Multi-dimensional single-phase grounding typical waveform extraction method based on multi-scale space-time isometric mapping

Abstract

The present application relates to the field of artificial intelligence and power distribution network single-phase grounding, and particularly relates to a multi-dimensional single-phase grounding typical waveform extraction method based on multi-scale space-time isometric mapping. The method comprises the following steps: S1, constructing a single-phase grounding waveform; S2, single-phase grounding waveform segment coarse-grained positioning; S3, single-phase grounding multi-dimensional mapping; S4, single-phase grounding typical waveform selection. The method can effectively reduce the dimension of multi-dimensional electrical quantity time series, can retain key features, analyze the distribution of waveform data after dimension reduction, select typical waveforms representative of faults, and reduce the dimension of multi-dimensional electrical quantity sequence data from the time and space angles. The present application can be well used for single-phase grounding fault detection of power distribution network equipment.

Description

Technical Field

[0001] This invention relates to the fields of artificial intelligence and single-phase grounding in power distribution networks, specifically to a method for extracting typical waveforms of multi-dimensional single-phase grounding based on multi-scale spatiotemporal isometric mapping. Background Technology

[0002] The power distribution network is closely connected to users, with a complex structure and operating conditions, making it prone to various faults. Single-phase grounding faults account for as much as 70% to 80% of these faults, making them the most common type of fault in power distribution systems. Single-phase grounding faults are often caused by factors such as tree obstructions, single-phase breakdown of insulators on distribution lines, and single-phase wire breaks. If these faults are not handled promptly, they can lead to serious consequences such as equipment insulation failure, personal injury, and fires. Therefore, timely detection of single-phase grounding faults is of paramount importance.

[0003] With the development of power distribution automation equipment technology, integrated primary and secondary equipment has gradually become the mainstream model for power distribution automation. The application of related equipment has greatly improved the standardization and integration level of power distribution automation equipment and increased the efficiency of on-site installation and commissioning. However, it has also brought certain technical challenges to the corresponding quality control work. For example, the testing approach is gradually shifting from independent testing of primary and secondary equipment to overall testing; the application of new technologies has put forward targeted testing requirements; and the control requirements for the single-phase grounding fault handling performance of individual equipment have increased to a certain extent. To address these issues, it is necessary to strengthen the testing and verification of the overall performance while maintaining the control of typical problems of traditional primary and secondary equipment. This poses a significant challenge to current testing and verification methods.

[0004] Single-phase grounding faults in distribution networks are mostly characterized by their evolving and gradual progression. Due to the complexity of fault conditions in distribution networks, numerous on-site operational interference factors, and limitations in device principles and processes, fault characteristics are characterized by rapid changes and abundant interference. This presents challenges in designing fault detection algorithms and related components, and also makes testing the quality of distribution automation equipment time-consuming and labor-intensive, failing to meet the current demands for intelligent distribution networks. Therefore, selecting typical fault waveforms for detection and balancing the efficiency and coverage of equipment quality testing remains a major challenge.

[0005] The rapid development of machine learning technologies in recent years has provided conditions for the application of multi-dimensional time series processing techniques in single-phase grounding detection. Multi-dimensional time series processing technology analyzes the time-domain characteristics of collected waveform data, fully utilizing the temporal and spatial information in the original waveform data in an automated manner. It can extract typical waveform features from real-world test data, thereby assisting power distribution automation equipment in detecting single-phase grounding faults. Summary of the Invention

[0006] The purpose of this invention is to address the impact of dimensionality reduction mapping of multi-dimensional time-series data on other sub-tasks. It provides a method for extracting typical waveforms of multi-dimensional single-phase grounding faults based on multi-scale spatiotemporal isometric mapping. Utilizing artificial intelligence and machine learning techniques, a novel multi-scale spatiotemporal isometric mapping model is proposed to perform dimensionality reduction mapping of multi-dimensional single-phase grounding fault waveform data from both temporal and spatial perspectives. Typical waveform data is selected using a hierarchical squared equilibrium iterative reduction and a typical waveform extraction model. The proposed model has achieved significant results in extracting typical waveforms for real-world single-phase grounding fault detection and shows great promise for application in the field of single-phase grounding fault detection and testing.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for extracting typical waveforms of a multi-dimensional single-phase grounding event based on multi-scale spatiotemporal isometric mapping includes the following steps:

[0009] S1. Construct a single-phase grounding waveform.

[0010] By using dynamic model and full-scale experiments of active distribution networks, multi-dimensional time-domain data of observable electrical quantities from multiple sources under faults and disturbances are obtained to construct a basic single-phase grounding sample set;

[0011] S2, single-phase grounding waveform segment coarse-grained positioning

[0012] Taking into account the timing characteristics of the normal waveform segment, transient fault segment, and steady-state fault segment, 50% of the maximum amplitude of the zero-sequence current is used as the transient fault initiation condition. One cycle is taken forward to form the normal steady-state waveform segment; two cycles are taken backward to form the transient waveform segment and the steady-state waveform segment.

[0013] S3, Single-phase grounding multi-dimensional mapping

[0014] Multi-dimensional Time and Space Isometric Mapping (MDTS-IM) is used to reduce the dimensionality of the extracted features by mapping them to the model in both the time and space domains.

[0015] S4. Typical waveform selection for single-phase grounding

[0016] A clustered electrical quantity feature tree is established, with nodes representing clustered electrical quantity features. The tree is classified using a hierarchical squared equilibrium iterative reduction and clustering method. The number of categories is determined based on similarity and the requirements of typical waveforms. The center waveform is selected as the typical waveform based on compactness.

[0017] Furthermore, the specific steps of step S1 are as follows:

[0018] S1-1. In a real-world distribution network demonstration scenario, conduct tests and experiments in a real environment to obtain fault data; including simulating real distribution network overhead lines and cable lines in a real-world demonstration field.

[0019] S1-2. On the physical dynamic simulation platform, use a voltage setting lower than the real scenario to conduct simulation tests. The simulation tests require simulating changes in the distribution network test environment; for example, proportionally reducing a 10 kV distribution network to 690 V.

[0020] Changing the distribution network test environment refers to altering the distribution network environment, including the neutral grounding method, system current capacity, unbalance, fault transition resistance, grounding medium, fault location, and fault closing angle. Among these, multi-dimensional time-domain data of electrical quantities under different grounding medium fault conditions can only be measured in a full-scale experimental field. Multi-dimensional time-domain data of electrical quantities under other disturbance conditions can be measured through both dynamic model platforms and full-scale experimental fields. By using relevant instruments to measure, sample, and calculate different distribution network environments, eight-dimensional time-series electrical data can be obtained, including the ABC three-phase current, zero-sequence current, ABC three-phase voltage, and zero-sequence voltage.

[0021] According to different neutral point grounding methods, they are divided into ungrounded, arc suppression coil grounding, and low resistance grounding.

[0022] The system current capacity is divided into 8A, 60A, 120A and 200A; where the system current capacity is the current when a single-phase ground fault occurs.

[0023] Based on different fault transition resistances, they are classified as stable, intermittent, 500, 1kΩ, 2kΩ, and 5kΩ. The fault transition resistance refers to the resistance between the transmission line and the zero potential point after a grounding fault in the transmission line.

[0024] Based on the different grounding media, they are classified as grassland, mud, asphalt, sand and gravel, trees, water and cement.

[0025] Based on the location of the fault, it can be divided into initial fault, intermediate fault, and final fault.

[0026] The fault closing angle is divided into 0°, 30°, 45°, 60° and 90°. The fault closing angle is the phase angle of the reference phase voltage at the moment of fault closing. Since the phases of the three-phase voltage and current are inconsistent, the closing angle is related to the fault type. In this invention, single-phase faults are calculated based on the fault phase.

[0027] S1-3. Collect multidimensional observable electrical quantity time-frequency characteristics under different initial conditions in a real-world distribution network scenario and a physical dynamic simulation platform. The different initial conditions refer to the transformation of the distribution network test environment described in step S1-2, including setting three different neutral grounding methods, setting seven different grounding media, and setting three types of fault transition resistance: stable, intermittent, and metallic. The time-frequency characteristics are divided into eight dimensions, including three-phase currents and three-phase voltages (A, B, and C), as well as zero-sequence current and zero-sequence voltage.

[0028] Furthermore, the specific steps of step S2, coarse-grained positioning of the single-phase grounding waveform segment, include the following:

[0029] S2-1. Extract the zero-sequence current dimension sequence from the multi-dimensional time-frequency sequence, obtain the maximum value of the zero-sequence current, and take the first 5% of the maximum value as the fault occurrence signal point.

[0030] S2-2. Taking the fault occurrence signal point described in step S2-1 as the origin, one cycle length is taken forward, which is called the normal waveform representative segment; two cycles lengths are taken backward, where the first cycle is the waveform cycle containing the transient fault, which is called the transient waveform representative segment, and the second cycle is the representative of the steady-state fault waveform segment, which is called the steady-state fault waveform representative segment.

[0031] At this point, step S2-2 uses preliminary positioning to remove redundant data from the normal waveform segment and the steady-state fault waveform segment, resulting in a waveform representative segment that combines the normal waveform representative segment, the transient waveform representative segment, and the steady-state fault waveform representative segment.

[0032] Furthermore, step S3, which involves dimensionality reduction mapping of the extracted features to the model from the time domain, specifically includes the following steps:

[0033] S3-1-1. The multidimensional electrical quantity time series data is spatially segmented into 8 dimensions, with each of the 8 dimensions forming a corresponding data matrix. These matrices are then combined to form the total sample set, D.

[0034] D = {X} Ia ,X Ib ,X Ic ,X I0 ,X Ua ,X Ub ,X Uc ,X U0}

[0035] Among them, the data matrix X has 8 dimensions. Ia ,X Ib ,X Ic ,X I0 ,X Ua ,X Ub ,X Uc,X U0 These are the phase A current matrix, phase B current matrix, phase C current matrix, zero-sequence current matrix, phase A voltage matrix, phase B voltage matrix, phase C voltage matrix, and zero-sequence voltage matrix, respectively. Let the phase A current matrix X... Ia For example, it contains the A-phase current time series of all samples:

[0036]

[0037] For sample x i The time series corresponding to the A-phase current dimension after 8-dimensional spatial segmentation. n is the total number of samples. and This is a way of expressing the dimension of a variable, representing a one-dimensional vector with a dimension of 1200 and a two-dimensional matrix with a dimension of n×1200, respectively.

[0038] The above method is used to perform time-angle metric mapping on the eight spatially partitioned matrices;

[0039] S3-1-2. For the eight dimensions, the method of connecting graphs is used to approximate the geodesic distance. Specifically, the k nearest points of each time dimension sequence are set, and a connecting graph is constructed. In this connecting graph, each data point is directly connected to the k nearest points, but not directly connected to other points. After constructing the adjacency matrix, the shortest path between any two points in the graph is found to replace the geodesic distance.

[0040] S3-1-3. Construct the time series distance matrix in the original space using the shortest path between two time series in the adjacency matrix; taking the A-phase current dimension as an example, calculate the inner product matrix B of the A-phase current dimension. Ia :

[0041]

[0042]

[0043]

[0044] in, The term in the i-th row and j-th column of the inner product matrix represents the i-th sample. and the j-th sample The inner product between them; n is the number of samples; For the i-th sample and the j-th sample The square of the distance, the distance function dist uses Euclidean distance.

[0045] S3-1-4, Matrix B of the above time series Ia Perform eigenvalue decomposition to obtain the time series eigenvalue matrix Λ Ia and time series eigenvector matrix V Ia The solution process is as follows:

[0046]

[0047] Where, X′ Ia The matrix after time dimension reduction; X′ Ia T Let X′ Ia transpose; Λ Ia V is a diagonal matrix composed of eigenvalues; Ia The eigenvectors corresponding to the eigenvalues; For V Ia The transpose of .

[0048] The matrix Y after time dimension reduction Ia The eigenvalue matrix Λ can be calculated based on the specific characteristics. Ia and eigenvector matrix V Ia Find:

[0049]

[0050] S3-1-5, Selecting the eigenvalue matrix Λ Ia The largest k1 term in V, and from V Ia By selecting the corresponding feature vector, the mapping and dimensionality reduction of the time dimension are achieved;

[0051] Taking the dimension matrix of phase A current as an example, the dimension-reduced phase A current matrix V is obtained. Ia :

[0052]

[0053] in, For Y Ia The A-phase current sequence of the i-th sample. k1 is the dimension after time dimensionality reduction, which can be preset and is set to 2 in this invention; this process reduces the dimension matrix of phase A current from 1200 dimensions to 2 dimensions.

[0054] Dimensionality reduction along the time dimension is performed on each of the eight data subsets, resulting in time-dimension-reduced matrices Y. Ia Y Ib Y Ic Y I0 Y Ua Y Ub Y Uc YU0 Each matrix belongs to

[0055] Furthermore, step S3, which involves dimensionality reduction mapping of the extracted features to the model from the spatial domain, specifically includes the following steps:

[0056] After stretching the data through time dimension reduction into a one-dimensional vector, spatial dimension reduction is then performed; the data matrix Y after stretching the data into a one-dimensional vector is:

[0057]

[0058] in, Indicates that Y Ia and Y Ib Concatenate the 8 matrices row by row. Perform dimensionality reduction on matrix Y.

[0059] Y = [y1, y2, ..., y i ,...,y n ] T

[0060] Among them, y i For the i-th sample after time-dimension reduction mapping,

[0061] S3-2-1, Calculate the inner product matrix B of data points in the spatial angle data space. s The distance is calculated using Euclidean distance.

[0062]

[0063]

[0064]

[0065] Among them, s ij Let B be the inner product matrix. s The item in the i-th row and j-th column; n is the number of samples; For the i-th sample y i and the j-th sample y j The square of the distance, the distance function dist uses Euclidean distance.

[0066] Perform eigenvalue decomposition on the matrix to obtain the eigenvalue matrix Λ and the eigenvector matrix V.

[0067]

[0068] Where Z is the sample matrix after dimensionality reduction in space; Z TFor the transpose of Z; Λ S V is a diagonal matrix composed of eigenvalues; s The eigenvectors corresponding to the eigenvalues; For V s The transpose of .

[0069] The matrix Z after dimensionality reduction can be derived from the eigenvalue matrix Λ s and eigenvector matrix V s Find:

[0070]

[0071] Take the eigenvalue matrix Λ s The eigenvectors corresponding to the largest k2-phase sums are used to achieve dimensionality reduction in the spatial dimension, denoted as Z:

[0072]

[0073] in, k1 is the dimension after time dimensionality reduction, which can be preset and is set to 2 in this invention; k2 is the dimension of the space after dimensionality reduction. For ease of visualization, it is set to 3 in this invention. This process reduces the matrix Y from 16 dimensions to 3 dimensions.

[0074] Furthermore, the specific steps of the clustering method for single-phase grounding waveforms described in step S4 are as follows:

[0075] S4-1-1. Read all electrical quantity data in sequence and build a clustered electrical quantity feature tree. Each node of the tree is composed of clustered electrical quantity features. The clustered electrical quantity feature is a triplet, i.e., F = (N, L, M).

[0076] Where F represents the clustered electrical quantity feature; N represents the number of samples in this clustered electrical quantity feature; L represents the sum vector of each feature dimension of the sample data points in the clustered electrical quantity feature; and M represents the sum of squares of each feature dimension of the sample points in this clustered electrical quantity feature.

[0077] S4-1-2. Filter the clustered electrical quantity feature tree and remove some abnormal clustered electrical quantity feature nodes, which are generally nodes with very few sample points.

[0078] S4-1-3. Using the centroids of all clustered electrical quantity feature nodes in the generated clustered electrical quantity feature tree as the initial centroids, cluster the samples from far to near.

[0079] Furthermore, the specific steps for selecting the single-phase grounding waveform in step S4 are as follows:

[0080] S4-2-1. Visualize the clustering results: visualize two-dimensional data as a two-dimensional graph and three-dimensional data as a three-dimensional graph.

[0081] S4-2-2 Select the waveform data closest to the center point in each category as the typical waveform.

[0082] The selected typical waveform satisfies the mean clustering of all other waveform data points in that category.

[0083] The typical waveform formula is selected as follows:

[0084]

[0085] Where, x choose The selected typical waveform sample points; C represents the category; the function dist is the distance function, which uses Euclidean distance here.

[0086] The final selected waveform can represent most of the fault waveform information in this category.

[0087] Beneficial effects:

[0088] 1. The present invention employs a multi-scale spatiotemporal isometric mapping method, which can effectively reduce the dimensionality of multidimensional electrical quantity time series while preserving key features.

[0089] 2. The present invention uses a hierarchical squared balanced iterative reduction and clustering method to perform waveform clustering, which can effectively analyze the distribution of waveform data after dimensionality reduction.

[0090] 3. This invention proposes a method for selecting the center point as the typical waveform based on dimensionality reduction clustering, which can select typical waveforms that are representative of the fault.

[0091] 4. This invention proposes to reduce the dimensionality of multidimensional electrical quantity sequence data by using both temporal and spatial perspectives.

[0092] 5. This invention defines and implements a complete method for extracting typical waveforms of single-phase grounding in distribution networks, which is used for single-phase grounding fault detection in distribution network equipment. Attached Figure Description

[0093] Figure 1 A flowchart of a method for extracting typical waveforms of a multidimensional single-phase grounding event based on multi-scale spatiotemporal isometric mapping;

[0094] Figure 2 A flowchart for constructing a basic single-phase grounding sample set;

[0095] Figure 3 A flowchart for coarse-grained positioning of a single-phase grounding waveform segment;

[0096] Figure 4A flowchart for multi-dimensional mapping of single-phase grounding;

[0097] Figure 5 A flowchart for selecting a typical waveform for single-phase grounding;

[0098] Figure 6 This is a schematic diagram of a multidimensional single-phase grounding typical waveform extraction device based on multi-scale spatiotemporal isometric mapping;

[0099] Figure 7 A schematic diagram of the structure of a multi-dimensional single-phase grounding typical waveform extraction model based on multi-scale spatiotemporal isometric mapping;

[0100] Figure 8 A partial screenshot of a representative waveform segment obtained after coarse-grained localization of a single-phase grounding waveform segment.

[0101] Figure 9 This is a schematic diagram of the fault waveform clustering results;

[0102] Figure 10 This is a schematic diagram of the typical waveform selection results. Detailed Implementation

[0103] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0104] Terminology Explanation:

[0105] Single-phase grounding is a common fault in power systems, indicating that a short circuit has occurred between one phase of a three-phase system and the ground.

[0106] Eigenvectors are an important concept in matrix theory with wide applications. Mathematically, an eigenvector of a linear transformation is a non-degenerate vector whose direction remains unchanged under the transformation.

[0107] like Figure 1 As shown, the specific steps of the method flow of the present invention are as follows:

[0108] Step 1: Constructing a single-phase grounding waveform.

[0109] Using dynamic and full-scale experiments on active power distribution networks, multi-source observable electrical quantities in multiple dimensions are acquired in the time domain to construct a basic single-phase grounding sample set, such as... Figure 2 As shown.

[0110] In a real-world distribution network demonstration scenario, tests and experiments are conducted in a realistic environment to obtain fault data. The demonstration site, covering 7,000 square meters, can simulate 10 kilometers of real distribution network overhead and cable lines. On the physical dynamic simulation platform, using voltage settings lower than in real-world scenarios, over 400 distribution network test environments are simulated.

[0111] In this invention, the tested distribution network environment changes include: neutral grounding method, system current capacity, unbalance, fault transition resistance, grounding medium, fault location, and fault closing angle. System current capacity refers to the current during a single-phase ground fault; transition resistance refers to the resistance between the transmission line and the zero potential point after a ground fault; fault closing angle is the phase angle of the reference phase voltage at the moment of fault closing. Based on the neutral grounding method, it can be divided into ungrounded, arc-suppression coil grounded, and low-resistance grounded systems. Based on the system current capacity, it can be divided into 8A, 60A, 120A, and 200A. Based on the unbalance, it can be divided into 0%, 3%, and 5%. Based on the fault transition resistance, it can be divided into stable, intermittent, 500, 1kΩ, 2kΩ, and 5kΩ systems. Based on the grounding medium, it can be divided into grassland, mud, asphalt, gravel, trees, water, and cement systems. Based on the fault location, it can be divided into initial fault, middle fault, and final fault systems. Based on the fault closing angle, it can be divided into 0°, 30°, 45°, 60°, and 90°. Among them, the multidimensional time-domain data of electrical quantities under different grounding medium fault conditions can only be measured from the real field, while the multidimensional time-domain data of electrical quantities under other disturbance conditions can be measured through the dynamic model platform and the real field.

[0112] This invention relies on a dynamic model platform and a real-world experimental field to collect the time-frequency characteristics of multidimensional observable electrical quantities under different initial conditions. The different initial conditions refer to the transformation distribution network test environment described in S1-2, including setting three different neutral grounding methods, setting seven different grounding media, and setting three types of fault transition resistances: stable, intermittent, and metallic. The time-frequency characteristics are divided into eight dimensions, including three-phase currents and three-phase voltages (A, B, and C), as well as zero-sequence current and zero-sequence voltage.

[0113] Step 2: Coarse-grained positioning of single-phase grounding waveform segments.

[0114] For each multidimensional electrical quantity time-frequency data, it experiences multiple normal waveform segments in the initial time period, at which time the distribution network is in normal operation. At a certain moment, fault and disturbance conditions occur, and the waveform changes instantaneously. At this time, the waveform segment shows a short period of drastic change, which is the transient fault waveform segment. After experiencing the transient fault waveform segment, the waveform gradually tends to stabilize and re-emerges periodically, but at this time the fault continues to exist, which is the steady-state fault waveform segment.

[0115] Different fault and disturbance conditions affect the characteristics of transient and steady-state fault waveform segments in multidimensional electrical quantity data. Complete multidimensional electrical quantity data exhibits relatively long normal and steady-state waveform segments, resulting in significant redundancy when used for single-phase grounding fault analysis. In this invention, preliminary localization is performed on the original electrical quantity data to locate waveforms containing normal, transient, and steady-state fault waveform segments for comprehensive analysis of transient and steady-state faults.

[0116] The location method of this invention is as follows: extract the zero-sequence current dimension sequence from the multi-dimensional time-frequency sequence, obtain the maximum value of the zero-sequence current, and take 5% of the first time the maximum value is reached as the fault occurrence signal point. Taking the occurrence signal point as the origin, one cycle length is intercepted forward, called the normal waveform representative segment; two cycle lengths are intercepted backward, where the first cycle is the waveform cycle containing the transient fault, called the transient waveform representative segment, and the second cycle is used as the representative of the steady-state fault waveform segment, called the steady-state fault waveform representative segment.

[0117] The waveform representative segment, which combines the located normal waveform representative segment, transient waveform representative segment, and steady-state fault waveform representative segment, is as follows: Figure 8 As shown (taking zero-sequence voltage, zero-sequence current, and phase A voltage as an example).

[0118] Preliminary localization removes redundant data from the normal waveform segments and steady-state fault segments in the original waveform data, thus making the located waveforms more representative. The purpose of this invention is to obtain representative typical waveform segments by clustering multidimensional waveform data under various fault and disturbance conditions.

[0119] like Figure 3 As shown, a dataset can be set up based on the multidimensional time-series data of the waveform segments after preliminary positioning for further analysis.

[0120] Step 3: Multi-dimensional mapping of single-phase grounding.

[0121] The raw electrical quantities represent waveform time-series data that are long and multi-dimensional, making direct clustering impossible. Simply connecting these multi-dimensional data will lead to the curse of dimensionality, resulting in an exponential increase in computation and excessively sparse data points in space, making it difficult to extract typical waveforms. Therefore, dimensionality reduction mapping is necessary. Mapping independently along the time dimension ignores the correlations between multi-dimensional time series.

[0122] Reference Figure 4This invention addresses the problems existing in the current task by proposing corresponding improvement methods. Step three uses Multi-dimensional Time and Space Isometric Mapping (MDTS-IM) to perform dimensionality reduction mapping on the extracted features from the time and space domains to the model.

[0123] The time dimension mapping steps include:

[0124] For electrical quantity time-frequency data, the period is 0.02s, the frequency is 50Hz, and the sampling frequency during raw data acquisition is 20000Hz, so each period contains 400 sampling points. Therefore, for the three-cycle representative waveform segment for positioning, each data point has 1200 dimensions in time and 8 dimensions in space, including the three-phase current and three-phase voltage of A, B, and C, as well as the zero-sequence current and zero-sequence voltage.

[0125] The electrical quantity data D is represented as follows:

[0126] D = {x1, x2, ..., x} n}

[0127] Where n is the number of samples; x i For the i-th electrical quantity data sample

[0128] Each electrical quantity data sample x i It can be represented as:

[0129]

[0130] Among them, each electrical quantity data sample x i There are 8 dimensions, indicated by superscripts. The waveform time series length for each dimension is 1200.

[0131] The multidimensional electrical quantity time series data is spatially segmented into 8 dimensions, with each of the 8 dimensions forming a corresponding data matrix. These matrices are then combined to form the overall sample set, D.

[0132] D = {X} Ia ,X Ib ,x Ic ,x I0 ,x Ua ,X Ub ,x Uc ,X U0}

[0133] Among them, the data matrix X has 8 dimensions. Ia ,X Ib ,X Ic ,X I0 ,X Ua ,XUb ,X Uc ,X U0 These are the phase A current matrix, phase B current matrix, phase C current matrix, zero-sequence current matrix, phase A voltage matrix, phase B voltage matrix, phase C voltage matrix, and zero-sequence voltage matrix, respectively. Let the phase A current matrix X... Ia For example, it contains the A-phase current time series of all samples:

[0134]

[0135] For sample x i The time series corresponding to the A-phase current dimension after 8-dimensional spatial segmentation. n is the total number of samples.

[0136] Assuming the original time series data follows the characteristics of a manifold distribution, the geodesic distance between points is used instead of the traditional Euclidean distance to represent the actual distance between two data points.

[0137] Because geodesic distance is difficult to calculate directly, a connected graph approach is used to approximate it. A connected graph is constructed by identifying the k nearest neighbors for each time dimension sequence. In this graph, the sum of the distances between each data point and its k nearest neighbors are directly connected, while other points are not directly connected. After constructing the adjacency matrix, the shortest path between any two points in the graph is calculated and used to replace the geodesic distance.

[0138] Construct the time series distance matrix in the original space using the shortest paths between two time series in the adjacency matrix; taking the A-phase current dimension subset as an example, calculate the inner product matrix B of the A-phase current dimension subset. Ia ,

[0139]

[0140]

[0141]

[0142] in, The term in the i-th row and j-th column of the inner product matrix represents the i-th sample. and the j-th sample The inner product between them; n is the number of samples; For the i-th sample and the j-th sample The square of the distance, the distance function dist uses Euclidean distance.

[0143] For the matrix B of the above time series IaPerform eigenvalue decomposition to obtain the time series eigenvalue matrix Λ Ia and time series eigenvector matrix V Ia The solution process is as follows:

[0144]

[0145] Among them, Y Ia The matrix after dimensionality reduction in the time dimension; Y Ia T For Y Ia transpose; Λ Ia V is a diagonal matrix composed of eigenvalues; Ia V is the eigenvector corresponding to the eigenvalue; la T For V Ia The transpose of .

[0146] The matrix Y after time dimension reduction Ia Based on the eigenvalue matrix Λ Ia and eigenvector matrix V Ia Find:

[0147]

[0148] Select the eigenvalue matrix Λ Ia The largest k1 term in V, and from V Ia By selecting the corresponding eigenvectors, the mapping and dimensionality reduction of the time dimension are achieved. Taking the A-phase current dimension subset as an example, and the A-phase current dimension matrix as an example, the dimensionality-reduced A-phase current matrix Y is obtained. Ia :

[0149]

[0150] in, k1 is the dimension after time dimensionality reduction, which can be preset and is set to 2 in this invention; For Y Ia The A-phase current sequence of the i-th sample.

[0151] Dimensionality reduction along the time dimension is performed on each of the eight data subsets, resulting in time-dimension-reduced matrices Y. Ia Y Ib Y Ic Y I0 Y Ua Y Ub Y Uc Y U0 Each matrix belongs to

[0152] After stretching the data through time dimension reduction into a one-dimensional vector, spatial dimension reduction is then performed; the data matrix Y after stretching the data into a one-dimensional vector is:

[0153]

[0154] in, This indicates that Y Ia and Y Ib Concatenate line by line Perform spatial dimensionality reduction on dataset Y.

[0155] Y = [y1, y2, ..., y i ,...,y n ] T

[0156] Among them, y i For the i-th sample after time-dimension reduction mapping,

[0157] Calculate the inner product matrix B of data points in the spatial angle data space. s .

[0158]

[0159]

[0160]

[0161] Among them, s ij Let B be the inner product matrix. s The item in the i-th row and j-th column; n is the number of samples; For the i-th sample y i and the j-th sample y j The square of the distance, the distance function dist uses Euclidean distance.

[0162] For matrix B s Perform eigenvalue decomposition to obtain the eigenvalue matrix Λ s and eigenvector matrix V s .

[0163] B s =ZZ T =V s Λ s V s T

[0164] Where Z is the sample matrix after dimensionality reduction in space; Z T For the transpose of Z; Λ s V is a diagonal matrix composed of eigenvalues; sV is the eigenvector corresponding to the eigenvalue; s T For V s The transpose of .

[0165] The matrix Z after dimensionality reduction can be derived from the eigenvalue matrix Λ s and eigenvector matrix V s Find:

[0166]

[0167] Take the eigenvalue matrix Λ s The eigenvectors corresponding to the largest k2-phase sums are used to achieve dimensionality reduction in the spatial dimension, denoted as Z:

[0168]

[0169] in, k1 is the dimension after time dimensionality reduction, which can be preset and is set to 2 in this invention; k2 is the dimension of the space after dimensionality reduction, which is set to 3 in this invention for ease of visualization.

[0170] Step 4: Single-phase grounding waveform clustering and typical waveform selection.

[0171] Reference Figure 5 Before extracting typical fault waveforms, hierarchical squared equilibrium iterative reduction and cluster analysis are performed on the data after dimensionality reduction by MDTS-IM to analyze the distribution characteristics of fault waveforms.

[0172] Construct a clustered electrical quantity feature tree, where each node of the tree consists of clustered electrical quantity features. Each clustered electrical quantity feature is a triplet.

[0173] F = (N, L, M)

[0174] Where F represents the clustered electrical quantity feature; N represents the number of samples in this clustered electrical quantity feature; L represents the sum vector of each feature dimension of the sample data points in the clustered electrical quantity feature; and M represents the sum of squares of each feature dimension of the sample points in this clustered electrical quantity feature.

[0175] The clustered electrical quantity feature tree has two properties: first, non-leaf nodes in the clustered electrical quantity feature tree have descendants; second, non-leaf nodes store the sum of the clustered electrical quantity features of their descendants. The clustered electrical quantity feature tree has three parameters: the maximum number of non-leaf nodes, the maximum number of clustered electrical quantity features contained in each leaf node, and the maximum radius threshold for each clustered electrical quantity feature in a leaf node.

[0176] First, all electrical quantity data are read in sequentially to build a clustered electrical quantity feature tree. The clustered electrical quantity feature tree is then filtered to remove some abnormal clustered electrical quantity feature nodes, which are generally nodes with very few sample points. Using the centroids of all clustered electrical quantity feature nodes in the generated clustered electrical quantity feature tree as the initial centroids, the samples are clustered from far to near.

[0177] This invention visualizes the clustering results, with two-dimensional data visualized as a two-dimensional graph and three-dimensional data visualized as a three-dimensional graph. The waveform data closest to the center point in each category is selected as the representative waveform. The selected representative waveform satisfies the condition that it is the closest to the average cluster of all other waveform data points in that category.

[0178] The typical waveform formula is selected as follows:

[0179]

[0180] Where, x choose The selected typical waveform sample points; C represents the category; the function dist is the distance function, which uses Euclidean distance here.

[0181] The waveforms selected in this invention represent most of the fault waveform information in this category. This can be seen from the visualized data.

[0182] Reference Figure 9 and Figure 10 Experimental results show that the method of this invention can effectively reduce dimensionality and cluster data. The waveform data of each category are closely distributed, indicating that the model of this invention can extract representative and typical waveforms.

[0183] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0184] Reference Figure 6 and Figure 7 A multi-dimensional single-phase grounding typical waveform extraction device based on multi-scale spatiotemporal isometric mapping includes:

[0185] The single-phase grounding waveform construction unit uses dynamic model and real-world experiments of active power distribution networks to obtain multi-dimensional time-domain data of multi-source observable electrical quantities under faults and disturbances, and constructs a basic single-phase grounding sample set.

[0186] The single-phase grounding waveform segment coarse-grained positioning unit comprehensively considers the timing characteristics of the normal waveform segment, transient fault segment and steady-state fault segment. It uses 5% of the maximum amplitude of the zero-sequence current as the transient fault initiation condition, and extracts one cycle forward to form the normal steady-state waveform segment, and extracts two cycles backward to form the transient waveform segment and the steady-state waveform segment.

[0187] The single-phase grounding multidimensional mapping unit performs dimensionality reduction mapping on the model from the time domain and the spatial domain by multi-scale time and space isometric mapping (MDTS-IM).

[0188] A typical waveform selection unit for single-phase grounding is established, and a clustered electrical quantity feature tree is constructed. The nodes are clustered electrical quantity features. The system classifies them using the hierarchical squared balance iterative reduction and clustering method. The number of categories is determined based on similarity and the requirements of typical waveforms. The center waveform is selected as the typical waveform using the compactness property.

[0189] Furthermore, the single-phase grounding multi-dimensional mapping unit also includes:

[0190] The time-angle mapping dimensionality reduction unit performs dimensionality reduction on time-dimensional sequence data. It constructs the time-series distance matrix in the original space by using the shortest path between two time series in the adjacency matrix, performs eigenvalue decomposition on the time-series matrix, selects the largest k1 item in the eigenvalue matrix, and selects the corresponding eigenvector. In this invention, k1 is set to 2.

[0191] The spatial angle mapping dimensionality reduction unit performs dimensionality reduction processing of spatial angles. It calculates the distance matrix of data points in the spatial angle data space, performs eigenvalue decomposition on the matrix to obtain the eigenvalue matrix and eigenvector matrix, and takes the eigenvectors corresponding to the largest k2 sums of the eigenvalue matrix, thereby realizing the dimensionality reduction of spatial angles. In this invention, k2 is set to 3.

[0192] Furthermore, the single-phase grounding typical waveform selection unit also includes:

[0193] The single-phase grounding clustering unit is responsible for grouping data that are relatively closely distributed into the same category to explore the distribution of the data.

[0194] The single-phase grounding typical waveform selection unit is responsible for selecting typical waveforms to cover fault characteristics.

[0195] A storage medium storing a plurality of instructions, which are loaded by a processor to execute the steps of the method described above.

[0196] An electronic device includes: the storage medium described above; and a processor for executing instructions in the storage medium.

Claims

1. A method for extracting typical waveforms of a multi-dimensional single-phase grounding event based on multi-scale spatiotemporal isometric mapping, characterized in that, Includes the following steps: S1. Construct a single-phase grounding waveform. Using dynamic and full-scale experiments on active power distribution networks, multi-dimensional time-domain data of observable electrical quantities from multiple sources under faults and disturbances are obtained to construct a basic single-phase grounding sample set. S2, single-phase grounding waveform segment coarse-grained positioning Taking into account the timing characteristics of the normal waveform segment, transient fault segment, and steady-state fault segment, 50% of the maximum amplitude of the zero-sequence current is used as the transient fault initiation condition. One cycle is taken forward to form the normal steady-state waveform segment; two cycles are taken backward to form the transient waveform segment and the steady-state waveform segment. S3, Single-phase grounding multi-dimensional mapping By using the multi-scale spatiotemporal isometric mapping MDTS-IM, the extracted features are dimensionality-reduced and mapped to the model in both the temporal and spatial domains. S4. Typical waveform selection for single-phase grounding A clustered electrical quantity feature tree is established, with nodes representing clustered electrical quantity features. The tree is classified using a hierarchical squared equilibrium iterative reduction and clustering method. The number of categories is determined based on similarity and the requirements of typical waveforms. The center waveform is selected as the typical waveform based on compactness. Step S3, which involves dimensionality reduction mapping of the extracted features to the model in the time domain, specifically includes the following steps: S3-1-1. The multidimensional electrical quantity time-series data is spatially segmented into 8 dimensions, with each of the 8 dimensions forming a corresponding data matrix. These matrices are then combined to form a total sample set. for: ； Among them, the data matrix has 8 dimensions. These are the phase A current matrix, phase B current matrix, phase C current matrix, zero-sequence current matrix, phase A voltage matrix, phase B voltage matrix, phase C voltage matrix, and zero-sequence voltage matrix, respectively; with the phase A current matrix as an example. For example, it contains the A-phase current time series of all samples: ； For the sample The time series corresponding to the A-phase current dimension after 8-dimensional spatial segmentation. n is the total number of samples. ; The above method is used to perform time-angle metric mapping on the eight spatially partitioned matrices; S3-1-2. For the eight dimensions, the method of connecting graphs is used to approximate the geodesic distance. Specifically, the k nearest points of each time dimension sequence are set, and a connecting graph is constructed. In this connecting graph, each data point is directly connected to the k nearest points, but not directly connected to other points. After constructing the adjacency matrix, the shortest path between any two points in the graph is found to replace the geodesic distance. S3-1-3. Construct the time series distance matrix in the original space using the shortest paths between two time series in the adjacency matrix; taking the A-phase current dimension as an example, calculate the inner product matrix of the A-phase current dimension. : ； ； ； in, For the inner product matrix, the first... Line number The item in the column, i.e., the first Sample and the Sample The inner product between; The number of samples; For the first Sample and the Sample Square of distance, distance function Use Euclidean distance; S3-1-4, Matrix of the above time series Perform eigenvalue decomposition to obtain the time series eigenvalue matrix. and time series eigenvector matrix The solution process is as follows: ； in, The matrix after dimensionality reduction in the time dimension; for transpose; It is a diagonal matrix composed of eigenvalues; The eigenvectors corresponding to the eigenvalues; for transpose; Matrix after time dimension reduction The eigenvalue matrix can be calculated based on the specific features. and eigenvector matrix Find: ； S3-1-5. Selecting the eigenvalue matrix The largest Item, and from By selecting the corresponding feature vector, the mapping and dimensionality reduction of the time dimension are achieved; Taking the dimension matrix of phase A current as an example, the dimension-reduced phase A current matrix is ​​obtained. : ； in, ; for The Middle A-phase current sequence of a sample, ; The dimension after time reduction can be preset, and is set to 2 in this invention; this process reduces the dimension matrix of phase A current from 1200 dimensions to 2 dimensions. Dimensionality reduction along the time dimension is performed on each of the eight data subsets, resulting in the following time-dimension-reduced matrices: , , , , , , , Each matrix belongs to .

2. The method for extracting typical waveforms of a multi-dimensional single-phase grounding event based on multi-scale spatiotemporal isometric mapping according to claim 1, characterized in that, The specific steps of step S1 are as follows: S1-1. In a real-world distribution network demonstration scenario, conduct tests and experiments in a real environment to obtain fault data; including simulating real distribution network overhead lines and cable lines in a real-world demonstration field. S1-2. On the physical dynamic simulation platform, use a voltage setting lower than the real scenario to conduct simulation tests. The simulation tests require simulating changes in the distribution network test environment. Changing the distribution network test environment refers to altering the distribution network environment, including the neutral grounding method, system current capacity, unbalance, fault transition resistance, grounding medium, fault location, and fault closing angle. Among these, multi-dimensional time-domain data of electrical quantities under different grounding medium fault conditions can only be measured in a real-world experimental field. Multi-dimensional time-domain data of electrical quantities under other disturbance conditions can be measured through both dynamic model platforms and real-world experimental fields. By measuring, sampling, and calculating with relevant instruments for different distribution network environments, eight-dimensional time-series electrical data can be obtained, including the ABC three-phase current, zero-sequence current, ABC three-phase voltage, and zero-sequence voltage. According to the different neutral point grounding methods, they can be divided into ungrounded, arc suppression coil grounding, and low resistance grounding; The system current capacity is classified into 8A, 60A, 120A and 200A; where the system current capacity is the current when a single-phase ground fault occurs. According to different fault transition resistances, they are divided into stable, intermittent, 500, 1k, 2k and 5kΩ. The fault transition resistance refers to the resistance between the transmission line and the zero potential point after a grounding fault in the transmission line. Based on the different grounding media, they are classified as grassland, mud, asphalt, sand and gravel, trees, water and cement; Based on the location of the fault, it can be divided into initial fault, middle fault and final fault; The fault closing angle is divided into 0°, 30°, 45°, 60° and 90°. The fault closing angle is the phase angle of the reference phase voltage at the moment of the fault. Since the phases of the three-phase voltage and current are inconsistent, the closing angle is related to the fault type. In this invention, single-phase faults are calculated based on the fault phase. S1-3. Collect multidimensional observable electrical quantity time-frequency characteristics under different initial conditions in a real-world distribution network scenario and a physical dynamic simulation platform. The different initial conditions refer to the transformation of the distribution network test environment described in step S1-2, including setting three different neutral grounding methods, setting seven different grounding media, and setting three types of fault transition resistance: stable, intermittent, and metallic. The time-frequency characteristics are divided into eight dimensions, including three-phase currents and three-phase voltages (A, B, and C), as well as zero-sequence current and zero-sequence voltage.

3. The method for extracting typical waveforms of a multi-dimensional single-phase grounding event based on multi-scale spatiotemporal isometric mapping according to claim 2, characterized in that, The specific steps of step S2, coarse-grained positioning of the single-phase grounding waveform segment, include the following: S2-1. Extract the zero-sequence current dimension sequence from the multi-dimensional time-frequency sequence, obtain the maximum value of the zero-sequence current, and take the first 5% of the maximum value as the fault occurrence signal point. S2-2. Taking the fault occurrence signal point described in step S2-1 as the origin, one cycle length is taken forward, which is called the normal waveform representative segment; two cycles lengths are taken backward, where the first cycle is the waveform cycle containing the transient fault, which is called the transient waveform representative segment, and the second cycle is the representative of the steady-state fault waveform segment, which is called the steady-state fault waveform representative segment. At this point, step S2-2 uses preliminary positioning to remove redundant data from the normal waveform segment and the steady-state fault waveform segment, resulting in a waveform representative segment that combines the normal waveform representative segment, the transient waveform representative segment, and the steady-state fault waveform representative segment.

4. The method for extracting typical waveforms of a multi-dimensional single-phase grounding event based on multi-scale spatiotemporal isometric mapping according to claim 3, characterized in that, Step S3, which involves dimensionality reduction mapping of the extracted features to the model from the spatial domain, specifically includes the following steps: After the data has undergone time-dimension reduction and been stretched into a one-dimensional vector, spatial-dimension reduction is performed; the resulting data matrix after being stretched into a one-dimensional vector. for: ； in, Indicates will and Concatenate the 8 matrices row by row. ; For matrices Perform spatial dimension reduction; ； in, For the first The samples after time-dimension reduction mapping ; S3-2-1 Calculate the inner product matrix of data points in the spatial angle data space. The distance is calculated using Euclidean distance. ； ； ； in, The inner product matrix No. Line 1 Items in the list; The number of samples; For the first Sample and the Sample Square of distance, distance function Use Euclidean distance; Perform eigenvalue decomposition on the matrix to obtain the eigenvalue matrix. and eigenvector matrix ; ； in, This is the sample matrix after dimensionality reduction in space. for Transpose of; It is a diagonal matrix composed of eigenvalues; The eigenvectors corresponding to the eigenvalues; for Transpose of; Matrix after spatial dimension reduction Based on the eigenvalue matrix and eigenvector matrix Find: ； Take the eigenvalue matrix The largest front Each phase and its corresponding eigenvector are used to achieve dimensionality reduction in space. This dimensionality reduction is expressed as: : ； in, , The dimension after time reduction; , The dimension is the reduced dimension of the space, for easier visualization.

5. The method for extracting typical waveforms of a multi-dimensional single-phase grounding event based on multi-scale spatiotemporal isometric mapping according to claim 4, characterized in that, The specific steps of the clustering method for single-phase grounding waveforms described in step S4 are as follows: S4-1-1. Read all electrical quantity data sequentially and build a clustered electrical quantity feature tree. Each node of the tree consists of clustered electrical quantity features; each clustered electrical quantity feature is a triplet, i.e. ; in, Clustering electrical quantity characteristics; This represents the number of samples in the electrical quantity features of this cluster. This is the sum vector of each feature dimension of the clustered electrical quantity feature sample data points; This is the sum of squares for each feature dimension of all sample points in this cluster of electrical quantity features; S4-1-2. Filter the clustered electrical quantity feature tree and remove some abnormal clustered electrical quantity feature nodes; S4-1-3. Using the centroids of all clustered electrical quantity feature nodes in the generated clustered electrical quantity feature tree as the initial centroids, cluster the samples from far to near.

6. The method for extracting typical waveforms of a multi-dimensional single-phase grounding event based on multi-scale spatiotemporal isometric mapping according to claim 5, characterized in that, The specific steps for selecting the single-phase grounding waveform in step S4 are as follows: S4-2-1. Visualize the clustering results: visualize two-dimensional data as a two-dimensional graph and three-dimensional data as a three-dimensional graph. S4-2-2. Select the waveform data closest to the center point in each category as the typical waveform; The selected typical waveform satisfies the mean clustering of all other waveform data points in that category; The typical waveform formula is selected as follows: ； in, These are the selected typical waveform sample points; For category; function The distance function is Euclidean distance; The final selected waveform can represent most of the fault waveform information in this category.

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