Adaptive cluster division method and device based on multi-dimensional similarity weighting

Abstract

The invention belongs to the technical field of cluster division, and particularly relates to a self-adaptive cluster division method and device based on multi-dimensional similarity weighting, and the method comprises the steps: constructing a power distribution network comprehensive cluster division index, and taking the index as a basis for comprehensive cluster division; the power distribution network comprehensive cluster division indexes comprise a modularity index, a power balance index, a cluster interaction comprehensive index and a source load coincidence rate index; based on a comprehensive cluster division index of the power distribution network, a self-adaptive cluster division algorithm based on multi-dimensional similarity weighting is constructed, cluster division is performed on nodes of the power distribution network, and the method comprises the following steps: normalization processing; constructing a comprehensive similarity matrix, and performing weighted fusion on each index; based on adaptive spectral clustering, constructing a similarity matrix between nodes; and obtaining an optimal cluster division result through eigenvalue decomposition and K-means clustering, and optimizing and evaluating the optimal cluster division result. According to the method, adaptive weighted fusion is realized, and the objectivity and flexibility of cluster division are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of cluster partitioning, and specifically relates to an adaptive cluster partitioning method and device based on multi-dimensional similarity weighting. Background Art

[0002] With the advancement of the construction process of the new power system, the proportion of distributed power sources connected to the grid gradually increases. With the development of renewable energy power generation technology in China, large-scale renewable energy is connected to the distribution network in a distributed manner, which has caused huge changes in the voltage distribution characteristics and power flow direction of the system, and thus affected the planning and operation of the distribution network.

[0003] First of all, the access of large-scale distributed renewable energy forms a group scale, and reverse power flow appears in the distribution network. The output of some distributed renewable energy is sent to some areas of the distribution network to supply power to the load points in adjacent areas. At this time, the circulation and interaction of power make the distributed renewable energy no longer independent individuals, but become distributed renewable energy clusters that can perform power interaction, communicate with each other, and coordinate scheduling. The distributed renewable energy cluster includes components such as lines and transformers in the distribution network, distributed renewable energy such as photovoltaic and wind power, and loads on the user side. The power flow in the cluster can flow bidirectionally, so that the distributed renewable energy in the cluster can achieve coordinated output, and thus be better consumed by the loads in the cluster.

[0004] The power coordinated scheduling and bidirectional power flow of distributed power sources in the cluster cannot exist in a large range in the distribution network, otherwise problems such as excessive network loss and voltage over-limit will occur. Therefore, it is necessary to reasonably divide the boundaries of the cluster, clarify the power coordinated scheduling range of distributed renewable energy, and perform cluster partitioning.

[0005] In terms of cluster partitioning, existing research mainly focuses on several key indicators: electrical distance, power balance, and system coupling. The electrical distance is usually defined based on the sensitivity of the voltage amplitude to the reactive power, while the power balance focuses on the active power balance within the cluster. The system coupling index analyzes the tightness of the connection within the cluster and the sparsity of the connection between clusters. These indicators provide important references for cluster planning, but many studies do not fully consider the impact of reactive power on planning and the impact of cluster scale on the planning results.

[0006] Since the application scenarios of different types of clusters are different, the metrics for cluster boundary division also vary with the application scenarios. Currently, the distribution network zoning methods studied by scholars mainly include clustering analysis methods, upward hierarchical classification methods, Tabu search methods, community mining methods, etc. Among them, the clustering analysis method mainly focuses on mining the similarity of sample data characteristics; while the community division method focuses on merging similar nodes within the network. These algorithms have problems with insufficient calculation accuracy when dealing with complex cluster division metrics and may fall into local optimal solutions. Summary of the Invention

[0007] Based on the above deficiencies in the prior art, the purpose of the present invention is to provide an adaptive cluster division method and device based on multi-dimensional similarity weighting, which realizes adaptive weighted fusion and significantly improves the objectivity and flexibility of cluster division.

[0008] To achieve the above objectives, the present invention provides an adaptive cluster division method based on multi-dimensional similarity weighting, including the following steps: S1. Construct a comprehensive cluster division index for the distribution network as the basis for comprehensive cluster division. The comprehensive cluster division index for the distribution network includes: S1.1. The modularity index Q, which is used to measure the comparison between the similarity of nodes within a cluster and the similarity of nodes between clusters; S1.2. The power balance index , which is used to evaluate the balance degree of active and reactive power within a cluster; S1.3. The comprehensive cluster interaction index , which is used to characterize the tightness and sparsity of the connection between clusters; S1.4. The source-load simultaneity rate index , which is used to reflect the power matching degree between the load and distributed power sources within a cluster; S2. Based on the comprehensive cluster division index for the distribution network, construct an adaptive cluster division algorithm based on multi-dimensional similarity weighting to divide the distribution network nodes into clusters. The steps include: S2.1. Perform normalization processing on , , ; S2.2. Construct a comprehensive similarity matrix and perform weighted fusion on each index; S2.3. Based on adaptive spectral clustering, construct a similarity matrix between nodes; S2.4. Through eigenvalue decomposition and K-means clustering, obtain the optimal cluster division result and optimize and evaluate it.

[0009] As a preferred solution of the present invention, in S1.2, the power balance index Specifically, first, define the active power balance index of the cluster : ; In the formula, is the number of clusters, c represents one of the clusters; T is the number of time instants, t represents one of the time instants; is the net power of cluster c at time t; Then, define the reactive power balance index of the cluster : ; In the formula, represents the maximum value of reactive power supply within the cluster; represents the demand value of reactive power within the cluster; Combining and , we get : ; In the formula, is the weight; is the weight.

[0010] As a preferred solution of the present invention, in S1.3, the comprehensive cluster interaction index Specifically, first, define the volatility : ; In the formula, is the number of interactive branches between clusters, l represents one of the branches; T is the number of time instants, t represents one of the time instants; , are the interactive power values flowing through the interactive branch l at time t and time t + 1 respectively; , are the weight coefficients; is the average value of the interactive power flowing through the interactive branch l; Then, define the fluctuation variance : ; Combining and , we get : ; In the formula, is the weight; is the The weight.

[0011] As a preferred embodiment of the present invention, in the above-mentioned S1.4, the source-load simultaneity rate index is the total cluster correlation coefficient, expressed as: ; In the formula, is the number of clusters, and c represents one of the clusters; is the internal correlation coefficient of cluster c.

[0012] As a preferred embodiment of the present invention, the above-mentioned is expressed as: ; In the formula, is the load set in cluster c, and x represents one of the loads; is the distributed PV set in cluster c, and y represents one of the distributed PVs; is the total number of loads in cluster c; is the total number of distributed PVs in cluster c; is the correlation coefficient between the xth load and the yth distributed PV, is to map to the standardized value in the range of [0, 1], expressed as: ; ; In the formula, represents the covariance; represents the standard deviation; is the power demand of the xth load; is the power output of the yth distributed PV.

[0013] As a preferred embodiment of the present invention, in the above-mentioned S2.1, Q is a standardized value and does not need to be normalized. For , , , map them to the range of [0, 1], and use , , to represent the normalized , , ; In S2.2, construct a comprehensive similarity matrix, and perform weighted fusion on each index. Specifically, define the comprehensive similarity distance between node i and node j. The comprehensive similarity distances between each node form a comprehensive similarity matrix, expressed as: ; wherein is the normalized distance of the modularity index corresponding to nodes i and j; is the normalized distance of the power balance degree index corresponding to nodes i and j; is the normalized distance of the comprehensive index of cluster interaction corresponding to nodes i and j; is the normalized distance of the source-load simultaneity rate index corresponding to nodes i and j; , , , are respectively , , , corresponding weights; is the weighted linear combination after normalization of each index.

[0014] As a preferred solution of the present invention, for the said , , , , the obtaining method is as follows: there are four indexes in total. For the m-th index, m = 1, 2, 3, 4, the similarity distribution ; wherein is the normalized value of the m-th index; N is the total number of nodes; the information entropy of the m-th index is expressed as: ; wherein, ln represents the natural logarithm function; Based on , calculate the weight of the m-th index: .

[0015] As a preferred solution of the present invention, in the said S2.3, based on adaptive spectral clustering, construct a similarity matrix S between nodes, that is, a matrix composed of the similarities of each node, wherein the similarity between nodes i and j is defined by the Gaussian kernel function: ; wherein, exp represents the exponential function; represents the Gaussian kernel parameter; Calculate the degree matrix D. The degree matrix D is a matrix composed of the degrees of each node, wherein the degree of node i is the weighted sum of the similarities of node i with all other nodes: 。

[0016] As a preferred solution of the present invention, in S2.4, the construction of the similarity matrix between nodes based on adaptive spectral clustering is specifically as follows: for the Laplacian matrix L, L = D - S; perform eigenvalue decomposition on L, select the eigenvectors corresponding to the smallest V eigenvalues, and form the eigenmatrix with these eigenvectors , where is the eigenvector corresponding to the v-th smallest eigenvalue; Regard each row of U as a sample point, the dimension of the row vector is V, and use the K-means algorithm to cluster these sample points to obtain V clusters; For the cluster division result, optimize and evaluate it through the following objective function F: ; In the formula, , , , are the weights of Q, , , respectively.

[0017] The adaptive cluster division device based on multi-dimensional similarity weighting includes a memory, a processor, and a computer program stored on the memory and capable of running on the processor. The above method is implemented by the processor executing the computer program.

[0018] The beneficial effects of the present invention are as follows: By comprehensively considering multi-dimensional indicators such as modularity, power balance degree, comprehensive index of cluster interaction, and source-load simultaneity rate, the present invention comprehensively depicts the complex requirements of distribution network cluster division, and solves the problem of limited division effect caused by traditional methods relying on a single indicator or manual setting of weights.

[0019] The present invention introduces the entropy weight method to dynamically adjust the indicator weights, combines spectral clustering with optimization algorithms, realizes adaptive weighted fusion, significantly improves the objectivity and flexibility of the division, avoids local optimal solutions, and at the same time optimizes the calculation efficiency, showing better modularity, power balance degree, and shorter calculation time in simulation experiments.

[0020] By reducing the energy exchange demand between clusters and enhancing the coordination ability of sources, loads, and storages within clusters, the present invention effectively improves the operation stability and economy of the distribution network. Its innovation lies in taking into account both the network topology structure and dynamic operation characteristics, providing a scientific and efficient technical path for cluster division in scenarios with high-proportion distributed energy access, and having significant practical value and promotion potential. Description of the Drawings

[0021] Figure 1 It is the process schematic diagram of the present invention; Figure 2 It is the distribution network topology diagram during the verification process of the present invention; Figure 3 It is the clustering result of the adaptive clustering division algorithm based on multi-dimensional similarity weighting during the verification process of the present invention; Figure 4 It is the clustering result of the ordinary clustering algorithm during the verification process of the present invention. Specific embodiments

[0022] The following further describes the embodiments of the present invention in conjunction with the accompanying drawings: Embodiment 1: As Figure 1 shown, the adaptive clustering division method based on multi-dimensional similarity weighting includes the following steps: S1. Construct a comprehensive clustering division index for the distribution network as the basis for comprehensive clustering division. The comprehensive clustering division index for the distribution network includes: S1.1. The modularity index Q, which is used to measure the comparison between the similarity of nodes within a cluster and the similarity of nodes between clusters; S1.2. The power balance index , which is used to evaluate the balance degree of active and reactive power within a cluster; S1.3. The comprehensive cluster interaction index , which is used to characterize the tightness and sparsity of the connection between clusters; S1.4. The source-load simultaneity rate index , which is used to reflect the power matching degree between the load and distributed power sources within a cluster; S2. Based on the comprehensive clustering division index for the distribution network, construct an adaptive clustering division algorithm based on multi-dimensional similarity weighting to perform clustering division on the distribution network nodes. The steps include: S2.1. Perform normalization processing on , , ; S2.2. Construct a comprehensive similarity matrix and perform weighted fusion on each index; S2.3. Based on adaptive spectral clustering, construct a similarity matrix between nodes; S2.4. Through eigenvalue decomposition and K-means clustering, obtain the optimal clustering division result and optimize and evaluate it.

[0023] For the calculation of the modularity index Q, it can be obtained by a well-known method. For example, the electrical distance between nodes is defined by voltage sensitivity. The electrical distance between node i and node j based on active voltage sensitivity is defined as: ; ; In the formula, and respectively represent the electrical distances of node i and node j based on the active and reactive voltage sensitivity matrices; and respectively represent the sensitivity coefficients of the active and reactive power injected by node i to its own voltage amplitude; and respectively represent the sensitivity coefficients of the active and reactive power injected by node j to its own voltage amplitude; and respectively represent the sensitivity coefficients of the active and reactive power injected by node j to the voltage amplitude of node i; and respectively represent the sensitivity coefficients of the active and reactive power injected by node i to the voltage amplitude of node j; The electrical distance between node i and node j is defined as: ; In the formula, the weight coefficients and respectively represent the recovery ratios of the active power regulation and reactive power compensation to the voltage violation amount when the voltage is violated; The modularity index Q is expressed as: ; In the formula, k i and k j are the degrees of node i and node j respectively (usually the number of edges); z is the sum of the weights of all nodes; is a 0-1 variable, indicating that node i and node j are in the same cluster, otherwise it is 0; is a function of the electrical distance between nodes, and its value is between [0, 1], and is expressed as: .

[0024] In S1.2, the power balance degree index Specifically, first, define the active power balance degree index of the cluster : ; In the formula, is the number of clusters, c represents one of the clusters; T is the number of time instants, t represents one of the time instants; is the net power of cluster c at time t; Then, define the reactive power balance degree index of the cluster : ; In the formula, represents the maximum value of the reactive power supply within the cluster; represents the demand value of the reactive power within the cluster; Combining and , we get : ; In the formula, is the weight; is the weight of

[0025] In S1.3, the comprehensive index of cluster interaction Specifically, first, define the volatility : ; In the formula, is the number of the interaction branches between clusters, l represents one of the branches; T is the number of moments, and t represents one of the moments; , are the interaction power values flowing through the interaction branch l at the moment t and the moment t + 1 respectively; , are the weight coefficients; is the average value of the interaction power flowing through the interaction branch l; Then, define the fluctuation variance : ; Combining and , we get : ; In the formula, is the weight of is the weight of

[0026] When designing the comprehensive index of cluster interaction, aiming at the interaction between clusters and the optimization of power flow, by quantifying and optimizing the power fluctuation, power flow between clusters, and the control effects inside and outside the clusters, the stability and efficiency of the entire distribution system are improved.

[0027] The designed , mainly analyzes the stability of the power fluctuation between clusters, so the fluctuation mean values of multiple branches are considered; the designed , which represents the active power of the interactive line l at time t. The subtraction represents the change in active power between two consecutive times t and t + 1, and dividing by max() is used to normalize the fluctuation amount. This formula reflects the active power fluctuation between clusters. The greater the fluctuation, the more unstable the power interaction between clusters. The volatility is mainly used to measure the amplitude of power change between two consecutive times. By calculating the power change between adjacent times and normalizing it, it is used to measure the rate of change of power over time, which is more suitable for reflecting the severity of power change in the short term.

[0028] It is used to measure the degree of deviation between the power and its average value, that is, the fluctuation size of the power relative to its average power during the entire time period T. It focuses on the long-term fluctuation relative to the average value, and it measures the overall deviation degree of the power during the entire time period.

[0029] Combining these two, the volatility can help evaluate the instantaneous fluctuation of power in the short term, while the fluctuation variance can be used to evaluate the stability of power during the entire time period. Together, they constitute a comprehensive evaluation of the power fluctuation of the system. The volatility formula combines the volatility of short-term and long-term power in a weighted manner to obtain a comprehensive volatility index (volatility). .

[0030] Designed In the calculation formula, the absolute value represents the absolute value of power flow, that is, without considering the direction, only focusing on the magnitude of power flow. This helps to evaluate the volatility of power flow without being affected by the direction of power flow. The purpose of this formula is to calculate the power flow volatility in the entire distribution system or a certain cluster within a time interval. Through this volatility measurement, the system can understand the change amplitude of power flow in different time steps and control the fluctuation of power flow by adjusting cluster division, load matching, etc., so as to improve the stability of the system.

[0031] Through the designed Related formulas, the purpose of this embodiment is to optimize and control the distribution network in multiple dimensions, especially considering the power fluctuation between clusters and the stability of power flow. This helps to improve the accuracy of cluster division and ensure that the distribution network can maintain a stable power flow in the case of large-scale distributed energy access. By measuring and minimizing the power fluctuation and power flow fluctuation in the system, the uncertainty and volatility of the system can be effectively reduced, the overall adaptive ability of the power grid can be improved, and the energy loss can be reduced. Dynamic weight coefficients are introduced into the formula, and these weight coefficients are adjusted according to the actual operation situation of the system to ensure that the stability and power transmission efficiency of the system can be optimized under different operating environments and demands.

[0032] In S1.4, the source-load simultaneity rate index That is the total correlation coefficient of the clusters, expressed as: ; In the formula, is the number of clusters, and c represents one of the clusters; is the internal correlation coefficient of cluster c.

[0033] The is expressed as: ; In the formula, is the load set in cluster c, and x represents one of the loads; is the distributed PV set in cluster c, and y represents one of the distributed PVs; is the total number of loads in cluster c; is the total number of distributed PVs in cluster c; is the correlation coefficient between the x-th load and the y-th distributed PV, is to map to the standardized value within the range of [0, 1], expressed as: ; ; In the formula, represents the covariance; represents the standard deviation; is the power demand of the x-th load; is the power output of the y-th distributed PV.

[0034] The acquisition formula of

[0035] is designed to optimize the cluster division by quantifying the source-load synchronization rate and ensure the best match between the load demand and the output of distributed power sources. Ideal synchronization means that the load demand can be fully absorbed by the power source, thereby reducing the power exchange demand across clusters and lowering the complexity and instability of system operation. Through this formula, the power system can adjust the cluster division in real time, enhance the coordination between the load and the power source, and make the power transmission and distribution more efficient. is the covariance between load x and distributed PV y, representing the consistency of the changes of these two parameters. If the load and the power source (i.e., the distributed PV) output have a high covariance, it means that their change trends are consistent, indicating a high degree of match between the two. is the standard deviation of the power demand of load x, that is, the volatility of the load demand, which measures the variation range of the load. is the standard deviation of the power output of distributed PV y, which measures the volatility of the power output. The formula of... calculates the correlation between the load and the power source, standardizes the covariance to measure the matching degree between the load and the power source. The larger the correlation coefficient, the higher the matching degree between the load and the power source, and the better the stability of the system.

[0036] After that, through map to the range of [0, 1] to ensure the standardization of the synchronization index for subsequent processing. According to the obtained correlation coefficient, calculate , and obtain the synchronization rate (internal correlation coefficient) between the load and the distributed power source in cluster c, which is used to measure the matching degree between all loads and power sources in the cluster. The higher the synchronization rate, the better the coordination between the load and the power source in the cluster. Finally, by summing and averaging the synchronization rates in all clusters c , the overall synchronization rate of the system is obtained. This synchronization rate helps to evaluate the overall stability of the system and ensure the coordination between the load and the power source across the entire system.

[0037] The acquisition formula of... optimizes the matching between the load and the power source, ensures the effective flow of power, avoids excessive power exchange and energy loss, and improves the operating efficiency of the system. The synchronization optimization makes the relationship between the load and the power source closer and reduces the ineffective energy transmission.

[0038] In S2.1, Q is the standardized value and does not need to be normalized. For , , , map them to the range of [0, 1], and use , , to represent the normalized , , ; The specific normalization method is as follows: ; ; ; According to the formula, and are within the range of [0, 1], is their weighted average, so also takes values within the range of [0, 1]. Therefore, 1 - Normalization method. Similarly, this normalization method can also be used.

[0039] For , through the formula , map from the original [-1, 1] to the standardized value within the range of [0, 1]. After adding conversion, all correlation coefficients become values within the range of [0, 1]. Therefore, the value range of

[0040] will also change from [-1, 1] to [0, 1], and this method can be used for normalization. In S2.2, to construct the comprehensive similarity matrix and perform weighted fusion on each index specifically, define the comprehensive similarity distance between node i and node j. The comprehensive similarity distances between each node form the comprehensive similarity matrix, ; In the formula, is the normalized distance of the modularity index corresponding to node i and node j; is the normalized distance of the power balance degree index corresponding to node i and node j; is the normalized distance of the comprehensive cluster interaction index corresponding to node i and node j; is the normalized distance of the source-load simultaneity rate index corresponding to node i and node j; , , , are respectively , , , the corresponding weights; is the weighted linear combination after normalizing each index.

[0041] , , , The acquisition method of is as follows. There are four indicators in total. For the mth indicator, m = 1, 2, 3, 4, the similarity distribution between node i and node j is: In the formula, is the normalized value of the mth indicator (i.e., , , or ); N is the total number of nodes; the information entropy Expressed as: ; In the formula, ln represents the natural logarithm function; Based on , calculate the weight of the m-th index : .

[0042] In S2.3, based on adaptive spectral clustering, construct the similarity matrix S between nodes, which is the matrix composed of the similarities of each node. The similarity between node i and node j is defined by the Gaussian kernel function: ; In the formula, exp represents the exponential function; represents the Gaussian kernel parameter; The degree matrix D is a matrix related to the similarity matrix S, representing the similarity weights of each node; calculate the degree matrix D, which is the matrix composed of the degrees of each node. The degree of node i is the weighted sum of the similarities between node i and all other nodes: .

[0043] In S2.4, based on adaptive spectral clustering, the construction of the similarity matrix between nodes is specifically as follows: for the Laplacian matrix L, L = D - S; perform eigenvalue decomposition on L, select the eigenvectors corresponding to the smallest V eigenvalues, and form the eigenmatrix from these eigenvectors, where is the eigenvector corresponding to the v-th smallest eigenvalue; Regard each row of U as a sample point, the dimension of the row vector is V, and use the K-means algorithm to cluster these sample points to obtain V clusters; For the cluster division result, optimize and evaluate it through the following objective function F: ; In the formula, , , , are the weights of Q, , , respectively.

[0044] When designing an adaptive cluster partitioning algorithm based on multi-dimensional similarity weighting, traditional clustering methods usually partition clusters based on a single metric (such as the distance or similarity between nodes). However, in practical applications, the similarity between nodes is jointly determined by multiple factors. For example, in a power system, there may be multiple aspects of similarity: load demand, power fluctuation, node synchronization, etc. The multi-dimensional similarity weighting algorithm more precisely measures the comprehensive similarity between nodes by considering information from multiple dimensions and assigning different weights to each dimension.

[0045] The formula design in the adaptive cluster partitioning algorithm based on multi-dimensional similarity weighting quantifies the similarity between nodes and uses multiple metrics (such as power balance, synchronization, modularity, etc.) to ensure that nodes can coordinate reasonably and optimize power flow. Dynamically adjust the weights according to the different characteristics of nodes, construct the similarity matrix between nodes, and finally achieve the optimal cluster partitioning through the clustering algorithm.

[0046] Normalize all metrics and map them to the range [0, 1] to ensure that metrics from different dimensions can be uniformly compared and combined, obtaining the weighted similarity distance between node i and node j , representing the similarity between nodes. Incorporating multiple factors (such as modularity, balance, volatility, and synchronization), the smaller this distance value, the more similar node i and node j are, and they are suitable to be partitioned into the same cluster.

[0047] Dynamically adjust the weights of each metric according to the importance of each metric (reflected by information entropy), thus affecting the final cluster partitioning. is the unnormalized distance value (normalized value) of the m-th metric, representing the difference measure between node i and node j under the m-th metric. The distance between each pair of nodes is transformed into a normalized similarity measure through the similarity distribution between node i and node j Calculate the information entropy of each metric , the higher the value of the information entropy, the more uniform the distribution of this metric, indicating that this metric has a weaker ability to distinguish nodes. The lower the information entropy, the stronger the discriminatory power of this metric. Use the information entropy formula to evaluate the distribution of each metric, and then calculate the weight of each metric 、 、 、 . The metrics with higher information entropy are given smaller weights because their distributions are more uniform and their discriminatory abilities are weaker.

[0048] After calculating the weights for each metric, they can be combined to calculate the weighted similarity between nodes. The Gaussian kernel function is used for calculation, which reflects the similarity between node pairs. Based on the similarity of each node, the distance between nodes is calculated, and the similarity matrix is constructed using the Gaussian kernel function to obtain Finally, the nodes are clustered using the K-means algorithm to finally obtain a reasonable cluster division.

[0049] The adaptive cluster division algorithm based on multi-dimensional similarity weighting can effectively improve the accuracy of cluster division, making the divided clusters more in line with actual needs. The algorithm measures the similarity between nodes by considering multiple metrics and performs the process of node cluster division based on these similarities. Different from traditional clustering methods, this algorithm is not only based on a single metric, but comprehensively considers multiple influencing factors and adopts a weighting strategy to ensure that the influence of each metric is adjusted according to its actual importance.

[0050] The verification process is as follows: Taking a certain actual distribution network as an example for simulation verification. The total load access capacity of this distribution network is 22.8 MVA, and the total photovoltaic power source access capacity is 7.5 MW. The geographical layout (topological diagram) of the distribution network is as Figure 2 shown. The detailed information about the installed photovoltaic capacity in this network is that for nodes 11, 15, 18, 24, 32, 35, 38, 44, 48, 51, 54, 64, 67, 71, 75, 77, 80, 81, 82, 83, the installed capacity is 500 kw each. The total length of the lines to be planned reaches 329.82 km.

[0051] Considering that different weights have different impacts on the cluster division results, in this embodiment, different weights are selected for simulation respectively, and the obtained results are shown in Table 1: Table 1 Influence of different weights on cluster division

[0052] When is dominant, the number of generated clusters is relatively large because modularity emphasizes cluster tightness rather than overall balance. When is dominant, the planning will give priority to the high matching between sources and loads within the cluster, forming a small number of larger clusters. It can be seen that when the weight of a single metric increases, although the performance of a specific metric can be optimized, the performance of other metrics will decline accordingly. Therefore, considering the balance of each metric comprehensively and uniformly allocating weights can avoid over-optimizing a single metric and causing the deterioration of other metrics, ensuring balanced performance in all aspects. At the same time, decision-makers can also select different weights according to their preferences.

[0053] To illustrate the superiority of the adaptive cluster partitioning algorithm based on multi-dimensional similarity weighting proposed in this embodiment in the distribution network cluster partitioning, the algorithm proposed in this embodiment is compared with the ordinary clustering algorithm, and the weights of the comprehensive cluster partitioning indicators are taken as = = = = 0.25. The cluster partitioning results of the adaptive cluster partitioning algorithm based on multi-dimensional similarity weighting are as shown in Figure 3 shown, and the cluster partitioning results of the ordinary clustering algorithm are as shown in Figure 4 shown.

[0054] From Figure 3 and Figure 4 it can be seen that based on the method of this embodiment, a total of 10 clusters are partitioned, the number of clusters is small, and the scale of each cluster is large. In the cluster partitioning results of the comparison algorithm, the number of clusters is large, a total of 13 clusters are partitioned, and the cluster scale is small; this is because larger clusters enable more load demands to be absorbed by distributed photovoltaics within the cluster, reducing the demand for cross-cluster energy exchange.

[0055] Table 2 Comparison of cluster partitioning results under different methods

[0056] As can be seen from Table 2, the solution speed of the cluster partitioning algorithm proposed in this embodiment is higher than that of the traditional clustering algorithm. In addition, from the cluster partitioning indicators in Table 2 and combined with Figure 3 and Figure 4 it can be seen that the optimization results of each cluster partitioning indicator under the algorithm of this embodiment are greater than those of the traditional clustering algorithm. The results show that the cluster partitioning algorithm proposed in this embodiment can make the cluster scale and the number of sizes more reasonable, ensuring that the electrical connection between nodes within the cluster is closer, thus achieving a more reasonable partitioning in terms of network structure.

[0057] Embodiment 2: An adaptive cluster partitioning device based on multi-dimensional similarity weighting includes a memory, a processor, and a computer program stored on the memory and capable of running on the processor. The method in Embodiment 1 is implemented by the processor executing the computer program.

Claims

1. An adaptive clustering method based on multi-dimensional similarity weighting, characterized by The following steps are involved: S1. Construct the comprehensive cluster division index of distribution network as the basis for comprehensive cluster division. The comprehensive cluster division index of distribution network includes: S1.1, modularity index Q, used to measure the comparison between the similarity of nodes within a cluster and the similarity of nodes between clusters; S1.2 Power balance index , used to evaluate the balance of active and reactive power within the cluster; S1.

3. Comprehensive indicators of cluster interaction , used to characterize the closeness of connections between clusters and the sparseness of connections between clusters; S1.

4. Source-load simultaneous rate index , used to reflect the power matching degree between the load and distributed generation within the cluster; S2. Based on the comprehensive clustering index of the distribution network, an adaptive clustering algorithm based on multi-dimensional similarity weighting is constructed to cluster the distribution network nodes. The steps include: S2.

1. Yes , , Perform normalization processing; S2.2, construct a comprehensive similarity matrix and perform weighted fusion of each indicator; S2.3, constructing similarity matrix between nodes based on adaptive spectral clustering; S2.

4. Through eigenvalue decomposition and K-means clustering, the optimal cluster division result is obtained, and it is optimized and evaluated.

2. The adaptive clustering method based on multi-dimensional similarity weighting according to claim 1, characterized in that: In S1.2, the power balance index Specifically, first, define the active power balance index of the cluster : ； In the formula, is the number of clusters, c represents one of the clusters; T is the number of moments, and t represents one of them; is the net power of cluster c at time t; Then, define the reactive power balance index of the cluster : ； In the formula, Indicates the maximum value of reactive power supply within the cluster; Indicates the reactive power demand value within the cluster; comprehensive and ,get : ； In the formula, For Weight; for The weight of .

3. The adaptive clustering method based on multi-dimensional similarity weighting according to claim 1, characterized in that: In S1.3, the cluster interaction comprehensive index Specifically, first, define volatility : ； In the formula, is the number of interaction branches between clusters, and l represents one of the branches; T is the number of moments, and t represents one of them; , are the interactive power values ​​flowing through the inter-cluster branch l at time t and time t+1 respectively; , is the weight coefficient; is the average value of the interaction power flowing through the inter-cluster branch l; Then, define the volatility variance : ； comprehensive and ,get : ； In the formula, for The weight of for The weight of .

4. The adaptive clustering method based on multi-dimensional similarity weighting according to claim 1, characterized in that: In S1.4, the source-load simultaneous rate indicator That is the total cluster correlation coefficient, expressed as: ； In the formula, is the number of clusters, c represents one of the clusters; is the internal correlation coefficient of cluster c.

5. The adaptive clustering method based on multi-dimensional similarity weighting according to claim 4 is characterized in that: The It is expressed as: ； In the formula, is the set of loads in cluster c, and x represents one of the loads; is the set of distributed photovoltaics in cluster c, and y represents one of the distributed photovoltaics; is the total number of loads in cluster c; is the total number of distributed photovoltaics in cluster c; is the correlation coefficient between the x-th load and the y-th distributed photovoltaic, Yes Mapped to a normalized value in the range [0, 1], expressed as: ； ； In the formula, represents covariance; represents standard deviation; is the power demand of the xth load; is the power output of the yth distributed photovoltaic.

6. The adaptive clustering method based on multi-dimensional similarity weighting according to claim 1, characterized in that: In S2.1, Q is a standardized value and does not need to be normalized. , , , map it to the range [0, 1], and use , , Respectively represent the normalized , , ; In S2.2, a comprehensive similarity matrix is ​​constructed to perform weighted fusion on each indicator. Specifically, the comprehensive similarity distance between node i and node j is defined as , the comprehensive similarity distance between each node constitutes a comprehensive similarity matrix, It is expressed as: ； In the formula, is the normalized distance between the modularity indexes of nodes i and j; is the normalized distance between the power balance indicators of nodes i and j; is the normalized distance of the cluster interaction comprehensive index corresponding to node i and node j; is the normalized distance between the source-load simultaneity index of the corresponding nodes i and j; , , , They are , , , The corresponding weights; It is the weighted linear combination of normalized indicators.

7. The adaptive clustering method based on multi-dimensional similarity weighting according to claim 6, characterized in that: The , , , The way to obtain is that there are four indicators in total. For the mth indicator, m=1, 2, 3, 4, the similarity distribution between node i and node j for: ； In the formula, is the normalized value of the mth indicator; N is the total number of nodes; the information entropy of the mth indicator It is expressed as: ； In the formula, ln represents the natural logarithm function; based on , calculate the weight of the mth indicator : 。 8. The adaptive clustering method based on multi-dimensional similarity weighting according to claim 7, characterized in that: In S2.3, based on adaptive spectral clustering, a similarity matrix S between nodes is constructed, which is a matrix composed of the similarities of each node, where the similarity between node i and node j is Defined by the Gaussian kernel function: ； Where, exp represents the exponential function; represents the Gaussian kernel parameter; Calculate the degree matrix D, which is a matrix composed of the degrees of each node, where the degree of node i is the weighted sum of similarities between node i and all other nodes: 。 9. The adaptive clustering method based on multi-dimensional similarity weighting according to claim 8, characterized in that: In the above S2.4, based on the adaptive spectral clustering, the similarity matrix between nodes is constructed as follows: for the Laplace matrix L, L=DS; Perform eigenvalue decomposition on L, select the eigenvectors corresponding to the smallest V eigenvalues, and form these eigenvectors into a feature matrix ,in is the eigenvector corresponding to the vth smallest eigenvalue; Consider each row of U as a sample point, the dimension of the row vector is V, and use the K-means algorithm to cluster these sample points to obtain V clusters; The cluster division results are optimized and evaluated by the following objective function F: ； In the formula, , , , They are Q, , , The weight of .

10. An adaptive clustering device based on multi-dimensional similarity weighting, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, and the method according to any one of claims 1 to 9 is implemented by executing the computer program by the processor.

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