A power distribution network distributed resource gaussian mixture model clustering method and system

Abstract

The application provides a power distribution network distributed resource Gaussian mixture model clustering method and system, and relates to the technical field of power systems. The non-spherical distribution characteristics of resource parameters are adapted by the Gaussian mixture model to improve the clustering adaptability of heterogeneous parameters. The Davies-Bouldin and Calinski-Harabasz indexes are improved, the Mahalanobis distance and sample weight mechanism are introduced respectively, the interference of abnormal values on clustering evaluation is effectively reduced, and multi-dimensional clustering effect evaluation is realized in combination with the profile coefficient. The clustering evaluation mixed index is constructed by relying on the entropy weight method to objectively weight, the optimal clustering number is accurately determined, the subjective randomness problem of the clustering number selection of the traditional method is completely solved, and the objectivity and accuracy of the clustering result are greatly improved. The clustering attribution result can provide reliable data support for the differentiated scheduling of the power distribution network distributed resources, and significantly improves the resource aggregation management and utilization efficiency.

Description

Technical Field

[0001] This application relates to the field of power system technology, and in particular to a Gaussian mixture model clustering method and system for distributed resources in power distribution networks. Background Technology

[0002] With the deepening of the construction of new power systems, the types and scale of distributed resources in distribution networks are showing a continuous growth trend, covering various forms such as energy storage devices, photovoltaic power generation units, wind power generation units, flexible loads, and electric vehicle charging facilities. These resources exhibit significant heterogeneity in key dimensions such as rated capacity, real-time power output characteristics, dynamic response speed, operating time constraints, and energy storage capacity, posing severe challenges to the power grid in implementing aggregated dispatch, coordinated control, and refined management. Traditional resource clustering methods mainly rely on the subjective experience of operators to set fixed thresholds or use simple rules for division, making it difficult to objectively and adaptively capture the complex similarity relationships and group behavior characteristics between resources. This can easily lead to biased clustering results, making dispatching strategies too general and failing to fully explore and leverage the potential value of various distributed resources.

[0003] Currently, although some studies attempt to introduce hard clustering algorithms such as K-means for resource classification, these methods implicitly assume that the data is spherically distributed and isotropic. However, the operating parameters of distributed resources in actual power distribution networks often exhibit non-spherical and heteroscedastic distribution characteristics. For example, power fluctuation curves often show long-tailed distributions or multiple peak phenomena, resulting in insufficient ability of hard clustering methods to fit the true distribution and poor clustering results. Furthermore, when evaluating clustering quality, existing technologies often rely on single indicators such as the silhouette coefficient, the Davidson-Bolding index, or the Kalinsky-Hallabus index. The silhouette coefficient focuses on the quality of individual sample assignment but has limited ability to reflect the global cluster structure; the Davidson-Bolding index emphasizes intra-cluster compactness and inter-cluster separation but is sensitive to outlier interference; the Kalinsky-Hallabus index focuses on the ratio of inter-cluster to intra-cluster divergence but assumes that the data follows a Gaussian distribution. A single indicator cannot comprehensively measure the clustering effect, especially when the data contains noise or has a complex distribution. The evaluation results fluctuate greatly, leading to a lack of objective basis in the selection of the optimal number of clusters, and exhibiting strong subjectivity and uncertainty. This uncertainty directly affects subsequent application stages. For example, when modeling resource aggregation, inaccurate typical operating curves may be generated. When formulating differentiated scheduling strategies, it is difficult to develop effective control schemes for different resource groups, thus limiting the practical application effect of distributed resources in improving the flexibility, reliability, and management sophistication of the power distribution network.

[0004] To address the aforementioned issues, existing technologies urgently need improvement. Summary of the Invention

[0005] This application provides a Gaussian mixture model clustering method and system for distributed resources in power distribution networks. It has the advantages of objectively determining the optimal number of clusters, adapting to the non-spherical distribution characteristics of distributed resources in power distribution networks, reducing subjective arbitrariness in evaluation, thereby improving clustering results and the accuracy of scheduling strategies.

[0006] Firstly, the Gaussian mixture model clustering method for distributed resources in power distribution networks provided in this application adopts the following technical solution: A clustering method for distributed resource Gaussian mixture model in power distribution networks includes: The operating characteristic parameters of multiple distributed resources within the distribution network area are obtained and standardized to construct a multidimensional feature dataset adapted to Gaussian mixture model clustering. The range of values ​​for the number of clusters k is determined based on the number of samples in the multidimensional feature dataset; The K-means algorithm is used to perform initial clustering on the multidimensional feature dataset, thereby initializing the cluster centers and covariance matrix of the Gaussian mixture model. By iteratively optimizing the mixing coefficients, cluster centers, and covariance matrix of the Gaussian mixture model using the expectation-maximization algorithm, fine clustering of multidimensional feature datasets is achieved. For each candidate cluster number k, the improved Davidson-Bolding index, the improved Kalinsky-Harabas index, and the silhouette coefficient adapted to the characteristics of distributed resource parameters in the distribution network are calculated respectively. The weights of the three indicators are objectively determined using the entropy weight method, and a cluster evaluation mixture index is constructed. The k corresponding to the maximum value of this index is taken as the optimal number of clusters. The clustering results of each distributed resource in the distribution network under the optimal clustering number are output, providing data support for the differentiated scheduling of distributed resources in the distribution network.

[0007] Alternatively, methods for constructing a multidimensional feature dataset include: Select distributed resources within the distribution network, wherein the distributed resources are one or more of the following: energy storage devices, photovoltaic power generation units, wind power generation units, flexible loads, and electric vehicle charging facilities; Extract at least three types of operational characteristic parameters from the distributed resource, including power-related, energy-related, and performance-related parameters; The extracted operational feature parameters were normalized using a standardization method to eliminate dimensional differences and obtain a multidimensional feature dataset.

[0008] Optionally, the method for determining the number of clusters and initializing the parameters of the Gaussian mixture model includes: The range of the number of clusters k is set to 2~ N is the number of samples in the multidimensional feature dataset; The multidimensional feature dataset is input into the K-means algorithm, and the cluster centers of each initial cluster are obtained through iterative calculation. Based on the sample distribution of the initial clusters, the covariance matrix of each cluster is calculated, and the cluster centers and covariance matrix of the Gaussian mixture model are initialized.

[0009] Optionally, methods for optimizing Gaussian mixture models and performing fine clustering based on the expectation-maximization algorithm include: Based on the initialized Gaussian mixture model parameters, the expectation step is performed to obtain the posterior probability of each sample belonging to each cluster. Perform a maximization step calculation and update the mixing coefficients, cluster centers, and covariance matrix of the Gaussian mixture model based on the posterior probability; Repeat the expected step and the maximization step until the model parameters converge or the preset number of iterations is reached. Then, complete the fine clustering of the dataset based on the converged model parameters.

[0010] Optionally, the calculation method of the Davidson-Bolding index can be improved, including: For each cluster after fine clustering, the average Mahalanobis distance from the samples within the cluster to the cluster center is calculated as the intra-cluster dispersion. The Mahalanobis distance calculation introduces the inverse of the cluster's covariance matrix to adapt to the non-spherical distribution characteristics of distributed resource parameters in the distribution network. Calculate the Mahalanobis distance between any two cluster centers based on the joint covariance matrix, and use it as the inter-cluster distance. The joint covariance matrix is ​​jointly determined by the covariance matrices of the two clusters. The similarity between two clusters is calculated based on intra-class dispersion and inter-class distance. The maximum similarity of each cluster relative to all other clusters is selected and the mean of these maximum similarities is calculated to obtain the improved Davidson-Bolding index. The smaller the index value, the better the clustering effect of distributed resources in the distribution network.

[0011] Optionally, the calculation method of the Kalinsky-Harabas index can be improved, including: For each cluster after fine clustering, sample weights are introduced to calculate the weighted covariance matrix within the cluster. The sample weights are determined by the mean of the squared distances from the sample to the cluster center. The weights of outlier samples are close to 0, which reduces the interference of abnormal parameters of distributed resources in the distribution network on the indicators. Based on the weighted covariance matrix of each cluster, the overall weighted within-class scatter matrix is ​​calculated, and its trace is solved. Calculate the inter-class scatter matrix of each cluster center relative to the global center, and solve for its trace. The global center is the mean of all samples in the multi-dimensional feature dataset of distributed resources in the distribution network. The improved Kalinsky-Harabas index is obtained by normalizing the ratio of the trace of the inter-class scatter matrix to the trace of the weighted intra-class scatter matrix. The larger the index value, the better the clustering effect of distributed resources in the distribution network.

[0012] Optionally, the method for calculating the contour coefficient includes: For each sample in the multidimensional feature dataset of distributed resources in the distribution network after fine clustering, calculate the average distance from the sample to all other samples in the same cluster, and denot it as the intra-cluster distance. Calculate the average distance from the sample to all samples in each other cluster, and select the minimum value as the inter-cluster distance; The silhouette coefficient of a sample is calculated based on the intra-cluster distance and the inter-cluster distance. The silhouette coefficient is the difference between the inter-cluster distance and the intra-cluster distance divided by the maximum of the two. Calculate the arithmetic mean of the profile coefficients of all samples to obtain the profile coefficient corresponding to the candidate cluster number k. The closer the coefficient is to 1, the better the sample clustering effect of the distributed resources of the distribution network is.

[0013] Optionally, methods for constructing cluster evaluation mixture indices using the entropy weight method include: Collect the improved Davidson-Bolding index, the improved Kalinsky-Harabs index, and the silhouette coefficient corresponding to each candidate cluster number k, and construct the original index matrix for distributed resource clustering of the distribution network. The original matrix of indicators is normalized. Different normalization formulas are used for positive and negative indicators to ensure that the normalized indicator values ​​fall within the range of [0.002, 1]. Calculate the information entropy of each indicator. The information entropy is obtained by the ratio of the indicator's normalized value to the logarithm. The ratio of an indicator is the ratio of a single normalized value to the sum of all normalized values ​​of that indicator. The entropy weight of each indicator is calculated based on the information entropy. The weight is the ratio of the complement of the information entropy to the sum of the complements of all indicators. The normalized index values ​​are summed with their corresponding entropy weights to obtain the hybrid index for distributed resource clustering evaluation of each candidate cluster number k.

[0014] Optionally, a method for determining the optimal number of clusters and outputting the clustering results of distributed resources in the distribution network includes: Iterate through all candidate cluster numbers k and select the cluster evaluation mixture index corresponding to the maximum index as the optimal cluster number for the Gaussian mixture model of distributed resources in the distribution network. Extract the refined clustering results of the Gaussian mixture model with the optimal number of clusters, and determine the cluster affiliation of each distributed resource sample in the distribution network; The clustering results are structured and output according to the distributed resource type and the dimension of operating characteristic parameters. The output results include the cluster number, the number of samples in each cluster, and the statistical values ​​of the characteristic parameters of each cluster, which can be directly used to guide the formulation of differentiated scheduling strategies for distributed resources in the distribution network.

[0015] Secondly, this application provides a Gaussian mixture model clustering system for distributed resources in power distribution networks, comprising: The data acquisition module is used to acquire the operating characteristic parameters of multiple distributed resources within the distribution network area and perform standardized processing to construct a multidimensional feature dataset adapted to Gaussian mixture model clustering. The value determination module is used to determine the range of values ​​for the number of clusters k based on the number of samples in the multidimensional feature dataset. The initial clustering module is used to perform initial clustering of the multidimensional feature dataset using the K-means algorithm, and to initialize the cluster centers and covariance matrix of the Gaussian mixture model. The fine clustering module is used to iteratively optimize the mixing coefficients, cluster centers, and covariance matrix of Gaussian mixture models based on the expectation-maximization algorithm, and to complete fine clustering of multidimensional feature datasets. The calculation module is used to calculate the improved Davidson-Bolding index, the improved Kalinsky-Harabas index, and the profile coefficient for each candidate cluster number k, respectively, to adapt to the characteristics of distributed resource parameters in the distribution network. The index construction module is used to objectively determine the weights of the above three indicators using the entropy weight method, construct a cluster evaluation hybrid index, and use the k corresponding to the maximum value of the index as the optimal number of clusters. The output module is used to output the clustering results of each distributed resource in the distribution network under the optimal clustering number, providing data support for the differentiated scheduling of distributed resources in the distribution network.

[0016] In summary, this application improves the clustering adaptability to heterogeneous parameters by adapting the non-spherical distribution characteristics of resource parameters to a Gaussian mixture model. It improves the Davidson-Bolding and Kalinsky-Hallas indices by introducing Mahalanobis distance and sample weighting mechanisms, effectively reducing the interference of outliers on clustering evaluation. Combined with the silhouette coefficient, it achieves multi-dimensional evaluation of clustering results. Based on the entropy weight method, it constructs a clustering evaluation mixture index to accurately determine the optimal number of clusters, completely solving the problem of subjective arbitrariness in the selection of cluster numbers in traditional methods, and significantly improving the objectivity and accuracy of clustering results. Its clustering results can provide reliable data support for the differentiated scheduling of distributed resources in the distribution network, significantly improving the efficiency of resource aggregation management and utilization. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the first embodiment of the Gaussian mixture model clustering method for distributed resources in the distribution network of this application; Figure 2 These are curves of various evaluation indicators in the first embodiment of the Gaussian mixture model clustering method for distributed resources in the distribution network of this application; Figure 3 This is a distribution diagram of the PCA dimensionality reduction clustering results of energy storage devices in the first embodiment of the Gaussian mixture model clustering method for distributed resources in the power distribution network of this application; Figure 4 This is a structural block diagram of the first embodiment of the Gaussian mixture model clustering system for distributed resources in the power distribution network of this application. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0019] Traditional distributed resource clustering methods for power distribution networks typically rely on manual experience or a single threshold for classification, making it difficult to objectively and adaptively characterize the complex similarities and group characteristics among resources. This can lead to coarse scheduling strategies. Existing clustering algorithms are not adaptable to the non-spherical and heteroscedastic distribution of resource parameters, and single evaluation indicators are easily affected by outliers, failing to comprehensively reflect the clustering quality. Consequently, the selection of the optimal number of clusters is subjective and uncertain.

[0020] To address this, this application provides a Gaussian mixture model clustering method for distributed resources in power distribution networks, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of the Gaussian mixture model clustering method for distributed resources in the power distribution network of this application.

[0021] In this embodiment, the Gaussian mixture model clustering method for distributed resources in the power distribution network includes the following steps: Step S10: Obtain the operating characteristic parameters of multiple distributed resources within the distribution network area and perform standardization processing to construct a multidimensional feature dataset adapted to Gaussian mixture model clustering.

[0022] It should be noted that, for ease of understanding, some key terms in this embodiment are explained below: Distributed resources refer to various small, decentralized power generation, energy storage, or load regulation devices connected to the distribution network, such as photovoltaic power generation units, wind power generation units, energy storage devices, electric vehicle charging facilities, and flexible loads. These resources are typically characterized by geographically dispersed locations, relatively small capacity, and diverse operating characteristics. Their aggregation and coordinated control play a crucial role in improving the operating efficiency and flexibility of the distribution network.

[0023] A Gaussian Mixture Model (GMM) is a probabilistic model used to represent a population containing multiple subpopulations that follow a Gaussian distribution. In clustering applications, GMM assumes that the data points in each cluster follow a Gaussian distribution. By learning the parameters of these Gaussian distributions (such as mean, covariance, and mixture coefficients), soft clustering can be performed on the data, that is, assigning a probability to each data point that it belongs to each cluster.

[0024] K-means is a hard clustering algorithm that aims to divide n data points into k clusters, such that each data point belongs to the cluster containing its nearest cluster center. This algorithm optimizes the clustering results by iteratively calculating cluster centers and reallocating data points, and is often used for initializing Gaussian mixture models.

[0025] The Expectation-Maximization (EM) algorithm is an iterative optimization algorithm used to find the maximum likelihood estimate of parameters in a probabilistic model, especially suitable for models with latent variables. In a Gaussian mixture model, the EM algorithm calculates the posterior probability of each data point belonging to each Gaussian component in the expectation step (E-step) and updates the model parameters (mixture coefficients, mean, and covariance) in the maximization step (M-step) until the model converges.

[0026] The improved Davidson-Baudin index is an internal metric for evaluating clustering performance. Its basic idea is to measure the ratio of intra-cluster compactness to inter-cluster separation. A smaller value indicates better clustering. By incorporating Mahalanobis distance and considering the covariance matrix, it can better accommodate non-spherical data characteristics.

[0027] The improved Kalinsky-Hallabus index is another internal clustering effectiveness metric that assesses clustering quality by calculating the ratio of between-cluster divergence to within-cluster divergence. A higher index value indicates better clustering performance. Introducing sample weights and a weighted covariance matrix can reduce the impact of outliers on the index calculation.

[0028] The silhouette coefficient is an internal metric used to evaluate clustering performance. It measures the similarity of a sample to its own cluster and its dissimilarity to other clusters. The silhouette coefficient ranges from -1 to 1. A value closer to 1 indicates a better clustering outcome, while a value closer to -1 suggests that the sample may have been assigned to the wrong cluster.

[0029] Entropy weighting is an objective weighting method that determines the weight of an indicator based on the degree of variation in its value. The lower the information entropy, the greater the degree of variation of the indicator, and the more information it provides; therefore, it should be assigned a higher weight. This method avoids the influence of subjective factors on the determination of indicator weights.

[0030] The clustering evaluation hybrid index is a comprehensive evaluation index obtained by combining multiple clustering effectiveness indicators, determining the weights of each indicator using an objective weighting method (such as the entropy weight method), and then summing them up. This index aims to more comprehensively and objectively reflect the quality of clustering results, thereby assisting in the selection of the optimal number of clusters.

[0031] It should be noted that the method for constructing the multidimensional feature dataset includes: screening distributed resources within the distribution network, wherein the distributed resources are one or more of energy storage devices, photovoltaic power generation units, wind power generation units, flexible loads, and electric vehicle charging facilities; extracting at least three types of operational feature parameters from the distributed resources, wherein the operational feature parameters include power-related, energy-related, and performance-related parameters; and normalizing the extracted operational feature parameters using a standardization method to eliminate dimensional differences, thereby obtaining the multidimensional feature dataset. Among these, performance-related parameters include: charge / discharge efficiency, power generation efficiency, response time, ramp rate, and self-discharge rate.

[0032] Understandably, the above technical solution achieves several key benefits. First, by selecting specific types of distributed resources within the distribution network, such as energy storage devices, photovoltaic power generation units, wind power generation units, flexible loads, and electric vehicle charging facilities, the constructed multidimensional feature dataset ensures that it only includes key assets that significantly impact the operation of the distribution network and require differentiated scheduling. This effectively avoids interference from irrelevant data in the clustering results and improves the focus of the analysis. Second, by extracting at least three types of operational feature parameters—power, energy, and performance parameters—the operational characteristics of each distributed resource can be comprehensively and deeply characterized from multiple dimensions. This multidimensional feature representation can more fully capture the complex behavioral patterns of distributed resources under different operating scenarios, providing rich information for subsequent Gaussian mixture models to identify their inherent differences. Finally, a standardization method is used to normalize the extracted operational feature parameters, successfully eliminating the influence of parameters with different dimensions and numerical ranges on the clustering distance calculation. This ensures that all features have equal weight and contribution in the clustering process, avoiding bias caused by certain features with larger values ​​dominating the clustering results. These measures work together to significantly improve the quality and representativeness of the multidimensional feature dataset, providing high-quality input for subsequent fine clustering based on the expectation-maximization algorithm. This enables the clustering results to more accurately and effectively reflect the actual operating mode and differentiated needs of distributed resources in the distribution network, laying a solid data foundation for formulating precise differentiated scheduling strategies.

[0033] Step S20: Determine the range of values ​​for the number of clusters k based on the number of samples in the multidimensional feature dataset.

[0034] Step S30: Use the K-means algorithm to perform initial clustering on the multidimensional feature dataset to complete the initialization of the cluster centers and covariance matrix of the Gaussian mixture model.

[0035] The method for determining the number of clusters and initializing the parameters of the Gaussian mixture model includes: setting the value of the number of clusters k to a range of 2~ N is the number of samples in the multidimensional feature dataset; the multidimensional feature dataset is input into the K-means algorithm, and the cluster center of each initial cluster is obtained through iterative calculation; based on the sample distribution of the initial clusters, the covariance matrix of each cluster is calculated, and the cluster center and covariance matrix of the Gaussian mixture model are initialized.

[0036] The above technical solution clarifies the reasonable search range for the number of clusters, k, avoiding blind selection and laying the foundation for determining the optimal number of clusters. Simultaneously, leveraging the efficiency and effectiveness of the K-means algorithm, high-quality initial cluster centers are provided for the Gaussian mixture model. More importantly, by calculating the covariance matrix of each cluster based on the sample distribution of the initial K-means clusters, the initialization parameters of the Gaussian mixture model can more accurately reflect the intrinsic structure and distribution characteristics of the data. This data-driven initialization method significantly improves the convergence speed and stability of the expectation-maximization algorithm, reducing its risk of getting trapped in local optima. This ensures the accuracy and reliability of the fine-grained clustering results of distributed resources in the distribution network, providing more solid data support for subsequent differentiated scheduling.

[0037] Step S40: Iteratively optimize the mixing coefficients, cluster centers, and covariance matrix of the Gaussian mixture model based on the expectation-maximization algorithm to complete the fine clustering of the multidimensional feature dataset.

[0038] The method for optimizing Gaussian mixture models and performing fine clustering based on the expectation-maximization algorithm includes: performing expectation step calculation based on the initialized Gaussian mixture model parameters to obtain the posterior probability of each sample belonging to each cluster; performing maximization step calculation to update the mixture coefficients, cluster centers, and covariance matrix of the Gaussian mixture model in combination with the posterior probability; repeatedly iterating the expectation step and maximization step until the model parameters converge or the preset number of iterations is reached, and performing fine clustering of the dataset based on the converged model parameters.

[0039] Through the above technical solution, after the initial clustering and Gaussian mixture model parameter initialization of the multidimensional feature dataset of distributed resources in the distribution network, this embodiment further introduces the expectation-maximization algorithm for iterative optimization. Specifically, the expectation step calculates the posterior probability of each distributed resource sample belonging to each cluster based on the current model parameters, realizing a soft evaluation of sample belonging. Subsequently, the maximization step uses these posterior probabilities to accurately update the mixing coefficients, cluster centers, and covariance matrix of the Gaussian mixture model, enabling the model parameters to more accurately reflect the true distribution of distributed resource data. By repeatedly iterating the expectation and maximization steps until the model parameters converge or reach the preset number of iterations, it ensures that the Gaussian mixture model can fully learn the intrinsic structure of the data, overcoming the limitations that may exist in the initial parameters. Finally, the refined clustering completed based on the converged model parameters can more accurately and robustly identify the clustering belonging of distributed resources in the distribution network, significantly improving the accuracy and reliability of the clustering results. This leads to a deeper understanding of the operating characteristics of distributed resources, providing more solid and refined data support for the subsequent formulation of differentiated scheduling strategies based on clustering results, thereby optimizing the operating efficiency and management level of the distribution network.

[0040] Step S50: For each candidate cluster number k, calculate the improved Davidson-Bolding index, the improved Kalinsky-Harabass index, and the silhouette coefficient that are adapted to the characteristics of distributed resource parameters in the distribution network.

[0041] An improved method for calculating the Davidson-Bolding index includes: for each cluster after fine clustering, calculating the average Mahalanobis distance from the samples within the cluster to the cluster center as the intra-cluster dispersion. The Mahalanobis distance calculation incorporates the inverse of the cluster's covariance matrix to adapt to the non-spherical distribution characteristics of distributed resource parameters in the distribution network; calculating the Mahalanobis distance between any two cluster centers based on the joint covariance matrix as the inter-cluster distance. The joint covariance matrix is ​​jointly determined by the covariance matrices of the two clusters; calculating the similarity between two clusters based on the intra-cluster dispersion and the inter-cluster distance; selecting the maximum similarity value of each cluster relative to all other clusters and calculating the mean of these maximum similarities to obtain the improved Davidson-Bolding index. The smaller the index value, the better the clustering effect of distributed resources in the distribution network.

[0042] In its implementation, the improved Davidson-Bolding index uses Mahalanobis distance instead of Euclidean distance to calculate intra-class dispersion and inter-class distance. Intra-class dispersion is defined as the average Mahalanobis distance from within a class sample to its class center, and inter-class distance is defined as the Mahalanobis distance between the two class centers based on their joint covariance matrix. The formula for calculating the intra-class dispersion of the improved Davidson-Bolding index is as follows: in Let be the sample set of the i-th cluster; Let be the number of samples in the i-th cluster; Belongs to cluster A sample vector; Let i be the cluster center of the i-th cluster; Let be the inverse of the covariance matrix of the i-th cluster. The improved Davidson-Boldt index is calculated using the following formula for the intra-class distance: in and Let i and j be the cluster centers of the i-th and j-th clusters; and Let be the covariance matrix of the i-th and j-th clusters. The physical meaning of is the Mahalanobis distance between the centers of two clusters. This distance is standardized using the joint covariance structure of the two clusters, thus reflecting the differences in shape and orientation between the two clusters. If the two clusters are similar in shape and have the same orientation, then... It will be smaller; if the shape or orientation differs greatly, then... It will increase. And the similarity This measures the similarity between cluster i and cluster j; a smaller value indicates better separation between the two clusters. and Let be the intra-class dispersion of clusters i and j, respectively. The average of the maximum similarity values ​​selected from the similarity scores is the improved Davidson-Bolding index. The smaller the index value, the better the classification effect. In actual distribution networks, the operating parameters (such as power, capacity, efficiency, and ramp rate) of distributed resources such as energy storage, photovoltaics, and flexible loads often exhibit multidimensional coupling and non-uniform distribution characteristics. Their parameter space is usually not an isotropic spherical structure, but rather an ellipse or more complex geometric shape with directional and scale differences. The improved Davidson-Bolding index uses Mahalanobis distance instead of Euclidean distance, considers the covariance matrix of each class, and makes the distance metric adapt to the distribution shape and direction, making it more sensitive and fairer to clustering results of non-spherical, heteroscedastic, and directed distributions.

[0043] Through the above technical solutions, after fine-grained clustering of distributed resources in the distribution network, an improved Davidson-Bolding index can be used to more accurately and robustly evaluate the clustering effect. Specifically, by introducing the inverse of the cluster covariance matrix into the calculation of intra-cluster dispersion, Mahalanobis distance can adapt to the non-spherical distribution characteristics of distributed resource parameters in the distribution network, thus more realistically reflecting the compactness of samples within a cluster. Simultaneously, using Mahalanobis distance based on the joint covariance matrix in the inter-cluster distance calculation comprehensively considers the distribution pattern of the two clusters, avoiding the bias that may occur when traditional Euclidean distance deals with non-spherical clusters, making the measurement of inter-cluster separation more accurate. This improved index can more effectively capture the complex structure of distributed resource data in the distribution network, providing a more reliable input for the subsequent entropy weight method to construct a mixed index for cluster evaluation, thereby improving the accuracy of selecting the optimal cluster number k, and ultimately providing more accurate data support for the differentiated scheduling of distributed resources in the distribution network.

[0044] In practical implementation, the calculation method of the Kalinsky-Hallas index is improved, including: for each cluster after fine clustering, sample weights are introduced to calculate the weighted covariance matrix within the cluster. The sample weights are determined by the mean of the squared distances from the sample to the cluster center, and the weights of outliers are close to 0 to reduce the interference of abnormal parameters of distributed resources in the distribution network on the index; based on the weighted covariance matrix of each cluster, the overall weighted intra-class scatter matrix is ​​calculated and its trace is solved; the inter-class scatter matrix of each cluster center relative to the global center is calculated and its trace is solved, where the global center is the mean of all samples in the multi-dimensional feature dataset of distributed resources in the distribution network; the normalized ratio of the trace of the inter-class scatter matrix to the trace of the weighted intra-class scatter matrix is ​​calculated to obtain the improved Kalinsky-Hallas index. The larger the index value, the better the clustering effect of distributed resources in the distribution network.

[0045] In its implementation, the improved Kalinsky-Harabas index introduces sample weights when calculating the within-class scatter matrix. To calculate the covariance matrix of the within-class data: Where k is the number of clusters, Cq is the sample set of the q-th cluster, and x is a sample vector belonging to cluster q. Let q be the cluster center of the q-th cluster. The weights of sample x, This is the mean of the squared distances from all samples within the cluster to the cluster center, i.e. This reduces the contribution of outliers to the within-class covariance matrix. The formula for the between-class covariance matrix in the Kalinsky-Harabas index is: in, The global center of the entire dataset, i.e. N is the total number of samples. The physical meaning of is to define the inter-class scatter matrix, reflecting the degree of dispersion of each cluster center relative to the global center. The final improved Kalinsky-Harabas index expression is: in The trace of the inter-class scatter matrix measures the degree of dispersion between classes. The trace of the weighted within-class scatter matrix measures the weighted dispersion of samples within a class. (Indicator) The larger the value, the greater the inter-class dispersion and the smaller the intra-class dispersion, meaning the better the clustering effect.

[0046] Through the above technical solution, this embodiment introduces a sample weighting mechanism when calculating the Kalinsky-Hallabas index, effectively suppressing the impact of outliers on intra-cluster divergence and thus improving the index's robustness to abnormal data. Simultaneously, by calculating the weighted covariance matrix, it can more accurately reflect the non-spherical distribution characteristics of distributed resource parameters in the distribution network, avoiding the limitations of traditional methods when dealing with complex data distributions. This improvement enables the Kalinsky-Hallabas index to more realistically and accurately evaluate the clustering effect of distributed resources in the distribution network under different numbers of clusters, especially when data quality is inconsistent or complex patterns exist. Therefore, when constructing a mixed index for cluster evaluation in subsequent steps, this improved index can provide a more reliable evaluation basis, helping to more accurately determine the optimal number of clusters, thereby providing stronger data support for differentiated scheduling of distributed resources in the distribution network and improving the effectiveness and economy of scheduling strategies.

[0047] The method for calculating the silhouette coefficient includes: for each sample in the multidimensional feature dataset of distributed resources in the distribution network after fine clustering, calculating the average distance from the sample to all other samples in the same cluster, denoted as the intra-cluster distance; calculating the average distance from the sample to all samples in other clusters, selecting the minimum value as the inter-cluster distance; calculating the silhouette coefficient of the sample based on the intra-cluster distance and the inter-cluster distance, the silhouette coefficient being the difference between the inter-cluster distance and the intra-cluster distance divided by the maximum of the two; calculating the arithmetic mean of the silhouette coefficients of all samples to obtain the silhouette coefficient corresponding to the candidate cluster number k, the closer the coefficient is to 1, the better the sample clustering belonging effect of the distributed resources in the distribution network.

[0048] In practice, the silhouette coefficient (SC) is used to measure the similarity between a sample point and other points in the same cluster. The silhouette coefficient of the i-th point is defined as follows: in It is the average distance from the i-th point to other points in the same cluster; Let be the minimum average distance from the i-th point to points in different clusters. The silhouette coefficient ranges from -1 to 1. The closer the silhouette coefficient is to 1, the better the match between the point and the category; conversely, the closer it is to 1, the worse the match. Then, the weights of the above three indicators are determined using the entropy weight method to construct a cluster evaluation mixture index.

[0049] Through the above technical solution, this embodiment introduces the silhouette coefficient as a clustering evaluation index. This index, by calculating the intra-cluster distance and inter-cluster distance of each distributed resource sample in the distribution network, can intuitively quantify the rationality of assigning a single sample to its respective cluster and its distinguishability from other clusters. By calculating the arithmetic mean of the silhouette coefficients of all samples, a quantitative evaluation of the overall clustering effect of distributed resources in the distribution network under the current candidate cluster number k can be obtained. This evaluation method not only considers the compactness and separation of clusters but also delves into the sample level, providing a strong basis for judging the refinement of the clustering results. This allows for a more accurate selection of the optimal number of clusters, ensuring the reliability of the clustering assignment results for distributed resources in the distribution network.

[0050] Step S60: Objectively determine the weights of the above three indicators using the entropy weight method, construct a cluster evaluation mixture index, and use the k corresponding to the maximum value of the index as the optimal number of clusters.

[0051] The method for constructing a mixed index for cluster evaluation using the entropy weight method includes: collecting the improved Davidson-Bolding index, the improved Kalinsky-Harabás index, and the silhouette coefficient corresponding to each candidate cluster number k to construct the original index matrix for distributed resource clustering in the distribution network; normalizing the original index matrix, using different normalization formulas for positive and negative indices to ensure that the normalized index values ​​fall within the range of [0.002, 1]; calculating the information entropy of each index, which is obtained by the ratio of the normalized index value to the logarithm, where the ratio is the ratio of a single normalized value to the sum of all normalized values ​​for that index; calculating the entropy weight of each index based on the information entropy, where the weight is the ratio of the complement of the information entropy to the sum of the complements of all index values; and weighting and summing the normalized index values ​​with their corresponding entropy weights to obtain the mixed index for distributed resource cluster evaluation in the distribution network corresponding to each candidate cluster number k.

[0052] In practical implementation, the steps for constructing the cluster evaluation mixture index using the entropy weight method are as follows: First, the three index values ​​are normalized to fall within the range of [0.002, 1]. The normalization processes for the positive and negative indices are as follows: in Let be the j-th index value of the i-th candidate cluster number k; The j-th indicator is the maximum value among all candidate k values; Let k be the minimum value of the j-th indicator among all candidate k values. Then, calculate the information entropy of each indicator, using the formula: in The weight of the j-th indicator value of the i-th candidate k-value is the proportion of the sum of all candidate k-values ​​for that indicator. Next, the weights of each indicator are determined based on information entropy: in , , These are the normalized values ​​of the three indicators corresponding to the k-th candidate cluster number.

[0053] This embodiment effectively addresses the problem of subjective weight setting and difficulty in objectively determining the optimal number of clusters when evaluating distributed resources in distribution networks, particularly in multi-indicator comprehensive evaluation. This method utilizes the entropy weight method to objectively determine the weights of each evaluation indicator based on its information content (i.e., dispersion) under different candidate cluster numbers, avoiding subjective biases caused by manually setting weights. Subsequently, these objective weights are weighted and summed with standardized indicator values ​​to form a comprehensive cluster evaluation hybrid index. This approach can more accurately and comprehensively evaluate the clustering effect under different cluster numbers, thereby selecting the optimal number of clusters that best reflects the intrinsic structure of distributed resources in the distribution network. This not only overcomes the limitations of single indicators but also significantly enhances the reliability and persuasiveness of the clustering results, providing more solid and scientific data support for the subsequent formulation of differentiated scheduling strategies for distributed resources in the distribution network.

[0054] Step S70: Output the clustering results of each distributed resource in the distribution network under the optimal clustering number, providing data support for the differentiated scheduling of distributed resources in the distribution network.

[0055] The method for determining the optimal number of clusters and outputting the clustering results of distributed resources in the distribution network includes: traversing all candidate clustering numbers k corresponding to clustering evaluation mixture indices, selecting the k corresponding to the maximum value of the index as the optimal number of clusters for the Gaussian mixture model clustering of distributed resources in the distribution network; extracting the refined clustering results of the Gaussian mixture model under the optimal number of clusters, and determining the cluster affiliation of each distributed resource sample in the distribution network; and outputting the cluster affiliation results in a structured manner according to the distributed resource type and the dimension of operating characteristic parameters. The output results include the cluster number, the number of samples in each cluster, and the statistical values ​​of the characteristic parameters of each cluster, which can be directly used to guide the formulation of differentiated scheduling strategies for distributed resources in the distribution network.

[0056] Through the above technical solution, this embodiment overcomes the limitation of insufficient information in guiding actual scheduling by traditional clustering results. First, by traversing and selecting k corresponding to the maximum value of the clustering evaluation mixture index as the optimal number of clusters, the objectivity and optimality of the clustering results are ensured, avoiding potential biases from subjective judgment. Second, based on the refined clustering results of the Gaussian mixture model under the optimal number of clusters, the cluster affiliation of each distributed resource sample can be accurately determined, laying the foundation for subsequent refined management. More importantly, this embodiment outputs the cluster affiliation results in a structured manner according to the distributed resource type and operational characteristic parameters, explicitly including the cluster number, the number of samples in each cluster, and the statistical values ​​of the characteristic parameters of each cluster. This highly integrated and generalized output format allows distribution network dispatchers to clearly grasp the typical operational characteristics and scale of each cluster, thus eliminating the need for additional data analysis or processing, and directly applying this insightful information to the formulation of differentiated scheduling strategies for distributed resources in the distribution network. This greatly improves the efficiency and accuracy of dispatching decisions, and helps to achieve refined management and optimized configuration of distributed resources of different types and operating characteristics, thereby improving the operational stability, economy and flexibility of the distribution network.

[0057] In specific implementation, firstly, the operating characteristic parameters of multiple distributed resources within the distribution network area are obtained, and the operating parameters are standardized to construct a multi-dimensional feature dataset. Distributed resources include, but are not limited to, one or more of energy storage devices, photovoltaic power generation units, wind power generation units, flexible loads, and electric vehicle charging facilities. The operating characteristic parameters of distributed resources include at least the following three categories: 1) Power parameters: maximum charging / discharging power, maximum generating power, and load baseline power; 2) Energy parameters: rated capacity, upper and lower limits of energy status, and initial energy; 3) Performance parameters: charging and discharging efficiency, generating efficiency, response time, ramp rate, and self-discharge rate.

[0058] It should be noted that the embodiments of this invention take energy storage device clustering as an example, with a total of 150 devices. The device operating characteristic parameters are selected from five items: capacity, power, efficiency, ramp rate, and self-discharge coefficient, and generated using the Monte Carlo method according to Table 1. Table 1 Then, the K-means algorithm is used to perform initial clustering of the dataset, initializing the cluster centers and covariance matrix of the Gaussian mixture model. Next, the parameters of the Gaussian mixture model are iteratively optimized using the expectation-maximization algorithm to complete the fine-grained clustering of the dataset. The number of candidate clusters k ranges from 2 to... Where N is the number of samples, for each candidate cluster number k, the improved Davidson-Bolding index, the improved Kalinsky-Harabas index, and the silhouette coefficient are calculated respectively. The improved Davidson-Bolding index uses Mahalanobis distance instead of Euclidean distance to calculate intra-class dispersion and inter-class distance. The formula for calculating intra-class dispersion is: in Let be the sample set of the i-th cluster; Let be the number of samples in the i-th cluster; Belongs to cluster A sample vector; Let i be the cluster center of the i-th cluster, i.e. ; is the inverse of the covariance matrix of the i-th cluster. The physical meaning of is to represent the average Mahalanobis distance from all samples within a cluster to the cluster center (Mahalanobis distance adapts to non-spherical distributions), and to measure the cluster compactness.

[0059] The improved formula for calculating the intra-class distance of the DB metric is as follows: in and Let i and j be the cluster centers of the i-th and j-th clusters; and Let be the covariance matrix of the i-th and j-th clusters. The physical meaning of is the Mahalanobis distance between the centers of two clusters. This distance is standardized using the joint covariance structure of the two clusters, thus reflecting the differences in shape and orientation between the two clusters. If the two clusters are similar in shape and have the same orientation, then... It will be smaller; if the shape or orientation differs greatly, then... It will increase. And the similarity This measures the similarity between cluster i and cluster j; a smaller value indicates better separation between the two clusters. and Let be the intra-class dispersion of clusters i and j, respectively. The average of the maximum similarity values ​​selected from the similarity scores is the improved Davidson-Bolding index. The smaller the index value, the better the classification effect. In actual distribution networks, the operating parameters (such as power, capacity, efficiency, and ramp rate) of distributed resources such as energy storage, photovoltaics, and flexible loads often exhibit multidimensional coupling and non-uniform distribution characteristics. Their parameter space is usually not an isotropic spherical structure, but rather an ellipse or more complex geometric shape with directional and scale differences. The improved DB index uses Mahalanobis distance instead of Euclidean distance, considers the covariance matrix of each class, and makes the distance metric adapt to the distribution shape and direction, making it more sensitive and fairer to clustering results of non-spherical, heteroscedastic, and directed distributions.

[0060] The improved CH index introduces sample weights when calculating the within-class scatter matrix. To calculate the covariance matrix of the within-class data: in This is the mean of the squared distances from all samples within the cluster to the cluster center, i.e. To reduce the contribution of outliers to the within-class covariance matrix, Let be the cluster center of the q-th cluster. Weights The properties are: the value range is (0,1], the closer the sample is to the cluster center, the closer the weight is to 1; the farther away the sample is, the closer the weight is to 0. This weight can reduce the contribution of outliers to the within-class covariance matrix, making the index more robust to noise and outliers. The formula for the between-class covariance matrix in the CH index is: in Let be the number of samples in the q-th cluster. Let q be the cluster center of the q-th cluster. The global center of the entire dataset, i.e. N is the total number of samples. The physical meaning of CH is to define the inter-class scatter matrix, which reflects the degree of dispersion of each cluster center relative to the global center. The final improved CH index expression is: in The trace of the inter-class scatter matrix measures the degree of dispersion between classes. The trace of the weighted within-class scatter matrix measures the weighted dispersion of samples within a class. (Indicator) The larger the value, the greater the inter-class dispersion and the smaller the intra-class dispersion, meaning the better the clustering effect.

[0061] The silhouette coefficient (SC) is used to measure the similarity between a sample point and other points in the same cluster. The silhouette coefficient of the i-th point is defined as follows: in It is the average distance from the i-th point to other points in the same cluster; The silhouette coefficient represents the minimum average distance from the i-th point to points in different clusters. The range of the silhouette coefficient is [-1, 1]. The closer the silhouette coefficient is to 1, the better the match between the point and the category; conversely, the worse the match, the lower the silhouette coefficient. Then, the weights of the three indicators are determined using the entropy weight method, and a clustering evaluation mixture index is constructed. The number of clusters corresponding to the maximum value of this index is taken as the optimal number of clusters. Finally, the clustering assignment results for each distributed resource under the optimal number of clusters are output.

[0062] The weights of the three indicators mentioned above are determined using the entropy weight method, a cluster evaluation mixture index is constructed, and the number of clusters corresponding to the maximum value of this index is taken as the final number of clusters k. The specific steps are as follows: First, there are m candidate cluster numbers (k values), each k value corresponds to 3 indicator values, and the original data matrix is ​​constructed. Where i = 1, 2, ..., m represents the i-th candidate k value; j = 1, 2, 3 correspond to "1" for the improved DB index, "2" for the improved CH index, and "3" for the silhouette coefficient, respectively. Next, normalization is performed to convert all indices into positive indices and compress them to the range [0.002, 1]. The normalization processes for positive and negative indices are as follows: in Let be the j-th index value of the i-th candidate cluster number k; The j-th indicator is the maximum value among all candidate k values; Let be the minimum value of the j-th index among all candidate k values. The normalized data matrix is: Then, calculate the information entropy of each indicator, using the following formula: in The weight of the j-th indicator value of the i-th candidate k-value is the proportion of the sum of all candidate k-values ​​for that indicator. Its satisfaction Next, the weights of each indicator are determined based on information entropy: satisfy The improved DB metric has an entropy weight of [value missing]. The improved CH index entropy weight is The contour coefficient index is Then, the normalized index values ​​are weighted and summed to construct the Cluster Evaluation Mixture Index (CEM). For each candidate cluster number k, we have: in , , These are the normalized values ​​of the three indicators corresponding to the k-th candidate cluster number. Finally, the candidate k with the largest CEM value is selected as the final optimal cluster number.

[0063] It should be noted that, Figure 2 The graphs for the various evaluation metrics in this embodiment are shown. The improved Davidson-Bauertin index is represented by a blue curve: the smaller the better, reflecting intra-class compactness and inter-class separation. The improved Kalinsky-Harabas index is represented by a green curve, the silhouette coefficient by a red curve, and the cluster evaluation mixture index by a purple curve. The three metrics are fused by the entropy weight method, and the maximum value corresponds to the optimal number of clusters. As can be seen from the graph, the CEM index value is the largest when k=5, so the final optimal number of clusters is k=5.

[0064] Figure 3 This is a distribution chart of the PCA dimensionality reduction clustering results for energy storage devices in this embodiment. Principal component analysis was used to reduce the 5-dimensional features to 2-dimensionality, showing the cluster distribution of 150 energy storage devices on the PC1-PC2 plane. Different colors represent different cluster categories, and red asterisks represent the cluster centers of each category. A histogram showing the distribution of the number of energy storage devices in each category is also included. The chart clearly shows that the clustering results match the proportion of the generated data.

[0065] By adapting the non-spherical distribution characteristics of resource parameters to a Gaussian mixture model, the clustering adaptability to heterogeneous parameters is improved. The Davidson-Bolding and Kalinsky-Harabas indices are improved by introducing Mahalanobis distance and sample weighting mechanisms, respectively, effectively reducing the interference of outliers on clustering evaluation. Combined with the silhouette coefficient, a multi-dimensional evaluation of clustering results is achieved. A clustering evaluation mixture index is constructed based on the entropy weight method for objective weighting, accurately determining the optimal number of clusters and completely solving the problem of subjective arbitrariness in the selection of cluster numbers in traditional methods, significantly improving the objectivity and accuracy of clustering results. The clustering results can provide reliable data support for differentiated scheduling of distributed resources in the distribution network, significantly improving the efficiency of resource aggregation management and utilization.

[0066] Reference Figure 4 , Figure 4 This is a structural block diagram of the first embodiment of the Gaussian mixture model clustering system for distributed resources in the power distribution network of this application.

[0067] like Figure 4 As shown in the embodiments of this application, the distributed resource Gaussian mixture model clustering system for distribution networks includes: The data acquisition module 10 is used to acquire the operating characteristic parameters of multiple distributed resources in the distribution network area and perform standardized processing to construct a multidimensional feature dataset adapted to Gaussian mixture model clustering. The value determination module 20 is used to determine the range of values ​​for the number of clusters k based on the number of samples in the multidimensional feature dataset; The initial clustering module 30 is used to perform initial clustering of the multidimensional feature dataset using the K-means algorithm, and to initialize the cluster centers and covariance matrix of the Gaussian mixture model. The fine clustering module 40 is used to iteratively optimize the mixing coefficients, cluster centers, and covariance matrix of the Gaussian mixture model based on the expectation-maximization algorithm, and to complete the fine clustering of the multidimensional feature dataset. Calculation module 50 is used to calculate the improved Davidson-Bolding index, the improved Kalinsky-Harabas index, and the profile coefficient for each candidate cluster number k, respectively, to adapt to the characteristics of distributed resource parameters of the distribution network. The index construction module 60 is used to objectively determine the weights of the above three indicators using the entropy weight method, construct a cluster evaluation hybrid index, and use the k corresponding to the maximum value of the index as the optimal number of clusters. Output module 70 is used to output the clustering results of each distributed resource in the distribution network under the optimal clustering number, providing data support for the differentiated scheduling of distributed resources in the distribution network.

[0068] It should be understood that the above are merely illustrative examples and do not constitute any limitation on the technical solution of this application. In specific applications, those skilled in the art can make settings as needed, and this application does not impose any restrictions on this.

[0069] This embodiment adapts the non-spherical distribution characteristics of resource parameters using a Gaussian mixture model, improving its clustering adaptability to heterogeneous parameters. The Davidson-Bolding and Kalinsky-Harabas indices are improved by introducing Mahalanobis distance and sample weighting mechanisms, effectively reducing the interference of outliers on clustering evaluation. A multi-dimensional clustering effect evaluation is achieved by combining the silhouette coefficient. A clustering evaluation mixture index is constructed based on the entropy weight method for objective weighting, accurately determining the optimal number of clusters and completely solving the problem of subjective arbitrariness in the selection of cluster numbers in traditional methods, significantly improving the objectivity and accuracy of clustering results. Its clustering results can provide reliable data support for differentiated scheduling of distributed resources in the distribution network, significantly improving the efficiency of resource aggregation management and utilization.

[0070] It should be noted that the workflow described above is merely illustrative and does not limit the scope of protection of this application. In practical applications, those skilled in the art can select some or all of it to achieve the purpose of this embodiment according to actual needs, and no restrictions are imposed here.

[0071] In addition, for technical details not described in detail in this embodiment, please refer to the method of Gaussian mixture model clustering of distributed resources in distribution networks provided in any embodiment of this application, which will not be repeated here.

[0072] Furthermore, it should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0073] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0074] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as read-only memory (ROM) / RAM, magnetic disk, optical disk), and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, or network device, etc.) to execute the methods of the various embodiments of this application. The above are only preferred embodiments of this application and do not limit the patent scope of this application. All equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A clustering method for distributed resources in a Gaussian mixture model of a power distribution network, characterized in that, include: The operating characteristic parameters of multiple distributed resources within the distribution network area are obtained and standardized to construct a multidimensional feature dataset adapted to Gaussian mixture model clustering. The range of values ​​for the number of clusters k is determined based on the number of samples in the multidimensional feature dataset; The K-means algorithm is used to perform initial clustering on the multidimensional feature dataset, thereby initializing the cluster centers and covariance matrix of the Gaussian mixture model. By iteratively optimizing the mixing coefficients, cluster centers, and covariance matrix of the Gaussian mixture model using the expectation-maximization algorithm, fine clustering of multidimensional feature datasets is achieved. For each candidate cluster number k, the improved Davidson-Bolding index, the improved Kalinsky-Harabas index, and the silhouette coefficient adapted to the characteristics of distributed resource parameters in the distribution network are calculated respectively. The weights of the three indicators are objectively determined using the entropy weight method, and a cluster evaluation mixture index is constructed. The k corresponding to the maximum value of this index is taken as the optimal number of clusters. The clustering results of each distributed resource in the distribution network under the optimal clustering number are output, providing data support for the differentiated scheduling of distributed resources in the distribution network.

2. The Gaussian mixture model clustering method for distributed resources in power distribution networks according to claim 1, characterized in that, Methods for constructing multidimensional feature datasets include: Select distributed resources within the distribution network, wherein the distributed resources are one or more of the following: energy storage devices, photovoltaic power generation units, wind power generation units, flexible loads, and electric vehicle charging facilities; Extract at least three types of operational characteristic parameters from the distributed resource, including power-related, energy-related, and performance-related parameters; The extracted operational feature parameters were normalized using a standardization method to eliminate dimensional differences and obtain a multidimensional feature dataset.

3. The Gaussian mixture model clustering method for distributed resources in power distribution networks according to claim 1, characterized in that, Methods for determining the number of clusters and initializing the parameters of a Gaussian mixture model include: The range of the number of clusters k is set to 2~ N is the number of samples in the multidimensional feature dataset; The multidimensional feature dataset is input into the K-means algorithm, and the cluster centers of each initial cluster are obtained through iterative calculation. Based on the sample distribution of the initial clusters, the covariance matrix of each cluster is calculated, and the cluster centers and covariance matrix of the Gaussian mixture model are initialized.

4. The Gaussian mixture model clustering method for distributed resources in power distribution networks according to claim 1, characterized in that, Methods for optimizing Gaussian mixture models and performing fine clustering based on the expectation-maximization algorithm include: Based on the initialized Gaussian mixture model parameters, the expectation step is performed to obtain the posterior probability of each sample belonging to each cluster. Perform a maximization step calculation and update the mixing coefficients, cluster centers, and covariance matrix of the Gaussian mixture model based on the posterior probability; Repeat the expected step and the maximization step until the model parameters converge or the preset number of iterations is reached. Then, complete the fine clustering of the dataset based on the converged model parameters.

5. The Gaussian mixture model clustering method for distributed resources in power distribution networks according to claim 1, characterized in that, Improvements to the calculation method of the Davidson-Boldt index include: For each cluster after fine clustering, the average Mahalanobis distance from the samples within the cluster to the cluster center is calculated as the intra-cluster dispersion. The Mahalanobis distance calculation introduces the inverse of the cluster's covariance matrix to adapt to the non-spherical distribution characteristics of distributed resource parameters in the distribution network. Calculate the Mahalanobis distance between any two cluster centers based on the joint covariance matrix, and use it as the inter-cluster distance. The joint covariance matrix is ​​jointly determined by the covariance matrices of the two clusters. The similarity between two clusters is calculated based on intra-class dispersion and inter-class distance. The maximum similarity of each cluster relative to all other clusters is selected and the mean of these maximum similarities is calculated to obtain the improved Davidson-Bolding index. The smaller the index value, the better the clustering effect of distributed resources in the distribution network.

6. The Gaussian mixture model clustering method for distributed resources in power distribution networks according to claim 1, characterized in that, Improvements to the calculation method of the Kalinsky-Harabas index include: For each cluster after fine clustering, sample weights are introduced to calculate the weighted covariance matrix within the cluster. The sample weights are determined by the mean of the squared distances from the sample to the cluster center. The weights of outlier samples are close to 0, which reduces the interference of abnormal parameters of distributed resources in the distribution network on the indicators. Based on the weighted covariance matrix of each cluster, the overall weighted within-class scatter matrix is ​​calculated, and its trace is solved. Calculate the inter-class scatter matrix of each cluster center relative to the global center, and solve for its trace. The global center is the mean of all samples in the multi-dimensional feature dataset of distributed resources in the distribution network. The improved Kalinsky-Harabas index is obtained by normalizing the ratio of the trace of the inter-class scatter matrix to the trace of the weighted intra-class scatter matrix. The larger the index value, the better the clustering effect of the distributed resources of the distribution network.

7. The Gaussian mixture model clustering method for distributed resources in power distribution networks according to claim 1, characterized in that, Methods for calculating the profile coefficient include: For each sample in the multidimensional feature dataset of distributed resources in the distribution network after fine clustering, calculate the average distance from the sample to all other samples in the same cluster, and denot it as the intra-cluster distance. Calculate the average distance from the sample to all samples in each other cluster, and select the minimum value as the inter-cluster distance; The silhouette coefficient of a sample is calculated based on the intra-cluster distance and the inter-cluster distance. The silhouette coefficient is the difference between the inter-cluster distance and the intra-cluster distance divided by the maximum of the two. Calculate the arithmetic mean of the profile coefficients of all samples to obtain the profile coefficient corresponding to the candidate cluster number k. The closer the coefficient is to 1, the better the sample clustering effect of the distributed resources of the distribution network is.

8. The Gaussian mixture model clustering method for distributed resources in power distribution networks according to claim 1, characterized in that, Methods for constructing cluster evaluation mixture indices using the entropy weight method include: Collect the improved Davidson-Bolding index, the improved Kalinsky-Harabs index, and the silhouette coefficient corresponding to each candidate cluster number k, and construct the original index matrix for distributed resource clustering of the distribution network. The original matrix of indicators is normalized. Different normalization formulas are used for positive and negative indicators to ensure that the normalized indicator values ​​fall within the range of [0.002, 1]. Calculate the information entropy of each indicator. The information entropy is obtained by the ratio of the indicator's normalized value to the logarithm. The ratio of an indicator is the ratio of a single normalized value to the sum of all normalized values ​​of that indicator. The entropy weight of each indicator is calculated based on the information entropy. The weight is the ratio of the complement of the information entropy to the sum of the complements of all indicators. The normalized index values ​​are summed with their corresponding entropy weights to obtain the hybrid index for distributed resource clustering evaluation of each candidate cluster number k.

9. The Gaussian mixture model clustering method for distributed resources in power distribution networks according to claim 1, characterized in that, Methods for determining the optimal number of clusters and outputting the clustering results of distributed resources in the distribution network include: Iterate through all candidate cluster numbers k and select the cluster evaluation mixture index corresponding to the maximum index as the optimal cluster number for the Gaussian mixture model of distributed resources in the distribution network. Extract the refined clustering results of the Gaussian mixture model with the optimal number of clusters, and determine the cluster affiliation of each distributed resource sample in the distribution network; The clustering results are structured and output according to the distributed resource type and the dimension of operating characteristic parameters. The output results include the cluster number, the number of samples in each cluster, and the statistical values ​​of the characteristic parameters of each cluster, which can be directly used to guide the formulation of differentiated scheduling strategies for distributed resources in the distribution network.

10. A Gaussian mixture model clustering system for distributed resources in a power distribution network, characterized in that, include: The data acquisition module is used to acquire the operating characteristic parameters of multiple distributed resources within the distribution network area and perform standardized processing to construct a multidimensional feature dataset adapted to Gaussian mixture model clustering. The value determination module is used to determine the range of values ​​for the number of clusters k based on the number of samples in the multidimensional feature dataset. The initial clustering module is used to perform initial clustering of the multidimensional feature dataset using the K-means algorithm, and to initialize the cluster centers and covariance matrix of the Gaussian mixture model. The fine clustering module is used to iteratively optimize the mixing coefficients, cluster centers, and covariance matrix of Gaussian mixture models based on the expectation-maximization algorithm, and to complete fine clustering of multidimensional feature datasets. The calculation module is used to calculate the improved Davidson-Bolding index, the improved Kalinsky-Harabass index, and the profile coefficient for each candidate cluster number k, respectively, to adapt to the characteristics of distributed resource parameters in the distribution network. The index construction module is used to objectively determine the weights of the above three indicators using the entropy weight method, construct a cluster evaluation hybrid index, and use the k corresponding to the maximum value of the index as the optimal number of clusters. The output module is used to output the clustering results of each distributed resource in the distribution network under the optimal clustering number, providing data support for the differentiated scheduling of distributed resources in the distribution network.

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