CN111104722A - Electric power communication network modeling method considering overlapping communities - Google Patents
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Abstract
The invention discloses a power communication network modeling method considering an overlapping community, belonging to the technical field of power communication network modeling. Based on the grid structure characteristics of an actual communication network, community division is carried out on the power network by using point-edge graph conversion and a Markov clustering algorithm, community overlapping nodes are further determined, a communication network model is established according to the overlapping community nodes, and the hierarchical topological structure and the coupling relation of the power communication network system are further established. The modeling result obtained by the method well reflects the actual networking characteristics, further reveals the characteristics of the power communication network, can provide more accurate simulation data for power grid workers, and has strong practical significance.
Description
Technical Field
The invention belongs to the technical field of power communication network modeling, and particularly relates to a power communication network modeling method considering an overlapping community.
Background
In recent years, with the rapid development of information communication technology, the construction of smart power grids is accelerated, and communication networks play an increasingly important role in power grid planning and scheduling. The deep integration of the power grid and the communication network is imperative, and the establishment of a power communication network model closer to the reality is the basis of research.
The existing methods for modeling the power communication network mainly comprise a complex network method and a hybrid modeling method. The complex network method comprises a dependent network method, an arbitration network control method, an incidence matrix construction method and the like. Among them, the dependent network method is most widely used. The dependent network method is to abstract the power network and the communication network into double-layer network coupling, analyze the self rule according to the coupling characteristic and the reliability, but only construct the connection topology of the power layer and the communication layer according to the hypothesis rule, and consider less modeling factors, which is not beneficial to the in-depth research. The hybrid modeling method mainly comprises a finite-state machine method, a multi-Agent intelligent simulation method, a hybrid logic dynamic method and the like. The multi-Agent intelligent simulation method is an important method for modeling the power communication network due to simple modeling and good effect, but the topological structures of the communication network and the power network are considered in less research, and the grid structure and the construction rule of the actual communication network are ignored, so that the model is separated from the reality, and the practicability is poor.
Aiming at the defects of the existing power communication network modeling method, the invention provides the power communication network modeling method considering the overlapping communities.
Disclosure of Invention
The invention aims to provide a power communication network modeling method considering overlapping communities, which is characterized by comprising the following steps of:
1) on the basis of a complex network theory, power equipment in the power grid topology is abstracted into power nodes to represent a node set of a power grid, a power transmission tie line is abstracted into a power grid connecting edge to represent an edge set of the power grid, and a power grid topological graph is obtained.
2) Because the space truss structure of the communication network access layer in the actual power communication network has strong topological similarity with the space truss structure of the power network, the communication network access layer topological structure is consistent with the power network topological structure, namely the number of nodes and topological connection of the communication network access layer are the same as those of the power network, and the communication network access layer and the power network are in one-to-one full coupling relationship.
3) Carrying out community division on the topological graph of the power network by using point edge graph conversion and a Markov clustering algorithm, further determining overlapped community nodes and mapping the overlapped community nodes to be nodes of a backbone network of the communication network, and finding a group of edge sets based on a greedy algorithm to ensure that the nodes among the backbone network point sets are connected to form an annular winding structure and the minimum path passed by the annular winding structure is shortest, thereby obtaining a backbone network topological structure of the communication network; the communication network backbone layer and the communication network access layer belong to a part of one-to-one coupling relationship, and the coupling nodes are overlapped nodes and have no direct coupling relationship with the power network nodes.
4) Finding out the overlapped nodes of the backbone layer of the communication network by adopting the same overlapped community searching algorithm as that in the step 3), mapping the overlapped nodes to be the nodes of the core layer of the communication network, and constructing a topology structure of the core layer of the communication network based on a greedy algorithm; the communication network core layer and the communication network backbone layer are in a part many-to-many coupling relationship, the coupling nodes are overlapped nodes of the communication network backbone layer, but the core layer, the communication network access layer and the power network are not in a direct coupling relationship.
5) And obtaining the adjacent matrix of the power communication network according to the corresponding coupling relation between the adjacent matrix of each layer of the power network and the communication network and the upper layer and the lower layer, thereby constructing a power communication network model.
The method comprises the steps that the phenomenon of community overlapping existing in the topology of an actual communication network is comprehensively considered, namely, cross overlapping areas exist among communication backbone rings, namely, the cross overlapping areas exist among the communication backbone rings, and nodes of the cross overlapping areas are often set as provincial dispatching centers or regional dispatching centers; the phenomenon can be better reflected by applying the overlapping community theory, so that the model is more reasonably established and is closer to an actual network.
According to the networking characteristics of multi-level and multi-service of an actual communication network, the communication network is divided into three layers, namely an access layer, a backbone layer and a core layer, and modeling is performed in sequence, so that the model is more in line with actual characteristics.
The specific steps of searching the overlapped nodes by the overlapped community searching algorithm are as follows:
step 401: defining a point diagram G ═ V, E, wherein V, E are respectively a node set and an edge set of the complex network, an adjacent matrix is A, and the point-edge conversion is carried out on the diagram G to obtain a new diagram Glink＝(Vlink，Elink) In which V islink、 ElinkRespectively carrying out point-edge conversion on the graph G to obtain a new graph GlinkThe edge set and the node set of (2), the adjacency matrix of which is Alink。
Step 402: obtaining a boundary graph G by using an LHN similarity matrix calculation methodlinkSimilarity matrix S oflinkMeasure each section of the edge mapNode similarity between a point and its neighbor nodes. The formula is as follows:
in the formula (1), mlinkShows a side graph GlinkThe number of edges of (c); lambda [ alpha ]linkRepresenting an edge graph adjacency matrix AlinkThe maximum eigenvalue of (d); k is a radical oflink(i) Degree of the edge graph node i; max (St) is the largest element of the matrix St; matrix I represents and AlinkColumn and row identity identical identity matrix, α is LHN similarity parameter.
Step 403: using Markov clustering algorithm to match similarity matrix SlinkPerforming expansion processing, wherein the formula is as follows:
in the formula (2), e is an expansion squaring coefficient; k is the number of iterations.
Step 404: using Markov clustering algorithm to match similarity matrix SlinkThe expansion treatment is carried out according to the following formula:
in the formula (3), r is an expansion point multiplication coefficient; k is the number of iterations.
Step 405: judging the similarity matrix SlinkWhether a preset condition is met or not, if so, finishing the algorithm; otherwise, go to step 403, enter next markov clustering algorithm processing. The predetermined conditions are as follows:
Slink (k+1)(i，j)＝(Slink (k+1)(i，j))2(4)
in the formula (4), SlinkIs a similarity matrix; k is the number of iterations.
Step 406: and performing excessive similarity processing on the node redundancy aspect, judging whether a preset condition is met, and if so, sequentially removing the nodes of the self community from large to small according to the community scale of the nodes until a threshold value is met. The predetermined conditions are as follows:
D(Vp(i))＞θ (5)
in the formula (5), D (V)p(i) Is the number of communities to which the node i of the point diagram belongs; theta is a defined threshold.
Step 407: and performing excessive similarity processing on the aspect of community redundancy, judging whether a preset condition is met, and if so, merging the two communities. The predetermined conditions are as follows:
Y(C(i)，C(j))＞ζ (6)
in the formula (6), C (i) is the ith community after division, Y (C (i), C (j)) is the node similarity of the two communities, and ξ is a limited threshold value.
Step 408: and searching out overlapped community nodes, namely nodes with the community number larger than 1 from the divided point communities C, classifying the nodes into an overlapped community node set and outputting.
The method has the advantages that the method for modeling the power communication network considering the overlapped communities is provided aiming at the defects of the existing method for modeling the power communication network, the phenomenon of community overlapping in the topology of the actual communication network is comprehensively considered, namely, the crossed overlapped areas exist among the communication backbone rings, namely, the crossed overlapped areas are community overlapped areas, and the nodes of the crossed overlapped areas are often set as provincial dispatching centers or regional dispatching centers; the phenomenon can be well embodied by adopting an overlapping community theory, so that the accuracy and the applicability of the model are improved; overlapping communities are searched by combining Markov clustering with an LHN similarity algorithm, so that the accuracy of the model is improved, and the phenomena of community division marginalization and community redundancy are avoided; the method can construct a more accurate and practical electric power communication network model, can provide more accurate simulation data for power grid workers, and has strong practical significance; the invention is easy to operate and suitable for practical network evaluation applications.
Drawings
Fig. 1 is a flowchart of a power communication network modeling method considering overlapping communities.
FIG. 2 is a diagram illustrating the division result of the IEEE39 node network community.
Fig. 3 is a schematic diagram for modeling an IEEE39 node power communication network.
Detailed Description
The invention provides a power communication network modeling method considering overlapping communities, which is described in detail below with reference to the accompanying drawings and specific embodiments.
Fig. 1 is a flowchart of a power communication network modeling method considering overlapping communities, which includes the following steps:
1) on the basis of a complex network theory, power equipment in the power grid topology is abstracted into power nodes to represent a node set of a power grid, a power transmission tie line is abstracted into a power grid connecting edge to represent an edge set of the power grid, and a power grid topological graph is obtained.
2) Because the space truss structure of the communication network access layer in the actual power communication network has strong topological similarity with the space truss structure of the power network, the communication network access layer topological structure is consistent with the power network topological structure, namely the number of nodes and topological connection of the communication network access layer are the same as those of the power network, and the communication network access layer and the power network are in one-to-one full coupling relationship.
3) Carrying out community division on the topological graph of the power network by using point edge graph conversion and a Markov clustering algorithm, further determining overlapped community nodes and mapping the overlapped community nodes to be nodes of a backbone network of the communication network, and finding a group of edge sets based on a greedy algorithm to ensure that the nodes among the backbone network point sets are connected to form an annular winding structure and the minimum path passed by the annular winding structure is shortest, thereby obtaining a backbone network topological structure of the communication network; the communication network backbone layer and the communication network access layer belong to a part of one-to-one coupling relationship, and the coupling nodes are overlapped nodes and have no direct coupling relationship with the power network nodes.
4) Finding out the overlapped nodes of the backbone layer of the communication network by adopting the same overlapped community searching algorithm as that in the step 3), mapping the overlapped nodes to be the nodes of the core layer of the communication network, and constructing a topology structure of the core layer of the communication network based on a greedy algorithm; the communication network core layer and the communication network backbone layer are in a part many-to-many coupling relationship, the coupling nodes are overlapped nodes of the communication network backbone layer, but the core layer, the communication network access layer and the power network are not in a direct coupling relationship.
5) And obtaining the adjacent matrix of the power communication network according to the corresponding coupling relation between the adjacent matrix of each layer of the power network and the communication network and the upper layer and the lower layer, thereby constructing a power communication network model.
The method comprises the steps that the phenomenon of community overlapping existing in the topology of an actual communication network is comprehensively considered, namely, cross overlapping areas exist among communication backbone rings, namely, the cross overlapping areas exist among the communication backbone rings, and nodes of the cross overlapping areas are often set as provincial dispatching centers or regional dispatching centers; the phenomenon can be better reflected by applying the overlapping community theory, so that the model is more reasonably established and is closer to an actual network.
According to the networking characteristics of multi-level and multi-service of an actual communication network, the communication network is divided into three layers, namely an access layer, a backbone layer and a core layer, and modeling is performed in sequence, so that the model is more in line with actual characteristics.
The specific steps of searching the overlapped nodes by the overlapped community searching algorithm are as follows:
step 401: defining a point diagram G ═ V, E, wherein V, E are respectively a node set and an edge set of the complex network, an adjacent matrix is A, and the point-edge conversion is carried out on the diagram G to obtain a new diagram Glink＝(Vlink，Elink) In which V islink、 ElinkRespectively carrying out point-edge conversion on the graph G to obtain a new graph GlinkThe edge set and the node set of (2), the adjacency matrix of which is Alink。
Step 402: obtaining a boundary graph G by using an LHN similarity matrix calculation methodlinkSimilarity matrix S oflinkTherefore, the node similarity between each node of the edge graph and the neighbor nodes of the edge graph is measured. The formula is as follows:
in the formula (1), mlinkShows a side graph GlinkThe number of edges of (c); lambda [ alpha ]linkRepresenting an edge graph adjacency matrix AlinkThe maximum eigenvalue of (d); k is a radical oflink(i) Degree of the edge graph node i; max (St) is the largest element of the matrix St; matrix I represents and AlinkThe number of rows and columns is the sameα is the LHN similarity parameter.
Step 403: using Markov clustering algorithm to match similarity matrix SlinkPerforming expansion processing, wherein the formula is as follows:
in the formula (2), e is an expansion squaring coefficient; k is the number of iterations.
Step 404: using Markov clustering algorithm to match similarity matrix SlinkThe expansion treatment is carried out according to the following formula:
in the formula (3), r is an expansion point multiplication coefficient; k is the number of iterations.
Step 405: judging the similarity matrix SlinkWhether a preset condition is met or not, if so, finishing the algorithm; otherwise, go to step 403, enter next markov clustering algorithm processing. The predetermined conditions are as follows:
Slink (k+1)(i，j)＝(Slink (k+1)(i，j))2(4)
in the formula (4), SlinkIs a similarity matrix; k is the number of iterations.
Step 406: and performing excessive similarity processing on the node redundancy aspect, judging whether a preset condition is met, and if so, sequentially removing the nodes of the self community from large to small according to the community scale of the nodes until a threshold value is met. The predetermined conditions are as follows:
D(Vp(i))＞θ (5)
in the formula (5), D (V)p(i) Is the number of communities to which the node i of the point diagram belongs; theta is a defined threshold.
Step 407: and performing excessive similarity processing on the aspect of community redundancy, judging whether a preset condition is met, and if so, merging the two communities. The predetermined conditions are as follows:
Y(C(i)，C(j))＞ζ (6)
in the formula (6), C (i) is the ith community after division, Y (C (i), C (j)) is the node similarity of the two communities, and ξ is a limited threshold value.
Step 408: and searching out overlapped community nodes, namely nodes with the community number larger than 1 from the divided point communities C, classifying the nodes into an overlapped community node set and outputting.
The invention takes an IEEE39 node power grid as an embodiment, applies the line grid structure, the unit capacity and the load capacity data in the embodiment, constructs a power communication network model based on an overlapped community theory on the basis of an MATPOWER toolbox data structure on MATLAB simulation software, and sets the relevant parameters as follows, wherein an LHN similarity parameter α is 0.3, and a similarity matrix S is adoptedlinkThe expansion square index e and the expansion point square index r are respectively 2 and 1.5, the threshold theta limited by the network scale is 2, and the node similarity exceeding threshold ξ is 0.5.
Firstly, carrying out community partitioning on the power network topology of IEEE39 nodes, and firstly calculating an IEEE39 node edge graph G by an LHN similarity algorithmlinkSimilarity matrix S oflinkThe calculation formula is as follows:
in the formula, mlinkShows a side graph GlinkThe number of edges of (c); lambda [ alpha ]linkRepresenting an edge graph adjacency matrix AlinkThe maximum eigenvalue of (d); k is a radical oflink(i) Degree of the edge graph node i; max (St) is the largest element of the matrix St; matrix I represents and AlinkThe unit matrixes with the same row and column number and the similarity parameter of LHN α are calculated to obtain the IEEE39 node edge graph GlinkSimilarity matrix S oflink。
Then according to the Markov algorithm, the similarity matrix S is alignedlinkAnd (3) processing to achieve the purpose of grouping, wherein the formula related to the algorithm is as follows:
wherein e is an expansion squaring coefficient; r is an expansion point multiplication coefficient; k is the number of iterations. Judging whether the Markov algorithm is ended or not according to a preset condition, wherein the preset condition is as follows:
Slink (k+1)(i，j)＝(Slink (k+1)(i，j))2
when the preset condition is met, outputting a similarity matrix SlinkAnd thus community division results are obtained, as shown in table 1.
TABLE 1 IEEE39 node Community partitioning results
| Community | Community member | |
| Community | ||
| 1 | 1，2，4，5，6，7，8，9，11，30，31，39 | 4，6，11 |
| |
4，6，10，11，12，13，14，15，32 | 4，6，11，15 |
| |
3，15，16，17，18，19，20，21，24，27，33，34 | 15，16，17，21，24，27 |
| |
16，21，22，23，24，35，36 | 16，21，24 |
| |
17，25，26，27，28，29，37，38 | 17，27 |
The division result of the network community of IEEE39 nodes is shown in fig. 2, where the red color part is the overlapping nodes found. Therefore, the power grid can be divided into 5 communities, 9 overlapping nodes are included in the power grid, most of the overlapping nodes belong to the center area of the whole system, the node topology centrality is high, and the setting area of an actual dispatching control center can be better embodied. In addition, the community 3 contains 6 overlapped nodes, namely the nodes 15, 16, 17, 21, 24 and 27, and the number of the overlapped nodes is the largest, if the nodes of the community 3 fail due to the attack of the malicious information, a series of cascading failures can be caused at the topological center of the system and spread to the edge of the system, the failure propagation range is large, and finally the system is damaged.
Then, constructing a communication network backbone layer topological structure by a greedy algorithm according to the 9 overlapped nodes; and similarly, searching the overlapped nodes of the communication network backbone layer according to the overlapped community theory, constructing a core layer topology network, and finally constructing a complete electric power communication network model according to the coupling relation between the electric power communication network layers. Fig. 3 shows a modeling schematic diagram of an IEEE39 node power communication network, and it can be seen that compared with a conventional modeling method, the method of the present invention can construct a simulation model closer to reality, and can lay a foundation for subsequent research and development.
The invention provides a power communication network modeling method considering overlapping communities, which considers the community overlapping phenomenon in the topology of an actual communication network and the networking characteristics of multiple layers and multiple services of the actual communication network, and constructs a power communication network model from the topological structures of the actual communication network and the power network according to a community overlapping theory so as to enable the power communication network model to be more consistent with the actual power communication network and more accurately reflect the relevant characteristics of the actual network.
The method selects the overlapping community theory to model the power communication network, well reflects the actual networking characteristics, and further reveals the characteristics of the power communication network. However, the above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (4)
1. A power communication network modeling method considering overlapping communities is characterized by comprising the following steps:
1) on the basis of a complex network theory, abstracting power equipment in a power grid topology into power nodes, representing a node set of a power grid, abstracting a power transmission tie line into a power grid connection edge, representing an edge set of the power grid, and obtaining a power grid topological graph;
2) because the space truss structure of the communication network access layer in the actual power communication network has strong topological similarity with the space truss structure of the power network, the communication network access layer topological structure is consistent with the power network topological structure, namely the number of nodes and topological connection of the communication network access layer are the same as those of the power network, and the communication network access layer and the power network are in one-to-one full coupling relation;
3) carrying out community division on the topological graph of the power network by using point edge graph conversion and a Markov clustering algorithm, further determining overlapped community nodes and mapping the overlapped community nodes to be nodes of a backbone network of the communication network, and finding a group of edge sets based on a greedy algorithm to ensure that the nodes among the backbone network point sets are connected to form an annular winding structure and the minimum path passed by the annular winding structure is shortest, thereby obtaining a backbone network topological structure of the communication network; the communication network backbone layer and the communication network access layer belong to a part of one-to-one coupling relationship, and the coupling nodes are overlapped nodes and have no direct coupling relationship with the power network nodes;
4) finding out the overlapped nodes of the backbone layer of the communication network by adopting the same overlapped community searching algorithm as that in the step 3), mapping the overlapped nodes to be the nodes of the core layer of the communication network, and constructing a topology structure of the core layer of the communication network based on a greedy algorithm; the communication network core layer and the communication network backbone layer are in a part many-to-many coupling relationship, the coupling nodes are overlapped nodes of the communication network backbone layer, but the core layer, the communication network access layer and the power network are not in a direct coupling relationship;
5) and obtaining the adjacent matrix of the power communication network according to the corresponding coupling relation between the adjacent matrix of each layer of the power network and the communication network and the upper layer and the lower layer, thereby constructing a power communication network model.
2. The method as claimed in claim 1, wherein a community overlapping phenomenon existing in an actual communication network topology is comprehensively considered, that is, cross overlapping areas exist between communication backbone rings, that is, community overlapping areas, nodes of the cross overlapping areas are often set as provincial dispatching centers or regional dispatching centers, and an overlapping community theory is applied to embody the phenomenon, so as to establish a model.
3. The electric power communication network modeling method considering the overlapping communities as claimed in claim 1 is characterized in that the communication network is divided into three layers, namely an access layer, a backbone layer and a core layer, according to the networking characteristics of multiple layers and multiple services of the actual communication network, and modeling is performed in sequence, so that the model is more in line with the actual characteristics.
4. The method as claimed in claim 1, wherein the step of searching for the overlapped nodes by the overlapped community searching algorithm comprises:
step 401: defining a point diagram G ═ V, E, wherein V, E are respectively a node set and an edge set of the complex network, an adjacent matrix is A, and the point-edge conversion is carried out on the diagram G to obtain a new diagram Glink＝(Vlink，，Elink) In which V islink、ElinkRespectively carrying out point-edge conversion on the graph G to obtain a new graph GlinkThe edge set and the node set of (2), the adjacency matrix of which is Alink。
Step 402: obtaining a boundary graph G by using an LHN similarity matrix calculation methodlinkSimilarity matrix S oflinkTherefore, the node similarity between each node of the edge graph and the neighbor nodes of the edge graph is measured, and the calculation formula is as follows:
in the formula (1), mlinkShows a side graph GlinkThe number of edges of (c); lambda [ alpha ]linkRepresenting an edge graph adjacency matrix AlinkThe maximum eigenvalue of (d); k is a radical oflink(i) Degree of the edge graph node i; max (St) is the largest element of the matrix St; matrix I represents and AlinkColumn and row identity identical identity matrix, α is LHN similarity parameter.
Step 403: similarity matrix S by using Markov clustering algorithmlinkPerforming expansion processing, wherein the calculation formula is as follows:
in the formula (2), e is an expansion squaring coefficient; k is the number of iterations.
Step 404: using Markov clustering algorithm to match similarity matrix SlinkCarrying out expansion treatment, wherein the calculation formula is as follows:
in the formula (3), r is an expansion point multiplication coefficient; k is the number of iterations.
Step 405: judging the similarity matrix SlinkWhether a preset condition is met or not, if so, finishing the algorithm; otherwise, go to step 403, enter next markov clustering algorithm processing. The predetermined conditions are as follows:
Slink (k+1)(i，j)＝(Slink (k+1)(i，j))2(4)
in the formula (4), SlinkIs a similarity matrix; k is the number of iterations.
Step 406: and performing excessive similarity processing on the node redundancy aspect, judging whether a preset condition is met, and if so, sequentially removing the nodes of the self community from large to small according to the community scale of the nodes until a threshold value is met. The predetermined conditions are as follows:
D(Vp(i))＞θ (5)
in the formula (5), D (V)p(i) Is the number of communities to which the node i of the point diagram belongs; theta is a defined threshold.
Step 407: and performing excessive similarity processing on the aspect of community redundancy, judging whether a preset condition is met, and if so, merging the two communities. The predetermined conditions are as follows:
Y(C(i)，C(j))＞ζ (6)
in the formula (6), C (i) is the ith community after division, Y (C (i), C (j)) is the node similarity of the two communities, and ξ is a limited threshold value.
Step 408: and searching out overlapped community nodes, namely nodes with the community number larger than 1 from the divided point communities C, classifying the nodes into an overlapped community node set and outputting.
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