A power communication network topology optimization method based on complex network theory

Abstract

The application discloses a power communication network topology optimization method based on a complex network theory; the method firstly establishes a graph model of the power communication network, embeds power network tidal flow parameters and communication network service flow parameters in a weight matrix of the graph model, quantifies interlayer coupling degree according to node similarity, and constructs a coupling model of the network. Then, an elasticity evaluation index of the power communication network is proposed, a dynamic form of Kirchhoff coefficient is used to evaluate elasticity of the power communication network at different times, and development and evolution of the network in a cascading failure process is tracked. Finally, the elasticity evaluation index is used as a target function, a simulated annealing method is used to establish an optimization model, and optimal elasticity topology of the network is solved. The application is a network topology planning method, considers coupling characteristics of the power and communication networks, can adjust the topology relationship of the communication network, enhances structural strength of the power communication network, and improves resistance of the network in a failure.

Description

Technical Field

[0001] This invention relates to the field of electrical engineering, and in particular to a method for optimizing the topology of power communication networks based on complex network theory. Background Technology

[0002] Complex networks consist of numerous nodes and intricate relationships between them. Abstracting the topology represents the relationships between different components in a real system. Graph models can effectively describe complex network structures, visualizing them while minimizing information loss. When establishing coupling between power and communication networks, communication equipment is typically installed directly at the location of power components for ease of measurement, and the topology of fiber optic transmission lines between these devices offers various options. Furthermore, the coupling between networks is not limited to physical connections but also relies on the exchange of information data. During fault events, numerous communication devices in the communication network can sense changes in the power network's operating status in real time, assisting the power communication network in implementing control strategies. However, simple network structure models struggle to reflect the dynamic characteristics of the system and cannot provide a resilient assessment of the power communication network after regulatory interventions are implemented.

[0003] To meet the needs of resilience analysis under changing operational states, a power communication network operation model reflecting real-time changes in information and power should be established based on the structural model. By introducing power flow and information flow parameters, the edge weight matrix simultaneously includes topological connectivity and operational state information. On the other hand, in real-world scenarios, the system undergoes a period of fault mitigation, during which losses are minimized by changing component operation methods or adjusting flexibility resources. Therefore, assessing operational resilience requires not only considering system operating parameters but also extending the time scale of resilience evaluation to establish a comprehensive evaluation index for the entire process after a fault. Based on this, using resilience indicators to guide network topology reconstruction can effectively utilize global information, predict post-fault trends, and further enhance system resilience. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a topology optimization method for power communication networks based on complex network theory; this method aims to achieve topology planning for power communication networks and improve their resilience in the face of faults.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A topology optimization method for power communication networks based on complex network theory includes the following steps:

[0007] (1) Establish a graph model of the power communication network, which includes a power network and a communication network, both of which are represented by a graph composed of nodes and edges; embed the power flow parameters in the power network and the service flow parameters in the communication network into the weight matrix of the graph model, quantify the coupling degree between layers based on the similarity of nodes, and construct a coupling model of the power communication network.

[0008] (2) Based on step (1), establish the cascading fault process of the power communication network; after the power node fails, the power flow is redistributed; the corresponding communication node fails, which in turn causes the redistribution of information flow and the failure of new communication nodes, and the corresponding power node also fails, until the entire power communication network reaches a stable state.

[0009] (3) Propose a resilience evaluation index for power communication networks, use the dynamic form of Kirchhoff coefficients to evaluate the resilience of power communication networks at different times, and track the development and evolution of power communication networks in the cascading fault process in step (2).

[0010] (4) Using the elasticity evaluation index proposed in step (3) as the objective function, an optimization model is established using the simulated annealing method to solve for the optimal elastic topology of the power communication network.

[0011] Furthermore, in step (1), the nodes in the power network represent generators, substations, and loads, and the edges represent transmission lines. The power proportion parameter of the power transmission line is introduced into the weight of the edge, and the edge weight value changes with the power flow distribution. The nodes in the communication network represent control centers, information sources, and information sinks, and the edges represent optical fiber transmission lines between nodes. The line information flow proportion parameter is introduced into the weight of the edge, and the edge weight value changes with the information service distribution. There is a one-to-one correspondence between power nodes and communication nodes, and the coupling model is represented by the correlation degree between the power nodes and the nodes connected to the communication nodes.

[0012] Furthermore, the power network is represented as Figure G. P =(V P E P W P ), where V P Let E be a set of N power nodes. P Let W be the set of edges. P Let the weight matrix be the weight matrix corresponding to the edge, which has the following expression:

[0013]

[0014] In the formula, W Pij (t) represents the line e at time t. ij The weights, F ij (t) represents the line e at time t. ijThe power, C ij For line e ij Power flow power limit;

[0015] The communication network is represented as Figure G. C =(V C E C W C ), where V C Let E be a set of N communication nodes. C Let W be the set of edges. C Let the weight matrix of the communication edge be given by the following expression:

[0016]

[0017] In the formula, W Cij (t) represents the line e at time t. ij Information network weight, T ij (t) represents the line e at time t. ij The communication traffic volume, S ij For line e ij bandwidth capacity;

[0018] The weight of a coupling edge represents the degree of correlation between the connected nodes; the coupling edge weight W sij The definition is as follows:

[0019] W Sij =|μ ij ρ ij |

[0020]

[0021]

[0022] In the formula, W is the weight matrix of the coupled network, and μ ij The binary discriminant variable ρ represents the connection relationship between nodes. ij The coupling degree represents the degree of mapping between nodes; the Spearman correlation coefficient is used to quantify the coupling degree of associated nodes, defined as follows:

[0023]

[0024] In the formula, Represents multiple attribute feature indicators for node i, R = 2, Ψ 1 The electrical betweenness of a node, Ψ 2 This represents the communication betweenness of a node in a communication network.

[0025] Furthermore, step (2) includes the following sub-steps:

[0026] (2.1) Attack k nodes in a power grid, and the attacked nodes become ineffective in the network;

[0027] (2.2) Based on the new power network topology, perform optimal power flow calculation, and consider nodes that are unloaded and edges that exceed the power flow limit as failures;

[0028] (2.3) Determine whether the power network has reached a stable state. If new loads are lost, repeat step (2.2). When the power network is stable, record all the failed power nodes as a set {Lp}.

[0029] (2.4) The node corresponding to the failed power node in the communication network is also failed, and the corresponding node does not include the communication center node;

[0030] (2.5) Based on the new communication network topology, perform communication power flow calculation. Nodes that cannot form a path with the control center and edges that exceed the power flow limit are considered invalid.

[0031] (2.6) Determine whether the communication network has reached a stable state. If new load is lost, repeat step (2.5). When the communication network is stable, denote all the failed communication nodes as the set {Lc}.

[0032] (2.7) Determine whether the coupled model has reached a stable state; if there is a newly added failed node in {Lc}, then the corresponding node in the power network is also failed, and repeat steps (2.2) to (2.5); if the set {Lp} is equal to the set {Lc}, then the cascading process ends.

[0033] Furthermore, in step (3), the dynamic Kirchhoff coefficient index Kd is used as an indicator for evaluating the resilience of the power communication network, and has the following expression:

[0034]

[0035] In the formula, t0 represents the initial moment of normal operation of the power communication network, t s The time when the power communication network reaches a steady state after a fault is represented by K(t), where K(t) represents the Kirchhoff coefficient at time t. The Kirchhoff coefficient K is defined as follows:

[0036] L=DW

[0037]

[0038]

[0039] In the formula, D represents the diagonal matrix composed of the degrees of all nodes, W represents the coupled network weight matrix, L is the Laplace matrix of the power communication network, and w ijLet n be the element in matrix W, n be the total number of nodes, and λ be the element in matrix W. i Let L be the eigenvalue of L, and V be the set of all nodes in the power communication network.

[0040] Furthermore, step (4) includes the following sub-steps:

[0041] (4.1) Set up the initial communication network G based on the given number of nodes and the number of communication lines. 0 The simulation parameters were initialized, and the resilience index Kd(G) of the power communication network coupled with the initial communication network was calculated under a single-node failure attack. 0 Set the iteration step count to τ = 1;

[0042] (4.2) Select a node j with at least one neighbor node, randomly select a connecting edge (i,j) in the communication network to disconnect it, and generate a connecting edge (i,k) to obtain a new graph G. τ ;

[0043] (4.3) Test chart G τ Is the graph connected? If the graph is not connected, return to step (4.2); if the graph is connected, calculate the dynamic Kirchhoff coefficient Kd(G) under a single-node attack. τ );

[0044] (4.4) Compare the current time τ graph G τ Plot G at time τ-1 τ-1 The new network replaces the previous network with a transition probability p, and the expression for the transition probability p is as follows:

[0045]

[0046] In the formula, parameter T is the cooling temperature;

[0047] (4.5) When the number of iterations reaches the preset maximum number of iterations τ max When the network adjacency matrix is ​​obtained, the optimization objective algorithm ends, and the optimal elastic topology of the power communication network is obtained; otherwise, τ = τ + 1 is executed and the process returns to step (4.2) to continue optimizing the network topology.

[0048] The beneficial effects of this invention are as follows:

[0049] (1) The network topology optimization method based on the resilience index of this invention can find the optimal communication network connection mode and reduce the network loss rate when a fault occurs. This method can effectively utilize global information, predict the trend of changes after a fault, and is more conducive to improving the resilience of power communication networks.

[0050] (2) This invention provides a flexible optimization scheme for the topology planning of power communication networks. Compared with the reconfiguration of transmission lines in power networks, the cost of changing communication lines in communication networks is relatively small. The network topology optimization process does not increase the total number of information transmission lines, but enhances the network's flexibility margin, reduces engineering modification costs, and has good engineering economics. Attached Figure Description

[0051] Figure 1 This is a flowchart of the method of the present invention;

[0052] Figure 2 This is a flowchart of the cascading fault process in the power communication network in this invention;

[0053] Figure 3 This is a schematic diagram of the topology optimization results in this invention; Figure 3 (a) in the diagram is a schematic diagram of the optimization result of the 30-sided structure. Figure 3 (b) in the diagram is a schematic diagram of the optimization result of the 50-sided structure. Detailed Implementation

[0054] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation examples.

[0055] like Figure 1 As shown, the present invention provides a power communication network topology optimization method based on complex network theory, comprising the following steps:

[0056] (1) Establish a graph model of the power communication network, which includes a power network and a communication network (the power communication network is a two-layer network structure composed of a power network and a communication network). Both the power network and the communication network are represented by a graph composed of nodes and edges. Embed the power flow parameters in the power network and the service flow parameters in the communication network into the weight matrix of the graph model. Quantify the coupling degree between layers according to the similarity of nodes to construct a coupling model of the network.

[0057] Specifically, a graph model of the power communication network is first established. The power communication network comprises both a power network and a communication network; both are represented by graphs consisting of nodes and edges. In the power network, nodes represent generators, substations, and loads, while edges represent transmission lines. The power proportion parameter of the power transmission lines is incorporated into the edge weights, which change with the power flow distribution. In the communication network, nodes (i.e., communication nodes) represent control centers, information sources, and information sinks, while edges represent fiber optic transmission lines between nodes. The proportion of information flow along the lines is incorporated into the edge weights, which change with the information service distribution. Power nodes and communication nodes are connected in a one-to-one manner, and the coupling model is represented by the correlation between the connected nodes of the power and communication nodes.

[0058] A power network can be represented as graph G. P =(V P E P W P ), where V P Let E be a set of N power nodes. P Let W be the set of edges. P Let be the weight matrix corresponding to the edges. Time-varying weights can reflect the elasticity of the power network at different time scales, and are defined as follows:

[0059]

[0060] In the formula, W Pij (t) represents the edge (i.e., the transmission line) e at time t. ij The weights, F ij (t) represents the line e at time t. ij The power, C ij For line e ij The power flow limit. To distinguish between cases where the line has a path but no power and cases where there is no path, add 1 to the power ratio and shift the weight range from [0,1] to [1,2].

[0061] The communication network is represented as graph G. C =(V C E C W C ), where V C Let E be a set of N communication nodes. C Let W be the set of edges. C This is the weight matrix for the communication edges. Nodes represent the control center, information source, and information sink, and edges represent the fiber optic transmission lines between nodes. The edge weights are represented as follows:

[0062]

[0063] In the formula, W Cij (t) represents the edge (i.e., the fiber optic transmission line) e at time t. ij Information network weight, T ij (t) represents the line e at time t. ij The communication traffic volume, S ij For line e ij The bandwidth capacity is determined. To distinguish between cases where the line has a path but no communication flow and cases where there is no path, the weight range is shifted from [0,1] to [1,2] by adding 1 to the power ratio. The number of power nodes and communication nodes are equal, and a one-to-one connection method is used.

[0064] The weight of a coupling edge represents the degree of correlation between the connected nodes; the coupling edge weight W sij The definition is as follows:

[0065] W Sij =|μ ij ρ ij |

[0066]

[0067]

[0068] In the formula, W is the weight matrix of the coupled network, and μ ij The binary discriminant variable ρ represents the connection relationship between nodes. ij To represent the degree of mapping between nodes, the Spearman correlation coefficient is used to quantify the degree of coupling between associated nodes, and is defined as follows:

[0069]

[0070] In the formula, Ψ i =[Ψ i 1 Ψ i 2 , ..., Ψ i R ] represents multiple attribute feature indicators of node i, R=2, Ψ 1 The electrical betweenness of a node, Ψ 2 This represents the communication betweenness of a node in a communication network.

[0071] (2) Figure 2 As shown, a cascading fault process in a power communication network is established. After a power node fails, the power flow is redistributed; the corresponding communication node fails, leading to a redistribution of information flow and the failure of new communication nodes, which in turn cause the corresponding power nodes to fail, until the entire power communication network reaches a stable state. The specific simulation sub-steps of the cascading fault process are as follows:

[0072] (2.1) Attack k nodes in a power grid, and the attacked nodes become ineffective in the network;

[0073] (2.2) Based on the new power network topology, perform optimal power flow calculation, and consider nodes that are unloaded and edges that exceed the power flow limit as failures;

[0074] (2.3) Determine whether the power network has reached a stable state. If new loads are lost, repeat step (2.2). When the power network is stable, record all the failed power nodes as a set {Lp}.

[0075] (2.4) The corresponding node in the communication network for a failed power node is also failed (except for the communication center node);

[0076] (2.5) Based on the new communication network topology, perform communication power flow calculation. Nodes that cannot form a path with the control center and edges that exceed the power flow limit are considered invalid.

[0077] (2.6) Determine whether the communication network has reached a stable state. If new load is lost, repeat step (2.5). When the communication network is stable, denote all the failed communication nodes as the set {Lc}.

[0078] (2.7) Determine whether the coupled network has reached a stable state. If there is a newly added failed node in {Lc}, then the corresponding node in the power network is also failed, and repeat the calculation of steps (2.2) to (2.5); if the set {Lp} is equal to the set {Lc}, then the cascading process ends.

[0079] (3) Propose a resilience evaluation index for power communication networks, use the dynamic form of Kirchhoff coefficients to evaluate the resilience of power communication networks at different times, and track the development and evolution of power communication networks in the cascading fault process in step (2).

[0080] Specifically, this paper proposes a resilience assessment index for power communication networks. A spectral metric is used to evaluate the overall resilience of the power communication network, and the static Kirchhoff coefficients are used to discover the network's structural characteristics. During a cascading fault, the power flow update within the power network is recorded as one moment, the propagation of the fault to other networks causing a redistribution of power flow is recorded as the next moment, and the end of the fault cycle is recorded when the entire power communication network reaches a stable state. The mean of the integrals of the static Kirchhoff coefficients at each moment within the cycle is used as the dynamic Kirchhoff coefficient index.

[0081] The dynamic Kirchhoff coefficient (Kd) is defined as an indicator of the resilience of power communication networks as follows:

[0082]

[0083] In the formula, t0 represents the initial moment of normal operation of the power communication network, t s The time when the power communication network reaches a steady state after a fault is represented by K(t), where K(t) represents the Kirchhoff coefficient at time t. The Kirchhoff coefficient K is defined as follows:

[0084] L=DW

[0085]

[0086]

[0087] In the formula, D represents the diagonal matrix composed of the degrees of all nodes, W represents the coupled network weight matrix, L is the Laplace matrix of the power communication network, and w ijLet n be the element in matrix W, n be the total number of nodes, and λ be the element in matrix W. i Let L be the eigenvalues ​​of L, and V be the set of all nodes in the power communication network. Kirchhoff coefficients can quantify the spatial distribution of nodes in the graph as eigenvalues ​​of a Laplace matrix, reflecting the compactness of the network structure.

[0088] (4) Using the elasticity evaluation index as the objective function, an optimization model is established using the simulated annealing method to solve for the optimal elastic topology of the power communication network.

[0089] A method for optimizing the topology of power communication networks. The goal is to find the optimal communication line topology with the objective of maximizing elasticity. Given a fixed number of nodes and communication edges as the state space, simulated annealing is used to solve for the optimal communication line topology connection method (i.e., the network adjacency matrix). The optimization objective of the power communication network topology is:

[0090] min Kd(G)

[0091] In the formula, the smaller the dynamic Kirchhoff coefficient index Kd, the stronger the elasticity of the power communication network. When the structure of the power network is already determined, the elasticity optimization process is actually about selecting the topology connection method for the communication lines of a certain number of nodes. The optimization problem is solved using the simulated annealing method to obtain the adjacency matrix of the communication network, thus obtaining the optimal elastic topology of the power communication network. The steps for elastic topology optimization of the power communication network using the simulated annealing method are as follows:

[0092] (4.1) Set up the initial communication network G based on the given number of nodes and the number of communication lines. 0 The simulation parameters were initialized, and the resilience index Kd(G) of the power communication network coupled with the initial communication network was calculated under a single-node failure attack. 0 Set the iteration step number to τ = 1.

[0093] (4.2) Select a node j with at least one neighbor node, randomly select a connecting edge (i,j) in the communication network to disconnect it, and generate a connecting edge (i,k) to obtain a new graph G. τ .

[0094] (4.3) Test chart G τ Is the graph connected? If the graph is not connected, return to step (4.2); if the graph is connected, calculate the dynamic Kirchhoff coefficient Kd(G) under a single-node attack. τ ).

[0095] (4.4) Compare the current time τ graph G τ Plot G at time τ-1 τ-1 The new network replaces the previous network with a transition probability p, which is calculated as follows:

[0096]

[0097] The parameter T is the cooling temperature, which is a decreasing function of time τ: T = T0θ τ-1 Where T0 is the initial temperature and the temperature cooling factor θ = 0.95.

[0098] (4.5) When the number of iterations reaches the preset maximum number of iterations τ max When the network topology optimization is complete, the optimization algorithm ends and the network adjacency matrix is ​​obtained; otherwise, τ = τ + 1 is executed and the process returns to step (4.2) to continue optimizing the network topology.

[0099] After the above steps, the adjacency matrix of the communication network is finally obtained, which is the optimal elastic topology of the power communication network.

[0100] In the optimization algorithm, the initial temperature T0 = 1000 and the maximum number of iterations is τ. max =1000. During the optimization process, the structure of the power network remains unchanged, and the node distribution of the communication network remains the same. The optimization focuses on the connection relationships between communication nodes. Using the static index K and the dynamic index Kd as elastic optimization objectives, the optimal structure of the communication network is found when the elasticity index is minimized.

[0101] To verify the effectiveness of the operational resilience index assessment, a comparison was made between the power communication network loss indices before and after the fault. The calculation methods for the load loss rate (Loss_p) in the power network, the service loss rate (Loss_c) in the communication network, and the overall network loss rate (Loss_net) are as follows:

[0102]

[0103]

[0104] Loss_net = (Loss_p + Loss_c) / 2

[0105] In the formula, Ω represents the set of load nodes, and PS i For the load reduction power of load i, PD i T represents the load power of node i; k E represents the service bandwidth on communication line k. c E represents the set of communication lines in the initial state of the communication network. s This represents the set of failed lines in the communication network, with the overall network loss rate being the average of the loss rates of the communication network and the power network.

[0106] Fifty communication network structures with varying communication line connection scales were randomly selected, and single-node failure attacks were conducted. The relationship between network loss rate and dynamic Kirchhoff coefficients is as follows: Figure 3As shown. Figure 3 (a) and Figure 3 Simulation results (b) show that when optimizing the network using static indices, the optimization result is not necessarily the optimal solution; the optimization effect is relatively better in a relatively compact network structure. When optimizing the network topology using dynamic indices, the optimization result has good flexibility in any structure. Therefore, the power communication network topology optimization method in this invention helps to improve flexibility and reduce network losses during faults.

Claims

1. A topology optimization method for power communication networks based on complex network theory, characterized in that, Includes the following steps: (1) Establish a graph model of the power communication network, which includes a power network and a communication network, both of which are represented by a graph composed of nodes and edges; embed the power flow parameters in the power network and the service flow parameters in the communication network into the weight matrix of the graph model, quantify the coupling degree between layers according to the similarity of nodes, and construct a coupling model of the power communication network. (2) Based on step (1), establish the cascading fault process of the power communication network; after the power node fails, the power flow is redistributed; the corresponding communication node fails, which in turn causes the redistribution of information flow and the failure of new communication nodes, and the corresponding power node also fails, until the entire power communication network reaches a stable state. (3) Propose a resilience evaluation index for power communication networks, use the dynamic form of Kirchhoff coefficients to evaluate the resilience of power communication networks at different times, and track the development and evolution of power communication networks in the cascading fault process in step (2). The dynamic Kirchhoff coefficient index Kd As a resilience assessment indicator for power communication networks, it has the following expression: ； In the formula, t 0 This indicates the initial moment of normal operation of the power communication network. t s This indicates the time when the power communication network reaches a stable state after a fault. K ( t )express t Kirchhoff coefficients at time t; Kirchhoff coefficients K Defined as follows: ； ； ； In the formula, D This represents a diagonal matrix consisting of the degrees of all nodes. W This represents the weight matrix of the coupled network. L For the Laplace matrix of the power communication network, w ij For matrix W The elements in n The total number of nodes. l i for L eigenvalues, V It is the set of all nodes in a power communication network; (4) Using the elasticity evaluation index proposed in step (3) as the objective function, an optimization model is established using the simulated annealing method to solve for the optimal elastic topology of the power communication network; include: (4.1) Set up the initial communication network based on the given number of nodes and communication lines. G 0 The simulation parameters were initialized, and the resilience index of the power communication network coupled with the initial communication network was calculated under a single-node failure attack. Kd ( G 0 Set the number of iteration steps to ). t =1; (4.2) Select a node that has at least one neighbor node. j Randomly select a connection edge in the communication network ( i , j Disconnect and generate a connection edge. i , k ), to obtain a new graph G t ; (4.3) Inspection chart G t Determine if the graph is connected; if not, return to step (4.2); if connected, calculate the dynamic Kirchhoff coefficients under a single-node attack. Kd ( G t ); (4.4) Compare with the current situation t Time map G t and t Graph at time -1 G t-1 and with transition probability p Replace the previous network with a new network, and the transition probability. p The expression is as follows: ； In the formula, the parameters T This refers to the cooling temperature. (4.5) When the number of iterations reaches the preset maximum number of iterations t max When the desired outcome is achieved, the optimization algorithm terminates, yielding the network adjacency matrix, which represents the optimal flexible topology of the power communication network; otherwise, the process continues. t = t +1 and return to step (4.2) to continue optimizing the network topology.

2. The power communication network topology optimization method based on complex network theory according to claim 1, characterized in that, In step (1), nodes in the power network represent generators, substations, and loads, and edges represent transmission lines. The power ratio parameter of the power transmission line is introduced into the edge weight, and the edge weight value changes with the power flow distribution. Nodes in the communication network represent control centers, information sources, and information sinks, and edges represent optical fiber transmission lines between nodes. The line information flow ratio parameter is introduced into the edge weight, and the edge weight value changes with the information service distribution. Power nodes and communication nodes correspond one-to-one, and the coupling model is represented by the correlation degree between the power nodes and the communication nodes connected to them.

3. The power communication network topology optimization method based on complex network theory according to claim 2, characterized in that, The power network is represented as a diagram. G P =( V P , E P , W P ),in V P for N A set of power nodes, E P Let be the set of edges. W P Let the weight matrix be the weight matrix corresponding to the edge, which has the following expression: ； In the formula, W Pij ( t )express t Timetable e ij The weight, F ij ( t )express t Timetable e ij power, C ij For the line e ij Power flow power limit; The communication network is represented as shown in the figure. G C =( V C , E C , W C ),in V C for N A set of communication nodes E C Let be the set of edges. W C Let the weight matrix of the communication edge be given by the following expression: ； In the formula, W Cij ( t )express t Timetable e ij Information network weight, T ij ( t )express t Timetable e ij The volume of communication services, S ij For the line e ij bandwidth capacity; The weight of a coupling edge represents the degree of correlation between the connected nodes. W sij The definition is as follows: ； ； ； In the formula, W This is the weight matrix of the coupled network. m ij The binary discriminant variable represents the connection relationship between nodes. r ij The coupling degree represents the degree of mapping between nodes; the Spearman correlation coefficient is used to quantify the coupling degree of associated nodes, defined as follows: ； In the formula, Y i =[ Y i 1 , Y i 2 ,..., Y i R ] represents a node i Multiple attribute feature indicators, R =2, Y 1 The electrical betweenness of a node, Y 2 This represents the communication betweenness of a node in a communication network.

4. The power communication network topology optimization method based on complex network theory according to claim 1, characterized in that, Step (2) includes the following sub-steps: (2.1) Attack k nodes in a power grid, causing the attacked nodes to become ineffective in the network; (2.2) Based on the new power network topology, perform optimal power flow calculation, and consider nodes that are unloaded and edges that exceed power flow limits as failures; (2.3) Determine whether the power network has reached a stable state. If new loads are lost, repeat step (2.2). When the power network is stable, record all the failed power nodes as a set {Lp}. (2.4) The node corresponding to the failed power node in the communication network is also failed, and the corresponding node does not include the communication center node; (2.5) Based on the new communication network topology, perform communication power flow calculation. Nodes that cannot form a path with the control center and edges that exceed the power flow limit are considered invalid. (2.6) Determine whether the communication network has reached a stable state. If new load is lost, repeat step (2.5). When the communication network is stable, denote all the failed communication nodes as the set {Lc}. (2.7) Determine whether the coupled model has reached a stable state; If a new failed node is added in {Lc}, then the corresponding node in the power network will also fail, and steps (2.2) to (2.5) will be repeated; if the set {Lp} is equal to the set {Lc}, then the cascading process ends.

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