A power distribution network high resistance ground fault detection method based on partial differential morphology
By using a partial differential morphology optimization model and an improved K-means clustering algorithm, the problems of insufficient accuracy and robustness of traditional morphology in signal feature extraction in power systems are solved, and reliable detection of high-resistance grounding faults in distribution networks is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SOUTH CHINA UNIV OF TECH
- Filing Date
- 2025-09-22
- Publication Date
- 2026-06-19
AI Technical Summary
Traditional mathematical morphology struggles to adaptively capture the local continuous features of signals in power systems, especially when dealing with complex and ever-changing fault signals. It cannot fully identify subtle morphological changes in signals, which limits the accuracy and robustness of feature extraction for high-resistance grounding fault detection in distribution networks.
A method based on partial differential morphology is adopted, which combines a partial differential morphology optimization model and partial differential morphology spectrum with an improved Kmeans clustering algorithm to achieve multi-scale analysis and adaptive processing of zero-sequence current data. Signal classification is performed using partial differential morphology discretization operators and Wasserstein distance.
It significantly improves the precision and robustness of signal feature extraction, accurately distinguishes normal signals from high-resistance grounding fault signals, and enhances the reliability and stability of high-resistance grounding fault detection in distribution networks.
Smart Images
Figure CN121234080B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of signal processing technology, and in particular to a method for detecting high-resistivity grounding faults in power distribution networks based on partial differential morphology. Background Technology
[0002] Traditional mathematical morphology, as a signal processing tool based on set theory, performs morphological operations on signals through structuring elements, demonstrating significant application value in fields such as image processing, pattern recognition, and power system fault diagnosis. However, this method faces a fundamental challenge: it relies on pre-set fixed structuring elements, making it difficult to adaptively capture the local continuous features of signals. Especially when processing complex and variable fault signals in power systems, it cannot fully identify subtle morphological changes in the signals, thus limiting the accuracy and robustness of feature extraction.
[0003] High-resistance grounding fault detection in distribution networks is a major technical challenge for ensuring the safe operation of power systems. When a fault occurs, the grounding impedance can reach several thousand ohms, and the fault current amplitude is close to the normal load level, making it difficult for traditional overcurrent protection devices to effectively identify. Existing detection methods based on transient signal analysis are easily limited by factors such as line topology, noise interference, and sampling frequency, resulting in a trade-off between sensitivity and reliability. Summary of the Invention
[0004] The purpose of this invention is to overcome the shortcomings and disadvantages of the prior art and propose a method for detecting high-resistivity grounding faults in distribution networks based on partial differential morphology. This method can effectively achieve adaptive processing and multi-scale analysis of local signal features, and complete the reliable detection of high-resistivity grounding faults in distribution networks.
[0005] To achieve the above objectives, the technical solution provided by this invention is: a method for detecting high-resistivity grounding faults in distribution networks based on partial differential morphology, comprising the following steps:
[0006] S1: At the first moment after a distribution network fault or disturbance occurs, collect the zero-sequence current data within the time window at the beginning of the feeder after that moment;
[0007] S2: Calculate the partial differential morphological spectrum of zero-sequence current data based on the defined partial differential morphological discretization operator and the mathematical expression of the partial differential morphological spectrum, and construct a dataset containing multiple partial differential morphological spectra. Specifically, based on the idea of partial differential equations, a partial differential morphological optimization model is defined. This model simulates the morphological evolution process of the signal through nonlinear partial differential equations, enabling the processing and analysis of local signal features. Unlike traditional morphology, the partial differential morphological optimization model dynamically adjusts the intensity of morphological operations through a continuous-scale diffusion process, preserving important edge information while significantly improving the refinement of feature extraction. A partial differential morphological discretization operator is derived, aiming to effectively preserve the key morphological features of one-dimensional signals while smoothing them. Based on the concept of traditional morphological spectra, a partial differential morphological spectrum is defined. Unlike the coarse-grained description of signal shape and size distribution in traditional morphological spectra, the partial differential morphological spectrum characterizes the sensitivity of the scale factor to area changes during signal processing, quantitatively describing the signal's variation characteristics on a continuous scale and accurately capturing the details of signal changes with scale.
[0008] S3: Perform cluster analysis on the obtained partial differential morphology spectra, calculate the Wasserstein distance between each partial differential morphology spectrum in the dataset, and use the improved K-means clustering algorithm to classify the partial differential morphology spectra of the obtained zero-sequence current data into two categories: normal or disturbance signals and high-resistance ground fault signals. The improved K-means clustering algorithm combines Wasserstein distance with traditional K-means clustering. This algorithm enhances the ability to identify overlapping distribution areas by introducing a density weighting strategy. From the perspective of clustering stability, the introduction of density weighting can effectively reduce the oscillation amplitude of center updates at the numerical iteration level.
[0009] S4: For the new zero-sequence current data input at the next moment, repeat the above steps S2 and S3. Based on the Wasserstein distance between the partial differential morphology spectrum of each new zero-sequence current data and the partial differential morphology spectrum of each category centroid, classify the category of each new zero-sequence current data into the category closest to the category centroid. In real time, distinguish between normal or disturbance signals and high-resistance grounding fault signals, thereby detecting whether a high-resistance grounding fault has occurred in the distribution network.
[0010] Furthermore, in step S2, a partial differential morphological optimization model is used to iteratively optimize the zero-sequence current data;
[0011] Based on the ideas of partial differential morphology, a partial differential morphological optimization model is proposed for a given original one-dimensional signal. The signal obtained through optimization is denoted as Objective function of partial differential morphological optimization model Described as:
[0012] ;
[0013] In the formula, The function is processed by the partial differential morphological optimization model. For a one-dimensional signal, the independent variable is... yes The first derivative is the gradient. For regularization terms, It is a balance parameter and This is used to adjust the relative weights of the regularization and fidelity terms. This is a fidelity-preserving term, used to maintain the similarity between the processed signal and the original signal;
[0014] The authenticity item is The regularization term is set as follows:
[0015] ;
[0016] In the formula, yes The second derivative of the function The sign function reflects the convexity or concavity of the signal at local points. It is convex. This indicates concavity, meaning it can adaptively adjust the smoothing direction based on the local convexity or concavity of the signal. It is a scaling factor used to control the degree to which regularization suppresses the gradient, and ;if The larger the value, the better. The faster the decay, the weaker the regularization magnitude when the gradient increases, and the more pronounced the preservation of edges; conversely, if The smaller the value, the less quickly the gradient is suppressed once it increases, and the partial differential morphological optimization model tends to smooth convex and concave edges more effectively; therefore, the scale factor... Corresponding to the size of structural elements in traditional morphology, based on this, the objective function is minimized. This partial differential morphological optimization model effectively preserves the convex and concave structure and significant edges of the signal while smoothing noise and small fluctuations.
[0017] To minimize the objective function The variational method is used to obtain the optimal conditions. The continuity equation is obtained:
[0018] ;
[0019] To achieve numerical computation and solution, the above continuity equation is discretized using the central difference approximation. The first and second derivatives are as follows:
[0020] ;
[0021] In the formula, This represents the signal value at coordinate i in the nth iteration. This represents the signal value at coordinate i+1 in the nth iteration. This represents the signal value at coordinate i-1 in the nth iteration. The spatial step size;
[0022] Will Substituting the first and second derivatives into the above continuity equation, we obtain the mathematical expression for the partial differential morphological discretization operator as follows:
[0023] ;
[0024] In the formula, This represents the signal value at coordinate i in the (n+1)th iteration. This represents the signal value at coordinate i in the original one-dimensional data. The step size is the scale step.
[0025] Furthermore, in step S2, a partial differential morphological spectrum is constructed using a partial differential morphological model based on physical driving characteristics.
[0026] Based on the concept of traditional morphological spectra, a partial differential morphological spectrum, referred to as PPS, is defined to characterize the scale factor. The mathematical expression for the sensitivity to area changes during signal processing is:
[0027] ;
[0028] In the formula, Indicates quantized signal Different scale factors Sensitivity to area changes during processing, scale factor A larger value means a larger structural element is used, resulting in a smoother processed signal but also greater loss of detail. Indicated by the scale factor as The structural elements of the original one-dimensional signal The signal obtained after performing a series of morphological operations. Indicates the processed signal area, To discretize the operator using partial differential morphology at the scale factor Signals processed below , The signal domain, and the signal domain and scale factor. Since it is irrelevant, exchanging the order of the differential and integral yields the partial differential morphological spectrum integral defined as:
[0029] ;
[0030] The partial differential morphological spectrum integral energy can be decomposed into a structure evolution term. With fidelity constraint Difference:
[0031] ;
[0032] when At that time, the partial differential morphological spectrum degenerates into pure morphological evolution:
[0033] ;
[0034] Partial differential morphology spectrometry (PDS) quantitatively describes the area distribution of a signal at different processing scale factors during diffusion, revealing the dynamic changes of the signal in multi-scale morphological operations. This helps in the analysis and understanding of the signal's structure and behavior. In other words, by using PDS, we can accurately capture the details of how the signal changes with scale factors, thus achieving a more in-depth and refined quantitative description in signal processing.
[0035] Furthermore, in step S3, an improved K-means clustering algorithm based on Wasserstein distance is used, as detailed below:
[0036] For two discrete probability distributions and ,in express The Middle The probability of an event or state. express The Middle The probability of an event or state. , Having the same quantity A possible outcome, and the relationships between them The order Wasserstein distance is defined as:
[0037] ;
[0038] In the formula, express and Between Wasserstein distance of order Let be the order of the distance, which is a real number and satisfies . , middle for and All joint distributions of , and their marginal distributions are respectively and , Let the set of all such joint distributions be represented. This represents the infimum, which is the minimum value that can be reached among all possible joint distributions. Represents the joint distribution The mathematical expectation, From Random variable pairs drawn from the sample. Representing variables and variables Norm distance between Ensure that the expectation exists, that is, the distribution has a finite value. Step moments; for each joint distribution Calculate all sampling distances Mathematical expectation ;
[0039] A Hadamard matrix is a special type of orthogonal matrix where all elements are either +1 or -1, and the rows and columns are mutually orthogonal. The Hadamard matrix is recursively defined as follows:
[0040] ;
[0041] The size of the Hadamard matrix is matrix order an integer power of 2 Indicates the order is The Hadamard matrix, Represents a positive integer, used in exponential expression, in the recursive definition. Let the current index be such that the matrix order is . ;
[0042] By integrating morphological gradient operations with the Hadamard matrix, an improved gradient morphological spectrum based on the Hadamard matrix, called HGPS, is proposed. This improved gradient morphological spectrum utilizes the rectangular wave structure elements generated by the Hadamard matrix, which expands the diversity of feature extraction and improves the robustness of signal processing.
[0043] For the original one-dimensional signal ,in Representing the real number field, the original one-dimensional signal The improved gradient morphology spectrum is defined as follows:
[0044] ;
[0045] In the formula, For the selected Hadamard matrix, Represents the original one-dimensional signal Given the Hadamard matrix The morphological gradient area spectrum value is a scalar value used to quantize the original one-dimensional signal. At a specific scale and row index Local mutation characteristics, Denotes the scale parameter of the matrix, where Represents all integers. The index for the selected row number. Indicates the use of the Hadamard matrix The corresponding structuring element corresponds to the original one-dimensional signal. The resulting function obtained after performing morphological gradient operations. As an area operator, it calculates the absolute area of the morphological gradient result; the improved gradient morphological spectrum captures the morphological differences of the signal at multiple scales through the rectangular wave structure elements corresponding to Hadamard matrices of different orders, and realizes a refined characterization of the local abrupt change features of the signal.
[0046] The improved K-means clustering algorithm enhances the ability to identify overlapping distribution regions by introducing a density-weighted strategy. In specific implementation, if the Wasserstein distance between a certain improved gradient morphology spectrum and the improved gradient morphology spectrum of the cluster center is smaller, and there are several samples with similar distribution to this improved gradient morphology spectrum nearby, then the weight is increased during the iterative optimization process; otherwise, it is decreased.
[0047] A set of improved gradient morphological spectra based on the Hadamard matrix for different signals ,in Representing the Each improved gradient morphology spectrum is a... dimensional vector, express dimensional real number field, Determined by the feature extraction process;
[0048] The process of improving the K-means clustering algorithm is as follows:
[0049] S31: Random selection Define an initial cluster center set. ,in It refers to the number of clusters, that is, the number of clusters into which the data is to be divided. Representing the The initial center of each cluster;
[0050] S32: Compute Set The Wasserstein distance between each improved gradient morphology spectrum and the improved gradient morphology spectrum of each cluster center is used to assign each improved gradient morphology spectrum to the nearest cluster center.
[0051] S33: Calculate local density weights:
[0052] ;
[0053] In the formula, Local density weights are used to calculate the first... The improved gradient morphology spectrum and the first The weights between the improved gradient morphology spectrum of the cluster centers Indicates the first The improved gradient morphology spectrum and the first The square of the Wasserstein distance between the improved gradient morphological spectra of the cluster centers For clusters The average of the squared Wasserstein distances between all improved gradient morphological spectra and the improved gradient morphological spectra of the cluster centers. It is an exponential function;
[0054] S34: Update cluster center:
[0055] ;
[0056] In the formula, at this time For the updated number Cluster centers, This represents the parameters that minimize the objective function; here, it's used to find the optimal cluster centers. Indicates the first Improved gradient morphology spectrum of a signal exist A probability distribution space with finite second moments over the real number field. Indicates the first Sum the improved gradient morphology spectra of all clusters. To be assigned to the The number of improved gradient morphology spectra for each cluster, Indicates assignment to the first The first cluster An improved gradient morphology spectrum Indicates the first The improved gradient morphology spectrum and the first The th cluster The square of the Wasserstein distance between each improved gradient morphological spectrum;
[0057] S35: Iterate through steps S32 to S34 until convergence, i.e., the cluster centers do not change significantly;
[0058] Through the above steps, the improved K-means clustering algorithm not only fully utilizes the advantages of Wasserstein distance in measuring distribution differences, but also improves the adaptability of the K-means clustering algorithm to complex distributions through a density-weighted strategy, thus exhibiting higher accuracy and stability in signal classification tasks.
[0059] Furthermore, in step S4, a high-resistance grounding fault in the distribution network is detected, as detailed below:
[0060] When a disturbance occurs in the measurement signal of the distribution network, but does not reach the protection action threshold, the disturbance signal is recorded and uploaded to the main station for fault identification. Specifically, a partial differential morphology optimization model and a partial differential morphology discretization operator are used to calculate the partial differential morphology spectrum of the disturbance signal, constructing a dataset containing multiple partial differential morphology spectra. Cluster analysis is performed on the obtained partial differential morphology spectra, calculating the Wasserstein distance between each partial differential morphology spectrum in the dataset. An improved K-means clustering algorithm is used to classify the partial differential morphology spectrum of the obtained disturbance signal into two categories: normal or disturbance signals and high-resistance ground fault signals. The partial differential morphology spectrum of the disturbance signal is assigned to the category closest to the centroid of the category, distinguishing between normal or disturbance signals and high-resistance ground fault signals in real time, and detecting whether a high-resistance ground fault has occurred in the distribution network.
[0061] Compared with the prior art, the present invention has the following advantages and beneficial effects:
[0062] 1. This invention defines a partial differential morphology optimization model and a partial differential morphology discretization operator, and introduces the concept of partial differential morphology spectrum, providing a theoretical tool for multi-scale signal analysis.
[0063] 2. The partial differential morphological discretization operator defined in this invention significantly reduces the interference of noise background while preserving the abrupt change positions of the original signal, and the extracted perturbation features are smoother and more consistent with the original features.
[0064] 3. The partial differential morphological spectrum constructed based on the physical driving characteristics of the partial differential morphological model provides an effective tool for further quantitatively describing the changes of the signal at continuous scales by quantitatively describing the area distribution of the signal at different processing scale factors during the diffusion process. It reveals the dynamic changes of the signal in multi-scale morphological operations and helps to analyze and understand the structure and behavior of the signal.
[0065] 4. The improved K-means clustering algorithm based on Wasserstein distance not only makes full use of the advantages of Wasserstein distance in measuring distribution differences, but also improves the adaptability of K-means clustering algorithm to complex distributions through density weighting strategy, thus showing higher accuracy and stability in signal classification tasks. Attached Figure Description
[0066] Figure 1 This is a schematic diagram of the overall process of the method of the present invention.
[0067] Figure 2 This is a flowchart illustrating the improved K-means clustering algorithm based on Wasserstein distance. Detailed Implementation
[0068] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.
[0069] like Figure 1 As shown in the figure, this embodiment discloses a method for detecting high-resistivity grounding faults in distribution networks based on partial differential morphology, the specific details of which are as follows:
[0070] S1: At the first moment after a distribution network fault or disturbance occurs, collect the zero-sequence current data within the time window at the beginning of the feeder after that moment;
[0071] S2: Calculate the partial differential morphological spectrum of zero-sequence current data based on the defined partial differential morphological discretization operator and the mathematical expression of the partial differential morphological spectrum, and construct a dataset containing multiple partial differential morphological spectra. Based on the idea of partial differential equations, a novel mathematical morphological optimization model is defined. This model simulates the morphological evolution of signals through nonlinear partial differential equations, enabling the processing and analysis of local signal features. Unlike traditional morphology, the partial differential morphological optimization model dynamically adjusts the intensity of morphological operations through a continuous-scale diffusion process, preserving important edge information while significantly improving the refinement of feature extraction. A partial differential morphological discretization operator is derived, aiming to effectively preserve key morphological features while smoothing one-dimensional signals. Based on the concept of traditional morphological spectra, a partial differential morphological spectrum (PPS) is defined. Unlike the coarse-grained description of signal shape and size distribution in traditional morphological spectra, the partial differential morphological spectrum characterizes the sensitivity of the scale factor to area changes during signal processing, quantitatively describing the signal's variation characteristics on a continuous scale and accurately capturing the details of signal changes with scale.
[0072] A partial differential morphological optimization model was used to iteratively optimize the zero-sequence current data;
[0073] For a given original one-dimensional signal The signal obtained through optimization is denoted as Objective function of partial differential morphological optimization model Described as:
[0074] ;
[0075] In the formula, The function is processed by the partial differential morphological optimization model. For a one-dimensional signal, the independent variable is... yes The first derivative is the gradient. For regularization terms, It is a balance parameter and This is used to adjust the relative weights of the regularization and fidelity terms. This is a fidelity-preserving term, used to maintain the similarity between the processed signal and the original signal;
[0076] The authenticity item is The regularization term is set as follows:
[0077] ;
[0078] In the formula, yes The second derivative of the function The sign function reflects the convexity or concavity of the signal at local points. It is convex. This indicates concavity, meaning it can adaptively adjust the smoothing direction based on the local convexity or concavity of the signal. It is a scaling factor used to control the degree to which regularization suppresses the gradient, and ;if The larger the value, the better. The faster the decay, the weaker the regularization magnitude when the gradient increases, and the more pronounced the preservation of edges; conversely, if The smaller the value, the less quickly the gradient is suppressed once it increases, and the partial differential morphological optimization model tends to smooth convex and concave edges more effectively; therefore, the scale factor... Corresponding to the size of structural elements in traditional morphology, based on this, the objective function is minimized. This partial differential morphological optimization model effectively preserves the convex and concave structure and significant edges of the signal while smoothing noise and small fluctuations.
[0079] To minimize the objective function The variational method is used to obtain the optimal conditions. The continuity equation is obtained:
[0080] ;
[0081] To achieve numerical computation and solution, the above continuity equation is discretized using the central difference approximation. The first and second derivatives are as follows:
[0082] ;
[0083] In the formula, This represents the signal value at coordinate i in the nth iteration. This represents the signal value at coordinate i+1 in the nth iteration. This represents the signal value at coordinate i-1 in the nth iteration. The spatial step size;
[0084] Will Substituting the first and second derivatives into the above continuity equation, we obtain the mathematical expression for the partial differential morphological discretization operator as follows:
[0085] ;
[0086] In the formula, This represents the signal value at coordinate i in the (n+1)th iteration. This represents the signal value at coordinate i in the original one-dimensional data. The scale step size;
[0087] The results show that the partial differential morphology discretization operator significantly reduces the interference of noise background while preserving the signal abrupt change position, and the extracted perturbation features are smoother and more consistent with the original features.
[0088] A partial differential morphological spectrum was constructed using a partial differential morphological model based on physical driving characteristics;
[0089] Based on the concept of traditional morphological spectrum, a partial differential morphological spectrum (PDE-based pattern spectrum, PPS) is defined to characterize the scale factor. The mathematical expression for the sensitivity to area changes during signal processing is:
[0090] ;
[0091] In the formula, Indicates quantized signal Different scale factors Sensitivity to area changes during processing, scale factor A larger value means a larger structural element is used, resulting in a smoother processed signal but also greater loss of detail. Indicated by the scale factor as The structural elements of the original one-dimensional signal The signal obtained after performing a series of morphological operations. Indicates the processed signal area, To discretize the operator using partial differential morphology at the scale factor Signals processed below , The signal domain, and the signal domain and scale factor. Since it is irrelevant, exchanging the order of the differential and integral yields the partial differential morphological spectrum integral defined as:
[0092] ;
[0093] The partial differential morphological spectrum integral energy can be decomposed into a structure evolution term. With fidelity constraint Difference:
[0094] ;
[0095] when At that time, the partial differential morphological spectrum degenerates into pure morphological evolution:
[0096] ;
[0097] Partial differential morphology spectrometry (PDS) quantitatively describes the area distribution of a signal at different processing scale factors during diffusion, revealing the dynamic changes of the signal in multi-scale morphological operations. This helps in the analysis and understanding of the signal's structure and behavior. In other words, by using PDS, we can accurately capture the details of how the signal changes with scale factors, thus achieving a more in-depth and refined quantitative description in signal processing.
[0098] S3: Perform cluster analysis on the obtained partial differential morphology spectra, calculate the Wasserstein distance between each partial differential morphology spectrum in the dataset, and use the improved K-means clustering algorithm to classify the partial differential morphology spectra of the obtained zero-sequence current data into two categories: normal or disturbance signals and high-resistance ground fault signals. The improved K-means clustering algorithm combines Wasserstein distance with traditional K-means clustering. This algorithm enhances the ability to identify overlapping distribution areas by introducing a density weighting strategy. From the perspective of clustering stability, the introduction of density weighting can effectively reduce the oscillation amplitude of center updates at the numerical iteration level.
[0099] like Figure 2 As shown, an improved K-means clustering algorithm based on Wasserstein distance was used, as detailed below:
[0100] For two discrete probability distributions and ,in express The Middle The probability of an event or state. express The Middle The probability of an event or state. , Having the same quantity A possible outcome, and the relationships between them The order Wasserstein distance is defined as:
[0101] ;
[0102] In the formula, express and Between Wasserstein distance of order Let be the order of the distance, which is a real number and satisfies . , middle for and All joint distributions of , and their marginal distributions are respectively and , Let the set of all such joint distributions be represented. This represents the infimum, which is the minimum value that can be reached among all possible joint distributions. Represents the joint distribution The mathematical expectation, From Random variable pairs drawn from the sample. Representing variables and variables Norm distance between Ensure that the expectation exists, that is, the distribution has a finite value. Step moments; for each joint distribution Calculate all sampling distances Mathematical expectation ;
[0103] A Hadamard matrix is a special type of orthogonal matrix where all elements are either +1 or -1, and the rows and columns are mutually orthogonal. The Hadamard matrix is recursively defined as follows:
[0104] ;
[0105] The size of the Hadamard matrix is matrix order an integer power of 2 Indicates the order is The Hadamard matrix, Represents a positive integer, used in exponential expression, in the recursive definition. Let the current index be such that the matrix order is . ;
[0106] By integrating morphological gradient operations with the Hadamard matrix, an improved gradient morphological spectrum based on the Hadamard matrix, called HGPS, is proposed. This improved gradient morphological spectrum utilizes the rectangular wave structure elements generated by the Hadamard matrix, which expands the diversity of feature extraction and improves the robustness of signal processing.
[0107] For the original one-dimensional signal ,in Representing the real number field, the original one-dimensional signal The improved gradient morphology spectrum is defined as follows:
[0108] ;
[0109] In the formula, For the selected Hadamard matrix, Represents the original one-dimensional signal Given the Hadamard matrix The morphological gradient area spectrum value is a scalar value used to quantize the original one-dimensional signal. At a specific scale and row index Local mutation characteristics, Denotes the scale parameter of the matrix, where Represents all integers. The index for the selected row number. Indicates the use of the Hadamard matrix The corresponding structuring element corresponds to the original one-dimensional signal. The resulting function obtained after performing morphological gradient operations. As an area operator, it calculates the absolute area of the morphological gradient result; the improved gradient morphological spectrum captures the morphological differences of the signal at multiple scales through the rectangular wave structure elements corresponding to Hadamard matrices of different orders, and realizes a refined characterization of the local abrupt change features of the signal.
[0110] The improved K-means clustering algorithm enhances the ability to identify overlapping distribution regions by introducing a density-weighted strategy. In practice, if the Wasserstein distance between an improved gradient morphology spectrum and the improved gradient morphology spectrum of the cluster center is smaller, and there are several samples with similar distributions to this improved gradient morphology spectrum nearby, then the weight is increased during the iterative optimization process; otherwise, it is decreased.
[0111] A set of improved gradient morphological spectra based on the Hadamard matrix for different signals ,in Representing the Each improved gradient morphology spectrum is a... dimensional vector, express dimensional real number field, Determined by the feature extraction process;
[0112] The process of improving the K-means clustering algorithm is as follows:
[0113] S31: Random selection Define an initial cluster center set. ,in It refers to the number of clusters, that is, the number of clusters into which the data is to be divided. Representing the The initial center of each cluster;
[0114] S32: Compute Set The Wasserstein distance between each improved gradient morphology spectrum and the improved gradient morphology spectrum of each cluster center is used to assign each improved gradient morphology spectrum to the nearest cluster center.
[0115] S33: Calculate local density weights:
[0116] ;
[0117] In the formula, Local density weights are used to calculate the first... The improved gradient morphology spectrum and the first The weights between the improved gradient morphology spectrum of the cluster centers Indicates the first The improved gradient morphology spectrum and the first The square of the Wasserstein distance between the improved gradient morphological spectra of the cluster centers For clusters The average of the squared Wasserstein distances between all improved gradient morphological spectra and the improved gradient morphological spectra of the cluster centers. It is an exponential function;
[0118] S34: Update cluster center:
[0119] ;
[0120] In the formula, at this time For the updated number Cluster centers, This represents the parameters that minimize the objective function; here, it's used to find the optimal cluster centers. Indicates the first Improved gradient morphology spectrum of a signal exist A probability distribution space with finite second moments over the real number field. Indicates the first Sum the improved gradient morphology spectra of all clusters. To be assigned to the The number of improved gradient morphology spectra for each cluster, Indicates assignment to the first The first cluster An improved gradient morphology spectrum Indicates the first The improved gradient morphology spectrum and the first The th cluster The square of the Wasserstein distance between each improved gradient morphological spectrum;
[0121] S35: Iterate through steps S32 to S34 until convergence, i.e., the cluster centers do not change significantly;
[0122] Through the above steps, the improved K-means clustering algorithm not only fully utilizes the advantages of Wasserstein distance in measuring distribution differences, but also improves the adaptability of the K-means clustering algorithm to complex distributions through a density-weighted strategy, thus exhibiting higher accuracy and stability in signal classification tasks.
[0123] S4: For the newly input zero-sequence current data at the next moment, repeat steps S2 and S3 above. Based on the Wasserstein distance between the partial differential morphology spectrum of each newly input zero-sequence current data and the partial differential morphology spectrum of each category centroid, classify the data into the category closest to the category centroid. This allows for real-time differentiation between normal or disturbance signals and high-resistance grounding fault signals, detecting whether a high-resistance grounding fault has occurred in the distribution network. Specific details are as follows:
[0124] When a disturbance occurs in the measurement signal of the distribution network, but does not reach the protection action threshold, the disturbance signal is recorded and uploaded to the main station for fault identification. Specifically, a partial differential morphology optimization model and a partial differential morphology discretization operator are used to calculate the partial differential morphology spectrum of the disturbance signal, constructing a dataset containing multiple partial differential morphology spectra. Cluster analysis is performed on the obtained partial differential morphology spectra, calculating the Wasserstein distance between each partial differential morphology spectrum in the dataset. An improved K-means clustering algorithm is used to classify the partial differential morphology spectrum of the obtained disturbance signal into two categories: normal or disturbance signals and high-resistance ground fault signals. The partial differential morphology spectrum of the disturbance signal is assigned to the category closest to the centroid of the category, distinguishing between normal or disturbance signals and high-resistance ground fault signals in real time, and detecting whether a high-resistance ground fault has occurred in the distribution network.
[0125] To comprehensively evaluate the adaptability and effectiveness of the improved high-resistance grounding fault detection scheme under complex operating conditions, this study uses the classic Emanuel high-resistance grounding fault model for simulation research. This model has the advantages of simple structure, intuitive parameter setting and no need for complex differential calculations, and can realistically simulate the randomness, asymmetry and non-stationary arc characteristics present in high-resistance grounding faults (HIF).
[0126] Considering that 666kV distribution networks generally adopt a neutral point non-effective grounding operation mode, this study builds a typical 10kV resonant grounding distribution network simulation model based on the PSCAD / EMTDC platform. The main transformer has a rated voltage of 110kV / 10.5kV, uses arc suppression coil grounding, and the distribution network topology includes overhead lines and cable lines. A 1MW photovoltaic module is connected to the system, with a load power of 1MW, and the sampling frequency is set to 10kHz.
[0127] In the simulation environment, zero-sequence current sensors are installed at the beginning of each feeder to collect zero-sequence current data for two power frequency cycles after a fault or disturbance in real time, and to perform morphological spectrum calculation and feature extraction based on this data. Furthermore, this study constructs a complete signal acquisition and data processing workflow based on the RTDS real-time digital simulation platform.
[0128] When calculating the partial differential morphological spectrum, a spatial step size ∆x=0.01, an initial scale s=0.1, a scale step size ∆s=0.1, and a fidelity term weight λ=0.2 were used. The overall performance of the scheme is shown in Table 1.
[0129] Table 1. Detection performance of partial differential morphological scheme in radial distribution network
[0130]
[0131] In a noise-free environment, all sampling frequencies (10kHz, 5kHz, and 1kHz) achieved 100% across all four performance indicators, verifying the reliability of the method under ideal conditions. As noise intensity increases, the performance indicators gradually decrease but remain at a high level. For example, at 30dB noise, the overall performance of the method remained stable above 99.4%, demonstrating its adaptability to typical noise levels in the measurement environment. Furthermore, the performance differences between different sampling frequencies were small, indicating that the method is insensitive to changes in the sampling rate.
[0132] To verify the feasibility of the proposed solution in a real-world scenario, actual distribution network fault waveform data was used for testing. Taking a radially connected distribution network as an example, under a 10kHz sampling frequency and noise-free conditions, the calculated cluster center coordinates for the four types of events were: [120.02 75.32 65.11 61.79 61.84], [142.65 87.20 75.17 65.44 70.69], [340.19 245.67 241.02 206.39 181.63], [218.05 199.63 206.88 174.30 162.97]. Based on these cluster centers, the actual waveform data was identified, and the results are shown in Table 2. All cases had the smallest Wasserstein distance to high-resistance grounding faults, indicating that the solution has a good ability to distinguish high-resistance grounding faults. In the table, HIF represents a high-resistance ground fault, LIF represents a low-resistance ground fault, CS represents capacitor switching, and LS represents load switching.
[0133] Table 2. Identification results of actual cases based on partial differential morphology spectrum.
[0134]
[0135] Experimental Conclusions: This invention proposes a method for detecting high-resistivity grounding faults in distribution networks based on partial differential morphology. The constructed partial differential morphological optimization model achieves a dynamic balance between edge preservation and noise suppression, exhibiting stronger local adaptive capabilities compared to traditional morphological operators. The proposed partial differential morphological spectrum effectively captures the multi-resolution morphological structure information of fault signals through continuous-scale integration, demonstrating more stable feature extraction capabilities within the 10kHz to 1kHz sampling range, laying the foundation for accurate characterization of fault signals.
[0136] Experimental results demonstrate that the proposed scheme exhibits good adaptability in complex power distribution networks. Verification using actual fault recording data further confirms that the proposed scheme achieves a 100% success rate in detecting high-resistivity faults, while also effectively distinguishing between interference events such as capacitor switching and load switching. These results highlight the robustness and practicality of the partial differential morphological spectrum scheme in complex power grid environments. To further promote the engineering application of this method in smart power distribution networks, future research will focus on the adaptive optimization mechanism of morphological parameters and explore FPGA-based hardware implementation to improve its real-time performance and engineering feasibility, making it worthy of wider application.
[0137] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.
Claims
1. A partial differential morphology-based method for detecting high impedance ground faults in a power distribution network, characterized in that, Includes the following steps: S1: At the first moment after a distribution network fault or disturbance occurs, collect the zero-sequence current data within the time window at the beginning of the feeder after that moment; S2: Calculate the partial differential morphological spectrum of zero-sequence current data based on the defined partial differential morphological discretization operator and the mathematical expression of the partial differential morphological spectrum, and construct a dataset containing multiple partial differential morphological spectra. Specifically, based on the idea of partial differential equations, a partial differential morphological optimization model is defined. This model simulates the morphological evolution process of the signal through nonlinear partial differential equations, enabling the processing and analysis of local signal features. Unlike traditional morphology, the partial differential morphological optimization model dynamically adjusts the intensity of morphological operations through a continuous-scale diffusion process, preserving important edge information while significantly improving the refinement of feature extraction. A partial differential morphological discretization operator is derived, aiming to effectively preserve the key morphological features of one-dimensional signals while smoothing them. Based on the concept of traditional morphological spectra, a partial differential morphological spectrum is defined. Unlike the coarse-grained description of signal shape and size distribution in traditional morphological spectra, the partial differential morphological spectrum characterizes the sensitivity of the scale factor to area changes during signal processing, quantitatively describing the signal's variation characteristics on a continuous scale and accurately capturing the details of signal changes with scale. A partial differential morphological optimization model was used to iteratively optimize the zero-sequence current data; Based on the idea of partial differential morphology, a partial differential morphology optimization model is proposed for a given original one-dimensional signal The signal obtained by optimization is denoted as The objective function of the partial differential morphology optimization model is described as follows ； wherein is a function of the model processed by the partial differential morphological optimization, is an independent variable of the one-dimensional signal, is a first derivative of , i.e. a gradient, is a regularization term, is a balancing parameter and is used to adjust the relative weight of the regularization term and the fidelity term, is a fidelity term used to maintain the similarity between the processed signal and the original signal; The fidelity term is taken as The regularization term is set as: ； In the formula, yes The second derivative of the function The sign function reflects the convexity or concavity of the signal at local points. It is convex. This indicates concavity, meaning it can adaptively adjust the smoothing direction based on the local convexity or concavity of the signal. It is a scaling factor used to control the degree to which regularization suppresses the gradient, and ;if The larger the value, the better. The faster the decay, the weaker the regularization magnitude when the gradient increases, and the more pronounced the preservation of edges; conversely, if The smaller the value, the less quickly the gradient is suppressed once it increases, and the partial differential morphological optimization model tends to smooth convex and concave edges more effectively; therefore, the scale factor... Corresponding to the size of structural elements in traditional morphology, based on this, the objective function is minimized. This partial differential morphological optimization model effectively preserves the convex and concave structure and significant edges of the signal while smoothing noise and small fluctuations. To minimize the objective function , the variational method is used to obtain the , the continuous equation is obtained: ； To realize the numerical calculation solution, the above continuous equation is discretized, and the central difference approximation is adopted, The first derivative and the second derivative are respectively: ； wherein denotes the signal value of coordinate i in the n-th iteration, denotes the signal value of coordinate i+1 in the n-th iteration, denotes the signal value of coordinate i-1 in the n-th iteration, is the spatial step size; The first derivative and the second derivative of the function f(x) are substituted into the above continuous equation to obtain the mathematical expression of the partial differential morphological discretization operator as follows: The first derivative and the second derivative of the function f(x) are substituted into the above continuous equation to obtain the mathematical expression of the partial differential morphological discretization operator as follows: ； wherein denotes the signal value of coordinate i in the n+1 iteration, denotes the signal value of coordinate i in the original one-dimensional data, is the step size of the scaling; S3: Perform cluster analysis on the obtained partial differential morphology spectra, calculate the Wasserstein distance between each partial differential morphology spectrum in the dataset, and use the improved K-means clustering algorithm to classify the partial differential morphology spectra of the obtained zero-sequence current data into two categories: normal or disturbance signals and high-resistance ground fault signals. The improved K-means clustering algorithm combines Wasserstein distance with traditional K-means clustering. This algorithm enhances the ability to identify overlapping distribution areas by introducing a density weighting strategy. From the perspective of clustering stability, the introduction of density weighting can effectively reduce the oscillation amplitude of center updates at the numerical iteration level. S4: For the new zero-sequence current data input at the next moment, repeat the above steps S2 and S3. Based on the Wasserstein distance between the partial differential morphology spectrum of each new zero-sequence current data and the partial differential morphology spectrum of each category centroid, classify the category of each new zero-sequence current data into the category closest to the category centroid. In real time, distinguish between normal or disturbance signals and high-resistance grounding fault signals, thereby detecting whether a high-resistance grounding fault has occurred in the distribution network.
2. The partial differential morphology based method for detection of high impedance ground faults in power distribution network as claimed in claim 1 wherein, In step S2, a partial differential morphological spectrum was constructed using a partial differential morphological model based on physical driving characteristics. Based on the concept of traditional morphological spectrum, partial differential morphological spectrum, called PPS, is defined to characterize the scale factor The sensitivity to area variation in the signal processing process is mathematically expressed as: ； In the formula, Indicates quantized signal Different scale factors Sensitivity to area changes during processing, scale factor A larger value means a larger structural element is used, resulting in a smoother processed signal but also greater loss of detail. Indicated by the scale factor as The structural elements of the original one-dimensional signal The signal obtained after performing a series of morphological operations. Indicates the processed signal area, To discretize the operator using partial differential morphology at the scale factor Signals processed below , The signal domain, and the signal domain and scale factor. Since it is irrelevant, exchanging the order of the differential and integral yields the partial differential morphological spectrum integral defined as: ； This partial differential morphological spectrum integral can be decomposed into the difference between the structural evolution term and the fidelity constraint term ； When the partial differential form degenerates into pure morphological evolution: ； Partial differential morphology spectrometry (PDS) quantitatively describes the area distribution of a signal at different processing scale factors during diffusion, revealing the dynamic changes of the signal in multi-scale morphological operations. This helps in the analysis and understanding of the signal's structure and behavior. In other words, by using PDS, we can accurately capture the details of how the signal changes with scale factors, thus achieving a more in-depth and refined quantitative description in signal processing.
3. The partial differential morphology based method for detection of high impedance ground faults in power distribution network as claimed in claim 2 wherein, In step S3, an improved K-means clustering algorithm based on Wasserstein distance was used, as detailed below: For two discrete probability distributions and ,in express The Middle The probability of an event or state. express The Middle The probability of an event or state. , Having the same quantity A possible outcome, and the relationships between them The order Wasserstein distance is defined as: ； In the formula, express and Between Wasserstein distance of order Let be the order of the distance, which is a real number and satisfies . , middle for and All joint distributions of , and their marginal distributions are respectively and , Let the set of all such joint distributions be represented. This represents the infimum, which is the minimum value that can be reached among all possible joint distributions. Represents the joint distribution The mathematical expectation, From Random variable pairs drawn from the sample. Representing variables and variables Norm distance between Ensure that the expectation exists, that is, the distribution has a finite value. Step moments; for each joint distribution Calculate all sampling distances Mathematical expectation ; A Hadamard matrix is a special type of orthogonal matrix where all elements are either +1 or -1, and the rows and columns are mutually orthogonal. The Hadamard matrix is recursively defined as follows: ； The size of the Hadamard matrix is matrix order an integer power of 2 Indicates the order is The Hadamard matrix, Represents a positive integer, used in exponential expression, in the recursive definition. Let the current index be such that the matrix order is ; By integrating morphological gradient operations with the Hadamard matrix, an improved gradient morphological spectrum based on the Hadamard matrix, called HGPS, is proposed. This improved gradient morphological spectrum utilizes the rectangular wave structure elements generated by the Hadamard matrix, which expands the diversity of feature extraction and improves the robustness of signal processing. For the original one-dimensional signal ,in Representing the real number field, the original one-dimensional signal The improved gradient morphology spectrum is defined as follows: ； In the formula, For the selected Hadamard matrix, Represents the original one-dimensional signal Given the Hadamard matrix The morphological gradient area spectrum value is a scalar value used to quantize the original one-dimensional signal. At a specific scale and row index Local mutation characteristics, Denotes the scale parameter of the matrix, where Represents all integers. The index for the selected row number. Indicates the use of the Hadamard matrix The corresponding structuring element corresponds to the original one-dimensional signal. The resulting function obtained after performing morphological gradient operations. This is an area operator that calculates the absolute area of the morphological gradient result; The improved gradient morphology spectrum captures the morphological differences of signals at multiple scales by using the rectangular wave structure elements corresponding to Hadamard matrices of different orders, thereby achieving a refined characterization of the local abrupt change features of the signal. The improved K-means clustering algorithm enhances the ability to identify overlapping distribution regions by introducing a density-weighted strategy. In specific implementation, if the Wasserstein distance between a certain improved gradient morphology spectrum and the improved gradient morphology spectrum of the cluster center is smaller, and there are several samples with similar distribution to this improved gradient morphology spectrum nearby, then the weight is increased during the iterative optimization process; otherwise, it is decreased. A set of improved gradient morphological spectra based on the Hadamard matrix for different signals ,in Representing the Each improved gradient morphology spectrum is a... dimensional vector, express dimensional real number field, Determined by the feature extraction process; The process of improving the K-means clustering algorithm is as follows: S31: Random selection Define an initial cluster center set. ,in It refers to the number of clusters, that is, the number of clusters into which the data is to be divided. Representing the The initial center of each cluster; S32: Compute Set The Wasserstein distance between each improved gradient morphology spectrum and the improved gradient morphology spectrum of each cluster center is used to assign each improved gradient morphology spectrum to the nearest cluster center. S33: Calculate local density weights: ； In the formula, Local density weights are used to calculate the first... The improved gradient morphology spectrum and the first The weights between the improved gradient morphology spectrum of the cluster centers Indicates the first The improved gradient morphology spectrum and the first The square of the Wasserstein distance between the improved gradient morphological spectra of the cluster centers For clusters The average of the squared Wasserstein distances between all improved gradient morphological spectra and the improved gradient morphological spectra of the cluster centers. It is an exponential function; S34: Update cluster center: ； In the formula, at this time For the updated number Cluster centers, This represents the parameters that minimize the objective function; here, it's used to find the optimal cluster centers. Indicates the first Improved gradient morphology spectrum of a signal exist A probability distribution space with finite second moments over the real number field. Indicates the first Sum the improved gradient morphology spectra of all clusters. To be assigned to the The number of improved gradient morphology spectra for each cluster, Indicates assignment to the first The first cluster An improved gradient morphology spectrum Indicates the first The improved gradient morphology spectrum and the first The th cluster The square of the Wasserstein distance between each improved gradient morphological spectrum; S35: Iterate through steps S32 to S34 until convergence, i.e., the cluster centers do not change significantly; Through the above steps, the improved K-means clustering algorithm not only fully utilizes the advantages of Wasserstein distance in measuring distribution differences, but also improves the adaptability of the K-means clustering algorithm to complex distributions through a density-weighted strategy, thus exhibiting higher accuracy and stability in signal classification tasks.
4. The method for detecting high-resistivity grounding faults in distribution networks based on partial differential morphology according to claim 3, characterized in that, In step S4, a high-resistance grounding fault in the distribution network is detected, as detailed below: When a disturbance occurs in the measurement signal of the distribution network, but does not reach the protection action threshold, the disturbance signal is recorded and uploaded to the main station for fault identification. Specifically, a partial differential morphology optimization model and a partial differential morphology discretization operator are used to calculate the partial differential morphology spectrum of the disturbance signal, constructing a dataset containing multiple partial differential morphology spectra. Cluster analysis is performed on the obtained partial differential morphology spectra, calculating the Wasserstein distance between each partial differential morphology spectrum in the dataset. An improved K-means clustering algorithm is used to classify the partial differential morphology spectrum of the obtained disturbance signal into two categories: normal or disturbance signals and high-resistance ground fault signals. The partial differential morphology spectrum of the disturbance signal is assigned to the category closest to the centroid of the category, distinguishing between normal or disturbance signals and high-resistance ground fault signals in real time, and detecting whether a high-resistance ground fault has occurred in the distribution network.