Single-phase ground fault location method and system for distribution network based on transient traveling wave

Abstract

The application relates to a power distribution network single-phase grounding fault positioning method and system based on a transient traveling wave, which comprises the following steps: 1. Collecting a zero-sequence current signal at the moment of single-phase grounding fault occurrence, decomposing the collected zero-sequence current signal through a variational mode decomposition algorithm, extracting features through a convolutional neural network, and optimizing the features through an alternating direction multiplier method; wherein the zero-sequence current simultaneously contains a high-frequency traveling wave component and a transient mutation characteristic; 2. Based on the optimized sampling signal in step 1, carrying out feature extraction from two dimensions of the transient mutation characteristic and the traveling wave propagation characteristic, and packaging the feature extraction into a fusion vector; 3. Identifying a fault line by means of a Gram angle and field method and an improved DenseNet; 4. Based on the fusion vector in step 2 and the fault line information determined in step 3, performing iterative operation by using an improved sparrow search algorithm, and outputting a finally determined fault section position result. The application meets the intelligent fault sensing and accurate response demand under a complex power distribution environment.

Description

Technical Field

[0001] This invention belongs to the field of power system fault detection and location technology, specifically relating to a method and system for locating single-phase grounding faults in distribution networks based on transient traveling waves. Background Technology

[0002] With the continuous evolution of new power distribution systems, the widespread integration of overhead lines, cable lines, and distributed power sources has made power distribution network structures increasingly complex. In medium-voltage power distribution networks, especially in low-current grounding systems, most faults are single-phase grounding faults. However, due to the weak zero-sequence current, short duration, and unclear traditional steady-state characteristics, conventional protection devices struggle to accurately identify them, leading to misjudgments and missed detections. Particularly in multi-branch, multi-feeder structures, traditional algorithms are easily affected by electrical parameter distribution, load changes, and the initial phase angle of the fault, making them prone to incorrect line selection or location deviations. Meanwhile, while the high-frequency traveling wave signal generated in the early stages of a fault has excellent ranging capabilities, it relies on extremely high-precision clock synchronization systems and high-speed sampling equipment, and is sensitive to noise, limiting its widespread application. On the other hand, machine learning methods based on transient signal characteristics are gradually being used for intelligent fault diagnosis in power systems, but their results typically rely on large-scale data model training, making it difficult to meet the dual requirements of real-time performance and accuracy. Therefore, there is an urgent need to build a multi-feature sensing system that integrates transient information and high-frequency traveling wave signals, and has the capabilities of BeiDou spatiotemporal synchronization, high-speed data acquisition and intelligent identification, so as to comprehensively improve the fault location accuracy of distribution network lines and form an overall solution for distribution network fault location that takes into account robustness, accuracy and response speed. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention proposes a single-phase grounding fault location system and method for power distribution networks based on transient traveling waves.

[0004] One of the above-mentioned objectives of the present invention is achieved by the following technical solution:

[0005] A method for locating single-phase ground faults in a distribution network based on transient traveling waves includes the following steps:

[0006] Step 1: Collect the zero-sequence current signal at the instant of a single-phase ground fault. Decompose the collected zero-sequence current signal using Variational Mode Decomposition (VMD) algorithm, extract features using Convolutional Neural Network (CNN), and optimize it using Alternating Direction Multiplier (ADMM) method. The zero-sequence current contains both high-frequency traveling wave components and transient change features.

[0007] Step 2: Based on the sampled signal optimized in Step 1, feature extraction is performed from two dimensions: transient change characteristics and traveling wave propagation characteristics, and then encapsulated into a fusion vector;

[0008] Step 3: The fusion vector established in Step 2 is converted into a two-dimensional image using Gram angle and field GASF methods. Then, the feature channels are adaptively weighted using a DenseNet network with SENet attention mechanism to deeply mine the local and global semantic information in the image, resulting in DenseNet image feature vectors enhanced by the attention mechanism. These feature vectors not only contain local details and global information, but also highlight the key features of the fault and suppress noise and secondary features through SENet's adaptive weighting mechanism. Finally, the enhanced DenseNet image feature vectors are combined with the fusion vector, and the Gini coefficient of random forest is used to achieve accurate identification of faulty lines.

[0009] Step 4: Randomly initialize the population of the improved sparrow search algorithm. Based on the fusion vector from Step 2 and the faulty line information determined in Step 3, initiate multiple rounds of iterative calculation to determine the optimal fitness position. In each iteration, the population position is updated based on fitness and aggregation state. When the maximum number of iterations is reached, the algorithm terminates and outputs the final determined faulty section location, accurately locating the faulty section.

[0010] Moreover, in step 1, the feeder terminal unit (FTU) deployed on the distribution network line collects the raw signal at the moment a single-phase ground fault occurs in real time, and realizes 10ns-level clock synchronization between each measuring point based on Beidou satellite time synchronization, and collects signals at a sampling frequency of more than 10MHz.

[0011] Furthermore, in step 1, the zero-sequence high-frequency components related to the fault transient are extracted from the current signal. The three-phase instantaneous currents ia(t), ib(t), and ic(t) are linearly transformed to obtain the zero-sequence current i0(t), and the calculation formula is as follows:

[0012] ;

[0013] The zero-sequence current is de-trended to obtain the processed signal. ;right Further normalization processing:

[0014] .

[0015] Furthermore, in step 1, the normalized zero-sequence current signal and voltage traveling wave signal are preprocessed using a variational mode decomposition algorithm; the original signal is decomposed into a set of finite modes with different center frequencies, and the mode components containing transient abrupt changes and high-frequency traveling wave characteristics are extracted:

[0016] Original signal: x(t);

[0017] Modal components: ;

[0018] Each mode satisfies:

[0019]

[0020] in, Let ωk be the k-th modal component, ωk be its center frequency, and the asterisk be the convolution symbol.

[0021] Furthermore, in step 1, Lagrange multipliers and penalty terms are introduced, and the alternating direction multiplier method (ADMM) is used to iteratively optimize the frequency domain representation of each mode; in each iteration, the mode... The frequency domain is updated as follows:

[0022]

[0023] The iterative formulas for the center frequencies of each mode are as follows:

[0024]

[0025] in, This is the Fourier transform of the original signal in the frequency domain; Let i be the frequency domain representation of the i-th mode; i ≠ k, indicating that when updating the k-th mode, the other modes are considered to be known. This is the frequency domain representation of the Lagrange multipliers, used to constrain the sum of all modes to equal the original signal; The penalty factor controls the strength of the modal bandwidth constraint; The center frequency of the kth mode; The energy spectral density of the k-th mode in the frequency domain.

[0026] Furthermore, in step 1, the selected modal components containing key signal elements are input into the convolutional neural network, and the network structure used is as follows:

[0027]

[0028] in: , These are the parameters of the convolutional layer. For the first Layer weight parameters, For the first Layer bias vector; For the first The output features of the layer For the next level (the first) The output of the current layer is used as the input of the current layer; ∗ is the convolution operation; f() is the non-linear activation function;

[0029] The parameter optimization form of the neural network based on ADMM is as follows:

[0030]

[0031] in, It is the set of all parameters of the neural network; The task loss function; For regularization terms; The regularization coefficient is used. , These are the matrices and vectors in the constraints used for ADMM optimization.

[0032] Moreover, step 2 includes:

[0033] Step 2.1: Perform Variational Mode Decomposition (VMD) on the sampled current and voltage traveling wave signals to extract the zero-sequence current high-frequency mode i0HF, voltage drop Δv, and energy spectrum changes;

[0034] Step 2.2: Using the nanosecond-level timestamp provided by BeiDou synchronization, combined with the initial current polarity identification at multiple measurement points, calculate the propagation delay Δt from the fault point to the measurement point, and construct the propagation path characteristics;

[0035] Step 2.3: Unify the extracted multimodal high-frequency features into a fusion vector to provide input for the subsequent fault line and localization network model. The fusion vector features include temporal abrupt changes, frequency domain energy, spatial propagation delay, and initial traveling wave current polarity features.

[0036] Furthermore, step 3 includes:

[0037] Step 3.1: Using the Gram angle and field method GASF, the one-dimensional zero-sequence current time-series signal is converted into a two-dimensional image, including:

[0038] Step 1: Scale the time series X = {x1, ..., xi, ..., xd} of length d to the range [-1, 1]. The calculation formula is:

[0039]

[0040] Step 2: Transform the scaled sequence according to the following formula, encoding the timestamp as a radius and the sequence value as a cosine angle, thus converting the signal to polar coordinates. The calculation formula is:

[0041]

[0042] In the formula: For polar coordinates, For radius, M is the timestamp, and M is the coordinate span adjustment constant;

[0043] Calculate the cosine sum function between each point to obtain the Gram angle and field. The calculation method is as follows:

[0044]

[0045] Step 3.2: Deeply mine the features in the image using DenseNet and SENet attention mechanisms to highlight key information;

[0046] The SENet attention module consists of squeezing and activation operations.

[0047] The extrusion operation is as follows:

[0048]

[0049] In the formula: The output feature vector is H, where H and W are the length and width of the feature map, respectively. The input matrix is ​​h and c, which are its rows and columns. The squash operation compresses the W×H×T feature map into a 1×1×T feature vector, where T is the number of output channels.

[0050] The incentive operation is as follows:

[0051]

[0052] In the formula: s is the weight vector with a dimension of 1×1×T; The input feature vector; It is the ReLU activation function; The Sigmoid function normalizes the obtained weights; W1 and W2 are two fully connected layer operations.

[0053] Furthermore, in step 4, the formula for calculating the nonlinear inertia weighting factor w used in the iterative calculation process is as follows:

[0054]

[0055] In the formula, α is 0.7 and β is 0.3;

[0056] The improved discoverer location update formula is shown below:

[0057]

[0058] The follower update formula is as follows:

[0059]

[0060] In the formula, To be the globally optimal position This is the worst position globally. A is a value of 1 or -1. Matrix;

[0061] The position update formula for the vigilant is as follows:

[0062] .

[0063] The second objective of this invention is achieved through the following technical solution:

[0064] A single-phase ground fault location system for distribution networks based on transient traveling waves is used to implement the above-mentioned single-phase ground fault location method for distribution networks based on transient traveling waves. The system includes a high-precision synchronous sampling unit, a transient-traveling wave fusion feature extraction module, a fault line module, and a fault section location module.

[0065] The high-precision synchronous sampling unit uses BeiDou <10ns-level clock synchronization and ≥10MHz high-frequency sampling to construct a spatiotemporal reference, collects high-frequency traveling wave signals in the early stage of the fault, decomposes the collected zero-sequence current signal through variational mode decomposition algorithm (VMD), extracts features through convolutional neural network (CNN), and optimizes it with ADMM, forming a "synchronization-capture-purification-learning" closed loop to achieve high-fidelity perception of fault signals.

[0066] The transient-traveling wave fusion feature extraction module is used to fuse time-domain transient quantities, frequency-domain energy spectrum and spatial propagation delay to construct a three-dimensional feature vector of "time-domain abrupt change + frequency-domain energy + spatial propagation".

[0067] The fault line module uses the Gram angle and field method GASF to map the one-dimensional zero-sequence current sequence into a two-dimensional image, and integrates the dense connection structure of DenseNet and the attention mechanism of SENet to deeply mine the local and global semantic information in the image; at the same time, it introduces random forest to replace the traditional classifier to achieve intelligent and accurate identification of fault lines in the distribution network.

[0068] The fault section location module is used to accurately locate the fault section by judging the fault direction based on the propagation characteristics of the initial traveling wave current polarity of the fused vector using the improved sparrow algorithm, thereby achieving efficient and accurate identification of distribution network faults.

[0069] The advantages and positive effects of this invention are as follows:

[0070] This invention proposes a system-level method for locating single-phase grounding faults in power distribution networks, constructing an integrated solution for high-precision sensing, intelligent identification, and rapid positioning driven by the BeiDou timescale. Through high-frequency synchronous sampling and multimodal feature extraction, combined with neural network classification and intelligent optimization algorithms, the system achieves over 95% identification accuracy for single-phase grounding faults in low-current grounding systems. By combining traveling wave initial polarity and propagation time difference modeling, the average response time for locating faulty lines and sections is less than 1 second, with positioning errors controlled within ±1.6 meters. The system structure possesses good topology adaptability and grounding type compatibility, exhibiting significant robustness in different feeder scenarios. It supports modular deployment and can be flexibly embedded in intelligent switching stations, distribution rooms, and remote master stations, meeting the needs for intelligent fault sensing and accurate response in complex power distribution environments. Attached Figure Description

[0071] Figure 1 This is a block diagram of the single-phase grounding fault location system for power distribution networks according to the present invention;

[0072] Figure 2 This is a flowchart of the data acquisition and synchronization process of this invention;

[0073] Figure 3 This is the zero-sequence current signal and its GASF image of lines L1 and L3 in an embodiment of the present invention;

[0074] Figure 4 This is the random forest structure diagram used in this invention;

[0075] Figure 5 This is a flowchart of the improved sparrow algorithm used in this invention. Detailed Implementation

[0076] The structure of the present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that these embodiments are descriptive and not limiting.

[0077] A method and system for locating single-phase grounding faults in distribution networks based on transient traveling waves is proposed. The system has BeiDou spatiotemporal synchronization, high-speed data acquisition and intelligent identification capabilities, which comprehensively improves the fault line and location accuracy of distribution networks, forming an overall solution for distribution network fault location that takes into account robustness, accuracy and response speed. This invention discloses a method for locating single-phase grounding faults in distribution networks. First, a high-precision synchronous sampling unit, based on BeiDou satellite timing, achieves 10ns-level clock synchronization between measurement points, capturing high-frequency traveling waves and abrupt changes in the initial stage of the fault at a sampling frequency of 10MHz or higher. The acquired zero-sequence current signal is decomposed using Variational Mode Decomposition (VMD), features are extracted using a Convolutional Neural Network (CNN), and optimized using the Alternating Direction Multiplier Method (ADMM). Then, a transient traveling wave fusion feature extraction module extracts features from two dimensions: transient abrupt changes and traveling wave propagation characteristics. Transient and traveling wave propagation features are extracted from the sampled signals and encapsulated into a fusion vector. Next, a fault line module identifies the faulty line using Gram angle and field method (GASF) and an improved DenseNet. Finally, a fault section location module uses an improved sparrow search algorithm to determine the fault direction and accurately locate the fault section based on the propagation characteristics of the initial traveling wave current polarity, ultimately achieving efficient and accurate fault identification in the distribution network.

[0078] This invention relates to a single-phase ground fault location system for distribution networks based on transient traveling waves, comprising the following components:

[0079] 1. High-precision synchronous sampling unit (HSTS):

[0080] The high-precision synchronous sampling module integrates several key technologies, including BeiDou time synchronization, high-frequency sampling, signal decomposition, and feature extraction. It constructs a high-fidelity data acquisition and processing front-end for distribution network fault identification, achieving a fusion of spatiotemporal benchmark enhancement, intelligent signal purification, and in-depth feature mining. This module achieves <10ns-level clock synchronization between measurement points via BeiDou satellites, ensuring precise alignment of fault transient signals in the time domain. With a sampling frequency exceeding 10MHz, it can completely capture high-frequency traveling wave signals in the initial stage of a fault. The introduction of the Variational Mode Decomposition (VMD) algorithm decomposes complex current signals into multi-scale high-frequency modes, significantly enhancing the ability to characterize weak abrupt changes. Combined with a Convolutional Neural Network (CNN) to automatically extract key local waveform features, and optimized for network convergence and robustness using the Alternating Direction Multiplier Method (ADMM), it innovatively constructs a high-precision fault perception unit that integrates synchronization mechanisms and deep sensing capabilities.

[0081] 2. Transient-Traveling Wave Fusion Feature Extraction Module TF-FEM:

[0082] The transient-traveling wave fusion feature extraction module innovatively integrates transient mutations and traveling wave propagation information to construct a physical perception feature system for distribution network faults. The module extracts the zero-sequence current high-frequency mode i0HF, the fault phase voltage drop ∆v, and the frequency domain energy spectrum through the variational mode decomposition algorithm VMD, comprehensively capturing the high-frequency disturbance characteristics in the early stages of a fault. Furthermore, by combining initial current polarity identification at multiple measurement points with nanosecond-level time differences supported by BeiDou timing, it accurately calculates the propagation delay ∆t, characterizing the propagation path of electromagnetic waves within the network. Finally, it fuses and encapsulates time-domain mutations, frequency-domain features, and spatial propagation behavior into a unified feature vector, constructing a fault behavior chain "from disturbance generation to path evolution," achieving deep perception and accurate modeling of fault types and locations. TF-FEM, through the three-dimensional fusion of "time-domain mutations + frequency-domain energy + spatial propagation," achieves for the first time a leap from signal analysis to behavioral chain cognition of distribution network faults.

[0083] 3. Faulty Line Module GASF-DenseNet:

[0084] The fault line module innovatively transforms the time-domain waveform of zero-sequence current in the distribution network into visual image features, enabling accurate identification of fault lines under weak signal conditions. The module employs the Gram angle and field method GASF to map the one-dimensional zero-sequence current sequence into a two-dimensional image, effectively enhancing the separability and visual representation of fault features. It integrates the dense connection structure of DenseNet and the attention mechanism of SENet to deeply mine local and global semantic information in the image. Simultaneously, it introduces random forest to replace the traditional classifier, improving the model's robustness and classification stability under complex operating conditions, thus constructing a high-precision line selection system from signal visualization to intelligent identification. GASF-DenseNet transforms fault signals into an image space (GASF) + dense connection feature reuse (DenseNet), achieving intelligent and accurate identification of fault lines in the distribution network.

[0085] 4. Fault Section Location Module ISSA-Locator:

[0086] The fault section location module, by introducing an intelligent optimization mechanism, constructs a high-precision and high-efficiency distribution network fault section search system. Based on the improved Sparrow Search Algorithm (ISSA), the module integrates nonlinear inertial factor weight control to dynamically balance global exploration and local convergence capabilities, significantly improving location accuracy and algorithm stability. It innovatively uses initial current polarity and high-frequency energy difference as fitness evaluation indicators to accurately characterize the physical area where the fault occurs. Internally, the algorithm employs a multi-role intelligent agent ("discoverer-follower-watcher") for collaborative iteration, rapidly completing the optimal search and identification of the fault section, constructing an integrated closed-loop mechanism from perception triggering to intelligent location. The introduction of a nonlinear inertial weight factor w improves the discoverer position update formula of the Sparrow Search algorithm, enabling ISSA to accurately locate fault sections.

[0087] This invention relates to a method for locating single-phase ground faults in distribution networks based on transient traveling waves, comprising the following steps:

[0088] Step 1: Acquire the zero-sequence current signal at the instant of a single-phase ground fault. The acquired zero-sequence current signal is decomposed using Variational Mode Decomposition (VMD), its features are extracted using a Convolutional Neural Network (CNN), and optimized using the Alternating Direction Multiplier Method (ADMM). The zero-sequence current simultaneously contains high-frequency traveling wave components and transient change characteristics. The specific implementation is as follows:

[0089] First, the system relies on the BeiDou satellite timing module to construct a high-precision clock synchronization mechanism, achieving clock synchronization accuracy of 10ns between various monitoring terminals. This ensures the alignment consistency of sampled data in the time domain from the source, providing a time reference for traveling wave propagation time difference analysis and fault location. Its basic principle is as follows:

[0090]

[0091] Where Δx represents the position error caused by clock error. Based on the traveling wave propagation speed, the positioning error can be calculated to be controlled within approximately 1.6 meters.

[0092] To fully capture transient and traveling wave signals during the initial stage of a fault, the system sampling frequency is set to 10MHz or higher. Transient signals primarily occur within tens of microseconds in the initial fault phase, covering a spectrum from hundreds of kHz to several MHz; the high-frequency traveling wave band is concentrated in the 100kHz~5MHz range. Using zero-sequence current as the key indicator, the zero-sequence high-frequency components related to the fault transient are extracted from the current signal. The three-phase instantaneous currents ia(t), ib(t), and ic(t) are linearly transformed to obtain the zero-sequence current i0(t), calculated using the following formula:

[0093]

[0094] Then, the zero-sequence current is de-trended to eliminate DC bias and low-frequency drift interference, improve sensitivity to abrupt changes, and obtain the processed signal. ,right Further normalization processing yields the following standard form:

[0095]

[0096] The normalization result is used as the input signal to be decomposed to the variational mode decomposition (VMD) algorithm unit.

[0097] It achieves a time reference innovation with 10ns-level high-precision clock synchronization, signal integrity guarantee above 10MHz, and feature extraction optimization of zero-sequence current processing and variational mode decomposition (VMD) algorithm.

[0098] Then, the normalized zero-sequence current signal and voltage traveling wave signal are preprocessed using the Variational Mode Decomposition (VMD) algorithm. VMD decomposes the original signal into a set of finite modes (IMFs) with different center frequencies, extracting the modal components that contain transient abrupt changes and high-frequency traveling wave characteristics.

[0099] Original signal: x(t)

[0100] Modal components:

[0101] Each mode satisfies:

[0102]

[0103] Where uk(t) is the k-th modal component, ωk is its center frequency, and the asterisk is the convolution symbol.

[0104] To improve decomposition stability, Lagrange multipliers and penalty terms are introduced, and the Alternating Direction Multiplier Method (ADMM) is used to iteratively optimize the frequency domain representation of each mode. In each iteration, the mode... The frequency domain is updated as follows:

[0105]

[0106] The iterative formulas for the center frequencies of each mode are as follows:

[0107]

[0108] We have achieved an innovative joint optimization of the variational mode decomposition algorithm VMD-ADMM to reduce the error in traveling wave mode extraction.

[0109] Then, the selected modal components containing key signal elements are input into the convolutional neural network (CNN). Leveraging the advantages of CNNs in local structure perception, the network automatically learns transient waveforms and high-frequency change patterns: convolutional layers perceive local changes and identify representative waveform structures in zero-sequence currents; activation functions preserve nonlinear abrupt changes; and pooling layers compress invalid information, enhancing representational capabilities. The network structure is as follows:

[0110]

[0111] in: , These are the parameters of the convolutional layer. For the first Layer weight parameters, For the first Layer bias vector; For the first The output features of the layer For the next level (the first) The output of the current layer is used as the input of the current layer; ∗ is the convolution operation; f() is the non-linear activation function;

[0112] To improve the convergence and robustness of model training, the Alternating Direction Multiplier Method (ADMM) is introduced to perform constraint decomposition and joint solution of the parameter optimization process of Convolutional Neural Networks (CNNs). The optimization problem is formalized as follows:

[0113]

[0114] in, It is the set of all parameters of the neural network; The task loss function; For regularization terms; The regularization coefficient is used. , These are the matrices and vectors in the constraints used for ADMM optimization.

[0115] By introducing auxiliary variables and Lagrange multipliers, ADMM decomposes the optimization objective into subproblems that are solved iteratively, thereby improving the stability and generalization ability of parameter updates.

[0116] Step 2: Feature extraction is performed from two dimensions—transient abrupt changes and traveling wave propagation characteristics—using the transient traveling wave fusion feature extraction module. Transient and traveling wave propagation features are extracted based on the sampled signal and encapsulated into a fusion vector. The specific implementation is as follows:

[0117] Traditional methods often use steady-state amplitude or instantaneous peak value as characteristics. This invention improves the physical consistency of the description of the fault evolution process by jointly modeling modal time-frequency characteristics and traveling wave propagation characteristics. Using propagation time difference and spatial distribution data of measurement points, a fault wave propagation trajectory map is constructed to achieve spatial reasoning and matching localization of the fault location. Specifically, the steps include:

[0118] Step 2.1: Perform Variational Mode Decomposition (VMD) on the sampled current and voltage traveling wave signals to extract the zero-sequence current high-frequency mode i0HF, voltage drop Δv, energy spectrum changes, etc.

[0119] Step 2.2: Using the nanosecond-level timestamp provided by BeiDou synchronization, combined with the initial current polarity identification at multiple measurement points, calculate the propagation delay Δt from the fault point to the measurement point, and construct the propagation path characteristics;

[0120] Step 2.3: The extracted multimodal high-frequency features are fused and encapsulated into a unified feature vector for behavior chain reconstruction and subsequent localization network modeling. The multimodal high-frequency features include temporal abrupt changes, frequency domain energy, and spatial propagation delay.

[0121] Step 3: The fusion vector established in Step 2 is converted into a two-dimensional image using Gram angle and field GASF methods. Then, a DenseNet network incorporating SENet attention mechanism is used to adaptively weight the feature channels, deeply mining the local and global semantic information in the image to obtain DenseNet image feature vectors enhanced by the attention mechanism. These feature vectors not only contain local details and global information but also, through SENet's adaptive weighting mechanism, highlight key fault features while suppressing noise and secondary features. Finally, the enhanced DenseNet image feature vectors are combined with the fusion vector, and the Gini coefficient of a random forest is used to achieve accurate identification of faulty lines. The specific implementation is as follows:

[0122] Step 3.1: Convert the one-dimensional zero-sequence current time-series signal into a two-dimensional image;

[0123] Due to the weak fault characteristics of low-current grounding systems and the nonlinear nature of zero-sequence current signals, various processing methods in the one-dimensional time domain are not very effective. Therefore, the one-dimensional time series signal can be transformed into a two-dimensional image signal to better reveal the detailed features of the fault signal. The GASF transform is a method for converting a one-dimensional time series into a two-dimensional image. This transform can characterize the relationship between the local and global parts of the sequence. The transformed image retains the time correlation on the diagonal while also reflecting the nonlinear characteristics within the signal. Using the GASF transform to convert the zero-sequence current signal into a two-dimensional image provides a prerequisite for subsequent feature mining using neural networks.

[0124] The GASF transformation steps are as follows:

[0125] Step 1: Scale the time series X = {x1, ..., xi, ..., xd} of length d to the range [-1, 1]. The calculation formula is:

[0126]

[0127] Step 2: Transform the scaled sequence according to the following formula, encoding the timestamp as a radius and the sequence value as a cosine angle, thus converting the signal to polar coordinates. The calculation formula is:

[0128]

[0129] In the formula: For polar coordinates, For radius, M is the timestamp, and M is the coordinate span adjustment constant. The encoded polar coordinates correspond to the time series, ensuring the uniqueness of the encoding.

[0130] Calculate the cosine sum function between each point to obtain the Gram angle and field. The calculation method is as follows:

[0131]

[0132] A single-phase ground fault was simulated on line L1 using simulation software. The zero-sequence current signal waveforms of the faulted line L1 and the non-faulted line L3 were subjected to GASF transformation. The results are as follows. Figure 3 As shown.

[0133] Through GASF transformation, the zero-sequence current signals of faulty and non-faulty lines show obvious differences in the image, such as differences in color distribution and intensity, thus providing a more intuitive and effective data foundation for subsequent feature extraction and classification.

[0134] Step 3.2: Deeply mine features in the image using DenseNet and SENet attention mechanisms to highlight key information.

[0135] Residual neural networks can solve the vanishing and exploding gradient problems by utilizing residual units. DenseNet avoids these problems through feature reuse and skip connections. DenseNet consists of alternating dense blocks (DBs) and transition layers (TLs). Dense blocks are the core structure of DenseNet. Each layer in a dense block is connected to all subsequent layers in a dense manner, enabling feature reuse.

[0136] To improve the feature extraction capability of the line selection model, improvements were made to the DenseNet neural network. The SENet attention module can highlight meaningful data features and suppress the network layers' attention to secondary features. At the same time, the SENet attention module has low complexity and can be easily integrated into existing networks.

[0137] The SENet attention module consists of squeezing operations and stimulus operations.

[0138] (1) The extrusion operation is as follows:

[0139]

[0140] In the formula: The output feature vector is H, where H and W are the length and width of the feature map, respectively. Let h be the input matrix; h and c are its rows and columns, respectively. The squeezing operation compresses the W×H×T feature map into a 1×1×T feature vector, where T is the number of output channels.

[0141] (2) Incentive operation:

[0142] Similar to the gate mechanism in recurrent neural networks, each feature channel can be adaptively weighted according to the loss function, and the activation operation is as follows:

[0143]

[0144] In the formula: s is the weight vector with a dimension of 1×1×T; The input feature vector; It is the ReLU activation function; The Sigmoid function normalizes the obtained weights; W1 and W2 are two fully connected layer operations that fuse the feature values ​​of each channel.

[0145] Step 3.3 uses the random forest algorithm as a classifier to accurately identify faulty lines based on the extracted features.

[0146] To shorten the time to failure of a faulty circuit, a random forest structure is integrated into a neural network. This allows the neural network to possess a certain degree of noise resistance without the need for a pre-processed data denoising stage. Random forest (RF) is an ensemble learning algorithm based on decision trees, and its structure is as follows: Figure 4 As shown. Random forests consist of many decision trees, which gives them good noise resistance.

[0147] Random forest algorithms effectively avoid the overfitting problem common to single decision trees, and can handle high-dimensional data and a large number of features. Using it as a classifier in a neural network can improve the generalization ability of the network. Decision trees in random forests select features based on the Gini coefficient. During the construction of the decision tree, the Gini coefficient is used to evaluate the purity of nodes to select the optimal splitting feature. The Gini coefficient ranges from [0,1]. When all samples under a node belong to the same class, the Gini coefficient is 0, indicating the highest purity and good classification performance. Conversely, the closer the Gini coefficient is to 1, the worse the classification performance of the node. Let the number of sample classes be *a*, and the probability that a sample belongs to class *j* be *pj*. Then the Gini coefficient of this probability distribution is:

[0148]

[0149] Step 4: Randomly initialize the population of the improved sparrow search algorithm. Based on the fusion vector from Step 2 and the faulty line information determined in Step 3, initiate multiple rounds of iterative calculation to determine the optimal fitness position. Each iteration updates the population position based on fitness and aggregation state. When the maximum number of iterations is reached, the algorithm terminates and outputs the final determined faulty section location, accurately locating the faulty section. Specifically:

[0150] To overcome the slow iteration speed of the original algorithm in fault segment localization, an optimized sparrow search algorithm is adopted. The best result of the previous iteration is combined into the finder position update formula, and a nonlinear inertial weight factor w is introduced to balance the convergence speed and global search range. Increasing the inertial weight factor w helps to expand the global search range; while decreasing the inertial weight factor w is more conducive to strengthening the local search capability. The population is initialized based on FTU fault current data, and the optimal fitness position is calculated through multiple iterations to achieve efficient and accurate fault segment localization. The calculation formula for the nonlinear inertial weight factor w is shown below:

[0151]

[0152] In the formula, α is 0.7 and β is 0.3.

[0153] The improved discoverer location update formula is shown below:

[0154]

[0155] Once an individual discoverer locates a suspected fault location, followers immediately update their own positions and move closer to that optimal position. This allows the population to quickly cluster around the fault area within the solution space, thereby accelerating the algorithm's localization speed and accuracy in the fault segment. The position update formula is shown below:

[0156]

[0157] In the formula To be the globally optimal position This is the worst position globally. A is a value of 1 or -1. The matrix; when If the i-th follower does not gather at the fault location, it needs to move to other suspected fault locations; otherwise, it means the follower is in the optimal position and can search for the fault location in the surrounding area.

[0158] In the population, 10%-20% of individuals are aware of danger. These individuals are randomly assigned positions within the population and are called vigilant individuals. The formula for updating the vigilant individuals' positions is as follows:

[0159]

[0160] Each iteration updates the population position based on fitness and aggregation state. After reaching the maximum number of iterations, the algorithm terminates and outputs the final determined fault segment location, achieving fault segment localization supported by BeiDou high-precision timescales. The fault segment localization process of the improved Sparrow Algorithm is as follows: Figure 5 As shown.

[0161] In summary, this system addresses the challenge of single-phase grounding fault detection and location in low-current grounding systems by constructing an integrated intelligent fault location system that combines BeiDou clock synchronization, high-frequency sampling, advanced signal processing, and intelligent recognition technologies. The system employs a BeiDou satellite timing module to achieve 10ns-level high-precision clock synchronization at the monitoring terminal, providing a unified time reference for traveling wave propagation analysis. High-frequency sampling above 10MHz accurately captures transient and traveling wave signals in the initial stage of the fault. Using zero-sequence current as the core analysis object, its high-frequency components are extracted and decomposed using the Variational Mode Decomposition (VMD) algorithm to obtain multi-modal features, suppressing interference and highlighting abrupt changes. The decomposed modal signals are input into an improved Convolutional Neural Network (CNN) model, combined with the Advanced Dynamic Model (ADMM) optimization algorithm to enhance learning stability and nonlinear feature perception capabilities. Simultaneously, the GASF transform is introduced to visualize the one-dimensional signal, further enhancing the spatial representation of weak fault features. To improve the network's expressiveness and robustness, the system integrates DenseNet and SENet attention mechanisms to achieve multi-scale feature reuse and adaptive channel weighting, enhancing attention to critical structures. After fault classification, the system employs an intelligent optimization method based on the improved Sparrow Search Algorithm (ISSA), efficiently locating faulty lines and sections with the support of a random forest model. This algorithm enhances search accuracy and convergence efficiency through nonlinear inertial weights and iterative behavior strategies, and achieves meter-level spatial positioning error control by combining BeiDou timescales. It comprehensively realizes accurate perception and rapid location of complex fault signals in the distribution network, exhibiting high robustness, high sensitivity, and adaptability to engineering deployment.

[0162] Although embodiments and drawings of the present invention have been disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, variations and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A method for locating single-phase-to-ground fault in power distribution network based on transient traveling wave, characterized in that: Comprising the following steps: Step 1, collect the zero sequence current signal at the moment of single-phase ground fault occurrence, decompose the collected zero sequence current signal by the variational mode decomposition algorithm VMD, extract features by the convolutional neural network CNN, and optimize by the alternating direction multiplier method ADMM; wherein the zero sequence current simultaneously contains high-frequency traveling wave components and transient mutation characteristics; Step 2, based on the optimized sampling signal of step 1, feature extraction is carried out from two dimensions of transient mutation characteristics and traveling wave propagation characteristics, and is packaged as a fusion vector; Step 3, the fusion vector established in step 2 is converted into a two-dimensional image by the Gram angle and field GASF method, the feature channels are adaptively weighted by using the DenseNet network combined with the SENet attention mechanism, the local and global semantic information in the image is deeply mined, and the DenseNet image feature vector enhanced by the attention mechanism is obtained; finally, the enhanced DenseNet image feature vector is combined with the fusion vector, and the precise identification of the fault line is realized by the Gini coefficient of the random forest; Step 4, randomly initialize the population of the improved sparrow search algorithm, based on the fusion vector of step 2 and the fault line information determined in step 3, then start multiple rounds of iteration to calculate the optimal fitness position, and update the population position according to the fitness and aggregation state each time iteration; when the maximum number of iterations is reached, the algorithm terminates and outputs the final determined fault section position result, accurately positioning the fault section.

2. The method of claim 1, wherein the method is characterized by: In step 1, the feeder terminal unit FTU deployed on the distribution network line collects the original signal at the moment of single-phase ground fault occurrence in real time, realizes 10ns-level clock synchronization between each measuring point based on Beidou satellite timing, and collects the signal at a sampling frequency of 10MHz or above.

3. The method of claim 1, wherein the method further comprises: In step 1, the zero sequence high-frequency component related to fault transient is extracted from the current signal, the three-phase instantaneous current ia(t), ib(t), ic(t) is linearly transformed to obtain the zero sequence current i0(t), and the calculation formula is as follows: ； detrimental effects of the zero sequence current are eliminated ; and further normalization processing: 。 4. The method of claim 1, wherein the method further comprises: In step 1, the normalized zero sequence current signal and the voltage traveling wave signal are preprocessed by the variational mode decomposition algorithm; the original signal is decomposed into a group of limited modes with different center frequencies, and the mode components containing transient mutation and high-frequency traveling wave characteristics are extracted: The original signal is x(t); Modal components: ; Each mode satisfies: ； wherein, is the kth modal component, ωkis its center frequency, and the asterisk denotes convolution.

5. The method of claim 1, wherein: In step 1, the introduction of Lagrange multipliers and penalty terms uses the alternating direction method of multipliers (ADMM) to iteratively optimize the frequency-domain representation of each modality; in each iteration, the modal The update in the frequency domain is as follows: ； The iteration formula of the center frequency of each mode is: ； wherein, is the Fourier transform of the original signal in the frequency domain; is the frequency domain representation of the i-th modality; i≠ k, indicating that other modalities are considered known when updating the k-th modality; is the Lagrange multiplier in the frequency domain, used to constrain the sum of all modalities to be equal to the original signal; is a penalty factor, controlling the strength of the modal bandwidth constraint; is the center frequency of the k-th modality; is the energy spectral density of the k-th modality in the frequency domain.

6. The method of claim 1, wherein: In step 1, the selected mode component containing the key signal component is input into the convolutional neural network, and the network structure adopted is as follows: ； wherein: , is a convolutional layer parameter, is a weight parameter of the i-th layer, is a bias vector of the i-th layer; is an output feature of the i-th layer, is an output of the previous layer as input to the current layer; * is a convolution operation; f() is a non-linear activation function; The neural network parameter optimization form based on ADMM is: ； wherein, is a set of all parameters of the neural network; is a task loss function; is a regularization term; is a regularization coefficient; , are matrices and vectors in the constraints for ADMM optimization.

7. The method of claim 1, wherein: The step 2 comprises: Step 2.1, the current and voltage traveling wave signals obtained by sampling are decomposed by the variational mode decomposition algorithm VMD, and the zero sequence current high-frequency mode i0HF, the voltage drop Δv and the energy spectrum change are extracted; Step 2.2, the nanosecond-level time stamp provided by Beidou synchronization is used to calculate the propagation delay Δt from the fault point to the measuring point, and the propagation path feature is constructed in combination with the initial current polarity identification of multiple measuring points; Step 2.3, the extracted multi-modal high-frequency features are uniformly packaged as a fusion vector, which provides an input for the subsequent network model of the fault line and positioning, wherein the fusion vector features include time domain mutation, frequency domain energy, spatial propagation delay and initial line wave current polarity features.

8. The method of claim 1, wherein: The step 3 comprises: Step 3.1, a one-dimensional zero sequence current time series signal is converted into a two-dimensional image by using the Gram angle and field method GASF, comprising: Step 1: Scale the time series X = {x1,..., xi,..., xd} of length d to the range of [-1, 1], and the calculation formula is: ； Step 2: Transform the scaled sequence according to the following formula, encode the timestamp as the radius, and encode the sequence value as the cosine angle, so that the signal is converted to the polar coordinate system, and the calculation formula is: ； wherein: is a polar coordinate angle, is a radius, is a time stamp, and M is a coordinate span adjustment constant. Calculate the cosine and function between each point to get the Gram angle and field, and the calculation method is as follows: ； Step 3.2, the features in the image are deeply mined through DenseNet and SENet attention mechanism, and the key information is highlighted; The SE-Net attention module is composed of squeezing operation and excitation operation; The squeezing operation is: ； wherein: is the output feature vector, H and W are the height and width of the feature map, respectively, is the input matrix; h, c are its rows and columns; the squeezing operation compresses the W x H x T feature map into a 1 x 1 x T feature vector, T is the number of output channels; The excitation operation is as follows: ； where s is a weight vector with dimension 1x1xT; is the input feature vector; is a ReLU activation function; is a Sigmoid function; W1 and W2 are two fully connected layer operations.

9. The transient traveling wave based single-phase grounding fault positioning method for distribution network according to claim 1, characterized in that: In step 4, the calculation formula of the nonlinear inertia weight factor w used in the iterative calculation process is as follows: ； In the formula, a is 0.7, and β is 0.3; The improved finder position update formula is as follows: ； The follower update formula is as follows: ； wherein is the globally optimal position, is the globally worst position; A is a value of 1 or -1 is a matrix; The position update formula of the guard is as follows: 。 10. A transient based traveling wave single-phase-to-ground fault location system for a power distribution network, characterized by: A method for implementing the transient traveling wave based single-phase grounding fault positioning method for distribution network according to any one of claims 1-9, comprising a high-precision synchronous sampling unit, a transient-traveling wave fusion feature extraction module, a fault line module and a fault section positioning module. The high-precision synchronous sampling unit constructs a time-space reference with Beidou <10ns clock synchronization and ≥10MHz high-frequency sampling to collect high-frequency traveling wave signals at the initial stage of the fault, and the collected zero sequence current signals are decomposed by the variational mode decomposition algorithm VMD, the features are extracted by the convolutional neural network CNN and optimized by the ADMM, forming a synchronous-capture-purification-learning closed loop to realize high-fidelity perception of the fault signals. The transient-traveling wave fusion feature extraction module is used to fuse the time domain transient quantity, the frequency domain spectrum and the spatial propagation delay to construct a three-dimensional feature vector of time domain mutation + frequency domain energy + spatial propagation. The fault line module maps the one-dimensional zero sequence current sequence to a two-dimensional image by using the Gram angle and field method GASF, and fuses the dense connection structure of DenseNet and the SE-Net attention mechanism to deeply mine the local and global semantic information in the image. At the same time, a random forest is introduced to replace the traditional classifier to realize intelligent and accurate identification of the fault line of the distribution network. The fault section positioning module is used to accurately locate the fault section based on the improved sparrow algorithm and the propagation characteristics of the initial line wave current polarity of the fusion vector to realize efficient and accurate identification of the fault of the distribution network.

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