Fault Detection in HVDC System with Gray Wolf Optimization Algorithm Based on Artiﬁcial Neural Network

: Various methods have been proposed to provide the protection necessitated by the high voltage direct current system. In this ﬁeld, most of the research is conﬁned to various types of DC and AC line faults and a maximum of two switching converter faults. The main contribution of this study is to use a new method for fault detection in HVDC systems, using the gray wolf optimization method along with artiﬁcial neural networks. Under this method, with the help of faulted and non-faulted signals, the features of the voltage and current signals are extracted in a much shorter period of the signal. Subsequently, differences are detected with the help of an artiﬁcial neural network. In the studied HVDC system, the behavior of the rectiﬁer, along with its controllers and the required ﬁlters are completely modeled. In this study, other methods, such as artiﬁcial neural network, radial basis function, learning vector quantization, and self-organizing map, were tested and compared with the proposed method. To demonstrate the performance of the proposed method the accuracy, sensitivity, precision, Jaccard, and F1 score were calculated and obtained as 99.00%, 99.24%, 98.74%, 98.00%, and 98.99%, respectively. Finally, according to the simulation results, it became evident that this method could be a suitable method for fault detection in HVDC systems.


Introduction
Due to their lower cost over long distances and their ability to transmit more power, high voltage direct current (HVDC) transmission systems have been widely used for power transmission projects with overhead transmission lines, bulk power, and asynchronous connections. Issues such as the long distance of the lines, the environments of the transmission lines, and adverse weather conditions in HVDC transmission lines have resulted in an increased error rate [1,2].
Currently, protection systems based on traveling waves and voltage derivatives are typically used as the main protection, as well as current differential protection and DC voltage reduction as backup protections for HVDC transmission lines. Protections based on traveling waves and voltage derivatives are sensitive to fault resistance and misdiagnose in detecting high impedance faults, as they use the rate of the voltage change to detect the fault. In addition, current differential protection has a relatively slow performance, due to the transmission line's charge and discharge currents. The main DC voltage reduction has low reliability in detecting faults inside and outside the protection zone [1,2]. Therefore, developing new protection schemes with better performance for HVDC transmission lines is necessary.
With the expansion of applications in AC/DC systems, the expectation of reliability in high-voltage direct current systems has increased dramatically. There are numerous advantages of these systems, such as no interference during transmission, the ability to connect two networks with different frequencies, and the selection of the optimal frequency according to the maximum efficiency of power plants for long distances, as well as high power transmission capacity and having two or more network connections [3,4].
Fault detection is the starting unit of the protection block. So, a fast and reliable method needs to detect the faults in HVDC protection systems. In this study, AI is used to get a fast response to fault detection. Actually, the AI algorithm needs time to learn, but after the learning step, the trained network is used for fault detection. In the testing step, fault detection by AI is very much faster than the logic algorithms.
The rest of the paper is organized into six sections. Section 2 includes a literature review. Section 3 includes the materials and methodologies for the HVDC fault detection method used in the proposed system. Section 4 describes the implementation of the selected methodology, illustrates the methods, and includes the analysis of the model. Section 5 discusses the proposed algorithm within the proposed system and analyzes it under various conditions. Lastly, Section 6 discusses the conclusion and future scope of the research.

Literature Review
The protection of HVDC converters has been the subject of much research. The first attempt was made by Kandil using classification algorithms in HVDC [7]. In this study, three types of neural networks were used, and comparisons were made among them. In [8], the radial basis function (RBF) neural network was used for fault detection in an HVDC sample system. This study used a classifier to reduce preprocessing data before entering the information into the neural network. A new scheme for reducing neural simulation data for neural network training used in HVDC monitoring is presented in [9]. Shang et al. [10] proposed a wavelet-based fault detection technique to protect the HVDC system. In [11], MR analysis of wavelet transform was used to extract important features of fault data for HVDC monitoring. Reference [12] used wavelet transform for HVDC protection.
Most studies [13][14][15][16][17] focus on the selection of the control function to provide the required protection, but, in separating the types of converter faults, a maximum of two types of converter faults are simulated and divided into steps: AC, DC fault, and converter fault. While controlling the performance of individual converters, thyristor valves can provide higher degrees of protection against DC and AC line faults as well as internal converter faults.
In [14], they used the wavelet transform to extract the feature of the fault. The three features of their method are the root means: the inverter's wavelet energy spectrum information entropy, wavelet energy skewness, and wavelet detail coefficients squared values.  [15]. They compared their method with bidirectional LSTM and convolutional neural networks and observed that the LSTM has a lower processing time and obtains 100% accurate results.
The bidirectional Gated Recurrent Unit was proposed in [16] for feature extraction on the bidirectional structure. With this method, detailed information and features are extracted and used to classify faults.
The discrete Fourier transform, based on the decision tree, was used in [18] for fault detection and classification. The discrete wavelet transform combined with the decision tree was used in [19] to diagnose faults. In [19], the wavelet transform was combined with S-transform to classify and detect the fault in grid-tied systems. The support vector machine and a naive classifier were used in [20] to declare the type of faults. They used the Hilbert-Huang transform for feature extraction in their work. The discrete wavelet transform, based on the extreme learning machine, was used to detect and classify faults in the microgrid [21]. The semi-supervised fault detection and classification methods were used in [21]. The discrete wavelet transform, based on ANN Taguchi, was used in [22].
The poor architecture used by machine learning and neural network-based methods [23][24][25] limits the system's ability to learn its complicated non-linear properties. Due to the abundance of features, most of which are insignificant, these approaches cannot effectively leverage the advantages of numerous features.
One of the most important problems in identifying faults in HVDC systems is that the machine learning systems (in this study, ANNs) with non-main features that do not play an important role in learning neural networks cause errors in learning. To address this problem, this study presents the GWO method to select the best features and uses this feature in the training of the neural network, containing several hidden layers that make it possible to increase classification accuracy by mastering the system's intricate non-linear features.
In this study, the types of faults in HVDC converters are introduced separately for the inverter and rectifier, then, using MATLAB software, the simulation and dynamic behavior of the rectifier, together with the relevant controller, are investigated. Then, using the GWO, the best features are determined, and the potential neural network is trained by extracting the properties of the best features of the fault signal and the original data. This way, the types of faults related to converters are distinguished from each other. Finally, to validate the results, a comparison of the test data output for the multilayer perceptron (MLP), radial basis function (RBF), learning vector quantization (LVQ), and self-organizing map (SOM) are given.

Materials and Methods
In this study, faulted and non-faulted signals were created to analyze HVDC fault detection. For this purpose, multiple signals with different types of AC and DC faults were created. The 12 features that depend on the voltage, current, and their components are extracted from these signals. Some of these features are unsuitable for the training of ANN [26,27], and using these features would result in errors and reduce detection accuracy. For this reason, the best and the most accurate features should be selected. Thus, the GWO method, first presented in [28], was used for the feature selection.
The summary of the proposed method is shown in Figure 1. As seen in Figure 1, the 13 faulted signals containing the AC and DC faulted signals were created manually by Simulink-MATLAB. Then, for each fault, the output signals were obtained. These signals contain a huge number of features, most of which are not suitable for training the neural network, and sometimes they can make mistakes in fault detection. For this reason, the best and most useful features have to be selected to train the network. The GWO method was used to select the best features, and these features were used to train the neural network. The GWO method scenario is shown on the right side of the flowchart. this reason, the best and the most accurate features should be selected. Thus, the GWO method, first presented in [28], was used for the feature selection. The summary of the proposed method is shown in Figure 1.  Primarily, the GWO performs by mimicking grey wolves' leadership hierarchy and hunting mechanisms, which they exhibit in the natural environment. Four grey wolf types exist in each pack, namely, the alpha, beta, delta, and omega. Moreover, their hunting process comprises three stages: searching, encircling, and attacking the prey, which are also performed during the optimization process. As Mirjalili suggests, GWO is a novel and robust meta-heuristic method [28]. It is also an easy-to-understand and feasible-toimplement algorithm because it is natural and animal-inspired. The main advantage of GWO is that it is adaptable, easy, and plain. A few recent studies have shown that GWO may provide satisfying results when compared to other popular and successful metaheuristic concepts. For example, Mirjalili compared GWO with the gravitational search algorithm (GSA), differential evolution (DE), PSO, evolution strategy, and evolutionary programming through 29 test functions.
The hierarchy of the gray wolves is shown in Figure 2.
detection. For this reason, the best and most useful features have to be selected to train the network. The GWO method was used to select the best features, and these features were used to train the neural network. The GWO method scenario is shown on the right side of the flowchart. Primarily, the GWO performs by mimicking grey wolves' leadership hierarchy and hunting mechanisms, which they exhibit in the natural environment. Four grey wolf types exist in each pack, namely, the alpha, beta, delta, and omega. Moreover, their hunting process comprises three stages: searching, encircling, and attacking the prey, which are also performed during the optimization process. As Mirjalili suggests, GWO is a novel and robust meta-heuristic method [28]. It is also an easy-to-understand and feasible-toimplement algorithm because it is natural and animal-inspired. The main advantage of GWO is that it is adaptable, easy, and plain. A few recent studies have shown that GWO may provide satisfying results when compared to other popular and successful metaheuristic concepts. For example, Mirjalili compared GWO with the gravitational search algorithm (GSA), differential evolution (DE), PSO, evolution strategy, and evolutionary programming through 29 test functions.
The hierarchy of the gray wolves is shown in Figure 2. The wolves' social hierarchy is mathematically modeled to solve any problem of optimization that requires the best solution, which is called alpha (α). The second and third best solutions are termed beta (β) and delta (δ), and other solutions are termed omega (ω).
The GWO method selects the best features from the voltage, current, and derivatives, which are then used to train the neural network. ANN is a numerical representation of the ANNs in an individual's cerebrum, which are made up of a massive number of nerve cells called neurons linked together. The average number of neurons in a human brain is approximately 10 11 [29,30].
The effect of contributions to the neuron is altered in ANNs using mathematical properties, which are referred to as loads. Before being conveyed to neurons, each piece of information is duplicated through comparing weight. Then, a neuron aggregates such weighted characteristics, despite the value of any predisposition, and passes the summation results, via actuation work, to determine the neuron's outcome. In addition, the bias values give the neuron more flexibility when changing the output value, depending on the features it needs to detect. When no bias is utilized, the neuron's output is 0 whenever inputs are 0 because the weights are multiplied by such inputs. As a result, the presence of bias value enables neurons to evaluate the needed output depending on the feature [31]. Equation (1) shows the synopsis S of inputs and the bias of neuron j [31]. The wolves' social hierarchy is mathematically modeled to solve any problem of optimization that requires the best solution, which is called alpha (α). The second and third best solutions are termed beta (β) and delta (δ), and other solutions are termed omega (ω).
The GWO method selects the best features from the voltage, current, and derivatives, which are then used to train the neural network. ANN is a numerical representation of the ANNs in an individual's cerebrum, which are made up of a massive number of nerve cells called neurons linked together. The average number of neurons in a human brain is approximately 10 11 [29,30].
The effect of contributions to the neuron is altered in ANNs using mathematical properties, which are referred to as loads. Before being conveyed to neurons, each piece of information is duplicated through comparing weight. Then, a neuron aggregates such weighted characteristics, despite the value of any predisposition, and passes the summation results, via actuation work, to determine the neuron's outcome. In addition, the bias values give the neuron more flexibility when changing the output value, depending on the features it needs to detect. When no bias is utilized, the neuron's output is 0 whenever inputs are 0 because the weights are multiplied by such inputs. As a result, the presence of bias value enables neurons to evaluate the needed output depending on the feature [31]. Equation (1) shows the synopsis S of inputs and the bias of neuron j [31].
The value x i represents the contributions of that neuron, w ij are loads to those contributions, and b j represents the neuron's bias. The visual layout of the way that a neuron grips the contributions to request registering results is shown in Figure 3.
The value represents the contributions of that neuron, are loads to those contributions, and represents the neuron's bias. The visual layout of the way that a neuron grips the contributions to request registering results is shown in Figure 3.

Simulink Model
Different models were studied to analyze and identify faults in the HVDC system. The HVDC converter acts on the AC side as the source of current harmonics and voltage harmonics on the DC side. The order of output harmonics depends on the number of converter valves (P), which, for AC current harmonics, is n = kP ± 1, and for DC voltage harmonics is n = kP, and k is an integer. For this purpose, AC filters on both sides of the rectifier and inverter were used to remove the current harmonics on the AC side. In the simulation, to solve the equations of the power system and control/protection system, the sampling time was performed with Ts = 50 μs. The main control of HVDC in this simulation was rectifier control on the rectifier side and power control on the inverter side.
The difference in the characteristics of the thyristors in a valve can cause severe stress during a normal operation. An improper operation of each pole causes a voltage drop on all thyristors of a valve, leading to a sudden decrease in transmitting power. Therefore, the HVDC converter must be protected as a stand-alone device.
The Simulink model for creating the different faults is shown in Figure 4.

Simulink Model
Different models were studied to analyze and identify faults in the HVDC system. The HVDC converter acts on the AC side as the source of current harmonics and voltage harmonics on the DC side. The order of output harmonics depends on the number of converter valves (P), which, for AC current harmonics, is n = kP ± 1, and for DC voltage harmonics is n = kP, and k is an integer. For this purpose, AC filters on both sides of the rectifier and inverter were used to remove the current harmonics on the AC side. In the simulation, to solve the equations of the power system and control/protection system, the sampling time was performed with Ts = 50 µs. The main control of HVDC in this simulation was rectifier control on the rectifier side and power control on the inverter side.
The difference in the characteristics of the thyristors in a valve can cause severe stress during a normal operation. An improper operation of each pole causes a voltage drop on all thyristors of a valve, leading to a sudden decrease in transmitting power. Therefore, the HVDC converter must be protected as a stand-alone device.
The Simulink model for creating the different faults is shown in Figure 4. Modern HVDC uses Voltage Source Converters (VSC). However, the model used in this study utilized thyristors. There are well-known and advanced protection strategies for thyristor-based two-terminal HVDC systems available in the literature [32][33][34]. Current protection challenges are related to VSC-based systems, particularly multi-terminal DC systems. In this study, the GWO method, the main subject, was used to evaluate the features and select the best form of voltage and current signal. In future studies, the authors recommend using a VSC-based HVDC system in simulation studies. The Simulink model used the neural network for testing the system is shown in Figure 5, where the trained neural network was used to test the system. This network was trained by the signals obtained from the model created for each fault. All the faults were used to train this network. Thus, neural network inputs used the features of the signals selected by the GWO method. In this study, the protection systems appeared to react to all types of faults. However, any protection algorithm in the HVDC system aimed to operate the relay for internal faults and to make it stable for external faults. The analysis of the system's stability was not the main aim of this paper.  Modern HVDC uses Voltage Source Converters (VSC). However, the model used in this study utilized thyristors. There are well-known and advanced protection strategies for thyristor-based two-terminal HVDC systems available in the literature [32][33][34]. Current protection challenges are related to VSC-based systems, particularly multiterminal DC systems. In this study, the GWO method, the main subject, was used to evaluate the features and select the best form of voltage and current signal. In future studies, the authors recommend using a VSC-based HVDC system in simulation studies. The Simulink model used the neural network for testing the system is shown in Figure 5, where the trained neural network was used to test the system. This network was trained by the signals obtained from the model created for each fault. All the faults were used to train this network. Thus, neural network inputs used the features of the signals selected by the GWO method. In this study, the protection systems appeared to react to all types of faults. However, any protection algorithm in the HVDC system aimed to operate the relay for internal faults and to make it stable for external faults. The analysis of the system's stability was not the main aim of this paper.

Results and Discussion
The proposed fault detection and class method's overall effectiveness are demonstrated in this section, along with individual parameter modifications. Specific values were displayed by the voltage and fault signals in grid-linked and island modes, respectively. Therefore, it became tough to lay out an incorporated fault category scheme. Thus, the proposed model's performance was analyzed separately for different gadget topologies and working modes.
The criteria of sensitivity, accuracy, F1-score, and precision were utilized to evaluate the suggested approach and were compared to the HVDC fault classification systems. The

Results and Discussion
The proposed fault detection and class method's overall effectiveness are demonstrated in this section, along with individual parameter modifications. Specific values were displayed by the voltage and fault signals in grid-linked and island modes, respectively. Therefore, it became tough to lay out an incorporated fault category scheme. Thus, the proposed model's performance was analyzed separately for different gadget topologies and working modes.
The criteria of sensitivity, accuracy, F1-score, and precision were utilized to evaluate the suggested approach and were compared to the HVDC fault classification systems. The accuracy percentage in best and worst cases were 0 and 100, and the proximity to the value of 100 indicated high accuracy of the classification algorithm. Equations (2)- (7) show the calculations of accuracy, sensitivity, specificity, precision, Jaccard, and F1 score, respectively [35][36][37]: In this equation, N TD presents the total wide variety of entered facts for the evolved model, and N CC implies the variety of correctly categorized information. The proposed network might function similarly even when the distribution line is relaxed. Table 1 shows the mean accuracy derived for each distribution line. As a result, the proposed classifier's best accuracy was recorded at 99.65% for the grid-related radial mode operation. The classifier performed higher than 99.6% for the other device configurations, which changed in keeping with the expectation. The TP (True Positive) index represents the subjects that had the fault classification correctly. TN (True Negative) represents the classifier that detects faults correctly that do not depend on the original signal. FP (False Positive) represents the subjects misidentified as fault signals. FN (False Negative) represents the subjects mistakenly diagnosed as nonfault signals, using the confusion matrix (CM), in which the 11 different fault classes were inserted into the x-axis and y-axis in the form of an 11 by 11 matrix. The vertical ranges symbolized the anticipated flaw elegantly, while the horizontal stages showed the true splendor. The rates of true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN) were also reported in the confusion matrix (CM). The confusion matrix of the proposed classifier is shown in Figure 6. the records was used to measure the validity of the introduced version, which had to be more specific than the trained records. The current and voltage waveforms for the individual datasets were combined and shuffled to create a total of 1600 samples. To test the efficiency of the suggested model, 35% of the records were then randomly selected. With the help of various system configurations and operating modes, the proposed device's overall performance for strains 1-3 was simulated. This performance was then visualized in Figure 7 As seen in Figure 6, the system checked the a-g fault 500 times in total and correctly found the fault 495 times. ANN found this type of fault mistily only five times. There were no faults for b-g, b-c, c-a, abc-g, and DC faults. As a result, this scenario showed that the selected features were the best for training and testing the network.

Average Accuracy (%)
Line one-three 99.23 Line one-two 99.44 In system learning, to test the model's overall performance, a listing of the pattern of the records was used to measure the validity of the introduced version, which had to be more specific than the trained records. The current and voltage waveforms for the individual datasets were combined and shuffled to create a total of 1600 samples. To test the efficiency of the suggested model, 35% of the records were then randomly selected. With the help of various system configurations and operating modes, the proposed device's overall performance for strains 1-3 was simulated. This performance was then visualized in Figure 7. However, the average accuracy could not provide accurate results about model performance. Therefore, the category's overall performance was evaluated via the F1 score to examine how the classifier behaved for error training. The F1 score parameter represents a feature of precision, sensitivity or recall, and accuracy, considered first-rate when it is equal to 1 and worst when it is equal to 0.
The accuracy, precision, recall, and F1 score results are shown below in Table 2. The graphical illustration of these results is shown in Figure 7. The proposed technique extracted features from three-phase current and voltage waveforms with a sampling frequency of 20 kHz. A sampling frequency lower than 20 kHz can be good, because of the restrictions of the information acquisition tool. Therefore, the overall performance of the proposed classifier's fault type was investigated by 99.8 100 a-g b-g c-g ab-g bc-g ac-g a-b b-c a-c abc-g Accuracy (%) 99. 16   As seen in Figure 6, the system checked the a-g fault 500 times in total and correctly found the fault 495 times. ANN found this type of fault mistily only five times. There were Energies 2022, 15, 7775 11 of 17 no faults for b-g, b-c, c-a, abc-g, and DC faults. As a result, this scenario showed that the selected features were the best for training and testing the network.
However, the average accuracy could not provide accurate results about model performance. Therefore, the category's overall performance was evaluated via the F1 score to examine how the classifier behaved for error training. The F1 score parameter represents a feature of precision, sensitivity or recall, and accuracy, considered first-rate when it is equal to 1 and worst when it is equal to 0.
The accuracy, precision, recall, and F1 score results are shown below in Table 2. The graphical illustration of these results is shown in Figure 7. The proposed technique extracted features from three-phase current and voltage waveforms with a sampling frequency of 20 kHz. A sampling frequency lower than 20 kHz can be good, because of the restrictions of the information acquisition tool. Therefore, the overall performance of the proposed classifier's fault type was investigated by converting the kind of input signal and the sampling rate. The sampling frequency used in these studies was changed to 5, 10, 15, 20, 25, and 30 kHz, and the kinds of input signals were voltage waveform or current waveform, blended current, and voltage waveform. The effects of sampling frequency and the precise signal were completed by performing the classification technique five times. After that, the average value of the accuracy was determined to acquire the very last effects, as shown in Figure 8.
The increase in accuracy type was expected for a higher sampling frequency, as it carried more precise fault information for an excellent short circuit fault class. Furthermore, combined current and voltage waveforms provided the highest overall performance for all when the sampling frequency was taken into consideration. At a lower sampling rate, a better category performance was found with the three-phase current waveform rather than with the three-phase voltage waveform. Moreover, the proposed gadget was completed with higher voltage signal records and with a better sampling frequency. Between 10 kHz and 20 kHz sampling frequencies, current waveform and blended current and voltage waveform showed nearly identical accuracy types. This scenario was anticipated because the voltage waveform incorporates much less low-frequency fault information than the modern-day waveform for the available fault class. However, the voltage waveform contained temporary mistakes that were appropriate for investigating at a better sampling rate.
The above evaluation suggested that the expected accuracy could not be executed with current or voltage waveforms alone. If each waveform was considered at the same time, a higher chance of faults in overall performance might be seen for the considered frequency degree. From the above study, it was determined that the idea of the use of current or voltage waveforms for the best accuracy classification was shaken. Instead, their fusion gave higher than 99% category accuracy in a large area when frequency range was taken into consideration, which confirmed the performance of the proposed method.
converting the kind of input signal and the sampling rate. The sampling frequency used in these studies was changed to 5,10,15,20,25, and 30 kHz, and the kinds of input signals were voltage waveform or current waveform, blended current, and voltage waveform. The effects of sampling frequency and the precise signal were completed by performing the classification technique five times. After that, the average value of the accuracy was determined to acquire the very last effects, as shown in Figure 8. The increase in accuracy type was expected for a higher sampling frequency, as it carried more precise fault information for an excellent short circuit fault class. Furthermore, combined current and voltage waveforms provided the highest overall performance for all when the sampling frequency was taken into consideration. At a lower sampling rate, a better category performance was found with the three-phase current waveform rather than with the three-phase voltage waveform. Moreover, the proposed gadget was completed with higher voltage signal records and with a better sampling frequency. Between 10 kHz and 20 kHz sampling frequencies, current waveform and blended current and voltage waveform showed nearly identical accuracy types. This scenario was anticipated because the voltage waveform incorporates much less lowfrequency fault information than the modern-day waveform for the available fault class. However, the voltage waveform contained temporary mistakes that were appropriate for investigating at a better sampling rate.
The above evaluation suggested that the expected accuracy could not be executed with current or voltage waveforms alone. If each waveform was considered at the same time, a higher chance of faults in overall performance might be seen for the considered frequency degree. From the above study, it was determined that the idea of the use of current or voltage waveforms for the best accuracy classification was shaken. Instead, their fusion gave higher than 99% category accuracy in a large area when frequency range was taken into consideration, which confirmed the performance of the proposed method. Table 3 compares the overall fault classification system for the HVDC fault classification using the proposed method and other methods, in accuracy, sensitivity, precision, Jaccard, and F1 Score.  Table 3 compares the overall fault classification system for the HVDC fault classification using the proposed method and other methods, in accuracy, sensitivity, precision, Jaccard, and F1 Score. Table 3. Accuracy, sensitivity, precision, Jaccard, and F1 score of the proposed method.

Method
Accuracy The proposed method used the GWO method to select the best features from the voltage, current, and their derivatives compared with other neural network architectures, such as multilayer perceptron (MLP), radial basis function (RBF), learning vector quantization (LVQ), and self-organizing map (SOM). The experiments demonstrated that the accuracies of ANN, RBF, LVQ, SOM, and the proposed method were 99.00%, 99.24%, 98.74%, 98.00%, and 98.99% for accuracy, sensitivity, precision, Jaccard, and F1 score, respectively. In terms of compared methods, the proposed method was the most accurate because, when the GWO algorithm was used with feature selection, the accuracy increased to 99.00%.
A sample of the fault detection system is shown in Figure 9. As seen in Figure 9, the a-g fault was given to the system, and the neural network correctly found this fault. First, the features of this signal were extracted, then the GWO algorithm was used to find the best and most suitable features to be used in the input of the neural network. Then, the trained neural network decided the fault type regarding the selected features. The model was tested many times and created the confusion matrix shown in Figure 6.
The faulted signals' varying fault resistances were tested, and the features were extracted from different resistance values. Furthermore, the input signals were fixed, and only the resistances were changed, and the scenarios of the faults were modified to extract the features from the signals. In this study, the computational and hardware requirement of this algorithm, considering the time required to clear the fault, were not analyzed.
The proposed method used the GWO method to select the best features from the voltage, current, and their derivatives compared with other neural network architectures, such as multilayer perceptron (MLP), radial basis function (RBF), learning vector quantization (LVQ), and self-organizing map (SOM). The experiments demonstrated that the accuracies of ANN, RBF, LVQ, SOM, and the proposed method were 99.00%, 99.24%, 98.74%, 98.00%, and 98.99% for accuracy, sensitivity, precision, Jaccard, and F1 score, respectively. In terms of compared methods, the proposed method was the most accurate because, when the GWO algorithm was used with feature selection, the accuracy increased to 99.00%.
A sample of the fault detection system is shown in Figure 9. As seen in Figure 9, the a-g fault was given to the system, and the neural network correctly found this fault. First, the features of this signal were extracted, then the GWO algorithm was used to find the best and most suitable features to be used in the input of the neural network. Then, the trained neural network decided the fault type regarding the selected features. The model was tested many times and created the confusion matrix shown in Figure 6.
The faulted signals' varying fault resistances were tested, and the features were extracted from different resistance values. Furthermore, the input signals were fixed, and only the resistances were changed, and the scenarios of the faults were modified to extract the features from the signals. In this study, the computational and hardware requirement of this algorithm, considering the time required to clear the fault, were not analyzed.
In this study, the classification performance of the proposed network was tested using a system that met the International Electrotechnical Commission standard. The analysis was done using MATLAB/Simulink; the discussion and the results are shown below. The explanation, the detailed results obtained, and the study's observations under specific conditions can also be listed accordingly when the figures are used in thesis work. In this study, the classification performance of the proposed network was tested using a system that met the International Electrotechnical Commission standard. The analysis was done using MATLAB/Simulink; the discussion and the results are shown below. The explanation, the detailed results obtained, and the study's observations under specific conditions can also be listed accordingly when the figures are used in thesis work. The transformation device was used with power electronic devices during this converter simulation in order to compare the outcomes of this analysis.
The voltage, current signals, and alpha order results are shown in Figure 10. The transformation device was used with power electronic devices during this converter simulation in order to compare the outcomes of this analysis. The voltage, current signals, and alpha order results are shown in Figure 10. This simulation results' control mode was arranged as 0, 1, 2, 3, 4, 5, and 6 for blocked case, current, voltage, alpha minimum, alpha maximum, forced alpha, and gamma. The three-phase voltage and current are shown in Figure 11. This simulation results' control mode was arranged as 0, 1, 2, 3, 4, 5, and 6 for blocked case, current, voltage, alpha minimum, alpha maximum, forced alpha, and gamma. The three-phase voltage and current are shown in Figure 11.
As seen in Figure 11, the faulted signal occurred in the first second of the simulation. In Figure 11, the (X) axis shows the simulation time, and the (Y) axis shows the voltage and current amplitude value. This simulation results' control mode was arranged as 0, 1, 2, 3, 4, 5, and 6 for blocked case, current, voltage, alpha minimum, alpha maximum, forced alpha, and gamma. The three-phase voltage and current are shown in Figure 11. As seen in Figure 11, the faulted signal occurred in the first second of the simulation. In Figure 11, the (X) axis shows the simulation time, and the (Y) axis shows the voltage and current amplitude value. Figure 12 shows the reliable state condition at the rectifier section without any abnormal behavior in DC.  As seen in Figure 12, the voltage and current signals did not have any faults. These signals were used to train ANN as non-faulted signals. In Figure 12 (as mentioned before), the (X) axis shows the simulation time, and the (Y) axis shows the amplitude value of the voltage and current. Figure 13 demonstrates no faults at the rectifier (transmitting point) or the inverter (receiving point). The data displayed in Figure 12 represents current and voltage. This diagram makes it quite evident that at a time t = 1 s, the voltage was not naturally steady at the rectifier side. The voltage at the side of the inverter, which was the receiving point, stabilized, or became constant, after some time had passed or elapsed, as can be properly seen or observed. With a slight delay, the voltage and current values at the receiving point and at the inverter were nearly identical to those at the transmitting point, which was the rectifier side, unlike the transmitting and receiving points. As seen in Figure 12, the voltage and current signals did not have any faults. These signals were used to train ANN as non-faulted signals. In Figure 12 (as mentioned before), the (X) axis shows the simulation time, and the (Y) axis shows the amplitude value of the voltage and current. Figure 13 demonstrates no faults at the rectifier (transmitting point) or the inverter (receiving point). The data displayed in Figure 12 represents current and voltage. This diagram makes it quite evident that at a time t = 1 s, the voltage was not naturally steady at the rectifier side. The voltage at the side of the inverter, which was the receiving point, stabilized, or became constant, after some time had passed or elapsed, as can be properly seen or observed. With a slight delay, the voltage and current values at the receiving point and at the inverter were nearly identical to those at the transmitting point, which was the rectifier side, unlike the transmitting and receiving points. diagram makes it quite evident that at a time t = 1 s, the voltage was not naturally steady at the rectifier side. The voltage at the side of the inverter, which was the receiving point, stabilized, or became constant, after some time had passed or elapsed, as can be properly seen or observed. With a slight delay, the voltage and current values at the receiving point and at the inverter were nearly identical to those at the transmitting point, which was the rectifier side, unlike the transmitting and receiving points.    The inverter malfunction produced an increase in the DC current Idc = 5.3 pu, while decreasing the DC voltage to Vdc = 0.5 pu. This further condition showed how a commutation failure can be readily caused by a fall in inverter voltage and an increase in current and how it can affect the stability of the AC grid supply.

Conclusions
In this paper, using the main characteristics measured on one side of the transmission line, based on voltage and current, an algorithm for fault detection in HVDC lines is proposed. In the proposed algorithm, when the start unit of the protection function in the protection system confirms the existence of a fault, the fault detection method uses the correlation level of voltage and fault current signals based on trained neural networks. In this study, firstly, the voltage and current signals are produced, which are used as feature signals. The GWO method is used to select the best and more effective features. The GWO algorithm selects the best features to train ANN. The GWO algorithm, based on ANN, can easily develop a fault locator with acceptable accuracy if a substantial quantity of data is used for training and learning. That is why the GWO algorithm, based on ANN, is becoming increasingly popular. This information was utilized to predict the results of unknown fault sites and different fault types simulated at various fault locations. For future work, the authors recommend using different types of wavelets for feature extraction and different metaheuristic methods, such as the ant colony optimization method, Harris Hawks optimization, and particle swarm optimization, to find the The inverter malfunction produced an increase in the DC current Idc = 5.3 pu, while decreasing the DC voltage to Vdc = 0.5 pu. This further condition showed how a commutation failure can be readily caused by a fall in inverter voltage and an increase in current and how it can affect the stability of the AC grid supply.

Conclusions
In this paper, using the main characteristics measured on one side of the transmission line, based on voltage and current, an algorithm for fault detection in HVDC lines is proposed. In the proposed algorithm, when the start unit of the protection function in the protection system confirms the existence of a fault, the fault detection method uses the correlation level of voltage and fault current signals based on trained neural networks. In this study, firstly, the voltage and current signals are produced, which are used as feature signals. The GWO method is used to select the best and more effective features. The GWO algorithm selects the best features to train ANN. The GWO algorithm, based on ANN, can easily develop a fault locator with acceptable accuracy if a substantial quantity of data is used for training and learning. That is why the GWO algorithm, based on ANN, is becoming increasingly popular. This information was utilized to predict the results of unknown fault sites and different fault types simulated at various fault locations. For future work, the authors recommend using different types of wavelets for feature extraction and different metaheuristic methods, such as the ant colony optimization method, Harris Hawks optimization, and particle swarm optimization, to find the different accuracy rates for fault detection scenarios.