#### Abstract

This paper proposes a continuous tracing framework for fault location in distribution network, which is divided into two stages: parameter correction and fault location. On the stage of parameter correction, it is capable of correcting line parameters based on data in the steady state. On the stage of fault location, it can locate the fault according to the one cycle signal after it occurs based on the corrected parameters in the former stage. The stage of parameter correction is beneficial to the fault location process. The core algorithm of the framework is parameter adaptive group search optimizer (PAGSO), which is a kind of improved metaheuristic optimization algorithm. The adjustment strategy and regulatory mechanism are introduced in exploitation, whereas the adaptive mechanism based on reinforcement learning (RL) is introduced in exploration. Improvements could enhance search capability and help the algorithm converge faster. The proposed framework is tested in IEEE 34-bus model. Other meta-heuristic algorithms are adopted for comparison, including genetic algorithms (GA), particle swarm optimization (PSO), grey wolf optimization (GWO), and the standard group search optimizer (GSO). For fault location, PAGSO has been verified under three cases, including ideal condition, noisy condition, and the system with renewable penetration. For line parameters, experiments are designed to prove the algorithm feasibility and verify the necessity of the correction.

#### 1. Introduction

Distribution network is characterized by complex structure, large scale, and wide coverage [1]. Compared with the transmission network, it is less reliable and more likely to develop a fault. The distribution line accounts for more than 90% in the lines of power system. Moreover, the system is allowed to continue to operate with a single phase-to-ground fault, which may cause a series of problems if the fault cannot be located as soon as possible [2]. An accurate fault location algorithm could reduce the time for line patrol and accelerate the maintenance process. Thus, it is crucial to propose a fast and accurate fault diagnosis method for distribution network [3]. Considering the dynamic environment in the power system, such as frequent changes in operation mode, network structure, load demand, and line parameters, it is a great challenge to diagnose the fault with a higher accuracy.

There are some disadvantages in the current fault location method. The travelling wave method [4] would bring some extra cost on account of auxiliary devices, which is too expensive to expand. The impedance-based method [5, 6] is very sensitive to the inaccurate line parameters and noise in the environment. It does not perform well in application. The data-driven method requires a large quantity of training data [7–9], which is difficult to obtain in the actual power system. In mathematical programming, the metaheuristic optimization algorithm (MOA) is a procedure that determines near-optimal solutions to an optimization problem. It could provide flexible techniques to solve hard problems with the advantage of simple implementation and low computational cost. It has been recognized and used in many areas, such as path planning for autonomous underwater vehicles [10], cloud service selection [11], and energy management [12]. Considering that MOA does not require auxiliary devices or a large amount of fault data, it is appropriate to apply MOA for fault location problem.

However, there are some shortcomings in the current MOAs. Genetic algorithm [13] (GA) is a kind of heuristic algorithm based on the ideas of natural selection and genetics. It explores the solution space by a series of operations, including selection, crossover, mutation, etc. However, these complex operations are not instructive to the member that has the minimal fitness value. Thus, it does not perform well in some cases. Particle swarm optimization [14] (PSO) is a kind of widely used MOA. It is much simpler than GA in the process, and it has clear procedure to make other particles come close to the minimum. However, it only considers the best one particle, which would cause some limitations in optimization. Grey wolf optimizer [15] (GWO), firstly, introduces the leadership hierarchy and hunting mechanism into the MOA. Compared with PSO, it not only makes use of the member with minimal fitness value but also fully considers the top three members, which could bring more information for optimization. However, the update mechanism is the same for all members in the optimization, which may lead to a negative effect to convergence. It could be more reasonable if the algorithm has a corresponding mechanism for exploration and exploitation. The group search optimizer [16] (GSO) is an effective MOA in a multimodal problem. It consists of three types of members, which are producers, scroungers, and rangers. Each member has its own update mechanisms, which are beneficial to implement exploration and exploitation. In conclusion, there are two main problems in the aforementioned MOAs. The first is that parameters in the algorithm are constant or random values, which could not adaptively adjust with the optimization process. Secondly, the experience obtained in the optimization process is not fully utilized. The latter step does not obtain valuable information from the former one, which results in a lot of important and useful information buried in the optimization process to be wasted. It would be a great contribution and improvement if the information could be adopted in the algorithm.

In general, system parameters could vary with operation mode, weather, and some other factors. Actual parameters could be quite different with design parameters. It is difficult to obtain accurate parameters in the actual power system. Moreover, the process of signal acquisition could introduce the noise. These inaccurate parameters or noise could lead to negative impacts and result in the rise of errors for fault location. In view of this, most current fault location methods could not perform well in application. Thus, it is necessary to propose a method that could deal with the impact of dynamic environment.

In conclusion, this paper transfers the fault location problem into a parameter estimation problem and proposes a continuous tracing framework for the fault location. It consists of two stages: parameter correction and fault location. The stage of parameter correction is dedicated to the dynamic environment. The core algorithm in the framework is parameter adaptive group search optimizer. It makes full use of the information buried in the optimization problem to make members adaptively adjust parameters based on the current situation. PAGSO would be implemented in both stages of fault location with different control variables and solving spaces. To verify the ability of the proposed algorithm, GA, PSO, GWO, and standard GSO are adopted for comparison. Experiments illustrate that the proposed framework could obtain accurate and robust results. Main contributions of this paper are shown as follows:(1)Considering the disadvantages of other fault location methods, this paper transfers the fault location problem into the parameter estimation problem. It does not need the extra cost or large amounts of data, and it could deal with some complex situations that could not be solved by current methods. More importantly, the proposed approach is quite flexible, which could be adapted to the change of system topology and renewable penetration.(2)Given that most MOAs have constant default parameters and could not vary flexibly according to specific situation, this paper fully utilized the information buried in the optimization process and introduced the adaptive mechanism. Based on it, the proposed algorithm could adaptively adjust its parameters along with optimization. The contribution is quite novel and creative. It would be of great benefit for faster convergence.(3)In the light of the difficulty in obtaining accurate parameters, we propose a framework that includes two stages: parameter correction and fault location. Parameter correction would be executed in an interval, which aims to make sure the method could deal with the dynamic environment and achieve more accurate location.

The rest of this paper is organized as follows: Section 2 briefly introduces the related work of fault location. Section 3 describes the framework of fault diagnosis. Sections 4 introduces the standard GSO and the improvements of PAGSO. Section 5 gives the explanation of simulation models, experimental settings, and comparison results. Finally, Section 6 serves as the conclusion of this paper.

#### 2. Related Work

Different from the transmission network, the distribution network has its own unique characteristics. The lines are distributed widely, and they penetrate areas with varied topographies. Most important of all, the length of the distribution line is very short in some cases, and the network could have multiple branches. The large number of branches and complex topology make great difficulties for fault location. Considering the reality of the power system, only a few of the buses could install sensors. The process of acquisition and transmission for signals could be mixed with some noise. Moreover, the system parameters are not static, and they could be changed with the system operation or some other factors. All of these have created great challenges for the fault location in the distribution network. At present, fault location methods could be divided into two categories: model-free method and model-based method.

The most common method in model-free is the travelling wave method. It locates the fault using the faulty travelling wave head [17]. They do not require any a priori knowledge of the topology. However, they bring some extra cost on account of auxiliary devices, such as remote-end synchronization and signal generator, which introduce additional complexity in the fault location process [18]. There are two types in the travelling wave method: the single-ended algorithm and the double-ended algorithm. The single-ended algorithm encounters difficulty in detecting the travelling wave reflected from the fault point when there are travelling waves reflected at branch points or junction points [19]. Thus, it is less applicable to the actual power system. The double-ended algorithm does not suffer from the disadvantage above as it requires travelling waves of both ends, however, the installation of sensors at all terminals is impractical in distribution networks. However, both methods are influenced by the accuracy of travelling wave speed in calculation [20]. The speed could be affected by many factors, such as sag, parasitic shunt capacitances in transformers [21], and attenuation or distortion in the process of spread. In a word, the travelling wave method is not suitable for the fault location in the distribution network, given the complex situation and the extra cost. It is usually applied in the transmission network.

Beside the travelling wave method, there is another model-free method based on the auxiliary devices. In reference [22], a hybrid Peterson coil combined with an electromagnetic element is applied to compensate fault current and locate the fault section. Since the method adopted the information of the primary substation, the accuracy of fault location would be affected by the limited availability of information because of the line with complicated laterals and different parameters of the line in distribution systems. Similarly, the method should utilize additional devices, which would increase the difficulty of field practice.

The impedance-based method is a kind of model-based method, which is calculated by the equations based on Kirchhoff’s mathematical law. However, it could be underdetermined and get several potential solutions since we could not install sensors in each node. Thus, it is necessary to find out some method to pick up the best one in the set of solutions. In reference [23], after getting several potential answers in calculation, it determines the final answer by comparing voltage signals generated from the reality and the simulation, respectively. Then, it picks up the fault point with minimal difference as the final answer. In reference [24], it applies fuzz-c mean clustering to determine the final answer after getting potential answers. It is noteworthy that the precision of parameters could have great impacts in the accuracy in nearly all impedance-based methods. However, parameters are not static in the actual system, which could vary with the pattern of operation, the weather, and some other factors. Thus, the impedance method cannot function effectively in reality [25].

The data-driven method [26] is also based on the system model, which has the ability of obtaining reasonable results with approximate parameters. It has strong ability to tackle the inaccurate parameters and noise in the environment. However, it demands a large quantity of training data, which is time-consuming for collecting fault data through simulation [27]. Reference [28] propose an approach based on 1-D convolutional neural network and waveform concatenation. It solves the problem of data volume by simplifying the neural network topology. Considering that it adopts zero-sequence signals as features, this approach is only available on the line-to-ground fault. Given that it is tested on the radial distribution network, this approach would be less applicable when the topology becomes complex. In fact, the data-driven method still needs more data with the increase of precision in the fault location. Huge amounts of data are needed for model construction, and the high computational cost has become a bottleneck of such methods. Besides, the trained network has fixed model constructure, which is difficult to be transferred and reused when the network topology changes [29]. The method could be invalid when sensors are failed and cannot collect signals.

#### 3. Parameter Correction and Fault Diagnosis

The dynamic environment has a great impact on the fault location, which refers to the variations of line parameters in the actual system. Parameters could be changed by the weather or operation mode. We assume that the simulation model is the same as the actual power system, like the digital twin. The goal is to find a set of variables to make simulation signals as close as signals obtained in the actual system, including the fault location, the region, etc. If the environment is dynamic and not the same as the simulation model, we cannot obtain same signals even if the fault location is set to the actual fault location. In other words, the inferential location could be inaccurate. Thus, parameter correction is vital to make the simulation model close to the actual system as much as possible. The fault diagnosis framework is divided into two parts: parameter correction and fault location. They are corresponded to two subproblems. Considering the dynamic changes in the line parameters of the power system, the optimization algorithm would trace the system state and correct line parameters during the steady state, including resistances, inductances, and capacitances. It is a timer interval-driven process. However, in the fault state, the optimization algorithm is aimed at finding out the fault location based on parameters corrected in the steady state. Assuming a distribution network with buses and lines, the objective functions of two subproblems are shown as follows:where and are the optimization objective functions that model the errors of the parameter correction and fault location, respectively. is the vector of dependent variables.which includes the bus voltages, , and the bus currents, . is a set of control variables in the second objective function . It is shown as follows:which includes all resistance, inductances, and capacitances of lines in the system. , , and represent the resistance, inductance, and capacitance at the line. Boundaries are as follows:where is the set of line indexes in the distribution network. According to reference [30], the variation range of line parameters in appalling weather is between 4% and 10%. To consider situations as much as possible, the lower boundary (, , and ) is 0.8 times the baseline, while the upper boundary (, , and ) is 1.2 times the baseline. The baseline is the standard value obtained in the system construction. is a set of control variables in the first objective function .where is the fault location distancing from the secondary windings of the distribution transformer, is the phase angle of the fault starting time. and are the fault resistance and region, respectively. Each distribution line between the two nodes is regard as a region. The boundaries are as follows:

Considering that we normalize the length of the line, its upper boundary is 1. is the upper boundary of the fault resistance, which is set to 1,000 in the paper. represents the number of the region, which is set according to the topology of the actual power system.

Although there are two subproblems that have different control variables, the evaluations of objective functions are similar. The goal is to minimize the fitness value, which is to evaluate the difference between the actual signal and signals generated by the simulation model. According to reference [31], the objective function is described as follows:where represents the fitness value, while and represent the number of sensors and the length of signal window, respectively. represents the actual signal, which is the sampling point collected from the sensor. is the sampling point in the sensor generated from the simulation model. and have the similar meanings with and . The smaller the fitness value, the more similarities between the simulation model and the fault. In other words, the inferred result is closer to the situation in the actual power system.

Figure 1 describes the whole procedure of the framework. There are two parts in it: parameter correction (green block) and fault location (orange block). In both of them, actual signals from the real system and simulation signals from the simulation system would be adopted as the inputs. Parameter correction is a self-circulation process. is the interval time, which means that parameters would be corrected on a timed interval. The objective function is calculated by equation (8). The output is a set of corrected parameters, which is shown in equation (4). It includes resistances, inductances, and capacitances. These parameters would be used in the fault location to modify the model. The fault location process would be triggered only when the fault occurs. Inputs are corrected line parameters and signals from both the real system and the simulation system. The variables that need to be estimated are , fault location, the phase angle of the fault, fault resistance, and region number. It is shown in equation (6).

#### 4. Parameter Adaptive Group Search Optimizer (PAGSO)

The group search optimizer (GSO) is an effective MOA in a multimodal problem. This paper makes some improvements in it to make it more adaptive and converge faster. The population of GSO is called a group, and each individual in the population is called a member. There are three types of members, namely producers, scroungers, and rangers. The former two members are based on the Producer-Scrounger model. Rangers are dispersed members that perform random walk motions. Usually, we assume that there is only one producer at each searching bout, which has the minimal fitness value, and the rest of the members are scroungers and rangers. However, GSO has some constant values in the algorithm. To make it more reasonable, some adaptive mechanisms are introduced to PAGSO. For the producer, the dynamic step length based on local search and the regulatory mechanism for angle adjustment are adopted. The parameter adjustment based on the previous experience is proposed for the scrounger.

##### 4.1. Producer

At each iteration, the member with the minimal fitness value is selected as the producer. It would stop and scan the environment to seek resources (optima). If it has a better resource than its current position, then it will fly to the new one. Otherwise, it will stay its current position and turn its head to a new randomly generated angle. is the head angle in the scanning field of vision. , which is an (*n* − 1)-dimensional vector. The scanning field is simplified and generalized to an n-dimensional space, which is characterized by the maximal pursuit angle and maximal pursuit distance . They both are constants. is , and is the singular value of solution ranges. is the number of iterations. The producer will find the best point with the best resource (fitness value).

The producer will sample three points in the scanning field. one point at zero degree, which is as follows: one point in the right-hand side hypercube, which is as follows: one point in the left-hand side hypercube, which is as follows:where is a normally distributed random number with a mean 0 and a standard deviation 1, and is a uniformly distributed random sequence in the range . The calculation of is shown in reference [23].

In exploitation, GWO proves that the top three members could bring in more information for optimization, and it is superior to others in some cases. Thus, we introduce the adaptive strategy and regulatory mechanism for the producer in PAGSO. It is based on leadership hierarchy, and it makes improvements to the framework of GSO. Instead of only making use of the member of minimal fitness value in original GSO, the proposed algorithm can adjust the step length and angle of producer based on more information. Details are shown as follows:

###### 4.1.1. Dynamic Step Length Based on Local Search

is a constant, which depends on boundary-value, and it would not change along with the optimization process. It is unreasonable since the step should be smaller when the member is close to the optima. Thus, we propose a more rational calculation method for step length. It is calculated as follows:where means a virtual member determined by three members closest to the current best position, , , and . is a random value in the range (0,1), which is used to generate small random disturbance. It could help the member break away from the local optima. In PAGSO, is replaced by in equations (9)–(11).

###### 4.1.2. Regulatory Mechanism for Angle Adjustment

If the producer cannot find a better area at this iteration, it will turn its head to a new angle in the next time, which is calculated as follows:where is the maximal turning angle in one movement. It is a constant value, , in standard GSO. Moreover, there is a counter in GSO that calculates how much degree the producer has searched. If the producer finds a better position or another member becomes the producer in the next movement, the counter of this producer would be cleared to zero. If the counter is more than , the producer will turn its head back to zero degree and keep exploring in this direction. It seems inefficient and could lead to be stuck in the current position. Thus, we introduce the regulatory mechanism for angle adjustment to prevent the producer from getting stuck.where is the decay rate, which is set to 0.1 in our experiments. represents the degree of counter. Operator means the remaining integer part of the value. Equation (14) has been modified into the following:

The exploration angle could be smaller if the producer could not find a better position during the search process. In conclusion, the improvements bring more meticulous and in-depth exploration for the producer.

##### 4.2. Scrounger

A few group members are selected as scroungers, which will keep searching for opportunities to join the resources found by the producer. At iteration, the scrounger can be modeled as a random walk toward the producer.where represents the step length of the exploration, which is a random sequence in the range under uniform distribution. Operator is the Hadamard product or Schur product, which calculates each element of the two vectors. It means that the scrounger would take a random step between the current position and the position of the producer. It seems that the scrounger does not make full use of the previous experience and the optimization progress.

One of the most significant contributions for PAGSO is to introduce the adaptive mechanism for the scrounger to speed up optimization and make it more reasonable. At the beginning, disperse members are far away from each other. The step length could be larger for faster convergence. When members are close to the optima, the step length should be smaller to avoid missing the optima. In other words, the step length should be adaptive during the optimization process. Thus, the adaptive mechanism based on reinforcement learning (RL) is introduced to adjust the in scrounger. There are six main parts in RL: environment, agent, state, action, policy, and reward. There is one-to-one correspondence between these and the optimization process. The solution space and each member in PAGSO are considered to be the environment and agent, respectively. State means the current fitness value of the member, whereas action is set to decide whether to increase or decrease the step length of the scrounger. Policy is the network required to be trained, and each agent has its own policy network. Reward is the mechanism, which is formulated to guide the agent to make more proper action based on current states. The detailed definitions are as follows: State It is a sequence that represents the changes of the member in PAGSO during the process of iterations. where is the state vector attached to a given agent at iteration . is the fitness value for agent at iteration . is the length of the sliding window. Function is defined as follows: Action : The action is corresponded to the adjustment of step length . A larger value of facilitates exploration, whereas a smaller value facilitates exploitation. There are three kinds of possible actions for the agent: increase, decrease, or remain. increase: this action commonly occurs when the member succeeds in previous iterations. The member intends to step up its exploration based on the current state. decrease: the oscillation of agent’s fitness value could lead to this action. It means that the member is close to the optima, and it should slow down to reach it. remain: the length of the step will remain the previous value if there is no motivation to either increase or decrease it. The actions mentioned above will directly affect the parameter in the next iteration. where is the step length of the member at iteration . It fluctuates within the range of , which is a constant. Equation (18) is modified into the following: Policy : The core of RL is the agent, which is also called the policy network. It is the mapping between state and action , which is usually modeled by the neural network. In the training process of the agent, state vectors as inputs would be sent into the neural network, and outputs are the action vectors, which are encoded by one-hot code. Reward vectors would be used to minimize the loss function of the neural network. The policy network would be continuously trained along with the optimization process. Reward represents the reward for the member at iteration . It is the feedback from the environment based on the action to the current state. If the member takes the action determined by and moves to a better position, which has a smaller fitness value than the previous one, it will receive the positive reward. On the contrary, the member will be punished and will get a negative reward if it moves to a worse position. The reward function is defined as follows:

The policy network would be continuously trained along with the optimization process. At last, the policy could make the most proper action based on the state.

The flow chart of adaptive mechanism is shown in Figure 2. The agent is a neural network, which requires to be trained. At each iteration , the agent could be in an observer state from the environment and determine the action . On account of the action, the agent would receive the reward and obtain a new state from the environment. The agent would repeat the steps above until it reaches the terminating condition. In practice, samples are continually generated from interactions between the agent and the environment. The number of samples would increase gradually as the process goes on. The network should be able to deal with these changes. Unlike other algorithms that have a fixed training dataset and sample the batch data from the dataset at each iteration, incremental learning (IL) is introduced to PAGSO to learn from fresh samples and update the network continuously. For achieving this, we build a buffer to store the newest state samples. The structure of the buffer is a queue. Previous data could be discarded when the number of the data is larger than the buffer size. The agent keeps interacting with the environment and generates new state vectors stored in the buffer. This mechanism makes sure the network could adapt the latest data and keep learning along with the process. In conclusion, the agent is a neural network to determine what actions it should take in a given state. Its target is to achieve a decision-making policy , which could obtain a higher reward during the interaction with the environment.

##### 4.3. Ranger

The rest of the group members, named rangers, will be dispersed from their current positions. Random walks, which are thought to be the most efficient searching methods for randomly distributed resources, are employed by the rangers. At iteration, it generates a random head angle using equation (14). In standard GSO, the ranger will move to a new position according to the following equation:where is calculated as follows:where is the dimension of the solution, and is a random value in range (0, 1). This strategy could avoid being trapped in the local optima and improve the ability of exploration.

If a scrounger or a ranger finds a better location than the rest of the members, it will switch to a producer in the next iteration. The previous producer will perform scrounging or random strategies. Moreover, to avoid searching a profitable patch, GSO set the strategy that the member which is outside the search space should turn back into to its previous position.

#### 5. Algorithms Background

##### 5.1. Genetic Algorithm

Genetic algorithm (GA) is a kind of heuristic algorithm based on the ideas of natural selection and genetics. The genetic algorithm repeatedly modifies a population of individual solutions. At each step, the genetic algorithm selects individuals from the current population to be parents and uses them to produce the children for the next generation. Over successive generations, the population “evolves” toward an optimal solution. The flow chart including the main algorithmic steps is shown in Figure 3.

##### 5.2. Particle Swarm Optimization

Particle swarm optimization (PSO) is an evolutionary approach by Kennedy and Eberhent. PSO may have some similarities with genetic algorithms, however, it is much simpler because it does not use mutation/crossover operators or pheromone. The movement of the particle consists of two major components: a stochastic component and a deterministic component [32]. Each particle is attracted toward the position of the current global best and its own best in history, while at the same time, it tends to move randomly. The flow chart of PSO is shown in Figure 4.

##### 5.3. Grey Wolf Optimization

Grey wolf optimizer (GWO) is proposed by Seyedali Mirjalili. It simulates the leadership hierarchy and hunting mechanism of grey wolves in nature. Wolves are divided into four types in GWO. The alpha wolf is considered the dominant wolf in the pack and his/her orders should be followed by the pack members. Beta are subordinate wolves, which help the alpha in decision-making and are considered the best candidates to be the alpha. Delta wolves have to submit to the alpha and beta, however, they dominate the omega. Omega wolves are considered to be the scapegoats in the pack, and they are the least important individuals in the pack and are only allowed to eat at last. Thus, the wolves that have the smallest three fitness value are wolf alpha, wolf beta, and wolf delta, respectively. Other wolves are omega wolves. The flow chart of GWO is shown in Figure 5.

#### 6. Experimental Study

##### 6.1. Settings and Criteria

The IEEE-34 bus model is applied to verify the framework of fault diagnosis, which is shown in Figure 6. The legend is in the top left corner. The number begins with the symbol “#,” e.g., #800, and it represents the node in the system. The number marked along with the line means the distance between the two nodes. Its unit is foot. More detailed parameters about lines, loads, generators, and transformers refer to reference [33]. Data is collected from the end of each branch. Nodes equipped with sensors are set red. For better comparison, we set different faults to verify the feasibility of PAGSO, including the single line-to-ground faults, double line-to-ground faults, line-to-line faults, and the three phase short-circuit fault. GA, PSO, GWO, and standard GSO are adopted for comparison. Maximum iteration and population size are set to 200 and 50, respectively. To testify the robustness of algorithms, each experiment repeats 30 times. *α* and *β* in equation (8) are set to 0.3 and 0.2, respectively. Some metaheuristics algorithms could be affected by the initialization. To make it fair, we ensure that all algorithms begin with the same situation. Different criteria are set to evaluate results. Accuracy, , is calculated as follows:where is the number of fault samples that infer the right regions, while is the number of total samples. The mean absolute percentage error (MAPE), , is calculated as follows:where is the variables to be evaluated, and is the prediction result. represents the number of total results. We also adopt standard deviation into criteria to evaluate the stability of the algorithm, which is calculated as follows:

In conclusion, we set , , and to evaluate the MAPEs of resistances, inductances, and capacitances in the line parameters correction experiments. Although there are four control variables in , the precisions of others do not matter as much. Thus, accuracy (), MAPE (), and standard deviation () are adopted for fault location experiments.

##### 6.2. Experiments of the Fault Diagnosis

To verify the proposed algorithm, we design four cases in experiments. Firstly, all algorithms are tested in the ideal condition to evaluate their performance in the fault location. Considering that signals could be accompanied by some noise in the actual system, Case 2 is designed to testify whether algorithms are still effective under noisy environment. Given that this paper proposes a framework that consists of parameter correction and fault location, Case 3 is used to reveal the performance of PAGSO in parameter correction and the necessity of it for fault location. With the development of renewable energy, Case 4 is set to testify whether the proposed method could work with the renewable penetration.

###### 6.2.1. Case 1: Ideal Environment with Correct Line Parameters

In this case, it is assumed that the parameters of lines are accurate and signals do not have noise. Experiments are executed 30 times. Each time, the fault is randomly set in the system. Experimental results are shown in Table 1. Accuracies, , are 100% in all compared algorithms, which illustrates that MOA is suitable for solving the fault location problem and could infer valid answers. In comparison, GA has the worst result ( is 4.82% and is 561.2), which illustrates that the optimization process could not benefit from the complex operations of GA. The major difference between GWO and others is that its update mechanism is based on top three members. If top three members are in different optima, this mechanism could slow down the process of convergence. It could be the explanation for the performance of GWO, in which is 0.78% and is 20.64. The update mechanism of the scrounger in GSO is similar to that in PSO, however, the update mechanisms of producer and ranger are different. In fact, the step length of the producer in GSO is a constant value based on the boundary of the solve space. This mechanism is not conductive to the convergence, especially in the latter process of optimization. Thus, its performance is poorer than PSO. In PAGSO, we fully consider the disadvantages of GSO in exploitation and introduce the adaptive strategy for step length and regulatory mechanism for angle adjustment. Moreover, RL principles are adopted to adaptively adjust the factor in the process of scrounger. Results show that PAGSO achieves the smallest (0.17%) and (3.11). It not only performs better than PSO but also achieves obvious improvements than standard GSO. In a word, the proposed PAGSO achieves the best performance among all compared algorithms.

For better visualization, we do repeated experiments with a fixed fault and draw the box-plot of all results. The fault is set to A-phase fault in the distribution line from #806 to #808 with 1 fault resistance and phase angle. The total length of the line is 32,230 ft. The actual fault location is 14,504 ft away from node #806. The prediction value should be as close to the actual value as possible. The box-plot is shown in Figure 7. The smaller subfigure attached in Figure 7 is the detailed display of the other four algorithms, except GA, since they cannot be seen clearly in the main figure. The ordinate represents the predictive fault location, whereas the abscissa is five algorithms for comparison. The blue dot line means the actual fault location, 14,504 ft. The main figure shows that the interquartile range of GA is the largest, and the maximal and minimal outliers are around 15,793 ft and 13,537 ft, respectively. They are far away from the answer compared with other algorithms. It means that the results of GA are not only inaccurate but also unstable. In the subfigure, GWO and GSO have similar interquartile ranges. The results of GWO are almost distributed on both sides equally, whereas most results in GSO are lower than the answer. However, there is one outlier at about 14,568 ft in GWO, which means that its performance is not stable in repeated experiments. Considering the interquartile range and outlier, PSO has the second-best result, which is benefitted from the update mechanism we analyze above. Compared with PSO, PAGSO has not only the smaller interquartile range but also the median that is closer to the actual fault location. The range between the upper whisker and lower whisker is smaller, which shows that PAGSO is more robust. In conclusion, Figure 7 draws a similar conclusion with Table 1. It proves that PAGSO obtains accurate and stable results.

###### 6.2.2. Case 2: Noisy Environment with Correct Line Parameters

In practice, noise contained in the signal could affect the accuracy of fault location. To testify whether algorithms are still effective under noisy environment, we add a 30 dB noise in both current and voltage signals obtained from the actual system in this case. Signal-Noise Ratio (SNR) is calculated as follows:where and are the power of signal and noise, respectively.

Table 2 illustrated the results in the noisy condition. and of GA are 6.05% and 742.69, respectively. They are much larger than other compared algorithms. It illustrates that GA still performs worst in this case, and it cannot converge well in the multimodal problem. GWO and GSO have slightly larger and than PSO and PAGSO, which is consistent with results in Case 1. They may be caused by similar reasons we analyzed above. and of PSO are 1.73% and 11.38, respectively. The performance proves the effectiveness of its update mechanism again. Considering that PAGSO is improved in both exploration and exploitation, it still achieves the best performance in all criteria. and are 1.51% and 11.14, respectively. Compared with Table 1, it is obvious that MAPEs under noisy condition are much larger than these under ideal condition. The results reveal that the noise has a certain impact on the accuracy of solution.

For better visualization, we also do repeated experiments with the same fixed fault under ideal condition and draw the box-plot, which is shown in Figure 8. Overall results are quite similar to Figure 7. Figure 8 illustrates that the interquartile range of GA still performs the worst, which is consistent with the aforementioned results. In the subfigure, all compared algorithms have more outliers than in Figure 8. Among them, GWO and GSO have outliers much far away from the answer, which means that these two algorithms do not have strong ability in the face of noise disturbance. s of GWO and GSO in Table 2 are much larger than PSO and PAGSO, which also proves the conclusion. For other two algorithms, outliers are smaller than those in GWO and GSO. PAGSO has a smaller interquartile range than PSO. It illustrates that PAGSO is still effective even under noisy environment. In conclusion, although noise has a negative impact on all algorithms, PAGSO achieves accurate and stable results under noisy conditions and performs better than others.

###### 6.2.3. Case 3: Parameter Correction under the Dynamic Environment

In this case, experiments are divided into two parts. The first part aims to reveal the feasibility of PAGSO in parameter correction. The later part verifies the necessity of parameter correction in the fault location. Parameters are set according to reference [33]. There are five types of lines in the 34-bus model, which are numbered from to . To fully test the impact of line type, we pick up one line in each type. Reference [30] states that the variation range of line parameters in appalling weather is between 4% to 10%. Thus, the variations of resistance, inductance, and capacitance are set to 4%, 6%, and 8%, respectively. MAPEs of line parameters after correction are shown in Table 3.

In Table 3, the first two columns indicate the number of line and its type. Five lines belong to five types. Different types of lines are adopted to prove that the proposed algorithm is general. , , and represent the MAPEs of line parameters after correction. According to settings, the variations of resistance, inductance, and capacitance are set to 4%, 6%, and 8%, respectively. Table 3 illustrates that MAPEs of all parameters are lower than 3% after correction. It fully proves that the proposed algorithm is quite effective in correcting line parameters. After proving the ability of the proposed algorithm in parameter correction, the following experiments are designed to figure out whether the performance could be improved after correction. The results are shown in Table 4.

In Table 4, we design experiments to verify the necessary and importance of parameter correction. Similar to Table 3, we set up five experiments according to five types of lines. Table 4 illustrates MAPEs with or without parameter correction in fault location. It is evident that MAPEs in all experiments decrease to some degree after parameter correction. For example, MAPE is 4.91% in the line from node #802 to node #806 before correction, whereas it is reduced to 1.06% after correction. Thus, the process of parameter correction does contribute to achieve more accurate results. In conclusion, experiments fully prove its necessity in the fault location and the effectiveness of the fault diagnosis framework we propose.

In a word, experiments in this case are sufficient to prove the availability of the proposed algorithm in parameter correction and the framework of fault diagnosis we propose. The correction does make a great help to enhance the performance of fault location.

###### 6.2.4. Case 4: Distribution Model with Renewable Penetration

To verify whether the proposed method could work in the system with the renewable penetration, we construct a PV farm (400 kW) to the IEEE-34 bus model at node #822. The PV farm consists of four PV arrays, delivering each a maximum of 100 kW at 1000 W/m2 sun irradiance. A single PV array block consists of 64 parallel strings. The model of PV farm is shown in Figure 9.

The proposed method is verified in the subsequent three scenarios, and results are shown in Table 5.(1)Ideal condition: assume that line parameters are accurate and noise does not contain signals.(2)Variation of parameter: assume that line parameters would change within 5%(3)Noisy condition: assume that signals are obtained with 30 dB noise.

Compared with Tables 1, 2, and 4, the results of system with the PV farm are in accordance with the system without the PV farm. MAPEs keep at the same level, and the trend is accordant. In Table 5, MAPEs rise with the increase of complexity in the environment. MAPE in an ideal condition is the smallest, whereas MAPE in a noisy condition is the largest. The inaccurate parameters have a certain negative impact on the proposed algorithm compared with the ideal condition. Reasons for these have been illustrated in Case 1 to Case 3. In general, Table 5 shows that the proposed algorithm still works in the system with renewable penetration. These results make sense. In model construction, we build the simulation model, which is the same as the actual power system, like the digital twin. It means that this simulation model and the related devices in the system could make similar actions with the actual system when the fault occurs. Then, the proposed algorithm would find out the fault location by minimizing the difference between signals in the simulation model and the actual system. In other words, whether the system is connected to the renewable penetration or distributed generator, the proposed algorithm has strong ability to adapt the variation of the system. It is one of the superiorities of the proposed algorithm.

#### 7. Conclusions

In conclusion, this paper proposes a fault diagnosis framework for the dynamic environment, which is divided into two stages: locate the fault in the fault state and line parameter correction in the steady state. In fault location, we compare several MOA algorithms in the ideal and noisy environments to better simulate the actual system. All algorithms could achieve 100% accuracy in the region number, which proves that MOA is suitable for applying in the fault location problem. In the ideal condition and noisy condition, PAGSO has the best performance in nearly all criteria, which proves that the proposed improvements are effective and help the algorithm converge faster. Experiments in case 3 are designed to verify the great significance of parameter correction. A more accurate fault location could be achieved with the process of parameter correction. Experiments in case 4 illustrate the performance in the system with renewable penetration. Results show that the proposed method is still effective, which benefits from its working mechanism.

In a word, this paper proposes a continuous tracing framework for fault diagnosis, and experiments have shown its accuracy and robustness. It has strong adaptability in a dynamic environment.

#### List of Symbols and Abbreviations:

PAGSO: | Parameter adaptive group search optimizer |

GA: | Genetic algorithm |

PSO: | Particle swarm optimization |

GWO: | Grey Wolf optimization |

GSO: | Group Search optimizer |

MOA: | Meta-heuristic optimization algorithm |

RL: | Reinforcement learning. |

#### Data Availability

The previously reported model and data were used to support this study. These prior studies (and datasets) are cited at relevant places within the text as references [33].

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

This research was funded by the National Natural Science Foundation of China (No.52077081) and Key-Area Research and Development Program of Guangdong Province (2020B010166004).