Power distribution network fault distance measurement and transition resistance estimation method based on physical information neural network

Abstract

The invention discloses a power distribution network fault distance measurement and transition resistance estimation method based on a physical information neural network, and relates to the technical field of power distribution network fault diagnosis and artificial intelligence deep learning, and the method comprises the following steps: collecting real-time voltage and current data after a power distribution network fault through measurement devices disposed on all lines; inputting the voltage and current data into a pre-trained physical information neural network model to obtain a fault distance estimation value and a transition resistance estimation value; wherein the physical information neural network model is constructed on the basis of a feedforward neural network model, is obtained by training a loss function fusing a data driving loss item and a physical constraint loss item, and is used for establishing a nonlinear mapping relationship between the voltage and current data and the fault distance as well as between the voltage and current data and the transition resistance. The method has the advantages that the accuracy and generalization ability of fault distance measurement are improved, and the dependence on a large number of fault samples is reduced.

Description

Technical Field

[0001] This invention relates to the fields of distribution network fault diagnosis and artificial intelligence deep learning technology, specifically to a method for distribution network fault location and transition resistance estimation based on physical information neural networks. Background Technology

[0002] Rapid and accurate location of line faults is a core requirement for distribution network fault handling. In actual distribution network operation, frequent line faults and their hidden locations make fault diagnosis difficult, thus affecting power supply reliability. Therefore, rapid and accurate fault location is of great significance for restoring power supply and ensuring distribution network reliability.

[0003] Existing fault location methods can be categorized into physical-driven methods and artificial intelligence methods. Physical-driven methods mainly include traveling wave methods, signal injection methods, and impedance methods. The traveling wave method detects transient traveling wave signals at the time of a fault occurrence and determines the fault distance using the wavefront propagation time difference, offering advantages such as high location accuracy and fast response speed. However, the traveling wave method relies on high-frequency / high-speed sampling and synchronization accuracy, resulting in relatively high implementation costs, thus hindering its practical application in conventional power distribution networks. The signal injection method identifies fault locations by injecting specific frequency signals into the system and analyzing reflected waves or impedance changes, but it also faces problems such as high equipment costs and signal attenuation.

[0004] Impedance method, based on steady-state power frequency measurements, calculates the equivalent impedance of the fault point by measuring terminal voltage and current, and then infers the fault distance. This method is simple to implement and fast to calculate, making it the most widely used fault location method in distribution networks. However, the presence of transition resistance causes voltage drops to be distributed along the grounding branch, especially when the transition resistance is large, leading to a systematic underestimation of the fault location result. Therefore, to improve the accuracy of distance measurement, some researchers have introduced a joint solution mechanism for fault distance and transition resistance during the modeling process to achieve a more accurate characterization of the voltage distribution along the fault path. Furthermore, the impedance method is prone to multiple location estimations in distribution systems with multiple branches, resulting in inaccurate location.

[0005] With the rapid popularization of machine learning and artificial intelligence, data-driven fault location methods for distribution networks have developed rapidly. The main idea is to model fault location as a regression problem, establishing a nonlinear mapping relationship between measurement information and fault distance to achieve end-to-end fault distance estimation. Preliminary applications of artificial neural networks (ANN), support vector machines (SVM), and other artificial intelligence models have demonstrated the feasibility and applicability of data-driven solutions in the field of distribution network fault location. These methods can automatically extract features, avoiding explicit parameter modeling, but they also have significant limitations: firstly, the sample labels for fault distance cannot be completely covered, resulting in an excessive dependence on the number of samples, while samples of different fault types are extremely scarce in actual distribution networks; secondly, purely data-driven methods lack electrical mechanism constraints, making it difficult to guarantee that the results conform to physical laws, and resulting in insufficient interpretability of the prediction results and insufficient reliability for practical applications.

[0006] In real-world distribution network environments, fault types are diverse, including single-phase ground faults, two-phase short-circuit faults, two-phase ground faults, and three-phase short-circuit faults. The magnitude of the transition resistance and the variation in fault distance under each fault type significantly impact the fault location results. Particularly in the case of high-resistance ground faults, the transition resistance can reach tens of ohms or even higher, leading to a significant increase in the fault location error of traditional impedance methods. Furthermore, the complex structure of distribution networks, with multiple branches and load points, complicates the fault current path, further increasing the difficulty of fault location.

[0007] Furthermore, the widespread integration of distributed generation sources in distribution networks alters the power flow distribution and fault characteristics of traditional distribution networks, making fault location more complex. The integration of distributed generation sources may cause changes in the direction of fault current, affecting the accuracy of traditional fault location methods based on single-ended measurements. Therefore, a fault location method is needed that can adapt to complex distribution network structures and consider the effects of various fault types and transition resistance.

[0008] While some existing technologies attempt to apply artificial intelligence to fault location, most methods rely solely on data-driven approaches and lack consideration for the physical laws governing power systems, resulting in insufficient generalization ability when faced with unseen fault scenarios. Furthermore, the scarcity of fault data in actual distribution networks makes it difficult for purely data-driven methods to obtain sufficient training samples, limiting their effectiveness in practical applications.

[0009] To address the aforementioned issues, existing technologies urgently need improvement. Summary of the Invention

[0010] In view of this, the present invention provides a method for fault location and transition resistance estimation in distribution networks based on physical information neural networks, which has the advantages of improving the accuracy and generalization ability of fault location and reducing the dependence on a large number of fault samples.

[0011] This invention provides a method for fault location and transition resistance estimation in distribution networks based on physical information neural networks, comprising the following steps: S1. Collect real-time voltage and current data after a power distribution network fault by using measuring devices installed on each line; S2. Input the voltage and current data into the pre-trained physical information neural network model to obtain the fault distance estimate and the transition resistance estimate. The physical information neural network model is constructed based on a feedforward neural network model and is trained by a loss function that integrates data-driven loss terms and physical constraint loss terms. It is used to establish a nonlinear mapping relationship between voltage and current data and fault distance and transition resistance.

[0012] As can be seen from the above, the fault location and transition resistance estimation method for distribution networks based on physical information neural networks provided in this application has the advantages of effectively improving the accuracy and generalization ability of fault location by integrating data-driven and physical constraints and establishing a nonlinear mapping relationship, while reducing the dependence on a large number of fault samples. Attached Figure Description

[0013] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0014] Figure 1 This is a flowchart illustrating a method for fault location and transition resistance estimation in a distribution network based on a physical information neural network, according to an embodiment of the present invention. Figure 2 This is a system architecture diagram of the physical information neural network model according to an embodiment of the present invention; Figure 3 This is a circuit diagram of the fault state network under a phase A ground fault according to an embodiment of the present invention. Figure 4 This is a topology diagram of a 10kV distribution network containing distributed power sources according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the entire fault location process according to an embodiment of the present invention; Figure 6The following are graphs showing the trends of the overall loss, physical constraint loss term, and data-driven loss term during the training iteration process of the training and test sets in this embodiment of the invention; wherein, (a) is a graph showing the trend of the overall loss during the training iteration process of the training and test sets; (b) is a graph showing the trend of the data-driven loss term during the training iteration process of the training and test sets; and (c) is a graph showing the trend of the physical constraint loss term during the training iteration process of the training and test sets. Figure 7 The following are graphs showing the trends of the estimation error and accuracy of fault distance and transition resistance as a function of the number of iterations in an embodiment of the present invention: (a) shows the trend of the estimation error of fault distance as a function of the number of iterations; (b) shows the trend of the estimation error of transition resistance as a function of the number of iterations; (c) shows the trend of the estimation accuracy of fault distance as a function of the number of iterations; and (d) shows the trend of the estimation accuracy of transition resistance as a function of the number of iterations. Figure 8 The figures shown are performance test results of the physical information neural network model under different fault types in the embodiments of the present invention; wherein, (a) is the performance test result of the physical information neural network model under single-phase ground fault; (b) is the performance test result of the physical information neural network model under two-phase short-circuit fault; (c) is the performance test result of the physical information neural network model under two-phase ground fault; and (d) is the performance test result of the physical information neural network model under three-phase short-circuit fault. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 embodiments of the present invention, not all embodiments. 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.

[0016] like Figure 1 As shown, this application proposes a method for fault location and transition resistance estimation in distribution networks based on physical information neural networks, including the following steps: Step S1: Collect real-time voltage and current data after a power distribution network fault by using measuring devices installed on each line.

[0017] Step S2: Input the voltage and current data into the pre-trained physical information neural network model to obtain the fault distance estimate and the transition resistance estimate.

[0018] Among them, the physical information neural network model is built on the feedforward neural network model and is trained by a loss function that integrates data-driven loss terms and physical constraint loss terms. It is used to establish a nonlinear mapping relationship between voltage and current data and fault distance and transition resistance.

[0019] Specifically, the physical information neural network model is a deep learning model whose training process not only relies on data but also explicitly embeds physical laws or equations as constraints through a loss function. Therefore, this model can maintain the physical consistency and interpretability of its predictions even when data is sparse or incomplete.

[0020] A feedforward neural network is a basic artificial neural network structure in which information is passed unidirectionally from the input layer through one or more hidden layers to the output layer. This model learns the nonlinear mapping between input and output to recognize and predict complex patterns.

[0021] The data-driven loss term is a part of the loss function used to measure the deviation between the model's predicted output and the actual observed data or labels. By minimizing this loss term, the model can better fit the training data, thereby improving the accuracy of predictions.

[0022] The physical constraint loss term is another part of the loss function, used to introduce known physical laws, equations, or boundary conditions as constraints into the training process of the neural network. By minimizing this loss term, the model is guided to generate predictions that conform to physical principles, enhancing the model's physical consistency and generalization ability.

[0023] A loss function is a mathematical function used to measure the difference between a model's predictions and the true values. During neural network training, optimization algorithms minimize the loss function, thereby updating the model's weights and biases and gradually improving the model's performance.

[0024] Measuring devices are equipment installed on various lines of a power distribution network to collect electrical quantity data such as voltage and current in real time. These devices typically include voltage transformers, current transformers, and data acquisition units, which can convert analog signals into digital signals for subsequent processing.

[0025] The fault distance estimate refers to the predicted distance from the fault point to the location of the measuring device, calculated using this method. This value is crucial information for fault location in the distribution network, guiding fault investigation and emergency repair.

[0026] The estimated transition resistance refers to the predicted equivalent resistance at the fault point calculated using this method. Transition resistance is a crucial factor affecting fault current and voltage distribution, and its accurate estimation is essential for improving fault location accuracy.

[0027] This embodiment provides a method for fault location and transition resistance estimation in distribution networks based on physical information neural networks. The method first collects real-time voltage and current data after a distribution network fault using measurement devices. Specifically, basic voltage and current sensors can be deployed on each line of the distribution network, continuously monitoring the electrical state of the lines. When a line anomaly is detected, such as a significant change in voltage or current, data recording can be initiated manually or through a simple threshold judgment mechanism to store the voltage and current waveform data for a period of time after the fault occurs. This raw electrical quantity data forms the input basis for subsequent fault analysis.

[0028] Subsequently, the collected voltage and current data are input into a trained physical information neural network model. This model receives these real-time measurement data as input and, based on its internally learned complex mapping relationships, outputs estimates of the fault distance and the transition resistance. For example, the collected voltage and current time-series data can be directly used as the model's input vector. After internal calculations, the model directly outputs two values ​​at the output layer, representing the distance from the fault point to the measurement location and the equivalent transition resistance at the fault point, respectively.

[0029] like Figure 2 As shown, the core of this physical information neural network model lies in its construction method and training mechanism. Specifically, the model is built based on a feedforward neural network model. A feedforward neural network typically contains an input layer, several hidden layers, and an output layer. Information is transmitted unidirectionally between layers, and calculations are performed through the connection weights and biases between neurons. For example, a feedforward neural network with three hidden layers can be used as the basic architecture, where the input layer receives voltage and current data, and the output layer outputs fault distance and transition resistance. The training process of this model is optimized by fusing a loss function with a data-driven loss term and a physical constraint loss term. The data-driven loss term ensures that the model can accurately fit historical fault data and learn patterns in the data; while the physical constraint loss term embeds the inherent physical laws and engineering experience of the distribution network into the training process. For example, it can require that the model's output results are physically reasonable or satisfy certain basic electrical balance relationships. Through this dual-constraint training method, the model can establish a more accurate and physically consistent nonlinear mapping relationship between voltage and current data and fault distance and transition resistance.

[0030] This embodiment effectively overcomes the limitations of traditional methods in distribution network fault location by integrating data-driven and physical constraints. These limitations include high cost, significant influence from transition resistance, multiple location estimations, and the strong sample dependence and lack of physical consistency inherent in purely data-driven methods. Therefore, this method can achieve high-precision coordinated estimation of fault distance and transition resistance in complex distribution network environments, while ensuring that the prediction results conform to electrical and physical laws, thus enhancing the reliability and interpretability of the model.

[0031] In one alternative implementation, the training method for the physical information neural network model includes the following steps: First, obtain voltage and current sample data covering various fault conditions, along with corresponding fault distance and transition resistance labels. Training a physical information neural network model requires a large amount of representative sample data. This sample data typically includes voltage and current data collected under different fault conditions, as well as the actual values ​​(i.e., labels) of fault distance and transition resistance, which serve as the model's learning targets. This data can be generated using a distribution network simulation model to simulate various fault types, fault locations, and fault resistance scenarios, ensuring the diversity and coverage of the training data. Alternatively, historical fault data can be organized and labeled, but simulation data is generally easier to control and generate large-scale datasets for.

[0032] Secondly, a feedforward neural network model is constructed. The feedforward neural network model is the fundamental structure of physical information neural networks, and its function is to establish a nonlinear mapping relationship between the input (voltage and current data) and the output (fault distance and transition resistance). This model typically consists of an input layer, multiple hidden layers, and an output layer. The hidden layers abstract and extract features from the input data layer by layer through a series of neurons and activation functions. The specific structure of the model, such as the number of hidden layers, the number of neurons in each layer, and the selected activation functions, can be designed and optimized according to the actual application requirements and data characteristics.

[0033] Specifically, the input to the feedforward neural network model is the voltage and current time-series signals obtained from the measuring device. These features reflect the transient changes in the fault signal, providing the model with high-dimensional dynamic input. The model's output is the fault distance estimate. Compared with the estimated value of transition resistance .

[0034] Feedforward neural network models include an input layer, There are one hidden layer and one output layer, and the input vector is given. Output , No. k Layer contains If there are 10 neurons, then the forward propagation process of this network model can be represented as: in, Indicates the first k Hidden layer output of the layer; and They represent the first k Layer weight matrix and bias vector; The activation function is tanh, which is used here to improve the smoothness and gradient stability of the model in nonlinear mappings. The mapping relationship of the output layer can be expressed as: in, and These are the weight matrix and bias vector of the output layer, respectively.

[0035] Next, a loss function is constructed. This loss function includes a data-driven loss term and a physical constraint loss term. The loss function is a key indicator that measures the difference between the model's predictions and the true values, and whether the model's output conforms to physical laws. In this method, the loss function is designed to include both a data-driven loss term and a physical constraint loss term. The data-driven loss term ensures that the model can learn the correct mapping relationship from the data, while the physical constraint loss term incorporates known physical laws and engineering knowledge into the model's training process, thereby improving the model's physical rationality and generalization ability. Specifically, the data-driven loss term is determined based on the deviation between the estimated values ​​of the feedforward neural network model output and their corresponding label values. The data-driven loss term aims to quantify the deviation between the fault distance estimate and the transition resistance estimate output by the feedforward neural network model and their corresponding true label values. Common implementations include mean squared error (MSE) or mean absolute error (MAE). By calculating these deviations and minimizing them, the model can progressively learn an accurate mapping from the input data to the target output. This loss term is the core of supervised learning, ensuring that the model can effectively extract features from the provided sample data and make predictions. The physical constraint loss term is used to embed physical laws as constraints into the training process of the feedforward neural network model. This physical constraint loss term is one of the core innovations of this method; its role is to mathematically embed the physical laws and engineering knowledge of distribution network faults into the training process of the feedforward neural network model. By introducing physical constraints, even with limited training data, the model can learn mapping relationships that conform to physical principles, avoiding unreasonable predictions. This not only improves the interpretability and reliability of the model but also helps enhance its generalization ability under unseen operating conditions.

[0036] Specifically, data-driven loss items The expression used to minimize the deviation between the estimated value and the true value of the feedforward neural network model is: ; Where N is the sample size. Indicates the first i The actual fault distance of each sample Indicates the first i Predicted fault distance for each sample Indicates the first i The actual transition resistance of each sample Indicates the first i Predict the transition resistance for each sample.

[0037] Finally, the feedforward neural network model is trained using the voltage and current sample data. The model parameters are updated by optimizing the loss function to obtain the trained physical information neural network model. The training process is an iterative optimization process. The acquired voltage and current sample data are input into the feedforward neural network model, and the loss between the model output and the true label value, as well as the physical constraints, is calculated. Subsequently, using the backpropagation algorithm and optimizer (such as Adam, SGD, etc.), the weights and biases within the model are gradually adjusted according to the gradient direction of the loss function. This process continues until the loss function converges to a preset threshold or the maximum number of training epochs is reached, ultimately resulting in a physical information neural network model that can accurately estimate fault distance and transition resistance and conforms to physical laws.

[0038] Through the aforementioned training method, this application can systematically construct and optimize a physical information neural network model. Specifically, by acquiring voltage and current sample data and corresponding labels containing various fault conditions, rich learning materials are provided for the model. Based on this, a loss function comprising a data-driven loss term and a physical constraint loss term is constructed, enabling the model to strictly adhere to the physical laws of the distribution network while learning data features. The data-driven loss term ensures the model can learn accurate mapping relationships from the data, while the physical constraint loss term integrates domain knowledge into the training process, effectively compensating for poor generalization ability that may result from insufficient data and avoiding situations where the model output does not conform to physical common sense. By optimizing this composite loss function to update the model parameters, the final physical information neural network model not only has high accuracy but also good physical rationality and robustness, thereby significantly improving the accuracy and reliability of distribution network fault location and transition resistance estimation, and solving the performance problems that may exist if relying solely on pre-trained models.

[0039] In one optional implementation, the method for acquiring voltage and current sample data specifically includes: Build a power distribution network simulation model; By changing the parameters of fault feeder, fault type, fault distance, transition resistance, and fault initial phase angle, various fault conditions are simulated; voltage and current waveform data under each fault condition are collected, and the corresponding fault distance and transition resistance are recorded as labels.

[0040] Specifically, building a distribution network simulation model refers to using specialized power system simulation software, such as PSCAD / EMTDC, DIgSILENT PowerFactory, ATP-EMTP, or MATLAB / Simulink, to accurately mathematically model the topology, line parameters, load characteristics, and protection configuration of the actual distribution network. This simulation model provides a safe, controllable, and repeatable environment for generating various distribution network operation data, especially fault data that is difficult to reproduce in the actual system. When building the model, detailed input of key parameters such as line impedance, cable parameters, transformer parameters, load model, and distributed generation connection points and capacities is required to ensure that the simulation results can highly realistically reflect the dynamic behavior of the actual distribution network.

[0041] Based on this, various fault conditions are simulated by changing the fault feeder, fault type, fault distance, transition resistance, and initial phase angle parameters. This process aims to systematically generate sample data covering a wide range of fault scenarios to ensure that the trained neural network model has good generalization ability and robustness. For example, different line segments can be selected as fault occurrence points in the simulation model to simulate various fault types such as single-phase ground faults, two-phase short-circuit faults, two-phase ground-to-short-circuit faults, and three-phase short-circuit faults. Regarding fault distance, fault points can be set on selected fault feeders at preset step sizes (e.g., every 1 kilometer or 1% of the total line length) to cover different locations from the beginning to the end of the line. The transition resistance can simulate everything from near-zero ohm metallic short circuits to high-resistance ground faults of hundreds or even thousands of ohms; for example, a setting of 0.1... 1 10 50 100 500 1000 Multiple discrete values ​​or continuous values ​​within a range can be used. The fault initial phase angle can simulate different voltage or current phase angles at the time of a fault, for example... , , , These parameters are used to reflect the randomness of the timing of the failure. By systematically combining and varying the above parameters, thousands or even tens of thousands of different failure conditions can be generated.

[0042] Subsequently, voltage and current waveform data under various fault conditions are collected, and the corresponding fault distance and transition resistance are recorded as labels. Under each simulated fault condition, the simulation model records the instantaneous voltage and current waveform data at various measuring devices in the distribution network at a sufficiently high sampling frequency (e.g., 10kHz or higher) within a preset time window (e.g., several cycles) after the fault occurs. Since this data is generated in the simulation environment, the true values ​​of the fault distance and transition resistance corresponding to that fault condition can be accurately obtained, and these true values ​​are stored as labels for that set of voltage and current waveform data. This data is typically stored in matrix or time series form and associated with the corresponding labels, providing high-quality input and output targets for subsequent neural network training.

[0043] The above technical solution effectively addresses the problems of difficulty in obtaining real distribution network fault data, insufficient data volume, and incomplete coverage of fault conditions. The simulation model can generate massive amounts of voltage and current waveform data covering various fault types, locations, transition resistances, and initial phase angles, greatly enriching the training dataset. Simultaneously, the simulation data comes with accurate fault distance and transition resistance labels, avoiding the difficulties or inaccuracies in label acquisition found in real data, providing high-quality training targets for supervised learning of physical information neural network models. This enables the trained model to better adapt to various complex faults that may occur in actual distribution networks, significantly improving the model's ranging and estimation accuracy under unknown fault conditions, thereby enhancing the model's generalization ability and robustness. Furthermore, this method avoids dangerous and expensive fault experiments in actual distribution networks, reducing research costs and risks.

[0044] In some alternative implementations, before performing step S1, the method further includes monitoring the amplitude change of the zero-sequence current in the distribution network; when the difference in the amplitude of the zero-sequence current between adjacent time windows exceeds a set threshold, a fault is determined to have occurred and step S1 is performed.

[0045] Specifically, the zero-sequence current in a distribution network is a crucial indicator reflecting system grounding faults. Under normal operating conditions, the three-phase currents are balanced, and the zero-sequence current is theoretically zero or close to zero. When a grounding fault occurs, the three-phase currents become unbalanced, and the amplitude of the zero-sequence current increases significantly. Therefore, by installing current transformers and other measuring devices at key nodes or feeder outlets in the distribution network to collect phase current data in real time and calculate the zero-sequence current, the operating status of the distribution network can be effectively reflected. This monitoring process can be continuous or periodic to ensure constant monitoring of the system's condition.

[0046] In detail, to avoid misjudgments caused by normal system fluctuations or measurement noise, this method does not simply rely on the absolute value of the zero-sequence current for judgment. Instead, it compares the changes in the zero-sequence current amplitude within adjacent time windows. First, the system defines a time window, such as several power cycles or tens of milliseconds, and calculates the amplitude of the zero-sequence current (e.g., RMS or peak value) within this window. Then, it compares the zero-sequence current amplitude of the current time window with that of the previous adjacent time window and calculates the difference. If this difference exceeds a preset threshold, it indicates that an abnormal and drastic change has occurred in the system, and a fault can be identified. This threshold needs to be reasonably calibrated based on the actual operating characteristics of the distribution network, the range of load changes, and possible background noise to balance the sensitivity and anti-interference capability of the detection. Once a fault is identified, the system immediately triggers step S1, which begins collecting real-time voltage and current data after the distribution network fault, providing accurate input for subsequent fault location and transition resistance estimation.

[0047] Through the above technical solution, this method can achieve rapid and accurate detection of distribution network faults. By continuously monitoring the amplitude change of zero-sequence current and employing a strategy of comparing the difference between adjacent time windows with a threshold, misjudgments caused by normal system fluctuations or transient interference are effectively avoided, thus improving the reliability of fault detection. Once a fault is accurately determined, the system can promptly initiate data acquisition in step S1, ensuring that the acquired voltage and current data are valid information that truly reflects the fault state. This provides high-quality input for subsequent fault distance estimation and transition resistance estimation based on a physical information neural network model, significantly improving the accuracy and real-time performance of fault location and transition resistance estimation, and avoiding resource waste and result deviations caused by processing non-fault data.

[0048] In one alternative implementation, the feedforward neural network model includes multiple hidden layers with the number of neurons configured as [256, 512, 512, 256]; and Dropout and layer normalization are introduced during training to improve the model's numerical stability and generalization ability.

[0049] Specifically, the feedforward neural network model is designed with multiple hidden layers responsible for layer-by-layer abstraction and feature extraction of the input data. The number of neurons in the hidden layers is configured as [256, 512, 512, 256], a configuration intended to provide sufficient learning capacity for the model to capture complex nonlinear patterns and potential correlations in distribution network fault data, thereby more accurately mapping the relationship between voltage and current data and fault distance and transition resistance. This deep structure helps the model learn more discriminative feature representations from the raw measurement data.

[0050] To further enhance the model's robustness and generalization ability, a Dropout mechanism was introduced during training. Dropout is an effective regularization technique that works by randomly and temporarily removing a portion of neurons and their connections from the neural network with a preset probability during each training iteration. This random deactivation operation forces the network to avoid over-reliance on any single neuron, thereby encouraging the model to learn more distributed and robust feature representations. In this way, Dropout can effectively suppress overfitting, enabling the trained model to maintain high prediction accuracy even when faced with unseen fault condition data.

[0051] Furthermore, this application introduces layer normalization (LN) technology. LN is a method for normalizing the inputs of neural network layers. It independently standardizes the inputs of each neuron in each layer for each training sample, making their mean 0 and variance 1. This process effectively stabilizes the distribution of inputs across different layers of the neural network, alleviating the common internal covariate bias problem during deep neural network training. By stabilizing the input distribution, LN improves the numerical stability of the model, accelerates the convergence speed of the training process, and reduces the model's sensitivity to hyperparameter selection such as learning rate and parameter initialization, thereby making the training process more efficient and stable.

[0052] In one alternative implementation, the physical constraint loss term includes at least one of the fault differential equation constraint term, boundary condition constraint term, and line parameter regularization constraint term.

[0053] The fault differential equation constraint term aims to embed the dynamic physical laws governing distribution network faults into the neural network training process. Specifically, it forces the model to learn a mapping relationship that conforms to physical principles by ensuring that the estimated values ​​(such as voltage and current) output by the model satisfy the differential equations describing the fault phenomena. Its role is to guide the model to generate physically reasonable predictions even with limited or noisy training data, thereby improving the model's generalization ability and robustness.

[0054] Boundary condition constraints are used to impose physical range limitations on the fault distance and transition resistance estimates output by the physical information neural network model. In actual distribution networks, the fault distance must be between zero and the total line length, and the transition resistance must also be a non-negative value. By introducing boundary condition constraints, it is possible to effectively avoid model outputs that do not conform to actual physical meaning, ensuring the physical rationality of the estimates, thereby improving the reliability of fault location and transition resistance estimation.

[0055] Line parameter regularization constraints are used to constrain the learnable line parameters that may exist in the physical information neural network model. In some implementations of physical information neural networks, parameters such as line impedance and susceptance may be set as learnable variables to accommodate the uncertainty of actual line parameters. The role of line parameter regularization constraints is to ensure that these learnable parameters do not deviate too far from their known or expected reference values ​​during training, thereby maintaining a close connection between the model and the actual physical system, preventing model overfitting, and improving the model's stability and interpretability.

[0056] By incorporating at least one of the following technical solutions—fault differential equation constraint terms, boundary condition constraint terms, and line parameter regularization constraint terms—into the physical constraint loss term, the physical information neural network model can more comprehensively and accurately follow the physical laws of the distribution network during training. The fault differential equation constraint terms ensure that the dynamic response output by the model conforms to the physical equations, improving the model's accuracy in simulating the fault process. The boundary condition constraint terms effectively avoid physically impossible situations in the estimated fault distance and transition resistance, enhancing the reliability of the estimation results. The line parameter regularization constraint terms ensure that the line parameters learned internally by the model remain consistent with the actual physical parameters, improving the model's stability and generalization ability. Therefore, this application can significantly improve the accuracy and physical rationality of fault location and transition resistance estimation in distribution networks. Especially under complex operating conditions with sparse data or noise, the model can still provide stable and reliable prediction results, thus providing strong support for rapid fault location and recovery in distribution networks.

[0057] In one optional implementation, the process of constructing the constraint terms of the fault differential equation specifically includes: First, measurement data is acquired within a preset time window after the fault occurs. The "preset time window" refers to a data acquisition interval of a certain duration from the moment the fault occurs, such as several cycles (e.g., 2-5 cycles) or tens of milliseconds (e.g., 20-100 ms) after the fault occurs. Choosing an appropriate time window length is crucial; it must include sufficient dynamic fault information while avoiding excessive interference from steady-state data. The measurement data is typically stored in discrete time series format, including the voltage, current, zero-sequence voltage, and zero-sequence current of the fault phase. This data forms the basis for analyzing fault characteristics and constructing physical constraints.

[0058] Secondly, based on the measurement data and the preset sampling frequency The first and second time derivatives of the voltage and current of the faulty phase, the zero-sequence voltage, and the zero-sequence current are calculated. To incorporate dynamic physical laws (usually expressed as differential equations) into neural network training, the instantaneous rate of change of the measured data needs to be obtained. The first time derivative reflects the rate of change of the signal, and the second time derivative reflects the rate of change of that rate of change. For discrete-time series data, its derivatives can be calculated numerically, such as using the central difference method, forward difference method, or backward difference method. For example, for a certain moment... t Measurement values Its first derivative can be approximated as The second derivative can be approximated as: ,in The sampling period (the reciprocal of the sampling frequency) is used. These derivatives are key components in constructing the constraint terms of the fault differential equation, enabling the capture of the transient response at the time of fault occurrence.

[0059] Next, the measured data, the calculated first and second time derivatives, and the estimated fault distance and transition resistance output by the feedforward neural network model are substituted into the preset fault differential equation to calculate the estimated voltage of the fault phase. The preset fault differential equation is derived based on the equivalent circuit model of the distribution network line and physical principles such as Kirchhoff's laws at the time of fault occurrence. This equation describes the dynamic relationship between the voltage, current, and their derivatives at the fault point and the fault distance and transition resistance. For example, for a single-phase ground fault, differential equations can be established between the fault phase voltage and current, the zero-sequence voltage and current, and line parameters (such as impedance and reactance) and fault point parameters (fault distance and transition resistance). By substituting the measured voltage, current, zero-sequence quantities, and their derivatives, as well as the estimated fault distance and transition resistance output by the feedforward neural network model in the current training iteration, into this differential equation, the theoretical "estimated voltage" of the fault phase under the current estimated parameters can be calculated according to physical laws. This estimated voltage is the model's understanding and prediction of physical laws.

[0060] Finally, based on the estimated and measured voltages of the faulty phase, residual terms are calculated, and the squares of these residual terms are averaged over the entire preset time window to obtain the constraint terms of the fault differential equation. A residual term is obtained by comparing the "estimated voltage" calculated by the physical model with the "measured voltage." This residual term reflects the extent to which the fault distance estimate and transition resistance estimate output by the current neural network model conform to physical laws. To optimize the model during training, the square of the residual term is typically used as a penalty term, and averaged over all sampling points within the entire preset time window to ensure that physical constraints are satisfied throughout the dynamic process. Specifically, for each sampling point within the time window... tCalculate the square of the difference between the estimated voltage and the measured voltage, then sum these squared differences and divide by the total number of sampling points within the time window. N This yields the constraint term for the fault differential equation. This constraint term, as part of the loss function, is minimized during training, prompting the neural network model to learn fault distances and transition resistances that conform to physical laws.

[0061] The expression for the constraint terms in the fault differential equation is: ; in, These are constraint terms in the fault differential equation; for t The measured value of phase A voltage at time t; for t The estimated value of phase A voltage at time; This represents the total number of sampling points within the time window.

[0062] The above technical solution involves substituting the measured data after a distribution network fault, its time derivative, and the fault distance and transition resistance estimates output by the neural network model into a pre-defined fault differential equation. The constraint terms of the fault differential equation are then constructed based on the residual between the estimated voltage calculated by the physical model and the measured voltage. This method directly embeds the dynamic physical laws of the distribution network into the training process of the physical information neural network model, ensuring that the model's output satisfies basic physical laws while learning data characteristics. This effectively solves the problem of potentially physically unreasonable estimation results from traditional data-driven models. Especially when the fault dynamic process is complex, the data noise is high, or the training samples are limited, it significantly improves the accuracy and robustness of fault location and transition resistance estimation, ensuring that the model's output fault distance and transition resistance estimates not only match the measured data but also possess physical rationality.

[0063] As an example, consider nodes in a distribution network. n With nodes n The three-phase line between +1 L n,n+1 The self-resistance and self-inductance per unit length of the line are respectively , The mutual resistance and mutual inductance per unit length of the line are respectively , ; This is the equivalent capacitance to ground per unit length of the line. When the distance from the node on the line... n The distance is d Location f A single-phase ground fault occurred at point (taking phase A ground fault as an example), and the transition resistance was... At that time, the equivalent fault state network is as follows: Figure 3As shown.

[0064] in, and Representing nodes respectively n The measuring devices configured at the location collect the three-phase voltage and current. Similarly, the voltage and current at the fault point are respectively measured using... and To indicate, For nodes n The equivalent three-phase ground capacitance current on the side.

[0065] For the faulty phase A, the fault differential equation can be obtained as follows: (4) The unknown quantity is the fault distance. d and transition resistance The expressions for the other parameters are shown in equation (5): (5) in, The positive sequence resistance per unit length of the line; The zero-sequence resistance per unit length of the line; The positive sequence inductance per unit length of line; The zero-sequence inductance per unit length of line; Equivalent capacitance to ground per unit length of line Half the value, that is ; Represents a node n The a-phase current collected by the measuring device configured at the location; To represent nodes n The zero-sequence current collected by the measuring device configured at the location; Represents a node n The voltage of phase a is collected by the measuring device configured at the location; Represents a node n The zero-sequence voltage collected by the measuring device configured at the location.

[0066] Referring to the derivation process of the single-phase ground fault above, it can be extended to the fault differential equations of other fault types, as shown in equation (6): (6) Wherein, parameter matrix Each element in the equation can be calculated from the line parameters and measurement data.

[0067] As can be seen from equation (6), although the network structure and sequence component coupling methods differ for different fault types, the fault phase voltage at the beginning of the line and the fault distance are the same. d Transition resistance The functional relationships between them have a consistent form of expression. This unified algebraic structure reveals the common characteristics of the physical mechanisms of various faults, providing a theoretical basis for combining fault differential equations with data-driven methods in the future.

[0068] Taking a phase A ground fault as an example, according to the previous formula (4), the measured data within a time window after the fault occurs are selected, including the phase A voltage. Phase A current Zero-sequence voltage Zero-sequence current Combined with sampling frequency Calculate its first and second derivatives. The fault distance estimate output by the current feedforward neural network model. Compared with the estimated value of transition resistance Then, the corresponding estimated voltage of phase A can be calculated. and define the residual term. for: (7) in, for t The measured value of phase A voltage at time t; for t The estimated value of phase A voltage at time A; the denominator term is used to maintain the numerical stability of the normalization process and prevent residual amplification and gradient instability when the voltage value is small or close to zero.

[0069] Over the entire time window, the squares of the residuals are averaged to form the constraint terms of the fault differential equation. : (8) in, This represents the total number of sampling points within the time window.

[0070] By minimizing the difference between the model-predicted voltage and the actual voltage, the neural network is guided to follow the dynamic characteristics and physical constraints of the electrical system during training. Similarly, for different fault types, the voltage and current components of the corresponding fault phase can be directly replaced by the fault differential equation given in equation (6), thereby achieving unified modeling and model training.

[0071] In one alternative implementation, boundary condition constraints are used to impose physical range limitations on the fault distance estimates and transition resistance estimates output by the feedforward neural network model.

[0072] The expression for the boundary condition constraint term is: ; in, These are boundary condition constraint terms; It is a linear rectified function; This is the total length of the line; This is the estimated distance to the fault; This is an estimated value for the transition resistance.

[0073] The core function of this boundary condition constraint is to introduce inherent and explicit boundary conditions from the physical world into the training process of the neural network. Specifically, it ensures that the fault distance estimate and transition resistance estimate output by the model are always within a reasonable physical range.

[0074] For example, fault distance d It should not be less than zero, nor should it be greater than the total length of the line. Transition resistance It should also not be less than zero: To prevent model predictions from exceeding actual physical boundaries during training, the aforementioned inequality constraints are transformed into a penalty form, resulting in boundary condition constraints. By adding this term to the loss function, the model is subject to additional "penalty" during optimization; when its output exceeds these physical boundaries, the loss value increases significantly, thereby guiding the model parameters to adjust in a direction that conforms to the physical boundaries. As a linear rectification function, when the prediction result violates the physical boundary, the penalty term will produce a non-zero value, thereby dynamically suppressing the prediction result that violates the constraint during the model optimization process, and prompting the model output to meet the actual operating conditions / physical feasibility of the power distribution line.

[0075] By introducing boundary condition constraints and applying physical range limitations to the fault distance and transition resistance estimates output by the feedforward neural network model using a linear rectification function, this application effectively addresses the problem of models generating estimates that do not conform to actual physical boundaries during training. Specifically, this constraint ensures that the fault distance estimate always lies between zero and the total length of the line, while guaranteeing that the transition resistance estimate is not negative. This mandatory embedding of physical boundaries requires the model to not only satisfy physical laws such as the fault differential equation when optimizing the loss function, but also to strictly adhere to the actual value range of physical quantities. This significantly improves the physical rationality, accuracy, and reliability of the fault distance and transition resistance estimates output by the physical information neural network model, avoids generating meaningless estimation results, and thus enhances the practicality and robustness of the entire fault location and transition resistance estimation method.

[0076] In one optional implementation, the line parameter regularization constraint term is used to constrain each learnable line parameter in the feedforward neural network model, so that the deviation between each learnable line parameter and the corresponding reference value is kept within a preset error radius. The expression for the line parameter regularization constraint is: in, This is a regularization constraint term for line parameters; In the feedforward neural network model, the first i Each learnable line parameter forms a vector. ; For the first i The reference values ​​for each line parameter can be determined based on the line measurement values ​​or typical design values. n The total number of learnable line parameters is preferably 5; e This is the error radius coefficient, typically set to [0.25, 0.30], used to limit the allowable error range of the parameters. This line parameter regularization constraint maintains the physical consistency of the parameter magnitudes and suppresses numerical instability during training by suppressing abnormal deviations in the parameters.

[0077] Specifically, the line parameter regularization constraint is a component of the physical constraint loss term. Its core function is to guide the feedforward neural network model during the learning process, ensuring that the line physical parameters involved or implicitly included within it maintain a high degree of consistency with the actual, known line parameters. By introducing this constraint, the model focuses not only on the accuracy of the output results but also on the rationality of its internal physical mechanisms. The learnable line parameters in the feedforward neural network model refer to the variables that represent the physical characteristics of the distribution network lines and can be optimized and adjusted during training. For example, they can be the resistance, inductance, or capacitance per unit length of the line. These parameters can be used as direct outputs of the neural network or as coefficients in the physical equations, and their values ​​are dynamically updated during model training to better fit the data and satisfy the physical constraints. The corresponding reference values ​​are the known or expected physical true values ​​of the distribution network line parameters. They are usually derived from line design specifications, historical operating data, actual measurement results, or engineering experience. These reference values ​​serve as "anchor points" during the training process, providing a physical benchmark for the learnable line parameters. The preset error radius... e This is a hyperparameter that defines the maximum permissible range of deviation of learnable line parameters from their reference values. The setting of this parameter reflects the tolerance for the physical accuracy of the line parameters. A smaller error radius *e* implies a higher requirement for the physical accuracy of the parameters, while a larger error radius... e This allows for greater deviation. This value is typically adjusted empirically or through cross-validation to strike a balance between model performance and physical consistency.

[0078] By introducing line parameter regularization constraints This approach further enhances the physical consistency and numerical stability of the model during training. Considering that in actual power distribution systems, the positive-sequence and zero-sequence parameters of the lines (including resistance, inductance, and capacitance to ground) undergo continuous and slow changes due to objective factors such as operating temperature, conductor lifespan, and current carrying capacity, these parameters have clearly defined prior ranges in engineering, and their deviations typically do not exceed the theoretical error radius. Arbitrary updates during training could lead to model divergence or loss of physical meaning. Therefore, the parameters should be set to satisfy allowable interval constraints. When the predicted parameters deviate from this interval, a penalty term is applied to the excess portion to achieve adaptive constraints on the parameters, thereby maintaining the physical consistency and rationality of the line parameters. Based on this, each line parameter is treated as a learnable variable, and a regularization constraint term is used to maintain a reasonable deviation between it and the reference value.

[0079] In one alternative implementation, the loss function is represented as a weighted sum of the data-driven loss term and the physical constraint loss term, and its expression is: in, For data-driven loss terms, For physical constraint loss terms, As a weighting factor; These are constraint terms in the fault differential equation; These are boundary condition constraint terms; This is a regularization constraint term for line parameters.

[0080] Data-driven loss term The loss term is determined based on the deviation between the estimated value output by the feedforward neural network model and the corresponding label value. It is typically expressed as mean squared error (MSE) or mean absolute error (MAE) and is used to measure how well the model fits the training data. Physical constraint loss term. It is a core component of the physical information neural network model, embedding the physical laws of the power distribution network as constraints into the training process of the feedforward neural network model. This physical constraint loss term... It can include constraint terms of the fault differential equation Boundary condition constraints and line parameter regularization constraints At least one of the following. Weighting factor This is an adjustable parameter, and its value range is usually a non-negative real number. In the early stages of training, a relatively large value can be set. The initial value is used to guide the model to quickly learn physical laws; in the later stages of training, it can be gradually reduced. The value allows the model to fit the data more precisely. Weighting factors The selection of parameters can be determined through hyperparameter optimization methods such as cross-validation, grid search, or Bayesian optimization to find the optimal balance point.

[0081] The above technical solution designs the loss function as a weighted sum of data-driven and physical constraint loss terms, enabling the physical information neural network model to flexibly balance data fitting ability and adherence to physical laws during training. (Weight factors) The introduction of this feature allows for dynamic adjustment of the model's dependence on empirical data and prior physical knowledge based on actual needs and data characteristics. This not only effectively addresses the problem of insufficient model generalization ability when data volume is limited or data quality is poor, but also ensures that the model's output fault distance estimates and transition resistance estimates are physically reasonable and interpretable. Specifically, when data drives the loss term... With physical constraint loss term Through weighting factors When performing weighted combinations, the model considers both prediction accuracy and physical consistency during the optimization process. This avoids overfitting or physically unreasonable predictions that may result from relying solely on data, and also avoids relying solely on physical laws while ignoring the complex nonlinear relationships inherent in the data. This weighting mechanism enables the model to estimate the fault distance and transition resistance of the distribution network more robustly and accurately, especially in the face of complex and variable fault conditions, providing more reliable diagnostic results.

[0082] The following example will provide a more detailed explanation of the above technical solution: A 10kV resonant grounded distribution network simulation model with distributed power sources was built on the MATLAB / Simulink simulation platform to verify the effectiveness and robustness of the proposed method. The overall topology of the system is as follows: Figure 4 As shown. The system consists of a power source, main transformer, distribution lines, loads, and distributed power sources, employing a typical radial structure with six outgoing lines, including a mix of overhead and cable lines. The length of each feeder is... Figure 4 All parameters are clearly marked and are shown in Table 1. Each feeder is connected to a load at its end, and some feeder ends are connected to distributed generation (DG) sources, including photovoltaic and wind power. The output of the DG is allowed to fluctuate within 0.2 to 0.8 times its rated capacity to simulate the random output characteristics of distributed generation. The neutral point on the low-voltage side of the main transformer is grounded via an arc suppression coil with 8% compensation. Measuring devices are installed at the beginning of each feeder to collect voltage and current signals at a sampling frequency of 10kHz.

[0083] Table 1

[0084] like Figure 5As shown, the specific process of the method of the present invention is as follows: 1) Simulation case design and sample library generation stage: A power distribution network fault simulation model was built using MATLAB / Simulink. Various typical fault conditions were constructed by changing key parameters such as fault type, fault distance, transition resistance, and initial phase angle. In each simulation scenario, the instantaneous voltage and current values ​​for three power frequency cycles after the fault occurred were selected as the sample window to fully extract fault features. The waveform sampling frequency was set to 10kHz to ensure high resolution of the time-domain waveform and dynamic continuity of the signal. A fault sample set was generated through the above process, with each sample containing voltage and current measurement signals and their corresponding labels (fault distance, transition resistance). The sample set was divided into a training set and a test set proportionally. The training set was used for iterative updates of network parameters, while the test set was used to monitor model convergence, parameter selection, ablation experiments, and model performance evaluation.

[0085] 2) Model training and parameter tuning stage: The preprocessed dataset was divided into training and test sets in a 7:3 ratio. The goal of model training was to minimize the defined overall loss function, thereby achieving joint optimality between data consistency and physical constraints, allowing the network output to approximate the true label while maintaining physical interpretability. The Adam optimizer was used during training, with an initial learning rate of 0.001. An adaptive learning rate decay strategy was introduced to accelerate convergence and avoid getting trapped in local optima. To ensure the correctness and computational accuracy of higher-order derivatives in the physical constraints, the model employed Automatic Differentiation (AD) to synchronously calculate the derivative information of each electrical quantity during backpropagation, achieving explicit embedding of fault differential equation constraints in parameter updates. Simultaneously, to prevent overfitting and maintain training stability, an early stopping strategy was introduced. When the network performs stably for several consecutive training rounds, the training process was automatically terminated, and the best-performing model weights were retained.

[0086] 3) Practical application stage: When an actual fault occurs, voltage and current waveform data are collected over three power frequency cycles following the fault occurrence, and preprocessed to reduce measurement noise interference. To avoid redundant detection and reduce the waste of computational resources, the zero-sequence current amplitude difference is used as the trigger criterion; that is, when the zero-sequence current amplitude difference between adjacent time windows exceeds 2A, a fault is determined to have occurred, and the proposed fault location process is initiated. Subsequently, the preprocessed voltage and current signals are input into the proposed physical information neural network to estimate the fault distance.

[0087] like Figure 6The diagram illustrates the iterative convergence process of the model during training, including the total loss, data-driven loss, and physical constraint loss on both the training and test sets. Figure 6 As can be seen, all loss terms continuously decrease with increasing iterations and stabilize after approximately 300 iterations, indicating that the model achieves smooth convergence during iteration. Meanwhile, the curves on the training and test sets show largely consistent trends, with no significant overfitting, demonstrating good generalization performance. Furthermore, the physics constraint loss term fluctuates significantly in the early stages of training before gradually converging to a lower level, indicating that the physical constraints are effectively satisfied in the later stages of model training. This result verifies the data-physical fusion concept proposed in this invention, namely, that by introducing physical information constraints, the physical consistency and interpretability of the model can be effectively improved.

[0088] like Figure 7 As shown, the model's performance on the test set during training, including the variation trend of the estimation errors of fault distance and transition resistance with the number of iterations, is illustrated. Figure 7 As training continues, both types of errors show a significant decreasing trend and stabilize after approximately 350 rounds, indicating that the model has achieved stable convergence in the later stages of training. At this point, the average relative error of the fault distance is controlled within 100m, and the average estimation error of the transition resistance is less than 5Ω, indicating that the model has high prediction accuracy and good convergence stability under various fault conditions. Furthermore, Figure 7 The statistical results show that the accuracy of fault distance prediction exceeds 95% within the range, and the accuracy of transition resistance estimation reaches 98% within the range. This result fully verifies the high-precision prediction capability and good physical consistency of the proposed physical information neural network under complex nonlinear conditions.

[0089] To evaluate the generalization ability of the method of this invention under different fault conditions, the model performance was tested under different fault types, fault distances, and transition resistance conditions. The simulation scenarios covered four typical fault types: single-phase ground fault, two-phase short-circuit fault, two-phase ground fault, and three-phase short-circuit fault. The model's performance under different fault distances and transition resistance conditions is shown below. Figure 8 As shown. By Figure 8It can be seen that the model's fault distance prediction error is less than 150m under different scenarios, the transition resistance estimation error is controlled within 10Ω, and the error distribution is uniform with no abnormal fluctuations or divergence. These results demonstrate that the method of this invention can maintain physical consistency and stable prediction performance under various complex fault conditions, thus exhibiting good generalization ability in diverse fault scenarios.

[0090] The method of this invention is compared with traditional methods to fully verify the advantages of the technical solution of this application, including two aspects: model localization accuracy and computation time. Considering the certain randomness in the model training and testing process, the model is repeatedly tested and the average is calculated. The results are shown in Table 2. The accuracy of the fault location result and the transition resistance estimation result is characterized by the mean, standard deviation, and median of the prediction error; computation time refers to the average inference time of the model for a single sample. As can be seen from Table 2, compared with the impedance method, this technical solution achieves joint estimation of fault distance and transition resistance, and has a significant advantage in accuracy. Furthermore, even though CNN and LSTM have higher computational efficiency, their fault location error is greater than that of this technical solution. It should be noted that in practical applications, the accuracy of fault localization is more important than computational speed. Therefore, sacrificing a small amount of computation time to obtain higher fault localization accuracy is acceptable for this technical solution.

[0091] Table 2

[0092] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method for fault location and transition resistance estimation in distribution networks based on physical information neural networks, characterized in that, Includes the following steps: S1. Collect real-time voltage and current data after a power distribution network fault by using measuring devices installed on each line; S2. Input the voltage and current data into the pre-trained physical information neural network model to obtain the fault distance estimate and the transition resistance estimate. The physical information neural network model is constructed based on a feedforward neural network model and is trained by a loss function that integrates data-driven loss terms and physical constraint loss terms. It is used to establish a nonlinear mapping relationship between voltage and current data and fault distance and transition resistance.

2. The method according to claim 1, characterized in that, The training method for the physical information neural network model includes: Acquire voltage and current sample data containing various fault conditions, along with corresponding fault distance and transition resistance labels; Construct a feedforward neural network model; Construct a loss function; the loss function includes a data-driven loss term and a physical constraint loss term; the data-driven loss term is determined based on the deviation between the estimated value output by the feedforward neural network model and the corresponding label value; the physical constraint loss term is used to embed physical laws as constraints into the training process of the feedforward neural network model; The feedforward neural network model is trained using the voltage and current sample data, and the model parameters are updated by optimizing the loss function to obtain a trained physical information neural network model.

3. The method according to claim 2, characterized in that, The method for obtaining the voltage and current sample data includes: Build a power distribution network simulation model; By changing the fault feeder, fault type, fault distance, transition resistance, and fault initial phase angle parameters, various fault conditions can be simulated. Collect voltage and current waveform data under various fault conditions, and record the corresponding fault distance and transition resistance as labels.

4. The method according to claim 1, characterized in that, Prior to S1, the method further includes: Monitor the amplitude change of zero-sequence current in the distribution network; When the difference in zero-sequence current amplitude between adjacent time windows exceeds a set threshold, a fault is determined to have occurred and S1 is executed.

5. The method according to claim 2, characterized in that, The feedforward neural network model contains multiple hidden layers with the number of neurons configured as [256, 512, 512, 256]. Dropout and layer normalization are introduced during training to improve the model's numerical stability and generalization ability.

6. The method according to claim 2, characterized in that, The physical constraint loss term includes at least one of the following: fault differential equation constraint term, boundary condition constraint term, and line parameter regularization constraint term.

7. The method according to claim 6, characterized in that, The process of constructing the constraint terms of the fault differential equation includes: Acquire measurement data within a preset time window after the fault occurs; the measurement data includes discrete time series of the voltage, current, zero-sequence voltage, and zero-sequence current of the fault phase. Based on the measured data and the preset sampling frequency, calculate the voltage of the fault phase, the current of the fault phase, the zero-sequence voltage, and the first and second time derivatives of the zero-sequence current. Substituting the measured data, the calculated first and second time derivatives, and the fault distance and transition resistance estimates output by the feedforward neural network model into the preset fault differential equation, the estimated voltage of the fault phase is calculated. Based on the estimated and measured voltages of the faulted phase, the residual terms are calculated, and the squares of the residual terms are averaged over the entire preset time window to obtain the constraint terms of the fault differential equation: ； in, These are constraint terms in the fault differential equation; for t The measured value of phase A voltage at time t; for t The estimated value of phase A voltage at time; This represents the total number of sampling points within the time window.

8. The method according to claim 7, characterized in that, The boundary condition constraint term is used to impose physical range restrictions on the fault distance estimate and transition resistance estimate output by the feedforward neural network model; The expression for the boundary condition constraint term is: ； in, These are boundary condition constraint terms; It is a linear rectified function; This is the total length of the line; This is the estimated distance to the fault; This is an estimated value for the transition resistance.

9. The method according to claim 8, characterized in that, The line parameter regularization constraint term is used to constrain each learnable line parameter in the feedforward neural network model, so that the deviation between each learnable line parameter and the corresponding reference value is kept within a preset error radius. The expression for the line parameter regularization constraint is: in, This is a regularization constraint term for line parameters; In the feedforward neural network model, the first i One learnable line parameter; For the first i Reference values ​​for each line parameter; n This represents the total number of learnable line parameters; e This is the error radius coefficient.

10. The method according to claim 9, characterized in that, The loss function is expressed as a weighted sum of the data-driven loss term and the physical constraint loss term, and its expression is: in, For data-driven loss terms, For physical constraint loss terms, As a weighting factor; These are constraint terms in the fault differential equation; These are boundary condition constraint terms; This is a regularization constraint term for line parameters.

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