VMDCNN-based single-phase earth fault section positioning method

Abstract

The invention relates to a VMDCNN-based single-phase earth fault section positioning method, and belongs to the technical field of power distribution network fault analysis. The method comprises the following steps: at the moment of determining a single-phase earth fault, collecting transient zero-sequence current and voltage derivative signals of each section of a power distribution network in a 1 / 4 period before and after the single-phase earth fault, and decomposing by using a variational mode decomposition method VMD to obtain characteristic mode components IMF with frequencies from low to high; ground fault property identification is provided according to the polar relation of transient zero sequence current and voltage derivatives, IMF1 waveforms of the transient zero sequence current and the voltage derivatives are normalized and combined into a feature image, and then the feature image is converted into a gray binary image. And taking the converted gray binarization image as input data of CNN classification network training, and training the CNN classification network to identify the properties of the single-phase earth fault section. According to the method, only the transient zero-sequence signal of 1 / 4 period before and after the fault is needed, data acquisition is simple, the applicability is high, and the fault section of the single-phase earth fault of the power distribution network can be accurately and rapidly positioned.

Description

Technical Field

[0001] The invention belongs to the technical field of distribution network fault analysis, and in particular relates to a single-phase grounding fault section locating method based on VMD_CNN. Background Art

[0002] The distribution network system is becoming increasingly large, with branches all over the place, and faults are inevitable during operation. Among them, single-phase grounding faults account for the highest proportion, reaching 80% of all faults. At present, the neutral point of my country's distribution network generally adopts a small current grounding method that is not grounded or grounded through an arc suppression coil. The fault current caused by single-phase grounding of the small current grounding distribution network is very small, and the system can continue to maintain operation. However, if the fault cannot be located and eliminated in time, the further expansion of the fault may cause greater harm to the distribution network. Therefore, realizing the location of the fault is a basic work to ensure the reliability of the distribution network system, which has important engineering significance.

[0003] At present, the research on the location of small current grounding faults at home and abroad can be divided into two categories: active and passive positioning, according to the different sources of fault signals. Among them, the active positioning method is greatly affected by the detection equipment and the structure of the distribution network, and its application positioning effect is poor. The passive positioning method determines the fault section by collecting and extracting the fault characteristics of the voltage and current signals in the line. With the increasing penetration rate of distributed power sources in the distribution network, it has brought great challenges to fault location. The access of distributed power sources has changed the structure and flow of the distribution network, among which the positive sequence network topology of the system has changed greatly, but the zero sequence network has little effect. Therefore, after access, there is no effect on the transient zero sequence current, that is, the distribution of the zero sequence current of the active distribution network in the system is the same as that of the traditional distribution network, and the transient positioning analysis method based on zero sequence current is still applicable. Summary of the invention

[0004] The purpose of the present invention is to take the transient zero-sequence current and voltage derivative polarity relationship as the research object, and provide a single-phase grounding fault section locating method based on VMD_CNN. The method only requires zero-sequence current and voltage derivative waveform data of 1 / 4 cycle before and after the fault. The data acquisition is simple, and it has the advantages of high sensitivity, obvious judgment characteristics, and strong adaptability. It meets the requirements of distribution network fault locating and has certain practical significance in the safe operation of the distribution network.

[0005] To achieve the above object, the technical solution of the present invention is: a single-phase grounding fault section location method based on VMD_CNN, comprising:

[0006] After a single-phase grounding fault occurs in the distribution network, determine the time of the single-phase grounding fault;

[0007] The transient zero-sequence current and voltage derivative signals of each section of the distribution network in the 1 / 4 cycle before and after the single-phase grounding fault occurs are collected, and the transient zero-sequence current and voltage derivative signals of each section of the distribution network are decomposed using the variational mode decomposition method VMD to obtain the characteristic mode components IMF with frequencies from low to high.

[0008] According to the polarity relationship of transient zero-sequence current and voltage derivative, the ground fault property identification is proposed. The characteristic modal component IMF1 of transient zero-sequence current and voltage derivative signals in each section of the distribution network is normalized and merged into a characteristic image, which is then converted into a grayscale binary image.

[0009] The converted grayscale binary image is used as the input data for CNN classification network training, and the CNN classification network is trained to identify the properties of the single-phase grounding fault section.

[0010] In one embodiment of the present invention, the method comprises the following steps:

[0011] Step S1, using the variational mode decomposition method VMD to decompose the transient zero-sequence current and voltage derivative signals of each section of the distribution network in the 1 / 4 cycle before and after the single-phase grounding fault occurs, the frequency of the characteristic mode components IMF from low to high, separate the characteristic mode components IMF1 of the transient zero-sequence current and voltage derivative signals, and merge them into a characteristic image after normalization;

[0012] Step S2, selecting 240 groups of original signals under various working conditions and processing them into feature images through step S1, and converting the feature images into grayscale binary images as CNN classification network training data sets and test data sets;

[0013] Step S3, using the training data set to train the CNN classification network, and optimizing and adjusting the network structure and network parameters according to the training results during the training process;

[0014] Step S4: Test the test data set with the trained CNN classification network to obtain the image classification result, thereby obtaining the single-phase grounding fault section classification result.

[0015] In one embodiment of the present invention, the variational mode decomposition method VMD decomposition process includes two parts: proposing a variational problem and solving the variational problem. The first part is proposing a variational problem. The variational model under constraints is expressed as:

[0016]

[0017] Where, δ(t) is the unit pulse function; is the gradient function; {u k} are the modal components and {u k}={u1,u2,···,u k}; {ω k} is the corresponding center frequency and {ω k}={ω1,ω2,···,ω k}; j refers to the imaginary part of the complex number;

[0018] The second part is to solve the variational problem. Here, we introduce the quadratic penalty factor α and the augmented Lagrange function λ(t) and transform it into an unconstrained variational model:

[0019]

[0020] Alternating Direction Multiplier Algorithm Stepwise Iterative Update and Thus, we get the saddle point of λ(t) and update for:

[0021]

[0022] In the formula Initialization is all set to zero, n is the iteration variable;

[0023] Convert the above formula into frequency domain:

[0024]

[0025] In the formula represents the spectrum of the kth mode after the nth iteration, represents the spectrum of the original signal, represents the adjustment variable used to control the bandwidth of the mode;

[0026] The formula of the center frequency in the frequency domain and the solution of each modal component are expressed as:

[0027]

[0028] Operator The update method is expressed as:

[0029]

[0030] The convergence condition is determined according to the convergence accuracy ε. If ε>0 and the following formula is satisfied, the iteration is stopped to obtain the modal components of k different frequency bands; otherwise, the loop is returned to update;

[0031]

[0032] In one embodiment of the present invention, the characteristic modal components IMF1 of the transient zero-sequence current and voltage derivative signals exhibit the same polarity in the healthy section, and the IMF1 waveforms have a high degree of similarity; the characteristic modal components IMF1 of the transient zero-sequence current and voltage derivative signals exhibit opposite polarities in the fault section, and the IMF1 waveforms are extremely different.

[0033] In one embodiment of the present invention, the image classification results of the feature images recognized by the CNN classification network are divided into two categories, there are large differences between the two categories of images and the same type of images have a high similarity.

[0034] In one embodiment of the present invention, the Otsu algorithm is used to select a threshold value during the image binarization process. The Otsu algorithm can adaptively perform binarization processing on the image.

[0035] In one embodiment of the present invention, the Otsu algorithm is used to perform image binarization, which is specifically implemented as follows:

[0036] The characteristic modal components IMF1 of the transient zero-sequence current and voltage derivative signals of each section of the distribution network are normalized and the combined characteristic images are converted into grayscale images. The grayscale images are converted into binary images using the Otsu algorithm. The optimization goal is:

[0037]

[0038] The final between-class variance formula is:

[0039]

[0040] Where m is the mean of the pixels, MG is the global mean, and pi is the frequency of occurrence of pixels with gray value i.

[0041] In one embodiment of the present invention, the pixels of the CNN classification network input image are 64×64, the convolution layer is 4 layers, a 7×7 convolution kernel is used, LeakReLU is used as the activation function of the CNN classification network, and the classification output result after the fully connected layer is adjusted to 2 categories.

[0042] In one embodiment of the present invention, the characteristic mode component IMF is expressed as follows:

[0043] u k (t) = A k (t)(cosψ k (t))

[0044] In the formula, u k (t) represents the kth eigenmode component, A k (t) is the amplitude envelope of the modal component, ψ k(t) represents the instantaneous phase. This expression shows that each modal component can be regarded as an amplitude modulated (AM) and frequency modulated (FM) signal.

[0045] In one embodiment of the present invention, the formula for normalizing the characteristic modal component IMF1 of the transient zero-sequence current and voltage derivative signals is as follows:

[0046]

[0047] Where: x i is an element in vector X, i=1,2,···,n, n is the number of sampling points of X; abs(·) is the calculation for absolute value; max(·) is the calculation for maximum value; For x i Normalized value.

[0048] The present invention also provides a single-phase grounding fault section positioning system based on VMD_CNN, including a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0049] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] 1. Variational modal decomposition is a new adaptive signal processing method that can accurately reflect the characteristics of the original signal. The present invention uses this method as a fault feature extraction tool to perform modal decomposition on the collected transient zero-sequence current and voltage derivative signals, obtain transient signal components with more significant fault features, eliminate random interference, highlight the dominant part, and improve the ability to distinguish ground faults.

[0052] 2. The single-phase grounding fault section location method proposed in the present invention distinguishes faults based on the polarity difference of the characteristic components of the fault waveform. It has the advantages of high sensitivity, obvious judgment characteristics, and strong adaptability. It meets the requirements of distribution network fault location and achieves the expected goal.

[0053] 3. The fault section identification of the present invention is independent of the fault type. The same neural network model can be used under different fault types and is not easily affected by changes in transition resistance and system load. At the same time, section positioning can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flow chart of a method in an embodiment of the present invention;

[0055] Figure 2 is the zero-sequence current distribution of the equivalent network in the embodiment of the present invention;

[0056] Figure 3 It is a simulation model of 10kV resonant grounding system;

[0057] Figure 4 It is the process of constructing the binary feature image of the fault section signal;

[0058] Figure 5 It is a process of constructing binary feature images of perfect segment signals. DETAILED DESCRIPTION

[0059] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0060] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0061] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0062] The present invention provides a single-phase grounding fault section location method based on VMD_CNN, comprising:

[0063] After a single-phase grounding fault occurs in the distribution network, determine the time of the single-phase grounding fault;

[0064] The transient zero-sequence current and voltage derivative signals of each section of the distribution network in the 1 / 4 cycle before and after the single-phase grounding fault occurs are collected, and the transient zero-sequence current and voltage derivative signals of each section of the distribution network are decomposed using the variational mode decomposition method VMD to obtain the characteristic mode components IMF with frequencies from low to high.

[0065] According to the polarity relationship of transient zero-sequence current and voltage derivative, the ground fault property identification is proposed. The characteristic modal component IMF1 of transient zero-sequence current and voltage derivative signals in each section of the distribution network is normalized and merged into a characteristic image, which is then converted into a grayscale binary image.

[0066] The converted grayscale binary image is used as the input data for CNN classification network training, and the CNN classification network is trained to identify the properties of the single-phase grounding fault section.

[0067] The following is the specific implementation process of the present invention.

[0068] 1. First, the technical solution of this embodiment is described in detail from the perspective of principle:

[0069] 1. Analysis of transient conditions of single-phase grounding fault

[0070] After a single-phase grounding fault occurs in a resonant grounding system, the transient zero-sequence currents of all non-fault lines flow from the busbar to the line with basically the same polarity, and the transient zero-sequence current of the faulty line flows from the line to the busbar. The zero-sequence current distribution of the equivalent network is shown in Figure 2. Figure 2 As shown in FIG. 1 , let the area between sampling point n and sampling point n+1 of the mth feeder be section n, and m = 1, 2, ..., M, n = 1, 2, ..., N, then C 0mn is the zero-sequence equivalent capacitance to ground of the section; R L and L are the equivalent resistance and inductance of the arc suppression coil respectively; R f is the fault ground resistance.

[0071] Ignoring the line impedance, for the healthy section, the relationship between the transient zero-sequence voltage derivative and the transient zero-sequence current is:

[0072]

[0073] For the fault section, the relationship between the transient zero-sequence voltage derivative and the transient zero-sequence current is:

[0074]

[0075] Where: u 0mn (t), i 0mn (t) are the transient zero-sequence voltage and transient zero-sequence current of sampling point n of the mth feeder; C 1mn C is the total equivalent zero-sequence capacitance to ground of each section between the sampling point n at the head end of the healthy section of the mth feeder and the end of the line; 2mn It is the sum of the zero-sequence equivalent capacitance to ground from the mth feeder ground fault point to the sampling point n+1 at the end of the fault section where it is located and the total equivalent capacitance to ground of all non-fault sections in the network; i L (t) is the inductance current of the arc suppression coil.

[0076] 2. Transient zero-sequence current and voltage derivative polarity analysis

[0077] From the first point, it can be seen that since the inductive current of the arc suppression coil is basically unchanged in the first half-wave after the fault occurs and can be approximated to zero, the zero-sequence voltage derivative of the sampling point upstream of the ground fault point is inversely proportional to the zero-sequence current and has opposite polarity. As the ground fault time increases, the arc suppression coil transitions to the over-compensation state, and the zero-sequence voltage derivative and zero-sequence current of the fault section no longer have an inverse relationship. Therefore, the image constructed by selecting the zero-sequence voltage derivative and zero-sequence current characteristic modal components of the 1 / 4 cycle before and after the fault has obvious differences, and the feature quantity constructed by it can be used to distinguish between healthy sections and fault sections.

[0078] 2. Figure 1 As shown, this embodiment provides a single-phase grounding fault section location method based on VMD_CNN, and the specific implementation steps are as follows:

[0079] Step S1, collecting transient zero-sequence current and voltage derivative signals of each section in the distribution network in a quarter cycle before and after a single-phase grounding fault occurs, using a variational mode decomposition method to decompose the transient zero-sequence current and voltage derivative signals of each section to obtain characteristic mode components IMF1, and normalizing them and merging them into a characteristic image;

[0080] Step S1 is specifically implemented as follows:

[0081] like Figure 2 As shown in the figure, a 10kV radial distribution network with a single busbar is built using the MATLAB / SIMULINK platform (see the simulation model of the 10kV resonant grounding system for details). Figure 3 ), the distribution network includes a 110kV power supply, a 110 / 10kV main transformer, a 10 / 0.4kV distribution transformer, 5 feeders (overhead lines and cable lines mixed) and 18 detection nodes, among which section 3 is set as the fault section. The sampling frequency of the network is set to 10kHz, the load is simulated by a constant load of 0.1MW, the line voltage amplitude of the power module is set to 110kV, and the power frequency is set to 50Hz. The line parameters of the 10kV resonant grounding system are shown in Table 1.

[0082] Table 1 10kV resonant grounding system line parameters

[0083]

[0084] After determining the time of the single-phase grounding fault, the zero-sequence current and zero-sequence voltage derivative signals of each section in the distribution network are collected in the 1 / 4 cycle before and after the single-phase grounding fault occurs. The variational mode decomposition method is used to decompose the zero-sequence current and zero-sequence voltage derivatives of each section to obtain the IMF characteristic mode components with low to high frequencies. The functions of each IMF component are:

[0085] u k (t) = Ak (t)(cosψ k (t))

[0086] In the formula, A k (t) is the instantaneous amplitude;

[0087] The VMD variational modal decomposition is used to separate the IMF1 characteristic modal components of the zero-sequence current and voltage derivatives. The decomposition process of the VMD is divided into two parts: proposing a variational problem and solving the variational problem. The first part is to propose a variational problem. The variational model under constraints can be expressed as:

[0088]

[0089] Where, δ(t) is the unit pulse function; is the gradient function; {u k} are the modal components and {u k}={u1,u2,···,u k}; {ω k} is the corresponding center frequency and {ω k}={ω1,ω2,···,ω k}.

[0090] The second part is to solve the variational problem. Here, we introduce the quadratic penalty factor α and the augmented Lagrange function λ(t) and transform it into an unconstrained variational model:

[0091]

[0092] Alternating Direction Multiplier Algorithm Stepwise Iterative Update and Thus, we can get the saddle point of λ(t) and update for:

[0093]

[0094] In the formula Initialization is all set to zero, n is the iteration variable;

[0095] Convert the above formula into frequency domain:

[0096]

[0097] In the formula represents the spectrum of the kth mode after the nth iteration, represents the spectrum of the original signal, represents the adjustment variable used to control the bandwidth of the mode;

[0098] The formula of the center frequency in the frequency domain and the solution of each IMF component are expressed as:

[0099]

[0100] Operator The update method is expressed as:

[0101]

[0102] The convergence condition is determined according to the convergence accuracy ε. If ε>0 and the following formula is satisfied, the iteration is stopped to obtain the IMF components of k different frequency bands; otherwise, the loop is returned to update.

[0103]

[0104] Then, the low-frequency characteristic modal component IMF1 of the zero-sequence current and zero-sequence voltage derivative is normalized and the waveform images are merged. The specific normalization formula is as follows:

[0105]

[0106] Where: x i is an element in vector X, i=1,2,···,n, n is the number of sampling points of X; abs(·) is the calculation for absolute value; max(·) is the calculation for maximum value; For x i Normalized value. This formula can be used to limit the elements in vector X to [-1,1].

[0107] Step S2, selecting a total of 240 groups of original signals under various working conditions and processing them into feature images through step S1, converting the feature images into grayscale images and binarizing the images as data sets for CNN training and testing;

[0108] In step S2, the feature image is converted into a grayscale image, and the grayscale image is converted into a binary image using the Otsu algorithm. The Otsu algorithm is simple to calculate and is not affected by image brightness and contrast. Its optimization goal is:

[0109]

[0110] The final between-class variance formula is:

[0111]

[0112] Where m is the mean of the pixels, MG is the global mean, and pi is the frequency of occurrence of pixels with gray value i.

[0113] According to the above method, the data of each segment is used to generate several binary images as the data set for CNN training and testing;

[0114] Figure 4 , Figure 5They are the binary feature image construction processes of fault section signal and sound section signal.

[0115] In step S2, in order to verify that the method of the present invention can be used for fault diagnosis under variable working conditions and can overcome the influence of the initial fault angle and the grounding resistance to a certain extent, fault data of 6 different initial angles and 6 different grounding resistances are selected, and binary images of 120 sets of training samples and test samples are generated according to Table 2.

[0116] Table 2 Parameters of simulation data training samples and test samples

[0117]

[0118] Step S3, using the generated binary image data set to train the convolutional neural network, and optimizing and adjusting the network structure and network parameters according to the training results during the training process;

[0119] Furthermore, in step S3, the convolutional neural network is selected by training, testing and comparing each group of networks designed in Table 3 one by one using the data set allocated in Table 2, and finally determining that the pixels of the input image are 64×64, the convolution layer is 4 layers, and the 7×7 convolution kernel is used. The CNN model using LeakReLU as the activation function adjusts the classification output result after the fully connected layer to 2 categories.

[0120] Table 3 CNN experiment grouping

[0121]

[0122] Step S4: Test the trained network on the test data set to obtain the image classification result, thereby obtaining the data segment classification, outputting the diagnosis result and analyzing the conclusion.

[0123] The present invention also provides a single-phase grounding fault section positioning system based on VMD_CNN, including a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0124] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0125] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0126] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0127] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0128] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0129] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A single-phase grounding fault section location method based on VMD_CNN, characterized in that: include: After a single-phase grounding fault occurs in the distribution network, determine the time of the single-phase grounding fault; The transient zero-sequence current and voltage derivative signals of each section of the distribution network in the 1 / 4 cycle before and after the single-phase grounding fault occurs are collected, and the transient zero-sequence current and voltage derivative signals of each section of the distribution network are decomposed using the variational mode decomposition method VMD to obtain the characteristic mode components IMF with frequencies from low to high. According to the polarity relationship of transient zero-sequence current and voltage derivative, the ground fault property identification is proposed. The characteristic modal component IMF1 of transient zero-sequence current and voltage derivative signals in each section of the distribution network is normalized and merged into a characteristic image, which is then converted into a grayscale binary image. The converted grayscale binary image is used as the input data for CNN classification network training, and the CNN classification network is trained to identify the properties of the single-phase grounding fault section.

2. The single-phase grounding fault section location method based on VMD_CNN according to claim 1 is characterized in that: The method comprises the following steps: Step S1, using the variational mode decomposition method VMD to decompose the transient zero-sequence current and voltage derivative signals of each section of the distribution network in the 1 / 4 cycle before and after the single-phase grounding fault occurs, the frequency of the characteristic mode components IMF from low to high, separate the characteristic mode components IMF1 of the transient zero-sequence current and voltage derivative signals, and merge them into a characteristic image after normalization; Step S2, selecting 240 groups of original signals under various working conditions and processing them into feature images through step S1, and converting the feature images into grayscale binary images as CNN classification network training data sets and test data sets; Step S3, using the training data set to train the CNN classification network, and optimizing and adjusting the network structure and network parameters according to the training results during the training process; Step S4: Test the test data set with the trained CNN classification network to obtain the image classification result, thereby obtaining the single-phase grounding fault section classification result.

3. A single-phase grounding fault section location method based on VMD_CNN according to claim 1 or 2, characterized in that: The variational mode decomposition method VMD decomposition process consists of two parts: proposing a variational problem and solving the variational problem. The first part is to propose a variational problem. The variational model under constraints is expressed as: Where, δ(t) is the unit pulse function; is the gradient function; {u k } are the modal components and {u k }={u1,u2,···,u k }; {ω k } is the corresponding center frequency and {ω k }={ω1,ω2,···,ω k }; j refers to the imaginary part of the complex number; The second part is to solve the variational problem. Here, we introduce the quadratic penalty factor α and the augmented Lagrange function λ(t) and transform it into an unconstrained variational model: Alternating Direction Multiplier Algorithm Stepwise Iterative Update and Thus, we get the saddle point of λ(t) and update for: In the formula Initialization is all set to zero, n is the iteration variable; Convert the above formula into frequency domain: In the formula represents the spectrum of the kth mode after the nth iteration, represents the spectrum of the original signal, represents the adjustment variable used to control the bandwidth of the mode; The formula of the center frequency in the frequency domain and the solution of each modal component are expressed as: Operator The update method is expressed as: The convergence condition is determined according to the convergence accuracy ε. If ε>0 and the following formula is satisfied, the iteration is stopped to obtain the modal components of k different frequency bands; otherwise, the loop is returned to update; 4. A single-phase grounding fault section location method based on VMD_CNN according to claim 1 or 2, characterized in that: The characteristic modal components IMF1 of the transient zero-sequence current and voltage derivative signals show the same polarity in the healthy section, and the IMF1 waveforms have a high degree of similarity; the characteristic modal components IMF1 of the transient zero-sequence current and voltage derivative signals show opposite polarities in the fault section, and the IMF1 waveforms are extremely different.

5. A single-phase grounding fault section location method based on VMD_CNN according to claim 1 or 2, characterized in that: The image classification results of the feature images recognized by the CNN classification network are divided into two categories. There are large differences between the two categories of images and the same type of images have a high similarity.

6. A single-phase grounding fault section location method based on VMD_CNN according to claim 1 or 2, characterized in that: In the process of image binarization, Otsu algorithm Otsu is used to select threshold value, and the Otsu algorithm Otsu can perform binarization processing on the image adaptively.

7. The single-phase grounding fault section location method based on VMD_CNN according to claim 6 is characterized in that: The Otsu algorithm is used to binarize the image. The specific implementation is as follows: The characteristic modal components IMF1 of the transient zero-sequence current and voltage derivative signals of each section of the distribution network are normalized and the combined characteristic images are converted into grayscale images. The grayscale images are converted into binary images using the Otsu algorithm. The optimization goal is: The final between-class variance formula is: Where m is the mean of the pixels, MG is the global mean, and pi is the frequency of occurrence of pixels with gray value i.

8. A single-phase grounding fault section location method based on VMD_CNN according to claim 1 or 2, characterized in that: The pixels of the CNN classification network input image are 64×64, the number of convolution layers is 4, a 7×7 convolution kernel is used, LeakReLU is used as the activation function of the CNN classification network, and the classification output result after the fully connected layer is adjusted to 2 categories.

9. A single-phase grounding fault section location method based on VMD_CNN according to claim 1 or 2, characterized in that: The characteristic mode component IMF is expressed as follows: u k (t)=A k (t)(cosψ k (t)) In the formula, u k (t) represents the kth eigenmode component, A k (t) is the amplitude envelope of the modal component, ψ k (t) represents the instantaneous phase. This expression shows that each modal component can be regarded as an amplitude modulated AM and frequency modulated FM signal.

10. A single-phase grounding fault section location method based on VMD_CNN according to claim 1 or 2, characterized in that: The formula for normalizing the characteristic modal component IMF1 of the transient zero-sequence current and voltage derivative signals is as follows: Where: x i is an element in vector X, i=1,2,···,n, n is the number of sampling points of X; abs(·) is the calculation for finding the absolute value; max(·) is the calculation for finding the maximum value; For x i Normalized value.

Images