Method for identifying relationship between power supply area and household based on spectral gap depth subspace clustering

Abstract

A method for identifying transformer substation relationships based on spectral gap deep subspace clustering includes: collecting effective voltage values ​​from the user side to obtain daily voltage sequences and constructing a user voltage matrix; constructing a deep subspace clustering network to encode the features of the collected user daily voltage curves, obtaining corresponding low-dimensional latent feature representations; generating a self-expression coefficient matrix representing the correlation between users based on self-expression constraints; constructing a graph Laplace matrix based on the self-expression coefficient matrix; determining the number of transformer substations based on spectral gap analysis; and identifying user transformer substations based on spectral clustering. This method can automatically extract the number of transformer substations and identify the substation to which a user belongs based on user voltage characteristics, and is suitable for low-voltage distribution network transformer substation relationship verification and topology identification applications.

Description

Technical Field

[0001] This invention relates to the field of low-voltage distribution network transformer-household relationship identification, and in particular to a transformer-household relationship identification method based on spectral gap depth subspace clustering. Background Technology

[0002] The connection between a user's electricity meter and a transformer or distribution area is a crucial aspect of studying the topology of a low-voltage distribution network. However, during the renovation or expansion of distribution lines, unauthorized alterations or changes to wiring by users often lead to complex user-transformer relationship structures, resulting in delays, omissions, or errors in the uploading of topology information. Furthermore, there is a lack of effective verification methods. Therefore, there is an urgent need to research a method that can accurately and efficiently identify user-transformer relationships.

[0003] Currently, traditional detection methods such as instantaneous power outage methods and carrier communication methods all require manual operation or on-site testing, resulting in high costs, low efficiency, and difficulty in large-scale application. With the increasing prevalence of smart meters, numerous methods based on correlation analysis of user voltage and power data have emerged, such as k-means, DBSCAN, and Gaussian mixture model clustering. However, these methods still have some limitations in practical applications: First, they typically rely on manually pre-setting the number of transformer areas (k); second, they have limited ability to characterize the nonlinear structures in voltage data; furthermore, these methods are sensitive to noise or outliers; finally, they cannot automatically detect subspatial distribution differences between different transformer areas, thus affecting identification accuracy and robustness.

[0004] Therefore, there is an urgent need for a new method for identifying the relationship between transformer substations and households that can automatically determine the number of transformer substations and is applicable to nonlinear voltage curves. Summary of the Invention

[0005] This invention proposes a method for identifying the relationship between transformer substations and households based on spectral gap depth subspace clustering. This method can automatically extract the number of transformer substations and identify the transformer substation to which the user belongs based on the user's voltage characteristics. It is applicable to the verification of transformer substation relationships and topology identification in low-voltage distribution networks.

[0006] The technical solution adopted in this invention is as follows:

[0007] A method for identifying the relationship between transformer substations and their customers based on spectral gap depth subspace clustering includes the following steps: Step 1: Collect the effective voltage value from the user side to obtain the daily voltage sequence and construct the user voltage matrix; Step 2: Construct a deep subspace clustering network to encode the features of the collected user daily voltage curves and obtain the corresponding low-dimensional latent feature representations; Step 3: Generate a self-expression coefficient matrix representing the correlation between users based on self-expression constraints; Step 4: Construct the graph Laplacian matrix based on the self-expression coefficient matrix; Step 5: Determine the number of stations based on spectral gap analysis; Step 6: Identify user station areas based on spectral clustering.

[0008] In step 1, if there are N users in the low-voltage distribution area of ​​the distribution network, the collected raw voltage data is represented as follows: (1); In formula (1): Represents the original voltage matrix; Indicates user At the point of time voltage value, , This indicates the number of users within the low-voltage distribution area of ​​the distribution network. , Indicates the number of time sampling points; Represents a real matrix with N rows and T columns; This indicates the number of users within the low-voltage distribution area of ​​the power distribution network.

[0009] Step 1 includes the following steps: Step 1.1: Handle missing and outlier values ​​in the raw voltage data: For missing values, linear interpolation is used for imputation: (2); In formula (2): Indicates user At the point of time The voltage value; Indicates user At the point of time The voltage value; Indicates user At the point of time The voltage value; For outliers, i.e., points exceeding the normal operating range, the daily average voltage value is used instead. Outliers are voltage values ​​in the power system that deviate from the normal permissible range. The daily average voltage value is: (3); In formula (3): express Outliers at any given time; This indicates the normal voltage value; This represents the number of time sampling points.

[0010] Step 1.2: Data Normalization: To avoid the impact of voltage level differences among different users on the training of the deep subspace clustering network, a minimum-maximum normalization method is used to normalize the voltage sequence of each user: (4); In equation (4): for Normalized column vectors; and They represent the first The maximum and minimum values ​​of voltage data for all users at any given time.

[0011] The normalized voltage data matrix is ​​represented as follows: (5); In formula (5): This is the normalized user voltage data matrix; From 1 to The normalized column vectors at all times; the upper right corner of the matrix. It is the matrix transpose symbol.

[0012] The obtained voltage data matrix The numerical range is limited to This is used for subsequent training of deep subspace clustering networks; Step 1.3: Data format conversion: For subsequent deep subspace clustering network processing, each user's voltage sequence is treated as a sample vector, such that the data satisfies: (6); In formula (6): From 1 to The normalized column vectors at all times; Through the above steps, the final user voltage matrix used as input to the deep subspace clustering network is obtained: (7); In equation (7): This represents an N-row, T-column voltage matrix after data normalization and format conversion. The user voltage matrix is ​​used as input to step 2 for the encoder to extract latent subspace features.

[0013] In step 2, the deep subspace clustering network consists of an encoder, a self-expression layer, and a decoder. The encoder module extraction process includes the following steps: Step 2.1: The original high-dimensional voltage sequence is mapped to a low-dimensional latent feature space using an encoder. The encoder network consists of multiple one-dimensional convolutional layers (1D-CNN) and fully connected layers (FC), and its structure is represented as follows: (8); In equation (8): For the nonlinear mapping function of the encoder network; A collection of network parameters; The latent feature matrix; For the latent feature dimension, satisfying ; Step 2.2: High-dimensional voltage feature extraction, as detailed below: Convolutional feature extraction layers extract temporal patterns and local variation features of voltage sequences within local time windows: (9); In equation (9): Indicates the kernel length; For the first Each convolutional kernel weight; For bias terms; It is a non-linear activation function; For at any time The local characteristic response.

[0014] By sliding the convolutional kernel along the time axis, linear filtering and nonlinear transformations are applied to nearby time points, thereby capturing periodic fluctuations, short-term peaks and troughs, and local amplitude variations. The sliding window diagram illustrates the movement of the convolutional kernel along the time axis. Figure 7 As shown. Linear filtering and nonlinear transformation are as follows. Figure 8 As shown, Figure 8 middle, Indicates the first The voltage sequence after normalization for each user.

[0015] Step 2.3: Map the high-dimensional voltage features extracted by the convolutional layer to a low-dimensional latent vector with discriminative capabilities. The details are as follows: The feature compression layer flattens the convolutional output and maps it to a low-dimensional latent feature space through a fully connected layer: (10); In formula (10): For users Latent space characteristics; , These are the parameters for the fully connected layer; This represents the number of convolutional layers.

[0016] The dimension is The real vector space; This indicates a flattening (vectorization) operation, which converts the multidimensional features output by the convolutional layer into a one-dimensional vector; The output features are obtained from the convolutional layer in step 2.2.

[0017] Step 2.4: Collect the low-dimensional latent vectors of all users Organized into a matrix by row As a unified form of "sample-feature" representation, it is as follows: The encoder maps each user's voltage sequence to a d-dimensional vector, ultimately forming a latent feature matrix: (11); In equation (11): Represents the transpose of the low-dimensional latent vectors of all users; Represents the matrix space; This represents the number of users in the low-voltage distribution area of ​​the power grid; this matrix is ​​the basis for the subsequent construction of the self-expression coefficient matrix C in the expression layer.

[0018] Step 2.5: Encoder training to minimize reconstruction error and self-expression error: To enable the encoder to learn potential feature representations that effectively characterize the original voltage data and satisfy the subspace structure characteristics, the network is jointly optimized and trained. Specifically, this is achieved by simultaneously minimizing the reconstruction error and the self-expression error.

[0019] First, based on the encoder and decoder, the input data is reconstructed, and the reconstruction error is defined as: (12); In equation (12): This represents the reconstruction error; This is the original voltage matrix; For encoder mapping functions; This is the decoder mapping function; Represents the calculation of the square of the F-norm; By introducing self-expression constraints into the latent feature space, and after encoding mapping, we can obtain: (13); In equation (13): Z is the deep subspace feature representation of the user voltage data, which serves as the input for constructing the self-expression coefficient matrix C in the next step; This represents the encoder function that takes the original voltage matrix as input.

[0020] Step 3, constructing the self-expression coefficient matrix C, includes the following steps: Step 3.1: Establish a self-expressive model: According to the self-expression hypothesis, the latent features satisfy: (14); In equation (14): For the deep subspace feature representation of user voltage data, This is the self-expression coefficient matrix; Formula (14) is based on the subspace assumption, which states that the voltage characteristics of users in the same distribution area are distributed in the same low-dimensional subspace in the potential space, and the points (user voltage characteristics) in the same space can be linearly represented by other points on the plane. The overall expression is Formula (14). Due to voltage fluctuations in different user voltage characteristics, the subspace is not strictly ideal, and there are errors in encoder learning, etc., they are approximately equal, but not completely equal.

[0021] This is the self-expression coefficient matrix. Represents the coefficient matrix space, Number of users in low-voltage distribution areas of the distribution network; its first Columns represent samples The coefficients linearly reconstructed from other samples.

[0022] Step 3.2: Solve for the self-expression coefficient : The self-expression coefficient is obtained by solving the following formula. : (15); In equation (15): For regularization weights; It is a regular term. This is used to enhance sparsity, so that each sample is associated with only a small number of relevant users; Denotes the square of the F-norm; The calculation of the 1-norm is consistent with the self-expression coefficient. Perform 1-norm calculation.

[0023] Step 3.3: Similarity Matrix Construction: To use the self-expression coefficient matrix for subsequent graph structure modeling and spectral clustering analysis, it needs to be transformed into a symmetric similarity matrix that satisfies the requirements of undirected graphs. Therefore, the self-expression coefficient matrix is ​​symmetricized to construct the similarity matrix. Its definition is: (16); Among them, symmetry processing refers to... This involves taking the absolute value of a matrix and then adding it to the absolute value of the transpose of that matrix.

[0024] In step 4, the graph Laplacian matrix L is constructed to describe the graph structure relationships between different users, including the following steps: Step 4.1: Calculate the degree matrix D: The similarity matrix D is defined as a diagonal matrix whose elements are similarity matrices. The sum of the weights in each row: (17); In equation (17): Represents the diagonal elements in the degree matrix; Among them, each diagonal element The calculation is as follows: (18); In formula (18): Let be the degree of the node, representing the degree of the node. "Total connection strength" of each user in the similarity graph; Indicates the number of users in the low-voltage distribution area of ​​the distribution network; Similarity matrix The similarity element in the data represents the user's identity. With users The degree of similarity between them.

[0025] Step 4.2: Construct the normalized graph Laplacian matrix L: Using the symmetric normalized graph Laplace matrix form: (19); In equation (19): D is the degree matrix in step 4.1; W is the similarity matrix in step 3.3; Step 4.3: To ensure that L satisfies the spectral clustering conditions, a symmetry check is performed to ensure that L is a symmetric positive semi-definite matrix and that the eigenvalue decomposition is accurate.

[0026] (20); In equation (20): This represents the transpose of the Graph Laplace matrix; It is the transpose symbol.

[0027] Step 5 includes the following steps: Step 5.1: Eigenvalue decomposition of the graph Laplacian matrix L: Eigenvalue decomposition of the graphical Laplacian matrix L: (twenty one); In equation (21): This represents the right multiplication of the graph's Laplacian matrix by its eigenvectors; These are the eigenvalues ​​of the graph Laplacian matrix; It is the eigenvector corresponding to each eigenvalue.

[0028] Obtain all eigenvalues and corresponding feature vectors .

[0029] Eigenvalues ​​sorted from smallest to largest: (twenty two); In equation (22): This is the first eigenvalue; This is the second eigenvalue; For the first There are 10 eigenvalues, and the number of eigenvalues ​​is equal to the number of components.

[0030] Step 5.2: Calculate the spectral gap sequence of eigenvalues ​​to estimate the number of clustered regions: Construct adjacent eigenvalue difference sequences: (twenty three); In equation (23): Indicates the first The nth difference value represents the nth difference value. With the The size of the interval between the feature values; It represents the difference between two adjacent eigenvalues, reflecting the magnitude of change in the spectral sequence at that position.

[0031] According to the spectral gap method, the position of the largest gap in the difference sequence is taken as the cluster number: (twenty four); In equation (24): That is, the number of transformer substations; This means taking the largest difference value in the difference value sequence as the largest difference value. The value of ; Indicates the first Each difference value.

[0032] In step 6, based on the spectral clustering method, the previous... Each user's Laplacian feature vector is mapped to a low-dimensional space and k-means clustering is performed to obtain the substation number for each user, thus achieving automatic identification of user-transformation relationships. This includes the following steps: Step 6.1: Sort the eigenvalues ​​and eigenvectors of the graphical Laplacian matrix L obtained in step S4, specifically: Sort all feature values ​​from smallest to largest: (25); In equation (25): They represent the 1st, 2nd...th respectively Small feature values ​​(after sorting).

[0033] Correspondingly, the feature vectors are rearranged in the same order: The eigenvectors corresponding to the k smallest eigenvalues ​​are used to form a new feature matrix: (26); In equation (26): It is the new feature matrix after reordering; These represent the 1st and 2nd positions after reordering. , No. eigenvectors; express OK The matrix space of columns; This refers to the number of users in the low-voltage distribution area of ​​the power distribution network. This refers to the number of TV stations.

[0034] Normalize each row of matrix U: (27); In equation (27): Represents the normalized i-th Row vectors; Represents the first... Row vectors; It represents a positive constant to prevent the denominator from being zero; This indicates the number of rows in matrix U.

[0035] The normalized feature matrix is ​​formed as follows: (28); In equation (28): This represents the normalized row vector. Each It is a matrix One of the lines represents the first After normalization, each user 3D feature vector; Represent a OK A matrix of real numbers in columns; This indicates the number of stations (clusters) automatically determined through spectral gap analysis (step 5).

[0036] Step 6.2: Perform k-means clustering on the normalized feature matrix: (29); In equation (29): Indicates the category to which each user belongs; It is the input normalized feature matrix data; k-means is a clustering algorithm; Equation (29) indicates that the clustering labels are output when k-means is executed.

[0037] Step 6.3: Output the user substation area number to form the final user-transformer relationship mapping: Based on the clustering results, assign a station area number to each user: (30); In equation (30): Refers to the first One user; Indicates the mapping relationship; The clustering algorithm using formula (29) is the first... Each user is assigned a zone (transformer) number label; Indicates all Each user executes this mapping definition.

[0038] The final user-station mapping can be represented as: (28); In equation (28): This represents the final set of household change relationship mappings; This indicates that the k-means clustering using formula (29) is the first... Each user is assigned a zone number.

[0039] This step converts the deep subspace features, self-expressive relationships, and graph structure information into the final substation division result, which is the final identification step of this invention.

[0040] A method for identifying the relationship between transformer substations and their customers based on spectral gap depth subspace clustering includes: In the first stage, a deep subspace clustering network is constructed to encode the features of the collected user daily voltage curves to obtain the corresponding low-dimensional latent feature representations. At the same time, a self-expression coefficient matrix representing the correlation between users is generated based on self-expression constraints. In the second stage, a graph Laplacian matrix is ​​constructed based on the self-expression coefficient matrix, and the number of stations k is determined using the spectral gap analysis method. The determined number of stations k is then used to cluster the deep features to obtain the preliminary grouping results for the users. In the third stage, the deep feature embedding results are combined with the spectral clustering output to form a connection mapping relationship between users and transformers, thereby outputting the corresponding user-transformer relationship identification results.

[0041] A transformer substation-household relationship identification system based on deep subspace clustering of spectral gaps includes: a deep subspace feature extraction module, a self-expression coefficient construction module, a spectral gap determination module, and a spectral clustering identification module. The deep subspace feature extraction module encodes the user's daily voltage curve through a deep subspace clustering network to obtain its low-dimensional latent feature representation. The deep subspace feature extraction module is a deep feature learning module based on an encoder-self-expression layer-decoder structure. It constructs a deep subspace network to perform nonlinear feature extraction and latent space representation learning on the input user daily voltage curves. This module can map high-dimensional voltage sequences to a low-dimensional latent feature space and generate a self-expression coefficient matrix reflecting the correlation between samples. In this invention, it is used to obtain deep features and construct subspace representation relationships between users.

[0042] The self-expression coefficient construction module generates a self-expression coefficient matrix based on encoding features, which is used to describe the association relationship between different users; The self-expressive coefficient matrix construction module is a matrix construction module based on the linear self-representation concept. By applying self-expressive constraints to deep features, it obtains a coefficient matrix between samples, which is used to describe the correlation structure between different users. This type of matrix is ​​widely used in subspace clustering and graph structure construction, and in this invention, it is used to form the similarity representation basis required for subsequent spectral clustering.

[0043] The spectral gap determination module constructs a graph Laplacian matrix using a self-expressing coefficient matrix and calculates the spectral gap based on its eigenvalue sequence to determine the number of stations to which the user belongs. The spectral gap determination module is a cluster number estimation module based on the graph Laplacian eigenvalue sequence. It constructs a corresponding graph Laplacian matrix using a self-expressed coefficient matrix, sorts its eigenvalues, and calculates the spectral gap to determine the potential number of clusters. This method is commonly used for adaptive cluster number determination in unsupervised clustering; in this invention, it is used to automatically determine the number of transformer areas, k.

[0044] The spectral clustering identification module clusters the deep features based on the number of transformer substations determined by the spectral gaps, outputs the connection relationship between users and transformer substations, and completes the identification of user-transformer relationship.

[0045] The spectral clustering identification module is a clustering module that uses graph embedding features to segment users. It uses the number of clusters obtained from the aforementioned spectral gap determination in a spectral clustering algorithm to cluster deep features and output the connection relationship between users and transformer substations. Spectral clustering is widely used for clustering tasks of graph-structured data, and in this invention, it is used to generate the final user-transformation relationship identification result.

[0046] This invention discloses a method for identifying the relationship between transformer substations and their customers based on spectral gap depth subspace clustering. The technical advantages are as follows: 1) Step 1 of this invention uses linear interpolation to repair missing values, ensuring the continuity of the voltage sequence; secondly, it replaces outliers with the daily average, effectively suppressing noise and disturbances and improving data robustness; then, it uses min-max normalization to scale the voltage of each user to the [0,1] interval, eliminating benchmark differences and enabling the model to focus on the fluctuation pattern of the learning curve; finally, it organizes the data into a regular matrix form, which is suitable for the input requirements of deep learning models.

[0047] 2) Step 2 of this invention constructs a deep subspace clustering network consisting of an encoder, a self-expression layer, and a decoder to automatically learn discriminative low-dimensional latent feature representations from high-dimensional voltage curves. The encoder effectively captures local temporal patterns and nonlinear fluctuation features in the voltage sequence using a one-dimensional convolutional layer, and then compresses them to a low-dimensional subspace through a fully connected layer. This step trains the network by jointly optimizing the reconstruction error and the self-expression error, ensuring that the learned features can both reconstruct the original data with high fidelity and satisfy the geometric constraint that user features in the same area are located in the same low-dimensional subspace. This provides a structured feature foundation for accurately constructing user relationships and clustering in the future.

[0048] 3) Step 3 of this invention explicitly models and optimizes the relationships between users by constructing a self-expression coefficient matrix. Based on the assumption that "samples within the same subspace can be linearly represented by other samples within that subspace," a self-expression model is established, and the coefficient matrix C is obtained by solving an optimization problem with L1 norm sparsity constraints. This makes the expression coefficients between users within the same substation area significant, while the coefficients between users in different substation areas approach zero, thus revealing the subspace structure to which users belong. By symmetricizing C, a similarity matrix W is obtained. This matrix quantitatively characterizes the association strength of user pairs, providing a robust similarity measurement basis that meets the requirements of undirected graphs for subsequent construction of the graph Laplacian matrix for spectral analysis.

[0049] 4) Step 4 of this invention transforms the relationships between users into a graph structure suitable for spectral analysis by constructing a normalized graph Laplacian matrix. The degree matrix D is calculated using the similarity matrix W derived from the self-expression coefficient matrix, and a symmetric normalized graph Laplacian matrix L is constructed. This matrix not only characterizes the global topological structure of the user relationship network but also eliminates the influence of differences in node degree (user connection strength) on the structure through normalization, improving the stability and comparability of the graph when the degree distribution is uneven. Simultaneously, this step ensures the symmetric positive semidefiniteness of the matrix through symmetry processing, laying a graph theory foundation for reliable eigenvalue decomposition and spectral gap analysis in subsequent step 5, and supporting the automatic determination of the number of clusters.

[0050] 5) Step 5 of this invention achieves fully automated determination of the number of transformer substations through spectral gap analysis. This method performs eigenvalue decomposition on the graph Laplacian matrix L representing the user association structure and calculates the adjacent intervals of its ordered eigenvalue sequence. Then, the index corresponding to the largest spectral gap is used as the optimal number of clusters k. This step is entirely based on the graph structure characteristics of the data itself, without any prior knowledge or manual preset, overcoming the limitation of traditional clustering methods that require pre-specifying the value of k. This makes the entire user-transformation relationship identification process adaptive and ensures the inherent consistency between the subsequent spectral clustering division and the actual distribution of transformer substations.

[0051] 6) Step 6 of this invention transforms the graph structure features learned in the preceding steps into accurate user partitioning results using spectral clustering. A low-dimensional embedding representation is constructed using the eigenvectors corresponding to the first k smallest eigenvalues ​​of the graph Laplacian matrix, and the rows of the eigenvector matrix are normalized to highlight the relative distribution of samples in the feature space. Subsequently, k-means clustering is performed based on the number of transformer substations k automatically determined in step 5, ultimately assigning a specific transformer substation number to each user. This directly and explicitly outputs the data's intrinsic structure revealed by deep subspace learning, self-expressive relationships, and graph analysis as a complete "user-transformer substation" mapping relationship, completing the closed loop of automatic identification of user-transformer relationships. Attached Figure Description

[0052] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a structural diagram of the deep subspace feature extraction module.

[0053] Figure 2 This is a schematic diagram of the overall structure of Deep Subspace Clustering (DSC).

[0054] Figure 3 Flowchart for constructing the feature association matrix.

[0055] Figure 4 A flowchart for constructing the graph Laplacian matrix L.

[0056] Figure 5 This is a flowchart for determining the number of stations k based on the spectral gap (Eigengap).

[0057] Figure 6 The overall flowchart for adaptive household change relationship identification.

[0058] Figure 7 A schematic diagram of a sliding window used to represent the rolling of the convolution kernel along the time axis.

[0059] Figure 8 This is a schematic diagram of linear filtering and nonlinear transformation.

[0060] Figure 9Comparison chart of data normalization preprocessing.

[0061] Figure 10 A scatter plot of t-SNE visualization representing low-dimensional latent features.

[0062] Figure 11 W is the user similarity matrix learned by the deep subspace clustering network.

[0063] Figure 12 Confusion matrix diagram for identification results. Detailed Implementation

[0064] A method for identifying the relationship between users and transformer substations based on deep subspace feature representation and spectral gap cluster number estimation is used to divide low-voltage user voltage curve data into substation areas. This method obtains the latent subspace structure of voltage data through a deep subspace network and determines the number of clusters using the spectral gap criterion to construct the connection relationship between users and substation areas.

[0065] The present invention will be further described with reference to the accompanying drawings: Figure 1 This is a structural diagram of the depth subspace feature extraction module of the present invention. Figure 1 The paper demonstrates the network architecture process from input user voltage data to output potential low-dimensional feature representations, including the process of the encoding network performing feature mapping on high-dimensional time series data to obtain the subspace features required for subsequent self-expressive modeling and cluster analysis.

[0066] Figure 2 This is a schematic diagram of the overall structure of the Deep Subspace Clustering (DSC) of the present invention. Figure 2 The overall structure of the deep subspace clustering method in this invention is presented, including several key modules such as encoder network, self-expression relation construction, similarity matrix generation, graph Laplacian matrix construction, spectral gap determination of station number, and spectral clustering output of user category, demonstrating a complete DSC clustering framework.

[0067] Figure 3 The flowchart for constructing the feature correlation matrix of this invention is shown below. Figure 3 The process of obtaining the self-expression coefficient matrix by solving the latent feature representation through the self-expression model, and generating the feature association matrix (similarity matrix) through symmetry processing, illustrates how the relationship between users is constructed at the matrix level.

[0068] Figure 4 Constructing a graph Laplacian matrix for this invention The flowchart. Figure 4 The process of calculating the degree matrix from the feature correlation matrix and generating the normalized graph Laplacian matrix is ​​demonstrated. This matrix is ​​used to characterize the graph structure relationships between users and provides an input basis for subsequent spectral gap analysis and spectral clustering.

[0069] Figure 5 This invention determines the number of stations based on the spectral gap (Eigengap). The flowchart. Figure 5 This demonstrates the eigenvalue decomposition of the Graph Laplacian matrix, the construction of eigenvalue difference sequences, the identification of the maximum spectral gap, and the automatic determination of the number of clusters based on this. The specific steps are used to achieve adaptive determination of the number of transformer areas.

[0070] Figure 6 This is the complete flowchart of the adaptive household change relationship identification of the present invention. Figure 6 From data input to final output of user station category, the entire process is demonstrated, including voltage data preprocessing, deep subspace feature extraction, feature correlation matrix construction, graph Laplacian matrix generation, spectral gap method to determine the number of stations, and spectral clustering to identify user station relationships, reflecting the systematic processing path of the overall method of this invention.

[0071] Figure 9 The results of data preprocessing are shown. Figure 9 The subplot above shows the raw daily voltage curves (220-230V) for three users. Figure 9 The subplot below shows the results after normalization to the [0,1] interval. This process eliminates the voltage amplitude differences between users while fully preserving the fluctuation patterns and relative temporal relationships of each curve. This allows the subsequent deep subspace clustering network to focus on learning curve shape patterns rather than absolute value deviations, providing standardized input for feature extraction.

[0072] Figure 10 This diagram illustrates the visualization results of user voltage features extracted by a deep subspace clustering network, reduced to two dimensions using t-SNE. Different colors in the diagram represent user samples from different transformer substations. The feature points form relatively clear clusters in space, indicating that the low-dimensional features learned by the network can effectively distinguish users from different substations, providing a separable feature base for subsequent accurate clustering.

[0073] Figure 11 This shows the user similarity matrix W learned by the deep subspace clustering network. Each point in the matrix represents the association strength between two users (the more yellow the color, the higher the similarity). Figure 11 As can be seen, there are several distinct yellow highlighted squares, which indicates that users have been automatically divided into multiple groups that are highly similar internally but significantly different externally, with each group corresponding to a potential TV station area.

[0074] Figure 12This demonstrates the final household-transformation relationship identification effect of the method of this invention. The horizontal axis represents the transformer substation categories predicted by the algorithm (1-4), and the vertical axis represents the actual transformer substation categories. Most cells in the matrix are white (value 0), with only a few off-diagonal cells having values, indicating that most users have been correctly clustered.

Claims

1. A method for identifying the relationship between transformer substations and their customers based on spectral gap depth subspace clustering, characterized by the following steps: Step 1: Collect the effective voltage value from the user side to obtain the daily voltage sequence and construct the user voltage matrix; Step 2: Construct a deep subspace clustering network to encode the features of the collected user daily voltage curves and obtain the corresponding low-dimensional latent feature representations; Step 3: Generate a self-expression coefficient matrix representing the correlation between users based on self-expression constraints; Step 4: Construct the graph Laplacian matrix based on the self-expression coefficient matrix; Step 5: Determine the number of stations based on spectral gap analysis; Step 6: Identify user station areas based on spectral clustering.

2. The method for identifying the relationship between a user and a distribution transformer in a low-voltage distribution area based on spectral gap depth subspace clustering according to claim 1, is characterized in that: in step 1, if there are N users in the low-voltage distribution area of ​​the distribution network, the collected raw voltage data is represented as: （1）； In formula (1): represents the original voltage matrix; represents the user at the time point , , represents the number of users in the low-voltage area of the power distribution network, , represents the number of time sampling points; represents an N-row, T-column real number matrix; represents the number of users in the low-voltage area of the power distribution network.

3. The method for identifying the relationship between transformer substations and households based on spectral gap depth subspace clustering according to claim 2, characterized in that: step 1 includes the following steps: Step 1.1: Handle missing and outlier values ​​in the raw voltage data: For missing values, linear interpolation is used for imputation: （2）； In formula (2): Indicates user At the point of time The voltage value; Indicates user At the point of time The voltage value; Indicates user At the point of time The voltage value; For outliers, i.e., points that exceed the normal operating range, the daily average voltage value is used instead; where outliers are voltage values ​​in the power system that deviate from the normal allowable range, and the daily average voltage value is: （3）； In formula (3): express Outliers at any given time; This indicates the normal voltage value; This represents the number of time sampling points; Step 1.2: To avoid the impact of voltage level differences among different users on the training of the deep subspace clustering network, the min-max normalization method is used to normalize the voltage sequence of each user: （4）； In equation (4): for Normalized column vectors; and They represent the first The maximum and minimum values ​​of all user voltage data at any given time; The normalized voltage data matrix is ​​represented as follows: （5）； In formula (5): This is the normalized user voltage data matrix; From 1 to The normalized column vectors at all times; the upper right corner of the matrix. It is the matrix transpose symbol; The obtained voltage data matrix The numerical range is limited to This is used for subsequent training of deep subspace clustering networks; Step 1.3: For subsequent deep subspace clustering network processing, treat each user's voltage sequence as a sample vector, ensuring the data satisfies: （6）； In formula (6): From 1 to The normalized column vectors at all times; Through the above steps, the final user voltage matrix used as input to the deep subspace clustering network is obtained: （7）； In equation (7): This represents an N-row, T-column voltage matrix after data normalization and format conversion.

4. The method for identifying the relationship between transformer substations and households based on spectral gap depth subspace clustering according to claim 3, characterized in that: In step 2, the deep subspace clustering network consists of an encoder, a self-expression layer, and a decoder; the encoder module extraction process includes the following steps: Step 2.1: The original high-dimensional voltage sequence is mapped to a low-dimensional latent feature space using an encoder. The encoder network consists of multiple one-dimensional convolutional layers (1D-CNN) and fully connected layers (FC), and its structure is represented as follows: （8）； In equation (8): is the nonlinear mapping function of the encoder network; A collection of network parameters; The latent feature matrix; For the latent feature dimension, satisfying ; Step 2.2: High-dimensional voltage feature extraction, as detailed below: Convolutional feature extraction layers extract temporal patterns and local variation features of voltage sequences within local time windows: （9）； In equation (9): Indicates the kernel length; For the first Each convolutional kernel weight; For bias terms; It is a non-linear activation function; For at any time Local characteristic response; By sliding the convolution kernel on the time axis, linear filtering and nonlinear transformation are performed on nearby time points to capture periodic fluctuations, short-term peaks and valleys, and local amplitude changes. Step 2.3: Map the high-dimensional voltage features extracted by the convolutional layer to a low-dimensional latent vector with discriminative capabilities. The details are as follows: The feature compression layer flattens the convolutional output and maps it to a low-dimensional latent feature space through a fully connected layer: （10）； In formula (10): For users Latent space characteristics; , These are the parameters for the fully connected layer; This represents the number of convolutional layers; The dimension is The real vector space; This indicates a flattening operation, which converts the multidimensional features output by the convolutional layer into a one-dimensional vector. The output features obtained from the convolutional layer in step 2.2; Step 2.4: Collect the low-dimensional latent vectors of all users Organized into a matrix by row As a unified form of "sample-feature" representation, it is as follows: The encoder maps each user's voltage sequence to a d-dimensional vector, ultimately forming a latent feature matrix: （11）； In equation (11): Represents the transpose of the low-dimensional latent vectors of all users; Represents the matrix space; The number of users in the low-voltage distribution area of ​​the distribution network; Step 2.5: Encoder training to minimize reconstruction error and self-expression error: First, based on the encoder and decoder, the input data is reconstructed, and the reconstruction error is defined as: （12）； In equation (12): This represents the reconstruction error; This is the original voltage matrix; For encoder mapping functions; This is the decoder mapping function; Represents the calculation of the square of the F-norm; By introducing self-expression constraints into the latent feature space, and after encoding mapping, we can obtain: （13）； In equation (13): Z is the deep subspace feature representation of the user voltage data, which serves as the input for constructing the self-expression coefficient matrix C in the next step; This represents the encoder function that takes the original voltage matrix as input.

5. The method for identifying the relationship between transformer substations and households based on spectral gap depth subspace clustering according to claim 4, characterized in that: Step 3, constructing the self-expression coefficient matrix C, includes the following steps: Step 3.1: Based on the self-expression hypothesis, the latent features satisfy: （14）； In equation (14): For the deep subspace feature representation of user voltage data, This is the self-expression coefficient matrix; This is the self-expression coefficient matrix. Represents the coefficient matrix space, Number of users in low-voltage distribution areas of the power distribution network; Step 3.2: Obtain the self-expression coefficients by solving the following formula. : （15）； In equation (15): For regularization weights; It is a regular term. This is used to enhance sparsity, so that each sample is associated with only a small number of relevant users; Denotes the square of the F-norm; The calculation of the 1-norm is consistent with the self-expression coefficient. Perform 1-norm calculation; Step 3.3: Symmetricize the self-expression coefficient matrix and construct the similarity matrix. Its definition is: （16）； Among them, symmetry processing refers to... This involves taking the absolute value of a matrix and then adding it to the absolute value of the transpose of that matrix.

6. The method for identifying the relationship between transformer substations and households based on spectral gap depth subspace clustering according to claim 5, characterized in that: In step 4, the graph Laplacian matrix L is constructed to describe the graph structure relationships between different users, including the following steps: Step 4.1: Calculate the degree matrix D: The similarity matrix D is defined as a diagonal matrix whose elements are similarity matrices. The sum of the weights in each row: （17）； In equation (17): Represents the diagonal elements in the degree matrix; Among them, each diagonal element The calculation is as follows: （18）； In formula (18): Let be the degree of the node, representing the degree of the node. "Total connection strength" for each user in the similarity graph; Indicates the number of users in the low-voltage distribution area of ​​the distribution network; Similarity matrix The similarity element in the data represents the user's identity. With users The degree of similarity between them; Step 4.2: Use the symmetric normalized graph Laplace matrix form: （19）； In equation (19): D is the degree matrix; W is the similarity matrix; Step 4.3: To ensure that L satisfies the spectral clustering conditions, a symmetry check is performed to ensure that L is a symmetric positive semi-definite matrix and that the eigenvalue decomposition is accurate; （20）； In equation (20): This represents the transpose of the Graph Laplace matrix; It is the transpose symbol.

7. The method for identifying the relationship between transformer substations and households based on spectral gap depth subspace clustering according to claim 6, characterized in that: Step 5 includes the following steps: Step 5.1: Perform eigenvalue decomposition on the graph Laplacian matrix L: （21）； In equation (21): This represents the right multiplication of the graph's Laplacian matrix by its eigenvectors; These are the eigenvalues ​​of the graph Laplacian matrix; It is the eigenvector corresponding to each eigenvalue; Obtain all eigenvalues and corresponding feature vectors ; Eigenvalues ​​sorted from smallest to largest: （22）； In equation (22): This is the first eigenvalue; This is the second eigenvalue; For the first There are 1 eigenvalues, and the number of eigenvalues ​​is equal to the number of components; Step 5.2: Calculate the spectral gap sequence of eigenvalues ​​to estimate the number of clustered regions: Construct adjacent eigenvalue difference sequences: （23）； In equation (23): Indicates the first The nth difference value represents the nth difference value. With the The size of the interval between the feature values; It represents the difference between two adjacent eigenvalues, reflecting the magnitude of change in the spectral sequence at that position; According to the spectral gap method, the position of the largest gap in the difference sequence is taken as the cluster number: （24）； In equation (24): That is, the number of transformer substations; This means taking the largest difference value in the difference value sequence as the largest difference value. The possible values ​​of ; Indicates the first Each difference value.

8. The method for identifying the relationship between transformer substations and households based on spectral gap depth subspace clustering according to claim 7, characterized in that: In step 6, based on the spectral clustering method, the previous... The Laplacian feature vectors of each graph are mapped to a low-dimensional space and k-means clustering is performed to obtain the transformer area number for each user, thereby achieving automatic identification of user-transformation relationships; including the following steps: Step 6.1: Sort the eigenvalues ​​and eigenvectors of the graph Laplacian matrix L obtained in step S4, specifically: Sort all feature values ​​from smallest to largest: （25）； In equation (25): They represent the 1st, 2nd...th respectively Small eigenvalues; The eigenvectors corresponding to the k smallest eigenvalues ​​are used to form a new feature matrix: （26）； In equation (26): It is the new feature matrix after reordering; These represent the 1st and 2nd positions after reordering. , No. eigenvectors; express OK The matrix space of columns; This refers to the number of users in the low-voltage distribution area of ​​the power distribution network. It refers to the number of TV stations; Normalize each row of matrix U: （27）； In equation (27): Represents the normalized i-th Row vectors; Represents the first... Row vectors; It represents a positive constant to prevent the denominator from being zero; This indicates the number of rows in matrix U; The normalized feature matrix is ​​formed as follows: （28）； In equation (28): Represents the normalized row vector; each It is a matrix One of the lines represents the first After normalization, each user 3D feature vector; Represent a OK A matrix of real numbers in columns; This indicates the number of stations automatically determined through spectral gap analysis; Step 6.2: Perform k-means clustering on the normalized feature matrix: （29）； In equation (29): Indicates the category to which each user belongs; It is the input normalized feature matrix data; k-means is a clustering algorithm; Equation (29) represents the output cluster labels when performing k-means; Step 6.3: Output the user substation area number to form the final user-transformer relationship mapping: Based on the clustering results, assign a station area number to each user: （30）； In equation (30): Refers to the first One user; Indicates a mapping relationship; The clustering algorithm using formula (29) is the first... A user-assigned area code label; Indicates all This mapping definition is executed by a user; The final user-station mapping is represented as follows: （28）； In equation (28): This represents the final set of household change relationship mappings; This indicates that the k-means clustering using formula (29) is the first... Each user is assigned a zone number.

9. A method for identifying the relationship between transformer substations and their customers based on spectral gap depth subspace clustering. Its special features include: In the first stage, a deep subspace clustering network is constructed to encode the features of the collected user daily voltage curves to obtain the corresponding low-dimensional latent feature representations. At the same time, a self-expression coefficient matrix representing the correlation between users is generated based on self-expression constraints. In the second stage, a graph Laplacian matrix is ​​constructed based on the self-expression coefficient matrix, and the number of stations k is determined using the spectral gap analysis method. The determined number of stations k is then used to cluster the deep features to obtain the preliminary grouping results for users. In the third stage, the deep feature embedding results are combined with the spectral clustering output to form a connection mapping relationship between users and transformers, thereby outputting the corresponding user-transformer relationship identification results.

10. A transformer substation relationship identification system based on spectral gap depth subspace clustering. Its special features include: The module includes a deep subspace feature extraction module, a self-expression coefficient construction module, a spectral gap determination module, and a spectral clustering recognition module. The deep subspace feature extraction module encodes the user's daily voltage curve through a deep subspace clustering network to obtain its low-dimensional latent feature representation. The self-expression coefficient construction module generates a self-expression coefficient matrix based on encoding features, which is used to describe the association relationship between different users; The spectral gap determination module constructs a graph Laplacian matrix using a self-expressing coefficient matrix and calculates the spectral gap based on its eigenvalue sequence to determine the number of stations to which the user belongs. The spectral clustering identification module clusters the deep features based on the number of transformer substations determined by the spectral gaps, outputs the connection relationship between users and transformer substations, and completes the identification of user-transformer relationship.

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