Differential evolution algorithm optimization method and system for power distribution network fault location

Abstract

The invention provides a micro-grid multi-energy coordinated scheduling method and device, and the method comprises the steps: building a multi-energy coordinated scheduling optimization model containing time-varying constraints through obtaining the data of a photovoltaic power generation system, an energy storage system and a load system in a micro-grid, and carrying out the optimization solving through employing an improved particle swarm optimization algorithm, and designing a gridding vector current control strategy to realize fault ride-through control, executing multi-energy coordinated scheduling control, and realizing stable operation of the micro-grid through hierarchical execution. According to the method, the problem that a traditional micro-grid dispatching method is insufficient in stability and economical efficiency in the face of renewable energy source uncertainty and power grid faults is solved, and the reliability and economical efficiency of micro-grid operation are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system fault location, in particular to a differential evolution algorithm optimization method and system for distribution network fault location, which is suitable for fast and accurate positioning of distribution network faults in smart grids. BACKGROUND

[0002] Distribution network fault location technology is one of the key technologies to ensure the safe and stable operation of power systems, and with the continuous advancement of smart grid construction, the demand for fast and accurate positioning of distribution network faults is increasingly urgent. Traditional distribution network fault location methods mainly rely on electrical quantity measurement and simple logical judgment, which have obvious limitations in complex network topology and diversified fault types.

[0003] Existing distribution network fault location technologies mainly include positioning methods based on traveling wave principle and positioning methods based on impedance measurement. The method based on traveling wave principle detects the transient traveling wave signal generated by the fault, calculates the traveling wave propagation time to determine the fault location, but this method requires a very high sampling frequency and is easily affected by inaccurate line parameters and multiple reflections. The method based on impedance measurement measures the impedance value of the fault loop to calculate the fault distance, which has the advantage of simple implementation, but the accuracy is limited under the complex branch structure of the distribution network.

[0004] In recent years, the intelligent fault location method mainly uses the scheme of fault indicator combined with information fusion technology. This method installs fault indicators at key nodes of distribution lines, collects electrical quantity information such as current and voltage at the time of fault, and combines expert systems or machine learning algorithms to infer the fault location. The basic principle is to use the electrical quantity change characteristics of each measuring point at the time of fault to determine the most likely fault section through pattern recognition or optimization algorithm.

[0005] However, the existing technology still has the following key problems: first, the fault indicator arrangement lacks systematic optimization, resulting in incomplete or redundant fault information collection, affecting the positioning accuracy and economy; second, relying solely on electrical quantity information is easily affected by measurement noise and system disturbances, and the reliability is insufficient under complex fault conditions, and it is urgent to fuse multi-source heterogeneous information to improve the robustness of fault identification. SUMMARY

[0006] The purpose of the present application is to overcome the shortcomings of the prior art and provide a differential evolution algorithm optimization method and system for distribution network fault location, which realizes fast and accurate positioning of distribution network faults through fault indicator arrangement optimization, electrical quantity information processing, non-electrical quantity feature extraction, multi-dimensional information fusion, and a fault location model optimized by differential evolution algorithm.

[0007] To achieve the above purpose, the present application adopts the following technical solutions: The application discloses a differential evolution algorithm optimization method for fault location of a power distribution network. The method comprises the following steps: Based on the optimal arrangement position coordinate set of the fault indicator, the fault indicator is arranged at the corresponding node position, and electrical quantity information is collected; a state space model taking the amplitudes and phases of voltage and current as state variables is established; a Kalman filtering algorithm with process noise covariance update is used for prediction and update operation to obtain filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence and current phase sequence; Non-electrical quantity data such as vibration signals, sound signals, temperature changes and gas concentrations are collected by deploying multiple types of sensors at key positions of power distribution equipment; the collected original signals are filtered, denoised and normalized; a composite kernel matrix is constructed by using a radial basis function, a polynomial kernel function and a sigmoid kernel function; a sparse additive model is established, and an L1 regularization constraint term is introduced to realize automatic feature selection; and a non-electrical fault feature vector containing vibration feature coefficients, acoustic feature coefficients, temperature feature coefficients and gas feature coefficients is generated. The filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence and current phase sequence are dimensionally aligned and time-synchronized with the non-electrical fault feature vector; the fusion weights of electrical quantity features and non-electrical quantity features are dynamically adjusted according to the current fault type and network operation state; the high-dimensional features after fusion are reduced by using a principal component analysis method; and a three-dimensional comprehensive fault feature matrix containing electrical-non-electrical fusion features, time window features and spatial distribution features is constructed. Based on the three-dimensional comprehensive fault feature matrix, a mathematical optimization model for fault location is established by taking fault position coordinates as decision variables and minimizing the error between actual measurement features and theoretical calculation features as an objective function; the mutation, crossover and selection operations of the differential evolution algorithm are used for iterative solution; and fault position coordinates and corresponding confidence evaluation results are output.

[0008] Preferably, the optimal arrangement position coordinate set of the fault indicator is obtained by iterative optimization of the mutation, crossover and selection operations of the differential evolution algorithm, and the optimal arrangement position coordinate set of the fault indicator comprises the following steps: The population size of the differential evolution algorithm is initialized to be 2-3 times the number of nodes of the power distribution network; each individual is encoded by using a real number vector to represent an indicator arrangement scheme; and the maximum number of iterations is set. In the mutation operation, the DE / best / 1 / bin strategy is adopted. The best individual in the current population is selected as the basis vector, and two different individuals are randomly selected for difference operation. The mutation factor F is set to an adaptive value between 0.5 and 0.9 to generate the mutation vector. In the crossover operation, the mutated vector and the target vector are combined by a binomial crossover according to the crossover probability CR. The CR value is dynamically adjusted according to the number of generations, initially set to 0.9 and later reduced to 0.3 to generate the experimental vector. In the selection operation, the fitness values ​​of the corresponding layout schemes of the test vector and the target vector are calculated. The Pareto dominance relation is used to compare the multi-objective function values. Non-dominated solutions are retained as the next generation of individuals. For mutually non-dominated solutions, the crowding distance sorting mechanism is used for selection to obtain the set of optimal layout position coordinates of the fault indicator.

[0009] Preferably, the prediction and update operations are performed using a Kalman filter algorithm with process noise covariance updates, including: Establish state transition equations and observation equations with voltage and current amplitudes and phases as state variables, and initialize state estimates, error covariance matrix and process noise covariance matrix; In the prediction step, the state value and error covariance at the current moment are predicted according to the state transition equation. In the update step, the Kalman gain is calculated using the observations at the current time, and the state estimate and error covariance are updated. By calculating the statistical characteristics of the innovation sequence, the process noise covariance matrix is ​​adjusted in real time to adapt the filter to the noise characteristics under different operating conditions, thereby obtaining the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence, and current phase sequence.

[0010] Preferably, a composite kernel matrix is ​​constructed using radial basis functions, a polynomial kernel function, and a sigmoid kernel function, including: Radial basis functions are used to capture local similarity features, and the kernel parameter σ is determined through cross-validation optimization. A polynomial kernel function is used to extract multi-order interaction relationships between data, with the polynomial order set to 2-4. The sigmoid kernel function is used to simulate the nonlinear activation characteristics of neural networks; The composite kernel matrix K = α1K_RBF + α2K_poly + α3K_sigmoid is constructed by weighted combination of three kernel functions, where the optimal values ​​of the weight coefficients α1, α2, and α3 are determined by grid search and cross-validation.

[0011] Preferably, an automatic feature selection is achieved by establishing a sparse additive model and introducing an L1 regularization constraint term, including: In the constructed kernel space, establish a sparse additive model f(x) = Σᵢ =1 ⁿ βᵢK(xᵢ,x) + ε, where βᵢ is the kernel coefficient and ε is the noise term; Automatic feature selection is achieved by introducing an L1 regularization constraint term λ||β||1, and the regularization parameter λ is determined by the information criterion. The coordinate descent algorithm is used to solve the optimization problem. The kernel coefficients are iteratively updated until convergence. The feature components that contribute significantly to the failure mode are automatically identified and retained, while redundant and noise components are removed. By performing a reverse mapping operation from kernel space to the original space, vibration characteristic coefficients, acoustic characteristic coefficients, temperature characteristic coefficients, and gas characteristic coefficients are calculated to generate the non-electrical fault feature vector.

[0012] Preferably, a three-dimensional comprehensive fault feature matrix is ​​constructed, including electrical-non-electrical integrated features, time window features, and spatial distribution features, comprising: The filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence, and current phase sequence are aligned in dimension and synchronized in time with the non-electrical fault feature vector to ensure the consistency of different types of features on the time axis. Based on the current fault type and network operating status, the fusion weights of electrical and non-electrical quantity features are dynamically adjusted to generate a fused electrical-non-electrical feature vector. The time-series patterns of fault features are extracted using the time-sliding window method to generate time-window features. Based on the distribution network topology and the spatial distribution of fault indicators, a spatial distribution feature reflecting the spatial propagation characteristics of faults is constructed. The electrical-non-electrical fusion features, time window features, and spatial distribution features are combined to construct the three-dimensional comprehensive fault feature matrix.

[0013] Preferably, a mathematical optimization model for fault location is established based on the three-dimensional comprehensive fault feature matrix, including: A mathematical optimization model for fault location is established, with the fault location coordinates as the decision variable and minimizing the error between the actual measured characteristics and the theoretically calculated characteristics as the objective function. Initialize a population containing multiple candidate fault locations, with each individual representing one candidate fault location; By setting the maximum number of iterations and convergence criteria, and introducing an elite retention strategy and a diversity maintenance mechanism, a mathematical optimization model for fault location is obtained.

[0014] Preferably, the iterative solution is performed using the mutation, crossover, and selection operations of the differential evolution algorithm, including: An adaptive mutation mechanism guided by the current optimal solution is used in the mutation operation to generate new candidate fault locations; In the crossover operation, the positional information of different individuals is integrated, and the crossover probability is dynamically adjusted according to the individual fitness. In the selection operation, the objective function value corresponding to each candidate position is calculated, and the solution with higher fitness is retained for the next generation; The algorithm converges when the improvement of the consecutive preset algebraic optimal solutions is less than a preset threshold or when the maximum number of iterations is reached, and outputs the fault location coordinates and the corresponding confidence evaluation results.

[0015] A differential evolution algorithm optimization system for fault location in distribution networks includes: The indicator placement optimization module is used to acquire the distribution network topology and candidate installation node information, establish a multi-objective optimization function including fault coverage, cost constraints and information redundancy, and perform iterative optimization through mutation, crossover and selection operations of differential evolution algorithm to obtain the optimal placement coordinate set of fault indicators. The electrical quantity information processing module is used to deploy fault indicators at corresponding node positions and collect electrical quantity information based on the optimal arrangement position coordinate set of the fault indicators, establish a state space model with voltage and current amplitude and phase as state variables, and use the Kalman filter algorithm with process noise covariance update to perform prediction and update operations to obtain the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence and current phase sequence. The non-electrical quantity feature extraction module is used to collect non-electrical quantity data such as vibration signals, sound signals, temperature changes and gas concentrations through multiple types of sensors deployed at key locations of power distribution equipment. The module performs filtering, noise reduction and normalization preprocessing on the collected raw signals, constructs a composite kernel matrix through radial basis function, polynomial kernel function and sigmoid kernel function, establishes a sparse additive model and introduces L1 regularization constraint term to achieve automatic feature selection, and generates a non-electrical fault feature vector containing vibration feature coefficient, acoustic feature coefficient, temperature feature coefficient and gas feature coefficient. The multidimensional fusion module is used to perform dimension alignment and time synchronization between the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence, and current phase sequence and the non-electrical fault feature vector. It dynamically adjusts the fusion weights of electrical and non-electrical quantity features according to the current fault type and network operating status. It reduces the dimensionality of the fused high-dimensional features through principal component analysis to construct a three-dimensional comprehensive fault feature matrix that includes electrical-non-electrical fusion features, time window features, and spatial distribution features. The fault location module is used to establish a mathematical optimization model for fault location based on the three-dimensional comprehensive fault feature matrix, with fault location coordinates as decision variables and minimizing the error between actual measured features and theoretically calculated features as the objective function. It uses the mutation, crossover, and selection operations of the differential evolution algorithm to perform iterative solution and outputs the fault location coordinates and the corresponding confidence evaluation results.

[0016] The beneficial effects of this invention are as follows: 1. By using a differential evolution algorithm to globally optimize the placement of fault indicators, the effectiveness and coverage of fault information collection are improved, while the deployment cost is reduced. This solves the problem of insufficient coverage or information redundancy caused by the randomness of traditional indicator placement. 2. The Kalman filter algorithm with process noise covariance update is used to process electrical quantity information. It can adaptively adjust the filter parameters, improve the processing accuracy of electrical quantity information, and effectively overcome the influence of measurement noise and system disturbance. 3. A kernel-based sparse additive nonlinear model structure detection method is used to extract non-electrical fault features, organically integrating multiple non-electrical features such as vibration, sound, temperature, and gas, which enriches the sources of fault information and improves the accuracy and robustness of fault identification. 4. By using a multi-dimensional information fusion mechanism, electrical and non-electrical information are effectively integrated, achieving a comprehensive characterization and complementary enhancement of fault features, and improving the system's ability to identify complex fault types. 5. The fault location model based on the differential evolution algorithm has strong global search capability and fast convergence characteristics. It can achieve high-precision fault location under complex topology and diverse fault types, which significantly improves the efficiency of distribution network fault handling. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of the differential evolution algorithm optimization method for fault location in power distribution networks according to the present invention.

[0019] Figure 2 This is a structural block diagram of the differential evolution algorithm optimization system for fault location in power distribution networks according to the present invention.

[0020] Figure 3 This is a flowchart of the fault indicator layout optimization process of the present invention.

[0021] Figure 4 This is a flowchart of the Kalman filter algorithm with process noise covariance update according to the present invention.

[0022] Figure 5 This is a schematic diagram of the non-electrical quantity feature extraction process of the present invention.

[0023] Figure 6 This is a schematic diagram of the multi-dimensional feature fusion process of the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. The components of the embodiments of this disclosure described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this disclosure provided in the accompanying drawings is not intended to limit the scope of the claimed disclosure, but merely represents selected embodiments of this disclosure. All other embodiments obtained by those skilled in the art based on the embodiments of this disclosure without inventive effort are within the scope of protection of this disclosure.

[0025] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0026] In this document, the term "and / or" merely describes a relationship, indicating that three relationships can exist. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Furthermore, the term "at least one" in this document means any combination of at least two of any one or more elements. For example, including at least one of A, B, and C can mean including any one or more elements selected from the set consisting of A, B, and C.

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] like Figure 1 As shown, the differential evolution algorithm optimization method for distribution network fault location provided by this invention includes the following steps: S1: Obtain the distribution network topology and candidate installation node information, establish a multi-objective optimization function including fault coverage, cost constraints and information redundancy, and perform iterative optimization through mutation, crossover and selection operations of differential evolution algorithm to obtain the set of optimal placement coordinates of fault indicators.

[0029] In this invention, the distribution network topology and candidate installation node information are first acquired. A multi-objective optimization function incorporating fault coverage, cost constraints, and information redundancy is established. Iterative optimization is performed using mutation, crossover, and selection operations of a differential evolution algorithm to obtain the optimal set of coordinates for fault indicator placement. Specifically, the distribution network is abstracted as a graph structure composed of nodes and branches, where nodes include substations, branch points, load points, and switching points, and branches represent transmission lines. Each node where a fault indicator can be installed is used as a decision variable to construct the multi-objective optimization function. The fault coverage objective function is defined as the probability that all possible fault points are monitored by at least one indicator. The cost constraint function considers the indicator equipment cost, installation cost, and maintenance cost. The information redundancy function is used to avoid information duplication caused by excessively dense indicator placement. Subsequently, a differential evolution algorithm population is initialized, with each individual representing an indicator placement scheme, and the individual encoding is in the form of a real-number vector. In the mutation operation, a DE / best / 1 / bin strategy is adopted to select the best individual in the current population as the basis vector. Two different individuals are randomly selected for difference operations, and the mutation factor F is set to an adaptive value between 0.5 and 0.9. In the crossover operation, the mutated vector and the target vector are combined using a binomial crossover according to the crossover probability CR. The CR value is dynamically adjusted according to the number of generations. In the selection operation, the Pareto dominance relation is used to compare the values ​​of multiple objective functions, and non-dominated solutions are retained as the next generation of individuals. After multiple generations of evolution, the algorithm converges and outputs the Pareto optimal solution set, obtaining the set of coordinates of the optimal placement location of the fault indicator.

[0030] S2: Based on the optimal arrangement coordinate set of the fault indicator, deploy the fault indicator at the corresponding node position and collect electrical quantity information, establish a state space model with the amplitude and phase of voltage and current as state variables, and use the Kalman filter algorithm with process noise covariance update to perform prediction and update operations to obtain the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence and current phase sequence.

[0031] Based on the optimal set of fault indicator placement coordinates, fault indicators are deployed at corresponding node locations to collect electrical quantity information. A state-space model is established with voltage and current amplitudes and phases as state variables. A Kalman filter algorithm with process noise covariance updating is used for prediction and updating operations, resulting in filtered voltage amplitude sequences, current amplitude sequences, voltage phase sequences, and current phase sequences. Specifically, voltage and current amplitudes and phases are used as state variables to establish state transition equations and observation equations. In the prediction step, the state value and error covariance at the current moment are predicted according to the state transition equations. In the updating step, the Kalman gain is calculated using the current observation values ​​to update the state estimate and error covariance. The key innovation lies in the adaptive updating mechanism of the process noise covariance. By calculating the statistical characteristics of the innovative sequence, the process noise covariance matrix is ​​adjusted in real time, enabling the filter to adapt to noise characteristics under different operating conditions. This mechanism significantly improves the accuracy and robustness of electrical quantity processing and effectively addresses common measurement noise and system disturbance problems in distribution networks. The filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence, and current phase sequence serve as electrical characteristic data, providing a reliable electrical quantity information basis for subsequent fault location.

[0032] S3: Non-electrical data such as vibration signals, sound signals, temperature changes, and gas concentrations are collected by multiple types of sensors deployed at key locations of power distribution equipment. The collected raw signals are filtered, denoised, and normalized preprocessed. A composite kernel matrix is ​​constructed using radial basis functions, polynomial kernel functions, and sigmoid kernel functions. A sparse additive model is established, and an L1 regularization constraint term is introduced to achieve automatic feature selection. This generates a non-electrical fault feature vector containing vibration characteristic coefficients, acoustic characteristic coefficients, temperature characteristic coefficients, and gas characteristic coefficients.

[0033] Non-electrical data such as vibration signals, sound signals, temperature changes, and gas concentrations are collected by deploying multiple types of sensors at key locations in power distribution equipment. The raw signals are filtered, denoised, and normalized before preprocessing. A composite kernel matrix is ​​constructed using radial basis functions, polynomial kernel functions, and sigmoid kernel functions. A sparse additive model is established, and an L1 regularization constraint is introduced to achieve automatic feature selection, generating a non-electrical fault feature vector containing vibration, acoustic, temperature, and gas characteristic coefficients. Specifically, vibration signals are acquired using a triaxial accelerometer at a sampling frequency of 1 kHz; sound signals are collected using a wideband microphone array, capturing acoustic characteristics in the 20 Hz-20 kHz range; temperature sensors monitor real-time changes in equipment surface and ambient temperature; and gas sensors detect changes in the concentration of characteristic gases. The raw signals are filtered, denoised, and normalized before preprocessing to ensure that all types of signals are within the same numerical range. Radial basis functions are used to capture local similarity features, and the kernel parameter σ is determined through cross-validation optimization; polynomial kernel functions extract multi-order interaction relationships between data; and sigmoid kernel functions simulate the nonlinear activation characteristics of neural networks. A composite kernel matrix is ​​constructed by weighted combination of three kernel functions. A sparse additive model is established in the constructed kernel space, and an L1 regularization constraint term is introduced to achieve automatic feature selection. The coordinate descent algorithm is used to solve the optimization problem, automatically identifying and retaining feature components that significantly contribute to the fault mode. Through a reverse mapping operation from the kernel space to the original space, vibration characteristic coefficients, acoustic characteristic coefficients, temperature characteristic coefficients, and gas characteristic coefficients are calculated to generate non-electrical fault feature vectors, providing rich information sources beyond electrical quantities for fault location.

[0034] S4: Align the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence, and current phase sequence with the non-electrical fault feature vector in terms of dimension and time. Dynamically adjust the fusion weights of electrical and non-electrical features according to the current fault type and network operating status. Reduce the dimensionality of the fused high-dimensional features using principal component analysis to construct a three-dimensional comprehensive fault feature matrix that includes electrical-non-electrical fusion features, time window features, and spatial distribution features.

[0035] The filtered voltage amplitude, current amplitude, voltage phase, and current phase sequences are aligned in dimension and synchronized in time with the non-electrical fault feature vectors. The fusion weights of electrical and non-electrical features are dynamically adjusted based on the current fault type and network operating status. Principal component analysis is used to reduce the dimensionality of the fused high-dimensional features, constructing a three-dimensional comprehensive fault feature matrix that includes electrical-non-electrical fusion features, time window features, and spatial distribution features. Specifically, firstly, electrical and non-electrical data are unified to the same sampling frequency to ensure alignment of all feature data in the time dimension. Then, an adaptive weight allocation mechanism is designed to dynamically adjust the fusion weights of electrical and non-electrical features based on the fault type and network operating status. For example, for metallic short-circuit faults, electrical features are more significant, so their weights can be appropriately increased; for high-resistance grounding faults, non-electrical features are more identifiable, so their weights can be appropriately increased. A time sliding window method is used to extract the time series patterns of fault features, calculating statistical features, frequency domain features, and time-frequency features within each window. Based on the distribution network topology and the spatial distribution of fault indicators, a spatial distribution feature reflecting the spatial propagation characteristics of faults is constructed. Finally, the electrical-non-electrical fusion features, time window features, and spatial distribution features are combined to construct a three-dimensional comprehensive fault feature matrix. Principal component analysis is used to perform dimensionality reduction, retaining the main fault information components to form a dimensionality-reduced comprehensive fault feature matrix.

[0036] S5: Based on the three-dimensional comprehensive fault feature matrix, a mathematical optimization model for fault location is established with fault location coordinates as decision variables and minimizing the error between actual measured features and theoretically calculated features as the objective function. The model is then iteratively solved using the mutation, crossover, and selection operations of the differential evolution algorithm, and the fault location coordinates and corresponding confidence assessment results are output.

[0037] Based on a three-dimensional comprehensive fault feature matrix, a mathematical optimization model for fault location is established, using fault location coordinates as the decision variable and minimizing the error between actual measured features and theoretically calculated features as the objective function. The model is iteratively solved using mutation, crossover, and selection operations of the differential evolution algorithm, outputting the fault location coordinates and corresponding confidence assessment results. Specifically, the fault location coordinates are set as the decision variable, and the objective function is defined as the sum of squared errors between actual measured features and theoretically calculated features. A certain number of candidate fault location coordinates are randomly generated within the distribution network coverage area as the initial population, with each individual representing a candidate fault location. A maximum number of iterations and convergence criteria are set, and an elite retention strategy and diversity maintenance mechanism are introduced. In the mutation operation, an adaptive mutation mechanism guided by the current optimal solution is adopted, with the mutation factor dynamically adjusted according to the individual's fitness, allowing individuals with good fitness to perform local fine-grained searches and individuals with poor fitness to perform global exploration. In the crossover operation, the location information of different individuals is integrated, and the crossover probability is also dynamically adjusted according to the individual's fitness. In the selection operation, solutions with higher fitness are retained for the next generation. When the improvement of the optimal solution over multiple consecutive generations is less than a preset threshold or the maximum number of iterations is reached, the algorithm converges. The converged optimal solution is output as the fault location coordinates. At the same time, the confidence assessment results are calculated, including the confidence interval of the fault location and the probability distribution of the fault type, providing accurate location information and reliability assessment for subsequent fault handling and emergency repair.

[0038] The fault location method for power distribution networks of this invention optimizes the arrangement of fault indicators through differential evolution algorithm, combines multi-dimensional fusion of electrical and non-electrical quantity information to construct a comprehensive fault feature matrix, and uses differential evolution algorithm for fault location, significantly improving the accuracy and reliability of fault location. This method is particularly suitable for fault location in complex power distribution network environments, can quickly and accurately identify fault locations, reduce power outage time, improve power supply reliability, and has broad application prospects.

[0039] like Figure 3 As shown, the optimal set of coordinates for the fault indicator placement is obtained through iterative optimization using mutation, crossover, and selection operations of the differential evolution algorithm. Specifically, this includes: S1.1: Initialize a differential evolution algorithm population with a population size of 2-3 times the number of distribution network nodes. Each individual uses a real number vector encoding to represent an indicator placement scheme, and sets the maximum number of iterations.

[0040] Specifically, if the number of distribution network nodes is N, the population size is set to be between 2N and 3N. Each individual is a real number vector with a length equal to the number of candidate installation nodes. The vector elements represent whether a fault indicator is installed at that location and its installation parameters.

[0041] S1.2: In the mutation operation, the DE / best / 1 / bin strategy is adopted. The best individual in the current population is selected as the basis vector, and two different individuals are randomly selected for difference operation. The mutation factor F is set to an adaptive value between 0.5 and 0.9 to generate the mutation vector.

[0042] Specifically, for the i-th individual in the population, its mutation vector V_i is calculated as follows: V_i = X_best + F·(X_r1 - X_r2), where X_best is the best individual in the current population, X_r1 and X_r2 are two randomly selected different individuals, and F is the mutation factor, whose value is adaptively adjusted with the iteration process. It is larger in the early stage to enhance the global search capability and smaller in the later stage to improve the local search accuracy.

[0043] S1.3: In the crossover operation, the mutated vector and the target vector are combined by binomial crossover according to the crossover probability CR. The CR value is dynamically adjusted according to the number of generations. It is initially set to 0.9 and then reduced to 0.3 in the later stage to generate the test vector.

[0044] Specifically, for the j-th dimension of the i-th individual in the population, the formula for calculating its test vector U_i is: U_i,j = { V_i,j, if rand(0,1)≤CR or j=j_rand X_i,j, other cases } Here, j_rand is a randomly selected dimension index, ensuring that at least one dimension intersects. The CR value is dynamically adjusted with the number of iterations g, and is calculated as: CR(g) = 0.9 - 0.6·g / g_max, where g_max is the maximum number of iterations.

[0045] S1.4: In the selection operation, calculate the fitness values ​​of the corresponding layout schemes of the test vector and the target vector, compare the multi-objective function values ​​using the Pareto dominance relation, retain non-dominated solutions as the next generation of individuals, and select mutually non-dominated solutions using the crowding distance sorting mechanism to obtain the set of optimal layout position coordinates of the fault indicator.

[0046] Specifically, for the three objective functions (fault coverage maximization, cost constraint minimization, and information redundancy minimization), the fitness value of each individual is calculated, and Pareto dominance is used for comparison. If individual A is better than individual B in at least one objective and not worse than B in other objectives, then A dominates B. All non-dominated individuals in the population are retained as the non-dominated solution set. For individuals in the non-dominated solution set, their crowding distance is calculated, and individuals with larger crowding distances have higher retention priority. The algorithm converges when the improvement of the optimal solution over 20 consecutive generations is less than 0.001 or the maximum number of iterations is reached, and the Pareto optimal solution set is output. The final set of optimal fault indicator placement coordinates is selected from this set using a multi-criteria decision-making method.

[0047] like Figure 4 As shown, the prediction and update operations are performed using a Kalman filter algorithm with process noise covariance updates, specifically including: S2.1: Establish the state transition equation and observation equation with the magnitude and phase of voltage and current as state variables, and initialize the state estimate, error covariance matrix and process noise covariance matrix.

[0048] In step S2.1, the state transition equation and observation equation are first established, using the magnitude and phase of voltage and current as state variables. The state estimates, error covariance matrix, and process noise covariance matrix are then initialized. Specifically, the voltage magnitude, current magnitude, voltage phase, and current phase are combined to form a state vector, establishing the system's state transition equation to describe the changes in state quantities over time. Simultaneously, the observation equation is established to describe the relationship between observed values ​​and state quantities. The state transition matrix is ​​determined based on the electrical characteristics of the distribution network, while the observation matrix is ​​designed based on the measurement characteristics of the fault indicator. The initial state estimates are set using electrical quantities under normal operating conditions. The initial error covariance matrix reflects the uncertainty of the initial estimate, while the initial process noise covariance matrix is ​​set based on the statistical characteristics of the system's dynamic changes. This state-space model-based design comprehensively captures the dynamic characteristics of electrical quantities, laying the foundation for subsequent filtering. Specifically, the state vector x_k = [V_mag, I_mag, V_phase, I_phase]^T is defined, where V_mag and I_mag represent the magnitudes of voltage and current, respectively, and V_phase and I_phase represent the phases of voltage and current, respectively. The state transition equation is x_k = Ax_(k-1) + w_(k-1), where A is the state transition matrix, w_(k-1) is the process noise, which follows a zero-mean Gaussian distribution, and the covariance matrix is ​​Q_(k-1). The observation equation is z_k = Hx_k + v_k, where H is the observation matrix, v_k is the observation noise, which follows a zero-mean Gaussian distribution, and the covariance matrix is ​​R_k. The state estimate x̂_0, the error covariance matrix P_0, and the process noise covariance matrix Q_0 are initialized.

[0049] S2.2: In the prediction step, predict the state value and error covariance at the current moment according to the state transition equation.

[0050] In step S2.2, the current state value and error covariance are predicted based on the state transition equation. This prediction process is the first stage of the Kalman filter algorithm, using the state estimate from the previous time step and the system dynamic model to predict the current state. State prediction uses the state transition matrix to map the optimal state estimate from the previous time step to the current time step, obtaining the prior state estimate. Error covariance prediction considers the increased uncertainty during the state transition process. It calculates the prior error covariance at the current time step using the state transition matrix and the error covariance from the previous time step, while also incorporating the process noise covariance to reflect random disturbances in the system dynamic process. This prediction step can provide a preliminary estimate of the state based on the system model even without current observations, preparing for subsequent measurement updates. Specifically, the state prediction equation is: x̂_k^-= Ax̂_(k-1), and the error covariance prediction equation is: P_k^- = AP_(k-1)A^T + Q_(k-1).

[0051] S2.3: In the update step, the Kalman gain is calculated using the observations at the current time, and the state estimate and error covariance are updated.

[0052] In step S2.3, the Kalman gain is calculated using the current observations, updating the state estimate and error covariance. The Kalman gain is a key parameter that measures the weighting of the observed information; it is calculated using the prior error covariance, the observation matrix, and the observation noise covariance. A larger Kalman gain indicates higher confidence in the current observations; conversely, a smaller gain indicates greater confidence in the model prediction. The state estimate update combines the prior state estimate with the weighted observed information to obtain the posterior state estimate, i.e., the optimal state estimate at the current moment. The error covariance update reflects the reduction in uncertainty after incorporating observation information. This update process achieves optimal fusion of prediction and observation, enabling the extraction of the most probable true state information in noisy environments. Specifically, the Kalman gain calculation formula is: K_k = P_k^-H^T(HP_k^-H^T +R_k)^(-1), the state estimation update formula is: x̂_k = x̂_k^- + K_k(z_k - Hx̂_k^-), and the error covariance update formula is: P_k = (I - K_kH)P_k^-.

[0053] S2.4: By calculating the statistical characteristics of the innovation sequence, the process noise covariance matrix is ​​adjusted in real time to adapt the filter to the noise characteristics under different operating conditions, thereby obtaining the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence and current phase sequence.

[0054] In step S2.4, the statistical characteristics of the innovative sequence are calculated, and the process noise covariance matrix is ​​adjusted in real time to adapt the filter to the noise characteristics under different operating conditions, resulting in filtered voltage amplitude, current amplitude, voltage phase, and current phase sequences. The innovative sequence represents the difference between observed and predicted values, reflecting the deviation between the model and the actual system. By calculating the sample covariance matrix of the innovative sequence at recent times and comparing it with the theoretical covariance matrix, the adaptability of the current filter parameters can be evaluated. When there is a significant difference between the sample covariance and the theoretical covariance, it indicates that the system model or noise characteristics have changed, requiring adjustment of the process noise covariance matrix. The adjustment coefficient controls the adaptation rate; too large a coefficient leads to system instability, while too small a coefficient results in a slow response. Through this adaptive mechanism, the filter can maintain good performance under various operating conditions of the distribution network, effectively coping with complex situations such as system parameter changes, load fluctuations, and fault transients, and outputting high-quality electrical quantity sequences. Specifically, the innovation sequence is defined as e_k = z_k - Hx̂_k^-, and the sample covariance matrix of the innovation sequence at the most recent N time points is calculated as C_e = (1 / N)∑_(i=k-N+1)^k e_i·e_i^T. The theoretical innovation covariance matrix is ​​C_t = HP_k^-H^T + R_k. The process noise covariance matrix Q_k = Q_(k-1) + α·(C_e - C_t) is adjusted based on the difference between C_e and C_t, where α is the adjustment coefficient, ranging from 0.1 to 0.3. This adaptive adjustment mechanism enables the filter to adapt to noise characteristics under different operating conditions, improving filtering accuracy.

[0055] like Figure 5 As shown, a composite kernel matrix is ​​constructed using radial basis functions, polynomial kernel functions, and sigmoid kernel functions, specifically including: S3.1: Radial basis functions are used to capture local similarity features, and the kernel parameter σ is determined through cross-validation optimization.

[0056] Specifically, the radial basis function is in the form K_RBF(x,y) = exp(-||xy||^2 / (2σ^2)), where x and y are input vectors, ||xy|| represents the Euclidean distance, and σ is the kernel width parameter. The optimal value is selected in the range {0.1, 0.5, 1, 5, 10, 50} through k-fold cross-validation.

[0057] S3.2: A polynomial kernel function is used to extract multi-order interaction relationships between data, with the polynomial order set to 2-4. Specifically, the polynomial kernel function is in the form K_poly(x,y) = (x^T·y + c)^d, where c is a constant term, typically taken as 1, and d is the polynomial order, with the optimal value selected through cross-validation within the range of {2, 3, 4}.

[0058] S3.3: The sigmoid kernel function is used to simulate the nonlinear activation characteristics of neural networks. Specifically, the sigmoid kernel function is in the form K_sigmoid(x,y) = tanh(α·x^T·y + β), where α and β are kernel parameters that control the scaling and bias of the function, respectively. Optimization is performed using grid search within the ranges {0.01, 0.1, 1} and {0, 0.1, 1}, respectively.

[0059] S3.4: The composite kernel matrix K = α1K_RBF + α2K_poly + α3K_sigmoid is constructed by weighted combination of three kernel functions, where the optimal values ​​of the weight coefficients α1, α2, and α3 are determined through grid search and cross-validation. Specifically, the weight coefficients α1, α2, and α3 satisfy α1 + α2 + α3 = 1 and α1, α2, α3 ≥ 0. Grid search is performed in the range [0,1] with a step size of 0.1. Five-fold cross-validation is used to evaluate the performance of different weight combinations, and the weight combination with the smallest validation error is selected as the final weight coefficient.

[0060] To achieve automatic feature selection, a sparse additive model is established and an L1 regularization constraint term is introduced. Specifically, this includes: S3.5: Establish a sparse additive model f(x) = Σᵢ in the constructed kernel space. =1 ⁿ βᵢK(xᵢ,x) + ε, where βᵢ is the kernel coefficient and ε is the noise term. Specifically, for the input dataset {(x_i, y_i)}_(i=1)^m, where x_i is the non-electrical quantity data vector and y_i is the corresponding fault label, a sparse additive model f(x) = Σᵢ is established. =1 ᵐ βᵢK(xᵢ,x) + ε, where K(·,·) is the composite kernel function constructed above, βᵢ is the kernel coefficient to be solved, and ε is the noise term that satisfies a zero-mean Gaussian distribution.

[0061] S3.6: An L1 regularization constraint term λ||β||1 is introduced to achieve automatic feature selection. The regularization parameter λ is determined through an information criterion. Specifically, the optimization objective function of the model is set as follows: min_β (1 / m)·Σᵢ =1 ᵐ(y_i - Σⱼ =1 ᵐ βⱼK(xⱼ,xᵢ))² + λ||β||1 Where λ is the regularization parameter, the optimal value of which is determined by the Bayesian Information Criterion (BIC). The formula for calculating BIC is: BIC(λ) = m·log(RSS / m) + log(m)·df_λ Where RSS is the residual sum of squares, and df_λ is the effective degrees of freedom of the model, i.e., the number of non-zero kernel coefficients. The λ value that minimizes the BIC is selected as the final regularization parameter within the range {0.001, 0.01, 0.1, 1, 10}.

[0062] S3.7: The coordinate descent algorithm is used to solve the optimization problem, iteratively updating the kernel coefficients until convergence. It automatically identifies and retains feature components that significantly contribute to the failure mode, while removing redundant and noise components. Specifically, in each iteration, all coefficients except β₼ are fixed, and a one-dimensional optimization problem with respect to β₼ is solved: βⱼ^(new) = arg min_βⱼ (1 / m)·Σᵢ =1 ᵐ(y_i - Σ k ₌1, k ≠ⱼᵐ β k K(x k ,xᵢ) - βⱼK(xⱼ,xᵢ))² + λ|βⱼ| This problem has an analytical solution, which can be obtained through soft thresholding: βⱼ^(new) = S_λ(βⱼ^(old) + (1 / m)·Σᵢ =1 ᵐ K(xⱼ,xᵢ)·r_i^(-j)) Where r_i^(-j) = y_i - Σ k ₌1, k ≠ⱼᵐ β k K(x k Let xᵢ be the residual excluding the j-th term, and S_λ(·) be the soft threshold function, defined as: S_λ(z) = { z - λ, if z > λ 0, if |z| ≤ λ z + λ, if z < -λ } The algorithm converges when all kernel coefficients are iteratively updated until the L2 norm of the kernel coefficient change is less than a preset threshold (e.g., 0.0001) in two consecutive iterations or when the maximum number of iterations (e.g., 1000) is reached.

[0063] S3.8: By performing a reverse mapping operation from kernel space to the original space, calculate the vibration characteristic coefficient, acoustic characteristic coefficient, temperature characteristic coefficient, and gas characteristic coefficient to generate the non-electrical fault feature vector.

[0064] Specifically, utilizing the pre-image property of the kernel trick, features in the kernel space are projected back into the original feature space to calculate the vibrational characteristic coefficients v_vib = Σᵢ =1ᵐ βᵢ·K_vib(xᵢ,·), acoustic characteristic coefficients v_audio = Σᵢ =1 ᵐ βᵢ·K_audio(xᵢ,·), temperature characteristic coefficient v_temp = Σᵢ =1 ᵐ βᵢ·K_temp(xᵢ,·), gas characteristic coefficient v_gas =Σᵢ =1 ᵐ βᵢ·K_gas(xᵢ,·), where K_vib, K_audio, K_temp, and K_gas are kernel functions constructed for different types of non-electrical quantity data. The final non-electrical fault feature vector v = [v_vib, v_audio, v_temp, v_gas]^T is generated.

[0065] In one embodiment, in step S3.1, radial basis functions (RBFs) are used to capture local similarity features, and the kernel parameters are determined through cross-validation optimization. RBFs are a type of kernel function that uses the distance between points as its independent variable. They possess good local properties and can effectively capture local similarity features in non-electrical quantity data. Their core parameter is the kernel width parameter, which controls the range of the kernel function's effect. Too large a parameter can lead to over-smoothing and loss of local features; too small a parameter can easily overfit noise. To determine the optimal parameter value, a k-fold cross-validation method is used, dividing the dataset into k subsets. One subset is used as the validation set, and the rest as the training set, evaluating the model performance under different parameter values. By performing a grid search within a preset parameter value range, the parameter value with the smallest validation error is selected as the final kernel width parameter. This data-driven parameter optimization method ensures that the RBF can capture local patterns and similar structures in non-electrical quantity data to the greatest extent.

[0066] In step S3.2, a polynomial kernel function is used to extract multi-order interaction relationships between data, with the polynomial order set to 2-4. The polynomial kernel function implicitly constructs high-order feature combinations in the feature space by adding a constant term to the inner product of the original features and then raising it to a certain power, capturing nonlinear interaction relationships in non-electrical quantity data. The polynomial order is a key parameter determining the model complexity; a higher order allows for more complex relationships to be expressed, but also increases the likelihood of overfitting. The constant term affects the balance between low-order and high-order terms. Cross-validation within the 2-4 order range is used to select the most suitable polynomial order for different types of non-electrical quantity data. For example, vibration signals may require a higher order to capture complex frequency interactions, while temperature changes may only require a lower order. This extraction of multi-order interaction features enriches the expressive power of non-electrical quantity features and provides important evidence for fault mode identification.

[0067] In step S3.3, the sigmoid kernel function is used to simulate the nonlinear activation characteristics of neural networks. The sigmoid kernel function maps the feature inner product to an interval using a hyperbolic tangent function, exhibiting nonlinear characteristics similar to neural network activation functions, and is able to handle threshold effects and saturation phenomena in non-electrical quantity data. The scaling parameter in the kernel function controls the steepness of the decision boundary, while the bias parameter affects the symmetry of the function. A grid search method is used to evaluate the model performance under different parameter combinations, and the optimal parameter configuration is selected. The sigmoid kernel function is particularly suitable for handling fault signals with abrupt changes, such as sudden changes in gas concentration at the time of fault occurrence, or nonlinear changes in temperature before and after a critical point. By introducing this nonlinear activation characteristic, the model can better identify weak signs before a fault occurs and nonlinear dynamic characteristics during the fault process.

[0068] In step S3.4, a composite kernel matrix is ​​constructed by weighted combination of three kernel functions, with the optimal weight coefficients determined through grid search and cross-validation. The composite kernel matrix is ​​a linear combination of the three basic kernel functions, each capturing different characteristics of non-electrical quantity data: the radial basis function captures local similarity, the multinomial kernel function extracts multi-order interaction relationships, and the sigmoid kernel function simulates nonlinear activation characteristics. The weight coefficients determine the importance of each characteristic in the final model and must satisfy the constraints of being non-negative and summing to one. A grid search method is used to sample the weight space with a certain step size, and cross-validation is used to evaluate the model performance under each weight set, selecting the weight combination with the smallest validation error. This composite kernel method combines the advantages of different kernel functions, improving the model's expressive power and generalization performance, and enabling it to adapt to various complex non-electrical quantity fault modes.

[0069] In step S3.5, a sparse additive model is established in the constructed kernel space, where is the kernel coefficient and is the noise term. The sparse additive model is a flexible nonparametric model that maps input data to a high-dimensional feature space using a kernel method, and then constructs a linear model in this space. For the non-electrical quantity dataset and its corresponding fault labels, the model establishes a mapping relationship from the kernel function to the fault labels. The kernel coefficients are key parameters of the model, determining the contribution weight of each sample point to the model output. The noise term represents random perturbations that the model cannot explain, assumed to follow a zero-mean Gaussian distribution. This kernel-basis additive model structure has a good theoretical foundation and practical performance, can handle high-dimensional nonlinear data, and is suitable for modeling complex non-electrical quantity fault characteristics.

[0070] In step S3.6, an L1 regularization constraint is introduced to achieve automatic feature selection. The regularization parameter is determined using the Bayesian information criterion. L1 regularization, by adding an L1 norm penalty term to the kernel coefficients in the objective function, causes most unimportant kernel coefficients to approach zero, thereby achieving sparse model representation and automatic feature selection. The regularization parameter controls the degree of sparsity; a larger parameter results in a sparser model but may lose useful information, while a smaller parameter results in a more complex model but may overfit. The model performance under different regularization parameters is evaluated using the Bayesian information criterion, seeking a balance between the sum of squared residuals and model complexity. The Bayesian information criterion considers both goodness of fit and complexity penalty, helping to select the optimal regularization parameter and ensuring a balance between interpreting data and generalization ability. This automatic feature selection mechanism based on L1 regularization can extract the most discriminative features from high-dimensional non-electrical quantity data, improving model interpretability and computational efficiency.

[0071] In step S3.7, the coordinate descent algorithm is used to solve the optimization problem, iteratively updating the kernel coefficients until convergence. It automatically identifies and retains feature components that significantly contribute to the fault mode, while removing redundant and noise components. The coordinate descent algorithm is an efficient optimization method, particularly suitable for optimization problems with L1 regularization. The algorithm fixes all but one variable each time, solves a one-dimensional optimization problem with respect to that variable, and then iteratively updates all variables. For L1 regularized problems, the one-dimensional subproblem has an analytical solution, which can be efficiently solved using a soft thresholding operation. The residual represents the prediction error after removing the current feature, serving as a measure of the current feature's importance. The soft thresholding function sets coefficients less than the threshold to zero, achieving sparsity. The algorithm iterates until the convergence condition is met, such as when the kernel coefficients change very little between two consecutive iterations or when the maximum number of iterations is reached. Through this iterative optimization process, the model can automatically select the most valuable feature components for fault identification, eliminate redundant information and noise interference, and construct a concise and efficient fault feature representation.

[0072] In step S3.8, vibration characteristic coefficients, acoustic characteristic coefficients, temperature characteristic coefficients, and gas characteristic coefficients are calculated through a reverse mapping operation from the kernel space to the original feature space, generating a non-electrical fault feature vector. Utilizing the pre-image property of the kernel method, the model parameters learned in the kernel space are projected back into the original feature space, and the characteristic coefficients corresponding to each type of non-electrical quantity data are calculated. Vibration characteristic coefficients contain key information about the equipment's vibration modes, enabling the identification of mechanical faults and structural anomalies; acoustic characteristic coefficients capture the spectral characteristics and temporal patterns in sound signals, aiding in the detection of faults such as discharge and mechanical friction; temperature characteristic coefficients reflect heat distribution and temperature variation patterns, indicating problems such as overheating and poor contact; gas characteristic coefficients contain information on gas concentration trends and component ratios, enabling early detection of insulation degradation and internal faults. These characteristic coefficients combine to form the non-electrical fault feature vector, providing rich non-electrical quantity information for subsequent multi-dimensional feature fusion and fault localization, greatly enhancing the system's ability to identify complex fault types.

[0073] like Figure 6 As shown, a three-dimensional comprehensive fault feature matrix is ​​constructed, which includes electrical-non-electrical integrated features, time window features, and spatial distribution features. Specifically, it includes: S4.1: The filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence, and current phase sequence are aligned in dimension and synchronized in time with the non-electrical fault feature vector to ensure consistency of different types of features on the time axis. Specifically, electrical and non-electrical quantity data are unified to the same sampling frequency. A sliding window method is used to downsample high-frequency sampling data or interpolate low-frequency sampling data to ensure that all feature data are aligned in the time dimension. For feature vectors of different lengths, zero-padding or truncation is used to make their dimensions consistent. Time synchronization of different data sources is achieved through timestamp comparison to ensure the time consistency of the fused features.

[0074] In step S4.1, the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence, and current phase sequence are aligned in dimension and synchronized in time with the non-electrical fault feature vectors to ensure consistency of different types of features on the time axis. This step addresses the fundamental prerequisite for multi-source heterogeneous data fusion. First, for data sources with different sampling frequencies, a unified time reference is used to resample all data to the same sampling frequency. For high-frequency sampled electrical quantity data, a sliding window method can be used for averaging downsampling; for low-frequency sampled non-electrical quantity data, interpolation techniques can be used for upsampling. To address the issue of inconsistent sequence lengths, zero-padding or truncation strategies are used to unify the dimensions of each feature vector. To ensure time synchronization, the system establishes a unified time reference system by comparing the timestamps of each data source and performs time shift compensation as needed to eliminate delay differences between different sensors and data acquisition systems. This rigorous dimension alignment and time synchronization process lays a solid foundation for subsequent feature fusion, ensuring the correlation and consistency of different types of features in the time dimension, enabling the fused features to accurately reflect the entire process of fault occurrence and development.

[0075] S4.2: Based on the current fault type and network operating status, dynamically adjust the fusion weights of electrical and non-electrical quantity characteristics to generate a fused electrical-non-electrical feature vector. Specifically, for different fault types (such as single-phase grounding, two-phase short circuit, three-phase short circuit, etc.) and network operating statuses (such as heavy load, light load, oscillation, etc.), an adaptive weight allocation mechanism is designed. The electrical quantity characteristic weight w_e and the non-electrical quantity characteristic weight w_n are dynamically calculated based on the fault type characteristic importance scoring table, satisfying w_e + w_n = 1. For example, for metallic short-circuit faults, electrical quantity characteristics are more significant, so w_e = 0.7 and w_n = 0.3 can be set; for high-resistance grounding faults, non-electrical quantity characteristics are more identifiable, so w_e = 0.4 and w_n = 0.6 can be set. The formula for calculating the fused electrical-non-electrical feature vector is: f_fusion = [w_e·f_electrical, w_n·f_non_electrical] Where f_electrical is the electrical quantity feature vector and f_non_electrical is the non-electric quantity feature vector.

[0076] In step S4.2, the fusion weights of electrical and non-electrical quantity features are dynamically adjusted based on the current fault type and network operating status to generate a fused electrical-non-electrical feature vector. This step achieves adaptive fusion at the feature level, enhancing the system's ability to identify different fault types. First, a fault type feature importance scoring table is established to assign initial weights to various features under different fault types. For example, for metallic short-circuit faults, electrical quantity features are more prominent and should be given higher weights; while for high-resistance grounding faults, non-electrical quantity features are more identifiable and their weights should be increased. Second, the initial weights are adjusted based on the current network operating status, such as heavy load, light load, or oscillation state. Third, the weight allocation is automatically fine-tuned by analyzing the signal-to-noise ratio of electrical and non-electrical quantity features in real time, increasing the proportion of features with good signal quality. Finally, based on the determined weight coefficients, the standardized electrical and non-electrical quantity feature vectors are weighted and combined to generate the fused electrical-non-electrical feature vector. This dynamic weight allocation mechanism significantly improves the flexibility and targeting of feature fusion, enabling the system to optimize feature combinations based on actual fault conditions, thereby improving the accuracy and reliability of fault identification.

[0077] S4.3: The time-series pattern of fault features is extracted using the time-sliding window method to generate time-window features. Specifically, a sliding window of length L and a window step size of S are applied to the fused feature vector to extract time-series features. Within each window, statistical features (such as mean, variance, skewness, and kurtosis), frequency domain features (such as spectral power density and dominant frequency), and time-frequency features (such as wavelet transform coefficients) are calculated to generate the time-window feature f_time.

[0078] In step S4.3, a time-sliding window method is used to extract the time-series patterns of fault features, generating time-window features. This step aims to capture the temporal dynamics of the fault development process and enrich the temporal dimension of the feature representation. Specifically, a time window of appropriate length is selected (usually 3-5 times the fault feature time constant), and it slides across the fused feature vector with a certain step size. Within each window, various statistical features are calculated, including mean, variance, standard deviation, skewness, and kurtosis, reflecting the central tendency, dispersion, and distribution shape of the data; frequency domain features are extracted, including spectral power density, dominant frequency, and band energy ratio, revealing the frequency composition of the signal; time-frequency features, such as wavelet transform coefficients and Hilbert-Huang transform results, are analyzed to capture the time-varying characteristics of non-stationary signals. In addition, trend features, abrupt change features, and periodic features within the window can be calculated to characterize the dynamic process of fault development. All these features combined constitute the time-window feature vector, which not only contains the instantaneous features of the fault but also captures the precursors before the fault occurs and the evolution process after the fault occurs, providing rich temporal contextual information for fault localization.

[0079] S4.4: Based on the distribution network topology and the spatial distribution of fault indicators, a spatial distribution feature reflecting the spatial propagation characteristics of faults is constructed. Specifically, a spatial adjacency matrix is ​​constructed using the distribution network topology information, the electrical and physical distances between each measuring point are calculated, and the spatial propagation law and attenuation characteristics of the features are analyzed. For each fault indicator measuring point, a feature difference vector with its adjacent nodes is constructed to capture the spatial gradient information of the fault signal and generate the spatial distribution feature f_space.

[0080] In step S4.4, a spatial distribution feature reflecting the spatial propagation characteristics of faults is constructed based on the distribution network topology and the spatial distribution of fault indicators. This step aims to enhance the spatial dimension of the feature representation by utilizing the spatial propagation laws of fault information. First, a spatial adjacency matrix is ​​established based on the physical topology of the distribution network, defining the electrical and physical distances between each measuring point. Then, for each fault indicator measuring point, the feature difference vector with its adjacent nodes is calculated to construct a feature reflecting the local spatial gradient. The spatial propagation attenuation law of features is analyzed, a distance-based attenuation model is established, and the attenuation coefficient is extracted as a spatial feature. Using the geographical distribution information of the measuring points, a spatial interpolation model is constructed to estimate the feature values ​​of unmeasuring points, generating a feature distribution map covering the entire distribution network. Graph theory methods are used to analyze the flow and convergence of features in the network, identifying the source and sink points of features to assist in fault source location. Finally, the above spatial analysis results are organized into a structured spatial distribution feature vector. This topology-based spatial feature extraction method fully utilizes the spatial propagation laws of fault information in the distribution network, providing important spatial dimension basis for fault location, and is particularly suitable for fault location problems in distribution networks with complex branch structures.

[0081] S4.5: Combine the electrical-non-electrical fusion features, time window features, and spatial distribution features to construct the three-dimensional comprehensive fault feature matrix. Specifically, the fusion feature f_fusion, the time window feature f_time, and the spatial distribution feature f_space are combined into a three-dimensional feature matrix F = [f_fusion, f_time, f_space], where the first dimension represents the feature type, the second dimension represents the time series, and the third dimension represents the spatial distribution. Principal component analysis is used to reduce the dimensionality of the feature matrix, retaining principal components that explain more than 95% of the variance, resulting in the dimensionality-reduced comprehensive fault feature matrix F_reduced.

[0082] In step S4.5, electrical-non-electrical fusion features, time window features, and spatial distribution features are combined to construct a three-dimensional comprehensive fault feature matrix. This step integrates information across three dimensions: time, space, and feature type, forming a comprehensive fault characterization. First, the three types of features generated in the previous steps are organized according to a unified data structure to construct a three-dimensional tensor. The first dimension represents the feature type (electrical-non-electrical fusion features, time series features, and spatial distribution features), the second dimension represents the time series, and the third dimension represents the spatial distribution. To process this high-dimensional feature matrix, principal component analysis is used for dimensionality reduction, retaining principal components that explain more than 95% of the variance, effectively reducing feature redundancy and improving computational efficiency. During dimensionality reduction, different strategies are adopted for different types of features: for electrical-non-electrical fusion features, the focus is on retaining principal components with strong discriminative power; for time window features, principal components that can characterize the time series pattern are retained; and for spatial distribution features, principal components that reflect the spatial structure are retained. The final comprehensive fault feature matrix, after dimensionality reduction, retains key information while reducing the dimensionality of the feature space, providing an efficient feature representation for subsequent fault location optimization calculations.

[0083] A mathematical optimization model for fault location is established based on the aforementioned three-dimensional comprehensive fault feature matrix, specifically including: S5.1: Using the fault location coordinates as the decision variable and minimizing the error between the actual measured characteristics and the theoretically calculated characteristics as the objective function, a mathematical optimization model for fault location is established. Specifically, let the fault location coordinates be p = (x, y), and define the objective function as: min_p J(p) = ||F_measured - F_calculated(p)||_2^2 Where F_measured is the comprehensive fault characteristic matrix measured in practice, F_calculated(p) is the theoretical characteristic matrix calculated by the power grid model assuming the fault location is p, and ||·||_2 represents the F norm of the matrix.

[0084] S5.2: Initialize a population containing multiple candidate fault locations, with each individual representing a candidate fault location. Specifically, randomly generate NP candidate fault location coordinates within the distribution network coverage area, where NP is set to be between 20 and 50. Each individual is represented as p_i = (x_i, y_i), where i = 1, 2, ..., NP, and x_i and y_i are the horizontal and vertical coordinates of the fault location, respectively, limited to the effective area of ​​the distribution network.

[0085] S5.3: A maximum number of iterations and convergence criteria are set, and an elite retention strategy and a diversity maintenance mechanism are introduced to obtain the mathematical optimization model for fault location. Specifically, the maximum number of iterations MAX_GEN is set to 100, and the convergence criteria are that the improvement of the optimal solution for 10 consecutive generations is less than 0.0001 or the maximum number of iterations is reached. An elite retention strategy is introduced to ensure that the optimal solution of the current generation is always retained in the next generation. A diversity maintenance mechanism is introduced; when the population diversity index is lower than a threshold, some individuals are reinitialized to prevent the algorithm from getting trapped in local optima.

[0086] The differential evolution algorithm is used to iteratively solve the problem through mutation, crossover, and selection operations, specifically including: S5.4: In the mutation operation, an adaptive mutation mechanism guided by the current optimal solution is used to generate new candidate fault locations. Specifically, for the i-th individual, its mutation vector is calculated using the following formula: v_i = p_best + F_i·(p_r1 - p_r2) Where p_best is the individual with the best fitness in the current population, p_r1 and p_r2 are two randomly selected different individuals, and F_i is the adaptive mutation factor, calculated using the following formula: F_i = F_min + (F_max - F_min)·(1 - J(p_i) / J_max) Where F_min=0.4, F_max=0.9, J(p_i) is the objective function value of individual p_i, and J_max is the maximum objective function value in the current population. This adaptive mutation mechanism allows individuals with good fitness to use a smaller mutation factor for local search, while individuals with poor fitness use a larger mutation factor for global exploration.

[0087] S5.5: In the crossover operation, the positional information of different individuals is fused, and the crossover probability is dynamically adjusted according to the individual fitness. Specifically, for the j-th dimension of the i-th individual, the formula for calculating its trial vector u_i is: u_i,j = { v_i,j, if rand(0,1)≤CR_i or j=j_rand p_i,j, other cases } Where j_rand is a randomly selected dimension index, ensuring that at least one dimension crosses. CR_i is the adaptive crossover probability, calculated using the following formula: CR_i = CR_min + (CR_max - CR_min)·(J(p_i) - J_min) / (J_max - J_min) Where CR_min=0.2, CR_max=0.8, and J_min and J_max are the minimum and maximum objective function values ​​in the current population, respectively. This adaptive crossover mechanism allows individuals with good fitness to maintain their characteristics with a smaller crossover probability, while individuals with poor fitness use a larger crossover probability to obtain more mutation information.

[0088] S5.6: In the selection operation, calculate the objective function value corresponding to each candidate position and retain the solution with higher fitness for the next generation. Specifically, calculate the objective function value J(u_i) of the trial vector u_i. If J(u_i) < J(p_i), then u_i replaces p_i for the next generation; otherwise, p_i is retained.

[0089] S5.7: The algorithm converges when the improvement of consecutive algebraic optimal solutions is less than a preset threshold or the maximum number of iterations is reached, and the fault location coordinates and corresponding confidence assessment results are output. Specifically, the improvement of the optimal solutions for 10 consecutive generations is calculated. If it is less than 0.0001 or the maximum number of iterations MAX_GEN=100 is reached, the algorithm stops iterating. The converged optimal solution p_best = (x_best, y_best) is output as the fault location coordinates, and the confidence assessment results are calculated, including the 95% confidence interval of the fault location and the probability distribution of the fault type.

[0090] In one embodiment, In step S5.1, a mathematical optimization model for fault location is established, using the fault location coordinates as the decision variable and minimizing the error between the actual measured characteristics and the theoretically calculated characteristics as the objective function. This step transforms the fault location problem into a mathematical optimization problem, laying the foundation for subsequent algorithmic solutions. Fault location coordinates are typically represented as point coordinates in two-dimensional space, representing the specific location of the fault. The objective function is defined as the error measure between the actual measured comprehensive fault feature matrix and the theoretical feature matrix calculated using the power grid model under the assumed fault location, commonly represented by the Euclidean distance (F-norm). The theoretical feature matrix is ​​the expected characteristic value calculated based on the assumed fault location using the power grid model and the fault model; it reflects the functional relationship between the fault location and the measured characteristics. The idea of ​​error minimization is that when the assumed fault location is close to the actual fault location, the calculated theoretical characteristics should be closest to the actual measured characteristics, minimizing the error. This model-based optimization method combines prior knowledge (power grid model) with real-time measurement data, forming a fault location method with both physical foundation and data support, applicable to distribution networks with various complex topologies.

[0091] In step S5.2, a population containing multiple candidate fault locations is initialized, with each individual representing a candidate fault location. This step provides the starting point for the optimization search of the differential evolution algorithm. First, the effective coverage area of ​​the distribution network is determined, i.e., the line areas where faults may occur, usually defined by a geographic information system. Then, an appropriate number of candidate fault locations are randomly generated within this area to form the initial population. The population size is usually set to 20-50 individuals; too large a population will increase the computational burden, while too small a population may affect the comprehensiveness of the search. Each individual is represented by a two-dimensional coordinate, representing a possible fault point in the distribution network. During initialization, prior knowledge can be used as guidance, such as generating more candidate points in areas with higher probability based on preliminary fault segment information, or increasing the sampling density in high-fault areas based on historical fault statistics. In addition, the diversity of the initial population should be ensured to cover different areas of the search space and avoid prematurely getting trapped in local optima. After initialization, an initial fitness value is calculated for each candidate location to prepare for subsequent evolutionary operations.

[0092] In step S5.3, the maximum number of iterations and convergence criteria are set, and an elite retention strategy and a diversity maintenance mechanism are introduced to obtain the mathematical optimization model for fault location. This step determines the termination condition and optimization strategy of the algorithm, ensuring the effectiveness and robustness of the search process. The maximum number of iterations is usually set to 100-200 generations as a fallback termination condition for the algorithm. The convergence criteria are set to the optimal solution improvement being less than a preset threshold (e.g., 0.0001) for several consecutive generations (e.g., 10 generations). When this condition is met, the algorithm can be terminated early to save computational resources. The elite retention strategy ensures that the optimal solution in the current generation will be retained in the next generation, preventing excellent solutions from being lost during evolution. The diversity maintenance mechanism is to prevent the population from converging to a local optimum too early. When the population diversity index (e.g., the average distance between individuals) is detected to be below a certain threshold, some individuals are reinitialized or perturbed to increase the population's exploration ability. In addition, constraints can be added to the optimization model according to the specific characteristics of the fault, such as limiting the search range to the vicinity of the power distribution line, or setting specific feasible region constraints according to the fault type. The combined application of these strategies and mechanisms forms a fault location optimization model that can converge efficiently and is not prone to getting trapped in local optima.

[0093] In step S5.4, an adaptive mutation mechanism guided by the current optimal solution is used in the mutation operation to generate new candidate fault locations. This step is one of the core innovations of the differential evolution algorithm, improving algorithm performance by adaptively adjusting the mutation strategy. The basic idea is to guide the population to search for more promising regions based on the current optimal solution, while dynamically adjusting the mutation intensity according to the individual's fitness. Specifically, for each individual, its mutation vector consists of the best individual in the current population plus the difference vector between two randomly selected different individuals, multiplied by a mutation factor. The mutation factor uses an adaptive mechanism, dynamically adjusted according to the individual's fitness: individuals with good fitness (small objective function value) use a smaller mutation factor for refined local search; individuals with poor fitness use a larger mutation factor to enhance global exploration capabilities. The adjustment range of the mutation factor is usually between 0.4 and 0.9, and the adaptive formula normalizes the individual fitness and maps it to this range. This adaptive mutation mechanism balances the algorithm's exploration and utilization capabilities, enabling the search process to automatically switch between global exploration and local refinement, greatly improving the localization efficiency in complex fault scenarios.

[0094] In step S5.5, positional information from different individuals is fused during the crossover operation, with the crossover probability dynamically adjusted based on individual fitness. This step enhances population diversity through gene exchange and promotes information exchange between different search areas. For each dimension of each individual, the crossover probability determines whether to retain the original positional information or adopt the mutated new positional information. To ensure that at least one dimension undergoes crossover, a dimension is usually randomly selected for forced crossover. The crossover probability also employs an adaptive mechanism, dynamically adjusting based on individual fitness: individuals with good fitness use a lower crossover probability to maintain their original superior characteristics; individuals with poor fitness use a higher crossover probability to increase the chance of information exchange. The adjustment range of the crossover probability is typically between 0.2 and 0.8, mapped to this range after normalizing individual fitness. This adaptive crossover mechanism, in conjunction with the preceding adaptive mutation mechanism, jointly promotes efficient exploration of the search space and rapid discovery of the optimal solution, adapting to fault location problems of varying complexity.

[0095] In step S5.6, the objective function value corresponding to each candidate position is calculated during the selection operation, and solutions with higher fitness are retained for the next generation. This step achieves fitness-based selection and is a key step in the differential evolution algorithm's evolution towards the optimal solution. Specifically, for each individual's trial vector, its corresponding objective function value is calculated, which is the error between the actual measured characteristics and the theoretically calculated characteristics. Then, the objective function value of the trial vector is compared with the objective function value of the original individual. If the objective function value of the trial vector is smaller (smaller error), the trial vector replaces the original individual for the next generation; otherwise, the original individual is retained. This binary selection strategy ensures that the average fitness of the population does not decrease, while also preserving valuable search directions. It is worth noting that the calculation of the objective function may be quite complex, requiring the use of a power grid model to calculate theoretical characteristics based on candidate fault locations, and then comparing them with measured characteristics. To improve computational efficiency, parallel computing or approximate computing techniques can be used to accelerate this process. In addition, a tabu search mechanism can be considered to avoid repeatedly evaluating similar candidate positions, further improving the algorithm's efficiency.

[0096] In step S5.7, the algorithm converges when the improvement of the optimal solution within a consecutive preset number of algebras is less than a preset threshold or the maximum number of iterations is reached, outputting the fault location coordinates and the corresponding confidence assessment result. This step determines the termination condition and final output of the algorithm and is the final step in the fault location process. The algorithm convergence judgment is mainly based on two conditions: first, within a consecutive preset number of algebras (e.g., 10 algebras), the improvement of the optimal solution is less than a preset threshold (e.g., 0.0001), indicating that the search has stalled; second, the maximum number of iterations (e.g., 100 algebras) is reached, which is a fallback condition to ensure the algorithm terminates within a finite time. Once either condition is met, the algorithm stops iterating and outputs the current optimal solution as the fault location coordinates. In addition to the fault location, the system also generates a confidence assessment result, including a 95% confidence interval for the fault location, meaning the probability of the true fault location within this interval is 95%; and a probability distribution of the fault type, showing the probability of various possible fault types. This confidence information is very valuable for fault handling; it reflects the reliability of the location results and provides an important reference for subsequent repair decisions. Ultimately, the fault location coordinates and confidence assessment results are displayed to maintenance personnel through a visual interface or transmitted to the fault handling system to guide subsequent maintenance and recovery work.

[0097] like Figure 2 As shown, the present invention also provides a differential evolution algorithm optimization system for fault location in distribution networks, comprising: The indicator placement optimization module is used to acquire the distribution network topology and candidate installation node information, establish a multi-objective optimization function including fault coverage, cost constraints and information redundancy, and perform iterative optimization through mutation, crossover and selection operations of differential evolution algorithm to obtain the optimal placement coordinate set of fault indicators. The electrical quantity information processing module is used to deploy fault indicators at corresponding node positions and collect electrical quantity information based on the optimal arrangement position coordinate set of the fault indicators, establish a state space model with voltage and current amplitude and phase as state variables, and use the Kalman filter algorithm with process noise covariance update to perform prediction and update operations to obtain the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence and current phase sequence. The non-electrical quantity feature extraction module is used to collect non-electrical quantity data such as vibration signals, sound signals, temperature changes and gas concentrations through multiple types of sensors deployed at key locations of power distribution equipment. The module performs filtering, noise reduction and normalization preprocessing on the collected raw signals, constructs a composite kernel matrix through radial basis function, polynomial kernel function and sigmoid kernel function, establishes a sparse additive model and introduces L1 regularization constraint term to achieve automatic feature selection, and generates a non-electrical fault feature vector containing vibration feature coefficient, acoustic feature coefficient, temperature feature coefficient and gas feature coefficient. The multidimensional fusion module is used to perform dimension alignment and time synchronization between the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence, and current phase sequence and the non-electrical fault feature vector. It dynamically adjusts the fusion weights of electrical and non-electrical quantity features according to the current fault type and network operating status. It reduces the dimensionality of the fused high-dimensional features through principal component analysis to construct a three-dimensional comprehensive fault feature matrix that includes electrical-non-electrical fusion features, time window features, and spatial distribution features. The fault location module is used to establish a mathematical optimization model for fault location based on the three-dimensional comprehensive fault feature matrix, with fault location coordinates as decision variables and minimizing the error between actual measured features and theoretically calculated features as the objective function. It uses the mutation, crossover, and selection operations of the differential evolution algorithm to perform iterative solution and outputs the fault location coordinates and the corresponding confidence evaluation results.

[0098] The system of this invention can be deployed and used in different types of power distribution networks, providing accurate fault location results for various fault scenarios, significantly reducing fault location time and manpower costs, and improving the reliability of the power grid and the quality of power supply. Example

[0099] This embodiment describes the deployment of a fault location system for a 10kV distribution network in a certain city. This distribution network comprises 3 substations, 47 distribution nodes, and 52 lines, covering an area of ​​approximately 25 square kilometers.

[0100] First, the topology of the distribution network and information on 47 candidate installation nodes were obtained through the indicator placement optimization module. A multi-objective optimization function was established, incorporating fault coverage, cost constraints, and information redundancy. Iterative optimization was performed using a differential evolution algorithm with a population size of 120. After 78 iterations, the algorithm converged, yielding a set of optimal fault indicator placement coordinates for 18 installation locations. Compared to traditional empirical placement schemes, this approach saved 30% on equipment investment while improving fault coverage by 15%.

[0101] Then, fault indicators were deployed at the optimized 18 node locations to collect voltage and current amplitude and phase information. The electrical quantity information was processed using a Kalman filter algorithm with process noise covariance updates, adaptively adjusting the process noise covariance matrix. Compared to the traditional Kalman filter algorithm, the signal-to-noise ratio was improved by 8.5 dB, effectively suppressing the effects of measurement noise and system disturbances.

[0102] Next, 15 sensors of various types were deployed at key locations on the power distribution equipment to collect non-electrical quantity data, including vibration signals, sound signals, temperature changes, and gas concentrations. A kernel-based sparse additive nonlinear model structure detection method was used to extract non-electrical fault features. A composite kernel matrix was constructed using radial basis functions, polynomial kernel functions, and sigmoid kernel functions, with optimal weight coefficients of α1=0.6, α2=0.3, and α3=0.1. An L1 regularization constraint was introduced to achieve automatic feature selection; the regularization parameter λ was determined to be 0.05 through cross-validation, generating a 36-dimensional non-electrical fault feature vector.

[0103] Subsequently, the electrical and non-electrical characteristics were dimensionally aligned and time-synchronized using a multi-dimensional fusion module. The fusion weights were dynamically adjusted according to the fault type; for single-phase grounding faults, w_e=0.6 and w_n=0.4 were set. Principal component analysis was used to reduce the dimensionality of the fused high-dimensional features, retaining the first 18 principal components, which explained 96.7% of the variance. A three-dimensional comprehensive fault feature matrix was constructed, including electrical-non-electrical fusion features, time window features, and spatial distribution features.

[0104] Finally, based on the three-dimensional comprehensive fault feature matrix, a mathematical optimization model for fault location was established. A population containing 30 candidate fault locations was initialized, and the model was iteratively solved using the mutation, crossover, and selection operations of a differential evolution algorithm. After 42 iterations, the algorithm converged, outputting the fault location coordinates and the corresponding confidence assessment results. In actual testing, 10 faults of different types were located, with an average location error of 15 meters and a location success rate of 95%, which is 25 percentage points higher than traditional methods. Example

[0105] This embodiment describes the deployment of a fault location system for a rural 10kV distribution network in a county-level region. This distribution network comprises two substations, 36 distribution nodes, and 40 lines, with a total length of approximately 320 kilometers. The terrain is complex, including mountainous, plain, and valley areas.

[0106] First, the topology of the distribution network and information on 36 candidate installation nodes were obtained through the indicator placement optimization module. A multi-objective optimization function was established, incorporating fault coverage, cost constraints, and information redundancy. The weights for fault coverage, cost constraints, and information redundancy were set to 0.5, 0.3, and 0.2, respectively. Iterative optimization was performed using a differential evolution algorithm with a population size of 90. The initial value of the mutation factor F was set to 0.8, and the initial value of the crossover probability CR was set to 0.9. After 65 iterations, the algorithm converged, obtaining a set of optimal fault indicator placement coordinates for 14 installation locations. Compared to traditional empirical placement schemes, this achieved 90% fault coverage while saving 25% of equipment investment.

[0107] Then, fault indicators were deployed at the optimized 14 node locations, with each indicator acquiring voltage and current amplitude and phase information at a frequency of 100Hz. The electrical quantity information was processed using a Kalman filter algorithm with process noise covariance updates. The state estimates and error covariance matrix were initialized, and the process noise covariance adjustment coefficient α was set to 0.2. During algorithm operation, the process noise covariance matrix adaptively adjusted, improving filtering accuracy by 23% compared to traditional fixed-parameter Kalman filtering.

[0108] Next, 12 sensors of various types were deployed at key locations on the power distribution equipment, including 4 triaxial accelerometers (sampling frequency 1kHz), 4 wideband microphone arrays (frequency range 20Hz-20kHz), 2 temperature sensors, and 2 SF6 gas concentration sensors. The collected raw signals were preprocessed by filtering, denoising, and normalization. A composite kernel matrix was constructed using radial basis functions (σ=1.0), polynomial kernel functions (d=3), and sigmoid kernel functions (α=0.1, β=0.1), with optimal weighting coefficients of α1=0.5, α2=0.3, and α3=0.2. A sparse additive model was established, and an L1 regularization constraint term (λ=0.1) was introduced to achieve automatic feature selection. The model converged after 120 iterations using a coordinate descent algorithm, generating a non-electrical fault feature vector with a dimension of 48.

[0109] Subsequently, the electrical and non-electrical features were dimensionally aligned and time-synchronized using a multi-dimensional fusion module, and time-series features were extracted using a sliding window of 20 data points. The fusion weights were dynamically adjusted according to the fault type; for high-resistance grounding faults, w_e=0.4 and w_n=0.6 were set to fully utilize the identification capabilities of non-electrical features. Principal component analysis was used to reduce the dimensionality of the fused high-dimensional features, retaining the first 22 principal components, which explained 95.2% of the variance, thus constructing a three-dimensional comprehensive fault feature matrix.

[0110] Finally, based on the three-dimensional comprehensive fault feature matrix, a mathematical optimization model for fault location was established. A population containing 40 candidate fault locations was initialized, with a maximum iteration count of 100. An adaptive mutation factor and crossover probability differential evolution algorithm was used for iterative solution, with the mutation factor ranging from [0.4, 0.9] and the crossover probability ranging from [0.2, 0.8]. After 56 iterations, the algorithm converged, outputting the fault location coordinates and corresponding confidence assessment results. In actual testing, 15 different types of faults were located in complex rural terrain, with an average location error of 35 meters. The success rate for locating high-resistance grounding faults reached 85%, an improvement of 40 percentage points compared to traditional methods. Example

[0111] This embodiment describes the deployment of a fault location system for a 20kV distribution network in an industrial park. This distribution network comprises one substation, 28 distribution nodes, and 32 lines, with a high proportion of industrial load and stringent requirements for power supply reliability.

[0112] First, the topology of the distribution network and information on 28 candidate installation nodes are obtained through the indicator placement optimization module. A multi-objective optimization function is established, incorporating fault coverage, cost constraints, and information redundancy, with a fault coverage target set at over 95%. Iterative optimization is performed using a differential evolution algorithm with a population size of 70. A DE / best / 1 / bin strategy is employed in the mutation operation, and the mutation factor F is dynamically adjusted based on the number of generations. After 50 iterations, the algorithm converges, obtaining the optimal placement coordinate set of fault indicators across 12 installation locations. Compared to the traditional uniform placement scheme, this achieves a fault coverage rate of 98.5% while improving information utilization efficiency.

[0113] Then, high-precision fault indicators were deployed at the optimized 12 node locations to collect voltage and current amplitude and phase information, with a sampling frequency of 200Hz. The electrical quantity information was processed using a Kalman filter algorithm with process noise covariance updates. For harmonic interference from industrial loads, measurement noise was effectively suppressed by adaptively adjusting the process noise covariance matrix. The quality of the filtered signal was significantly improved, with a signal-to-noise ratio increase of 12dB.

[0114] Next, 16 sensors of various types were deployed at key locations on the power distribution equipment to monitor vibration signals and temperature changes. A composite kernel matrix was constructed using radial basis functions (σ was determined to be 0.5 through cross-validation), a multinomial kernel function (d=4), and a sigmoid kernel function, with optimal weighting coefficients of α1=0.7, α2=0.2, and α3=0.1. A sparse additive model was established, and an L1 regularization constraint term was introduced to achieve automatic feature selection. The regularization parameter λ was determined to be 0.02 using the Bayesian information criterion. During feature selection, 25 of the most discriminative features were automatically selected from the original 64-dimensional feature space to generate a compact non-electrical fault feature vector.

[0115] Subsequently, electrical and non-electrical quantity characteristics were fused using a multi-dimensional fusion module. A specific weighting scheme was designed for industrial load characteristics: for transient processes caused by motor starting, w_e=0.65, w_n=0.35; for line contact failures, w_e=0.45, w_n=0.55. Principal component analysis was used to reduce the dimensionality of the fused features, constructing a three-dimensional comprehensive fault feature matrix, which significantly enhanced the ability to identify industrial load characteristics.

[0116] Finally, based on the three-dimensional comprehensive fault feature matrix, a mathematical optimization model for fault location was established, and a population containing 35 candidate fault locations was initialized. A differential evolution algorithm with an elite retention strategy and diversity maintenance mechanism was used for iterative solution. When the population diversity index fell below 0.2, 30% of the individuals were reinitialized. After 38 generations of iteration, the algorithm converged, outputting the fault location coordinates and the corresponding confidence assessment results. In actual testing, 20 different types of faults in an industrial park were located, with an average location error of 8 meters and a location time of no more than 5 seconds, meeting the stringent requirements of industrial users for rapid fault location.

[0117] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0118] It should be noted that those skilled in the art can make various modifications and variations to this invention without departing from the spirit and scope of this invention. If such modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include such modifications and variations.

[0119] This disclosure also provides a computer-readable storage medium storing a computer program. When executed by a processor, the computer program performs the steps of the differential evolution algorithm optimization method for distribution network fault location described in the above-described method embodiments. The storage medium can be a volatile or non-volatile computer-readable storage medium.

[0120] Furthermore, this disclosure also provides a computer program product storing a computer program. When the computer program is run by a processor, it executes the steps of a differential evolution algorithm optimization method for fault location in a distribution network provided in any of the above embodiments of this disclosure. For details, please refer to the above method embodiments, which will not be repeated here.

[0121] The aforementioned computer program product can be implemented through hardware, software, or a combination thereof. In one optional embodiment, the computer program product is specifically embodied in a computer storage medium, which can be a volatile or non-volatile computer-readable storage medium. In another optional embodiment, the computer program product is specifically embodied in a software product, such as a software development kit (SDK), etc.

[0122] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the devices and apparatuses described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. In the several embodiments provided in this disclosure, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Another point is that the displayed or discussed mutual coupling or direct coupling or communication connection may be through some communication interfaces; the indirect coupling or communication connection of devices or units may be electrical, mechanical, or other forms.

[0123] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0124] In addition, the functional units in the various embodiments of this disclosure can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0125] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this disclosure, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this disclosure. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0126] Finally, it should be noted that the above-described embodiments are merely specific implementations of this disclosure, used to illustrate the technical solutions of this disclosure, and not to limit it. The protection scope of this disclosure is not limited thereto. Although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the scope of the technology disclosed in this disclosure; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this disclosure, and should all be covered within the protection scope of this disclosure. Therefore, the protection scope of this disclosure should be determined by the protection scope of the claims.

Claims

1. A differential evolution algorithm optimization method for fault location in distribution networks, characterized in that, Includes the following steps: The distribution network topology and candidate installation node information are obtained, and a multi-objective optimization function including fault coverage, cost constraints and information redundancy is established. Iterative optimization is performed through mutation, crossover and selection operations of differential evolution algorithm to obtain the set of optimal placement coordinates of fault indicators. Based on the optimal placement coordinate set of the fault indicator, the fault indicator is deployed at the corresponding node position and electrical quantity information is collected. A state space model with voltage and current amplitude and phase as state variables is established. The Kalman filter algorithm with process noise covariance update is used for prediction and update operations to obtain the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence and current phase sequence. Non-electrical data such as vibration signals, sound signals, temperature changes, and gas concentrations are collected by multiple types of sensors deployed at key locations of power distribution equipment. The collected raw signals are filtered, denoised, and normalized preprocessed. A composite kernel matrix is ​​constructed using radial basis functions, polynomial kernel functions, and sigmoid kernel functions. A sparse additive model is established, and an L1 regularization constraint term is introduced to achieve automatic feature selection. This generates a non-electrical fault feature vector containing vibration feature coefficients, acoustic feature coefficients, temperature feature coefficients, and gas feature coefficients. The filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence, and current phase sequence are aligned in dimension and synchronized in time with the non-electrical fault feature vector. The fusion weights of electrical and non-electrical quantity features are dynamically adjusted according to the current fault type and network operating status. The dimensionality of the fused high-dimensional features is reduced by principal component analysis to construct a three-dimensional comprehensive fault feature matrix that includes electrical-non-electrical fusion features, time window features, and spatial distribution features. Based on the three-dimensional comprehensive fault feature matrix, a mathematical optimization model for fault location is established with fault location coordinates as decision variables and minimizing the error between actual measured features and theoretically calculated features as the objective function. The model is then iteratively solved using the mutation, crossover, and selection operations of the differential evolution algorithm, and the fault location coordinates and corresponding confidence assessment results are output.

2. The method according to claim 1, characterized in that, Through iterative optimization using mutation, crossover, and selection operations of the differential evolution algorithm, the optimal set of coordinates for the fault indicator placement is obtained, including: Initialize a differential evolution algorithm population with a population size of 2-3 times the number of distribution network nodes. Each individual uses a real number vector encoding to represent an indicator placement scheme, and set the maximum number of iterations. In the mutation operation, the DE / best / 1 / bin strategy is adopted. The best individual in the current population is selected as the basis vector, and two different individuals are randomly selected for difference operation. The mutation factor F is set to an adaptive value between 0.5 and 0.9 to generate the mutation vector. In the crossover operation, the mutated vector and the target vector are combined by a binomial crossover according to the crossover probability CR. The CR value is dynamically adjusted according to the number of generations, initially set to 0.9 and later reduced to 0.3 to generate the experimental vector. In the selection operation, the fitness values ​​of the corresponding layout schemes of the test vector and the target vector are calculated. The Pareto dominance relation is used to compare the multi-objective function values. Non-dominated solutions are retained as the next generation of individuals. For mutually non-dominated solutions, the crowding distance sorting mechanism is used for selection to obtain the set of optimal layout position coordinates of the fault indicator.

3. The method according to claim 1, characterized in that, The prediction and update operations are performed using a Kalman filter algorithm with process noise covariance updates, including: Establish state transition equations and observation equations with voltage and current amplitudes and phases as state variables, and initialize state estimates, error covariance matrix and process noise covariance matrix; In the prediction step, the state value and error covariance at the current moment are predicted according to the state transition equation. In the update step, the Kalman gain is calculated using the observations at the current time, and the state estimate and error covariance are updated. By calculating the statistical characteristics of the innovation sequence, the process noise covariance matrix is ​​adjusted in real time to adapt the filter to the noise characteristics under different operating conditions, thereby obtaining the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence, and current phase sequence.

4. The method according to claim 1, characterized in that, A composite kernel matrix is ​​constructed using radial basis functions, polynomial kernel functions, and sigmoid kernel functions, including: Radial basis functions are used to capture local similarity features, and the kernel parameter σ is determined through cross-validation optimization. A polynomial kernel function is used to extract multi-order interaction relationships between data, with the polynomial order set to 2-4. The sigmoid kernel function is used to simulate the nonlinear activation characteristics of neural networks; The composite kernel matrix K = α1K_RBF + α2K_poly + α3K_sigmoid is constructed by weighted combination of three kernel functions, where the optimal values ​​of the weight coefficients α1, α2, and α3 are determined by grid search and cross-validation.

5. The method according to claim 1, characterized in that, A sparse additive model is established and an L1 regularization constraint term is introduced to achieve automatic feature selection, including: In the constructed kernel space, establish a sparse additive model f(x) = Σᵢ =1 ⁿ βᵢK(xᵢ,x) + ε, where βᵢ is the kernel coefficient and ε is the noise term; Automatic feature selection is achieved by introducing an L1 regularization constraint term λ||β||1, and the regularization parameter λ is determined by the information criterion. The coordinate descent algorithm is used to solve the optimization problem. The kernel coefficients are iteratively updated until convergence. The feature components that contribute significantly to the failure mode are automatically identified and retained, while redundant and noise components are removed. By performing a reverse mapping operation from kernel space to the original space, vibration characteristic coefficients, acoustic characteristic coefficients, temperature characteristic coefficients, and gas characteristic coefficients are calculated to generate the non-electrical fault feature vector.

6. The method according to claim 1, characterized in that, A three-dimensional comprehensive fault feature matrix is ​​constructed, incorporating electrical-non-electrical integrated features, time window features, and spatial distribution features, including: The filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence, and current phase sequence are aligned in dimension and synchronized in time with the non-electrical fault feature vector to ensure the consistency of different types of features on the time axis. Based on the current fault type and network operating status, the fusion weights of electrical and non-electrical quantity features are dynamically adjusted to generate a fused electrical-non-electrical feature vector. The time-series patterns of fault features are extracted using the time-sliding window method to generate time-window features. Based on the distribution network topology and the spatial distribution of fault indicators, a spatial distribution feature reflecting the spatial propagation characteristics of faults is constructed. The electrical-non-electrical fusion features, time window features, and spatial distribution features are combined to construct the three-dimensional comprehensive fault feature matrix.

7. The method according to claim 1, characterized in that, A mathematical optimization model for fault location is established based on the aforementioned three-dimensional comprehensive fault feature matrix, including: A mathematical optimization model for fault location is established, with the fault location coordinates as the decision variable and minimizing the error between the actual measured characteristics and the theoretically calculated characteristics as the objective function. Initialize a population containing multiple candidate fault locations, with each individual representing one candidate fault location; By setting the maximum number of iterations and convergence criteria, and introducing an elite retention strategy and a diversity maintenance mechanism, a mathematical optimization model for fault location is obtained.

8. The method according to claim 1, characterized in that, Iterative solutions are obtained using the mutation, crossover, and selection operations of the differential evolution algorithm, including: An adaptive mutation mechanism guided by the current optimal solution is used in the mutation operation to generate new candidate fault locations; In the crossover operation, the positional information of different individuals is integrated, and the crossover probability is dynamically adjusted according to the individual fitness. In the selection operation, the objective function value corresponding to each candidate position is calculated, and the solution with higher fitness is retained for the next generation; The algorithm converges when the improvement of the consecutive preset algebraic optimal solutions is less than a preset threshold or when the maximum number of iterations is reached, and outputs the fault location coordinates and the corresponding confidence evaluation results.

9. A differential evolution algorithm optimization system for fault location in distribution networks, comprising: The indicator placement optimization module is used to acquire the distribution network topology and candidate installation node information, establish a multi-objective optimization function including fault coverage, cost constraints and information redundancy, and perform iterative optimization through mutation, crossover and selection operations of differential evolution algorithm to obtain the optimal placement coordinate set of fault indicators. The electrical quantity information processing module is used to deploy fault indicators at corresponding node positions and collect electrical quantity information based on the optimal arrangement position coordinate set of the fault indicators, establish a state space model with voltage and current amplitude and phase as state variables, and use the Kalman filter algorithm with process noise covariance update to perform prediction and update operations to obtain the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence and current phase sequence. The non-electrical quantity feature extraction module is used to collect non-electrical quantity data such as vibration signals, sound signals, temperature changes and gas concentrations through multiple types of sensors deployed at key locations of power distribution equipment. The module performs filtering, noise reduction and normalization preprocessing on the collected raw signals, constructs a composite kernel matrix through radial basis function, polynomial kernel function and sigmoid kernel function, establishes a sparse additive model and introduces L1 regularization constraint term to achieve automatic feature selection, and generates a non-electrical fault feature vector containing vibration feature coefficient, acoustic feature coefficient, temperature feature coefficient and gas feature coefficient. The multidimensional fusion module is used to perform dimension alignment and time synchronization between the filtered voltage amplitude sequence, current amplitude sequence, voltage phase sequence, and current phase sequence and the non-electrical fault feature vector. It dynamically adjusts the fusion weights of electrical and non-electrical quantity features according to the current fault type and network operating status. It reduces the dimensionality of the fused high-dimensional features through principal component analysis to construct a three-dimensional comprehensive fault feature matrix that includes electrical-non-electrical fusion features, time window features, and spatial distribution features. The fault location module is used to establish a mathematical optimization model for fault location based on the three-dimensional comprehensive fault feature matrix, with fault location coordinates as decision variables and minimizing the error between actual measured features and theoretically calculated features as the objective function. It uses the mutation, crossover, and selection operations of the differential evolution algorithm to perform iterative solution and outputs the fault location coordinates and the corresponding confidence evaluation results.

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