A Single-Phase Ground Fault Detection Method for Distribution Networks Based on Gram Corner Field and Improved Convolutional Neural Network

By combining Gram angle field and improved convolutional neural network, the problems of feature loss and topology change in single-phase grounding faults in distribution networks are solved, and efficient and accurate fault detection and diagnosis are achieved.

CN119247026BActive Publication Date: 2025-12-02STATE GRID FUJIAN ELECTRIC POWER RES INST +2
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Patent Information

Application Number
CN202411302666.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-09-18
Publication Date
2025-12-02
Estimated Expiration
2044-09-18

AI Technical Summary

Technical Problem

Existing technologies for handling single-phase grounding faults in distribution networks suffer from problems such as easy loss of fault features, excessive feature extraction, lack of online learning capabilities, and inability of the model to accurately predict changes in network topology.

Method used

Gram corner field is used to convert one-dimensional time series into two-dimensional virtual images. Multi-scale feature extraction and attention mechanism are combined by improving convolutional neural network, and fine-tuning transfer learning method is used to adapt to network topology changes.

Benefits of technology

It improves the accuracy of fault diagnosis and noise resistance, achieves efficient fault detection under different online conditions, and has good generalization performance.

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Abstract

This invention relates to a method for detecting single-phase grounding faults in distribution networks based on Gram angle field and an improved convolutional neural network, comprising the following steps: S1, analyzing the characteristics of the grounding fault, acquiring measurement data from the distribution network through a phasor measurement unit (PMU), and then obtaining a two-dimensional virtual image from the acquired measurement data using a Gram angle field (GAF); S2, analyzing the obtained two-dimensional virtual image using an improved convolutional neural network (ICNN) with a multi-scale feature extraction module and an attention module, extracting and focusing on key features between the fault data; S3, constructing a fault detection model for single-phase grounding faults in the distribution network, dividing the fault detection model into offline and online stages, and performing fault detection for different online conditions. This method can improve fault diagnosis performance under different online conditions.
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Description

Technical Field

[0001] This invention relates to the field of power distribution network fault diagnosis technology, specifically to a method for detecting single-phase grounding faults in power distribution networks based on Gram angle field and improved convolutional neural network. Background Technology

[0002] In China, Japan, and parts of Europe, the neutral point of the power distribution network is mostly grounded with a small current. Most faults in the distribution network are single-phase grounding faults, accounting for approximately 80% of all faults. Among these, the single-phase grounding fault current is relatively small and unstable. The phase voltage of the non-faulty phases will increase significantly, causing electrical equipment to operate under overvoltage conditions. If the faulty line is not cleared in time, it can easily damage cable insulation, leading to incalculable harm. Therefore, timely and accurate fault detection of transmission lines is of great importance.

[0003] Single-phase ground fault location in most distribution networks can be divided into steady-state signal analysis and transient signal analysis. In the steady-state signal method, the generated power frequency and harmonic signals are typically used for feature analysis. Recently, feature analysis based on transient fault signals has become a focus of related research. To address this issue, a ground fault location method based on Hilbert-Huang transform is proposed, where different high-frequency signals are obtained through empirical mode decomposition, and then the faulty line is detected by the polarity of the signals. Due to the singularity of the criterion, this method is easily affected by interference from the power grid operating environment. Furthermore, a method is proposed to obtain multiple fault features from the synchronous current obtained from the fault recorder, and to classify the fault features using the K-means clustering algorithm to locate the fault area. Existing ground fault location methods use transient zero-sequence current or specific mode components as the analysis object, but these methods are susceptible to noise interference and are difficult to handle in complex fault environments. With the development of data monitoring systems, the amplitude of harmonic components can be extracted using Fourier transform as input features, and then the KNN algorithm can be used for fault detection. Simultaneously, wavelet transform can be used to extract high-frequency components of high-voltage line signals, and SVM can be used to classify the high-frequency components to achieve fault location of transmission lines. While these methods have good classification capabilities, they consume a lot of memory and runtime when processing large amounts of data, and are prone to problems such as local optimization and overfitting.

[0004] Convolutional Neural Networks (CNNs), as a typical deep learning model, have been widely applied in power systems. They are independent of manually designed feature extraction sessions, automatically extracting features from input data and performing inductive classification through training on massive amounts of data. These characteristics of CNNs demonstrate the feasibility and advantages of deep learning for their application in power systems. Existing research has proposed a fault diagnosis method combining CNNs and Long Short-Term Memory (LSTM) networks to extract fault information features more efficiently. Alternatively, the first half of the zero-sequence current waveforms of different faulty lines can be acquired and fused as feature inputs for CNNs to achieve fault line detection in resonant grounding distribution systems. However, in these studies, CNNs are applied to one-dimensional signals; since there are differences between two-dimensional images and the original signals, they may not work well in complex network topologies.

[0005] To overcome these challenges, GAF (Gaussian Image Processing) is used to convert time series data into images, preserving all information in the original signal while maximizing the extraction of fault sample features. However, this process also faces the issues of losing subtle fault features and extracting an excessive number of features from the hidden layers. Furthermore, online learning capabilities are lacking. Typically, fault diagnosis models are designed for specific topologies. When the actual power distribution network structure is reconfigured, fault diagnosis models trained offline cannot accurately predict various unknown new situations. Therefore, improving this process is a pressing issue. Summary of the Invention

[0006] The purpose of this invention is to provide a method for detecting single-phase grounding faults in distribution networks based on Gram angle field and improved convolutional neural network, which can improve fault diagnosis performance under different online conditions.

[0007] To achieve the above objectives, the technical solution adopted by this invention is: a method for detecting single-phase grounding faults in distribution networks based on Gram angle field and improved convolutional neural networks, comprising the following steps:

[0008] S1. Analyze the characteristics of grounding faults, obtain measurement data from the distribution network through the phasor measurement unit (PMU), and then obtain a two-dimensional virtual image from the obtained measurement data through the Gram angle field (GAF).

[0009] S2. By improving the convolutional neural network ICNN, the obtained two-dimensional virtual image is analyzed using a multi-scale feature extraction module and an attention module to extract and focus on the key features between fault data.

[0010] S3. Construct a fault detection model for single-phase grounding faults in the distribution network, and divide the fault detection model into offline and online stages, and perform fault detection for different online conditions.

[0011] Furthermore, in step S1, the characteristics of the ground fault are analyzed, and the characteristics of the zero-sequence current during a ground fault are analyzed using the equivalent network of the ungrounded distribution network.

[0012] Furthermore, in step S1, waveform data with precise time stamps is measured in real time by PMU, the measured data is transmitted back to the main station, and then the obtained one-dimensional time series data is scaled using GAF. Then, it is converted from a rectangular coordinate system to a polar coordinate system, and the temporal correlation of different time points is identified by considering the angle between different points, thereby converting the one-dimensional time series into a two-dimensional virtual image.

[0013] Furthermore, in step S1, the one-dimensional time series data is converted into a two-dimensional virtual image using GAF. The specific method is as follows:

[0014] S1-1, The zero-sequence current obtained by PMU measurement is X={x1,x2,…,x n}, where each time series sample x i It is obtained by individual sampling, where n is the number of sampling points;

[0015] S1-2. Normalize each time series sample, scaling it to the range [0,1]:

[0016]

[0017] in, It is a time series sample x i The normalized value;

[0018] S1-3, Normalize the values The data is encoded as angle cosines, and the timestamps are encoded as radii, thus transforming the time series data into a polar coordinate system. Specifically:

[0019]

[0020] In the formula, θ i Let t be the coded angle of the i-th polar coordinate point, where i = 1, 2, ..., n. i For timestamp; N is a constant factor for adjusting the range of the polar coordinate system; With θ i For the meaning mapping relationship, the coordinate r and the timestamp t i A linear relationship exists;

[0021] S1-4. By summing the trigonometric functions at different sampling points, the time series correlation between sampling points is identified from the perspective, as shown in the following formula. The matrix based on GAF is defined as F.

[0022]

[0023] The inner product can be represented using Cartesian coordinates, as shown in the following formula:

[0024]

[0025] In the formula, This represents the value of the i-th element in the normalized time series data.

[0026] Furthermore, the method for implementing step S2 is as follows:

[0027] S2-1. Construct a multi-scale feature extraction module, designing three channels in the convolutional layer; the first channel has a 5×5 kernel with 8 kernels; the second channel has 3×3 and 1×1 concatenated kernels with 8 and 16 kernels respectively; the third channel has 8×8 and 3×3 concatenated kernels with 4 and 8 kernels respectively; simultaneously, batch normalization and activation functions are used after each convolutional kernel, and the feature dimensions of different channels are stacked together through a Concat layer to maximize the extraction of fault feature information from the input data;

[0028] S2-2. Construct an attention module that includes a channel attention module and a spatial attention module. In the channel attention module, the input features are first subjected to average pooling and max pooling, and then fed into a multilayer perceptron for further processing. The features output by the multilayer perceptron are weighted to generate a channel attention feature map N. C As shown in the following formula:

[0029] N C (E)=σ(MLP(AvgPool(E))+MLP(MaxPool(E)))

[0030] In the formula, E is the input feature; AvgPool represents average pooling; MaxPool represents max pooling; σ is the sigmoid function;

[0031] S2-3. The spatial attention module takes the channel attention feature map output by the channel attention module as input, performs max pooling and average pooling on it, and generates the spatial attention feature map N. S As shown in the following formula:

[0032] N S (W)=σ(f([AvgPool(W);MaxPool(W)]))

[0033] In the formula, W is the output of the channel attention module, and f represents the convolution operation.

[0034] Furthermore, in step S2, the improved convolutional neural network performs layer-by-layer convolution and pooling calculations on the input data through multiple feature filters; the original image is respectively processed by multi-channel convolution kernel K. L Filtering to generate feature maps, the pooling layer filters the features from the previous layer. L-1 Compression is performed using the following expression:

[0035]

[0036] In the formula, L represents the number of layers in the improved convolutional neural network; b L To improve the bias of the Lth layer of a convolutional neural network; These are the features after pooling.

[0037] Furthermore, the implementation method of step S3 is as follows:

[0038] S3-1. After a ground fault occurs in the power distribution network, the original signal is first obtained from the multi-source database, then the original signal is converted into a two-dimensional virtual image, and then the parameters of the ICNN model are adjusted. The feature data after being converted into a two-dimensional virtual image is used as the input of the ICNN model to realize the fault location and fault type determination of the transmission line.

[0039] S3-2. In the online phase scenario, the offline phase model is transferred to the target domain, and the pre-trained model is quickly updated through fine-tuning training. Feature knowledge is learned from the large dataset of the source domain, and then the model weights and bias parameters are adjusted. Feature data is shared across tasks in the target domain.

[0040] Furthermore, in step S3, a fine-tuning-based transfer learning method is used to construct a pre-trained model during the online phase. When the distribution network topology changes, the fault detection model in the source domain is transferred to the target domain. The source domain is fine-tuned using a new dataset. The parameters of the fully connected layer and classification layer of the pre-trained model are adjusted using training samples, while other layers remain frozen to achieve fault detection under different conditions.

[0041] Compared with existing technologies, this invention has the following advantages: Addressing the single-phase grounding fault problem in complex distribution networks, this invention provides a single-phase grounding fault detection method for distribution networks based on Gram angle field and an improved convolutional neural network. This method converts one-dimensional time-domain signals into image domain signals through GAF algorithm processing; it fully utilizes the advantages of ICNN in image recognition to confirm the location of fault features in the image; while retaining all information of the original signal, the fault features are more obvious; by introducing a multi-scale feature extraction module and attention mechanism into the traditional CNN, the training accuracy of GAF-ICNN can be effectively improved under different fault conditions, and the noise resistance of the GAF-ICNN model is also improved under different noise environments; this invention also introduces a fine-tuning transfer learning method, improving the performance of the fault diagnosis model under different online conditions. The method provided by this invention only requires a small number of samples for fine-tuning the pre-trained model, and the detection accuracy remains at a high level, therefore, this method has excellent generalization performance. Attached Figure Description

[0042] Figure 1 This is a flowchart of a single-phase grounding fault detection method for power distribution networks based on Gram angle field and improved convolutional neural network according to an embodiment of the present invention;

[0043] Figure 2 This is a flowchart illustrating the implementation of single-phase grounding fault detection in a power distribution network in an embodiment of the present invention. Detailed Implementation

[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0045] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0046] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0047] Figure 1 This is a flowchart of the single-phase grounding fault detection method for distribution networks based on Gram angle field and improved convolutional neural network provided in this embodiment. Figure 1 As shown, this method specifically includes the following steps:

[0048] S1. Analyze the characteristics of ground faults, obtain measurement data from the distribution network through a phasor measurement unit (PMU), and then obtain a two-dimensional virtual image from the obtained measurement data through a Gram angle field (GAF).

[0049] S2. By improving the convolutional neural network (ICNN), and utilizing the added multi-scale feature extraction module and attention module, the obtained two-dimensional virtual image is analyzed to extract and focus on the key features between fault data.

[0050] S3. Construct a fault detection model for single-phase grounding faults in the distribution network, and divide the fault detection model into offline and online stages, and perform fault detection for different online conditions.

[0051] In this embodiment, the implementation process for single-phase ground fault detection in the distribution network is as follows: Figure 2 As shown.

[0052] In step S1, it is necessary to analyze the characteristics of ground faults and use the equivalent network of the ungrounded distribution network to analyze the characteristics of the zero-sequence current during ground faults.

[0053] By measuring waveform data with precise time stamps in real time using a PMU, and transmitting this measured data back to the main station via communication technology, it provides a data foundation for power grid fault detection based on machine learning. Then, the obtained one-dimensional time series data is scaled using GAF, and then transformed from a rectangular coordinate system to a polar coordinate system. By considering the angles between different points, the temporal correlation of different time points is identified, thereby converting the one-dimensional time series into a two-dimensional virtual image.

[0054] The method for converting one-dimensional time series data into a two-dimensional virtual image using GAF is as follows:

[0055] S1-1. First, the zero-sequence current is obtained by measuring the PMU, i.e., the one-dimensional time series data is X={x1,x2,…,x n}, where each time series sample x i Datax sampled separately n The composition is given by n, where n is the number of sampling points.

[0056] S1-2. Normalize each time series sample, scaling it to the range [0,1]:

[0057]

[0058] in, It is a time series sample x i The normalized value.

[0059] S1-3, Normalize the values The data is encoded as angle cosines, and the timestamps are encoded as radii, thus transforming the time series data into a polar coordinate system. Specifically:

[0060]

[0061] In the formula, θ i Let t be the coded angle of the i-th polar coordinate point, where i = 1, 2, ..., n. i For timestamp; N is a constant factor for adjusting the range of the polar coordinate system; With θ i For the meaning mapping relationship, the coordinate r and the timestamp t i They have a linear relationship.

[0062] S1-4. By summing the trigonometric functions at different sampling points, the time series correlation between sampling points is identified from the perspective, as shown in the following formula. The matrix based on GAF is defined as F.

[0063]

[0064] In the formula, θ i (i = 1, 2, ..., n) represents the coded angle of the i-th polar coordinate point; n represents the length of the time series data.

[0065] The inner product can be represented using Cartesian coordinates, as shown in the following formula:

[0066]

[0067] In the formula, The index is the value of the i-th element in the normalized time series data, and n is the number of sampling points.

[0068] The implementation method of step S2 is as follows:

[0069] S2-1. Construct a multi-scale feature extraction module, designing three channels in the convolutional layer. The first channel has a 5×5 convolutional kernel with 8 kernels; the second channel has cascaded 3×3 and 1×1 kernels with 8 and 16 kernels respectively; the third channel has cascaded 8×8 and 3×3 kernels with 4 and 8 kernels respectively. Simultaneously, batch normalization and activation functions are used after each convolutional kernel. The feature dimensions of different channels are stacked together through a Concat layer to maximize the extraction of fault feature information from the input data.

[0070] S2-2. The attention module is designed sequentially as a channel attention module and a spatial attention module. In the channel attention module, the input features are first subjected to average pooling and max pooling, and then fed into a multilayer perceptron for further processing. The features output by the multilayer perceptron are weighted to generate the channel attention feature map N. CAs shown in the following formula:

[0071] N C (E)=σ(MLP(AvgPool(E))+MLP(MaxPool(E)))

[0072] In the formula, E is the input feature; AvgPool represents average pooling; MaxPool represents max pooling; and σ is the sigmoid function.

[0073] S2-3. The spatial attention module takes the channel attention feature map output by the channel attention module as input, performs max pooling and average pooling on it, and generates the spatial attention feature map N. S As shown in the following formula:

[0074] N S (W)=σ(f([AvgPool(W);MaxPool(W)]))

[0075] In the formula, W is the output of the channel attention module, and f represents the convolution operation.

[0076] Based on the methods in steps S2-1 to S2-3, the improved convolutional neural network performs layer-by-layer convolution and pooling calculations on the input data using multiple feature filters; the original image is then processed with multi-channel convolution kernels K. L Filtering to generate feature maps, the pooling layer filters the features from the previous layer. L-1 Compression is performed to reduce redundant information. The specific expression is as follows:

[0077]

[0078]

[0079] In the formula, L represents the number of layers in the improved convolutional neural network; b L To improve the bias of the Lth layer of a convolutional neural network; These are the features after pooling.

[0080] The implementation method of step S3 is as follows:

[0081] S3-1. After a ground fault occurs in the power distribution network, the original signal is first obtained from the multi-source database. Then, based on the above method, the original signal is converted into a two-dimensional virtual image. The parameters of the ICNN model are then adjusted. The converted feature set is used as the input of the ICNN model to realize the fault location and fault type determination of the transmission line.

[0082] S3-2. In the online phase scenario, the offline phase model is transferred to the target domain, and the pre-trained model is quickly updated through fine-tuning training. Feature knowledge is learned from the big data set in the source domain, and then the model weights and bias parameters are adjusted. The feature parameters are shared across the target domain task.

[0083] In step S3, a pre-trained model needs to be constructed. During the online phase, a fine-tuning-based transfer learning method is used to construct the pre-trained model. This invention proposes a transfer learning method suitable for ICNN. When the distribution network topology changes, it is only necessary to transfer the fault detection model from the source domain to the target domain. The source domain is fine-tuned using a new dataset. The parameters of the fully connected layers and classification layers of the pre-trained model are adjusted using training samples, while other layers remain frozen to achieve fault detection under different conditions.

[0084] This invention provides a solution for single-phase grounding faults in distribution networks based on GAF and ICNN. The method first analyzes the characteristics of grounding faults, utilizing the equivalent network of an ungrounded distribution network to analyze the characteristics of zero-sequence current during grounding faults. Secondly, it transforms the time-series signal into polar coordinates using GAF, and then converts the encoded signal into a visual virtual image through GAF's inner product calculation. An improved CNN, ICNN, is formed, whose convolutional layers add multi-scale modules and attention mechanisms compared to general CNNs. The virtual image obtained from GAF is then directly imported into ICNN for feature extraction and classification of samples. Finally, a transfer learning method suitable for ICNN is proposed. When the distribution network topology changes, only the fault detection model in the source domain needs to be transferred to the target domain. The source domain is fine-tuned using a new dataset to achieve fault detection under different conditions.

[0085] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0086] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0087] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0088] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0089] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for detecting single-phase grounding faults in distribution networks based on Gram angle field and improved convolutional neural network, characterized in that, Includes the following steps: S1. Analyze the characteristics of grounding faults, obtain measurement data from the distribution network through the phasor measurement unit (PMU), and then obtain a two-dimensional virtual image from the obtained measurement data through the Gram angle field (GAF). S2. By improving the convolutional neural network ICNN, the obtained two-dimensional virtual image is analyzed using a multi-scale feature extraction module and an attention module to extract and focus on the key features between fault data. S3. Construct a fault detection model for single-phase grounding faults in the distribution network, and divide the fault detection model into offline and online stages, and perform fault detection for different online conditions; The implementation method of step S3 is as follows: S3-1. After a ground fault occurs in the power distribution network, the original signal is first obtained from the multi-source database, then the original signal is converted into a two-dimensional virtual image, and then the parameters of the ICNN model are adjusted. The feature data after being converted into a two-dimensional virtual image is used as the input of the ICNN model to realize the fault location and fault type determination of the transmission line. S3-2. In the online stage scenario, the offline stage model is transferred to the target domain, the pre-trained model is quickly updated through fine-tuning training, feature knowledge is learned from the big data set in the source domain, and then the model weights and bias parameters are adjusted. The feature data is shared on the task in the target domain. In step S3, a fine-tuning-based transfer learning method is used to construct a pre-trained model during the online phase. When the distribution network topology changes, the fault detection model in the source domain is transferred to the target domain. The source domain is fine-tuned using a new dataset. The parameters of the fully connected layer and classification layer of the pre-trained model are adjusted using training samples, while other layers remain frozen to achieve fault detection under different conditions.

2. The method for detecting single-phase grounding faults in distribution networks based on Gram angle field and improved convolutional neural network according to claim 1, characterized in that, In step S1, the characteristics of ground faults are analyzed, and the characteristics of zero-sequence current during ground faults are analyzed using the equivalent network of the ungrounded distribution network.

3. The method for detecting single-phase grounding faults in distribution networks based on Gram angle field and improved convolutional neural network according to claim 1, characterized in that, In step S1, waveform data with precise time stamps is measured in real time by PMU, the measured data is transmitted back to the main station, and then the obtained one-dimensional time series data is scaled using GAF. Then, it is converted from a rectangular coordinate system to a polar coordinate system. Then, the temporal correlation of different time points is identified by considering the angle between different points, thereby converting the one-dimensional time series into a two-dimensional virtual image.

4. The method for detecting single-phase grounding faults in distribution networks based on Gram angle field and improved convolutional neural network according to claim 3, characterized in that, In step S1, one-dimensional time series data is converted into a two-dimensional virtual image using GAF. The specific method is as follows: S1-1, The zero-sequence current obtained by PMU measurement is X={x1,x2,…,x n }, where each time series sample x i Obtained by individual sampling, where n is the number of sampling points, i = 1, 2, ..., n; S1-2. Normalize each time series sample, scaling it to the range [0,1]: in, It is a time series sample x i The normalized value; S1-3, Normalize the values The data is encoded as angle cosines, and the timestamps are encoded as radii, thus transforming the time series data into a polar coordinate system. Specifically: In the formula, θ i Let t be the coded angle of the i-th polar coordinate point, where i = 1, 2, ..., n. i For timestamp; N is a constant factor for adjusting the range of the polar coordinate system; With θ i For the meaning mapping relationship, coordinate r i With timestamp t i A linear relationship exists; S1-4. By summing the trigonometric functions at different sampling points, the time series correlation between sampling points is identified from the perspective, as shown in the following formula. The matrix based on GAF is defined as F. The inner product can be represented using Cartesian coordinates, as shown in the following formula:

5. The method for detecting single-phase grounding faults in distribution networks based on Gram angle field and improved convolutional neural network according to claim 1, characterized in that, The method for implementing step S2 is as follows: S2-1. Construct a multi-scale feature extraction module, designing three channels in the convolutional layer; the first channel has a 5×5 kernel with 8 kernels; the second channel has 3×3 and 1×1 concatenated kernels with 8 and 16 kernels respectively; the third channel has 8×8 and 3×3 concatenated kernels with 4 and 8 kernels respectively; simultaneously, batch normalization and activation functions are used after each convolutional kernel, and the feature dimensions of different channels are stacked together through a Concat layer to maximize the extraction of fault feature information from the input data; S2-2, Construct an attention module that includes a channel attention module and a spatial attention module; In the channel attention module, the input features are first subjected to average pooling and max pooling, and then fed into a multilayer perceptron for processing. The features output by the multilayer perceptron are weighted to generate the channel attention feature map N. C As shown in the following formula: N C (E)=σ(MLP(AvgPool(E))+MLP(MaxPool(E))) In the formula, E is the input feature; AvgPool represents average pooling; MaxPool represents max pooling; σ is the sigmoid function; S2-3. The spatial attention module takes the channel attention feature map output by the channel attention module as input, performs max pooling and average pooling on it, and generates a spatial attention feature map N. S As shown in the following formula: N S (W)=σ(f([AvgPool(W);MaxPool(W)])) In the formula, W is the output of the channel attention module, and f represents the convolution operation.

6. The method for detecting single-phase grounding faults in distribution networks based on Gram angle field and improved convolutional neural network according to claim 1, characterized in that, In step S2, the improved convolutional neural network performs layer-by-layer convolution and pooling calculations on the input data using multiple feature filters; the original image is processed by multi-channel convolution kernel K. L Filtering to generate feature maps, the pooling layer filters the features from the previous layer. L-1 Compression is performed using the following expression: In the formula, L represents the number of layers in the improved convolutional neural network; b L To improve the bias of the Lth layer of a convolutional neural network; These are the features after pooling.

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