A grid map maximum common subgraph discovery method based on seed-expansion heuristic search

Abstract

The application discloses a power grid atlas maximum common subgraph discovery method based on seed-expansion heuristic search, which is used for topology structure comparison between power grid atlases in homologous physical power networks and different application scenes, discovers the maximum common subgraph and comprises the following steps: 1. constructing a similarity score function of nodes between atlases according to node labels and degrees of the atlases; 2. a power grid atlas global comparison method based on seed-expansion heuristic search, and then discovering the maximum common subgraph between atlases. The application converts two compared power grid atlases into undirected graphs, establishes corresponding comparison graphs, and then converts the structure comparison problem of two networks into a common subgraph problem, calculates the similarity between all nodes according to the defined node similarity measurement method and the topological structure relationship between nodes, and finally solves the problem by means of the seed-expansion-based heuristic search to obtain the maximum common subgraph between homologous power grid atlases.

Description

Technical Field

[0001] This invention relates to the field of global comparison technology of power grid maps, specifically a method for discovering the maximum common subgraph of a power grid map based on seed-expansion heuristic search. Background Technology

[0002] A power grid is a physical network consisting of a large and complex system, characterized by stability and openness. In a power grid, power plants, transmission towers, substations, and electrical equipment are nodes, while the transmission and distribution lines connecting these nodes are edges. This topology is well-suited for use with graph databases for storage, description, and modeling.

[0003] For the same physical power network in reality, different application scenarios and systems employ different data models and representations of data entities due to varying application requirements. This results in topological differences in the power grid maps of the same physical power network across different application scenarios that are difficult to detect intuitively. Large power companies often have their applications and data intertwined, resulting in an "application-hijacked data" problem. This creates multiple information silos and information chimneys, making collaboration between various functional departments and business processes extremely difficult. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention proposes a seed-expansion heuristic search method for discovering the maximum common subgraph of a power grid map. This method aims to automatically compare the topological structures of power grid maps of multiple systems to discover the globally unique and accurate maximum common subgraph. This enables automatic comparison of power grid topology differences between control systems and information systems, as well as automatic matching of equipment names, thereby promoting system integration and business association.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] The present invention provides a method for discovering the maximum common subgraph of a power grid graph based on seed-expansion heuristic search, characterized by the following steps:

[0007] Step 1: Construct a similarity scoring function between nodes in the power grid map based on the node labels:

[0008] Step 1.1: Take all bus units in the digital power networks corresponding to any two business systems under the same physical power network as nodes, and the lines with power connections between bus units as edges, so as to obtain two power grid maps; set the label of the bus unit as the category of the component;

[0009] The two power grid maps are converted into a first undirected graph G = G(U,E) and a second undirected graph H = H(V,F), respectively, where U and V represent the sets of bus units in the first power grid map G and the second power grid map H, respectively, and E and F represent the sets of transmission lines between the bus units in the first power grid map G and the second power grid map H, respectively.

[0010] Step 1.2: Based on the automorphism of the power grid graph and the degree of the nodes, connect the two undirected nodes... Figure 1 Divide the grid into Δ tracks, and use equation (1) to calculate the distance D at the i-th track for any bus unit node u∈U in the first power grid map G and any bus unit node v∈V in the second power grid map H. i (u,v):

[0011]

[0012] In equation (1), u i v i w represents the number of times bus unit nodes u and v touch the i-th track. i Let represent the weight of the i-th orbit, which is obtained from equation (2):

[0013]

[0014] In equation (2), O i This represents the number of times the i-th orbit is affected by itself and other orbits;

[0015] Step 1.3: Calculate the overall distance D(u,v)∈[0,1] between nodes u and v of the bus unit using equation (3):

[0016]

[0017] In equation (3), when D(u,v) = 0, it means that the labels of bus unit nodes u and v are the same;

[0018] Step 1.4: Calculate the label similarity S(u,v) between bus unit nodes u and v using equation (4):

[0019] S(u,v)=1-D(u,v) (4)

[0020] Step 1.5: Construct the similarity score C(u,v) between bus unit nodes u and v using equation (5):

[0021]

[0022] In equation (5), deg(u) and deg(v) represent the number of nodes connected to bus unit nodes u and v, respectively, which is the degree; max_deg(G) and max_deg(H) represent the maximum degree of bus unit nodes in the first power grid map G and the second power grid map H, respectively, and the parameter α∈[0,1] is the weight of the label similarity and degree of the bus unit nodes.

[0023] Step 2, Seed Node Selection:

[0024] Step 2.1: Calculate the similarity scores between all nodes in the first power grid map G and the second power grid map H according to equation (5), and construct the score matrix C;

[0025] Step 2.2: Based on the connection relationship between nodes in the first power grid map G and the second power grid map H, use the Jerrca clustering algorithm to cluster all bus unit nodes in the first power grid map G and the second power grid map H, obtain the clustered node sets and use them as the functional modules in the power grid maps G and H, and store them in sets Z1 and Z2 respectively.

[0026] Step 2.3: For any k-th functional module cl in Z1 k Any j-th functional module cl in Z2 j The module pair formed (cl) k ,cl j Based on the similarity score matrix c, the Hungarian algorithm is used to analyze the module pairs (cl). k ,cl j The module is compared between every two busbar unit nodes to obtain the module pair (cl). k ,cl j The set of node pairs M of each bus unit in ) H ;

[0027] The module pair (cl) is calculated according to equation (6). k ,cl j The similarity score matrix simcl(cl) k ,cl j This allows us to obtain similarity scores between pairs of functional modules in the power grid maps G and H, and form the final matrix sim. cl :

[0028]

[0029] In equation (6), (a,b) represents the set of node pairs M. H In the node pair, C(a,b) is calculated using equation (5) for the i-th functional module cl. i The middle bus unit node a and the j-th functional module clj Similarity score of node b in the middle busbar unit;

[0030] Step 2.3: Based on the module's similarity score matrix sim cl The Hungarian algorithm is used to compare the functional modules in the first power grid map G and the second power grid map H to obtain the module pair set M. cl According to M cl The third and fourth quantiles of the similarity score distribution of each node pair in each module pair are used to select the top quartile of bus unit node pairs as seed node pairs, thus forming the initial comparison set M from all seed node pairs. s ;

[0031] Step 3: Global comparison of the power grid graph based on seed-expansion heuristic search to find the largest common subgraph among the graphs:

[0032] Step 3.1: Calculate the seed node pair set M according to equation (7). s Any seed node pair (u) s ,v s The neighboring nodes of u) s ′,v s Structural similarity score stru (u s ′,v s ′):

[0033] Score stru (u s ′,v s ′)=|{(u s ,v s )|(u s ,v s )∈M}| (7)

[0034] In equation (7), u s ′ represents the seed node u s The neighboring node, v s ' is the seed node v s The neighboring nodes;

[0035] Step 3.2: Traverse the set M of seed node pairs s The set of seed node pairs M is obtained by considering all neighboring nodes of all seed node pairs in the set M, and then using equation (7). s Structural similarity scores between all neighboring nodes of all seed node pairs;

[0036] Step 3.3: For the seed node pair set M sThe structural similarity scores of all neighbor nodes of all seed node pairs are sorted in descending order, and the neighbor node pairs with the highest scores are added to the comparison set M. s ;

[0037] If multiple neighbor node pairs with the highest scores exist, calculate the degree difference between the neighbor node pairs, and then select the neighbor node pair with the smallest degree difference from the highest-scoring neighbor node pairs to add to the comparison set M. s ;

[0038] If there are multiple neighbor node pairs with the minimum degree difference, then calculate the similarity score of each neighbor node pair according to equation (5), and select the neighbor node pair with the highest similarity score to add to the comparison set M. s ;

[0039] Step 3.4: Return to step 3.2 and execute sequentially until no neighbor node pairs are added to the comparison set M. s until;

[0040] Step 3.5: Output the comparison set M s The set of bus unit nodes formed by the first node of all node pairs or the set of bus unit nodes formed by the second node of all node pairs is the largest common subgraph of the global power grid map.

[0041] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in performing the discovery of the maximum common subgraph among the common sources of the power grid, and the processor is configured to execute the program stored in the memory.

[0042] This invention discloses a computer-readable storage medium on which a computer program is stored, characterized in that the computer program, when executed by a processor, performs the discovery of the maximum common subgraph among common source graphs of power grids. Compared with the prior art, the advantages of this invention are:

[0043] 1. This invention transforms two compared power grid maps into undirected graphs, and further establishes a new approach and method for establishing cross-references based on the topological relationships of the power grid maps. This transforms the problem of comparing power grid maps of multiple systems into the problem of finding the maximum common subgraph on a comparison graph, thereby improving the efficiency and accuracy of global comparison of power grid maps.

[0044] 2. This invention calculates the similarity between all nodes based on a defined node similarity measurement method and the topological relationships between nodes. It then uses a seed-expansion heuristic search employing a greedy strategy with a seed-growth approach to solve the problem, obtaining the maximum common subgraph among power grid maps originating from the same source. In the obtained maximum common subgraph, the topological structures of power grid maps from different systems are completely consistent along the same line, in the same dimension, and generated automatically. This solves the problem of the difficulty in intuitively identifying topological differences between power grid maps, facilitating system integration and business connections between various functional departments and business processes. Attached Figure Description

[0045] Figure 1 This is a flowchart of the method for discovering the maximum common subgraph of a power grid graph based on seed-expansion heuristic search, as described in this invention. Detailed Implementation

[0046] In this embodiment, a method for discovering the maximum common subgraph of a power grid graph based on seed-expansion heuristic search is presented. Figure 1 As shown, the procedure is as follows:

[0047] Step 1: Construct a similarity scoring function between nodes in the power grid map based on the node labels:

[0048] Step 1.1: Take all bus units (such as transformers, switches, fuses, etc.) in the digital power network corresponding to any two business systems (e.g., the "Resource Platform" system and the "Integration Platform" system) under the same physical power network as nodes, and the lines that connect the bus units as edges, so as to obtain two power grid maps; set the label of the bus unit as the category of the component;

[0049] Two power grid maps (e.g., the power grid map of Baohe District, Hefei City in the "Resource Platform" system and the power grid map of Baohe District, Hefei City in the "Integration Platform" system) are automatically converted into a first undirected graph G = G(U,E) and a second undirected graph H = H(V,F) through power grid mapping, respectively, and stored and visualized with the help of Neo4j graph database. Here, U and V represent the set of bus units in the first power grid map G and the second power grid map H, respectively, and E and F represent the set of transmission lines between the bus units in the first power grid map G and the second power grid map H, respectively.

[0050] Step 1.2: Based on the automorphism of the power grid graph and the degree of the nodes, connect the two undirected nodes... Figure 1 Divide the grid into Δ tracks, and use equation (1) to calculate the distance D at the i-th track for any bus unit node u∈U (e.g., a transformer in the "Resource Platform" system) in the first power grid map G and any bus unit node v∈V (e.g., a fuse in the "Integration Platform" system).i (u,v):

[0051]

[0052] In equation (1), u i v i w represents the number of times bus unit nodes u and v touch the i-th track. i Let represent the weight of the i-th orbit, which is obtained from equation (2):

[0053]

[0054] In equation (2), O i This represents the number of times the i-th orbit is affected by itself and other orbits;

[0055] Step 1.3: Calculate the overall distance D(u,v)∈[0,1] between nodes u and v of the bus unit using equation (3):

[0056]

[0057] In equation (3), when D(u,v) = 0, it means that the labels of bus unit nodes u and v are the same, such as the fuse in the "Resource Platform" system and the fuse in the "Integration Platform" system.

[0058] Step 1.4: Calculate the label similarity S(u,v) between bus unit nodes u and v using equation (4):

[0059] S(u,v)=1-D(u,v) (4)

[0060] Step 1.5: Construct the similarity score C(u,v) between bus unit nodes u and v using equation (5):

[0061]

[0062] In equation (5), deg(u) and deg(v) represent the number of nodes connected to bus unit nodes u and v, respectively, which is the degree; max_deg(G) and max_deg(H) represent the maximum degree of bus unit nodes in the first power grid map G and the second power grid map H, respectively, and the parameter α∈[0,1] is the weight of the label similarity and degree of the bus unit nodes.

[0063] Step 2, Seed Node Selection:

[0064] Step 2.1: Calculate the similarity scores between all nodes in the first power grid graph G and the second power grid graph H according to equation (5). Use the toolkit in Python to read the node information of the two undirected graphs stored in the Neo4j graph database, and program the calculation process of equations (1)-(5) to finally output the score matrix C.

[0065] Step 2.2: Based on the connection relationships between nodes in the first power grid map G and the second power grid map H, the existing Jerrca clustering algorithm calculation toolkit in Python is used to cluster all bus unit nodes in the first power grid map G and the second power grid map H, obtaining the clustered node sets as the functional modules in the power grid maps G and H, and storing them in sets Z1 and Z2 respectively, and storing them in the graph database by the Python database operation package;

[0066] Step 2.3: For any k-th functional module cl in Z1 k Any j-th functional module cl in Z2 j The module pair formed (cl) k ,cl j Based on the similarity score matrix C, the existing Hungarian algorithm toolkit in Python is used to analyze the module pairs (cl). k ,cl j The module is compared between every two busbar unit nodes to obtain the module pair (cl). k ,cl j The set of node pairs M of each bus unit in ) H ;

[0067] The module pair (cl) is calculated according to equation (6). k ,cl j The similarity score matrix sim cl (cl k ,cl j This allows us to obtain similarity scores between pairs of functional modules in the power grid maps G and H, and form the final matrix sim. cl Then, use Python's open() function to read and store the data as a file for later use.

[0068]

[0069] In equation (6), (a,b) represents the set of node pairs M. H In the node pair, C(a,b) is calculated using equation (5) for the i-th functional module cl. i The middle bus unit node a and the j-th functional module cl j Similarity score of node b in the middle busbar unit;

[0070] Step 2.3: Read the stored module's similarity score matrix sim cl Using the existing Hungarian algorithm toolkit in Python, the functional modules in the first power grid map G and the second power grid map H are compared to obtain the module pair set M. cl According to M cl The similarity scores of each node pair in each module pair are calculated, and the third and fourth quantiles of the similarity score distribution are obtained using the quantile function in the NumPy package. The top quartile of the bus unit node pairs are selected as seed node pairs, and thus the initial comparison set M is formed from all the seed node pairs. s And store them in a list containing tuples;

[0071] Step 3: Global comparison of the power grid graph based on seed-expansion heuristic search to find the largest common subgraph among the graphs:

[0072] Step 3.1: Calculate the seed node pair set M according to equation (7). s Any seed node pair (u) s ,v s Neighboring nodes of ) (u s ′,v s Structural similarity score stru (u s ′,v s ′):

[0073] Score stru (u s ′,v s ′)=|{(u s ,v s )|(u s ,v s )∈M}| (7)

[0074] In equation (7), u s ′ represents the seed node u s The neighboring node, v s ' is the seed node v s The neighboring nodes;

[0075] Step 3.2: Use a for loop in Python to read and iterate through the seed node pair set M. s The set of seed node pairs M is obtained by considering all neighboring nodes of all seed node pairs in the set M, and then using equation (7). s The structural similarity scores between all neighbor nodes of all seed node pairs are calculated and stored using a dictionary data type in the form of a key2list.

[0076] Step 3.3: Pair seed nodes with set M using dictionary keys and list elements. s Structural similarity scores are calculated among all neighboring nodes of all seed node pairs, and the results are sorted in descending order using the sort() function. The neighboring node pairs with the highest scores are then added to the comparison set M. s ;

[0077] If multiple neighbor node pairs with the highest scores exist, calculate the degree difference between the neighbor node pairs, and then select the neighbor node pair with the smallest degree difference from the highest-scoring neighbor node pairs to add to the comparison set M. s ;

[0078] If there are multiple neighbor node pairs with the minimum degree difference, then calculate the similarity score of each neighbor node pair according to equation (5), and select the neighbor node pair with the highest similarity score to add to the comparison set M. s ;

[0079] Step 3.4: Return to step 3.2 and execute sequentially until no neighbor node pairs are added to the comparison set M. s until;

[0080] Step 3.5: Create an array and use a for loop to read collection M. s The node pairs are stored in an array to store either the first node or the second node of the output node pair. The graph consisting of all the nodes stored in this array is the maximum common subgraph of the global power grid graph. The common subgraph is visualized using Gephi software.

[0081] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the methods described above, and the processor is configured to execute the program stored in the memory.

[0082] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

Claims

1. A method for discovering the maximum common subgraph of a power grid graph based on seed-expansion heuristic search, characterized in that, The procedure is as follows: Step 1: Construct a similarity scoring function between nodes in the power grid map based on the node labels: Step 1.1: Take all bus units in the digital power networks corresponding to any two business systems under the same physical power network as nodes, and the lines with power connections between bus units as edges, so as to obtain two power grid maps; set the label of the bus unit as the category of the component; Convert the two power grid graphs into the first undirected graph respectively. Second undirected graph ,in, and These represent the first power grid diagram. Second power grid map The set of busbar units in the middle, and These represent the first power grid diagram. Second power grid map The collection of transmission lines between busbar units in the system; Step 1.2: Based on the automorphism of the power grid graph and the degree of the nodes, divide the two undirected graphs into Δ tracks, and use equation (1) to calculate the first power grid graph. Any bus unit node in Second power grid map Any bus unit node in In the Distance at each track : (1) In equation (1), , Represents busbar unit node , Touching the first Number of orbits, Indicates the first The weights of each orbital are determined by equation (2): (2) In equation (2), Indicates the first The number of orbits affected by themselves and other orbits; Step 1.3: Calculate the busbar unit nodes using equation (3). , Overall distance between : (3) In equation (3), when When, it indicates the bus unit node. and The tags are the same; Step 1.4: Calculate the busbar unit nodes using equation (4). , Tag similarity between : (4) Step 1.5: Construct bus unit nodes using equation (5) , Similarity score between : (5) In equation (5), , These represent the busbar unit nodes respectively. , The number of connected nodes is called the degree. , Representing the first power grid diagram Second power grid map The maximum degree of the nodes in the middle busbar element, parameter It is the weighting of label similarity and degree among the nodes of the balancing bus unit; Step 2, Seed Node Selection: Step 2.1: Calculate the first power grid diagram according to equation (5). Second power grid map The similarity scores between all nodes are calculated and a score matrix is ​​constructed. ; Step 2.2: Based on the first power grid diagram Second power grid map The connection relationships between internal nodes were analyzed using the Jerrca clustering algorithm for the first power grid map. Second power grid map All bus unit nodes are clustered to obtain the clustered node sets, which are then used as the power grid map. , Each functional module in the process is stored in a corresponding collection. , middle; Step 2.3, for Any of the following Functional modules , Any of the following Functional modules The modules formed Based on the similarity score matrix The module is processed using the Hungarian algorithm. The module compares every two busbar unit nodes to obtain the module's... The set of node pairs of each bus unit ; The module pair is calculated according to equation (6). Similarity score matrix Thus, the power grid map is obtained. , The similarity scores between each pair of functional modules are used to form the final matrix. : (6) In equation (6), Represents a set of node pairs Node pairs in The first is calculated using equation (5). Functional modules Middle busbar unit node and the Functional modules Middle busbar unit node Similarity score; Step 2.4: Based on the module's similarity score matrix The Hungarian algorithm was used to analyze the first power grid map. Second power grid map The various functional modules are compared to obtain a set of module pairs. ,in accordance with The third and fourth quantiles of the similarity score distribution of each node pair in each module pair are used to select the top quartile of bus unit node pairs as seed node pairs, thus forming the initial comparison set from all seed node pairs. ; Step 3: Global comparison of the power grid graph based on seed-expansion heuristic search to find the largest common subgraph among the graphs: Step 3.1: Calculate the comparison set of seed nodes according to equation (7). Any seed node pair Between neighboring nodes Structural similarity score : (7) In equation (7), Seed node The neighboring nodes, Seed node The neighboring nodes; Step 3.2: Traverse the comparison set of seed nodes The set of comparisons for all seed node pairs is obtained by using equation (7) to find all neighboring nodes of all seed node pairs. Structural similarity scores between all neighboring nodes of all seed node pairs; Step 3.3: Comparison set of seed nodes The structural similarity scores between all neighbor nodes of all seed node pairs are sorted in descending order, and the neighbor node pairs with the highest scores are added to the comparison set. ; If multiple neighbor node pairs with the highest scores exist, calculate the degree difference between the neighbor node pairs, and then select the neighbor node pair with the smallest degree difference from the highest-scoring neighbor node pairs to add to the comparison set. ; If there are multiple neighbor node pairs with the minimum degree difference, then calculate the similarity score of each neighbor node pair according to equation (5), and select the neighbor node pair with the highest similarity score to add to the comparison set. ; Step 3.4: Return to step 3.2 and execute sequentially until no neighbor node pairs are added to the comparison set. until; Step 3.5: Output the comparison set The set of bus unit nodes formed by the first node of all node pairs or the set of bus unit nodes formed by the second node of all node pairs is the largest common subgraph of the global power grid map.

2. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store programs that support the processor in executing the maximum common subgraph discovery method of the power grid map as described in claim 1, and the processor is configured to execute the programs stored in the memory.

3. A computer-readable storage medium storing a computer program, characterized in that, The computer program is executed by the processor to perform the maximum common subgraph discovery method of the power grid map as described in claim 1.

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