A Multi-Region Power System Defense Method Based on Virtual Networks

Abstract

This invention discloses a multi-regional power system defense method based on a virtual network, specifically comprising: constructing a physical network of the power system; dividing the entire physical network of the power system into multiple mutually coupled regions; calculating the comprehensive key index of the i-th region; determining key regions based on the comprehensive key index; constructing a virtual network based on the existing physical topology of the power system, and allocating resources to key regions during the construction of the virtual network; then introducing a coupling matrix between the physical network and the virtual network to connect the virtual network and the physical network; optimizing the constructed virtual network; and using the optimized virtual network to absorb and disperse attack signals. This invention improves the collaborative defense capability and operational resilience of the smart grid when subjected to false data injection attacks, while also taking into account cost control and system feasibility.

Description

Technical Field

[0001] This invention belongs to the field of power system security protection technology, and in particular relates to a multi-regional power system defense method based on virtual networks. Background Technology

[0002] With the continuous development of smart grids, traditional power systems are gradually evolving towards a highly information-based and networked direction, and the measurement, communication, and control links in the system are increasingly reliant on information networks. However, this deep integration of cyber and physical systems exacerbates the vulnerability of power systems to malicious attacks. False data injection (FDI) attacks, as a typical and highly covert form of cyberattack, can manipulate power system measurement data without being detected by traditional anomaly detection methods, inducing the control system to make incorrect decisions, and even leading to system instability and large-scale power outages.

[0003] Current research on defense against spoofed data injection attacks in smart grids has made some progress, covering multiple directions such as anomaly detection in state estimation, optimization of frequency control mechanisms, and communication security hardening. However, existing research mainly focuses on local or single-region scenarios, and the following prominent problems remain in the identification of system structural vulnerabilities and multi-region collaborative defense:

[0004] 1. Lack of multi-regional system coupling modeling and collaborative defense mechanisms

[0005] Existing research employs the Federation Transformer-FL detection method to collaboratively identify FDI attacks across nodes. However, this method focuses on data collaboration and privacy protection, without delving into modeling the system structure and electrical coupling mechanisms; its defensive capabilities are significantly limited when facing cross-regional collaborative attacks. In smart grids, existing defense mechanisms struggle to accurately assess the comprehensive structural and electrical importance of different regions within the power system, resulting in a lack of targeted and scientific allocation of defense resources.

[0006] 2. The defense methods are too simplistic and lack the ability to combine structural and electrical features for reinforcement.

[0007] Most current defense strategies only focus on single aspects such as electrical anomaly detection (e.g., voltage / frequency offset) or communication path encryption, lacking modeling and identification of system structural vulnerabilities (e.g., concentrated load paths, critical connection edges), and thus cannot support joint defense mechanisms optimized for regional structures. Faced with the costs and operational difficulties of large-scale deployment, existing physical reconfiguration methods lack flexibility and feasibility, making it difficult to control system transformation costs while ensuring defense effectiveness.

[0008] 3. Lack of deployable and controllable network defense structure optimization methods

[0009] Some research has begun to introduce virtual network construction or deep learning methods to enhance system robustness, but these often suffer from problems such as model complexity, high training costs, and lack of engineering feasibility. Especially in strongly constrained and tightly coupled physical systems like power grids, there is a lack of network topology optimization schemes that balance global defense capabilities, deployment cost control, and real-time performance. Traditional heuristic-based network optimization methods are prone to getting trapped in local optima, making it difficult to achieve optimal allocation of defense resources from a global perspective, and they lack the ability to balance cost and defense effectiveness. Summary of the Invention

[0010] Purpose of the invention: In order to solve the problems existing in the prior art, the present invention provides a multi-regional power system defense method based on virtual networks.

[0011] Technical Solution: This invention provides a multi-regional power system defense method based on a virtual network, specifically including the following steps:

[0012] Read the parameters of generators, loads and branches in the power system to construct the physical network of the power system;

[0013] The physical network of the entire power system is divided into multiple mutually coupled regions;

[0014] Based on the structural characteristics of the i-th region and key electrical indicators Calculate the comprehensive key indicators for the i-th region. ;

[0015] Key areas were identified based on comprehensive key indicators;

[0016] Based on the topology of the power system, a virtual network is constructed, and resources are tilted towards key areas during the construction of the virtual network; then a coupling matrix between the physical network and the virtual network is introduced to connect the virtual network and the physical network.

[0017] Optimize the constructed virtual network;

[0018] An optimized virtual network is used to absorb and disperse attack signals.

[0019] Furthermore, the physical network of the power system is divided into multiple mutually coupled regions using the following strategy:

[0020] 1. Group nodes whose physical connection edge density exceeds a preset density threshold into the same region;

[0021] 2. Group nodes whose distance is less than a preset distance threshold into the same region;

[0022] 3. Nodes whose tidal power flow intensity is greater than the preset power flow intensity threshold are grouped into the same region;

[0023] 4. If the density of power transmission in a certain area is higher than the preset power transmission density threshold, the nodes in that area will be classified into the same area.

[0024] Furthermore, the structural features of the i-th region The expression is as follows:

[0025] ;

[0026] Where j1 is the adjacent region of the i-th region. Let i be the set of adjacent regions of the i-th region. and Let j1 be the degree centrality of the adjacent region and i be the degree centrality of the i-th region, respectively. The expression is:

[0027] ;

[0028] Where m is the total number of regions. Let be the correlation coefficient between the i-th region and the j-th region. If the i-th region and the j-th region are adjacent, then... ,otherwise .

[0029] Furthermore, the key electrical indicators for the i-th region The expression is as follows:

[0030] ;

[0031] in, For the initial power distribution of the power system, Let be the power of the power system when a fault occurs in the i-th region.

[0032] Furthermore, the comprehensive key indicators for the i-th region The expression is as follows:

[0033]

[0034] in, and All are weighting coefficients. and These represent the normalized structural characteristics and key electrical indicators, respectively.

[0035] Furthermore, determining key areas based on comprehensive key indicators specifically involves designating areas where the value of the comprehensive key indicator is greater than a preset indicator threshold as key areas.

[0036] Furthermore, the construction of the virtual network specifically involves constructing the virtual network based on the following model:

[0037] ;

[0038] in, This represents the local state matrix of all generators in the physical network of the power system. Composed of multiple Composed of vertical stacking, for The first derivative, Indicates the first The local state matrix of the generator. , and These are the generator's rotor angle and angular frequency offset, respectively. , ,in It is the generator's coefficient of inertia. It is the damping coefficient of the generator. For the steady-state input of the physical network of the power system; For the state variables of the virtual network, for The first derivative, For the system matrix of virtual networks, This represents the coupling matrix between the physical network and the virtual network. These are the steady-state initial values ​​of the physical network. Let I be the constant to be designed, I be the identity matrix, and L be the Laplace matrix of the physical network.

[0039] Furthermore, the virtual network is optimized using the annealing algorithm, specifically as follows:

[0040] Step 1: Set the initial temperature, the final temperature, and the cooling rate;

[0041] Step 2: Generate the current neighborhood solution E and the coupling matrix between the physical network and the virtual network during the current iteration. The neighborhood solution is the topology of the virtual network. The feasibility of the generated neighborhood solution E is checked to ensure that it meets the system constraints.

[0042] Calculate the following objective function based on E and T. :

[0043] ;

[0044] Where m represents the total number of regions, The cost of constructing the virtual network and coupling matrix; This represents the offset of the j-th region in the system after the attack.

[0045] Step 3: Subtract the value of the objective function at the current iteration from the value of the objective function at the previous iteration to obtain the increment value. ;

[0046] Step 4: If Alternatively, if the Metropolis criterion is satisfied, then retain the E and E generated in the current iteration. The current neighborhood solution and coupling matrix are used as the first solution; otherwise, the neighborhood solution and coupling matrix generated in the previous iteration are used as the current neighborhood solution and coupling matrix. The Metropolis criterion is... ,in A random number between 0 and 1, where Temp is the temperature at the current iteration;

[0047] Step 5: Calculate the value of the objective function based on the current neighborhood solution and coupling matrix. And the value of the objective function calculated based on the optimal neighborhood solution and the coupling matrix. Compare; if Then the current neighborhood solution and coupling matrix are taken as the optimal solution;

[0048] Step 6: Perform a temperature update operation, repeating steps 2-5 until the current temperature drops to the set termination temperature. The algorithm then terminates, outputting the optimal virtual network topology and coupling matrix.

[0049] A computer device includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the computer program to implement the aforementioned multi-regional power system defense method based on a virtual network.

[0050] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned method for defending a multi-regional power system based on a virtual network.

[0051] Beneficial Effects: The virtual network designed in this invention can effectively absorb disturbances from low-frequency attacks while maintaining low deployment costs. When attack resources are preferentially concentrated in critical areas with high criticality in the system, this invention, through area identification and virtual buffering mechanisms, can still effectively limit the state deviation of critical areas and maintain the overall stability of the system. Under frequent disturbance attacks, this invention effectively buffers the shock waves of high-frequency disturbances through the structural decoupling and energy absorption mechanisms of the virtual network. When attacks are frequent and concentrated on high-criticality areas, this invention, on the one hand, deploys a virtual network buffer layer in advance through early warning area identification, and on the other hand, optimizes the virtual network topology structure with simulated annealing algorithms, achieving high stability of the state of critical areas while maintaining deployment cost control. This invention improves the collaborative defense capability and operational resilience of smart grids when subjected to false data injection attacks, and also takes into account cost control and system feasibility. Attached Figure Description

[0052] Figure 1 This is a flowchart of the present invention;

[0053] Figure 2 The response diagrams of the virtual network constructed by this invention and the physical network of the original power system under scenario one;

[0054] Figure 3 The response diagrams of the virtual network constructed by this invention and the physical network of the original power system under scenario two are shown.

[0055] Figure 4 The response diagrams of the virtual network constructed by this invention and the physical network of the original power system under scenario three are shown.

[0056] Figure 5 The response diagrams of the virtual network constructed by this invention and the physical network of the original power system are shown in Scenario 4. Detailed Implementation

[0057] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0058] like Figure 1 As shown, this invention discloses a multi-regional power system defense method based on a virtual network, specifically as follows:

[0059] Power network topology model construction

[0060] This embodiment constructs a power network topology model based on the IEEE 39-bus standard test system. ,in: This represents the set of nodes in a power system, including generator nodes and load nodes; This represents the set of connecting edges between nodes, where each edge corresponds to a transmission line (branch) in the power grid.

[0061] The PYPOWER power system simulation tool library was used to import EEE 39-node system data, read generator, load, and branch parameters, and construct the following mapping relationship:

[0062] (1) Each generator corresponds one-to-one with a generator node in the topology model;

[0063] (2) Each load corresponds one-to-one with a load node in the topology model;

[0064] (3) Each branch corresponds one-to-one with an edge in the topology model.

[0065] The final topology It satisfies the following characteristics:

[0066] (1) The total number of nodes is ;

[0067] (2) All nodes satisfy Kirchhoff constraints on voltage and current.

[0068] Power system regional division

[0069] To implement differentiated defense strategies for multi-regional systems, this invention is based on a constructed power network topology map. The system is divided into regions.

[0070] Regional division strategy

[0071] The entire power network The system is divided into multiple coupled physical regions, each containing several adjacent generator nodes and load nodes. The division principles include the following two aspects:

[0072] (1) Structural adjacency: Prioritize grouping nodes with dense physical connection edges and close node distances into the same region;

[0073] (2) Electrical coupling: Consider the power flow intensity between nodes, and prioritize nodes in dense power transmission areas to be classified as a unified area.

[0074] Alternatively, a method based on structural clustering (such as spectral clustering or fuzzy clustering) can be used to divide the node set V into m structural-electrical coupling regions.

[0075] Based on the topology of the IEEE 39-node system, this embodiment divides the power grid into three regions, defining the set of nodes contained in each region:

[0076] Region 1: Nodes {1, 4-14, 31, 32, 39};

[0077] Region 2: Nodes {2, 3, 17, 18, 25-30, 37, 38};

[0078] Region 3: Nodes {15,16,19-24,33-36}.

[0079] Importance assessment model based on regional multidimensional features

[0080] This invention provides an importance assessment model based on regional multidimensional features to identify critical regions in a multi-regional power system when facing FDI attacks, in order to support subsequent differentiated defense resource configuration.

[0081] (1) Key structural features: The connectivity complexity and structural redundancy of the region in the power grid are quantified by mapping entropy;

[0082] For a multi-region power system, define an adjacency symmetric matrix between each region. m represents the total number of regions. For the region With the region The correlation coefficient, if the region With the region Adjacent, Otherwise 0, no. The set of adjacent regions of each region is denoted as: . No. Degree centrality of each region It can then be expressed as:

[0083] ;

[0084] Based on this, mapping entropy is introduced to obtain the criticality of structural features. :

[0085] ;

[0086] (3) Key Electrical Indicators: In order to quantify the electrical characteristics of different areas in the power grid, this embodiment introduces the Outage Distribution Factor (ODF) to establish a dynamic correlation model between line outages and power redistribution. The initial power distribution of the system, This describes the system power distribution after a power outage. Key electrical indicators are defined as follows:

[0087] ;

[0088] in, For the initial power distribution of the power system, Let be the power of the power system when a fault occurs in the i-th region.

[0089] Normalized index and After that, I received and Determine the first using the entropy weight method Comprehensive key indicators for each region As shown below:

[0090] ;

[0091] Then, and and represent weights, respectively. The two types of features mentioned above are combined to form a regional criticality index, which is used to quantitatively measure the criticality of each region in system stability and attack propagation. Through regional criticality, the system can prioritize the identification and protection of high-risk areas vulnerable to cross-regional FDI attacks, laying the foundation for differentiated defense deployment. t represents time.

[0092] for This embodiment utilizes the admittance matrix. Based on the power flow results, calculate the power disturbance response of each region under fault conditions. Specifically: for each region... Calculate the disturbance response matrix from the set of relevant branches S. :

[0093] ;

[0094]

[0095] in, It is a diagonal matrix formed by the reciprocals of the branch impedances. for The inverse matrix, Let T be the branch-node incidence matrix; T represents the matrix transpose, and I represents the identity matrix.

[0096] In the IEEE 39-node standard test system, the comprehensive key performance indicators for each region calculated in this embodiment are shown in Table 1 below:

[0097] Table 1

[0098]

[0099] As shown in Table 1 above, Region 3 has the highest overall criticality and should be given special protection.

[0100] Multi-regional power grid collaborative defense strategy based on virtual networks

[0101] To enhance the collaborative defense capabilities of multi-regional power systems against FDI attacks, this invention introduces a virtual defense network. Through logical mapping, a low-cost buffering and coordination mechanism is achieved without altering the original physical structure. Furthermore, simulated annealing algorithms are used to optimize the topology and coupling methods of the virtual network, achieving a balance between performance and cost.

[0102] In power systems, the dynamic behavior of generators plays a crucial role in system stability. The motion of a synchronous generator can be described by the swing equation:

[0103] ;

[0104] In the equation, This indicates the generator's output power. , This indicates the mechanical input power of the generator. This indicates the injected power of the generator. and These are the generator's rotor angle and angular frequency offset, respectively. for The first derivative, for The first derivative, It is the generator's coefficient of inertia. This is the damping coefficient of the generator. After simplification, it becomes:

[0105] ;

[0106] in, , It is the first The local state (two-dimensional vector) of a generator. It is to put all the generators The overall state after vertical stacking. for The first derivative; , , Let I be the number of generator bus nodes, I be the identity matrix, and L be the Laplace matrix of the physical network. This is the input to the physical network.

[0107] This invention proposes a collaborative defense strategy based on regional criticality using a virtual hidden network. By constructing a virtual network coupled with the physical power grid, it absorbs and buffers FDI attacks, thereby improving the overall robustness of the system. The designed model is as follows:

[0108] ;

[0109] In the model, These are the steady-state initial values ​​of the physical network. For the steady-state input of the physical network, This represents the coupling matrix between the physical network and the virtual network. For the constant to be designed, For the state variables of the virtual network, for The first derivative, This is the system matrix for virtual networks.

[0110] The virtual network design strategy in this embodiment is as follows:

[0111] First, based on the aforementioned criticality indicators, identify the target areas that require key protection; in the virtual network topology optimization, resources should be selectively allocated to key areas to achieve differentiated configuration.

[0112] Then, without changing the existing physical topology, a layer of virtual hidden network is introduced, whose node structure forms a one-to-one mapping relationship with the physical area nodes;

[0113] Establish a virtual-physical network coupling matrix to describe the intensity of the interaction between virtual network nodes and physical network nodes.

[0114] After an attack signal enters the system, it can first be absorbed and dispersed in the virtual network, thereby reducing the direct impact of the attack on critical areas of the physical network.

[0115] When the physical state deviates from the normal range, the virtual network immediately senses it and generates compensation items. By injecting into the physical layer, feedback suppression and energy buffering of attack disturbances can be achieved, enhancing defense resilience without deforming the system, and avoiding the high cost and engineering infeasibility problems caused by directly optimizing or modifying the actual power grid.

[0116] A Global Optimization Method for Virtual Network Topology Based on Simulated Annealing Algorithm

[0117] To improve the defense performance and deployment efficiency of virtual networks, this invention further proposes a virtual network topology optimization method based on simulated annealing algorithm. This method achieves a low-cost buffering and coordination mechanism without altering the original physical structure through logical mapping. Furthermore, it combines simulated annealing algorithm to optimize the topology and coupling methods of the virtual network, achieving a balance between performance and cost, thus realizing joint performance-cost optimization.

[0118] This embodiment uses the simulated annealing algorithm to generate the virtual network and its coupling matrix. The index function of the simulated annealing algorithm is designed as follows:

[0119]

[0120] In the function, To account for the cost of constructing virtual networks and coupled networks, These are the key regional indicators derived above. This represents the offset of the j-th region after the attack.

[0121] The key steps of this method include:

[0122] (1) Define the optimization objective function, taking into account the following:

[0123] The degree of steady-state shift of the system under attack disturbance;

[0124] Regional criticality weight;

[0125] The deployment cost of virtual network nodes and coupled connections;

[0126] (2) Initialize the virtual network topology and coupling matrix;

[0127] (3) Apply simulated annealing algorithm to iteratively search for the optimal solution. In each iteration:

[0128] Local perturbation topology;

[0129] Evaluate changes in the objective function;

[0130] Update the network structure according to the acceptance probability criterion;

[0131] It outputs a virtual network topology and coupling configuration scheme with optimal defense performance and controllable deployment costs.

[0132] The annealing algorithm in this embodiment is as follows:

[0133] 1. Virtual Network Construction

[0134] Design a configurable virtual network Its topology is independent of the physical topology of the power grid, serving as a logical layer security defense platform. Virtual Node Represented as virtual monitoring points; edge This indicates its communication or response path.

[0135] 2. Optimize configuration using simulated annealing algorithm.

[0136] The steps are as follows:

[0137] First, set the initial temperature. Termination temperature and cooling rate And initialize the solution structure.

[0138] In each iteration, perform the following steps:

[0139] Generate a neighborhood solution of the current solution. and the corresponding coupling matrix This step calls a predefined neighborhood perturbation function; the neighborhood solution is also the topology of the virtual network.

[0140] Perform a feasibility check on the generated neighborhood solutions to ensure that they meet the system constraints.

[0141] Calculate the objective function value corresponding to the current solution based on the objective function (i.e., the index function mentioned above). And the solution from the previous round The difference is calculated to obtain the increment value. ;

[0142] If the increment value Or it satisfies the Metropolis criterion, i.e., random numbers. If so, then the current neighborhood solution is accepted as the new current solution;

[0143] If the objective function value of the new current solution is better than the objective function value of the historical best solution, then update the historical best record and save the optimal structure simultaneously.

[0144] Perform a temperature update operation: Set the current temperature Gradually reduce the "acceptance probability" during the search process.

[0145] Repeat the above process until the current temperature drops to the set termination temperature. The algorithm terminates here. The final optimal topology is: The coupling matrix is .

[0146] This embodiment sets up four scenarios.

[0147] Scenario 1: Low-frequency, non-targeted attack

[0148] This scenario simulates an attacker launching a low-frequency, non-directional FDI attack on a power grid system under resource constraints. Attack resources are evenly distributed across regions, and regional importance is not considered, simulating situations where the attacker lacks system structure information or employs a random strategy.

[0149] The specific system response results are as follows: Figure 2 As shown. In this baseline scenario, the virtual network designed in this invention can effectively absorb disturbances caused by low-frequency attacks while maintaining low deployment costs, thus ensuring the stability of system operation.

[0150] Scenario 2: Low-frequency – Targeted attack

[0151] To maintain a low attack frequency, this scenario introduces an attack resource allocation mechanism based on regional criticality indicators. Attack resources are preferentially concentrated in critical areas of the system with high criticality, simulating attackers with knowledge of the system structure.

[0152] Compared to scenario one, targeted attacks significantly enhance the ability to disrupt critical areas of the system. Specific system response results are as follows: Figure 3 As shown, the present invention can still effectively limit the state shift of critical areas under the action of region identification and virtual buffering mechanism.

[0153] Scenario 3: High-frequency – non-targeted attacks

[0154] This scenario simulates an attacker using a high-frequency dynamic injection method to disrupt system operation. The attack resources are still evenly distributed, similar to the random strategy in scenario one, but the attack pace is significantly increased.

[0155] Under frequent disturbances, system stability faces greater challenges. For example... Figure 4 As shown, this invention effectively buffers the shock waves of high-frequency disturbances through the structural decoupling and energy absorption mechanism of virtual networks, significantly reducing the drastic fluctuations of critical system state variables.

[0156] Scenario 4: High-frequency – targeted attacks

[0157] This scenario combines high-frequency attack execution with a resource-focused strategy based on criticality indicators, simulating an extreme case of a powerful attacker with system knowledge launching a coordinated attack. The attacks are frequent and concentrated in high-criticality areas, making it an important test scenario for evaluating system resilience.

[0158] like Figure 5 As shown, this invention exhibits the strongest defensive capability in this scenario: on the one hand, it pre-deploys a virtual network buffer layer through early warning area identification; on the other hand, it optimizes the virtual network topology using simulated annealing algorithms, achieving high stability of the critical area state while maintaining deployment cost control. Experimental results verify the significant resilience advantage of this method under high-intensity, intelligent attack conditions.

[0159] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

Claims

1. A multi-regional power system defense method based on virtual networks, characterized in that, Specifically, the steps include the following: Read the parameters of generators, loads and branches in the power system to construct the physical network of the power system; The physical network of the entire power system is divided into multiple mutually coupled regions; Based on the structural characteristics of the i-th region and key electrical indicators Calculate the comprehensive key indicators for the i-th region. ; Key areas are identified based on comprehensive key indicators; Based on the topology of the power system, a virtual network is constructed, and resources are tilted towards key areas during the construction of the virtual network; Then, a coupling matrix between the physical network and the virtual network is introduced to connect the virtual network and the physical network; Optimize the constructed virtual network; An optimized virtual network is used to absorb and disperse attack signals.

2. The method for multi-regional power system defense based on virtual networks according to claim 1, characterized in that, The physical network of the power system is divided into multiple coupled regions using the following strategy:

1. Group nodes whose physical connection edge density exceeds a preset density threshold into the same region; 2. Group nodes whose distance is less than a preset distance threshold into the same region; 3. Nodes whose tidal power flow intensity is greater than the preset power flow intensity threshold are grouped into the same region; 4. If the density of power transmission in a certain area is higher than the preset power transmission density threshold, the nodes in that area will be classified into the same area.

3. The method for multi-regional power system defense based on virtual networks according to claim 1, characterized in that, Structural features of the i-th region The expression is as follows: ； Where j1 is the adjacent region of the i-th region. Let i be the set of adjacent regions of the i-th region. and Let j1 be the degree centrality of the adjacent region and i be the degree centrality of the i-th region, respectively. The expression is: ； Where m is the total number of regions. Let be the correlation coefficient between the i-th region and the j-th region. If the i-th region and the j-th region are adjacent, then... ,otherwise .

4. A multi-regional power system defense method based on a virtual network according to claim 1, characterized in that, Key electrical indicators for the i-th region The expression is as follows: ； in, For the initial power distribution of the power system, Let be the power of the power system when a fault occurs in the i-th region.

5. A multi-regional power system defense method based on a virtual network according to claim 1, characterized in that, The comprehensive key indicators of the i-th region The expression is as follows: ； in, and All are weighting coefficients. and These represent the normalized structural characteristics and key electrical indicators, respectively.

6. A multi-regional power system defense method based on a virtual network according to claim 1, characterized in that, The key areas determined by comprehensive key indicators are those areas whose comprehensive key indicator values ​​are greater than preset threshold values.

7. A multi-regional power system defense method based on a virtual network according to claim 1, characterized in that, The construction of the virtual network specifically involves constructing the virtual network based on the following model: ； in, This represents the local state matrix of all generators in the physical network of the power system. Composed of multiple Composed of vertical stacking, for The first derivative, Indicates the first The local state matrix of the generator. , and These are the generator's rotor angle and angular frequency offset, respectively. , ,in It is the generator's coefficient of inertia. It is the damping coefficient of the generator. For the steady-state input of the physical network of the power system; For the state variables of the virtual network, for The first derivative, For the system matrix of virtual networks, This represents the coupling matrix between the physical network and the virtual network. The steady-state initial values ​​of the physical network, Let I be the constant to be designed, I be the identity matrix, and L be the Laplace matrix of the physical network.

8. A multi-regional power system defense method based on a virtual network according to claim 1, characterized in that, The virtual network is optimized using the annealing algorithm, specifically as follows: Step 1: Set the initial temperature, the final temperature, and the cooling rate; Step 2: Generate the current neighborhood solution E and the coupling matrix between the physical network and the virtual network during the current iteration. The neighborhood solution is the topology of the virtual network. The feasibility of the generated neighborhood solution E is checked to ensure that it meets the system constraints. Calculate the following objective function based on E and T. : ； Where m represents the total number of regions, The cost of constructing the virtual network and coupling matrix; This represents the offset of the j-th region in the system after the attack. Step 3: Subtract the value of the objective function at the current iteration from the value of the objective function at the previous iteration to obtain the increment value. ; Step 4: If Alternatively, if the Metropolis criterion is satisfied, then retain E generated in the current iteration and The current neighborhood solution and coupling matrix are used as the first solution; otherwise, the neighborhood solution and coupling matrix generated in the previous iteration are used as the current neighborhood solution and coupling matrix. The Metropolis criterion is... ,in A random number between 0 and 1, where Temp is the temperature at the current iteration; Step 5: Calculate the value of the objective function based on the current neighborhood solution and coupling matrix. And the value of the objective function calculated based on the optimal neighborhood solution and the coupling matrix. Compare; if Then the current neighborhood solution and coupling matrix are taken as the optimal solution; Step 6: Perform a temperature update operation, repeating steps 2-5 until the current temperature drops to the set termination temperature. The algorithm then terminates, outputting the optimal virtual network topology and coupling matrix.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, When the processor executes the computer program, it implements a multi-regional power system defense method based on a virtual network as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements a multi-regional power system defense method based on a virtual network as described in any one of claims 1 to 8.

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