A Two-Stage Fault Localization Method for Active Distribution Networks Based on COA-SVM Model and Cosine Similarity

Abstract

To address the issues of low efficiency and poor noise immunity in traditional active distribution network (ADN) fault location methods based on swarm intelligent optimization algorithms, this paper proposes a two-stage fault location method utilizing the COA-SVM model and cosine similarity. First, this paper constructs the fault signature database for the target distribution network by randomly simulating single- and multi-point faults using the fault current state equation. Next, this paper introduces the COA-SVM classification model, establishing the high-dimensional mapping relationship between the fault current direction matrix and the fault zones through model training. The well-trained COA-SVM classification model is used to identify the fault zones, which include the fault line segments. Finally, for each identified fault zone, this paper calculates the cosine similarity of the fault current direction information of adjacent line segments, accurately pinpointing the fault line segments by identifying mutation points of the cosine similarity. Using the modified IEEE 33 node test distribution network as an example, simulation results demonstrate that the proposed two-stage fault location method offers higher accuracy and resistance to signal interference compared to fault location methods based on swarm intelligence optimization algorithms. The COA-SVM classification model surpasses conventional models, achieving high accuracy and excellent noise resilience. It accurately identifies fault segments within the test distribution network with a remarkable 100% precision. Moreover, the accuracy of fault localization remains above 83% when the FTU encounters fewer than three abnormal signals.

1. Introduction

With the continuous grid connection of distributed energy resources such as rooftop photovoltaics, small wind turbines, and fuel cells, the structure of distribution systems becomes more complex and intelligent [1]. Fault location in ADN is one of the core components of distribution automation systems. In a distribution automation system, the rapid and accurate identification and location of fault points is crucial for ensuring a continuous power supply and stable operation of the system [2]. For highly automated ADNs with robust communication infrastructures, feeder terminal unit (FTU) data can serve to localize faults. This approach enhances system intelligence, achieving zero-perception power outages. By monitoring and analyzing the fault current direction information uploaded via the FTU in real-time, the distribution network control system can quickly identify the exact location of the fault and automatically isolate the affected segment. Simultaneously, it can adjust the network’s operating status to restore power to non-fault areas, thus reducing downtime and minimizing the impact on users [3]. The exploration of grid-connected distributed generation (DG) has significant implications for managing both upstream and downstream fault currents within the associated power line. By thoroughly analyzing the fault current data captured via FTUs and considering the impact of grid-connected DGs, this paper aims to develop a fault localization methodology tailored for ADNs, which represents a key area of contemporary research interest.

Due to the complex influence of DG on the amplitude of fault currents, researchers have proposed various advanced algorithms and technologies to locate the fault line segments based on the fault current information uploaded via FTUs. Among these, the matrix theory-based method [4,5,6], artificial intelligence method [7,8], and the swarm intelligence algorithm [9,10] stand out as relatively cutting-edge and effective approaches. However, the matrix algorithm is susceptible to data noise interference, which impacts positioning accuracy and shows poor adaptability in complex networks with distributed power sources. By collecting and analyzing real-time data from SCADA systems, FTUs, and various sensors, artificial intelligence algorithms employ machine learning or deep learning technology for feature extraction and pattern recognition. They also train models that can predict the location of faults. Ref. [11] proposes a graph convolutional network model for fault location in power distribution systems. This model preserves the spatial correlation of lines, integrates information from multiple measurement units, and classifies fault lines by extracting and synthesizing features layer by layer. In Ref. [12], models for fault detection, line classification, and positioning were constructed using data from phasor measurement units. The robust deep filtering convolutional neural network (RDGCNN) model captures spatial and temporal features, maintaining high accuracy even in high-noise environments. Ref. [13] utilizes a fast Fourier transform to analyze the spectrum of voltage and current waveforms. It employs a multi-layer perceptron neural network and standard backpropagation technology to classify and locate shunt faults in medium-voltage distribution systems. The artificial intelligence algorithm can quickly and accurately analyze large amounts of data, enabling rapid fault location to reduce outage time and enhance the reliability of the power supply. Nonetheless, it has its inherent drawbacks, including the necessity for comprehensive and precise historical data, intricate algorithmic structures, and considerable real-time data processing. Most recent studies use fault current direction data from FTUs to identify fault locations. Researchers develop an optimization model and solve it using swarm intelligence algorithms. This approach seeks to create a model that minimizes the difference between the actual fault current direction data detected via FTUs and the expected fault current direction information. The model undergoes refinement through iterative solutions via a swarm intelligence algorithm to extract relevant details about the fault location. In ref. [14], distortion and missing fault information are integrated into the fitness function, while the ant colony algorithm for fusion pattern search addresses the problem. The fault location can still be determined under conditions of fault distortion, remaining unaffected by noise and data loss. Ref. [15] proposes a fault location method that combines an improved matrix algorithm with a genetic algorithm. The matrix algorithm locates and verifies the fault region. If a verification error occurs, the genetic tabu algorithm identifies the suspicious fault region, greatly improving fault accuracy and tolerance. Ref. [16] introduces a master–slave fault location method. In the main stage, the genetic algorithm determines the fault location and number, while the secondary stage predicts the fault location using an artificial neural network based on local voltage and current information, reducing dependence on the communication system. In ref. [17], the improved Cuckoo algorithm generates random states for all fault lines, converting these to the expected state of each switch, updating the fault line state, and outputting the specific fault location via the final model. Ref. [18] constructs the mathematical model of unipolar and bipolar short-circuit faults, introducing the artificial bee colony algorithm to enhance the slime mold algorithm, which tends to fall into local optima, to obtain the fault point from the optimization search. In summary, the aforementioned research does not consider the context of fault location in high-dimensional, large-scale distribution networks. Due to the complex network structure, increasing dimensions, and massive data volumes, swarm intelligence algorithms face an explosion of information. This leads to an excessively large search space, resulting in issues such as slow convergence speed, high computational costs, and local optima, thereby affecting the accuracy and efficiency of fault localization. This issue is notably amplified in complex network configurations and when confronted with multi-source faults. Consequently, it is crucial to improve the resilience and generalization capabilities of these algorithms.

Currently, support vector machines (SVMs) can efficiently construct classification boundaries by learning a small number of key samples. They effectively distinguish different types of faults even in high-dimensional space, which has garnered much research interest. Ref. [19] employs SVMs for classification and uses wavelet transform, Fourier transform, and minimum redundancy maximum correlation algorithm to select features. Ref. [20] utilizes SVMs to classify different fault locations, fault impedance, and load changes. It determines the fault location by injecting inter-harmonic current and measuring the generated voltage when a distribution network fault is detected. In Ref. [21], faults are classified according to the reactance characteristics of fault paths by combining SVM and feedforward neural networks. Principal component analysis reduces the dimensionality of measured values from substations, circuit breakers, and relays to extract key features. Ref. [22] quantitatively analyzes uncertain factors in the distribution network through data mining. It combines artificial neural networks and SVM to identify the state of the distribution network and enables adaptive reconfiguration based on state recognition results. However, the performance of SVM highly depends on the selection of kernel functions and parameter settings, such as penalty coefficients and kernel function parameters. Improper parameter selection may lead to overfitting or underfitting of the model. Therefore, this paper adopts the crayfish optimization algorithm (COA) [23] to optimize the hyperparameters of SVM, converging in a short time and reducing the computational resources and time costs required for hyperparameter tuning.

During the operation of the distribution network, single-phase and three-phase ground faults are regarded as the most severe types of faults due to their potential for high current and significant impact on system stability. In order to realize rapid fault location in an ADN and ensure its safe and reliable operation, a two-stage fault location method for ADNs based on the COA-SVM model and cosine similarity is proposed, taking into account the influence of DG on fault current direction. Firstly, based on the operation topology of the target ADN, the random simulation of single- and multi-point faults is carried out, and the fault feature database of the target distribution network is constructed by combining the fault current state equation. Subsequently, the offline training of the COA-SVM model was finalized utilizing the fault signature database. The SVM model was employed to construct the high-dimensional mapping relationship between the fault current direction matrix and the fault zone labels. COA was applied to optimize the hyperparameters of SVM, thereby enhancing its generalization capability, and the model was utilized for the initial localization of the fault zones within the distribution network. Finally, for each fault zone located, the cosine similarity of the fault current direction information detected via the FTU is calculated, and the precise location of the fault line segments in the fault zone is realized via the cosine similarity mutation position. The proposed fault location method can establish the mapping relationship between the fault current direction matrix and fault zone only through limited offline fault simulation. The trained COA-SVM model has the characteristics of a small online call computing power requirement and strong fault tolerance and avoids the shortcomings of the fault location method based on the swarm intelligence optimization algorithm, such as poor scalability, slow calculation speed, and poor anti-interference ability.

The full paper is organized as follows: Section 1 serves as the introduction to this paper. In Section 2, a two-stage fault location strategy framework is presented. Section 3 develops the fault signature database for the ADN. In Section 4, the two-stage fault location method is introduced in detail. The first stage involves the offline training of the COA-SVM classification model, while the second stage employs the well-trained COA-SVM model to perform the online identification of fault zones, and the cosine similarity algorithm accurately pinpoints the exact location of the fault line segments. Section 5 presents a simulation case based on an enhanced IEEE 33-node network. Finally, Section 6 serves as the conclusion of this paper.

2. Overall Framework of the Proposed Two-Stage Fault Localization Strategy

The two-stage fault location strategy relies primarily on the fault current direction information detected via FTUs, as well as the status information of DG and off-grid conditions. It identifies fault line segments through the fault location functional module, with the overall deployment diagram shown in Figure 1.

The traditional fault localization method based on swarm intelligence optimization algorithms requires extensive iterative calculations to ensure that the solutions obtained are as close as possible to the global optimal solution; however, it suffers from slow convergence rates, making it challenging to meet the real-time requirements of fault localization. To address the slow resolution speed and poor real-time performance of traditional fault location methods, this paper employs a two-stage fault location approach based on a combination of the COA-SVM classification model and cosine similarity. The first stage involves offline training of the COA-SVM model with a customized fault signature database. The objective of the second stage is to identify the fault zones online using the well-trained COA-SVM model and then locate the fault line segments based on the cosine similarity of the fault current direction of adjacent line segments. Unlike traditional fault location methods that directly identify specific fault lines, this approach effectively determines the general fault range even when there are fluctuations in node data quality. This reduces the sensitivity of location results to data quality and alleviates the workload of maintenance personnel. The overall strategy framework is illustrated in Figure 2.

In stage one, it begins with a randomized simulation of single-point and multi-point fault scenarios in the target regional distribution network. This utilizes the fault current direction discrimination function to establish a fault characteristic library. Based on this, offline training for the COA-SVM classification model is completed, creating a high-dimensional mapping relationship between FTU-detected fault current direction information and the identification numbers of fault zones. In stage two, the fault current direction feature vector of the target distribution network is extracted from the FTU’s real-time monitoring information and sent to the trained COA-SVM model, which quickly identifies the fault zones. For each fault zone identified, the cosine similarity of fault current direction information between each segmented line and its adjacent lines is calculated. By detecting sudden changes in fault current direction, the precise location of the faulty line segment is determined. This two-stage fault localization strategy ensures timely fault localization while improving accuracy.

3. Construction of Fault Signature Database of ADN

In the fault feature extraction stage, the focus is on the fault current direction as the key feature of short-circuit faults in the ADN. The FTU monitors the fault information characteristics in real time and determines the fault current direction of each segment line when a short-circuit fault occurs. Additionally, given the presence of DG in the ADN, the influence of DG on the fault current direction of its branches and the entire distribution network during a short-circuit fault must be taken into account. Thus, to fully explore the correlation between the fault current direction characteristics at the FTU monitoring points in the ADN and fault point location under various fault conditions, random simulations of single- and multi-point faults should be conducted on the target distribution network. The fault current direction discriminant function will analyze the current direction change rule when faults occur, and fault samples will be collected. A fault current direction feature database, which includes multiple-fault conditions, is constructed to support offline training of the COA-SVM classification model. This section emphasizes the fault state index and the fault current direction discriminant function of the distribution network line, which are essential for fault feature extraction.

3.1. Characteristics Analysis of Fault Current Directions

To analyze the direct implications of fault current directions across various faults, a practical urban distribution network feeder is modeled in the PSCAD/EMTDC environment, with its single-line diagram presented in Figure 3. The 110 kV/10.5 kV substation transformer features a capacity of 16 MW, with its neutral point ungrounded. The total electrical load is rated at 6 MW. To explore the effects of DG on the upstream fault current direction, a 4 MW solar PV system is integrated at the feeder end, complete with comprehensive power conversion and control circuit modeling. The fault location is established at the midpoint of line AB, considering three fault types: single-phase-to-ground, double-phase-to-ground, and three-phase-to-ground. The fault impedance is fixed at 5 Ω. The fault initiates at 1.5 s and is cleared at 1.7 s, with the measurement point located at the outgoing of Bus A. Here, the voltage and current values in phase A are provided below for analysis.

During a single-phase-to-ground fault, the voltage and current measurements appear as shown in Figure 4. The single-phase-to-ground fault has a minimal effect on upstream buses, even with the solar PV system connected to the downstream feeder. Notably, the current waveform leads the voltage waveform by 30 degrees.

During a double-phase-to-ground fault, the short-circuit current amplitude spikes to 1.3 kA. This is nearly ten-times greater than the normal current, as illustrated in Figure 5. Furthermore, the short-circuit current flows in the opposite direction. This results in a phase difference between voltage and current of approximately 180 degrees. Similarly, when a three-phase-to-ground fault occurs, the short-circuit current can peak at 2 kA. Its phase angle shifts in the opposite direction of the voltage waveform, as shown in Figure 6. Therefore, it can be concluded that the change in fault current direction can be an effective criterion for double- and three-phase-to-ground fault localization of a feeder with DG, while it is not applicable to the single-phase-to-ground fault condition.

3.2. Distribution Network Line Fault Status Indicators

When a fault occurs in a certain line segment of the distribution network, the FTU responds immediately. It captures the electrical parameter changes at the moment of the fault in real time using built-in current and voltage sensors and other detection elements. The control center receives this information for further fault confirmation and location.

The fault status of any line i in an ADN is represented by the indicator $S_i$. When this indicator is 0, it means line i has no fault; when it is 1, it indicates that a fault has occurred on line i. Considering the impact of the DG on both on-grid and off-grid states on the fault current direction, another indicator $S_{\mathrm{g},i}$ represents the state of DG at line i. If there is no DG connected or the connected DG is in off-grid mode, the indicator is 0; otherwise, it is 1.

After the DG connects to the distribution network, the fault current direction flowing through the branch where the DG is located becomes more complex. Traditional distribution network fault current direction uses only 0 and 1, which cannot reflect the role of the DG in injecting short-circuit current to the fault point. Therefore, this paper uses an indicator $S{L}_i$ to define the fault current direction flowing through line i. When the detected fault current on line i flows from the system power supply side to the end of the branch, it is considered a positive fault current direction ($S{L}_i=1$); conversely, it is a negative fault current direction ($S{L}_i=-1$). If no fault current is detected, it is 0. For an ADN with DG connected, when there is a DG downstream of line i and the upstream line experiences a fault, the indicator $S{L}_i$ is 0; if the downstream line has a fault, the indicator $S{L}_i$ is 1. Conversely, if there is DG upstream of line i and the upstream line has a fault, the indicator $S{L}_i$ is 0; if the downstream line has a fault, the indicator $S{L}_i$ is 1. Thus, the fault current direction of line i is influenced solely by its downstream DG.

In conclusion, the fault current direction flowing through any line i in an ADN is determined by three factors: the grid topology, the location of the fault point, and the DG’s on and off-grid state.

3.3. Fault Current Direction Discriminant Function

To further quantify the impact of grid topology, the location of fault points, and the states of DG connected or isolated from the grid on the fault current direction indicator $S{L}_i$ of any line i, this section proposes a fault current direction discrimination function, as shown in Equation (1).

$$\left\{\begin{array}{l}S{L}_i=S{L}_{\mathrm{dw},i}-S{G}_i\left(1-S{L}_{\mathrm{dw},i}\right)S{L}_{\mathrm{up},i}\hfill \\ S{L}_{\mathrm{dw},i}={\displaystyle \prod _i^{m_{1,i}}{S}_i}\hfill \\ S{L}_{\mathrm{up},i}={\displaystyle \prod _i^{m_{2,i}}{S}_i}\hfill \\ S{G}_i={\displaystyle \prod _i^{n_i}{S}_{\mathrm{g},i}}\hfill \end{array}\right.$$

(1)

where $S{L}_{\mathrm{dw},i}$ and $S{L}_{\mathrm{up},i}$ represent the fault status of downstream and upstream areas of line i (1 for fault, 0 otherwise); $S{G}_i$ indicates whether there is DG connected downstream of line i (1 for connected, 0 otherwise); $m_{1,i}$ and $m_{2,i}$ represent the total number of segmented lines downstream and upstream of line i, respectively; $n_i$ denotes the total number of DGs downstream of line i; $\prod$ represents logical OR; for any line i, upstream refers to the direction from its position to the system power supply side, while downstream refers to the direction from its location to the end of the branch where line i is situated.

By utilizing Equation (1), one can achieve large-scale simulation of single-point and multi-point short circuit faults under complex operating conditions of ADNs and quickly extract fault current direction information under various faults, thereby improving the efficiency of building a fault characteristic database for ADNs. By employing Equation (1), it is possible to conduct extensive simulations of both single-point and multi-point short circuit faults within the complex operational scenarios of ADNs. This approach facilitates the rapid extraction of fault current directional data across diverse fault conditions, thereby enhancing the efficiency of constructing a fault characteristic database for ADNs.

4. Two-Stage Fault Localization Strategy for ADN

4.1. Stage One: Off-Line Training for the COA-SVM-Based Fault Zone Identification Model

SVM is a supervised learning algorithm that utilizes kernel functions to map input feature samples into a high-dimensional space, thereby identifying the optimal hyperplane for achieving linear separability of the samples.

However, because SVM typically selects vectors and parameters based on existing empirical knowledge and within specific bounds, this conventional approach may lead to issues such as insufficient learning or overfitting. Additionally, the random selection of parameters can introduce significant randomness that may impact the accuracy of the test set. To address these challenges, this paper employs COA to identify the optimal penalty factor c and kernel function parameter g. COA, introduced by Jia Heming [23], is a novel intelligent optimization algorithm. The COA algorithm is inspired by the behavior of freshwater crayfish during foraging, thermoregulation, and competition, and its execution process is divided into three phases: thermoregulation, competition, and foraging. The thermoregulation phase corresponds to the exploration process of the algorithm, while the competition and foraging phases correspond to the exploitation process.

Crayfish transition between the exploration and exploitation phases based on environmental temperature changes; they enter the competition or thermoregulation phase when the temperature is too high and switch to the foraging phase when the temperature is optimal for searching for food. The COA algorithm calculates the environmental temperature according to Equation (2), determining the temperature value temp at the start of each iteration within a range of 20 °C to 35 °C, with the ideal foraging temperature for crayfish set at 25 °C. The COA algorithm uses a mathematical model to describe the feeding amount p of crayfish, taking into account the influence of environmental temperature temp. The specific equation is as follows:

$$temp=rand\times 15+20$$

(2)

$$p=C_1\times \left({\displaystyle \frac{l}{\sqrt{2\times \pi }\times \sigma }}\times exp\left(-{\displaystyle \frac{{(temp-\mu )}^2}{2{\sigma }^2}}\right)\right)$$

(3)

where rand is a random number within the range of 0 to 1. μ represents the optimal environmental temperature for crayfish foraging, which is 25 °C. C₁is a constant of 0.2, and the value of σ is 3. By adjustingC₁and σ, the feeding amount of crayfish at different temperatures can be controlled.

(1)

Summer escape stage

When the environmental temperature exceeds 30 °C, crayfish choose to retreat into caves to avoid the dangers posed by high temperatures. The expression for the cave location $X_{shade}$ is as follows:

$$X_{shade}=(X_G+X_L)/2$$

(4)

where $X_G$ represents the best position obtained so far during the iteration process, and $X_L$ denotes the best position of the current population.

When rand < 0.5, meaning there are no other crayfish competing for the cave, the crayfish will enter the cave directly using Equation (5) for relief from the heat:

$$X_{i,j}^{t+l}=X_{i,j}^t+C_2\times rand\times (X_{shade}-X_{i,j}^t)$$

(5)

$$C_2=2-(t/t_{\max })$$

(6)

where t indicates the current iteration number, $X_{i,j}^t$ represents the j-th dimension position of the i-th crayfish in the t-th iteration, and $C_2$ is a coefficient that linearly decreases from 2 to 0, calculated as per Equation (5).

(2)

Competition stage

When the environmental temperature exceeds 30 °C and rand ≥ 0.5, it indicates the presence of other crayfish within the cave. At this point, competition for the cave will ensue among the crayfish. Each crayfish, denoted as $X_{i,j}^t$, will adjust its position based on the location of another randomly selected crayfish, denoted as $X_{z,j}^t$. The relationship is defined as follows:

$$X_{i,j}^{t+l}=X_{i,j}^t{X}_{z,j}^t+X_{shade}$$

(7)

$$z=round(rand\times (P-1))+1$$

(8)

where P represents the population of crayfish, and z signifies another randomly selected individual.

(3)

Foraging stage

When the environmental temperature is at or below 30 °C, crayfish will move towards the food source. Upon locating the food, they will first assess its size. If the food is too large, the crayfish will tear it apart with their pincers and alternate the use of their second and third legs to consume it; conversely, if the food is of moderate size, they will approach it directly and begin feeding. The position of the food can be represented as $X_{food}$, defined as $X_{food}=X_G$, with the size of the food denoted as $Q$. This is expressed as follows:

$$Q=C_3\times rand\times (fitnes{s}_i/fitnes{s}_{food})$$

(9)

where $C_3$ represents the food factor, a constant value indicating the maximum food size, specifically valued at 3, while $fitnes{s}_i$ represents the fitness value of the i-th crayfish, and $fitnes{s}_{food}$ represents the fitness value of the food.

When the size of the food $Q$ is less than or equal to ($C_3$ + 1)/2, the crayfish simply moves towards the food’s location and starts feeding. The equation is as follows:

$$X_{i,j}^{t+I}=(X_{i,j}^t-X_{food})\times p+p\times rand\times X_{i,j}^t$$

(10)

When the size of the food $Q$ exceeds ($C_3$ + 1)/2, it implies that the food is too large. In such cases, the crayfish will alternately pick up and place the food. To simulate this process, Equation (12) integrates sine and cosine functions to depict the actions of the crayfish using their second and third pincers to alternately move the food towards their mouth.

$$X_{food}=\exp (-{\displaystyle \frac{1}{Q}})\times X_{food}$$

(11)

$$X_{i,j}^{t+l}=X_{i,j}^t+X_{food}\times p\times (cos(2\times \pi \times rand)-sin(2\times \pi \times rand))$$

(12)

By iteratively optimizing the objective function to identify the optimal parameter combinations, the predictive performance of the COA-SVM model is enhanced. The adaptive hyperparameter optimization workflow for the COA-SVM model is illustrated in Figure 7.

The optimized COA-SVM model allows for the rapid localization of fault zones through online invocation. Specifically, the fault current direction information monitored in real time via the FTU is inputted into the trained COA-SVM model. This model independently analyzes the fault current based on its directional characteristics by identifying the optimal hyperplane in the feature space, learning the characteristics and labels of fault currents from the fault feature repository, and establishing a fault current classification model. Consequently, this enables the determination of the specific zone where a fault occurs.

4.2. Stage Two: Online Fault Localization Based on COA-SVM Model and Cosine Similarity

Cosine similarity is a mathematical method used to measure the similarity between two non-zero vectors, as depicted in Figure 8. It evaluates the closeness of their directions by calculating the cosine of the angle between two high-dimensional vectors and is widely applied in fields such as document similarity calculation and image analysis.

For n-dimensional vectors A = (A₁, A₂, …, A_n) and B = (B₁, B₂, …, B_n), Equation (13) provides the calculation of cosine similarity [24].

$$\cos (A,B)={\displaystyle \frac{{\displaystyle \sum _{i=1}^n}{A}_i·B_i}{\sqrt{{\displaystyle \sum _{i=1}^n}{A}_i^2}·\sqrt{{\displaystyle \sum _{i=1}^n}{B}_i^2}}}$$

(13)

In this paper, the n-dimensional vector A = (A₁, A₂, …, A_n) refers to the fault current direction information SL_i of the current line, while B = (B₁, B₂, …, B_n) refers to the fault current direction information SL_i+1 of the next line. To prevent the denominator in Equation (13) from being zero, the status index $S{L}_i$ of lines without fault current is set to $-\epsilon$, where $\epsilon$ is a small constant. The result of cosine similarity strictly lies within the closed interval [−1, 1]; a value closer to 1 indicates a stronger positive correlation between the two vectors, while a value closer to −1 signifies a stronger negative correlation, with a value of 0 indicating no correlation. If two adjacent lines, which have not experienced faults, detect fault current in the same direction via their respective FTUs, the cosine similarity is 1. Conversely, if any one of the two adjacent lines experiences a fault, regardless of whether the DG is connected to the grid, the resulting cosine similarity will be −1. This method allows for precise localization of the specific fault line segment based on the fault zones localization.

5. Case Studies

5.1. Basic Information of the Simulation Case

To verify the accuracy of the method proposed in this paper, the modified IEEE 33-node network is selected as the test distribution network. Its network topology is shown in Figure 9. The test network contains three DG connections. The off-grid states of DG1–DG3 are controlled with switches K1–K3, respectively. The four 0–1 states of switches K1–K3 correspond to four fault scenarios. When a short circuit fault occurs in the branch of any DG, the DG injects short circuit current into the fault point. Additionally, except for the backbone lines L1 and L2, the remaining lines are divided into five zones from Z1 to Z5. The lines in each zone are shown in Figure 9. The simulation environment uses a Windows 64-bit operating system with an Intel (R) Core (TM) i9-8800 CPU @3.6GHz and 64 GB memory.

The fault signature database generates 496 groups of fault samples in batches by randomly creating single- and multi-point faults in the five zones. Based on the fault zone where the fault line segment is located, all fault feature samples are categorized into 15 different types, represented by labels C1–C15. The number combinations of the fault zone where the fault resides and the corresponding line sets are shown in

Table 1. Fault classification based on zone of line.

Label	Zone	Line Set	Label	Zone	Line Set
C1	Z1	L30~33	C9	Z1, Z5	L6~17, L30~33
C2	Z2	L18~21	C10	Z2, Z3	L3~5, L18~21
C3	Z 3	L3~5	C11	Z2, Z4	L18~21, L22~29
C4	Z 4	L22~29	C12	Z2, Z5	L6~17, L18~21
C5	Z 5	L6~17	C13	Z3, Z4	L3~5, L22~29
C6	Z1, Z2	L18~21, L30~33	C14	Z3, Z5	L3~5, L6~17
C7	Z1, Z3	L3~5, L30~33	C15	Z4, Z5	L6~17, L22~29
C8	Z1, Z4	L22~29, L30~33

.

Subsequently, by integrating the fault current direction identification function, the fault current direction matrix corresponding to each fault scenario can be obtained, thus constructing a fault sample library containing diverse fault conditions. The dataset from the fault sample library is split into training and testing sets in a 7:3 ratio and is input into the COA-SVM model for training. The relevant parameter settings for the COA-SVM model are detailed in

Table 2. The parameters set for the classifier algorithm of COA-SVM.

Parameters	Values
Optimal Temperature temp	25
Food Factor $C_3$	3
Feeding Amount $p$	$C_1=0.2$, $\sigma =3$
Population Size of Crayfish	5
Number of Optimization Parameters	2
Upper Limit of Optimization Parameter Goals	penalty factor $c=100$ kernel function parameter $g=100$
Lower Limit of Optimization Parameter Goals	penalty factor $c=0.01$ kernel function parameter $g=0.01$

.

5.2. Simulation Results Analysis

5.2.1. Single-Point Fault Localization

In this section, single-point fault location tests are performed in four scenarios combining DG1–DG3 in off-grid conditions, as detailed in

Table 3. Simulation case of single-point failure localization.

Fault Scenario	Distributed Power Supply and Off-Grid Conditions	Fault Setting Line	FTU Device Reporting Information	Fault Line Segment Positioning Output Results	Positioning Results
1	[0,0,0]	L7	[1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]	[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]	L7
2	[0,1,0]	L18	[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]	[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]	L18
3	[1,0,1]	L24	[1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0]	[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]	L24
4	[1,1,1]	L19	[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,−1,−1,0,0,0,0,0,0,0,0,0,0,0,0]	[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]	L19

. Fault Scenario 1 corresponds to the switch states [K1,K2,K3] = [0,0,0], indicating that DG1–DG3 are all off-grid, and the branches of the distribution network are all passive. When a fault occurs on line L7, the FTU device uploads fault current direction information and utilizes the COA-SVM model trained in stage one to determine that this fault line segment belongs to Z5, thereby initially localizing the fault range. Subsequently, for each segmented line within region Z5, we calculate the cosine similarity with adjacent lines using Formula (13). Taking lines L6 and L7 in region Z5 as an example, the cosine similarity calculation formula is shown in Equation (14). The cosine similarity gradient map for region Z5 is illustrated in Figure 10, where the cosine similarity calculated for the fault line segment L7 shows a significant deviation compared to other lines, confirming that the specific fault line segment is L7, achieving accurate localization of the fault line segment within the fault zone. The simulation calculations for single-point fault localization across the four fault scenarios are presented in Table 3.

$$\left\{\begin{array}{l}\cos (S{L}_6,S{L}_7)={\displaystyle \frac{{\displaystyle \sum _{j=1}^{33}}S{L}_{6,j}·S{L}_{7,j}}{\sqrt{{\displaystyle \sum _{j=1}^{33}}S{L}_{6,j}^2}·\sqrt{{\displaystyle \sum _{j=1}^{33}}S{L}_{7,j}^2}}}\\ \cos (S{L}_7,S{L}_8)={\displaystyle \frac{{\displaystyle \sum _{j=1}^{33}}S{L}_{7,j}·S{L}_{8,j}}{\sqrt{{\displaystyle \sum _{j=1}^{33}}S{L}_{7,j}^2}·\sqrt{{\displaystyle \sum _{j=1}^{33}}S{L}_{8,j}^2}}}\end{array}\right.$$

(14)

In this context, $S{L}_6$, $S{L}_7$, and $S{L}_8$ represent the fault current directions for lines 6, 7, and 8, respectively, and j denotes the test distribution network node number, thus $S{L}_6=(S{L}_{6,1},S{L}_{6,2},\dots ,S{L}_{6,33})$.

5.2.2. Multi-Point Fault Localization

Similarly, four multi-point fault scenarios are selected for multi-point fault localization, as shown in

Table 4. Simulation case of multiple-points failure localization.

Fault Scenario	Distributed Power Supply and Off-Grid Conditions	Fault Setting Line	FTU Device Reporting Information	Fault Line Segment Positioning Output Results	Positioning Results
1	[0,0,0]	L9, L30	[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0]	[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0]	L9, L30
2	[0,1,0]	L4, L19	[1,1,1,1,−1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,−1,−1,−1,−1,−1,−1,−1,−1,0,0,0,0]	[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]	L4, L19
3	[1,0,1]	L6, L9, L21	[1,1,1,1,1,1,1,1,1,−1,−1,−1,−1,−1,−1,−1,−1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]	[0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0]	L6, L9, L21
4	[1,1,1]	L5, L23, L29	[1,1,1,1,1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0]	[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0]	L5, L23, L29

. Fault Scenario 2 corresponds to the switch states [K1,K2,K3] = [0,1,0], indicating that only DG2 is connected to the distribution network, with faults set to occur on lines L4 and L19. Based on the fault current direction information reported via the FTU, we utilize the COA-SVM model trained in stage one to determine that the fault line segments belong to Z2 and Z3. The specific fault line segments are localized using the cosine similarity anomaly information in zones Z2 and Z3. The localization results for the fault line segments are summarized in Table 4, and the cosine similarity gradient maps for fault line segments L4 and L19 are shown in Figure 11. The simulation calculations for multi-point fault localization across the four fault scenarios are presented in Table 4.

5.2.3. Algorithm Comparison

ADN fault localization can utilize either swarm intelligence or machine learning algorithms. The former employs a single-layer approach, creating an optimization model and solving it iteratively. In contrast, the latter establishes a high-dimensional mapping relationship between fault current direction data and corresponding fault segment labels for effective localization. To validate the superiority of the proposed fault location method over those based on swarm intelligence optimization algorithms and machine learning algorithms, three mainstream swarm intelligence optimization algorithms were selected, including Particle Swarm Optimization (PSO) [25], Grey Wolf Optimization (GWO) [26], and the Whale Optimization Algorithm (WOA) [27], which possess strong global search capabilities, high adaptability, and can handle multi-objective problems. Similarly, for traditional machine learning algorithms, the Back Propagation Neural Network (BPNN) [28], Long Short-Term Memory Network (LSTM) [29], and Extreme Learning Machine (ELM) [30] were selected due to their strong classification capabilities, high adaptability, and capacity to process large-scale data, serving as comparative bases. The fault location method based on swarm intelligence optimization algorithms uses the fault current direction measured via the FTU as input information and constructs the objective function as shown in Equation (15). By iteratively solving this model, the fault line location information is obtained.

$$\min f={\displaystyle \sum _{i=1}^N\left|S{L}_i-S{L}_i^{\ast }\right|}+0.5{\displaystyle \sum _{i=1}^N\left|S_i\right|}-100$$

(15)

where $S{L}_i$ and $S{L}_i^{\ast }$, respectively, represent the actual fault current direction identified via the FTU installed on line i and the anticipated fault current direction derived from Equation (1).

The fault location method based on machine learning algorithms utilizes the fault feature library of the target distribution network to conduct offline training of classification models. It achieves sectional fault localization of the faulty line through online invocation of the trained classification models. To this end, this paper employs cross-validation, splitting the dataset from the fault sample library into training and testing sets. Here, 70% of the dataset is used as a training set for classifier training, while the remaining sample data serves as the testing set for evaluating model accuracy. The confusion matrix helps in comprehensively understanding the classification performance of the model, where a specific element of the final confusion matrix shown in Figure 12 represents the cumulative sum of elements from all folds in cross-validation. To minimize the simulation environment’s impact on the results, each fault localization model runs 20 times, and the median accuracy is taken as the final accuracy of that model.

The confusion matrix obtained from testing the COA-SVM model in the first stage of the proposed two-stage fault localization method is shown in Figure 12. The diagonal numbers in Figure 12 indicate the number of samples where the predicted fault classifications align with the actual fault classifications. The more matching samples there are, the richer the color appears along the diagonal. The horizontal percentages represent the proportion of correctly classified predictions for a particular fault category, while the vertical percentages illustrate the proportion of actual classifications that were correctly predicted. It is evident from Figure 12 that the COA-SVM model can accurately localize all fault samples.

Correct classification occurs when the predicted fault classification matches the actual fault classification.

Table 5. Comparison analysis table of fault line segment location results.

Fault Location Method		Classification Result
		Correct Identification of Numbers	Accuracy/%	Simulation Time/s
Swarm intelligence optimization algorithm	PSO	360	72.58	128.75
	GWO	388	78.23	57.78
	WOA	376	75.81	63.27
Machine learning algorithms	BPNN	382	77.02	1.787
	LSTM	483	97.98	0.256
	ELM	488	98.39	0.063
Method of this paper		496	100	0.238

describes the accuracy of fault line localization based on the ratio of correctly classified samples to the total number of samples, reflecting the model’s recognition capabilities. The classification accuracy is calculated using Formula (16). Furthermore, the simulation time for each classification model in Table 5 is obtained via the tic and toc modules in Simulink. By comparing the simulation times of different models on the same testing set, one can assess the execution efficiency of each classification method.

$$ACC={\displaystyle \frac{N_T}{N}}\times 100\%$$

(16)

where $N_T$ refers to the total number of correctly identified samples, and $N$ is the total number of samples.

Table 5 presents results from a performance comparison involving the method proposed in this paper, alongside a swarm intelligence optimization algorithm and a machine learning algorithm for fault location in power grids. It assesses both the accuracy of locating single- and multi-point faults as well as the time required for online identification. The findings indicate that the proposed method achieves a fault location accuracy of 100%, with an online identification time of under 1 s. Conversely, the machine learning-based method shows an accuracy range of 77% to 98%, outperforming the swarm intelligence method. Despite the machine learning approach requiring offline training, it still manages to complete online fault location in less than 2 s. In contrast, the swarm intelligence algorithm achieves an accuracy between 72% and 78%, but its online fault location time varies significantly, needing between 57 and 128 s due to iterative calculations.

This analysis reveals that the two-stage fault location method introduced in this paper has significant advantages in both accuracy and time efficiency for the tested distribution network. It effectively ensures precise fault identification while allowing for rapid fault location. Compared to common classification models such as BPNN, LSTM, and ELM, the COA-SVM classification model proposed here offers superior accuracy and reduced online recognition times in identifying fault line segments. This improvement arises from its adaptive hyperparameter optimization capabilities and robust generalization ability, culminating in the best overall performance.

To visually assess the advantages of the proposed method against group intelligence optimization algorithms, this study focuses on accuracy and computational demands for online fault location. Figure 13 and Figure 14 show the convergence curves of the objective function f for both single- and multiple-fault scenarios. The analysis indicates that the effectiveness of group intelligence optimization algorithms in solving the fault location optimization model is largely dependent on the algorithm used. Notably, WOA and GWO converge faster than PSO. In multiple-fault scenarios, PSO tends to settle into local optima, leading to incorrect fault line segment identifications. In contrast, the proposed method uses an offline-trained classification model for online fault location, thus providing accurate fault line segment position outputs.

5.3. Fault-Tolerance Analysis

The operational landscape of FTU devices is complex and often unpredictable. This intricacy frequently results in data loss and misinformation when these devices transmit details regarding the direction of fault currents, especially during instances involving atypical FTU signals. To thoroughly evaluate the interference resilience of the two-stage fault location technique introduced in this study, this paper generated a range of abnormal FTU signals randomly, corresponding to the 15 fault types specified in Table 1. The number of abnormal FTUs fluctuated from 0 to 6. This manuscript examined the data on transmitted fault current directions, which was inclusive of these abnormal signals, employing a trained COA-SVM model to ascertain its efficacy in accurately classifying the fault zone. This study replicated the experiment 200 times and subjected the resultant accuracy metrics to statistical scrutiny, as illustrated in Figure 15 and

Table 6. The influence of different numbers of abnormal FTU signals on the accuracy of the fault localization method in this paper and the optimization algorithm based on swarm intelligence.

Method	The Accuracy of Fault Location under Different Numbers of Abnormal FTU Signals/%
	0	1	2	3	4	5	6
PSO	[71.2 75.3]	[38.8 64.4]	[32.9 58.6]	[20.6 43.8]	[11.5 38.8]	[4.8 31.6]	[0.2 22.3]
GWO	[76.0 80.1]	[60.8 72.1]	[50.2 64.5]	[36.4 52.9]	[28.3 46.8]	[22.2 42.7]	[13.1 40.0]
WOA	[72.5 77.2]	[66.3 74.1]	[60.2 73.3]	[52.1 64.9]	[34.7 49.1]	[26.2 40.1]	[16.2 34.3]
Method of this paper	[100 100]	[91.3 99.3]	[84.7 96.7]	[82.7 94.7]	[74.7 91.2]	[69.3 90.7]	[65.3 86.0]

. The findings reveal that an increase in the quantity of abnormal FTU signals correlates with a decline in the accuracy of both the proposed methodology and the fault localization approach based on a swarm intelligence optimization algorithm. Nevertheless, the presented methodology demonstrates significantly greater resilience to FTU abnormal signal interference in comparison to the swarm intelligence-driven localization technique. Importantly, when the number of abnormal FTU signals remains under three, the fault location accuracy surpasses 83%.

6. Conclusions

This paper considers the effect of distributed generation on fault currents upstream and downstream of the line after grid connection. It explores the fault current detection information from the FTU while addressing the impact of distributed generation. A two-stage fault location method for ADNs is proposed, based on the COA-SVM algorithm alongside cosine similarity measures. This method features low online computing power requirements and strong fault tolerance. It overcomes the issues of poor scalability, slow convergence, and low fault tolerance present in existing fault location methods based on swarm intelligence optimization algorithms. Thus, it meets the demands for real-time performance, accuracy, and robustness in active distribution network fault location. Initially, a fault signature database for the target distribution network is established through randomized simulations of both single- and multiple-fault scenarios utilizing the fault current state equation. Subsequently, an enhanced SVM classification model integrated with COA is proposed for the preliminary identification of fault line segments. Ultimately, the precise identification of the specific fault line segment is achieved through the application of cosine similarity mutation points corresponding to the fault zone. The findings are summarized as follows:

(1)

In contrast to conventional swarm intelligent optimization algorithms utilized for fault localization in distribution networks, the proposed approach first segments the distribution network lines, effectively minimizing the search dimensions for subsequent specific fault segments, thereby reducing the fault localization duration and enhancing efficiency;

(2)

Relative to other traditional classification models, the COA-SVM classification framework introduced herein exhibits reduced training duration and elevated classification accuracy, successfully pinpointing the fault segment in the testing distribution network with a 100% success rate;

(3)

This paper takes into account the impact of varying numbers of abnormal FTU signals on the precision of the proposed two-stage fault localization strategy. Compared to traditional swarm intelligence optimization techniques, the proposed method demonstrates superior fault tolerance, making it more applicable in real-world scenarios characterized by signal anomalies in FTUs.