ., S p , M ]. The index p varies from 1 to N whereas the index varies from 1 to M . The two equations below can be used to mathematically express the updated positions of each particle in the search space for classical PSO: where a 1 and a 2 are two acceleration factors, b 1 and b 2 are two randomly generated values between [0, 1], whereas w represents the inertia weight of the population's current movement. The best individual in the population up to iteration n is represented by AG n p,r , whereas the best individual in the population as a whole is represented by PE n p,r , which stands for the best r th component of the p th individual personally. Each particle's starting location is represented by their initial PE, while the initial AG represents the initial optimal particle position within the randomly started population.
where ψ (Y ) is the objective function subject to minimization. Until a stop condition is satisfied, such as the predetermined number of iterations, the updating procedure should be restarted. After finishing, the PSO algorithm's AG n and ψ (AG n ) are provided as the solution. As is evident, the capacity of the particles to converge towards the closest optimal point as a consequence of the value of inertia weight being smaller than 1 makes the PSO convergence quicker than many swarm intelligence algorithms (between 0.4 and 0.9). Each particle's velocity in the search space decreases when this factor is present. Because each particle is unable to significantly modify its position after a given number of iterations, their velocity decreases and they become caught in a local optimum. The worst particles are planned to be replaced with MPSO in order to increase each particle's velocity vector and enable large thrusts that will drive the particles away from the local optimum. The suggested MPSO swaps out the worst particle for a mutant-particle created at random by choosing one or more PE components from some or all the conventional PSO's particles. A vector with the same size as every particle, the mutant particle is known as MP. The following MP may VOLUME 11, 2023 be produced for a population of size N×M, where N is the swarm size and M is the dimension of each particle: For r = 1:M MP n = PE (Rand(N ,1), r) End where rand(N,1) is a function that produces an integer in the range of 0 and N evenly. Thus, a total of M integers is created in the for-loop above, and the appropriate component from each column is chosen from matrix PE to build a vector called MP.
This paper proposes Parameters optimization of support vector machine for diagnosis of 500 kV long OHTL faults. Fig. 10 depicts the general organization of an optimized SVM employing MPSO parameter selection.
It can be noted that the proposed approach is fed by the outed features of SVD. Its input consists of the maximum value of diagonal S of the SVD of three currents from each phase, which is then normalized. With the input data represented as two sets of vectors in an n-dimensional space, an SVM will create a separating hyperplane in that space that maximizes the margin between the two data sets. To compute the margin, two parallel hyperplanes created, which are then superimposed on the two sets of data. Intuitively, the hyperplane with the greatest distance to the neighboring data points of both classes achieves a good separation. The expectation is that the generalization error of the classifier will decrease with increasing the margin or gap between these parallel hyperplanes.
The SVM model is trained using the SRM to reduce any potential training error. C and γ are controlled by the suggested mutant PSO, which may result in training error improvement. The most suited parameters are those that have the fewest errors in regulation. The SVM model is retrained using the optimal SVM parameters. When a certain number of iterations has been achieved, training is terminated. Following the training stage, the MPSO-SVM classifier is prepared to recognize the new samples in the testing stage. The output of this enhanced SVM classifier is five fault types (LG, LL, LL-G, LLL, LLL-G). The proposed MPSO-SVM flowchart for diagnosing 500 kV long OHTL faults is shown Fig.11.
The parameters of support vector machines (SVMs), such as kernel parameters and the penalty parameter, have a great influence on the accuracy and complexity of the classification models. The previous techniques are quite successful, but they suffer from being caught in local optima and also have a very long time requirement. A better approach is proposed to address these difficulties. The mutant particle swarm optimization (Mutant-PSO) approach has been devised, which removes the worst particle by generating a mutant particle at random and utilizing the personal best components of traditional PSO. The mutant particle attempts to avoid the other particle at the local optima. In order to diagnose fault types in OHTL, the suggested Mutant-PSO is used to optimize SVM parameters. The proposed algorithm's efficiency and reliability have been shown under different fault situations (noise, fault resistances (R) and inception angles (⊖)).
Our next objective is to identify the fault type once the faulty phases have been identified; at this point, the OSVM classifier is turned on. There are two stages to the fault classification method that is suggested. In the first, features are extracted using FRFT, then reduced using SVD, and in the second, features are classified using an OSVM classifier. One feature for each phase is derived from the maximum singular value of each fault state in the first stage previously discussed. The maximum singular value of the FRFT for just one phase yields one feature.

A. NOISE IMMUNITY OF THE PROPOSED ALGORITHM
The popular disturbance occurs on transmission line is corona noise. The fault signals have been combined with Gaussian white noise to create noise-contaminated fault signals. By adjusting the SNR level, the fault waveform noise level can also be adjusted in four steps. A more significant point is that the proposed model is assessed at a high noise level of 15 dB SNR, which is higher than the typical noise level used in most research. The impact of this undesirable noise is considered even when variations in fault type, location, and fault resistance occur concurrently. FRFT creates a signal's intermediate time-frequency representations. SVD has a dimension reduction strategy because it expresses the feature matrix as a collection of singular values. Additionally, the singular values are stable. The maximum SVD of the FRFT for a single phase yields a single feature (max value S matrix). Three features are chosen for each fault state in OHTL. FRFT-SVD thus eliminates the impact of noise on discrimination. In this work, the noise immunity property is also studied. A comparison of the maximum Singular value for direct standardized fault signals and that of its filtered form is shown in Tables 2-6. The observations demonstrate that filtering has no discernible impact on the FRFT-SVD algorithm's results as there is no noticeable change in the magnitudes of max Singular value. Using the suggested FRFT-SVD based fault analyzer has this as a major benefit. By doing away with the need for filtering, FRFT-SVD can lessen the computational load. SNR is varied for this purpose to observe the variation in max Singular value, and the proposed algorithm is then run under more challenging conditions with higher noise levels. The maximum single values in Tables 2-6 show how the results of analyzing the filtered and unfiltered signals using maximum singular value are extremely similar. Filtering thus becomes unnecessary at max Singular value, saving vital computation and processing time. This demonstrates the inherent ability of FRFT-SVD to largely ignore the effect of noise.

B. RESULTS OF MPSO-SVM CLASSIFIER
Results of a 500 kV Long OHTL Faults diagnosis using an SVM classifier are shown in Table 7 both before and after using MPSO parameter selection. Table 7 shows that the SVM without optimization achieves a classification accuracy of 90.14%. The regularization parameter C is set to 1000 in this instance, and the parameter is set to 0.4. After the MPSO is used to optimize the SVM classifier's parameters, this result is significantly improved, reaching 99.85%. Using the suggested mutant PSO, the SVM classifier's C and optimum values are 887and 8.19, respectively. As shown in Table 7, the training time of the MPSO-based SVM is also about 200 times (0.015 s) shorter than that of the SVM without (2.38 s), which is another interesting finding.

C. FAULT DETECTION USING MPSO-SVM
The main goal is to determine exactly which 500 kV long OHTL is faulty or unfaulty. To accomplish this, the MPSO-SVM classifier is fed training data derived from DFRFT and SVD. The proposed method for classifying faults consists of two steps. Feature extraction done first via DFRFT followed by reduction via SVD, and the second is classification via MPSO-SVM. In the mentioned above, one feature for each phase is obtained from the maximum singular value of DFRFT for each fault state. One feature is obtained from VOLUME 11, 2023     the maximum singular value of DFRFT for one phase only. For 500 kV long OHTL, 3 features are extracted for each fault state. Therefore, the size of the feature vector, which consists of three-phase transient current characteristics, has    The features of the DFRFT spectrum for a real signal are conjugated symmetric, i.e., the first half of the DFRFT spectrum is a mirrored conjugate to the second half. Hence, the features can be determined based on only one half of the DFRFT spectrum. This will reduce the complexity and save a lot of time. DFRFT and SVD provide optimal representation of signals by packing most of the information in a few coefficients for a given signal. The MLP and ELMAN take a lot of time because the computations are difficult and   time-consuming, and the proper functioning of the model depends on the quality of the training data. If the model does  not work properly, generalization problems arise. As shown in the above Figs. 11, and 12, utilizing MPSO-SVM, the better results were attained, which achieved 98.85 % performance levels and required less training time than the others since MPSO-SVM is trained using only support vectors rather than the entire training data set. As a result, MPSO-SVM is the optimal choice for classification tasks. While the MPSO-SVM has the best classification performance, these results could have been obtained by chance. A second validation test is required to evaluate the MPSO-SVM classifier's results. Table 8 summarizes the results of the 10-fold cross-validation test. The dataset is randomly divided into ten exclusive subsets of approximately equal size for 10-fold cross-validation, and the proposed method is repeated ten times. Each time, one of the ten subsets is used as the test set, while the remaining nine are combined to form the training set. The average percentage error across all five trials is then calculated. It is irrelevant how the data is divided in this method. Each data point appears exactly once in a test set VOLUME 11, 2023    and four times in a training set. As illustrated in Table 8, all fault types are correctly classified.

D. MPSO-SVM BASED FAULT TRACKING
When the MPSO-SVM classifier identifies the long transmission line faulty phases, our next objective of determining the fault distance to the sending side is initiated. Using inputs that contain data on three-phase current, the MPSO-SVM tries to determine the precise position of the fault. Numerous fault types have been considered, including LG, LL, LL-G, LLL, and LLL-G. An SVM was trained and tested using data corresponding to faults occurring at various points along the 200 km long OHTL (approximately 19 data points for each case). Additionally, the resistance and inception angles of faults are altered to demonstrate the SVM's performance under various operating conditions. After determining the fault types, the MPSO-SVM were used to predict the locations of LG, LL, LL-G, LLL, and LLL-G faults, respectively. The distinct high-frequency characteristics of each type of fault were determined using DFRFT and SVD and were then used in the second step of the algorithm to obtain the corrected location of the fault. The test case-specific estimation error was determined by looking at the results for each test case. This error, which gauges the accuracy of the method, was quantified as the difference between the estimated fault location (A) and the actual fault location (B) for the test instance. The greatest estimation error over the entire length range of the OHTL for all possible fault types can be characterized as the overall accuracy, E, expressed as a percentage of the total OHTL length (L).
Tables 9-13 illustrate the testing results, which demonstrate that in the worst-case situation, the greatest percentage inaccuracy in identifying the issue is restricted to (0.00085% of L) kilometres. The highest estimating mistakes occur at the receiving end of the closest spots on the line. Furthermore, various fault resistances R s are evaluated to assess the performance MPSO-SVM under a variety of operating scenarios. Tables 14-18 show the actual and expected locations  of faults with different fault resistances at (R=10 , R=50 , R=100 , R=150 , and R=200 , respectively). The worst situation was discovered at R=200 is restricted to 0.00092%. As seen in the tables, variable fault resistance levels have no influence on correct fault location categorization. Tables 19  show the  and O=90 o at the cable receiving end, the highest error (0.00098%) in fault location occurs (190 km). The simulation findings show that MPSO-SVM coupled with FRFT and SVD is an effective approach for identifying faults in a realistic for Diagnosis of 500 kV Long OHTL Faults. Under various settings, the suggested approach may conveniently, rapidly, and precisely locate the fault site.

VII. CONCLUSION
For fault classification and location in a three-phase, 200Km long, 500-kV OHTL single circuit system in Egypt, the mutant particle swarm optimization (MPSO) method is utilised to optimise the parameters of a support vector machine (SVM). For the purpose of feeding this information into our proposed technique, the ATP/EMTP simulator first models a variety of fault types with varied locations and parameters. Then, by combining FRFT with SVD, MPSO-SVM, and fault classification with SVD, the suggested technique optimised the performances of fault classification, location, and execution time, respectively. The proposed strategy performed better than previous methods in simulations when it came to accurately (maximum error between MPSO-SVM output and actual output is 0.00098 %), rapidly (0.012 s), and efficiently detecting, classifying, and tracking faults. Thus, in general, the proposed method has all the opportunity to become an efficient way for predicting the distance to a fault, which may help in the creation of a reliable transient-based power system protection strategy. Finally, there are many other scenarios like CT saturation, switching conditions, external faults etc. that can be considered.