A power distribution network optimization partitioning method considering three-phase power imbalance

Abstract

The application discloses a power distribution network optimization partitioning method considering three-phase power imbalance, relates to the technical field of large-scale power distribution network partitioning, and comprises the following steps: according to local sensitivity calculation, combining line admittance parameters of a power distribution network, calculating a voltage sensitivity matrix between nodes, and deducing electrical distance; then taking the electrical distance as an edge weight of a power distribution network topology, combining the concept of modularity, and using a Louvain algorithm to obtain a preliminary partitioning result; then according to a partitioning number constraint, selecting a flow method or a hierarchical flow method to perform sub-region merging, and obtaining a non-overlapping partitioning result; finally, according to a distributed algorithm requirement, the non-overlapping partitioning result can be overlapped based on a maximum information interaction principle. The application not only solves the influence of three-phase imbalance on partitioning, but also speeds up the partitioning algorithm, and has more advantages in partitioning effect and partitioning stability.

Description

Technical Field

[0001] This invention belongs to the field of large-scale distribution network zoning technology, specifically relating to an optimized zoning method for distribution networks that considers three-phase power imbalance. Background Technology

[0002] Community detection algorithms provide a good approach for distribution network partitioning algorithms. The literature [Xiao Chuanliang, Zhao Bo, Zhou Jinhui, et al. High-proportion distributed photovoltaic cluster voltage control based on network partitioning in distribution networks [J]. Automation of Electric Power Systems, 2017, 41(21): 147–155.] proposes a partitioning method based on reactive / active voltage sensitivity, and uses an improved modularity method and community detection algorithm for partitioning. This method does indeed obtain partitioning results with tight internal electrical coupling, but the number of partitions and the size of sub-regions are uncontrollable, making it difficult to apply effectively in large-scale distribution networks. The literature [Network Partition-Based Zonal Voltage Control for Distribution Networks With Distributed PV Systems] proposes a partitioning method also based on voltage / reactive sensitivity matrices and community detection algorithms, while using a greedy algorithm to obtain partitioning results with similar sizes between sub-regions. However, the greedy algorithm is prone to getting trapped in local optima, and both active and reactive sensitivity methods depend on power flow results, making them unsuitable for three-phase imbalance scenarios.

[0003] On the other hand, some research has begun on distribution network partitioning methods for three-phase unbalanced distribution networks. The literature [Community-detection-based approach to distribution network partition] proposes a sensitivity calculation method based on the voltage / admittance matrix. This method is decoupled from power flow, but the sensitivity calculation results are not proportional to the size of the electrical distance. This method subsequently obtains sub-regions of similar size through community detection-greedy-tabu search algorithm, but excessive use of heuristic algorithms can lead to instability in the partitioning results. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a distribution network optimization zoning method that considers three-phase power imbalance.

[0005] The objective of this invention can be achieved through the following technical solution: a distribution network optimization zoning method considering three-phase power imbalance, the method comprising the following steps:

[0006] Based on the local sensitivity calculation method and combined with the real-world distribution network line admittance parameters, the voltage sensitivity matrix between nodes is calculated to derive the electrical distance between nodes;

[0007] Using the electrical distance between nodes as the weight of the edges between nodes in the network topology, the preliminary network partitioning results are obtained based on the Louvain algorithm, which has high computational efficiency among community detection algorithms.

[0008] Based on the network size, the total number of partitions is determined using the preliminary network partitioning results. Then, the sub-regions of the network are merged using the flow method or the hierarchical flow method based on the total number of partitions. The non-overlapping partitioning results with a similar size to the sub-regions are solved and output using the branch and bound method.

[0009] According to the requirements of subsequent distributed algorithms, if the regions are divided into overlapping partitions, then based on the non-overlapping partition results, the overlapping partition results are generated based on the principle of maximizing the degree of network topology nodes, that is, the principle of maximizing information interaction.

[0010] Preferably, the local sensitivity calculation method includes:

[0011] (1)

[0012] In the formula, Let i be the voltage amplitude of phase p at node i. The current amplitude injected into phase q at node j is given by, where, The node injection current is obtained from the node voltage and the elements in the node admittance matrix:

[0013] (2)

[0014] In the formula, The admittance value between phase p at node i and phase q at node j; the sensitivity of phase p at node i and phase q at node j. The expression is represented by the impedance matrix:

[0015] (3).

[0016] Preferably, the method for calculating the electrical distance between nodes includes:

[0017] (4)

[0018] In the formula, This represents the electrical distance between node i and node j. According to formula (4), this represents the positive correlation between the electrical distance between nodes and the sensitivity. The higher the electrical coupling between the two nodes, the greater the electrical distance between the nodes. For two nodes that are not directly connected by a line, the electrical distance between the nodes is 0.

[0019] Preferably, the process of using the electrical distance between nodes as the weight of the edges between nodes in the network topology, and obtaining the preliminary network partitioning results based on the computationally efficient Louvain algorithm in community detection algorithms, includes:

[0020] Based on the modularity criterion, the Louvain algorithm is used for initial partitioning. The concept of modularity is as follows:

[0021] (5)

[0022] In the formula, A represents the adjacency matrix of the distribution network topology. ij This represents the connection relationship between nodes i and j; 1 indicates adjacency and 0 indicates non-adjacency. C represents a community; P is the set of communities in the network. This indicates the community to which vertex i belongs; This indicates that if vertices i and j belong to the same community, the value is 1; otherwise, it is 0. i and k j Let be the degree of the vertex, represent the sum of the weights of all edges connected to vertex i or vertex j, and m be the sum of the weights of all edges in the network; the function The variables u and v are both corresponding to , The intermediate quantities for calculation.

[0023] Preferably, the Louvain algorithm process includes the following steps:

[0024] Treat each vertex as an initial sub-community;

[0025] For each individual node, extract the nodes from its community and then add them sequentially to the communities of the nodes adjacent to it. Calculate the modularity gain in each community. If the largest at this time If so, the node will be returned to its original community. If the largest node at this time... If so, the node will be placed in the community with the greatest gain;

[0026] Repeat the above steps until the module gain is less than or equal to zero each time it is calculated;

[0027] The modularity gain The calculation method is as follows:

[0028] (6)

[0029] In the formula, It is the sum of the edge weights within the community; It is the sum of the weights of all connected nodes within the community; It is the sum of the weights between node i and community C, where the electrical distance between the nodes is used as the weight of each edge.

[0030] Preferably, the method for determining the total number of partitions based on the network size is as follows:

[0031] (7)

[0032] In the formula, N F The theoretical maximum number of partitions is taken as an empirical value. ,in n This represents the number of network nodes. N min The minimum value for network partitioning is set to 2; N max The maximum value for a network partition is the number of nodes containing measurements in the distribution network, incremented by 1; when selecting the number of partitions, when... N When the number of partitions is greater than 6, select the total number of partitions that can be factored into integers. If all partitions can be factored into integers, then selecting integers will result in more similar decomposition values. Number of partitions N ; and when N When the value is small and there is no need to select the stratified flow method, take the median of all candidate values ​​that meet the constraints.

[0033] Preferably, the flow method or stratified flow method is as follows:

[0034] Based on the initial network partitioning results, each partition is treated as a new node, and the weight of the new node is the number of original nodes contained in each original partition. Simultaneously, based on the network topology of the original nodes, the new node inherits all the connections between the original nodes, thus generating a new undirected graph. (G,ω) and G=(V,E) ,in G Represents the new undirected graph. ω It is the vertex weight set. V Represents a vertex set. E Represents the edge weight set;

[0035] For undirected graphs that require merging partitions using either the flow method or the hierarchical flow method. (G,ω) and G=(V,E) A new directed graph needs to be constructed. D The construction method is as follows: replace each undirected edge with two directed edges with the same endpoints but different directions, and then add a directed edge. N A set of vertices S={s 1 ,...,s N } As the source, and from S each vertex to GAdd a directed edge to each vertex in S, pointing from the vertex in S to... G By identifying the vertices in the set, a new set of vertices and edges is obtained. Therefore... D vertex set V(D) = V∪S, D edge set A(D)={(u,v),(v,u):{u,v}∈E}∪{(s i ,v):i∈[N],v∈V} ;

[0036] After obtaining the new directed graph D, that is, for the new directed graph... D The flow method or stratified flow method can be used. The steps of the flow method are as follows:

[0037] S In k Each source has a total of ω(G) Traffic, ω(G) This represents the sum of the weights of all vertices in G; furthermore, it forces each non-source vertex to... ν Only from D A single vertex in the process receives traffic and consumes it. ω(ν) The received traffic, ω(ν) This represents the weight of a single vertex, thus allowing each source vertex to... S i Traffic is sent to a single non-source vertex, then propagates to other vertices, and is consumed in the process until it reaches zero. S i The vertices traversed after departure correspond to the vertices contained in partition i. To balance the size of the sub-regions, the objective function is defined as minimizing the difference between the maximum and minimum flow sources, and the branch and bound method is used to solve it to ensure the globally optimal solution is obtained. The following formula is constructed:

[0038] (8)

[0039] (9)

[0040] (10)

[0041] (11)

[0042] (12)

[0043] (13)

[0044] (14)

[0045] (15)

[0046] In the above formulas, the function This represents the sum of the weights of the directed edges connected to the vertex. The positive or negative superscript indicates whether a directed edge flows out of or into that node. The function represents the remaining weight of edge a. This indicates the number of edges flowing into or out of this node. This means that the number of outflow sources i is 1, while This indicates that the number of nodes flowing into node v is 1; It is a binary variable used to indicate whether any edge partition exists in edge set A(D); Non-negative real numbers.

[0047] Preferably, the solution method of the flow method is as follows:

[0048] Search method: Based on the requirements of the branch and bound method, a queue is used as the data storage structure to store the flow process of each source. The subsequent expansion node is selected according to the first-in-first-out principle. Based on the number of sub-partitions N, all feasible solutions are listed. For each feasible solution, the neighbors of the root node of each source are found and used as child nodes. Each child node is judged to determine whether it can be pruned. At the same time, if a child node generates more sub-regions after selection, and there is a sub-region that is not connected to other partitioned regions, then the sub-region is selected as the node.

[0049] Pruning conditions: When a source in a feasible solution cannot find a new node, the difference between the largest and smallest subregion sizes is determined. Based on experience, if the difference between the largest and smallest subregion sizes is greater than three-quarters of the size of each sub-node, then pruning is performed. If the smallest source found temporarily in a feasible solution is smaller than the smallest source in other known feasible solutions, then pruning is performed.

[0050] Preferably, the principle of the stratified flow method is as follows:

[0051] The original process involving a large number of partitions is broken down into two sub-processes. The first process decomposes the large region into a few sub-regions using a flow method. The second process further divides each sub-region using a second flow method to achieve the required total number of partitions. Therefore, the integer decomposition of the total number of partitions N represents the number of partitions at each level. Furthermore, based on the determined N, it is decomposed into integers, specifically into only two numbers. The selected combination of decompositions should meet the following requirements:

[0052] Two numbers that should be factored into an integer should be close to each other. ;

[0053] The order of the decomposed numbers should be as follows: smaller numbers as the first layer and larger numbers as the second layer.

[0054] Preferably, the process of generating overlapping partitioning results includes the following steps:

[0055] Based on the non-overlapping partitioning results, candidate overlapping nodes are selected using the following method: For any non-overlapping region that is a neighbor, find two neighboring nodes belonging to the two sub-regions respectively; these neighboring node pairs are candidate overlapping nodes. Based on the principle of maximum information interaction, the interaction value of each candidate overlapping node is calculated. H The calculation method is as follows:

[0056] (16)

[0057] In the formula, The adjacency matrix represents the network topology, while The electrical distance between two nodes; by considering candidate node pairs i and j H i , H j Perform calculations and comparisons. H i and H j The size of the H value is used to select the node with the larger H value as the overlapping node to obtain the overlapping region division result.

[0058] The beneficial effects of this invention are:

[0059] This invention focuses on the uncertainties involved in the optimization and partitioning of large-scale distribution networks under three-phase imbalance conditions, and proposes a two-stage partitioning method framework based on the flow method. It utilizes a voltage sensitivity method based on the admittance matrix to avoid the impact of three-phase power imbalance on distribution network partitioning. The Louvain algorithm is used to obtain preliminary partitioning results, ensuring tight coupling within sub-regions and sparse coupling between regions. Sub-region merging algorithms based on the flow method or hierarchical flow method are designed to ensure reasonable sub-region sizes and similar sizes between regions, while also guaranteeing algorithm stability. Finally, an overlapping partitioning method based on the principle of maximum information interaction is proposed to meet the subsequent requirements of distributed algorithms for information interaction between regions. This invention further improves the computational efficiency and stability of the partitioning algorithm while ensuring high cohesion and low coupling in the partitioning results. Attached Figure Description

[0060] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0061] Figure 1 This is a schematic diagram of the framework of the method of the present invention;

[0062] Figure 2This is a diagram illustrating the process of vertex i moving to the community of adjacent vertex j based on the Louvain algorithm in an embodiment of the present invention.

[0063] Figure 3 This is a schematic diagram of the topology of the Louvain algorithm partitioning result in an embodiment of the present invention;

[0064] Figure 4 The embodiments of the present invention are based on Figure 3 A schematic diagram of the topology modification;

[0065] Figure 5 The embodiments of the present invention are based on Figure 4 A schematic diagram of the partitioning results from the flow method;

[0066] Figure 6 This is a schematic diagram of the flow method solution strategy according to an embodiment of the present invention;

[0067] Figure 7 This is a schematic diagram of the initial partitioning of the IEEE-123 nodes based on the Louvain algorithm in an embodiment of the present invention;

[0068] Figure 8 This is a schematic diagram of the non-overlapping partitioning results of the IEEE-123 nodes based on the flow method in an embodiment of the present invention;

[0069] Figure 9 This is a schematic diagram of the overlapping partitioning results of IEEE-123 nodes based on the flow method in an embodiment of the present invention;

[0070] Figure 10 This is a schematic diagram of the initial partitioning of IEEE-8500 nodes based on the Louvain algorithm in an embodiment of the present invention;

[0071] Figure 11 This is a schematic diagram of the non-overlapping partitioning results of IEEE-8500 nodes based on the 3-4 layered flow method in an embodiment of the present invention;

[0072] Figure 12 This is a schematic diagram of the non-overlapping partitioning results of IEEE-8500 nodes based on the 2-6 layered flow method in an embodiment of the present invention;

[0073] Figure 13 This is a schematic diagram of the non-overlapping partitioning results of IEEE-8500 nodes based on the 2-3-2 layered flow method in an embodiment of the present invention;

[0074] Figure 14 This is a schematic diagram of the non-overlapping partitioning result of IEEE-8500 nodes based on the greedy tabu algorithm in an embodiment of the present invention. Detailed Implementation

[0075] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0076] like Figure 1 As shown, a distribution network optimization zoning method considering three-phase power imbalance is proposed. The method includes the following steps:

[0077] Based on the local sensitivity calculation method and combined with the real-world distribution network line admittance parameters, the voltage sensitivity matrix between nodes is calculated to derive the electrical distance between nodes;

[0078] Using the electrical distance between nodes as the weight of the edges between nodes in the network topology, the Louvain algorithm, which has high computational efficiency among community detection algorithms, is used to obtain the preliminary network partitioning results. However, since the number of these preliminary partitions is generally large, it is necessary to further merge the sub-regions using the flow method or the hierarchical flow method.

[0079] The total number of partitions is determined based on the network size. Then, the sub-regions of the network are merged using the flow method or the hierarchical flow method based on the total number of partitions. The branch and bound method is used to solve and output non-overlapping partition results with a sub-region size similar to the sub-region size.

[0080] According to the requirements of subsequent distributed algorithms, if the regions are divided into overlapping partitions, then based on the non-overlapping partition results, the overlapping partition results are generated based on the principle of maximizing the degree of network topology nodes, that is, the principle of maximizing information interaction.

[0081] The local sensitivity calculation method includes:

[0082] (1)

[0083] In the formula, Let i be the voltage amplitude of phase p at node i. The current amplitude injected into phase q at node j is given by, where, The node injection current is obtained from the node voltage and the elements in the node admittance matrix:

[0084] (2)

[0085] In the formula, This represents the admittance value between phase p at node i and phase q at node j; therefore, it represents the sensitivity of phase p at node i and phase q at node j. The expression is represented by the impedance matrix:

[0086] (3).

[0087] Preferably, the method for calculating the electrical distance between nodes includes:

[0088] (4)

[0089] In the formula, This represents the electrical distance between node i and node j. According to formula (4), this represents the positive correlation between the electrical distance between nodes and the sensitivity. The higher the electrical coupling between the two nodes, the greater the electrical distance between the nodes. For two nodes that are not directly connected by a line, the electrical distance between the nodes is 0.

[0090] The process of using the electrical distance between nodes as the weight of the edges between nodes in the network topology and obtaining the preliminary network partitioning results based on the Louvain algorithm includes:

[0091] Based on the modularity criterion, the Louvain algorithm is used for initial partitioning. The concept of modularity is as follows:

[0092] (5)

[0093] In the formula, A represents the adjacency matrix of the distribution network topology. ij This represents the connection relationship between nodes i and j; 1 indicates adjacency and 0 indicates non-adjacency. C represents a community; P is the set of communities in the network. This indicates the community to which vertex i belongs; This means that if vertices i and j belong to the same community, the value is 1; otherwise, it is 0. Let be the degree of a vertex, represent the sum of the weights of all edges connected to vertex i, and m be the sum of the weights of all edges in the network; the function The variables u and v are both corresponding to , Intermediate quantities are used to simplify the expression of formulas.

[0094] The Louvain algorithm process includes the following steps:

[0095] Treat each vertex as an initial sub-community;

[0096] For each individual node, extract the nodes from its community and then add them sequentially to the communities of the nodes adjacent to it. Calculate the modularity gain in each community. If the largest at this time If so, the node will be returned to its original community. If the largest node at this time... If so, the node will be placed in the community with the greatest gain;

[0097] Repeat the above steps until the module gain is less than or equal to zero each time it is calculated;

[0098] The modularity gain The calculation method is as follows:

[0099] (6)

[0100] In the formula, It is the sum of the edge weights within the community; It is the sum of the weights of all connected nodes within the community; It is the sum of the weights between node i and community C, where the electrical distance between the nodes is used as the weight of each edge.

[0101] It should be noted that the method for determining the total number of partitions based on network size is as follows:

[0102] (7)

[0103] In the formula, N F The theoretical maximum number of partitions is taken as an empirical value. ,in n This represents the number of network nodes. N min The minimum value for network partitioning is set to 2; N max The maximum value for a network partition is the number of nodes containing measurements in the distribution network, incremented by 1; when selecting the number of partitions, when... N When the number of partitions is greater than 6, select the total number of partitions that can be factored into integers. If all partitions can be factored into integers, then selecting integers will result in more similar decomposition values. Number of partitions N ; and when N When the value is small and there is no need to select the stratified flow method, take the median of all candidate values ​​that meet the constraints of equation (7).

[0104] It should be noted that the flow method or stratified flow method is as follows:

[0105] Based on the initial network partitioning results, each partition is treated as a new node, and the weight of the new node is the number of original nodes contained in each original partition. Simultaneously, based on the network topology of the original nodes, the new node inherits all the connections between the original nodes, thus generating a new undirected graph. (G,ω) and G=(V,E) ,in G Represents the new undirected graph. ω It is the vertex weight set. V Represents a vertex set. E Represents the edge weight set;

[0106] For undirected graphs that require merging partitions using either the flow method or the hierarchical flow method. (G,ω) and G=(V,E) A new directed graph needs to be constructed. D The construction method is as follows: replace each undirected edge with two directed edges with the same endpoints but different directions, and then add a directed edge. N A set of vertices S={s 1 ,...,s N } As the source, and from S each vertex to G Add a directed edge to each vertex in S, pointing from the vertex in S to... G By identifying the vertices in the set, a new set of vertices and edges is obtained. Therefore... D vertex set V(D) = V∪S, D edge set A(D)={(u,v),(v,u):{u,v}∈E}∪{(s i ,v):i∈[N],v∈V} ;

[0107] After obtaining the new directed graph D, that is, for the new directed graph... D The flow method or stratified flow method can be used. The steps of the flow method are as follows:

[0108] S In k Each source has a total of ω(G) Traffic, ω(G) This represents the sum of the weights of all vertices in G; furthermore, it forces each non-source vertex to... ν Only from D A single vertex in the process receives traffic and consumes it. ω(ν) The received traffic, ω(ν) This represents the weight of a single vertex, thus allowing each source vertex to... S i Traffic is sent to a single non-source vertex, then propagates to other vertices, and is consumed in the process until it reaches zero. S i The vertices traversed after departure correspond to the vertices contained in partition i. To balance the size of the sub-regions, the objective function is defined as minimizing the difference between the maximum and minimum flow sources, and the branch and bound method is used to solve it to ensure the globally optimal solution is obtained. The following formula is constructed:

[0109] (8)

[0110] (9)

[0111] (10)

[0112] (11)

[0113] (12)

[0114] (13)

[0115] (14)

[0116] (15)

[0117] In the above formulas, the function This represents the sum of the weights of the directed edges connected to the vertex. The positive or negative superscript indicates whether a directed edge flows out of or into that node. The function represents the remaining weight of edge a. This indicates the number of edges flowing into or out of this node. This means that the number of outflow sources i is 1, while This indicates that the number of nodes flowing into node v is 1; It is a binary variable used to indicate whether any edge partition exists in edge set A(D); Non-negative real numbers.

[0118] The solution method of the flow method is as follows:

[0119] Search method: Based on the requirements of the branch and bound method, a queue is used as the data storage structure to store the flow process of each source. The subsequent expansion node is selected according to the first-in-first-out principle. Based on the number of sub-partitions N, all feasible solutions are listed. For each feasible solution, the neighbors of the root node of each source are found and used as child nodes. Each child node is judged to determine whether it can be pruned. At the same time, if a child node generates more sub-regions after selection, and there is a sub-region that is not connected to other partitioned regions, then the sub-region is selected as the node.

[0120] Pruning conditions: When a source in a feasible solution cannot find a new node, the difference between the largest and smallest subregion sizes is determined. Based on experience, if the difference between the largest and smallest subregion sizes is greater than three-quarters of the size of each sub-node, then pruning is performed. If the smallest source found temporarily in a feasible solution is smaller than the smallest source in other known feasible solutions, then pruning is performed.

[0121] The principle of the stratified flow method is as follows:

[0122] The original process involving a large number of partitions is broken down into two sub-processes. The first process decomposes the large region into a few sub-regions using a flow method. The second process further divides each sub-region using a second flow method to achieve the required total number of partitions. Therefore, the integer decomposition of the total number of partitions N represents the number of partitions at each level. Furthermore, based on the determined N, it is decomposed into integers, specifically into only two numbers. The selected combination of decompositions should meet the following requirements:

[0123] Two numbers that should be factored into an integer should be close to each other. ;

[0124] The order of the decomposed numbers should be as follows: smaller numbers as the first layer and larger numbers as the second layer.

[0125] It should be noted that the process of generating the overlapping partitioning results includes the following steps:

[0126] Based on the non-overlapping partitioning results, candidate overlapping nodes are selected using the following method: For any non-overlapping region that is a neighbor, find two neighboring nodes belonging to the two sub-regions respectively; these neighboring node pairs are candidate overlapping nodes. Based on the principle of maximum information interaction, the interaction value of each candidate overlapping node is calculated. H The calculation method is as follows:

[0127] (16)

[0128] In the formula, The adjacency matrix represents the network topology, while The electrical distance between two nodes; by considering candidate node pairs i and j H i , H j Perform calculations and comparisons. H i and H j The size of the H value is used to select the node with the larger H value as the overlapping node to obtain the overlapping region division result.

[0129] Example:

[0130] The proposed distribution network zoning method was verified and analyzed using the flow method and the hierarchical flow method, respectively, using IEEE-123-node and IEEE-8500-node examples. The algorithm proposed in this invention was analyzed on a computer with a CPU frequency of 5.2 GHz and 16 GB of memory, using the Python platform.

[0131] First, the flow method is used to analyze the IEEE-123 node case. The IEEE-123 node case includes 123 nodes and 122 feeder branches (excluding tie lines). First, the sensitivity matrix needs to be calculated based on the distribution network line parameters. Taking nodes 7 and 8 as examples, their admittance matrices are:

[0132] (17)

[0133] According to the voltage sensitivity calculation method based on the admittance matrix, we can obtain:

[0134] (18)

[0135] Clearly, the sensitivity calculation method based on the admittance matrix can be decoupled from power flow, eliminating the impact of three-phase imbalance on the partitioning. Meanwhile, the electrical distance between the two nodes is:

[0136] (19)

[0137] The Louvain algorithm is then used to perform initial network partitioning. For a network with n vertices, each vertex is first initialized as its own independent community, resulting in n distinct communities. Then, for each vertex i and all its neighboring vertices j, the module degree increment of moving vertex i from its community to the community of vertex j is calculated. Move vertex i to The community containing the largest and non-negative neighboring vertex j, the movement process is as follows: Figure 2 As shown, vertex i is moved from its community. The move is to the community to which j belongs. to form a new community and If all If all values ​​are less than 0, then vertex i remains in its original community. This process is applied sequentially to all vertices and repeated iteratively until no vertices move, meaning that moving any vertex will not increase the modularity Q. Figure 7 This shows the partitioning of the IEEE-123 node example after using the Louvain algorithm.

[0138] Depend on Figure 3 , Figure 4 and Figure 5 The basic process of the flow method is given. Based on... Figure 3 The Louvain partitioning result shown is an undirected topology graph, with circles representing sub-partitions. v This represents the number of nodes contained in the sub-partition, and also the weight of that node. Before applying the flow method, the undirected graph needs to be modified, such as... Figure 3As shown. First, based on the constraint of the number of partitions, the graph will be divided into two sub-regions. Therefore, two new source nodes are added to the topology graph. S 1 and S 2 Secondly, replace the original undirected edges with two directed edges in opposite directions. Finally, starting from each source, add a directed line to each vertex for each source to obtain the modified new topology. D Subsequently, based on the mathematical model of the flow method, the optimal solution can be searched, where... Figure 6 The search method is illustrated. For the search process shown in the left figure, yellow represents... S 1 The search process, and blue represents... S 2 The search process. When this step is reached, nodes 10 and 7, which can be considered independent subgraphs, are both only related to... S 2 Since they are connected, these two nodes can be directly assigned. S 2 ,like Figure 6 As shown in the middle right figure.

[0139] Based on the above-mentioned flow-based partitioning principle, it is possible to base it on Figure 7 The partitioning results shown yield the following: Figure 8 The non-overlapping sub-region partitioning map is then generated. Based on each candidate overlapping partition pair, its... H The value is ultimately obtained. Figure 9 The overlapping partitioning results are shown in the figure, with red nodes representing overlapping nodes.

[0140] Furthermore, the stratified flow method is used to analyze the IEEE-8500 node case. The IEEE-8500 node case actually has 2519 medium-pressure geographic nodes, so it is only necessary to partition these 2519 nodes. Similar to the IEEE-123 node case, the Louvain algorithm will not be elaborated upon further.

[0141] Based on the partition number constraint, the IEEE-8500 node computation can be divided into 11, 12, or 13 partitions. Since 11 and 13 are prime numbers, 12 is chosen as the final partition number. In practice, 12 partitions can be further divided into 3-4 partitions, 2-6 partitions, or even three layers, such as 2-3-2 partitions. Taking 3-4 partitions as an example, the IEEE-8500 node computation is first divided into 3 sub-regions, and then each sub-region is further decomposed into 4 smaller sub-regions, resulting in 12 relatively balanced sub-regions. To verify the effectiveness of the layering strategy, the three different layering methods are compared, yielding... Figure 11 , Figure 12 and Figure 13 Simultaneously, the stratification time and the size difference (maximum size difference) between the largest and smallest partitions were analyzed for the three stratification methods, resulting in Table 1 below:

[0142] Table 1. Stratified flow method partitioning data

[0143] Results based on Hierarchical flow method

[0144]

[0145] Furthermore, to verify the effectiveness, speed, and stability of the algorithm proposed in this invention, it is compared with the greedy-taboo algorithm. The optimal result of the greedy-taboo algorithm is as follows: Figure 14 As shown in Table 2, since both the greedy algorithm and the tabu search algorithm are heuristic algorithms, they are sensitive to initial values ​​and have poor stability. Therefore, the statistics of ten partitioning tests based on the greedy-tabu algorithm are given. The parameters of the tabu algorithm are set as follows: the length of the selected candidate set is 9, the tabu step size is 6, no amnesty criterion is set, and the maximum number of searches is 300.

[0146] Table 2. Partition data for the Greedy-Taboo Algorithm

[0147] Results based on Greedy-Tabu algorithm

[0148]

[0149] A comparison of the computation time, maximum difference, and algorithm stability between the method of this invention and the greedy-taboo algorithm reveals that the greedy-taboo algorithm generally has a longer computation time, and the time to find the optimal value is also generally longer than that of the layered flow method proposed in this invention. Although the greedy-taboo algorithm can also find the same better solution as the layered flow method, its results are not stable.

[0150] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0151] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A method for optimizing the zoning of a distribution network considering three-phase power imbalance, characterized in that, The method includes the following steps: Based on the local sensitivity calculation method and combined with the real-world distribution network line admittance parameters, the voltage sensitivity matrix between nodes is calculated to derive the electrical distance between nodes; Using the electrical distance between nodes as the weight of the edges between nodes in the network topology, the preliminary network partitioning results are obtained based on the Louvain algorithm, which has high computational efficiency among community detection algorithms. Based on the network size, the total number of partitions is determined using the preliminary network partitioning results. Then, the sub-regions of the network are merged using the flow method or the hierarchical flow method based on the total number of partitions. The non-overlapping partitioning results with a similar size to the sub-regions are solved and output using the branch and bound method. The methods of flow method or stratified flow method are as follows: Based on the initial network partitioning results, each partition is treated as a new node, and the weight of the new node is the number of original nodes contained in each original partition. Simultaneously, based on the network topology of the original nodes, the new node inherits all the connections between the original nodes, thus generating a new undirected graph. (G,ω) and G=(V,E) ,in G Represents the new undirected graph. ω It is the vertex weight set. V Represents a vertex set. E Represents the edge weight set; For undirected graphs that require merging partitions using either the flow method or the hierarchical flow method. (G,ω) and G=(V,E) A new directed graph needs to be constructed. D The construction method is as follows: replace each undirected edge with two directed edges with the same endpoints but different directions, and then add a directed edge. N A set of vertices S={s 1 ,...,s N } As the source, and from S each vertex to G Add a directed edge to each vertex in S, pointing from the vertex in S to... G By identifying the vertices in the set, a new set of vertices and edges is obtained. Therefore... D vertex set V(D) = V∪S, D edge set A(D)={(u,v),(v,u):{u,v}∈E}∪{(s i ,v):i∈[N],v∈V} ; After obtaining the new directed graph D, that is, for the new directed graph... D The flow method or stratified flow method can be used. The steps of the flow method are as follows: S In k Each source has a total of ω(G) Traffic, ω(G) This represents the sum of the weights of all vertices in G; furthermore, it forces each non-source vertex to... ν Only from D A single vertex in the process receives traffic and consumes it. ω(ν) The received traffic, ω(ν) This represents the weight of a single vertex, thus allowing each source vertex to... S i Traffic is sent to a single non-source vertex, then propagates to other vertices, and is consumed in the process until it reaches zero. S i The vertices traversed after departure correspond to the vertices contained in partition i. To balance the size of the sub-regions, the objective function is defined as minimizing the difference between the maximum and minimum flow sources, and the branch and bound method is used to solve it to ensure the globally optimal solution is obtained. The following formula is constructed: (8) (9) (10) (11) (12) (13) (14) (15) In the above formulas, the function This represents the sum of the weights of the directed edges connected to the vertex. A positive superscript indicates a directed edge flowing out of that node. A negative superscript indicates a directed edge flowing into that node. The function represents the remaining weight of edge a. This indicates the number of edges flowing into or out of this node. This means that the number of outflow sources i is 1, while This indicates that the number of nodes flowing into node v is 1; It is a binary variable used to indicate whether any edge partition exists in edge set A(D); Non-negative real numbers; The solution method of the flow method is as follows: Search method: Based on the requirements of the branch and bound method, a queue is used as the data storage structure to store the flow process of each source. The subsequent expansion node is selected according to the first-in-first-out principle. Based on the number of sub-partitions N, all feasible solutions are listed. For each feasible solution, the neighbors of the root node of each source are found and used as child nodes. Each child node is judged to determine whether it can be pruned. At the same time, if a child node generates more sub-regions after selection, and there is a sub-region that is not connected to other partitioned regions, then the sub-region is selected as the node. Pruning conditions: When a source in a feasible solution cannot find a new node, the difference between the largest and smallest subregion sizes is determined. Based on experience, if the difference between the largest and smallest subregion sizes is greater than three-quarters of the size of each sub-node, then prune. If the smallest source found temporarily in a feasible solution is smaller than the smallest source in other known feasible solutions, then prune. The principle of the stratified flow method is as follows: The original process involving a large number of partitions is broken down into two sub-processes. The first process decomposes the large region into a few sub-regions using a flow method. The second process further divides each sub-region using a second flow method to achieve the required total number of partitions. Therefore, the integer decomposition of the total number of partitions N represents the number of partitions at each level. Furthermore, based on the determined N, it is decomposed into integers, specifically into only two numbers. The selected combination of decompositions should meet the following requirements: Two numbers that should be factored into an integer should be close to each other. ; The order of the decomposed numbers should be as follows: smaller numbers as the first layer and larger numbers as the second layer. According to the requirements of subsequent distributed algorithms, if the regions are divided into overlapping partitions, then based on the non-overlapping partition results, the overlapping partition results are generated based on the principle of maximizing the degree of network topology nodes, that is, the principle of maximizing information interaction.

2. The method for optimizing the zoning of a distribution network considering three-phase power imbalance according to claim 1, characterized in that, The local sensitivity calculation method includes: (1) In the formula, Let i be the voltage amplitude of phase p at node i. The current amplitude injected into phase q at node j is given by, where, The node injection current is obtained from the node voltage and the elements in the node admittance matrix: (2) In the formula, The admittance value between phase p at node i and phase q at node j; the sensitivity of phase p at node i and phase q at node j. The expression is represented by the impedance matrix: (3)。 3. The method for optimizing the zoning of a distribution network considering three-phase power imbalance according to claim 2, characterized in that, The method for calculating the electrical distance between nodes includes: (4) In the formula, This represents the electrical distance between node i and node j. According to formula (4), this represents the positive correlation between the electrical distance between nodes and the sensitivity. The higher the electrical coupling between the two nodes, the greater the electrical distance between the nodes. For two nodes that are not directly connected by a line, the electrical distance between the nodes is 0.

4. The method for optimizing the zoning of a distribution network considering three-phase power imbalance according to claim 1, characterized in that, The process of using the electrical distance between nodes as the weight of edges between nodes in the network topology, and obtaining the preliminary network partitioning results based on the computationally efficient Louvain algorithm in community detection algorithms, includes: Based on the modularity criterion, the Louvain algorithm is used for initial partitioning. The concept of modularity is as follows: (5) In the formula, A represents the adjacency matrix of the distribution network topology. ij This represents the connection relationship between nodes i and j; 1 indicates adjacency and 0 indicates non-adjacency. C represents a community; P is the set of communities in the network. This indicates the community to which vertex i belongs; This indicates that if vertices i and j belong to the same community, the value is 1; otherwise, it is 0. i and k j Let be the degree of the vertex, represent the sum of the weights of all edges connected to vertex i or vertex j, and m be the sum of the weights of all edges in the network; the function The variables u and v are both corresponding to , The intermediate quantities for calculation.

5. A distribution network optimization zoning method considering three-phase power imbalance according to claim 4, characterized in that, The Louvain algorithm process includes the following steps: Treat each vertex as an initial sub-community; For each individual node, extract the nodes from its community and then add them sequentially to the communities of the nodes adjacent to it. Calculate the modularity gain in each community. If the largest at this time If so, the node will be returned to its original community. If the largest node at this time... If so, the node will be placed in the community with the greatest gain; Repeat the above steps until the module gain is less than or equal to zero each time it is calculated; The modularity gain The calculation method is as follows: (6) In the formula, It is the sum of the edge weights within the community; It is the sum of the weights of all connected nodes within the community; It is the sum of the weights between node i and community C, where the electrical distance between the nodes is used as the weight of each edge.

6. The method for optimizing the zoning of a distribution network considering three-phase power imbalance according to claim 1, characterized in that, The method for determining the total number of partitions based on network size is as follows: (7) In the formula, N F The theoretical maximum number of partitions is taken as an empirical value. ,in n This represents the number of network nodes. N min The minimum value for network partitioning is set to 2; N max This is the maximum value for the network partition, plus 1 for the number of nodes containing measurements in the distribution network; When selecting the number of partitions, when N When the number of partitions is greater than 6, select the total number of partitions that can be factored into integers. If all partitions can be factored into integers, then selecting integers will result in more similar decomposition values. Number of partitions N ; and when N When the value is small and there is no need to select the stratified flow method, take the median of all candidate values ​​that meet the constraints.

7. The method for optimizing the zoning of a distribution network considering three-phase power imbalance according to claim 1, characterized in that, The process of generating overlapping partitioning results includes the following steps: Based on the non-overlapping partitioning results, candidate overlapping nodes are selected using the following method: For any non-overlapping region that is a neighbor, find two neighboring nodes belonging to the two sub-regions respectively; these neighboring node pairs are candidate overlapping nodes. Based on the principle of maximum information interaction, the interaction value of each candidate overlapping node is calculated. H The calculation method is as follows: (16) In the formula, The adjacency matrix represents the network topology, while The electrical distance between two nodes; by considering candidate node pairs i and j H i , H j Perform calculations and comparisons. H i and H j The size of the H value is used to select the node with the larger H value as the overlapping node to obtain the overlapping region division result.

Images