A three-phase unbalanced power distribution network fast partitioning method based on electrical coupling strength

Abstract

The application discloses a three-phase unbalanced power distribution network fast partitioning method based on electrical coupling strength, comprising: data preprocessing of obtained power distribution network related data, construction of power distribution network electrical data set; definition of electrical distance adjustment parameter, calculation of three-phase comprehensive electrical distance between nodes; conversion of three-phase comprehensive electrical distance between nodes into connection weight between nodes, construction of weighted undirected graph model reflecting electrical coupling strength; generation of initial partition by using modularity optimized greedy community discovery algorithm, output of high cohesion initial partition set; construction of merging evaluation function fusing both; iterative execution of area merging, output of final partition result. The application quantifies real electrical correlation between nodes accurately, realizes collaborative optimization of electrical cohesion and balance of sub-region scale, guarantees high efficiency and stability of partition calculation, and provides reliable partition support for power distribution network parallel computing, distributed control and fault self-healing scenes.

Description

Technical Field

[0001] This invention belongs to the field of power grids and relates to distribution network zoning technology, specifically to a rapid zoning method for three-phase unbalanced distribution networks based on electrical coupling strength. Background Technology

[0002] With the increasing penetration of distributed generation (DG) in distribution networks, the traditional unidirectional power supply architecture has been disrupted, resulting in significant three-phase imbalances in the power grid. This presents new challenges to the safe and stable operation, dispatch control, and fault self-healing of the distribution network. Distribution network partitioning, as a fundamental technology for realizing distributed control, parallel computing, and optimized resource allocation, directly impacts the overall operating efficiency and power supply reliability of the distribution network, and therefore has attracted widespread attention in the industry.

[0003] Current distribution network zoning methods are mainly based on geographical topology, single electrical indicators, or traditional clustering algorithms. However, in three-phase unbalanced distribution network scenarios with a high proportion of distributed generation, these methods have gradually revealed significant limitations. Some methods zonify solely based on node geographical location or physical connection relationships, completely ignoring the impact of three-phase impedance differences and distributed generation power injection on the electrical connections between nodes. This results in zoning results that fail to reflect the true electrical coupling state of the power grid, exhibiting problems such as "insufficient cohesion and unreasonable boundary division," making it difficult to adapt to subsequent control and scheduling requirements.

[0004] Other methods, while incorporating electrical indicators, fail to achieve multi-objective collaborative optimization. They either overemphasize electrical cohesion, leading to excessively large differences in sub-region size, or simply pursue load balancing at the expense of realistic electrical coupling. This results in some regions having concentrated loads while others have idle resources, failing to meet the load balancing requirements of parallel computing. Furthermore, most existing partitioning algorithms are highly complex, computationally time-consuming, poorly adaptable to dynamic changes in distribution network operation, and their results from repeated calculations lack stability, making it difficult to meet the real-time and reliability requirements of online engineering applications.

[0005] Therefore, given the characteristics of three-phase unbalanced distribution networks, developing a partitioning method that can accurately quantify electrical coupling relationships, take into account both partition cohesion and balance, and possess efficient and stable computational performance has become a key issue that urgently needs to be addressed in the current distribution network technology field. Summary of the Invention

[0006] Purpose of the invention: To address the problems of unrealistic electrical coupling, insufficient multi-objective coordination, and poor computational efficiency and stability in existing three-phase unbalanced distribution network zoning methods, this invention provides a fast zoning method for three-phase unbalanced distribution networks based on electrical coupling strength. This method accurately quantifies the real electrical connections between nodes, achieves coordinated optimization of electrical cohesion and sub-region scale balance, and ensures the high efficiency and stability of zoning calculations. It provides reliable zoning support for scenarios such as parallel computing, distributed control, and fault self-healing in distribution networks.

[0007] Technical Solution: To achieve the above objectives, this invention provides a method for rapid zoning of a three-phase unbalanced distribution network based on electrical coupling strength, comprising the following steps:

[0008] S1: Perform data preprocessing on the acquired distribution network-related data to construct a distribution network electrical dataset;

[0009] S2: Based on the distribution network electrical dataset, and considering the three-phase imbalance characteristics and the power impact of distributed generation, define electrical distance adjustment parameters, integrate the three-phase self-impedance of nodes and the per-unit value of DG injected power, calculate the comprehensive three-phase electrical distance between nodes, and quantify the degree of electrical coupling between nodes.

[0010] S3: Convert the three-phase integrated electrical distance between nodes into connection weights between nodes, and use an indicator function to limit the effectiveness of the weights of physically connected nodes to construct a weighted undirected graph model that reflects the electrical coupling strength;

[0011] S4: Based on the weighted undirected graph model, each node is regarded as an independent initial community. The greedy community detection algorithm with modularity optimization is used to generate initial partitions and output a set of highly cohesive initial partitions.

[0012] S5: Define a dual objective function for electrical cohesion and load balancing, introduce weighting coefficients to balance the priorities of the two objectives, construct a combined evaluation function that integrates the two objectives, and calculate the combined comprehensive benefit of all adjacent sub-region pairs.

[0013] S6: Iterative execution of region merging: Identify adjacent sub-region pairs and perform virtual merging, select the region pair with the greatest overall merging benefit for actual merging, update the partition set and target value until the preset number of partitions is reached, and output the final partitioning result.

[0014] Furthermore, the formula for calculating the three-phase integrated electrical distance between nodes in step S2 is as follows:

[0015]

[0016] in, The three-phase comprehensive electrical distance between nodes; For nodes exist Phase self-impedance; For nodes exist Phase self-impedance; For electrical distance adjustment parameters; For nodes The per-unit value of DG injection power; For nodes The per-unit value of DG injection power.

[0017] Furthermore, the method for converting the three-phase comprehensive electrical distance between nodes into inter-node connection weights in step S3 includes:

[0018] node With nodes Connection weights between The calculation formula is:

[0019]

[0020] in, For indicator functions, if node With nodes If there is a direct line connection between them, then ,otherwise ; It is a very small positive number.

[0021] Furthermore, the method for generating the initial partition using the modularity-optimized greedy community detection algorithm in step S4 includes: based on the modularity... Calculate the change in modularity after node migration. Only retain The migration operation iterates until the global modularity no longer increases, and outputs a set of initial partitions with high cohesion.

[0022] Furthermore, in step S4, the modularity... The calculation formula is:

[0023]

[0024] in, The total weight of the weighted undirected graph; Represents a node The weight of the node, i.e. The sum of the weights of all connected edges; Represents a node The weight of the node, i.e. The sum of the weights of all connected edges; For indicator functions, , They are nodes ,node The community logo to which it belongs.

[0025] Furthermore, the electrical cohesion objective function in step S5 is expressed as follows:

[0026]

[0027] in, The target value for electrical cohesion; sub-region The number of nodes; the denominator sub-region The total number of internal node pairs; u and v are any two nodes in the distribution network; represents the electrical connection weight between node u and node v; h represents the preset number of partitions.

[0028] Furthermore, the load balancing objective function in step S5 is expressed as follows:

[0029]

[0030] in, This represents the number of nodes in each sub-region under ideal conditions. This is the target value for load balancing.

[0031] Furthermore, the expression of the merging evaluation function in step S5 is as follows:

[0032]

[0033]

[0034]

[0035] in, Indicates the combined benefits of the merger. This indicates merging adjacent sub-regions. and Subsequently, the change in the electrical cohesion target, of which The target value for electrical cohesion after the merger. The target value for electrical cohesion before the merger; This indicates merging adjacent sub-regions. and Afterwards, the change in the load balancing target, where The target value for load balancing after consolidation. This represents the target load balancing value before the merger. This represents the change in the electrical cohesion target after merging all possible adjacent regions. The maximum value; This represents the change in the electrical cohesion target after merging all possible adjacent regions. The maximum value; These are the weighting coefficients.

[0036] Furthermore, the iterative process of merging regions in step S6 includes:

[0037] A1: Calculate the current number of partitions ,like , If the preset number of partitions is not reached, the iteration will terminate and the output will be displayed. Otherwise, proceed to step A2;

[0038] A2: Identify all adjacent sub-region pairs For each region pair, a virtual merge is performed to obtain a temporary set of partitions. ;

[0039] A3: Calculation corresponding , and target change , and determine the current region pairs. and ;

[0040] A4: Calculate the combined benefits of merging pairs of regions. ,choose The largest region pair will be actually merged;

[0041] A5: Update Corresponding and Repeat steps A1 to A4 until the number of partitions reaches the target. Output the final set of partitions .

[0042] Beneficial Effects: Compared with existing technologies, this invention aims to solve the technical problem of balancing the realism of electrical coupling, the balance of sub-region size, and computational efficiency in the partitioning of three-phase unbalanced distribution networks. The method of this invention first uses the node impedance matrix to define electrical distance to quantify the coupling strength between nodes. Based on this, a modularity-optimized community detection algorithm is used for initial partitioning, resulting in multiple highly cohesive initial sub-regions. Subsequently, a multi-objective region merging strategy is proposed. This strategy comprehensively considers two optimization objectives: electrical cohesion and load balance. It iteratively merges adjacent sub-regions with the strongest electrical coupling and the smallest size until a preset number of partitions is reached, thereby ensuring close electrical connections within each sub-region while achieving relative balance in the size of each sub-region. Attached Figure Description

[0043] Figure 1 This is a flowchart of the method of the present invention;

[0044] Figure 2 Preliminary non-overlapping partition map for the IEEE-123 system;

[0045] Figure 3 This is the final non-overlapping partition map for the IEEE-123 system.

[0046] Figure 4 A comparison chart of performance metrics for different partitioning methods. Detailed Implementation

[0047] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0048] Example 1:

[0049] like Figure 1 As shown in the figure, this embodiment provides a method for rapid zoning of a three-phase unbalanced distribution network based on electrical coupling strength, including the following steps:

[0050] S1: Obtain the topology, node parameters, line impedance, and distributed generation power injection data of the distribution network, complete the data format unification and outlier removal, and construct a complete distribution network electrical dataset;

[0051] S2: Based on the distribution network electrical dataset, and considering the three-phase imbalance characteristics and the power impact of distributed generation, define electrical distance adjustment parameters, integrate the three-phase self-impedance of nodes and the per-unit value of DG injected power, calculate the comprehensive three-phase electrical distance between nodes, and quantify the degree of electrical coupling between nodes.

[0052] The formula for calculating the three-phase integrated electrical distance between nodes is:

[0053]

[0054] in, The three-phase comprehensive electrical distance between nodes; For nodes exist Phase self-impedance; For nodes exist Phase self-impedance; For electrical distance adjustment parameters; For nodes The per-unit value of DG injection power; For nodes The per-unit value of DG injection power.

[0055] S3: Convert the three-phase integrated electrical distance between nodes into connection weights between nodes, limit the validity of the weights of physically connected nodes through an indicator function, introduce a minimal positive number to avoid the denominator being zero, and construct a weighted undirected graph model that reflects the electrical coupling strength;

[0056] node With nodes Connection weights between The calculation formula is:

[0057]

[0058] in, For indicator functions, if node With nodes If there is a direct line connection between them, then ,otherwise ; It is a very small positive number.

[0059] S4: Based on the weighted undirected graph model, each node is regarded as an independent initial community. The greedy community detection algorithm with modularity optimization is used to generate initial partitions and output a set of highly cohesive initial partitions.

[0060] The greedy community detection algorithm with modularity optimization generates initial partitions in the following ways: based on modularity... Calculate the change in modularity after node migration. Only retain The migration operation iterates until the global modularity no longer increases, and outputs a set of initial partitions with high cohesion.

[0061] Modularity The calculation formula is:

[0062]

[0063] in, The total weight of the weighted undirected graph; Represents a node The weight of the node, i.e. The sum of the weights of all connected edges; Represents a node The weight of the node, i.e. The sum of the weights of all connected edges; For indicator functions, , They are nodes ,node The community logo to which it belongs.

[0064] S5: Define a dual objective function for electrical cohesion and load balancing, introduce weighting coefficients to balance the priorities of the two objectives, construct a combined evaluation function that integrates the two objectives, and calculate the combined comprehensive benefit of all adjacent sub-region pairs.

[0065] The objective function for electrical cohesion is expressed as follows:

[0066]

[0067] in, The target value for electrical cohesion; sub-region The number of nodes; the denominator sub-region The total number of internal node pairs; u and v are any two nodes in the distribution network; The electrical connection weights between nodes u and v; h is the preset number of partitions; electrical cohesion objective. The larger the value, the tighter the electrical connection within the sub-region, and the better the electrical performance of the partition.

[0068] The objective function for load balancing is expressed as follows:

[0069]

[0070] in, This represents the number of nodes in each sub-region under ideal conditions. This is the target value for load balancing. The range of values ​​is The closer the value is to 1, the smaller the size difference between the sub-regions, and the better the load balancing; when all sub-regions are of completely identical size... .

[0071] The combined evaluation function is expressed as follows:

[0072]

[0073]

[0074]

[0075] in, Indicates the combined benefits of the merger. This indicates merging adjacent sub-regions. and Subsequently, the change in the electrical cohesion target, of which The target value for electrical cohesion after the merger. The target value for electrical cohesion before the merger; This indicates merging adjacent sub-regions. and Afterwards, the change in the load balancing target, where The target value for load balancing after consolidation. This represents the target load balancing value before the merger. This represents the change in the electrical cohesion target after merging all possible adjacent regions. The maximum value; This represents the change in the electrical cohesion target after merging all possible adjacent regions. The maximum value; These are the weighting coefficients.

[0076] S6: Iterative execution of region merging: Identify adjacent sub-region pairs and perform virtual merging, select the region pair with the greatest overall merging benefit for actual merging, update the partition set and target value until the preset number of partitions is reached, and output the final partitioning result that satisfies constraints such as integrity and mutual exclusion.

[0077] The iterative process of merging regions includes:

[0078] A1: Calculate the current number of partitions ,like , If the preset number of partitions is not reached, the iteration will terminate and the output will be displayed. Otherwise, proceed to step A2;

[0079] A2: Identify all adjacent sub-region pairs For each region pair, a virtual merge is performed to obtain a temporary set of partitions. ;

[0080] A3: Calculation corresponding , and target change , and determine the current region pairs. and ;

[0081] A4: Calculate the combined benefits of merging pairs of regions. ,choose The largest region pair will be actually merged;

[0082] A5: Update Corresponding and Repeat steps A1 to A4 until the number of partitions reaches the target. Output the final set of partitions .

[0083] Example 2:

[0084] To verify the effectiveness of the method of the present invention, this embodiment uses the IEEE-123 node distribution network system for simulation analysis. This system contains multiple sets of three-phase load information, which can fully reflect the three-phase imbalance characteristics of the distribution network.

[0085] In the partitioning process, the association weights between nodes are first obtained by quantifying the electrical coupling strength to generate preliminary partitioning results; then, the regions are merged by combining a multi-objective region merging algorithm, and the final partitioning results are obtained by iterative solution.

[0086] Specifically, Figure 2 This paper presents a non-overlapping preliminary partitioning of the IEEE-123 system. The results are based on the original network topology and initial electrical coupling weights to complete the first round of community partitioning. It can be seen that although the preliminary partitioning results generally follow the topological connectivity between nodes, there are differences in the internal node connectivity of each region, and the scale imbalance of some regions is quite obvious. It does not yet fully meet the topological constraints and load balancing requirements of actual distribution network operation and maintenance.

[0087] Figure 3 The non-overlapping final partitioning of the IEEE-123 system is demonstrated. It is evident that after iterative optimization and multi-objective merging strategies using the method of this invention, the network is divided into several clearly structured sub-regions. Compared to the initial partitioning, the final partitioning result achieves relative balance in region size while maintaining the electrical cohesion of each sub-region, and all partitions satisfy connectivity constraints. Furthermore, the partition boundaries are clearer, effectively reducing cross-regional electrical coupling and making it more suitable for the practical engineering configuration of distributed control and protection in distribution networks.

[0088] To demonstrate the effectiveness of the method of the present invention, this embodiment compares the method of the present invention with existing partitioning methods and analyzes them from the perspective of core performance. Figure 4 This section presents a comparison of performance metrics for different partitioning methods, from... Figure 4 It can be seen that the method of this invention has significant advantages in all core evaluation indicators: under the premise of ensuring that the partitioning execution time is within a reasonable range, the electrical cohesion index of the method of this invention is significantly better than that of the comparative method, indicating that the internal electrical coupling is tighter after partitioning; at the same time, the method of this invention also performs well in terms of partitioning scale balance and network connectivity maintenance, effectively verifying the superiority and feasibility of the method of this invention in terms of solution accuracy and computational efficiency.

Claims

1. A method for rapid zoning of a three-phase unbalanced distribution network based on electrical coupling strength, characterized in that, Includes the following steps: S1: Perform data preprocessing on the acquired distribution network-related data to construct a distribution network electrical dataset; S2: Based on the distribution network electrical dataset, and considering the three-phase imbalance characteristics and the power impact of distributed generation, define electrical distance adjustment parameters, integrate the three-phase self-impedance of nodes and the per-unit value of DG injected power, calculate the comprehensive three-phase electrical distance between nodes, and quantify the degree of electrical coupling between nodes. S3: Convert the three-phase integrated electrical distance between nodes into connection weights between nodes, and use an indicator function to limit the effectiveness of the weights of physically connected nodes to construct a weighted undirected graph model that reflects the electrical coupling strength; S4: Based on the weighted undirected graph model, each node is regarded as an independent initial community. The greedy community detection algorithm with modularity optimization is used to generate initial partitions and output a set of highly cohesive initial partitions. S5: Define a dual objective function for electrical cohesion and load balancing, introduce weighting coefficients to balance the priorities of the two objectives, construct a combined evaluation function that integrates the two objectives, and calculate the combined comprehensive benefit of all adjacent sub-region pairs. S6: Iterative execution of region merging: Identify adjacent sub-region pairs and perform virtual merging, select the region pairs with the greatest overall merging benefit for actual merging, update the partition set and target value until the preset number of partitions is reached, and output the final partitioning result; The objective function for electrical cohesion in step S5 is expressed as follows: ； in, The target value for electrical cohesion; sub-region The number of nodes; the denominator sub-region The total number of internal node pairs; u and v are any two nodes in the distribution network; The electrical connection weight between node u and node v; h is the preset number of partitions; The load balancing objective function in step S5 is expressed as follows: ； in, This represents the number of nodes in each sub-region under ideal conditions. This is the target value for load balancing. The expression for the combined evaluation function in step S5 is as follows: ； ； ； in, Indicates the combined benefits of the merger. This indicates merging adjacent sub-regions. and Subsequently, the change in the electrical cohesion target, of which The target value for electrical cohesion after the merger. The target value for electrical cohesion before the merger; This indicates merging adjacent sub-regions. and Afterwards, the change in the load balancing target, where The target value for load balancing after consolidation. This represents the target load balancing value before the merger. This represents the change in the electrical cohesion target after merging all possible adjacent regions. The maximum value; This represents the change in the electrical cohesion target after merging all possible adjacent regions. The maximum value; These are the weighting coefficients.

2. The method for rapid zoning of a three-phase unbalanced distribution network based on electrical coupling strength according to claim 1, characterized in that, The formula for calculating the three-phase integrated electrical distance between nodes in step S2 is as follows: ； in, The three-phase comprehensive electrical distance between nodes; For nodes exist Phase self-impedance; For nodes exist Phase self-impedance; For electrical distance adjustment parameters; For nodes The per-unit value of DG injection power; For nodes The per-unit value of DG injection power.

3. The method for rapid zoning of a three-phase unbalanced distribution network based on electrical coupling strength according to claim 2, characterized in that, The method for converting the three-phase comprehensive electrical distance between nodes into inter-node connection weights in step S3 includes: node With nodes Connection weights between The calculation formula is: ； in, For indicator functions, if node With nodes If there is a direct line connection between them, then ,otherwise ; It is a positive number.

4. The method for rapid zoning of a three-phase unbalanced distribution network based on electrical coupling strength according to claim 3, characterized in that, The method for generating the initial partition using the modularity-optimized greedy community detection algorithm in step S4 includes: based on the modularity... Calculate the change in modularity after node migration. Only retain The migration operation iterates until the global modularity no longer increases, and outputs a set of initial partitions with high cohesion.

5. A method for rapid zoning of a three-phase unbalanced distribution network based on electrical coupling strength according to claim 4, characterized in that, Modularity in step S4 The calculation formula is: ； in, The total weight of the weighted undirected graph; Represents a node The weight of the node, i.e. The sum of the weights of all connected edges; Represents a node The weight of the node, i.e. The sum of the weights of all connected edges; For indicator functions, , They are nodes ,node The community logo to which it belongs.

6. A method for rapid zoning of a three-phase unbalanced distribution network based on electrical coupling strength according to claim 5, characterized in that, The iterative process of merging regions in step S6 includes: A1: Calculate the current number of partitions ,like , If the preset number of partitions is not reached, the iteration will terminate and the output will be displayed. Otherwise, proceed to step A2; A2: Identify all adjacent sub-region pairs For each region pair, a virtual merge is performed to obtain a temporary set of partitions. ; A3: Calculation corresponding , and target change , and determine the current region pairs. and ; A4: Calculate the combined benefits of merging pairs of regions. ,choose The largest region pair will be actually merged; A5: Update Corresponding and Repeat steps A1 to A4 until the number of partitions reaches the target. Output the final set of partitions .

Images