A New Method for Fault Detection and Location in a Low-Resistance Grounded Power Distribution Network Using Voltage Phasor of D-PMUs Data

. Electric power grids are always afected by numerous unexpected faults. Occurrence of these faults will have a negative impact on network availability and reliability indices of the network. But the indicators of reliability and quality of electrical energy in the network can be augmented by locating the fault in the shortest time. Special features of distribution networks such as load and network imbalance, existence of diferent types of load with diferent connections, existence of multiphase branches, efects related to diferent conductors, capacitive efects of distribution lines, and limited numbers of measuring devices complicate the process of fault localization in distribution networks. On the other hand, increasing penetration of distributed generation units has caused conventional methods of fault localization. Terefore, it is mandatory to introduce new methods of fault locating by considering the mentioned features. Hence, in the current study, nonlinear methods are presented for identifying the location of ground faults in the power distribution network with the help of voltage phasor measurement at diferent network buses by the D-PMU phased distribution unit. In the frst technique, the genetic optimization algorithms and particle swarm optimization for nonlinear modeling of fault position along the distribution line have been utilized for diferent single-phase, two-phase, and three-phase faults, and in the second technique, neural fuzzy network training has been proposed by diferent phasor measurement devices. In this case, it is enough to access the phase information of the network bus voltage. In order to show the efectiveness of the proposed algorithms, a 9-bus system is defned by MATLAB software and also defning diferent line lengths and line characteristics in diferent buses. Moreover, after applying single-phase, two-phase, and three-phase faults, as well as presenting the results, fault localization is detected in the shortest time.


Introduction
Nowadays, distribution and super-distribution networks have the highest number of diferent faults. Tus, the expansion of these networks and also the high volume of recorded information make these systems more complex. Consequently, it is imperative to implement a system in order to perform fault detection at the lowest possible time and with high reliability in distribution networks [1,2]. Te transmission line is an important component of the electrical power system and its protection is essential to ensure the stability of the system and reduce the damage done to the equipment due to a short connection in transmission lines [3][4][5]. Transmission line relays have three important functions: detecting, classifying, and locating transmission line faults. Fast detection of a transmission line fault facilitates the fast separation of the faulted line from service; hence, it protects the system from harmful efects of the fault [6,7]. Fault classifcation is the identifcation of the type of fault, and this information is essential for locating the fault and assessing the extent of repairs [8]. High accuracy of fault location is essential to facilitate rapid repair and separation of faulty line, improve reliability, and access to power source [9]. Various fault location (FL) schemes have been used in real systems, including phasor-based fault location (PHFL) techniques, which are still the most common [10]. Tese solutions require estimation of the basic phases of voltage and current which are used as inputs to the FL formulae. Backup protection may be local, remote, or both [11,12]. To realize the support of remote sensing protection, the use of phasor measurement units (PMU) has been subject to university and industry attention in several years.
Short circuit faults are common in transmission lines and are the worst type of faults that cause many hazards in lines such as reduced component life, increased power and heat loss of cables, and damage to insulation [13,14]. Various types of short circuit faults occur during daily work and are mainly classifed into two symmetric and asymmetric faults. Symmetric or balanced faults, which keep the system balanced, include three-line ground (LLLG) and triple-line (LLL) lines and are unlikely to occur, but they are the most severe type of short circuit faults, which include large destruction efects and damage to system equipment [15,16]. Asymmetric or unbalanced faults that unbalance the power system during a fault include two-line ground (LLG), ground-to-line (LG), and line-to-line (LL) lines. Although their intensity is lower compared to balanced rivals, they are of great importance because one-to-ground faults are more than 80% likely to occur [17]. In this work, ground connection faults have been worked on.
In [18][19][20], smart meters (SMs) are placed in several system buses so that they do not synchronize prefault and fault voltage measurements. From the voltage drop vector, the fow distribution vector is calculated. Te substation and all buses of DG have to be equipped with digital fault recorders (DFR). Te amount of fault current is obtained through the sum of the currents injected by each DG and the source of the post. Knowing the system impedance matrix and fault current, diferent voltage drops are calculated for all buses with DG. Since the actual voltage sag is recorded on each bus with DG, the voltage drop calculated with the lowest fault, compared to the actual voltage drop, related to the fault location can be used [21,22]. Terefore, such a method is based on classical analysis and does not require complicated mathematical techniques and load data; the fault occurrence position can be calculated with the help of voltage drop information at the beginning and end of the transmission line.
In the current study, a new method for locating faults in the distribution network using voltage phase information is introduced. Finding fault location in four stages is accomplished: frst, the voltage before and during the fault is received by the phasor measurement equipment installed at the network buses. In the next step, utilizing the values of voltage drop in various phases of the power system, the types of single-phase, two-phase, and three-phase faults are calculated and estimated in proportion to each of these received voltage drops, and the segments with potential for fault are calculated according to the number of buses. In the third stage, using two nonlinear modeling methods using phasor measurement methods in each fault line, fault location for each of the fault types is extracted, and fnally, due to the proposed techniques of genetic algorithm and swarm optimization of PSO particles and ANFIS neural fuzzy, the fault event location is achieved relative to the potential bus. In addition, the algorithm utilizes an optimization of the coefcients of the third-order nonlinear model to investigate the range of faults estimated by minimizing the objective function to a detailed model to determine the fault location based on phasor measurement voltages of buses. Te proposed method uses intelligent measuring equipment and D-PMU phase-measuring equipment to obtain voltage drooping. Distributed generation and loads were modeled as fxed impedance and then studied in the network. Te proposed method is implemented in the IEEE 9 bus test distribution network as well as in the MATLAB simulator environment.
In this work, an endeavor is made to implement fault position detection in distribution networks using neural fuzzy network and optimization algorithms. Due to high volume of information in distribution networks, information monitoring is often encountered problems. Terefore, here, it has been tried to use voltage-phasor measurement information in buses. So, there is no longer the need for complicated mathematical calculations in other methods of fault detection such as impedance methods. Terefore, the phase voltage information is applied directly as input to the estimator system and with nonlinear modeling and according to fxed network information such as length and characteristics of network lines and types of single-phase, two-phase, and three-phase fault positions in the network, fault positions are tracked in the shortest possible time.
Te contents of this paper are as follows. In Section 2, the study of the work carried out in the feld of detection and positioning of events and faults is discussed in the power distribution network. Section 3 deals with background studies and provides basic concepts. Section 4 describes the proposed algorithms and techniques for accurate positioning and fault type. In Section 4, the 9-bus system studied under the MATLAB simulator and the results of the proposed techniques are discussed, and in the end, the performance evaluation of the method is presented according to the intended scenarios. Eventually, Section 5 summarizes the results of the study.

Literature Review
In [23], a model-free scheme is introduced which is capable of identifying the topology changes in distribution networks using the data of phase measurement units at the distribution level (DPMU). In this work, algebraic tools of behavioral system theory are utilized to progress easy-toimplement algorithms and the inherent problems associated with the D-PMU measurement and their proposed solution are discussed as an additional challenge to implement the proposed algorithms.
Frequency disturbance events (FDEs) occur due to various events such as generator trip (GT), blackout line (LO), and load interruption (LD) that afect the stability of power systems. Depending on the intensity of the disorder, small properties strongly afect the performance of the integrated system. Accurate and rapid recognition of the event and its location in monitoring the adequacy of resources and 2 International Transactions on Electrical Energy Systems preventing the economic loss and extinction is very imperative. Te article [24], by concentrating on an advanced online hierarchical process, frst recognizes the event and then identifes its classifcation.  [25]. An imperative subject for fault classifcation in power distribution systems is the restriction of fault data for training classifers to recognize types of power outages for repair. Measuring data from power systems are generally not labeled without specifc types of faults, and labeled data with very limited types of faults are very limited and challenge educational classifers with sufcient accuracy. Present fault classifcation methods for dealing with labeled small samples ascertain the underlying structures between labeled and unlabeled data. However, this line of methods has incorrect assumptions about nonlabel and labeled data and sufers from loss of accuracy when dealing with limited data that have a tag. Te paper [26] suggests a novel latent structure learning under a multitask learning framework to supplement the information and address the challenges of limitedtagged data for fault organization. Te proposed process not only uses the underlying structure of unlabeled data that is not used efectually but also eliminates the boundaries of learning the underlying structure by avoiding classifers from being equipped with unlabeled data.
Rapid and accurate localization of electrical faults along power grids increases the reliability and continuity of the source, the rapid recovery of the power supply, and the consequent reduction of downtime. Te paper [27] presents a method of locating network fault through multidata source information fusion. Te compressed sensing algorithm is used to reconstruct the electrical signal twice and the rough fault amplitude and the degree of fault are achieved, respectively. Ten, to attain the degree of switching fault of each element in the anomalous fault range, the Bayesian network is used. Finally, the DS evidence theory combines these two degrees of fault to obtain the result of spatial location. In [28], a new technique for online fault location tracking in distribution networks based on existing systems measurement using phaser units (PMUs) and iterative support detection (ISD) is presented. Trough the fault event and by default, voltages are measured by PMUs that are optimally located along the network. From the voltage change vector and the system impedance matrix, the fow change vector contains a nonzero element with the faulty part. Since PMUs are not located in all crossings, the system equation has already been determined. Hence, to solve a fow vector that has a rare nature, ISD method is utilized. Te paper [29] considers the fault location algorithm suitable for medium unbalanced overhead distribution systems with or without distribution generation (DG). It should be noted that the proposed algorithm uses only simultaneous voltage measurement from two measurement points within the distribution system. Utilizing the basic fault analysis based on the bus matrix and the base impedance, objective algorithm estimates the fault position for each type of accurate short circuit fault. Fault resistance is considered in the algorithm, but it is not explicitly used in the transmission line impedance matrix.
To improve the sensitivity and reliability of system protection, detection, identifcation, and location are fundamental. Tis allows power systems to preserve stable performance. However, it is challenging in large-scale multidevice power systems. Te authors in [30] present three new models of classifcation and deep learning regression (DL) based on deep neural networks (DNNs) for fault area identifcation (FRI), fault type classifcation (FTC), and fault location prediction (FLP). Tese new models ascertain transient data from pre-and postfault cycles for reliable decision making, while current and voltage signals are measured by phasor measurement units (PMU) at diferent terminals and are used as input features in DNN models. Here, sequential deep learning (SDL), through long short-term memory (LSTM) and highdimensional multivariate features are utilized to model spatiotemporal series to accomplish accurate classifcation and prediction results.
Among the methods of fault localization, the most common of these methods is based on fundamental phase-based methods, whose approximation tends to converge with the stable state structure prior to opening the circuit breaker. Tus, conventional troubleshooters typically consider phase estimates obtained from shield relays or class P phase-measuring units, which show the time of flter delay less than the phasor measurement units of the class M. However, it is usually assumed that phasor measurement samples of M class are not suitable for fault location applications due to inherent fltering delays; studies on the possibility of using class M data-based fault locating programs are still scarcely found in literature [31]. Te paper [32] was introduced to investigate whether the phasor measurement units of class M could be used in real location fault localization schemes using previously used measurement systems. In order to do so, the real fault events on the Brazilian electricity network are investigated and the performance of four diferent phasor measurement algorithms is assessed when phasor measurement models are used in a traditional protection relay algorithm and from the phasor measurement units of class M. As opposed to initial expectations, the obtained results indicate that the M-class phase measurements can be used in fault location applications because in the phase-based fault localization methods, faults are expected at the expected levels.

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Te authors in [33] present an approach that enables the fault location across the system using a small set of phase measurements. Te proposed algorithm combines the prediction of voltage after fault and the scatter estimation. Te obtained method allows for practical use of the scattering formula using Prony analysis to predict stable state voltages after faults at those buses equipped with phasor measurement units. A short transient recording is required for prediction only, which is usually accessible before the protective relays are activated. After the prediction stage, recognizing the location of the fault is essential from the least-angle scatter regression-based scattering estimation algorithm. However, for certain circumstances that are usually associated with small fault currents, the scattered estimate algorithm may not be able to accurately diagnose the location of the fault. To lessen this problem, ordinary least squares are used to increase the strength of the proposed method.
It is worthy to note that local protective elements such as fuses and relays are the frst protection mechanism to overcome the fault and separation of the damaged portion of the power network. Although the capability of choice, speed, and sensitivity of these initial protective devices are relatively high and they cannot be considered fawless, there is small percentage of events for which the relays experience a fault occurrence. For these scenarios, a redundant arrangement can be made through backup protection. In [34], a centralized remote protection method based on two techniques, the Delta algorithm, and the least squares technique have been proposed. Te proposed method identifes the transmission line, fault type, and distance to fault. Moreover, the phasor measurement unit data is utilized and is nonreproducible. According to phase measurement units, the network is divided into a number of subregions in order to accurately determine the location of the fault location. In the frst stage, the afected area is located and then a deep search in the fault zone is carried out to determine the fault line. Ultimately, the fault distance is determined according to the distributed model of the transmission line.
In [35], a new high-voltage transmission line fault location scheme based on the use of support vector regression (SVR) has been proposed. Te proposed scheme will only use the amplitude of the fault voltage wave amplitudes, measured at one end of the line. Te various types of faults are investigated in diferent locations with diferent default impedance and types of fault initiation angles in the voltage transmission line of 400 kv and 300 km. Fault voltages are attained from the signals of the 1/8 cycle after the fault and also the removal of noise using a low-pass flter. Te amplitude of the fault voltage signals is used as features for the SVR training. Subsequently, the SVR is used in the precise location of the fault on the transmission line. Compared to other fault locating schemes, the proposed scheme for estimating fault locations requires no information and a smaller data window. However, the proposed scheme gives more accurate estimates, regardless of fault types, fault initiation angles, and default impedance.
Te paper [36] proposes a real-time fault detection technique and fault line detection capability obtained by calculating synchronous phase-based estimators. Each state estimator is characterized by diferent and reinforced topology in order to contain a foating fault bus. It should be noted that the choice of state estimator that afords the correct solution is made by a criterion that calculates the sum of the weighted residues. Te proposed process design is validated using a real-time simulation platform in which an active fow distribution network with a PMU-based monitoring system is simulated. It is postulated that the proposed process for active and passive networks, with neutral ground connection and without neutral ground connection, is appropriate for low and high impedance faults of any kind (symmetric and asymmetric) that occur in diferent places.
Te authors in [37] present an innovative method for fault localization in distribution networks based on the analysis of classical circuits. Two synchronized and few nonsynchronized pre-and during-fault voltages are required in few buses beside the impedance matrix. A new impedance matrix manipulation method is suggested to survey the distribution system in partitions under multiple subsystems. Tis method allows the fault localization process to be solved by solving the equations of equations that are determined and this method is technically available. Tis fault is determined by analyzing the voltage drop across the terminal-bus of each subsystem separately.
Owing to the presence of diferent branches in the electric distribution network and the only accessible information on voltage and current at the beginning of the line and the unavailability of information at the end of the network, the detection of fault section in the distribution network is very essential. Smart meters are now used to measure voltage and fow of network lines, but due to limitations of installation sites, it is not possible to use these devices in all network lines. In [38], two techniques have been used to ascertain the fault section and the fault occurrence location in the network to estimate the fault distance at the beginning of the line with the current estimation at the end of each network line. Terefore, in this project, by installing smart meters in the main branch of the network, as well as information obtained from the current in the normal state of the network, we have tried to practically estimate the voltage and current at the beginning and end of each distribution. Te network line in this method uses more power fow to compute the voltage drop and voltage estimation of the voltage and current at the end of the network lines to determine the fault area.

Conception
In power distribution networks, for accurate positioning of fault, diferent network states must be considered in fault estimation. In this section, we try to defne concepts that are addressed and devoted to this article. First, the types of faults studied in this work are modeled and investigated for two fault detection systems in the network with no distributed generation sources and the impact of fault on the network will be discussed.

Types of Faults (Considered in Tis Study).
Basically, the faults that may occur in a distribution feeder are singlephase to ground faults with ground resistance R f and twophase faults to ground with R arc arc resistance and ground resistors R f in diferent phases, and three-phase connection faults to ground. Before presenting the fault locating algorithm, these three types of short circuit faults are modeled as shown in Figure 1.

Single-Phase to Ground-Fault Modeling.
A singlephase short-to-ground fault with ground resistance R f at distance d in terms of prionite from the node at the beginning of the fault section is shown in Figure 2. According to the fgure, the relationship between the voltage at the beginning of the section and the location of the fault can be written as follows: On the other hand, it can be written as follows: Te value of the current phasor, I′ a , is obtained by implementing the load distribution algorithm presented in [39] in the downstream distribution feeder of point f holding the V fa voltage phasor. However, since the location of point f, i.e., distance d, is unknown, so with a good approximation, the downstream distribution feeder of point S can be loaded without considering the fault with the existing voltage phase of V a and the calculated current I a instead of the current value I′ a used.
By substituting (2) in (1) and decomposing the result into two real and imaginary components, the values of R f and d can be obtained; the value of d is given in the following relation:

d �
Im Re V a -j * Im V a * Re I a -I′ a + j * Im I a -I′ a Im Re z 11 I a + z 12 I b + z 13 I c -j * Im z 11 I a + z 12 I b + z 13 I c * Re I a -I′ a + j * Im I a -I′ a .

Modeling Two-Phase Fault to Each Other and to
Ground. In this case, a two-phase fault to each other and to ground occurred at a distance d from the beginning of the fault section with R arc arc resistance and ground resistance R f , which is shown in Figure 3. As in the previous case, based on equation (1), the voltage of the faulty phases at the beginning of the desired section and the fault location can be written as the following equations: Regarding the aforementioned relations, the following relations are presented: On the other hand, it can be written according to Figure 3: By substituting (6) in (5), the values of R f and d can be obtained as in the single-phase ground mode, with the fault distance d: Re I a -I′ a + j * Im I a -I′ a Im Re z 11 − z 21 I a + z 12 − z 22 I b + z 13 − z 23 I c -j * Im z 11 − z 21 I a + z 12 − z 22 I b + z 13 − z 23 I c * Re I a -I′ a + j * Im I a -I′ a .  International Transactions on Electrical Energy Systems

Fault Locating in the Distribution Network.
In the frst part, the fault location in the distribution network can be discussed without the presence of production sources and in the second part of the fault location in the distribution network with the presence of distributed generation sources. Te fault of connecting three phases to ground is described here.

Fault Finding without the Presence of Distributed
Generation Sources. Te distribution network consists of all diferent branches. Branch is a part of the distribution network between two successive buses and there is only one line between which there is no other element. Te single-line view of each section is shown in Figure 4(a). In this part, the π line model has been used for accurate modeling of each part. Terefore, the circuit model of each section can be extracted as shown in Figure 4(b).
To determine the fault distance according to the π model, the voltage line of point n at distance l from equation (8) is calculated [35].
Te coefcients a, b, c, and d are calculated from the following equations [21]: (12) Figure 6 shows the general model of the fault. According to Figure 6, the fault-point voltage matrix is defned as follows: Te fault phase has an opposite current of zero, so equation (13) in phase k is given equal to equation (12) and (14) results.
where I F includes the sum of the fault currents in all phases.
It should be noted that the results are from n equations where n represents the total number of fault phases. By dividing relation (14) into two parts, real and imaginary, and considering the pure resistance of Z Fa , Z Fg and Z Fc , Z Fb , respectively, the results are obtained: where r represents the real part and i represents the imaginary part and is obtained by removing R Fk from equations (16), (17), and (18). Im is the imaginary part and Re is the real part.     Figure 6: General view of resistance fault.

International Transactions on Electrical Energy Systems
Given that the multiplication of two complex numbers in one's conjugate is equal to a real number and its imaginary part is zero, as well as the faults in the resistive power system, equation (14) has been rewritten from equations (11) and (12).
In general, equation (21) can be rewritten according to So,

Fault Location in the Distribution Network with the Presence of Distributed Generation Sources.
To determine the fault distance in this section, an algorithm is frst implemented for one section and this algorithm is generalized to more sections. Having the voltage and current at the beginning of the feeder and the voltage and current at the end of the feeder, which is the same voltage and current towards the distributed sources, the fault distance π is determined using the impedance algorithm based on the π model. Figure 7 shows a single-line view and circuit model of a distribution feeder with the presence of distributed generation sources. Now, suppose fault occurs in the system. Figure 8 shows the error in the system. Fault point voltage is displayed with V f . Te fault point voltage is obtained by using the source voltage and the line model matrix π line, or by using the distributed source voltage, or, in other words, the line end voltage and the line matrix π model. Te fault point voltage is equal from the source side and from the distributed generation sources.
Assume that the fault point voltage is calculated according to equation (8) by the source at distance x from Te voltage of the fault point is calculated from equation (25) from the distributed generation sources that is located at the l − x distance.
Te fault voltage from the distributed generation sources is set equal to the fault voltage from the source. A quadratic equation gives the following results: In general, equation (26) can be rewritten according to So,

Genetic Algorithm (GA).
Genetic algorithm is a computational model that solves optimization problems by imitating genetic processes and evolution theory [40,41].
Solutions of a population set are used to form a new population set. Tis is hoped that the new population will be better than the previous population. Te solutions that make new solutions are chosen according to their ftness: the more appropriate they are, the more likely they are for reproduction. Tis is repeated until some conditions (e.g., a number of generations or improvement in the best solution) are met. In traditional GA, all variables of interest must frst be encoded as binary digits (genes) of a string (chromosome). To minimize a function f(x 1 , x 2 , . . . ., x k ) using GA, each x i is frst encoded as a dual or foating string of length m.
where x 1 , x 2 , . . . . . . ., x k is called a chromosome and x i is a gene. Ten, three standard genetic operations, namely, reproduction, crossover, and mutation, are accomplished to produce the new generation [42,43]. Such procedures are repeated until the number of predetermined generations can be achieved or accurately required. Te results are illustrated by chromosomes and the methods are known as the ftness function. Te evolution of the GAs is shown in Figure 9, while the original methods are introduced with three main defnitions. Selection: the process in which solutions must be maintained or entitled to disappear or be selected (or authorized solutions). Te best solution is selected and others are eliminated. Here, the ftness function and the optimization are quantitatively determined.
Crossover: a new solution is created from existing solutions after the selection process. 8 International Transactions on Electrical Energy Systems Mutation is the occasional introduction of new features into a solution string of the population. Mutation happens to preserve diversity within the population and prevent premature convergence.

Fuzzy Logic and Adaptive Neural-Fuzzy Inference System (ANFIS)
. Fuzzy logic is defned as a type of artifcial methods used in the classifcation of fuzzy logic resource classifcation. Fuzzy logic theory is unclear in the scope of its activities or observations. In fact, fuzzy sets are developed, but it contains certain types of activities, such as "true-false" or numeric "1-0." Fuzzy logic is known for its simplicity and ease in the design of the algorithm, but when increasing the complexity of the system, you have difculty to determine the appropriate set of rules and functions. In general, fuzzy rules and membership function are based on the behavior of the method learned by the neural network using input and output data [44]. Figure 10 shows an example of the membership functions created by the fuzzy rule generator.
In this study, the use of ANFIS is introduced. ANFIS is the intersection of an artifcial neural network (ANN) and a fuzzy logic inference system. An artifcial neural network is designed to mimic features of the human brain and includes a set of artifcial neural cells. An adaptive system is a multilayer system in which each node (neuron) plays the capacity of the input signals. You can read more about the structure of ANFIS in [45][46][47]. Figure 11 shows a general diagram of the structure of ANFIS. In this fgure, fxed nodes with a circle and adaptive nodes with a square are shown. Te ANFIS technique uses the Sugeno fuzzy model [49], in which the fuzzy rules (if-then) are formulated by  International Transactions on Electrical Energy Systems where n represents the number of rules. Note that M 1i and M 2i represent fuzzy membership functions. p n , q n , and r n represent the linear parts of the corresponding n law. Note that the frst layer of ANFIS contains the initial fuzzifcation in which the degree of membership functions is represented using the input variable. Typically, each node in the layer represents an adaptive function formulated by [50] M 1i 1 where (a i , b i , c i ) represent the set of parameters. Note that layer 2 stands for the product inference layer in which each node called P is controlled by a specifc fuzzy rule. Note that the w i output of the layer is displayed as follows: In turn, the third layer shows a normalization layer, while the transfer power calculated from the previous layer is normalized: Layer 4 receives the normalized values from the third layer. Note that each node in this layer represents a defuzzifcation mode with the node function as follows [51,52]: where (p, q, r), the result parameter, is set when u represents the control signal passed. Note that in the last layer, you have to calculate the sum of all the internal signals to collect the output of the rules [48]:

The Proposed Method
Here, we describe our proposed process for detecting and locating faults in a default power distribution network.
Regarding the studied faults, three models of single-phase, two-phase, and three-phase are studied, which can be generalized to other types of faults and only pay attention to ground connection faults. According to theoretical studies, as observed, the fault location estimation contains many complications and, on the other hand, the availability of branch fow or sections is critical and the problem of computation in diferent branches will require a series of computational complexity. Tis is while the voltage calculation at the feeder is independent of the path and the graph in the distribution network. Here, we focus our attention on the calculation of the error distance with the help of the voltage phasor measurement and not the calculation of the branch fow in the distribution network. In the proposed technique, we need only the amount of voltage phasor in the buses. Based on this, in a single network studied at a point of a unit D, PMU feeder is responsible for measuring the total voltages and is measured at any moment of time. Te basis of our work in this paper is to calculate the voltage drop in each feeder when the error occurs when the fault occurs. It is also based on the proposed scheme to identify fault location after 0.1 s. Figure 12 shows the fowchart of the proposed scheme. In this scheme, the phasor measurement voltage of each bus is checked regularly, and then the moment of the fault occurrence is detected by sudden voltage drop, which is determined in the next stage; according to the efective voltage drop in each phase, the type of ground connection fault of one, two, and three phases is determined and we enter the next stage. In this section, the diference between the voltage drop of each bus and the bus on the other side of each branch is calculated and aggregated for 0.1 seconds. Nodes with a more severe voltage drop are introduced, respectively, and any bus with a higher voltage drop is identifed as a node subject to fault. Terefore, the fault must be calculated in the branches close to it. In the following, the calculated values of the diference in voltage drop of the branch are given to the fault positioning systems. In addition, information including line length and line length impedance according to model π is extracted for the fault event branch and this information is given to the fault location estimation system. In the last phase, the fault location estimation system analyzes these data factors and informs the operator the exact location of fault.

Fault Location Estimation
System along the Line. In this paper, we use three techniques to estimate the location of the fault along the line. Te test data are extracted to investigate the faults and their information. Ten, using a nonlinear model, we choose the location of the faults with the help of fuzzy neural methods, particle swarm optimization, and genetic algorithm. We have achieved an optimal model for estimating fault location in diferent types in the ANFIS method. In the following techniques, a nonlinear model of the third-order Taylor expansion is used, and we use the squares of the diference between the values of the nonlinear function and the real value as the objective function to determine the coefcients of the third-order nonlinear model, expressed in equation (36). With the help of the algorithms described above, these optimal coefcients are calculated: Te target variables in this system are x 1 , x 2 , x 3 , and x 4 , which are defned as nonlinear models according to the input and output variables y 1 and y 2 .

Simulation Results
In this section, the performance results of the proposed design based on three methods of location estimation including fuzzy neural network and nonlinear model optimized with genetic algorithm and particle swarm algorithm are reviewed and compared. In this work, the 9 bus network studied is shown in Figure 13. Information about each line in the network is collected and uploaded under MATLAB software. In this case, when for a grid defned in terms of the length and connections and impedance of the lines, the proposed systems are trained for the next steps for detection and test data, it works completely fast and in real time. Te specifcations of the computer used in this work are Intel Core i5 M480 @ 2.67 GHz. Figure 14 illustrates the voltage drop for the error event in a branch between the 7 and 8 buses and displays the impact of this single phase error on the voltage drop at the diferent buses. Te 25 km line has the highest voltage drop on the 7 and 8 bus. In Table 1, diferent fault cases have been investigated and selected, and for diferent fault lengths, it has been determined as the frst option. According to Figure 14, the amount of voltage drop is diferent for diferent types of faults and the type of fault can be determined with a demarcation. Figures 15-17 show the results of estimating the fault position with ANFIS, GA, and PSO methods, respectively, based on the comparison of actual and estimated results, and Table 2 shows the average fault percentage of the performance of all three methods. Based on the reviewed results, ANFIS method has provided more accurate results.
According to Table 1, for the types of faults taught to the estimator systems, in the frst step, the location of the fault bus is identifed, and in the second step, the exact position of the error is identifed. First, the phasor voltage of each bus is regularly checked, and then the moment of the fault is detected by the sudden voltage drop. In this part, the amount of diference between the voltage drop of each bus and the bus on the other side of each branch is calculated, and according to the order of priority in the voltage drop that occurred in the buses, the locations of the buses with the most voltage drop are prioritized according to Table 1. In the next step, according to the efective voltage drop in each phase, the grounding fault type of one, two, and three phases is determined and we enter the next step. Te frst and second priority busses with the middle branch are prone to errors. Terefore, the error should be calculated in the branches close to it. In the following, the calculated values of the voltage drop diference of the branch are given to the fault location systems, along with that, the information including line length and line length impedance is extracted International Transactions on Electrical Energy Systems  according to the π model for the same branch where the fault occurred, and this information is given to the fault location estimation system to be. In the last step, the fault location estimation system checks these information factors and informs the operator of the exact distance of the fault from the bus with the frst priority. Table 2 shows the possible error in distance estimation for diferent proposed methods.
Tis means the estimated distance for grounding event with this amount of distance estimation tolerance.
According to Table 2, neural fuzzy methods and GA genetic algorithms and PSO particle swarm have been used as diferent and comparative techniques to estimate the location and distance of diferent errors. Among these, the ANFIS neural fuzzy method has been able to identify the

Conclusion
Due to the increasing use of distributed generation sources in distribution networks, new proposed methods for fnding fault in distribution network were provided by the presence of distributed generation sources to determine the fault location using the voltage information recorded at the beginning and end of the feeder and the distributed generation source. Due to the extent of distribution networks and the existence of multiple branches, fault locating in distribution networks is complicated into two parts: fault spacing in the distribution network without the presence of distributed generation sources and fault spacing in the distribution network with the presence of distributed generation sources.
In this paper, the fault location was performed using a nonlinear quadratic equation model optimized with GA and PSO algorithms and the ANFIS neural fuzzy intelligent model without the presence of distributed generation sources in the distribution network with the presence of distributed generation sources using circuit relationships. Te proposed methods were placed in diferent conditions such as single-phase, two-phase, and three-phase ground connection faults in diferent locations in the 9-bus network, and the results show the high accuracy of the proposed methods. Among these, the ANFIS method has shown better performance for correct fault locating.

Data Availability
Te data used to support the study are available from the corresponding author upon request.