Power distribution network hierarchical partition topology design method based on graph computation

Abstract

The application relates to the technical field of power system data processing, in particular to a power distribution network hierarchical partition topology design method based on graph calculation, which comprises the following steps: constructing a radial initial operation graph according to fixed connection edges in a weighted physical topology graph and switch connection edges with an initial state being closed; performing graph division on the radial initial operation graph to obtain a plurality of power supply partitions meeting preset power supply distance constraints; for each power supply partition, constructing a tree-shaped power supply path structure with a power supply node as a root node according to the power supply node and the voltage level of each node in the power supply partition to obtain an initial hierarchical partition topology forest composed of a plurality of tree-shaped power supply path structures; iteratively searching for candidate switch operation pairs, adjusting the current switch state according to the load balance degree of each power supply partition to obtain a target hierarchical partition topology forest, so that the operation rationality of the topology structure and the adaptability to network state changes are improved.

Description

Technical Field

[0001] This application relates to the field of power system data processing technology, specifically to a method for designing a hierarchical and partitioned topology structure for distribution networks based on graph computation. Background Technology

[0002] With the large-scale integration of new power equipment such as distributed power sources and electric vehicle charging stations, the operation of distribution networks is becoming increasingly complex, and the network topology is constantly changing dynamically. The high proportion of distributed power sources makes the operation of distribution networks more flexible and versatile, placing higher demands on the rationality and adaptability of the distribution network topology.

[0003] Currently, the hierarchical and zoning design of distribution networks mainly relies on manual experience or simple rules for partitioning. Existing technologies include methods for partitioning power grid nodes based on clustering or community detection algorithms, as well as research on topology analysis and reconstruction based on graph theory. However, most of these methods use only a single indicator as the partitioning criterion, often treating hierarchical and zoning separately, lacking a unified technical framework. Furthermore, existing methods are mostly static designs for the power grid state at a fixed moment. When the power grid topology changes, the original partitioning scheme often becomes invalid and cannot flexibly adapt to changes in network conditions.

[0004] Therefore, how to rationally design the distribution network topology based on its electrical characteristics and topology, so that the resulting topology can both meet the basic constraints of distribution network operation and adapt to changes in network conditions, is a problem that urgently needs to be solved. Summary of the Invention

[0005] To address the technical challenge of designing distribution network topologies that balance operational rationality with adaptability to network state changes, this application aims to provide a graph-based method for hierarchical and partitioned distribution network topology design. The specific technical solution adopted is as follows: This application provides a graph-based method for designing a hierarchical and partitioned topology structure for a power distribution network. The method includes: constructing a weighted physical topology graph based on the equipment attribute information and connection relationships between electrical devices in the power distribution network; constructing a radial initial operating graph based on fixed connection edges and initially closed switch connection edges in the weighted physical topology graph; partitioning the radial initial operating graph to obtain multiple power supply partitions that satisfy preset power supply distance constraints; for each power supply partition, constructing a tree-like power supply path structure with power supply nodes as root nodes based on the power supply nodes and their voltage levels, resulting in an initial hierarchical and partitioned topology forest composed of multiple tree-like power supply path structures; iteratively searching for candidate switch operation pairs and adjusting the current switch state according to the load balance of each power supply partition to obtain the target hierarchical and partitioned topology forest.

[0006] One possible approach to constructing a weighted physical topology graph includes: mapping each electrical device in the distribution network to a node in the weighted physical topology graph, and configuring corresponding device attribute information for each node; mapping each direct connection relationship to an edge in the weighted physical topology graph, and setting connection type information and electrical parameter information for each edge; and determining the comprehensive weight of each edge based on its electrical parameter information and topological location information to obtain the weighted physical topology graph.

[0007] One possible approach is to use the electrical parameters of the line corresponding to each edge, including transmission capacity parameters, electrical connection tightness parameters, and conductivity efficiency parameters, to determine the comprehensive weight of each edge. This includes: determining the corresponding electrical parameter vector based on the transmission capacity parameters, electrical connection tightness parameters, and conductivity efficiency parameters of the line corresponding to each edge; determining the topological criticality index of each edge in the weighted physical topology graph; determining the sample weighting coefficients of each edge based on the topological criticality index, and then performing weighted standardization processing on the electrical parameter vector based on the sample weighting coefficients to obtain a standardized feature vector; determining the principal component direction based on the standardized feature vector, projecting the standardized feature vector onto the principal component direction, and determining the component obtained from the projection as the comprehensive weight of the edge.

[0008] As one possible approach, the process of constructing a radial initial running graph includes: constructing a temporary graph using fixed connection edges and switch connection edges that are initially closed in the weighted physical topology graph as candidate edges; increasing the weight values ​​of the fixed connection edges in the temporary graph to be greater than the sum of the weights of all candidate edges in the temporary graph; performing de-loop processing on the temporary graph after weight increase, traversing the candidate edges in descending order of weight value; if the current candidate edge does not form a loop after being added, it is retained; if the current candidate edge forms a loop after being added and is a switch connection edge, it is removed and marked as pending disconnection in the weighted physical topology graph; if the current candidate edge forms a loop after being added and is a fixed connection edge, it is forcibly retained; and determining the subgraph formed by all retained edges as the radial initial running graph.

[0009] As one possible approach, the radial initial operating graph is partitioned, including: horizontally partitioning the radial initial operating graph using a pre-defined community detection algorithm based on the comprehensive weight of each edge, resulting in multiple initial power supply partitions. For each initial power supply partition, using the power nodes within the partition as the source, the shortest power supply path from each load node to the power node is determined. Based on the physical length of different voltage level segments within the shortest power supply path, it is determined whether the power supply distance of each load node meets the pre-defined maximum allowable power supply distance. For initial power supply partitions with load nodes exceeding the power supply distance limit, the boundary switch connection edge with the lowest partition suitability index is disconnected to split the initial power supply partition into two sub-partitions. The power supply distance verification and splitting operations are then recursively performed on the newly split sub-partitions to obtain power supply partitions that meet the power supply distance constraints.

[0010] As a possible implementation, assuming all power supply zones meet the power supply distance constraints, the method further includes: marking load nodes with power values ​​greater than a preset power threshold as critical load nodes based on the power values ​​of each load node. For each critical load node in the current zone, a dual-power supply condition existence check is performed in the weighted physical topology graph to determine if there are two non-intersecting paths connecting two different power supply nodes. If no non-intersecting paths exist, the switch connection edge with the highest zone suitability index is selected from the disconnected switch connection edges in the weighted physical topology graph as the backup switch connection edge, and this backup switch connection edge is marked as a tie-back edge and kept disconnected to establish a backup power supply channel between the current zone and another zone. For the zones marked with tie-back edges, the dual-power supply condition existence check is re-performed until all critical load nodes meet the dual-power supply conditions.

[0011] As one possible approach, the process of determining the zoning suitability index includes: calculating the number of nodes in each of the two sub-zonings formed after disconnecting the candidate switch connection edge, and determining the ratio of the smaller number of nodes to the larger number of nodes as the basic size factor. The candidate switch connection edge is then deleted from the weighted physical topology graph. The physical length of the bypass path between the nodes at both ends of the candidate switch connection edge is determined, and the electrical coupling factor is determined based on the physical length of the bypass path. Finally, the zoning suitability index for the candidate switch connection edge is determined based on the basic size factor and the electrical coupling factor.

[0012] One possible approach is to construct a tree-like power supply path structure with power nodes as root nodes. This includes: for each power supply zone that meets the power supply distance constraints, dividing all nodes within the power supply zone into at least two voltage levels based on the voltage level of each node, and selecting a power node from the highest voltage level as the root node. Within the highest voltage level, using the root node as the source point, constructing the highest voltage level tree using a pre-defined spanning tree algorithm based on comprehensive weights. Then, sequentially performing access operations on the adjacent next voltage level: obtaining the transformer between the current voltage level and the next voltage level, using the transformer's outgoing line side as the access point, and selecting nodes directly connected to the transformer in the next voltage level as nodes to be accessed. Using a pre-defined spanning tree algorithm based on comprehensive weights, these nodes are then accessed into the existing tree structure until all nodes in all voltage levels are accessed. Finally, performing path power supply distance verification on the load nodes in the constructed tree-like power supply path structure, for load nodes whose power supply distance exceeds the limit, tracing back along the parent chain, redirecting the parent node of the load node with an ancestor node that meets the constraints to the nearest ancestor node that meets the constraints, thus obtaining the tree-like power supply path structure.

[0013] One possible approach involves iteratively searching for candidate switch operation pairs and adjusting the current switch state based on the load balancing of each power supply zone. This includes: using the variance of the total load value of each power supply zone in the current operating topology as the current load balancing. Selecting a switch connection edge currently in an open state from the weighted physical topology graph as the edge to be closed, and identifying all closed switch connection edges in the loop formed after closing the edge to be closed in the current operating topology. Forming candidate switch operation pairs with the edges to be closed and each closed switch connection edge to constitute a candidate operation set. Executing the candidate switch operation pairs in the candidate operation set, applying the corresponding closing and opening operations to the current operating topology to obtain a candidate operating topology. Calculating the candidate load balancing for candidate operating topologies that satisfy radial constraints and power supply distance constraints. If the candidate load balancing is less than the current load balancing, the candidate operating topology and candidate load balancing are used as the updated current operating topology and current load balancing, respectively. Iteratively searching the candidate operation set until the load balancing no longer decreases after traversing all candidate switch operation pairs, using the operating topology where the load balancing no longer decreases as the target hierarchical partitioned topology forest.

[0014] As one possible approach, equipment attribute information includes the equipment type, voltage level, rated capacity, and load power of each electrical device. Direct connection relationships include the connection type between electrical devices, physical line length, line rated current, line impedance, and the initial state of the switches. Connection types include fixed connections and switch connections.

[0015] This application has the following beneficial effects: By constructing a radial initial operating graph, performing graph partitioning under power supply distance constraints, and establishing a tree-like power supply path structure rooted at power supply nodes, the resulting topology ensures that it meets multiple operational constraints, including radial operation, power supply radius, and clear voltage hierarchy relationships. This results in tight electrical connections within each power supply zone and distinct power supply path hierarchies, effectively improving the reliability and power quality of the distribution network. Furthermore, by iteratively searching for candidate switch operation pairs while satisfying basic constraints and dynamically adjusting switch states using load balancing as the optimization objective, the resulting hierarchical partitioned topology forest can flexibly adjust partition boundaries and power supply paths when the network topology changes. This balances the operational rationality of the topology with its adaptability to network state changes, thereby improving the overall performance of the distribution network topology design in complex dynamic scenarios. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating a graph-based distribution network hierarchical and partitioned topology design method provided in one embodiment of this application. Figure 2 This is a schematic diagram of the system architecture of a distribution network hierarchical and partitioned topology design system based on graph computation, provided as an embodiment of this application. Detailed Implementation

[0017] The following description, in conjunction with the accompanying drawings, details a specific scheme for a graph-based distribution network hierarchical and partitioned topology design method provided in this application.

[0018] Please see Figure 1 It illustrates a flowchart of a graph-based distribution network hierarchical and partitioned topology design method according to an embodiment of this application, as shown below. Figure 1 As shown, the method includes the following steps: S100. Construct a weighted physical topology diagram based on the equipment attribute information of each electrical device in the distribution network and the connection relationship information between the devices.

[0019] The aforementioned power distribution network includes multiple electrical devices, specifically including but not limited to transformers, busbars, circuit breakers, load switches, distribution transformers, load nodes, and distributed power source access points. Device attribute information may include the device type, voltage level, rated capacity, and load power of each electrical device. Connection information between devices includes direct and indirect connections. A direct connection refers to a relationship where two electrical devices are directly connected by a conductor or switch; this relationship can be directly mapped to an edge in a weighted physical topology graph. Direct connections include the connection type between each electrical device, the physical length of the line, the rated current of the line, the line impedance, and the initial state of the switch. Indirect connections refer to a relationship where two electrical devices are connected through multiple intermediate devices. Connection types include fixed connections and switch connections.

[0020] Because different electrical devices are interconnected through complex mesh-like relationships via wires or switches, this mesh-like connection cannot be directly used for partitioning and hierarchical calculations. Therefore, the physical structure of the distribution network is mapped as a graph structure, with electrical devices representing the nodes and the direct connections between them representing the edges. The attribute information of the electrical devices and the connection relationship information are configured as attributes of the nodes and edges of the graph structure, thus forming a weighted physical topology graph. Each edge in the weighted physical topology graph is assigned a comprehensive weight, which is used to quantify the overall importance of each edge in electrical performance and topology.

[0021] S200. Based on the fixed connection edges and the switch connection edges that are initially closed in the weighted physical topology diagram, construct a radial initial operation diagram.

[0022] The aforementioned radial initial operating graph refers to an acyclic connected graph composed of edges currently participating in power transmission. This radial initial operating graph contains no loop paths; each node is connected to a power source node via a single path. Understandably, a distribution network must satisfy the radial constraint under normal operating conditions; otherwise, loop paths will lead to circulating currents, endangering the safe operation of electrical equipment and lines.

[0023] The weighted physical topology diagram fully preserves all fixed connection edges and all switch connection edges in the distribution network. Fixed connection edges are always conductive and constitute an inoperable network structure; switch connection edges can be closed or open, and their initial state is determined by the collected switch state information. However, not all edges in the weighted physical topology diagram participate in power transmission at the current moment: switch connection edges initially open are not conductive and do not constitute an actual power supply path; only fixed connection edges and switch connection edges initially closed participate in power transmission. Therefore, it is necessary to extract all fixed connection edges and all switch connection edges initially closed from the weighted physical topology diagram to form a radial initial operating diagram. Since this temporary diagram may contain loop paths formed by fixed connection edges and switch connection edges initially closed, these loop paths do not conform to the radial constraints and require loop removal processing to eliminate all loops.

[0024] S300. Divide the radial initial operation diagram into multiple power supply zones that meet the preset power supply distance constraints.

[0025] In this embodiment, graph partitioning refers to dividing the set of nodes in the radial initial operating graph into multiple non-overlapping subsets, each subset corresponding to a power supply zone. Power supply distance refers to the physical length of the power supply path from the power source node to the load node. Preset power supply distance constraints refer to the maximum allowable power supply distance preset for different voltage levels; for example, the maximum allowable power supply distance for a 35kV high-voltage line is 40km, for a 10kV medium-voltage line it is 15km, and for a 0.4kV low-voltage line it is 0.5km. Power supply distance directly affects the voltage quality of the load node; an excessively long power supply path can lead to excessive voltage drop across the line, causing the load-side voltage to deviate from the allowable range and affecting power supply reliability.

[0026] While the radial initial operation diagram eliminates loops, all nodes in the network remain in the same connected graph, without horizontal partitioning. In a distribution network, power supply partitioning should ensure that the load within each partition is rationally distributed within that partition, with minimal power exchange between partitions. Therefore, the radial initial operation diagram needs to be divided into multiple power supply partitions, with close electrical connections within each partition and loose electrical connections between partitions.

[0027] S400. For each power supply zone, based on the power supply nodes and voltage levels of each node within the power supply zone, construct a tree-like power supply path structure with the power supply nodes as the root nodes, resulting in an initial hierarchical partition topology forest composed of multiple tree-like power supply path structures.

[0028] The aforementioned tree-like power supply path structure refers to a radial power supply path organization where a single power source node is the root node, and electrical energy is transmitted step-by-step from the root node down the tree-like path to each load node. Voltage level refers to the voltage level at which each electrical device in the distribution network is located, including high-voltage, medium-voltage, and low-voltage levels. Each power supply zone contains electrical equipment of different voltage levels; electrical energy at the high-voltage level needs to be transformed step-by-step through transformers to the medium-voltage and low-voltage levels before being supplied to the loads.

[0029] After the graph partitioning is completed, each power supply zone contains nodes at multiple voltage levels, but the power supply path relationships between the nodes are not yet determined. That is, the power source of the load nodes and the organization of the power transmission path are not clear. The power supply path of the distribution network should be presented in a tree structure, starting from the power source node and extending from top to bottom according to the voltage level to each load node, with each node having a unique parent node.

[0030] Therefore, for each power supply zone, a vertical hierarchy is established based on the voltage level of each node. Using the power supply nodes within the zone as root nodes, a tree-like power supply path structure is constructed layer by layer according to the voltage level from top to bottom. When constructing the tree-like power supply path structure, each node has a unique parent node, and the voltage level decreases progressively along the path from the root node to any load node. The tree-like power supply path structures of all power supply zones together constitute the initial hierarchical partitioned topology forest.

[0031] S500 iteratively searches for candidate switch operation pairs, adjusts the current switch state according to the load balance of each power supply zone, and obtains the target hierarchical partition topology forest.

[0032] The aforementioned candidate switch operation pair refers to the combination of operations that simultaneously close the connecting side of a switch that is currently open and open the connecting side of a switch that is currently closed. Load balance refers to the dispersion of the total load value across different power supply zones, used to quantify the uniformity of load distribution among these zones. A lower load balance indicates that the total load across different power supply zones is closer and the load distribution is more uniform.

[0033] In this embodiment, although the initial hierarchical partitioned topology forest satisfies the radial constraint and power supply distance constraint, and forms a complete tree-like power supply path structure, the load distribution among the power supply partitions may not be uniform. Since the initial partitions are mainly determined based on the tightness of electrical connections and power supply distance constraints, without considering the balanced distribution of load among the power supply partitions, some partitions may be overloaded while others are underloaded. Uneven load distribution can lead to overload risks for equipment in heavily loaded partitions and low utilization efficiency for equipment in lightly loaded partitions, which is detrimental to the economic operation and long-term safety of the distribution network.

[0034] Therefore, by adjusting the switch states to change the boundaries of each power supply zone, the load is transferred from the heavily loaded zone to the lightly loaded zone, making the load distribution among the power supply zones more uniform. The switch state adjustment method is to enumerate all feasible switch operation pairs. Each switch operation pair includes closing a currently open switch connection edge and opening a currently closed switch connection edge on the loop formed after the closure. For each candidate switch operation pair, the corresponding closing and opening operations are performed to obtain a candidate operating topology. The load balance degree corresponding to the candidate operating topology is calculated. If the candidate load balance degree is better than the current load balance degree, the candidate operation is accepted and the current operating topology is updated. The target hierarchical partitioned topology forest is obtained by iteratively searching until the load balance degree cannot be further improved.

[0035] As one possible approach, the process of constructing a weighted physical topology graph includes: S101. Map each electrical device in the distribution network to a node in the weighted physical topology graph, and configure the corresponding device attribute information for each node.

[0036] In this embodiment, each actual electrical device in the power distribution network is mapped to a node in a weighted physical topology graph. Each node is assigned a unique identifier, and the device attribute information corresponding to that node is recorded.

[0037] S102. Map each direct connection relationship to an edge of the weighted physical topology graph, and set the connection type information and electrical parameter information for the edge.

[0038] For any two electrical devices, determine whether a direct connection exists between them based on the design drawings or actual connection relationships. If the two electrical devices are directly connected by a wire or a switch, establish an undirected edge between their corresponding graph nodes and set the connection type information and electrical parameter information for this edge.

[0039] The connection type information identifies whether the connection is a fixed connection or a switching connection. A fixed connection refers to a direct connection between two devices via a wire, without any on / off components, and its on / off state is not affected by switch operation. A switching connection refers to a connection between two devices via a switching device, where the switch can be in a closed or open state.

[0040] S103. Based on the electrical parameter information and topological location information of each edge, determine the comprehensive weight of each edge to obtain the weighted physical topology graph.

[0041] The overall weight is a quantitative value representing the importance of each edge in the weighted physical topology graph. Its magnitude reflects the overall importance of the corresponding line in terms of electrical performance and topology. The larger the overall weight, the more important the edge is in the distribution network.

[0042] The aforementioned comprehensive weights are used to quantify the importance of each edge in the distribution network. Their determination requires a comprehensive consideration of each edge's performance in two dimensions: electrical characteristics and topological location. Electrical characteristics reflect the physical performance of the line itself, including transmission capacity, electrical connectivity, and conductivity; topological location reflects the edge's role as a connecting bridge in the network structure.

[0043] As one possible approach, the electrical parameters of each edge's corresponding line include transmission capacity parameters, electrical connection density parameters, and conductivity efficiency parameters. Based on the electrical parameters and topological location information of each edge, the comprehensive weight of each edge is determined, including: S1031. Determine the corresponding electrical parameter vector based on the transmission capacity parameter, electrical connection tightness parameter, and conductivity efficiency parameter of the line corresponding to each edge.

[0044] Specifically, for each edge in the weighted physical topology graph Three-dimensional feature parameters are extracted from the electrical parameter information of the corresponding line edge to form the electrical parameter vector of that edge. The transmission capacity parameter refers to the rated current of the line. This parameter represents the maximum current that the line is allowed to carry continuously, directly reflecting the line's power transmission capacity. A higher rated current indicates that the line can carry more active power and has a stronger electrical transmission capacity. Line physical length reciprocal This is a parameter for the tightness of electrical connection. The shorter the physical length of the line between two electrical devices, the smaller the electrical distance between them, the tighter the electrical connection, and the less energy is lost during transmission. Therefore, the reciprocal of the physical length of the line is used to quantify the tightness of the electrical connection. The conductivity efficiency parameter refers to the line impedance. The reciprocal of the modulus Line impedance reflects the resistance of a line to current. The smaller the impedance, the lower the active and reactive power losses during power transmission, and the higher the conductivity. Therefore, the reciprocal of the line impedance modulus is used to quantify conductivity.

[0045] Based on the above three feature parameters, the edge electrical parameter vector Defined as: in, The unit is ampere (A). The unit is kilometers (km) and the value is a positive number. For complex impedance ( ), This represents the magnitude of the impedance, measured in ohms (Ω). The unit is the reciprocal of kilometers (1 / km). The unit is the reciprocal of the ohm (1 / Ω). The above three parameters describe the electrical performance of the line from three dimensions: transmission capacity, electrical distance, and conductivity efficiency, and together they constitute the electrical parameter vector of this side.

[0046] S1032. Determine the topological criticality index of each edge in the weighted physical topology graph.

[0047] In this embodiment, betweenness centrality is used to quantify the connectivity of each edge in the network topology. Betweenness centrality reflects the degree to which an edge acts as a bridge connecting other nodes in the graph; a higher value indicates that the edge is more critical to the network topology.

[0048] side betweenness centrality The calculation formula is: in, Represents a weighted physical topology graph The set of all nodes in the set. For the node To the node The total number of shortest paths between them. For the node To the node In the shortest path between, passing through the edge The number of paths. When When, the corresponding fractional terms This term is meaningless; it is not included in the summation.

[0049] S1033. Determine the sample weighting coefficients of each edge based on the topological key indicators, and perform weighted standardization processing on the electrical parameter vector based on the sample weighting coefficients to obtain the standardized feature vector.

[0050] In this embodiment, betweenness centrality is converted into sample weighting coefficients. The formula is: The embodiments of this application can use sample weighting coefficients to perform weighted standardization processing on electrical parameter vectors in order to eliminate the interference of differences in numerical magnitude and dimensions of different features on the analysis results.

[0051] Specifically, firstly, based on the sample weighting coefficients Calculate the weighted mean vector of electrical parameter vectors : Among them, the summation symbol This represents all edges in the weighted physical topology graph. Summation, This represents the set of all edges in the weighted physical topology graph.

[0052] Secondly, based on the sample weighting coefficients Calculate the weighted standard deviation of each dimension of the electrical parameter vector. : The calculation of the square root of the sum of squares is performed separately for each component of the electrical parameter vector. Is with For vectors of the same dimension, each component corresponds to the weighted standard deviation of that dimension. The weighted standard deviation measures the dispersion of each electrical parameter after considering topological importance.

[0053] Finally, the electrical parameter vector of each edge is standardized to obtain the standardized feature vector. : The division is performed separately for each component of the electrical parameter vector. If the weighted standard deviation... If one component of the denominator is 0, the denominator in the standardized calculation is zero, rendering the calculation meaningless. For example, if the rated current of all sides... If all values ​​are the same, then the weighted standard deviation for that dimension is 0. If a component of the vector is 0, it indicates that the electrical parameter of that dimension has the same value on all edges and there is no degree of dispersion. In this case, the dimension does not participate in the standardization process, and the corresponding standardized eigenvector component is directly set to 0.

[0054] After the above standardization process, different electrical characteristics are transformed to the same scale, eliminating the differences in the numerical magnitude and dimensions of rated current, reciprocal of length, and reciprocal of impedance.

[0055] S1034. Determine the principal component direction based on the standardized eigenvector, project the standardized eigenvector onto the principal component direction, and determine the component obtained from the projection as the comprehensive weight of the edge.

[0056] In this embodiment, principal component analysis (PCA) is used to extract the main directions of change in the standardized eigenvectors. PCA is a data dimensionality reduction method that transforms the original data into a new coordinate system through linear transformation, such that the data has the maximum variance along the first coordinate axis of the new coordinate system.

[0057] Based on sample weighting coefficients For standardized feature vectors Weighted calculation of covariance matrix The formula is as follows: in, express The transpose of the eigenvector is such that the product of the eigenvector and its transpose is... Matrix. Solving for the weighted covariance matrix. The eigenvector corresponding to the largest eigenvalue is used as the direction of the first principal component. .

[0058] Each edge Standardized feature vectors Projected onto the direction of the first principal component Above, the projection value is obtained. : in, This represents the vector dot product operation. That is, the edge The overall weight reflects the overall importance of the edge in terms of electrical performance and topology. The larger the value, the higher the overall importance of that edge.

[0059] As one possible approach, the process of constructing a radial initial running graph includes: S201. Using the fixed connection edges and the switch connection edges that are initially closed in the weighted physical topology graph as candidate edges, construct a temporary graph.

[0060] The above weighted physical topology diagram It includes all electrical equipment and direct connections in the distribution network. To construct the initial operating graph, a temporary graph is built using fixed connection edges and switch connection edges that are initially closed in the weighted physical topology graph as candidate edges. Although the switch connection edge that is initially disconnected exists in the weighted physical topology graph, it does not participate in power transmission at the current moment and is not included in the temporary graph.

[0061] S202. Increase the weight value of the fixed connection edge in the temporary graph to be greater than the sum of the combined weights of all candidate edges in the temporary graph.

[0062] Specifically, for temporary graphs Each fixed connection edge in , and its overall weight Improve in the following ways: in, As a preset value, its value should satisfy: in, Temporary graph The sum of the weights of all candidate edges in the temporary graph. In this way, the weight of any boosted fixed connection edge is greater than the sum of the weights of all candidate edges in the temporary graph, thus ensuring that fixed connection edges are processed first during traversal.

[0063] S203. Perform deloop processing on the temporary graph after weight value enhancement. Traverse the candidate edges in descending order of weight value. If the current candidate edge does not form a cycle after being added, retain the current candidate edge. If the current candidate edge forms a cycle after being added and is a switch connection edge, remove the current candidate edge and mark the current candidate edge as pending disconnection in the weighted physical topology graph. If the current candidate edge forms a cycle after being added and is a fixed connection edge, force the current candidate edge to be retained.

[0064] After the weight boosting is completed, the temporary graph is... Perform cycle removal. Specifically, a cycle removal strategy based on the maximum spanning tree is adopted: Temporary diagram All edges are sorted in descending order of their updated weights. Each edge is iterated over and added to the currently constructed subgraph. Before each addition operation, a cycle check is performed to determine whether adding the edge to the currently constructed subgraph will create a cycle.

[0065] If the current candidate edge does not form a cycle after being added, it is directly retained and incorporated into the currently constructed subgraph. If the current candidate edge forms a cycle after being added, the connection type of the current candidate edge is further determined: if the current candidate edge is a switch connection edge, it is removed and marked as pending disconnection in the weighted physical topology graph; if the current candidate edge is a fixed connection edge, it is forcibly retained, even if it forms a cycle, and is not cut off. Cycle verification can be implemented using a disjoint-set data structure, which is a data structure that supports efficient set merging and querying.

[0066] After the above processing, all the remaining edges form an acyclic connected graph, which is the radial initial operating graph. For all the removed switch connection edges, their state is marked as pending disconnection in the weighted physical topology graph.

[0067] S204. Determine the subgraph formed by all retained edges as the radial initial running graph.

[0068] In this embodiment, the subgraph formed by all edges retained after delooping is determined as the radial initial running graph. .

[0069] As one possible approach, the radial initial running graph is partitioned, including: S301. Based on the comprehensive weight of each edge, a preset community detection algorithm is used to perform horizontal partitioning of the radial initial operation graph to obtain multiple initial power supply partitions.

[0070] The aforementioned horizontal partitioning refers to the process of dividing the set of nodes in the radial initial operating diagram into multiple power supply areas along the horizontal direction. Each power supply area has close electrical connections within itself, while the electrical connections between areas are loose.

[0071] The pre-defined community detection algorithm is a graph clustering algorithm that divides nodes into communities based on the graph topology. A community is a subset of nodes in a graph where the connections between nodes within the subset are relatively close, while the connections between subsets are relatively sparse. Applying the community detection algorithm to the horizontal partitioning of a radially initialized graph can fully utilize the comprehensive weight information of each edge to group electrically connected nodes into the same power supply partition. For example, the pre-defined community detection algorithm can employ the Louvain algorithm. The Louvain algorithm is a hierarchical community detection algorithm based on modularity optimization, capable of efficiently processing large-scale graph data and supporting edge weight input.

[0072] Modularity It is an evaluation indicator for measuring the quality of community zoning. Modularity A higher value indicates a denser expected network of connections between nodes within the community compared to random connections, resulting in a higher quality community partitioning. Weighted Modularity The calculation formula is: in, This represents all pairs of nodes in the graph (including...). Summation is performed in the case of (the situation described above). For nodes With nodes The combined weight of the edges between nodes, if nodes With nodes If there is no direct connection between them, then .when hour, . For nodes The weighted degree, i.e., the degree of the node The sum of the weights of all connected edges reflects the node's overall weight. Connection strength in a network. It is the sum of the combined weights of all edges in the initial radial graph, i.e., the total weighted weight of the network. For nodes The community logo to which it belongs. Let Kronecker function be used when and If the values ​​are the same, the value is 1; otherwise, the value is 0. Its function is to include only the contribution of node pairs within the same community in the summation calculation.

[0073] It should be noted that when there are edges with negative overall weights in the initial radial running graph, It may be less than 0. In this case, although the modularity calculation can still be performed, its physical meaning deviates from the standard interpretation of modularity. If If the total weighted weight of the initial radial graph is 0 (possibly due to the absence of effective edges or the cancellation of positive and negative weights), then community detection is not performed, and each node is directly treated as an independent power supply partition. In this embodiment, since the comprehensive weight is a relative value obtained through principal component projection, a preset offset can be applied to the comprehensive weight of each edge before the modularity calculation in practical applications, so that all edge weights are positive. The magnitude of the offset can be preset according to the actual data distribution, for example, taking the absolute value of the minimum comprehensive weight of all edges plus 1 as the offset. This processing method does not change the relative magnitude relationship of the comprehensive weights of each edge and does not affect the final partitioning result of the community detection algorithm.

[0074] In the above formula, Represents a node With nodes Modularity is defined as the deviation between the actual connection weights and the randomly expected connection weights. A positive deviation indicates that the actual connection strength between nodes exceeds the random expectation, and grouping them into the same community helps improve modularity. A negative deviation indicates that the connection strength is lower than the random expectation, and grouping them into the same community will reduce modularity. The goal of modularity optimization is to maximize the sum of deviations of all node pairs within a community, thereby optimizing the quality of community partitioning.

[0075] The specific execution process of Louvain's algorithm is as follows: First, each node in the radial initial running graph is regarded as an independent community, and the number of communities is equal to the number of nodes.

[0076] During the node movement optimization phase, each node is traversed sequentially. For the currently traversed node, it is moved to the community of each of its neighboring nodes. The weighted modularity increment after each move is calculated, which is the difference between the modularity before and after the move. If there is a move with a positive weighted modularity increment, the move with the largest weighted modularity increment is selected and executed, updating the community affiliation of the current node. If the weighted modularity increments of all candidate moves are not positive, the community affiliation of the current node remains unchanged. After completing one traversal of all nodes, the above node traversal and movement optimization operations are repeated until the community affiliation of all nodes no longer changes, at which point the modularity reaches a local maximum.

[0077] During the community aggregation phase, all nodes currently in the same community are aggregated into a single supernode. The edge weights between supernodes are the sum of the combined weights of all edges between the original two communities. This aggregation results in a new graph structure.

[0078] On the new graph structure, the above node movement optimization and community aggregation operations are performed iteratively until the modularity no longer increases, thus completing the horizontal partitioning.

[0079] S302. For each initial power supply zone, taking the power nodes within the initial power supply zone as the source point, determine the shortest power supply path from each load node to the power node within the initial power supply zone. Based on the physical length of the different voltage level sections in the shortest power supply path, determine whether the power supply distance of each load node meets the preset maximum allowable power supply distance.

[0080] After obtaining the initial power supply zones, the power supply distance of each power supply zone is verified to ensure that the power supply voltage quality of each load node meets the engineering requirements.

[0081] For each initial power supply zone, the power nodes within that zone are first determined. If power nodes exist within the initial power supply zone, the one with the highest voltage level is selected as the power node for that zone. .

[0082] If there are no power nodes in the initial power supply zone, then the initial power supply zone is merged with the adjacent power supply zone containing power nodes along the boundary edge with the largest comprehensive weight among the boundary edges of the initial power supply zone, and the merged power supply zone is used as the processing object for power supply distance verification; or the power node with the highest voltage level in the adjacent power supply zone is used as the alternative source point for calculating the shortest power supply path of the initial power supply zone.

[0083] For each load node in the initial power supply zone With power nodes Using Dijkstra's algorithm as the source, the algorithm is used to calculate the value from the source. arrive Shortest power supply path Dijkstra's algorithm is a shortest path algorithm that can find the shortest path from a single source node to all other nodes in a weighted graph. In this embodiment, the edge weights are the physical lengths of the corresponding lines. Shortest power supply path Composed of several edges They are connected sequentially to form a whole.

[0084] Obtain the shortest power supply path After that, separate statistics are required. The physical length of sections at different voltage levels. For the path Each edge on Obtain the voltage levels of the nodes at both ends of the edge, and take the higher value as the voltage level of the segment where the edge is located. According to the distribution network voltage level classification standard, three counters are defined: high voltage length... Medium pressure length Low-pressure length The initial values ​​are all 0.

[0085] if Then the edge The physical length is accumulated to ;if Then the edge The physical length is accumulated to ;if Then the edge The physical length is accumulated to After checking all edges After iterating and accumulating, the path is obtained. Total length of the upper high-voltage section Total length of medium-pressure section and the total length of the low-voltage section .

[0086] Will , , Each segment is compared with the maximum allowable power supply distance for the corresponding voltage level. If the length of all three segments does not exceed the allowable value for the corresponding voltage level, the power supply distance of the load node is qualified; if the length of any segment exceeds the allowable value for the corresponding voltage level, the power supply distance of the load node is out of specification.

[0087] S303. For an initial power supply zone with load nodes that exceed the power supply distance limit, select the boundary switch connection edge with the smallest zone suitability index and disconnect it to split the initial power supply zone into two sub-zones. Then, recursively perform power supply distance verification and splitting operations on the new sub-zones to obtain a power supply zone that meets the power supply distance constraint.

[0088] In this embodiment, if there are load nodes in the initial power supply zone that exceed the power supply distance limit, a splitting operation needs to be performed on the initial power supply zone. The purpose of the splitting operation is to separate the load nodes (usually located at the edge or far end of the zone) from the original initial power supply zone by cutting off the appropriate boundary switch connection edges, thereby shortening their power supply distance.

[0089] Specifically, iterate through all switch connection edges (excluding fixed connection edges) within the initial power supply zone, and for each candidate switch connection edge... The partition suitability index is calculated. The partition suitability index is used to evaluate whether the switch connection edge is suitable as a partition boundary. Candidate switch connections are sorted in ascending order of partition suitability index, and each candidate switch connection edge is selected for verification: It is verified whether each of the two sub-partitions formed after disconnecting the candidate switch connection edge contains at least one power node. If neither sub-partition contains a power node, the split candidate is rejected, and the next candidate switch connection edge is verified. If both sub-partitions contain power nodes, the candidate switch connection edge is selected as the boundary switch connection edge and disconnected, thus deleting it from the current operating diagram and splitting the original initial power supply partition in two. If, after traversing all candidate switch connections, the condition that each of the two sub-partitions contains at least one power node cannot be met, the splitting operation of the initial power supply partition is abandoned, and the initial power supply partition is marked as an unsplittable partition. In subsequent dual-power reinforcement operations, power support is provided to the overload nodes within the initial power supply partition through the backup power channel.

[0090] The power supply distance verification in S302 above is recursively performed on the two newly generated sub-partitions after the split. If there are still load nodes in the sub-partitions whose power supply distance exceeds the limit, the split operation is continued. The above process is recursively repeated until all power supply partitions meet the power supply distance constraints.

[0091] As one possible approach, assuming all power supply zones meet the power supply distance constraints, the method also includes: S304. Based on the power value of each load node, mark the load nodes whose power value is greater than the preset power threshold as critical load nodes.

[0092] Specifically, obtain the power value of each load node. Calculate the average power value of all load nodes. Will satisfy Load nodes are marked as critical load nodes. Critical load nodes are load nodes within a power supply zone whose power values ​​exceed a preset power threshold.

[0093] S305. For the current partition where each critical load node is located, perform a dual power supply condition existence check in the weighted physical topology graph to determine whether there are two non-intersecting paths that connect to two different power supply nodes.

[0094] In this embodiment, for each critical load node located in the current power supply zone, the weighted physical topology diagram is used to check whether the critical load node meets the dual power supply conditions. The reason for using the weighted physical topology diagram as the basis for the check is that when the switch connection edge in the current operation diagram is in the open state, the physical connection corresponding to the open switch connection edge still exists in the weighted physical topology diagram and can be used as a backup power supply channel.

[0095] Dual-power-condition existence checking refers to determining whether there are two non-intersecting paths starting from the critical load node, each connecting to a different power supply node. Non-intersecting paths mean that there are no shared nodes between the two paths besides the starting point (the critical load node itself), ensuring that the two paths are physically independent and will not fail simultaneously due to the failure of a single intermediate node. For example, a non-intersecting path search algorithm (such as the Suurballe algorithm) can be used to search for non-intersecting paths from the critical load node to each power supply node in a weighted physical topology graph.

[0096] S306. If there are no paths between two non-intersecting nodes, select the switch connection edge with the largest partition suitability index from the switch connection edges that are in the disconnected state in the weighted physical topology graph as the backup switch connection edge, mark the backup switch connection edge as the connection backup edge and keep the backup switch connection edge in the disconnected state, so as to establish a backup power channel between the current partition and another partition.

[0097] In this embodiment of the application, if the above dual power supply condition existence check result is non-existent, that is, the current partition where the critical load node is located is only powered by a single power supply, then a backup power supply channel needs to be established.

[0098] The disconnected switch connection edge with the highest partition suitability index is selected as the backup switch connection edge from the weighted physical topology diagram. During splitting operations, the switch connection edge with the lowest partition suitability index is disconnected; during backup channel establishment operations, the switch connection edge with the highest partition suitability index is selected for connection. A higher partition suitability index indicates that the two sub-partitions formed after disconnecting the switch connection edge are closer in size and have shorter electrical distances between their endpoints, thus minimizing the impact of using the switch connection edge as a connection channel on the normal operation of the system.

[0099] The selected standby switch connection is marked as a backup connection, but it remains disconnected in the operation diagram and does not participate in the current power transmission, ensuring that the distribution network continues to operate radially. This backup connection is only activated by closing the connection via switch operation when the original power supply to the critical load zone fails.

[0100] S307. For partitions marked with a backup connection edge, re-perform the dual power supply condition existence check until all critical load nodes meet the dual power supply condition.

[0101] In this embodiment, for the partition marked with a backup connection edge, the dual power supply condition existence check in S305 above is re-executed. If it still does not meet the requirement, the second largest partition suitability index switch connection edge is selected from the remaining disconnected switch connection edges as the second backup connection edge. The above process is repeated until all critical load nodes meet the dual power supply condition.

[0102] It should be noted that, to prevent the splitting and merging reinforcement operations from getting stuck in an infinite loop, a maximum number of iterations can be set. For example, the maximum number of iterations can be set to 20. In each iteration, power supply distance verification and splitting are performed first, followed by dual-power supply reinforcement.

[0103] As one possible approach, the process of determining the zoning suitability index includes: S3031. Calculate the number of nodes in each of the two sub-partitions formed after disconnecting the candidate switch connection edge, and determine the ratio of the smaller number of nodes to the larger number of nodes as the basic size factor.

[0104] For candidate switch connection edge Assuming that the candidate switch connection edge is removed from the current operating diagram, the power supply zone will be divided into two sub-zones. and ,in Includes nodes The connected component in which it is located, Includes nodes The connected components in which they reside. Statistical analysis is performed separately. and The number of nodes contained in each, denoted as and .

[0105] Basic size factor Calculate using the following formula: The range of the basic scale factor is: . The closer the value is to 1, the closer the sizes of the two sub-partitions formed after disconnecting the switch connection edge are. The smaller the value, the greater the difference in size between the two sub-partitions.

[0106] S3032. Delete candidate switch connection edges in the weighted physical topology graph, determine the physical length of the bypass path between the two nodes of the candidate switch connection edge, and determine the electrical coupling factor based on the physical length of the bypass path.

[0107] In the weighted physical topology graph, candidate switch connection edges are deleted. The physical length of the shortest bypass path between the two ends of each candidate switch connection edge is then determined. The bypass path refers to the alternative connecting path between the two ends of the candidate switch connection edge after deletion. If no alternative connecting path exists between the two ends of the candidate switch connection edge after deletion, the physical length of the shortest bypass path is positive infinity. A positive infinity value indicates no alternative electrical connection between the two endpoints, and this value is 0 when calculating the electrical coupling factor.

[0108] The electrical coupling factor is used to quantify the strength of the electrical connection between the two nodes of a candidate switch connection edge through alternative paths. The electrical coupling factor is determined as follows: using 1 as the numerator and the sum of 1 and the physical length of the shortest bypass path as the denominator, the numerator is divided by the denominator. The physical length of the shortest bypass path is in kilometers. The range of the electrical coupling factor is (0, 1). The longer the physical length of the shortest bypass path, the weaker the electrical connection between the two nodes of the candidate switch connection edge, and the closer the electrical coupling factor is to 0; the shorter the physical length of the shortest bypass path, the stronger the electrical connection between the two nodes of the candidate switch connection edge, and the closer the electrical coupling factor is to 1. If the shortest bypass path does not exist, the electrical coupling factor is 0.

[0109] S3033. Determine the zoning suitability index of candidate switch connection sides based on the basic scale factor and electrical coupling factor.

[0110] The zoning suitability index is used to evaluate whether candidate switch connection edges are suitable as zoning boundaries or connection channels. The zoning suitability index is determined according to the following formula: in, Indicators representing the suitability of zoning Represents the basic size factor. This represents the electrical coupling factor. The range of the zoning suitability index is... .

[0111] A smaller partition suitability index indicates a greater difference in size between the two sub-partitions formed after disconnecting the candidate switch connection edge, and a greater electrical distance between the two nodes of the candidate switch connection edge. This makes the switch connection edge more suitable as a partition boundary to be cut off. Conversely, a larger partition suitability index indicates closer similarities in size between the two sub-partitions formed after disconnecting the candidate switch connection edge, and a closer electrical distance between the two nodes of the candidate switch connection edge. This makes the switch connection edge more suitable as a connection channel between partitions. Therefore, in the partition splitting operation after power supply distance verification, the switch connection edge with the smallest partition suitability index is selected for disconnection; in the dual power supply reinforcement operation, the switch connection edge with the largest partition suitability index is selected as the backup connection edge.

[0112] As one possible approach, a tree-like power supply path structure with power nodes as root nodes is constructed, including: S401. For each power supply zone that meets the power supply distance constraint, divide all nodes in the power supply zone into at least two voltage levels according to the voltage level of each node, and select a power supply node from the highest voltage level as the root node.

[0113] For each power supply zone that meets the power supply distance constraint, vertical stratification is performed based on the voltage level of each node. All nodes within the power supply zone are divided into high-voltage, medium-voltage, and low-voltage levels according to their voltage levels. Nodes with a voltage level of 35kV and above belong to the high-voltage level; according to the distribution network voltage level classification standard, nodes with voltage levels of 6kV, 10kV, or 20kV belong to the medium-voltage level; and nodes with a voltage level of 0.4kV belong to the low-voltage level. For example, the voltage levels can be divided as follows: the high-voltage level is typically a single voltage level, such as 35kV; the medium-voltage level is 10kV; and the low-voltage level is 0.4kV. For each power supply zone, one power node from the high-voltage level is selected as the root node. If there are multiple power nodes in the high-voltage level, the power node with the highest degree centrality is selected as the root node. Degree centrality refers to the number of edges connected to that node.

[0114] S402. Within the highest voltage level, the highest voltage level tree is constructed using the root node as the source node and a preset spanning tree algorithm based on the comprehensive weight.

[0115] Within the highest voltage level (high-voltage level) of the power supply zone, using the root node selected in S401 above as the source node, a pre-defined spanning tree algorithm is used to construct the highest voltage level tree. The pre-defined spanning tree algorithm can be the maximum spanning tree algorithm, which prioritizes edges with larger overall weights, maximizing the total weight of all edges in the resulting spanning tree. The tree structure constructed using the maximum spanning tree algorithm ensures that the power transmission paths in the high-voltage level have high electrical performance and topological importance.

[0116] S403. Perform access operations sequentially on the next adjacent voltage level: Obtain the transformer between the current voltage level and the next voltage level, take the output side of the transformer as the access point, take the node in the next voltage level that is directly connected to the transformer as the node to be accessed, and use the preset spanning tree algorithm according to the comprehensive weight to access the node to be accessed into the existing tree structure until all nodes of all voltage levels have been accessed.

[0117] After completing the tree construction of the highest voltage level (high voltage level), the tree is expanded downwards level by level according to voltage level: from the current voltage level to the next adjacent voltage level (i.e., from the high voltage level to the medium voltage level, or from the medium voltage level to the low voltage level), until all voltage level nodes are connected to the tree structure.

[0118] Taking the expansion from the high-voltage level to the medium-voltage level as an example: First, the high-voltage / medium-voltage transformer connecting the high-voltage and medium-voltage levels is identified. Using the transformer's outgoing line side (medium-voltage side) as the access point, nodes directly connected to the transformer's outgoing line side are searched within the medium-voltage level and designated as nodes to be connected. Using the transformer's outgoing line side as the source point, a pre-defined spanning tree algorithm is employed based on comprehensive weights to sequentially connect the nodes to be connected to the existing tree structure.

[0119] For each medium-voltage node connected, its parent node is set as the upper-level node it connects to (the transformer outgoing side node or the medium-voltage node above it), and the level depth of the medium-voltage node (the number of hops relative to the root node) is recorded. After the medium-voltage hierarchical tree is constructed, it continues to expand to the low-voltage level: extract the medium-voltage / low-voltage distribution transformers between the medium-voltage and low-voltage levels, take the outgoing side (low-voltage side) of the distribution transformer as the access point, and take the nodes in the low-voltage level that are directly connected to the distribution transformer as the nodes to be connected. According to the comprehensive weight, the preset spanning tree algorithm is used to connect the nodes to be connected to the existing tree structure.

[0120] For each low-voltage node connected, set its parent node to the upper-level node connected to it (the outgoing node of the distribution transformer or the medium-voltage node above it), and record the hierarchy depth of the low-voltage node (the number of hops relative to the root node).

[0121] S404. Perform path power supply distance verification on the load nodes in the constructed tree-like power supply path structure. For load nodes whose power supply distance exceeds the limit, backtrack upwards along the parent chain and redirect the parent node of the load node that has an ancestor node that satisfies the constraint to the nearest ancestor node that satisfies the constraint, thus obtaining the tree-like power supply path structure. If no ancestor node that satisfies the constraint is found after backtracking upwards along the parent chain, then keep the current parent node of the load node unchanged.

[0122] The specific calculation method for path power supply distance verification is as follows: Starting from the root node, the physical length of the line on each side of the parent chain is accumulated to obtain the total length of the power supply path from the root node to the load node. The total length of the power supply path is compared with the maximum allowable power supply distance for the corresponding voltage level of the load node. If the total length of the power supply path does not exceed the maximum allowable power supply distance, the path power supply distance of the load node is qualified; if the total length of the power supply path exceeds the maximum allowable power supply distance, the path power supply distance of the load node exceeds the standard.

[0123] The constructed tree-like power supply path structure meets the voltage level hierarchical requirements, but the actual physical length of the power supply path for some load nodes may exceed the maximum allowable power supply distance for the corresponding voltage level. For load nodes whose path power supply distance exceeds the limit, backtracking is performed along the parent chain of that load node (the path from the load node upwards to the root node). For each ancestor node, the path length from the root node to that ancestor node is calculated. If there exists an ancestor node such that the sum of the path length from the root node to that ancestor node and the actual line length from that ancestor node to the load node satisfies the power supply distance constraint, then the presence of a directly connected physical cable and corresponding switching equipment between the load node and that ancestor node is verified in the weighted physical topology diagram. If the verification passes, the parent node of the load node is redirected from the current parent node to the nearest ancestor node that satisfies the constraint (i.e., the ancestor node with the longest path length from the root node that satisfies the constraint), in order to shorten the power supply path length of the load node while maintaining the acyclic nature of the tree structure.

[0124] After performing the above operations on all load nodes whose power supply distance exceeds the limit, a tree-like power supply path structure that satisfies the path power supply distance constraint is obtained.

[0125] As one possible approach, the steps of iteratively searching for candidate switch operation pairs and adjusting the current switch state based on the load balancing of each power supply zone include: S501. Use the variance of the total load value of each power supply zone in the current operating topology as the current load balance degree.

[0126] In this embodiment, the obtained initial hierarchical partitioned topology forest is used as the initial state of the currently running topology. Let the initial hierarchical partitioned topology forest contain a total of... Each power supply zone, with As a benchmark for the number of zones in load balance calculation, This remains unchanged in subsequent iterations. The actual number of power supply zones existing in the current running topology is denoted as... , It may change due to switching operations during the iteration process.

[0127] If an initial power supply zone no longer exists in the current operating topology, its total load value is recorded as 0. If a new power supply zone is created due to inter-zone merging or other reasons, the new power supply zone is not counted as an independent power supply zone in the load balancing calculation; its load is merged into the corresponding receiving power supply zone. The total load value of each power supply zone is recorded in the order of its initial power supply zone number. .

[0128] Current load balance Calculate using the following formula: in, This represents the average total load across all power supply zones. Load balance The smaller the value, the more uniform the load distribution among the power supply zones; The larger the value, the more uneven the load distribution among the power supply zones.

[0129] S502. In the weighted physical topology graph, select a switch connection edge that is currently in the open state as the edge to be closed, and determine all closed switch connection edges in the loop formed after closing the edge to be closed in the current running topology. Combine the edge to be closed with each closed switch connection edge to form a candidate switch operation pair, thus forming a candidate operation set.

[0130] In this embodiment of the application, in order to make the load distribution of each power supply zone more uniform, it is necessary to adjust the switch states in the current operating topology. The adjustment method is as follows: close one switch connection edge that is currently in the open state, and simultaneously disconnect another switch connection edge that is currently in the closed state, so as to keep the total number of edges in the operating topology unchanged, thereby maintaining the radial constraint.

[0131] Specifically, in the weighted physical topology graph In the process, select a switch connection side that is currently in an open state as the side to be closed. Since the edge to be closed is currently disconnected in the current running topology, it is not connected in the current running topology. If... If you close the loop and add it to the current running topology, it will form a unique loop in the current running topology (because the current running topology is a forest structure, adding an edge connecting two different tree nodes will inevitably form a loop).

[0132] Determine the topological changes that occur after closing the edge to be closed: If the closure operation causes a loop to form between nodes within the same tree in the current running topology, then determine all switch connection edges that are currently in a closed state on the loop path, denoted as . .

[0133] If the closure operation bridges two independent trees in the current running topology without forming a loop, then trace back up the main path formed by the merged interconnection to the root nodes of both trees, adding the currently closed switch connection edges on the tracing path to the set to be removed, denoted as... .

[0134] For each closed-state switch connection edge in the set to be deselected ,Will Forming a candidate switch operation pair indicates closure. and disconnect Collect all candidate switch operation pairs to form a candidate operation set.

[0135] S503. Execute candidate switch operation pairs in the candidate operation set, perform corresponding closing and opening operations on the current operating topology to obtain candidate operating topologies, and calculate the candidate load balance degree for candidate operating topologies that satisfy radial constraints and power supply distance constraints.

[0136] For each candidate switch operation pair in the obtained candidate operation set Perform the corresponding closure and open operations: based on the current running topology, The state changes from open to closed, The state changes from closed to open, forming a new candidate running topology.

[0137] First, verify whether the candidate running topology satisfies the radial constraint. Since the candidate running topology is generated by "closing a broken edge and then breaking a closed edge that forms a loop", this operation keeps the total number of edges unchanged and does not introduce loops. Therefore, the candidate running topology naturally satisfies the radial constraint, but it is still necessary to confirm that the topology after the operation is a connected forest.

[0138] Secondly, verify whether the power supply distance of each power supply zone in the candidate operating topology meets the preset maximum allowable power supply distance. The verification method is the same as S302 and S404 above, and will not be repeated here. If the candidate operating topology meets all the above constraints, calculate the candidate load balancing degree of the candidate operating topology according to the method in step S501. .

[0139] S504. If the candidate load balancing degree is less than the current load balancing degree, then the candidate operating topology and the candidate load balancing degree shall be used as the updated current operating topology and the current load balancing degree, respectively.

[0140] In this embodiment of the application, the calculated candidate load balancing degree Compared with the current load balance Compare. If If the candidate operation results in a more even load distribution among the power supply zones, then the candidate operation is accepted, the candidate operating topology is used as the updated current operating topology, and the candidate load balance is adjusted accordingly. As an updated current load balancing degree.

[0141] like If the candidate operation fails to improve the uniformity of load distribution, the candidate operation is rejected, and the current operating topology and current load balance remain unchanged.

[0142] S505, iteratively search the candidate operation set until the load balance no longer decreases after traversing all candidate switching operation pairs, and use the running topology when the load balance no longer decreases as the target hierarchical partitioned topology forest.

[0143] In this embodiment of the application, during one iteration, the judgments in S503 and S504 are performed sequentially on all candidate switch operation pairs in the current candidate operation set. After traversing all candidate switch operation pairs, if at least one candidate operation is accepted, the current running topology has been updated, the new current running topology generates a new candidate operation set, and the next iteration continues.

[0144] If no candidate operation is accepted in a complete traversal (i.e., the candidate load balance corresponding to all candidate operations is not less than the current load balance), it means that the current load balance has reached a local optimum and cannot be further improved by single-step switching operations. At this point, the iterative search terminates, and the current running topology is used as the final target hierarchical partitioned topology forest.

[0145] To prevent the algorithm from getting stuck in an infinite loop or running for too long, a maximum number of iterations can be set. For example, the maximum number of iterations can be set to 50. When the maximum number of iterations is reached, the iterative search terminates regardless of whether the load balancing continues to decrease, and the currently running topology is used as the target hierarchical partitioned topology forest.

[0146] Please see Figure 2 This document illustrates a system architecture diagram of a graph-based distribution network hierarchical and partitioned topology design system according to an embodiment of this application. The system includes: a physical topology graph construction unit 201, an initial running graph construction unit 202, a graph partitioning unit 203, a power supply path construction unit 204, and a dynamic reconfiguration unit 205. The units communicate bidirectionally via communication links to ensure real-time interaction of collected data and analysis results. These communication links can employ wired or wireless transmission methods.

[0147] The physical topology construction unit 201 is used to construct a weighted physical topology diagram based on the equipment attribute information and the connection relationship information between the electrical devices in the distribution network. The specific construction method performed by the physical topology construction unit 201 can be referred to S100, S101 to S103 above, and will not be repeated here.

[0148] The initial operation graph construction unit 202 is used to construct a radial initial operation graph based on the fixed connection edges and the switch connection edges that are initially closed in the weighted physical topology graph. The specific construction method executed by the initial operation graph construction unit 202 can be referred to in S200, S201 to S204 above, and will not be repeated here.

[0149] The graph division unit 203 is used to divide the radial initial operation graph into multiple power supply zones that meet the preset power supply distance constraints. The specific division method performed by the graph division unit 203 can be referred to in S300, S301 to S303, S3031 to S3033 and S304 to S307 above, and will not be repeated here.

[0150] The power supply path construction unit 204 is used to construct a tree-like power supply path structure with the power supply nodes as the root nodes for each power supply zone, based on the power supply nodes and the voltage levels of each node within the power supply zone, thus obtaining an initial hierarchical partition topology forest composed of multiple tree-like power supply path structures. The specific construction method executed by the power supply path construction unit 204 can be referred to in S400, S401 to S404 above, and will not be repeated here.

[0151] The dynamic reconfiguration unit 205 is used to iteratively search for candidate switch operation pairs and adjust the current switch state according to the load balance of each power supply zone to obtain the target hierarchical partition topology forest. The specific adjustment method performed by the dynamic reconfiguration unit 205 can be referred to S500, S501 to S505 above, and will not be repeated here.

[0152] The embodiments described above are merely examples of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application.

Claims

1. A method for designing a hierarchical and partitioned topology of a distribution network based on graph computation, characterized in that, include: A weighted physical topology diagram is constructed based on the equipment attribute information of each electrical device in the power distribution network and the connection relationship information between the devices. Based on the fixed connection edges and the switch connection edges that are initially closed in the weighted physical topology diagram, a radial initial operation diagram is constructed. The radial initial operation diagram is divided into multiple power supply zones that satisfy preset power supply distance constraints. For each power supply partition, a tree-like power supply path structure with the power supply node as the root node is constructed according to the power supply node in the power supply partition and the voltage level of each node, resulting in an initial hierarchical partition topology forest composed of multiple tree-like power supply path structures. Iteratively search for candidate switch operation pairs, adjust the current switch state according to the load balance of each power supply zone, and obtain the target hierarchical partition topology forest.

2. The method for designing a hierarchical and partitioned topology of a distribution network based on graph computation according to claim 1, characterized in that, The process of constructing the weighted physical topology graph includes: Each electrical device in the power distribution network is mapped to a node in the weighted physical topology graph, and corresponding device attribute information is configured for each node; Each direct connection is mapped to an edge of the weighted physical topology graph, and connection type information and electrical parameter information are set for the edge; Based on the electrical parameter information and topological location information of each edge, the comprehensive weight of each edge is determined to obtain the weighted physical topology graph.

3. The method for designing a hierarchical and partitioned topology of a distribution network based on graph computation according to claim 2, characterized in that, The electrical parameter information of the line corresponding to each edge includes transmission capacity parameters, electrical connection tightness parameters, and conductivity efficiency parameters. The determination of the comprehensive weight for each edge includes: Based on the transmission capability parameter, the electrical connection tightness parameter, and the conductivity efficiency parameter, determine the corresponding electrical parameter vector; Determine the topological criticality index of each edge in the weighted physical topology graph; The sample weighting coefficients of each edge are determined based on the topological key indicators, and the electrical parameter vector is weighted and standardized based on the sample weighting coefficients to obtain a standardized feature vector. The principal component direction is determined based on the standardized feature vector, the standardized feature vector is projected onto the principal component direction, and the projected component is determined as the comprehensive weight of the edge.

4. The method for designing a hierarchical and partitioned topology of a distribution network based on graph computation according to claim 2, characterized in that, The process of constructing the radial initial running map includes: A temporary graph is constructed using the fixed connection edges and the switch connection edges that are initially closed in the weighted physical topology graph as candidate edges; Increase the weight value of the fixed connection edge in the temporary graph to be greater than the sum of the combined weights of all candidate edges in the temporary graph; The temporary graph after weighting is improved is subjected to delooping. Candidate edges are traversed in descending order of weight. If the current candidate edge does not form a cycle after being added, the current candidate edge is retained. If the current candidate edge forms a cycle after being added and is a switch connection edge, the current candidate edge is removed and marked as pending disconnection in the weighted physical topology graph. If the current candidate edge forms a cycle after being added and is a fixed connection edge, the current candidate edge is forcibly retained. The subgraph formed by all retained edges is determined as the radial initial running graph.

5. The method for designing a hierarchical and partitioned topology of a distribution network based on graph computation according to claim 4, characterized in that, The process of dividing the radial initial running map includes: Based on the comprehensive weight of each edge, a preset community detection algorithm is used to horizontally partition the radial initial operation graph to obtain multiple initial power supply partitions; For each initial power supply zone, taking the power node in the initial power supply zone as the source point, the shortest power supply path from each load node in the initial power supply zone to the power node is determined. Based on the physical length of each voltage level segment in the shortest power supply path, it is determined whether the power supply distance of each load node meets the preset maximum allowable power supply distance. For an initial power supply zone with load nodes that exceed the power supply distance limit, the boundary switch connection edge with the smallest zone suitability index is selected and disconnected to split the initial power supply zone into two sub-zones. The power supply distance verification and splitting operations are then recursively performed on the new sub-zones to obtain power supply zones that meet the power supply distance constraints.

6. The method for designing a hierarchical and partitioned topology of a distribution network based on graph computation according to claim 5, characterized in that, When all power supply zones meet the power supply distance constraints, the method further includes: Based on the power values ​​of each load node, load nodes with power values ​​greater than a preset power threshold are marked as critical load nodes; For each critical load node in the current partition, a dual power condition existence check is performed in the weighted physical topology graph to determine whether there are two non-intersecting paths that connect to two different power nodes respectively. If there is no non-intersecting path between the two nodes, the switch connection edge with the largest partition suitability index is selected from the switch connection edges that are in the disconnected state in the weighted physical topology graph as the backup switch connection edge, and the backup switch connection edge is marked as a communication backup edge and kept in the disconnected state, so as to establish a backup power channel between the current partition and another partition. For the partition marked with the aforementioned backup connection edge, the dual power supply condition existence check is re-executed until all critical load nodes meet the dual power supply condition.

7. The method for designing a hierarchical and partitioned topology of a distribution network based on graph computation according to claim 5, characterized in that, The process of determining the zoning suitability index includes: Calculate the number of nodes in each of the two sub-partitions formed after disconnecting the candidate switch connection edge, and determine the basic size factor by the ratio of the smaller number of nodes to the larger number of nodes. In the weighted physical topology graph, the candidate switch connection edge is deleted, the physical length of the bypass path between the two nodes of the candidate switch connection edge is determined, and the electrical coupling factor is determined based on the physical length of the bypass path. Based on the basic scale factor and the electrical coupling factor, the zoning suitability index of the candidate switch connection edge is determined.

8. The method for designing a hierarchical and partitioned topology of a distribution network based on graph computation according to claim 6, characterized in that, The construction of the tree-like power supply path structure with the power node as the root node includes: For each power supply zone that meets the power supply distance constraint, all nodes in the power supply zone are divided into at least two voltage levels according to the voltage level of each node, and a power node from the highest voltage level is selected as the root node. Within the highest voltage level, the highest voltage level tree is constructed using the root node as the source point and a preset spanning tree algorithm based on the comprehensive weights. The access operation is performed sequentially on the next adjacent voltage level: the transformer between the current voltage level and the next voltage level is obtained, the output side of the transformer is used as the access point, the node in the next voltage level that is directly connected to the transformer is used as the node to be accessed, and the node to be accessed is used to access the existing tree structure according to the comprehensive weight using the preset spanning tree algorithm, until all nodes of all voltage levels are accessed. Perform path power supply distance verification on the load nodes in the completed tree power supply path structure. For load nodes whose power supply distance exceeds the limit, backtrack upwards along the parent chain and redirect the parent node of the load node that has an ancestor node that satisfies the constraint to the nearest ancestor node that satisfies the constraint, thus obtaining the tree power supply path structure.

9. The method for designing a hierarchical and partitioned topology of a distribution network based on graph computation according to claim 8, characterized in that, The step of iteratively searching for candidate switch pairs and adjusting the current switch state according to the load balance of each power supply zone includes: The variance of the total load value of each power supply zone in the current operating topology is used as the current load balance degree; In the weighted physical topology graph, select a switch connection edge that is currently in an open state as the edge to be closed, and determine all closed switch connection edges in the loop formed after closing the edge to be closed in the current running topology. Combine the edge to be closed with each of the closed switch connection edges to form a candidate switch operation pair, thus forming a candidate operation set. Execute the candidate switch operation pairs in the candidate operation set, perform the corresponding closing and opening operations on the current operating topology to obtain the candidate operating topology, and calculate the candidate load balance degree for the candidate operating topology that satisfies the radial constraint and the power supply distance constraint; If the candidate load balancing degree is less than the current load balancing degree, then the candidate operating topology and the candidate load balancing degree are respectively used as the updated current operating topology and the current load balancing degree; The candidate operation set is iteratively searched until the load balance no longer decreases after traversing all candidate switch operation pairs. The operating topology when the load balance no longer decreases is used as the target hierarchical partition topology forest.

10. The method for designing a hierarchical and partitioned topology of a distribution network based on graph computation according to claim 2, characterized in that, The equipment attribute information includes the equipment type, voltage level, rated capacity, and load power of each electrical device; the direct connection relationship includes the connection type between each electrical device, the physical length of the line, the rated current of the line, the line impedance, and the initial state of the switch, and the connection type includes fixed connection and switch connection.

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