A power network topology comparison method based on a divide-and-conquer strategy

Abstract

The application discloses a power network topology comparison method based on a divide-and-conquer strategy, comprising the following steps: 1. constructing a source power network and a target power network into a weightless and undirected graph containing node information and path information; 2. establishing a mapping relationship for the source power network and the target power network based on a node similarity function of the constructed power network; 3. performing k-hop neighborhood subgraph division on the source power network graph and the target power network graph based on a k-hop neighborhood concept; 4. performing random walk graph kernel matching calculation on each k-hop neighborhood subgraph of the power network graph and each corresponding neighborhood subgraph; and 5. obtaining an optimal matching network based on a pairwise matching comparison result between the k-hop neighborhood subgraphs of the power network graph. The application can improve the analysis efficiency of cross-service power network graphs and improve the identifiable ability of distribution network topology architecture in various professions in the power industry.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of graph network matching, in particular to a power network topology comparison method based on a divide-and-conquer strategy. BACKGROUND

[0002] With the vigorous development of information and communication technology, human society has entered the era of big data, and a large amount of data information connects people and various transactions, and in practice, many information data can be abstracted as graph topology data, thereby converting actual problems into graph structure calculation problems.

[0003] The topology structure of the power network is that the circuit breakers and other switching devices through which the power passes link busbars, generators, synchronous motors, load points and other elements, abstract them into nodes regardless of their styles, and abstract the power lines connecting these nodes into lines, and then represent the relationship between these nodes in the form of a topology graph. With the participation of various data of power consumers, the power network is no longer a single transmission function in the traditional sense, but has added various social elements. However, in the power system, due to the different functions of each department of the power system, and the fact that the existing data models of the power distribution profession are independent and difficult to share, the power network graphs constructed by each department are not the same, which easily hinders the exchange and cooperation between departments. With the rapid development of informationization construction of the power business system, there are more and more business needs for high-performance power grid topology analysis for power grid planning, equipment management, fault diagnosis, etc. The demand for data standardization, unified storage of data resources, and rapid access to data resources is also becoming more and more urgent. SUMMARY

[0004] In order to overcome the problem of insufficient matching technology for different forms of homologous networks in the prior art, the present application provides a power network topology comparison method based on a divide-and-conquer strategy, so as to improve the efficiency of cross-business power network graph analysis by comparing and matching the topology structures of the power network graphs of each department, and provide support for cross-business data completion based on sub-network matching, and improve the identifiable ability of the power distribution network topology architecture in various professions in the power industry.

[0005] In order to achieve the above-mentioned application purposes, the following technical solutions are adopted:

[0006] The power network topology comparison method based on the divide-and-conquer strategy is characterized in that the following steps are performed:

[0007] Step 1, the unweighted and undirected graph of the source power network G1 is denoted as G1(V1, E1), and the unweighted and undirected graph of the target power network G2 is denoted as G2(V2, E2); wherein, denotes the node set of G1; Represents the set of nodes in G2. This represents the x-th node in G1. Let E1 represent the y-th node in G2, n represent the total number of nodes in G1, and m represent the total number of nodes in G2; E1 and E2 represent the path sets of G1 and G2, respectively; each node in G1 and G2 corresponds to several feature labels.

[0008] Step 2: Establish the mapping relationship between the source power network G1 and the target power network G2:

[0009] Step 2.1: Construct the x-th node in G1 using equation (1). For the y-th node in G2 Node similarity function

[0010]

[0011] In equation (1), Represents the x-th node and the y-th node Labels with the same characteristics Quantity, Represents a node Feature tags The total number;

[0012] Step 2.2: Calculate the x-th node using equation (2). and the y-th node node homology

[0013]

[0014] In equation (2), Represents the y-th node in G2 For the x-th node in G1 The node similarity function;

[0015] Step 2.3: Use equation (3) to determine the x-th node in G1. With the y-th node in G2 Does a mapping relationship exist? like Represents the x-th node in G1 With the y-th node in G2 There is a mapping relationship; if Represents the x-th node With the y-th node There is no mapping relationship; therefore, an n-row, m-column mapping matrix P is constructed to represent the mapping relationship between nodes of G1 and nodes of G2.

[0016]

[0017] In formula (3), Δ represents a threshold value;

[0018] Step 3, performing neighborhood subgraph division on the source power network graph G1(V1, E1) and the target power network graph G2(V2, E2) based on a k-hop neighborhood concept:

[0019] Step 3.1, giving a parameter k;

[0020] traversing G1(V1, E1) and G2(V2, E2) in a depth-first manner, and using a two-component clusterer of the JUNG framework to respectively extract a k-hop neighborhood subgraph set H1={C i (L i , O i )|1≤i≤l} in G1(V1, E1) and a k-hop neighborhood subgraph set H2={Z j (W j , Q j )|1≤j≤w} in G2(V2, E2), wherein C i (L i , O i ) represents an i-th k-hop neighborhood subgraph in G1(V1, E1), L i represents a node set of the i-th k-hop neighborhood subgraph, O i represents a path set of the i-th k-hop neighborhood subgraph, l represents a total number of the extracted k-hop neighborhood subgraphs in G1(V1, E1), Z j (W j , Q j ) represents a j-th k-hop neighborhood subgraph in G2(V2, E2), W j represents a node set of the j-th k-hop neighborhood subgraph, Q j represents a path set of the j-th k-hop neighborhood subgraph, and w represents a total number of the extracted k-hop neighborhood subgraphs in G2(V2, E2), and

[0021] Step 3.2, obtaining a matching node set with a mapping relationship of 1 with the x-th node from a node set V2 of G2(V2, E2) according to a mapping matrix P;

[0022] obtaining a k-hop neighborhood subgraph corresponding to each matching node in the matching node set from H2, thereby constructing a k-hop neighborhood subgraph set related to the x-th node in G2(V2, E2)

[0023] Step 4: Include the x-th node in the neighborhood subgraph set H1. Let C be any r-th k-hop neighborhood subgraph. r，x (L r，x O r，x ); where L r，x Represents the neighborhood subgraph C r，x (L r，x O r，x The set of nodes of ) O r，x Represents the neighborhood subgraph C r，x (L r，x O r，x The set of paths;

[0024] Set of neighborhood subgraphs In and C r，x (L r，x O r，x The corresponding neighborhood subgraph is denoted as Z. r′，x (W r′，x Q r′，x ); where W r′，x Represents the neighborhood subgraph Z r′，x (W r′，x Q r′，x The set of nodes of Q r′，x Represents the neighborhood subgraph Z r′，x (W r′，x Q r′，x The set of paths;

[0025] Step 4.1: Calculate the product graph G r，x，r′ (V r，x，r′ E r，x，r′ ) = C r，x (L r，x O r，x )×Z r′，x (W r′，x Q r′，x ); where V r，x，r′ Indicated by L r，x Each node in the array is associated with W. r′，x The set of node pairs formed by pairing each node in sequence; E r，x，r′ V represents the set of node pairs. r，x，r′ The set of paths corresponding to each pair of nodes in L is only valid if they belong to L. r，x The two nodes in C r，x (L r，x O r，x There is a path in ) that belongs to W r′，x The two nodes in Z r′，x (Wr′，x Q r′，x When a path also exists in the node pair, a path exists between the two node pairs.

[0026] Step 4.2: Calculate the product graph G r，x，r′ (V r，x，r′ E r，x，r′ The adjacency matrix D r，x，r′ =[d ab ] g×g , where d ab Let V be the element in the a-th row and b-th column of the adjacency matrix. r，x，r′ There exists a path between any two nodes a and b in the d array. ab The value is 1, otherwise d ab =0; g is the direct product graph G r，x，r′ (V r，x，r′ E r，x，r′ The number of node pairs;

[0027] P-step random walks are performed using equation (4), and the r-th k-hop neighborhood subgraph C is calculated. r，x (L r，x O r，x ) and neighborhood subgraph Z r′，x (W r′，x Q r′，x The similarity K(C) between ) r，x Z r′，x ):

[0028]

[0029] In equation (4), Let D be the adjacency matrix r，x，r′ p-th power matrix, This represents the (a, b)th element in a p-th power matrix, i.e., the direct product graph G. r，x，r′ (V r，x，r′ E r，x，r′ The number of distinct paths of length p between node pair a and node pair b, |V r，x，r′ |For the product graph G r，x，r′ (V r，x，r′ E r，x，r′ The number of node pairs, λ p Let λ represent the walk length of the p-th random variable, and let λ be the walk length of the p-th random variable. p ∈λ, where λ is a set sequence of variables that control the walk length of random variables, and P is the maximum length of the random walk between the two graphs;

[0030] Step 4.3: Following the process in Steps 4.1-4.2, divide the neighborhood subgraph C... r，x (L r，x Or，x ) respectively with each neighborhood subgraph in the set , until the similarity between each neighborhood subgraph reaches the maximum value, to obtain the optimal matching result of the neighborhood subgraph;

[0031] Step 5, the similarity corresponding to the multiple pairs of optimal matching results of the source power network subgraph and the target power network subgraph is calculated by averaging, and the source power network and the target power network corresponding to the maximum average value are taken as the optimal paired network.

[0032] The electronic device comprises a memory and a processor, and the memory is used to store a program supporting the processor to perform the power network topology comparison, and the processor is configured to execute the program stored in the memory.

[0033] The computer readable storage medium stores a computer program, and when the computer program is executed by a processor, the power network topology comparison is performed.

[0034] Compared with the prior art, the power network topology comparison method has the following beneficial effects:

[0035] 1. The original power network is decomposed into multiple sub-networks based on the divide-and-conquer strategy and the modularization idea, so that the comparison between the original networks is converted into the comparison between multiple sub-networks, the sub-network comparison is completed by means of the graph kernel matching function, and the mapping relationship of different power network topologies is obtained, so that the model can be recognized when the power business is applied across the professions.

[0036] 2. The power network is divided into modules based on the modularization idea of the divide-and-conquer strategy, and the matching of the original network is completed by means of the comparison between multiple modules. This idea reduces the difficulty of graph network topology matching on the one hand, and on the other hand, it can fully utilize local information to speed up the matching process according to the characteristics of module comparison, effectively improve the analysis efficiency of the power network topology, and realize high-performance network topology matching. DETAILED DESCRIPTION

[0037] In this embodiment, a power network topology comparison method based on the divide-and-conquer strategy is used to decompose the original power network into multiple sub-networks, convert the comparison between the original networks into the comparison between multiple sub-networks, complete the sub-network comparison by means of the graph kernel matching function, and use the method for the comparison between multiple power networks, so as to improve the problem of different morphologies between homologous networks. Specifically, the following steps are performed:

[0038] Step 1, the unweighted and undirected graph of the source power network G1 is recorded as G1(V1, E1), and the unweighted and undirected graph of the target power network G2 is recorded as G2(V2, E2); wherein, a set of nodes representing G1; a set of nodes representing G2, the xth node in G1, the yth node in G2, n represents the total number of nodes in G1, and m represents the total number of nodes in G2; E1 and E2 represent the path sets of G1 and G2, respectively; each node in G1 and G2 corresponds to a number of feature labels, respectively;

[0039] Step 2, establish the mapping relationship between the source power network G1 and the target power network G2:

[0040] Step 2.1, use formula (1) to construct the xth node in G1 the node similarity function of the yth node in G2

[0041]

[0042] In formula (1), the number of feature labels that the xth node and the yth node have in common, the total number of feature labels of the node

[0043] Step 2.2, use formula (2) to calculate the node homology of the xth node and the yth node

[0044]

[0045] In formula (2), the node similarity function of the yth node in G2 to the xth node in G1;

[0046] Step 2.3, use formula (3) to determine whether the xth node in G1 and the yth node in G2 have a mapping relationship If indicates that the xth node in G1 and the yth node in G2 have a mapping relationship; if indicates that the xth node and the yth node ​​​​​​There is no mapping relationship; thereby constructing a mapping matrix P of n rows and m columns, which is used to represent the mapping relationship between the nodes of G1 and the nodes of G2;

[0047]

[0048] In formula (3), Δ represents a threshold value, and in the embodiment, Δ takes a value of 60%.

[0049] Step 3, based on the k-hop neighborhood concept, the source power network graph G1(V1, E1) and the target power network graph G2(V2, E2) are divided into neighborhood subgraphs:

[0050] Step 3.1, given a parameter k, in the embodiment, k takes any value in the set [1; 2; 3];

[0051] G1(V1, E1) and G2(V2, E2) are traversed in a depth-first manner, and a two-component clusterer of the JUNG framework is used to extract a k-hop neighborhood subgraph set H1={C i (L i , O i )|1≤i≤l} in G1(V1, E1) and a k-hop neighborhood subgraph set H2={Z j (W j , Q j )|1≤j≤w} in G2(V2, E2), wherein C i (L i , O i ) represents the i-th k-hop neighborhood subgraph in G1(V1, E1), L i represents the node set of the i-th k-hop neighborhood subgraph, O i represents the path set of the i-th k-hop neighborhood subgraph, l represents the total number of the extracted k-hop neighborhood subgraphs in G1(V1, E1), Z j (W j , Q j ) represents the j-th k-hop neighborhood subgraph in G2(V2, E2), W j represents the node set of the j-th k-hop neighborhood subgraph, Q j represents the path set of the j-th k-hop neighborhood subgraph, w represents the total number of the extracted k-hop neighborhood subgraphs in G2(V2, E2), and

[0052] Step 3.2, according to the mapping matrix P, the matching node set with the mapping relationship of 1 is obtained from the node set V2 of G2(V2, E2) for the x-th node in G1(V1, E1);

[0053] Obtain the k-hop neighborhood subgraph corresponding to each matching node in the matching node set from H2, thereby constructing the x-th node in G2(V2, E2). Related k-hop neighborhood subgraph set

[0054] Step 4: Include the x-th node in the neighborhood subgraph set H1. Let C be any r-th k-hop neighborhood subgraph. r，x (L r，x O r，x ); where L r，x Represents the neighborhood subgraph C r，x (L r，x O r，x The set of nodes of ) O r，x Represents the neighborhood subgraph C r，x (L r，x O r，x The set of paths;

[0055] Set of neighborhood subgraphs In and C r，x (L r，x O r，x The corresponding neighborhood subgraph is denoted as Z. r′，x (W r′，x Q r′，x ); where W r′，x Represents the neighborhood subgraph Z r′，x (W r′，x Q r′，x The set of nodes of Q r′，x Represents the neighborhood subgraph Z r′，x (W r′，x Q r′，x The set of paths;

[0056] Step 4.1: Calculate the product graph G r，x，r′ (V r，x，r′ E r，x，r′ ) = C r，x (L r，x O r，x )×Z r′，x (W r′，x Q r′，x ); where V r，x，r′ Indicated by L r，x Each node in the array is associated with W. r′，x The set of node pairs formed by pairing each node in sequence; E r，x，r′ V represents the set of node pairs r，x，r′ The set of paths corresponding to each pair of nodes in L is only valid if they belong to L. r，x The two nodes in Cr，x (L r，x , r，x ) exist paths between two nodes in Z r′，x (W r′，x , Q r′，x ) exist paths between two nodes in Z r′，x ;

[0057] Step 4.2, calculate the adjacency matrix D r，x，r′ of the direct product graph G r，x，r′ (V r，x，r′ , E r，x，r′ ) = [d ab ] g×g , where d ab is the element in the a-th row and b-th column of the adjacency matrix, when there exists a path between any two node pairs a and b in V rx，r′ , d ab takes the value 1, otherwise d ab is 0; g is the number of node pairs of the direct product graph G r，x，r′ (V r，x，r′ , E r，x，r′ ) ;

[0058] P-step random walk is performed using formula (4), in this embodiment, the maximum step length P of the random walk is randomly taken from the set [1; 2; 3; 4; 5], and the r-th k-hop neighborhood subgraph C r，x (L r，x , O r，x ) and the similarity K(C r′，x , Z r′，x ) between the neighborhood subgraph Z r′，x (W r，x , Q r′，x ) are calculated:

[0059]

[0060] In formula (4), is the p-th power matrix of the adjacency matrix D r，x，r′ , represents the (a, b)-th element in the p-th power matrix, that is, the number of different paths with a random walk length of p between node pair a and node pair b in the direct product graph G r，x，r′ (V r，x，r′ , E r，x，r′ ), |V r，x，r′ | is the number of node pairs of the direct product graph G r，x，r′ (V r，x，r′ , E r，x，r′ ), and λ p represents the p-th random variable walk length, and λ p∈λ, λ is a set variable sequence for controlling the length of random variable walk, P is the maximum length of random walk between two graphs;

[0061] Step 4.3, according to the process of step 4.1-step 4.2, the neighborhood subgraph C r，x (L r，x , O r，x ) respectively with each neighborhood subgraph in the set , until the similarity between each neighborhood subgraph reaches the maximum value, the optimal matching result of the neighborhood subgraph is obtained;

[0062] Step 5, the similarity corresponding to the optimal matching result of the multiple pairs of source power network subgraph and target power network subgraph is calculated, and the source power network and the target power network corresponding to the maximum average value are taken as the optimal paired network.

[0063] In this embodiment, an electronic device includes a memory for storing a program supporting the processor to execute the above method, and a processor configured to execute the program stored in the memory.

[0064] In this embodiment, a computer readable storage medium has a computer program stored thereon, and the computer program is run by a processor to execute the steps of the above method.

Claims

1. A power network topology comparison method based on a divide-and-conquer strategy, characterized in that, The procedure is as follows: Step 1: Denote the unweighted, undirected graph of the source power network G1 as G1(V1,E1), and the unweighted, undirected graph of the target power network G2 as G2(V2,E2); where, Represents the set of nodes in G1; Represents the set of nodes in G2. This represents the x-th node in G1. Let E1 represent the y-th node in G2, n represent the total number of nodes in G1, and m represent the total number of nodes in G2; E1 and E2 represent the path sets of G1 and G2, respectively; each node in G1 and G2 corresponds to several feature labels. Step 2: Establish the mapping relationship between the source power network G1 and the target power network G2: Step 2.1: Construct the x-th node in G1 using equation (1). For the y-th node in G2 Node similarity function In equation (1), Represents the x-th node and the y-th node Labels with the same characteristics Quantity, Represents a node Feature tags The total number; Step 2.2: Calculate the x-th node using equation (2). and the y-th node node homology In equation (2), Represents the y-th node in G2 For the x-th node in G1 The node similarity function; Step 2.3: Use equation (3) to determine the x-th node in G1. With the y-th node in G2 Does a mapping relationship exist? like Represents the x-th node in G1 With the y-th node in G2 There is a mapping relationship; if Represents the x-th node With the y-th node There is no mapping relationship; therefore, an n-row, m-column mapping matrix P is constructed to represent the mapping relationship between nodes of G1 and nodes of G2. In equation (3), Δ represents the threshold; Step 3: Based on the k-hop neighborhood concept, partition the source power network graph G1(V1,E1) and the target power network graph G2(V2,E2) into neighborhood subgraphs: Step 3.1: Given parameter k; The depth-first search algorithm traverses G1(V1,E1) and G2(V2,E2), and uses the two-component clusterer of the JUNG framework to extract the set H1={C} of k-hop neighborhood subgraphs in G1(V1,E1) whose paths are within k hops. i (L i O i The set of k-hop neighborhood subgraphs H2={Z} in G2(V2,E2) where the path is within k hops, 1≤i≤l}. j (W j Q j )|1≤j≤w}, where C i (L i O i ) represents the i-th k-hop neighborhood subgraph in G1(V1,E1), L i Let O represent the set of nodes in the i-th k-hop neighborhood subgraph. i Let Z represent the path set of the i-th k-hop neighborhood subgraph, l represent the total number of k-hop neighborhood subgraphs extracted from G1(V1,E1), and Z represent the path set of the i-th k-hop neighborhood subgraph. j (W j Q j ) represents the j-th k-hop neighborhood subgraph in G2(V2,E2), W j Let Q represent the set of nodes in the j-th k-hop neighborhood subgraph. j Let G2(V2,E2) represent the path set of the j-th k-hop neighborhood subgraph, and w represent the total number of k-hop neighborhood subgraphs extracted from G2(V2,E2). Step 3.2: Based on the mapping matrix P, obtain the node corresponding to the x-th node from the node set V2 of G2(V2,E2). The set of matching nodes whose mapping relationship is 1; Obtain the k-hop neighborhood subgraph corresponding to each matching node in the matching node set from H2, thereby constructing the x-th node in G2(V2,E2). Related k-hop neighborhood subgraph set Step 4: Include the x-th node in the neighborhood subgraph set H1. Let C be any r-th k-hop neighborhood subgraph. r,x (L r,x O r,x ); where L r,x Represents the neighborhood subgraph C r,x (L r,x O r,x The set of nodes of ) O r,x Represents the neighborhood subgraph C r,x (L r,x O r,x The set of paths; Set of neighborhood subgraphs In and C r,x (L r,x O r,x The corresponding neighborhood subgraph is denoted as Z. r',x (W r',x Q r',x ); where W r',x Represents the neighborhood subgraph Z r',x (W r',x Q r',x The set of nodes of Q r',x Represents the neighborhood subgraph Z r',x (W r',x Q r',x The set of paths; Step 4.1: Calculate the product graph G r,x,r' (V r,x,r' E r,x,r' ) = C r,x (L r,x O r,x )×Z r',x (W r',x Q r',x ); where V r,x,r' Indicated by L r,x Each node in the array is associated with W. r',x The set of node pairs formed by pairing each node in sequence; E r,x,r' V represents the set of node pairs r,x,r' The set of paths corresponding to each pair of nodes in L is only valid if they belong to L. r,x The two nodes in C r,x (L r,x O r,x There is a path in ) that belongs to W r',x The two nodes in Z r',x (W r',x Q r',x When a path also exists in the node pair, a path exists between the two node pairs. Step 4.2: Calculate the product graph G r,x,r' (V r,x,r' E r,x,r' The adjacency matrix D r,x,r' =[d ab ] g×g , where d ab Let V be the element in the a-th row and b-th column of the adjacency matrix. r,x,r' There exists a path between any two nodes a and b in the d array. ab The value is 1, otherwise d ab =0; g is the direct product graph G r,x,r' (V r,x,r' E r,x,r' The number of node pairs; P-step random walks are performed using equation (4), and the r-th k-hop neighborhood subgraph C is calculated. r,x (L r,x O r,x ) and neighborhood subgraph Z r',x (W r',x Q r',x The similarity K(C) between ) r,x Z r',x ): In equation (4), Let D be the adjacency matrix r,x,r' p-th power matrix, This represents the (a,b)th element in a p-th power matrix, i.e., the direct product graph G. r,x,r' (V r,x,r' E r,x,r' The number of distinct paths of length p between node pair a and node pair b, |V r,x,r' |For the product graph G r,x,r' (V r,x,r' E r,x,r' The number of node pairs, λ p Let λ represent the walk length of the p-th random variable, and let λ be the walk length of the p-th random variable. p ∈λ, where λ is a set sequence of variables that control the walk length of random variables, and P is the maximum length of the random walk between the two graphs; Step 4.3: Following the process in Steps 4.1-4.2, divide the neighborhood subgraph C... r,x (L r,x O r,x ) respectively with set The optimal matching result of the neighborhood subgraphs is obtained by randomly walking through each neighborhood subgraph until the similarity between the neighborhood subgraphs reaches the maximum value. Step 5: Calculate the average similarity of the multiple optimal matching results of the source power network subgraph and the target power network subgraph, and take the source power network and its target power network corresponding to the maximum average as the optimal matching network.

2. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the power network topology comparison of claim 1, and the processor is configured to execute the program 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 power network topology comparison as described in claim 1.

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