Time sequence attack sequence optimization method for cyber-physical power network based on intelligent evolution algorithm

Abstract

The application discloses a time sequence attack sequence optimization method of a cyber-physical power network based on an intelligent evolution algorithm, and comprises the following steps: 1, initializing the cyber-physical power network; 2, optimizing the time sequence attack sequence of the cyber-physical network based on an improved evolution algorithm of NSGA-II. The application simulates a real attack scene by using a time sequence attack model from the perspective of an attacker, and finds the most vulnerable power network component by using an intelligent evolution algorithm, thereby providing important decision support for the resilience and robustness of the augmented reality cyber-physical power network.

Description

Technical Field

[0001] This invention relates to the field of complex intelligent power networks, and more specifically to a method for finding the optimal attack strategy in a time-series attack simulation of cyber-physical power networks (CPPS) based on an intelligent evolutionary algorithm. Background Technology

[0002] With the development of the energy internet, the scale of power systems is constantly expanding, and the speed of communication infrastructure construction is significantly improving. Modern power systems are gradually transforming into coupled networks composed of physical power grids and communication networks, namely Cyber-Physical Power Systems (CPPS). CPPS achieves close integration of computing, communication, and power resources, making it more resilient, secure, reliable, and manageable, and ensuring the connectivity of power grid components. However, it also introduces new vulnerabilities; the inter-layer coupling relationship allows system faults to transform between the information layer and the physical layer. To mitigate this potential risk, it is necessary to study the generation, attack scenarios, and propagation mechanisms of cascading failures in cyber-physical power systems (CPPS).

[0003] Current power grid vulnerability analysis is mainly divided into the following categories:

[0004] The first category is traditional graph theory modeling methods based purely on topological information: the mechanism of fault propagation in power systems is closely related to the physical properties of the power system and is determined by nonconvex nonlinear power flow equations. However, many studies on cascading fault propagation in power systems neglect power flow equations. These studies focus on the system's topology, using complex network theory to model fault propagation, which makes it difficult to incorporate the physical mechanisms of cascading failures into topological metrics. This is because in a power grid, flow is driven by Kirchhoff's laws and cannot be described using network flow models. When a fault occurs in the power grid, the power flow is redistributed in the rest of the network, and some components may overload and fail, leading to cascading failures. Therefore, without detailed power grid information, methods based on complex network theory yield widely varying results, potentially leading to erroneous conclusions about the vulnerability of the power grid.

[0005] The second category involves using single-layer power grid structures or DC power flow modeling methods. With the development of the energy internet, the scale of power systems is constantly increasing, and the speed of communication infrastructure construction is significantly accelerating. Modern power systems are gradually becoming coupled networks composed of physical power grids and communication networks, namely Cyber-Physical Power Systems (CPPS). Therefore, traditional single-layer power grid modeling methods can no longer meet research needs. DC power flow modeling methods study the physical problems in cascading failures in power systems through linearized power flow equations. However, it has been shown that cascading failure simulations under DC power flow models (e.g., ignoring power losses, reactive power flow, and voltage amplitude variations) can lead to inaccurate and overly optimistic cascading predictions. More specifically, using DC power flow to study cascading failures in large networks often overestimates the number of components still in use after fault propagation stops, because DC power flow cannot accurately capture nonlinear mechanisms such as voltage collapse or dynamic instability in power systems. Therefore, using DC models for cascading predictions may lead to incorrect representations of cascading severity.

[0006] The third category of attack methods in power networks can be divided into single attacks and multiple attacks. A single attack method refers to an attack that removes only one node or link from the system. The robustness of a system to a single attack is known as the N-1 security problem. However, many industrial reliability standards often require a system to withstand the failure of a single component; therefore, a single attack usually does not cause serious consequences for most real-world systems. Multiple attack methods extend the original N-1 problem (removing one node from a network of N nodes) to Nk (removing k nodes from N nodes). For multiple attack methods, the removal operations can be performed simultaneously or sequentially. Many existing works assume that multiple attacks are carried out simultaneously; this is called a simultaneous multiple attack. However, some literature has demonstrated that sequential attacks can achieve better results.

[0007] The fourth category is the formulation of attack strategies. Existing attack strategies often employ random attacks or attack strategies based on network characteristics, such as node degree centrality, node betweenness centrality, etc. However, since CPPS not only has network characteristics but also electrical characteristics, it is impossible to carry out effective attacks based solely on network characteristics, and it is also impossible to simultaneously consider both the network structure and functional characteristics of CPPS as attack targets. Summary of the Invention

[0008] To overcome the shortcomings of existing technologies, this invention proposes a time-series attack sequence optimization method for cyber-physical power networks based on intelligent evolutionary algorithms. The aim is to find the optimal attack sequence in the modeled CPPS network and optimize the attack effect of CPPS in terms of both network structure and functional characteristics, thereby achieving the best attack effect and providing a more reliable and accurate basis for attack and protection decisions in real-world CPPS.

[0009] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0010] The present invention provides a method for optimizing the temporal attack sequence of cyber-physical power networks based on an intelligent evolutionary algorithm, characterized by the following steps:

[0011] Step 1. Initialization of the cyber-physical power network:

[0012] Step 1.1. Based on the number of nodes in the power network G1(N1, E1), construct a scale-free network G2(N2, E2) with the same number of nodes and use it as the communication layer of the cyber-physical power network; where, Represents the set of power nodes in power network G1; E1 represents the set of communication nodes in the scale-free network G2; E2 and E1 represent the undirected path information of G1 and G2, respectively. This represents the i-th power node in power network G1. Let u represent the u-th communication node in the scale-free network G2, and o represent the total number of nodes;

[0013] Step 1.2. Based on degree centrality, sort the nodes in G1 and G2 in descending order to obtain the sorted set of power nodes N′1 and the set of communication nodes N′2.

[0014] The nodes in the sorted power node set N′1 are coupled one by one with the nodes in the communication node set N′2 to obtain the cyber-physical power network and its coupling matrix B = [B (i，u) ], where B (i，u) Represents the i-th power node after sorting. With the u-th communication node The coupling value, if B (i，u) =1, which indicates the i-th power node. With the u-th communication node There exists an edge between B and B. (i，u) =0 indicates the i-th power node With the u-th communication node There is no edge between them;

[0015] Step 1.3. Make assumptions about each power node and the transmission branch represented by the edge in the power network G1:

[0016] (1) Let the states of each power node and edge in the power network G1 include: failure state and normal state;

[0017] (2) If any power node is in a failed state, the connected edges will also be in a failed state.

[0018] Step 2. Optimize the timing attack sequence for cyber-physical networks using an evolutionary algorithm improved from NSGA-II;

[0019] Step 2.1. Construct the timing attack target function using equations (1) and (2) respectively:

[0020] f1=o′ max / o (1)

[0021]

[0022] In equations (1) and (2), f1 represents structural indicators, f2 represents functional indicators, and o′ max P represents the maximum number of nodes in the connected subnet of power network G1 after a time-series attack, and o′ represents the number of power nodes in power network G1 after a time-series attack; i Represents the i-th power node in power network G1 Load before the timing attack, P i′ This represents the i′-th power node in power network G1 after it has been subjected to a timing attack. The load capacity;

[0023] Step 2.2. Population Coding:

[0024] Define the population size as S, the number of evolutions as G, and the maximum number of generations as G. max The crossover probability of the population is P. c The population mutation probability is P m and initialize G = 1;

[0025] Based on the nodes in the cyber-physical power network, the Gth generation population A (G) Encode, Represents population A of generation G (G) The s-th individual represents the s-th temporal attack sequence; and Represents the s-th individual The j-th gene represents the j-th node number to be attacked; m is the length of the temporal attack sequence.

[0026] Step 2.3. Calculate the i-th power node in the power network G1 using equation (3). Importance indicators

[0027]

[0028] In equation (3), p and q are two weights. Represents the i-th power node The degree, Represents the i-th power node The load;

[0029] The u-th communication node in the scale-free network G2 is calculated using equation (4). Importance indicators

[0030]

[0031] In equation (4), Represents the u-th communication node The degree;

[0032] Step 2.4. For population A in generation G. (G) Perform a crossover operation, and replace all duplicate nodes in the resulting individuals with other unique nodes from the corresponding individuals, thereby generating the G-th generation crossover population A′. (G) ;

[0033] Step 2.5. According to P m Determine the crossover population A′ of generation G. (G) If each offspring individual mutates, and if so, the genes in the offspring individuals are sorted in descending order according to their importance index, thus obtaining the gene sequence number of each offspring individual. The probability of selecting each gene in the offspring individual for mutation is then allocated based on the gene sequence number, with earlier sequence numbers indicating lower probabilities. One gene from each offspring individual is selected for mutation according to probability, resulting in the mutated offspring individual; thus, the mutated population A″ of the Gth generation is obtained. (G) , for A″ (G) Identical offspring individuals are discarded to obtain the Gth generation offspring population.

[0034] Step 2.6. Place A (G) and After merging, the Gth generation merged population is obtained. Any individual in the group is denoted as express The j-th gene in the sequence; initialize j = 1;

[0035] Step 2.7. The system inputs information to launch an attack on the physical network, and the attacked network is identified by the number [number to be inserted]. Remove the nodes, their coupled nodes, and the edges that are connected to them;

[0036] Step 2.8. Detect and configure failed nodes in the removed cyber-physical network;

[0037] Step 2.9. Perform AC power flow calculations on the cyber-physical network after the configuration fails to determine whether the processed cyber-physical network has reached equilibrium;

[0038] After assigning j+1 to j in step 2.10, if j>m, then it means... The attack ends, and step 2.11 is executed; otherwise, return to step 2.7 and execute sequentially.

[0039] Step 2.11. Calculate according to equations (1) and (2). The fitness value of the first objective function f1 And the fitness value of the second objective function f2

[0040] Step 2.12. Obtain the following steps: Steps 2.7-2.11 The fitness values ​​of all individuals are determined, and adjustments are made based on these fitness values. Individuals in the population are subjected to a fast non-dominated sorting and crowding distance is calculated, thereby obtaining population A in generation G+1 using a tournament selection strategy. (G+1) ;

[0041] Step 2.13. After assigning G+1 to G, determine if G > G. max Check if the condition is met. If it is met, the final population A is obtained; otherwise, return to step 2.4 and execute sequentially.

[0042] Step 2.14. Take all individuals in the first level of the final population A as the Pareto optimal solution set, and take the timing attack scheme corresponding to the Pareto optimal solution set as the optimal timing attack scheme.

[0043] The method for optimizing the timing attack sequence of cyber-physical power networks based on intelligent evolutionary algorithms described in this invention is also characterized in that step 2.8 includes:

[0044] Step 2.8.1. For the removed power network, set the isolated node as the failed node, and also set all power nodes in the power subnet without generator nodes as failed nodes. Update the coupling matrix B and set the row and column of the failed node to "0".

[0045] For the removed communication network, the communication nodes that are not connected to the largest connected communication subnet are set as failed nodes, the coupling matrix B is updated, and the row and column of the failed node are set to "0";

[0046] Step 2.8.2. Check if the remaining unfailed nodes have a value of "1" in the row and column of the coupling matrix B. If not, determine that the corresponding node is unfailed and return to step 2.8; otherwise, proceed to step 2.9.

[0047] Step 2.9 includes:

[0048] Step 2.9.1. If there is no balancing node in other power subnets, then randomly designate a generator node as the balancing node;

[0049] Step 2.9.2. Based on the specified slack node, perform AC power flow calculations on all power subnets respectively, and obtain the AC power flow calculation results;

[0050] Step 2.9.3. If the power flow calculation result does not converge, reduce the load on the nodes of the overloaded edge in the power subnet and return to step 2.9.2. If multiple load reductions still fail to converge, remove the edge with the most severe overload and return to step 2.8 to execute sequentially. If the AC power flow calculation result converges, it means that the processed cyber-physical network has reached equilibrium, and step 2.10 is executed.

[0051] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the timing attack sequence optimization method, and the processor is configured to execute the program stored in the memory.

[0052] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program is executed by a processor to perform the steps of the timing attack sequence optimization method.

[0053] Compared with existing technologies, the beneficial effects of this invention are reflected in:

[0054] 1. The method of this invention proposes a time-series attack model based on cyber-physical power networks, which can perform sequential attack cascading simulations on the power grid according to a specified attack sequence. This simulation not only considers the cascading fault propagation at the power grid level and the cascading fault propagation at the communication layer network, but also considers the fault propagation between the two layers of networks, thereby overcoming the limitations of existing models. The simulation results are closer to the real situation and provide a more reliable and accurate basis for decision-making.

[0055] 2. The method of this invention, at the physical layer of cyber-physical power networks, employs complete AC power flow equations and engineering constraints in the power grid, such as load-generation balance and islanding operation criteria, which have been used to appropriately address the physical problems of power systems. This invention considers multi-component faults and is based on an AC cascading fault model. This model captures branch overflow, bus load reduction, and branch faults through AC power flow and optimal power flow analysis, thereby overcoming the inaccurate and overly optimistic cascading prediction problems that DC power flow may cause. This improves the accuracy of power network simulation in CPPS, and the results obtained are more valuable for reference.

[0056] 3. This invention primarily improves the mutation part of the NSGA-II algorithm by incorporating the characteristics of complex networks and the electrical features of actual power grid nodes into the algorithm. Before optimizing the algorithm, the cyber-physical power network is analyzed, and nodes are ranked by importance based on the network's structural and electrical characteristics. During mutation, nodes with high importance are retained with a certain probability. Therefore, instead of randomly selecting genes for mutation, mutation is performed probabilistically after considering gene importance, significantly accelerating the convergence speed. This allows the algorithm to find the optimal attack sequence in a shorter time, facilitating rapid decision-making.

[0057] 4. This invention optimizes two objectives simultaneously, utilizing multi-objective optimization techniques to obtain multiple attack sequence schemes that are superior in both objectives. This allows cyber-physical network decision-makers to select the most suitable scheme based on actual conditions, thereby achieving the goal of balancing the structure and function of cyber-physical networks. Attached Figure Description

[0058] Figure 1 A schematic diagram of the cyber-physical network of this invention;

[0059] Figure 2 A schematic diagram of the timing attack sequence optimization process of this invention;

[0060] Figure 3 . Cross diagram of the present invention;

[0061] Figure 4 Schematic diagram of variations of this invention;

[0062] Figure 5 A schematic diagram of the timing attack simulation process of this invention. Detailed Implementation

[0063] In this embodiment, a method for optimizing the timing attack sequence of a cyber-physical power network based on an intelligent evolutionary algorithm includes the following steps:

[0064] Step 1. Initialization of the cyber-physical power network:

[0065] Step 1.1. Since the communication layer of the cyber-physical power network has scale-free characteristics, based on the number of nodes in the power network G1(N1, E1), a scale-free network G2(N2, E2) with the same number of nodes is constructed and used as the communication layer of the cyber-physical power network; where, Represents the set of power nodes in power network G1; E1 represents the set of communication nodes in the scale-free network G2; E2 and E1 represent the undirected path information of G1 and G2, respectively. This represents the i-th power node in power network G1. This represents the u-th communication node in the scale-free network G2, where o represents the total number of nodes. In the power network, nodes represent generators, transformers, loads, etc., while nodes in the communication layer represent sensors, which are responsible for reading and controlling the information of the corresponding power network nodes.

[0066] Step 1.2. Based on degree centrality, sort the nodes in G1 and G2 in descending order to obtain the sorted set of power nodes N′1 and communication nodes N′2. Communication layer nodes and power grid nodes are one-to-one correspondences and interdependent; power nodes require corresponding communication layer nodes for information reading and control, and communication layer nodes require power grid nodes for power supply. Couple the power grid layer and communication layer nodes one-to-one according to their degree centrality. The coupled cyber-physical network is as follows: Figure 1 As shown.

[0067] The nodes in the sorted power node set N′1 are coupled one by one with the nodes in the communication node set N′2 to obtain the cyber-physical power network and its coupling matrix B = [B (i，u) ], where B (i，u) Represents the i-th power node after sorting. With the u-th communication node The coupling value, if B (i，u) =1, which indicates the i-th power node. With the u-th communication node There exists an edge between B and B. (i，u) =0 indicates the i-th power node With the u-th communication node There is no edge between them;

[0068] Step 1.3. Make assumptions about each power node and the transmission branch represented by the edge in the power network G1:

[0069] (1) Let the states of each power node and edge in the power network G1 include: failure state and normal state;

[0070] (2) If any power node is in a failed state, the connected edges will also be in a failed state.

[0071] Step 2. Optimize the timing attack sequence for cyber-physical networks using an evolutionary algorithm improved from NSGA-II; the overall process is as follows: Figure 2 As shown.

[0072] Step 2.1. Construct the timing attack target function using equations (1) and (2) respectively:

[0073] f1=o′ max / o (1)

[0074]

[0075] In equations (1) and (2), f1 represents structural indicators, f2 represents functional indicators, and o′ max P represents the maximum number of nodes in the connected subnet of power network G1 after a time-series attack, and o′ represents the number of power nodes in power network G1 after a time-series attack; i Represents the i-th power node in power network G1 Load before the timing attack, P i′ This represents the i′-th power node in power network G1 after it has been subjected to a timing attack. The load capacity;

[0076] Step 2.2. Population Coding:

[0077] Define the population size as S, the number of evolutions as G, and the maximum number of generations as G. max The crossover probability of the population is P. c The population mutation probability is P m and initialize G = 1;

[0078] Based on the nodes in the cyber-physical power network, the Gth generation population A (G) Encode, Represents population A of generation G (G) The s-th individual represents the s-th temporal attack sequence; and Represents the s-th individual The j-th gene represents the j-th node number to be attacked; m is the length of the temporal attack sequence.

[0079] Step 2.3. Calculate the i-th power node in the power network G1 using equation (3). Importance indicators

[0080]

[0081] In equation (3), p and q are two weights. Represents the i-th power node The degree, Represents the i-th power node The load; the importance of power nodes is considered from both the structural and functional characteristics of the power network.

[0082] The u-th communication node in the scale-free network G2 is calculated using equation (4). Importance indicators

[0083]

[0084] In equation (4), Represents the u-th communication node The degree;

[0085] Step 2.4. For population A in generation G. (G) To perform a crossover operation, two individuals are randomly selected from the population, and a single-point crossover method is used. A gene is randomly selected as the crossover point, and the process is as follows: Figure 3 The crossover process is shown. After the crossover operation, all duplicate nodes in the resulting individuals are replaced with other unique nodes from the corresponding individuals, thus generating the G-th generation crossover population A′. (G) ;

[0086] Step 2.5. According to P m Determine the crossover population A′ of generation G. (G) If each offspring individual mutates, then the genes in the offspring individuals are sorted in descending order according to their importance index, resulting in a gene sequence number for each offspring individual. The probability of selecting each gene for mutation is then allocated based on this sequence number, with earlier sequences having lower probabilities. The probability of selecting each gene can be set as the gene sequence number divided by the sum of all gene sequence numbers. This allows for the selection of one gene from an offspring individual for mutation according to probability, resulting in the mutated offspring individual. The mutation process is as follows: Figure 4 As shown, the variant population A″ of the Gth generation is thus obtained. (G) , for A″ (G) Identical offspring individuals are discarded to obtain the Gth generation offspring population.

[0087] Step 2.6. Place A (G) and After merging, the merged population of generation G is obtained. Any individual in the group is denoted as express The j-th gene in the population; initialize j = 1; each individual in the population is equivalent to a temporal attack sequence, and the cyber-physical network is simulated to be attacked according to the sequence order. Steps 2.7-2.11 describe all the steps of the temporal attack, such as... Figure 5 As shown.

[0088] Step 2.7. The system attacks the initialized cyber-physical network and assigns the number of the attacked network to this system. Remove the nodes, their coupled nodes, and the edges that are connected to them;

[0089] Step 2.8. Inspect the removed cyber-physical network;

[0090] Step 2.8.1. For the removed power network, set the isolated node as the failed node, and also set all power nodes in the power subnet without generator nodes as failed nodes. Update the coupling matrix B, and set the row and column of the failed node to "0". When a power network node fails, its dependency relationship with the corresponding communication layer node also disappears.

[0091] For the removed communication network, the communication nodes that are not connected to the largest connected communication subnet are set as failed nodes, the coupling matrix B is updated, and the row and column of the failed node are set to "0"; when a communication network node fails, its dependency relationship with the corresponding power network node also disappears.

[0092] Step 2.8.2. Check if any of the remaining undone nodes have a value of "1" in the row and column of the coupling matrix B. If not, determine that the corresponding node is invalid and return to step 2.8; otherwise, proceed to step 2.9. If a power network node loses its corresponding communication layer node, it fails due to a lack of information reading and control. Similarly, if a communication layer node loses its corresponding power network node, it fails due to a loss of power supply.

[0093] Step 2.9. Perform AC power flow calculations on the cyber-physical network after the configuration fails:

[0094] Step 2.9.1. If there is no balancing node in other power subnets, then randomly designate a generator node as the balancing node;

[0095] Step 2.9.2. Based on the specified slack node, perform AC power flow calculations on all power subnets respectively, and obtain the AC power flow calculation results;

[0096] Step 2.9.3. If the power flow calculation result does not converge, reduce the load on the nodes of the overloaded edge in the power subnet and return to step 2.9.2. If multiple load reductions still fail to converge, remove the edge with the most severe overload and return to step 2.8 to execute sequentially. If the AC power flow calculation result converges, it means that the processed cyber-physical network has reached equilibrium, and step 2.10 is executed.

[0097] After assigning j+1 to j in step 2.10, if j>m, then it means... The attack ends, and step 2.11 is executed; otherwise, return to step 2.7 and execute sequentially.

[0098] Step 2.11. Calculate according to equations (1) and (2). The fitness value of the first objective function f1 The fitness value of the second objective function f2

[0099] Step 2.12. Following the process of steps 2.7-2.11, we obtain... The fitness values ​​of all individuals are determined, and adjustments are made based on these fitness values. Individuals in the population are subjected to a fast non-dominated sorting and crowding distance is calculated, thereby obtaining population A in generation G+1 using a tournament selection strategy. (G+1) ;

[0100] Step 2.13. After assigning G+1 to G, determine if G > G. max Check if the condition is met. If it is met, the final population A is obtained; otherwise, return to step 2.4 and execute sequentially.

[0101] Step 2.14. Take all individuals in the first level of the final population A as the Pareto optimal solution set, and take the timing attack scheme corresponding to the Pareto optimal solution set as the optimal timing attack scheme.

[0102] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0103] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

Claims

1. A method for optimizing the temporal attack sequence of a cyber-physical power network based on an intelligent evolutionary algorithm, characterized in that, Includes the following steps: Step 1. Initialization of the cyber-physical power network: Step 1.

1. Based on the power network To construct a scale-free network with the same number of nodes, use the same number of nodes. And it serves as the communication layer of the cyber-physical power network; among which, Represents power network The set of power nodes; Represents scale-free networks The set of communication nodes; and They represent and Undirected path information; Represents power network No. i One power node, Represents scale-free networks The Middle One communication node, Indicates the total number of nodes; Step 1.

2. Based on degree centrality, for and Sort the nodes in the array in descending order to obtain the sorted set of power nodes. and communication node set ; The sorted set of power nodes The set of nodes and communication nodes in The nodes in the network are coupled one by one to obtain the cyber-physical power network and its coupling matrix B=[ ,in, Indicates the sorted order of the first... i Power nodes With the Communication nodes The coupling value, if =1, then it means the first i Power nodes With the Communication nodes There exists an edge between them, if =0, then it means the first i Power nodes With the Communication nodes There is no edge between them; Step 1.

3. For the power network Assumptions are made regarding the power nodes and transmission branches represented by the edges in the data: (1) Make the power network The states of each power node and edge in the data include: failure state and normal state; (2) If any power node is in a failed state, the connected edges will also be in a failed state. Step 2. Optimize the timing attack sequence for cyber-physical networks using an evolutionary algorithm improved from NSGA-II; Step 2.

1. Construct the timing attack target function using equations (1) and (2) respectively: (1) (2) In equations (1) and (2), Indicates structural indicators, Indicates functional indicators, Represents power network The maximum number of nodes in a connected subnet after a time-series attack. Represents power network The number of power nodes after a timing attack; Represents power network The i-th power node Load before being subjected to a timing attack Represents power network The first time after being subjected to a timing attack Power nodes The load capacity; Step 2.

2. Population Coding: Define population size as Number of evolutions Maximum number of generations The crossover probability of the population is The population mutation probability is and initialize ; Based on the nodes in the cyber-physical power network, the Gth generation population Encode, , Represents the Gth generation population The s-th individual represents the s-th temporal attack sequence; and , Represents the s-th individual The j-th gene represents the j-th node number to be attacked; m is the length of the temporal attack sequence. Step 2.

3. Calculate the power network using equation (3). The Middle i Power nodes Importance indicators : (3) In equation (3), p and q are two weights. Representing the i Power nodes The degree, Representing the i Power nodes The load; Calculate the scale-free network using equation (4) The middle of Communication nodes Importance indicators : (4) In equation (4), Representing the Communication nodes The degree; Step 2.

4. For the Gth generation population Perform a crossover operation, and replace all duplicate nodes in the resulting individuals with other unique nodes from the corresponding individuals, thereby generating the first... Crossover population ; Step 2.

5. According to Determine the first Crossover population If each offspring individual mutates, and if so, the genes in the offspring individuals are sorted in descending order according to their importance index to obtain their gene sequence numbers. The probability of selecting each gene in the offspring individual for mutation is then allocated based on these sequence numbers; the earlier the sequence number, the lower the probability. One gene from each offspring individual is selected for mutation according to these probabilities, resulting in the mutated offspring individual. This process yields the [number of offspring individuals]. Generational variant population ,right Discard identical offspring individuals to obtain the first generation. Offspring population ; Step 2.

6. and After merging, we get the first Merging populations , Any individual in the group is denoted as , express The j-th gene in the sequence; initialize j=1; Step 2.

7. The system inputs information to launch an attack on the physical network, and the attacked network is identified by the number [number to be inserted]. Remove the nodes, their coupled nodes, and the edges that are connected to them; Step 2.

8. Detect and configure failed nodes in the removed cyber-physical network; Step 2.

9. Perform AC power flow calculations on the cyber-physical network after the configuration fails to determine whether the processed cyber-physical network has reached equilibrium; After assigning j+1 to j in step 2.10, if j>m, then it means... The attack ends, and step 2.11 is executed; otherwise, return to step 2.7 and execute sequentially. Step 2.

11. Calculate according to equations (1) and (2). The first objective function fitness value and the second objective function fitness value ; Step 2.

12. Obtain the following steps: Steps 2.7-2.11 The fitness values ​​of all individuals are determined, and adjustments are made based on these fitness values. The individuals in the pool are subjected to a fast non-dominated sort and crowding distance is calculated, thereby employing a tournament selection strategy to obtain the [number]th [unit / item]. Generations of population ; Step 2.

13. After assigning G+1 to G, determine... If the condition is met, it means the final population has been obtained. Otherwise, return to step 2.4 and execute sequentially. Step 2.

14. Obtain the final population All individuals in the first level are considered as the Pareto optimal solution set, and the timing attack scheme corresponding to the Pareto optimal solution set is taken as the optimal timing attack scheme.

2. The method for optimizing the temporal attack sequence of cyber-physical power networks based on intelligent evolutionary algorithms according to claim 1, characterized in that, Step 2.8 includes: Step 2.8.

1. For the removed power network, set the isolated node as the failed node, and also set all power nodes in the power subnet without generator nodes as failed nodes. Update the coupling matrix B and set the row and column of the failed node to "0". For the removed communication network, the communication nodes that are not connected to the largest connected communication subnet are set as failed nodes, the coupling matrix B is updated, and the row and column of the failed node are set to "0"; Step 2.8.

2. Check if the remaining non-failed nodes have a value of "1" in the row and column of the coupling matrix B. If not, determine that the corresponding node is failed and return to step 2.8 to execute; otherwise, execute step 2.

9.

3. The method for optimizing the temporal attack sequence of cyber-physical power networks based on intelligent evolutionary algorithms according to claim 2, characterized in that, Step 2.9 includes: Step 2.9.

1. If there is no balancing node in other power subnets, then randomly designate a generator node as the balancing node; Step 2.9.

2. Based on the specified slack node, perform AC power flow calculations on all power subnets respectively, and obtain the AC power flow calculation results; Step 2.9.

3. If the power flow calculation result does not converge, reduce the load on the nodes of the overloaded edge in the power subnet and return to step 2.9.

2. If multiple load reductions still fail to converge, remove the edge with the most severe overload and return to step 2.8 to execute sequentially. If the AC power flow calculation result converges, it means that the processed cyber-physical network has reached equilibrium, and step 2.10 is executed.

4. 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 any of the timing attack sequence optimization methods of claims 1-3, and the processor is configured to execute the program stored in the memory.

5. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program, when executed by the processor, performs the steps of the timing attack sequence optimization method according to any one of claims 1-3.

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