Method, device and medium for identifying key nodes of a power coupling network

Abstract

The application relates to a key node identification method, device, equipment and medium of an electric power coupling network. A power station and a power-on relay in an electric power system are taken as an application node and a transition node of a physical layer network respectively, a logical node is constructed by the application node, a logical layer network of a structure of an undirected and weightless graph representing communication capability is built, the electric power system is modeled into a physical-logical coupling network, a logical edge centrality score in the logical layer network is calculated by using a hybrid centrality measurement, a logical edge criticality list is arranged in descending order according to the scores, a target logical edge is selected according to the sequence, corresponding transition nodes in the physical layer network are determined, a plurality of shortest paths between the two are calculated, path nodes are taken as candidate nodes to be removed, the candidate nodes and corresponding logical edges are removed, a change of a maximum connected component of the logical layer network is taken as a damage rate, and when the damage rate reaches a preset value, the removed nodes are key nodes. The method can effectively and quickly identify key nodes of an electric power network.

Description

Technical Field

[0001] This application relates to the field of power system technology, and in particular to a method, apparatus, device, and medium for identifying key nodes in a power coupled network. Background Technology

[0002] In the power system field, with the continuous expansion of power grid scale and intelligent development, the stability and security of power coupled networks are crucial. Currently, traditional power coupled network analysis methods have limitations in identifying critical nodes. On the one hand, many methods do not fully consider the coupling characteristics between the physical and logical layers, failing to accurately locate nodes that play a key supporting role in the overall network function. On the other hand, existing technologies struggle to accurately measure the impact of nodes on network connectivity and reliability when dealing with complex power transmission and communication relationships. This leads to a failure to quickly implement effective countermeasures when the power grid suffers faults or attacks, potentially causing serious consequences such as widespread power outages.

[0003] Therefore, there is an urgent need for a more efficient and accurate method for identifying key nodes in power coupling networks to ensure the stable operation of the power system and improve the reliability and security of power supply. Summary of the Invention

[0004] Therefore, it is necessary to provide a method, apparatus, device, and medium for identifying key nodes in a power coupling network that can accurately identify key network nodes, addressing the aforementioned technical problems.

[0005] A method for identifying key nodes in a power coupling network, the method comprising:

[0006] Obtain relevant information about a power system, which includes multiple interconnected power plants and power relays;

[0007] A physical layer network is constructed based on the relevant information of the power system. Power plants and power relays are respectively used as application nodes and transition nodes in the physical layer network. Corresponding logical nodes are constructed based on the application nodes in the physical layer network. A logical layer network representing communication capabilities is constructed based on each logical node. The logical layer network is an undirected and unweighted graph structure. Based on the physical layer network and the logical layer network, the power system is modeled as a physical-logical coupled network.

[0008] The centrality score of each logical edge in the logical layer network is calculated using a mixed centrality metric, and the logical edges are arranged in descending order according to the scores to obtain a list of the criticality of logical edges;

[0009] Select logical edges as target logical edges in the logical edge criticality list in order, determine two corresponding application nodes in the physical layer network based on the target logical edges, calculate multiple shortest paths between the two application nodes, construct a total path set, and take all nodes in the total path set as candidate nodes to be removed.

[0010] While removing the candidate nodes to be removed in the physical layer network, the corresponding logical edges in the logical layer network are deleted. The maximum change in the connected components of the logical layer network after the logical edge deletion is used as the damage rate. When the damage rate meets a preset value, all the nodes removed are critical nodes.

[0011] In one embodiment, the attributes of each node in the physical layer network are represented as follows:

[0012] ;

[0013] In the above formula, The two-dimensional coordinates of the node represent the location of the corresponding power station or power relay. Indicate whether the node is an application node or a transition node.

[0014] In one embodiment, in the logical layer network, the attributes of each logical node are represented as two-dimensional coordinates of the corresponding application node, and the relationship between the corresponding logical nodes is constructed based on the power transmission and communication requirements between each power station.

[0015] In one embodiment, the centrality score of each logical edge in the logical layer network is calculated using the following formula:

[0016] ;

[0017] In the above formula, This represents the corresponding logical edge under an infinite number of random walks. The steady-state access probability, Represents the corresponding logical edge Intermediation centrality in logical networks Represents the corresponding logical edge Degree centrality, , , This represents the weighting coefficient.

[0018] In one embodiment, calculation Use the following formula:

[0019] ;

[0020] In the above formula, Indicates the first Step random walk path, Indicates the probability of restarting. This represents the initial edge from which the journey begins.

[0021] In one embodiment, determining the two corresponding application nodes in the physical layer network based on the target logical edge, calculating multiple shortest paths between these two nodes, and constructing a total path set includes:

[0022] Using the K-shortest path method, multiple shortest paths are calculated between two nodes, and a first set of paths is constructed.

[0023] Starting from one of the two nodes, the breadth-first search algorithm is used to explore the physical layer network layer by layer until the other node is reached, resulting in multiple paths, and a second path set is constructed.

[0024] The union of the first path set and the second path set is taken as the total path set.

[0025] This application also provides a critical node identification device for a power coupling network, the device comprising:

[0026] The relevant information acquisition module is used to acquire relevant information about the power system, which includes multiple interconnected power plants and power relays;

[0027] The physical-logical coupled network construction module is used to construct a physical layer network based on relevant information of the power system. Power plants and power relays are respectively used as application nodes and transition nodes in the physical layer network. Corresponding logical nodes are constructed based on the application nodes in the physical layer network, and a logical layer network representing communication capabilities is constructed based on each logical node. The logical layer network is an undirected and unweighted graph structure. Based on the physical layer network and the logical layer network, the power system is modeled as a physical-logical coupled network.

[0028] The logical edge criticality list construction module is used to calculate the centrality score of each logical edge in the logical layer network using a mixed centrality metric, and to sort the logical edges in descending order according to the scores to obtain the logical edge criticality list.

[0029] The module for generating candidate nodes to be removed is used to select logical edges as target logical edges in the list of logical edge criticality in order, determine two corresponding application nodes in the physical layer network according to the target logical edges, calculate multiple shortest paths between the two nodes, construct a total path set, and take all nodes in the total path set as candidate nodes to be removed.

[0030] The critical node identification module is used to remove the candidate nodes to be removed in the physical layer network and delete the corresponding logical edges in the logical layer network. The maximum connected component change of the logical layer network after the logical edge deletion is used as the damage rate. When the damage rate meets a preset value, all the removed nodes are critical nodes.

[0031] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps:

[0032] Obtain relevant information about a power system, which includes multiple interconnected power plants and power relays;

[0033] A physical layer network is constructed based on the relevant information of the power system. Power plants and power relays are respectively used as application nodes and transition nodes in the physical layer network. Corresponding logical nodes are constructed based on the application nodes in the physical layer network. A logical layer network representing communication capabilities is constructed based on each logical node. The logical layer network is an undirected and unweighted graph structure. Based on the physical layer network and the logical layer network, the power system is modeled as a physical-logical coupled network.

[0034] The centrality score of each logical edge in the logical layer network is calculated using a mixed centrality metric, and the logical edges are arranged in descending order according to the scores to obtain a list of the criticality of logical edges;

[0035] Select logical edges as target logical edges in the logical edge criticality list in order, determine two corresponding application nodes in the physical layer network based on the target logical edges, calculate multiple shortest paths between the two application nodes, construct a total path set, and take all nodes in the total path set as candidate nodes to be removed.

[0036] While removing the candidate nodes to be removed in the physical layer network, the corresponding logical edges in the logical layer network are deleted. The maximum change in the connected components of the logical layer network after the logical edge deletion is used as the damage rate. When the damage rate meets a preset value, all the nodes removed are critical nodes.

[0037] A computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0038] Obtain relevant information about a power system, which includes multiple interconnected power plants and power relays;

[0039] A physical layer network is constructed based on the relevant information of the power system. Power plants and power relays are respectively used as application nodes and transition nodes in the physical layer network. Corresponding logical nodes are constructed based on the application nodes in the physical layer network. A logical layer network representing communication capabilities is constructed based on each logical node. The logical layer network is an undirected and unweighted graph structure. Based on the physical layer network and the logical layer network, the power system is modeled as a physical-logical coupled network.

[0040] The centrality score of each logical edge in the logical layer network is calculated using a mixed centrality metric, and the logical edges are arranged in descending order according to the scores to obtain a list of the criticality of logical edges;

[0041] Select logical edges as target logical edges in the logical edge criticality list in order, determine two corresponding application nodes in the physical layer network based on the target logical edges, calculate multiple shortest paths between the two application nodes, construct a total path set, and take all nodes in the total path set as candidate nodes to be removed.

[0042] While removing the candidate nodes to be removed in the physical layer network, the corresponding logical edges in the logical layer network are deleted. The maximum change in the connected components of the logical layer network after the logical edge deletion is used as the damage rate. When the damage rate meets a preset value, all the nodes removed are critical nodes.

[0043] The aforementioned method, apparatus, equipment, and medium for identifying key nodes in a power-coupled network constructs a physical layer network based on relevant information from the power system. Power plants and energized relays are designated as application nodes and transition nodes in the physical layer network, respectively. Corresponding logical nodes are constructed based on the application nodes in the physical layer network, and a logical layer network representing communication capabilities is built based on each logical node. The logical layer network is an undirected, unweighted graph structure. Based on the physical and logical layer networks, the power system is modeled as a physical-logical coupled network. A mixed centrality metric is used to calculate the centrality score of each logical edge in the logical layer network, and the logical edges are then categorized according to their scores. Arrange the logical edges in descending order to obtain a list of logical edge criticality. Select logical edges from the list in order as target logical edges. Identify two corresponding transition nodes in the physical layer network based on the target logical edges. Calculate multiple shortest paths between these two nodes to construct a total path set. All nodes in the total path set are considered candidate nodes to be removed. Simultaneously, remove the candidate nodes from the physical layer network and delete the corresponding logical edges in the logical layer network. The maximum change in the maximum connectivity component of the logical layer network after edge removal is used as the damage rate. When the damage rate meets a preset value, all removed nodes are considered critical nodes. This method can effectively and quickly identify critical nodes in power networks. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating a method for identifying key nodes in a power-coupled network in one embodiment.

[0045] Figure 2 This is a schematic diagram of the power coupling network in one embodiment;

[0046] Figure 3 This is a schematic diagram illustrating the removal of application nodes in one embodiment;

[0047] Figure 4 This is a schematic diagram illustrating the removal of a transition node in one embodiment;

[0048] Figure 5 This is a diagram illustrating the effect of removing power system nodes in a simulation experiment. Figure 5 (a) represents the attack effect of each strategy when the logical network is a random network. Among them, the CENS strategy, represented in blue, has the highest attack efficiency. Figure 5 (b) represents the attack effect of each strategy when the logical network is a small-world network. Figure 5 (c) represents the attack effect of each strategy when the logical network is a regular network;

[0049] Figure 6 This is a schematic diagram of a large-scale network verification in a simulation experiment. Figure 6 (a) represents the attack effect of each strategy when the logical network is a random network. Among them, the CENS strategy, represented in blue, has the highest attack efficiency. Figure 6 (b) represents the attack effect of each strategy when the logical network is a small-world network. Figure 6 (c) represents the attack effect of each strategy when the logical network is a regular network;

[0050] Figure 7 This is a schematic diagram showing the result of random network node removal in a simulation experiment of a logic layer network.

[0051] Figure 8 This is a schematic diagram illustrating the removal of nodes in a small-world network used in a simulation experiment of the logic layer network.

[0052] Figure 9 This is a structural block diagram of a key node identification device for a power coupling network in one embodiment;

[0053] Figure 10 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0055] Traditional key point identification methods in coupled networks often assume that each layer has symmetrical physical attack capabilities. However, these methods fail when logical nodes, such as algorithm modules or abstract migration paths, lack physical form and cannot be directly attacked. This application addresses this issue by... Figure 1 As shown, a method for identifying key nodes in a power coupling network is provided, which specifically includes the following steps:

[0056] Step S100: Obtain relevant information about the power system, which includes multiple interconnected power plants and power relays.

[0057] Step S110: Construct a physical layer network based on relevant information of the power system. Power plants and power relays are respectively used as application nodes and transition nodes in the physical layer network. Construct corresponding logical nodes based on the application nodes in the physical layer network, and construct a logical layer network representing communication capabilities based on each logical node. The logical layer network is an undirected and unweighted graph structure. Based on the physical layer network and the logical layer network, the power system is modeled as a physical-logical coupled network.

[0058] Step S120: Calculate the centrality score of each logical edge in the logical layer network using a mixed centrality metric, and sort the logical edges in descending order according to the scores to obtain a list of criticality of logical edges.

[0059] Step S130: Select logical edges as target logical edges from the logical edge criticality list in order, determine the corresponding two application nodes in the physical layer network based on the target logical edges, calculate multiple shortest paths between the two application nodes, construct a total path set, and take all nodes in the total path set as candidate nodes to be removed.

[0060] In step S140, while removing the candidate nodes to be removed in the physical layer network, the corresponding logical edges in the logical layer network are deleted. The maximum connected component change in the logical layer network after the logical edge deletion is used as the damage rate. When the damage rate meets the preset value, all the nodes removed are key nodes.

[0061] This approach proposes a unique Critical Edge-to-Node Removal (CENS) strategy. This strategy focuses on prioritizing the identification of physical nodes supporting high-value logical edges, accurately identifying their crucial role in maintaining logical connectivity. Traditional methods often overlook the asymmetry between physical resources and business services, while the CENS strategy, through actionable targeted analysis of the physical layer (similar to attack simulation), can inversely deduce and indirectly clarify the factors that critically impact logical layer functionality, thereby effectively identifying critical nodes. This strategy provides a novel perspective for identifying critical nodes in power coupled networks, fully considering the dependence of abstract logical layer connectivity paths on the integrity of physical infrastructure. Breaking through traditional limitations, it facilitates more efficient and accurate identification of nodes playing a key role in maintaining network functionality, providing strong support for ensuring stable operation and risk prevention in power systems.

[0062] In step S100, the relevant information of the power system includes the location information of power plants and power relays, as well as their functions. The functions determine whether there are corresponding node mappings for power plants and power relays at the logical layer.

[0063] In this embodiment, the power system is modeled as a physical-logical coupled network, consisting of a physical node layer and a virtual communication layer. The physical-logical coupled network will be introduced first below.

[0064] Since both layers in the physically-logically coupled network framework are modeled as undirected networks, different notation conventions are used to avoid ambiguity and enhance the clarity of the symbolic representation: node pairs are represented by brackets. This represents an unordered combination of vertices at any level. Directly adjacent edges between nodes are explicitly indicated by angle brackets. , strictly represents physical / logical connection.

[0065] Specifically, the physical layer consists of application nodes and transition nodes. Application nodes are crucial for some critical tasks; for example, they are directly responsible for the existence of logical layer nodes. Transition nodes are used to transmit information between different application nodes. The virtual communication layer, or logical layer, is an abstraction of the physical node layer, as shown in the diagram. It means that, among them, Represents a communication layer node. This indicates a communication layer connection. Each Each application node in the physical layer is directly connected to an application node in the physical layer. Conversely, each application node in the physical layer is directly connected to a logical layer node. Represents logical nodes and The communication link between them. It is worth noting that the edges... Limited by the network node connections in the physical node layer.

[0066] Furthermore, the entire physical-logical coupled network framework exhibits an "edge-centric one-to-many coupling paradigm." Each logical edge in the virtual communication layer, i.e., the logical layer, maps to an application node in the physical layer. and A set of paths between ,in These physical paths can be maintained by interconnected transition nodes. Only when at least one valid path exists in the physical layer... At that time, logical edge Only then is it considered operational:

[0067] ;

[0068] In the above formula, Indicated by , This represents the running status of the logical edge at the endpoint, where 1 indicates it is valid and runnable, and 0 indicates it is not runnable. This is the set of physical paths between corresponding node pairs at the physical layer. This represents a physical path in the path set, and the path is marked as 1 if it is operational.

[0069] like Figure 2 The diagram shown is a schematic of a physical-logical coupled network framework.

[0070] Therefore, in step S110, based on the functional hierarchy, in addition to spatial relationships, nodes in the physical layer are assigned different attributes to characterize their operational capabilities. The physical layer network can be represented as follows: ,in It is a collection of physical entity nodes, including the application node collection. and transition node set ,Right now , It is the set of edges in the network. In this embodiment, the generator and the communication relay are respectively used as the application node and the transition node.

[0071] Furthermore, the attributes of each node in the physical layer network are represented as follows:

[0072] ;

[0073] In the above formula, The two-dimensional coordinates of the node represent the location of the corresponding power station or power relay. This indicates whether the node is an application node or a transition node. Application nodes are directly connected to nodes in the logical layer and are marked as... .

[0074] On the other hand, transition nodes are not directly connected to nodes in the logic layer; they only transmit electrical signals, denoted as... , is represented as:

[0075] ;

[0076] In this embodiment, the logical layer network representing communication capabilities is an undirected, unweighted graph, represented as follows: ,in, It is a collection of communication nodes. These are the two-dimensional coordinates of the logical nodes. Based on structural characteristics, it can be determined that for each node in the logical layer network, there is an application node in the physical layer that is in the same position and directly connected to it.

[0077] Specifically, in the logical layer network, the attributes of each logical node are represented as two-dimensional coordinates of the corresponding application node, and the relationships between the corresponding logical nodes are constructed based on the power transmission and communication requirements between the power plants.

[0078] Furthermore, in a physical-logical coupled network, the edges between nodes are defined according to a given dataset. The edges between nodes only need to satisfy the condition that there are connected node pairs on the logical network and that there are connected paths between the corresponding node pairs on the physical network.

[0079] This method employs a reverse approach to identify key points, focusing on how to rapidly dismantle a power network by removing nodes. Given the immaterial nature of logical layer network nodes, directly physically removing them during modeling presents significant challenges. Therefore, in physically-logically coupled networks, a node failure mechanism is specifically designed to remove only physical layer nodes. This approach aligns with existing research paradigms in cyber-physical system security, prioritizing tangible infrastructure components in penetration testing.

[0080] A two-layer network satisfies the prerequisite that all logical nodes can find their corresponding application nodes in the physical layer, and for reachable pairs of logical nodes, there must exist a reachable path in the physical layer. In multi-layer network fault propagation analysis, removing a physical layer node triggers a cascading effect through two different mechanisms: one is intra-layer connectivity loss, where all physical links associated with the removed node immediately fail, leading to the disintegration of the underlying physical topology. The other is cross-layer functional dependency, i.e., the role characteristic parameters of the node (… This determines its impact on the logic layer.

[0081] Furthermore, by analyzing the impact of removing application nodes and transition nodes in the aforementioned physical-logical coupled network, a theoretical foundation is laid for the subsequent steps of this method.

[0082] Remove application nodes from the physical layer ( First, it will cause all adjacent physical links to disconnect, resulting in a loss of connectivity within the layer. Crucially, the cascading failure mechanism is manifested through cross-layer functional dependencies: when a retired physical entity maintains a direct service provision relationship with a logical node, the corresponding logical node and its interconnecting links will be simultaneously eliminated, and the application node will be removed as well. Figure 3 As shown.

[0083] Removing a transition node leads to a decrease in intra-layer connectivity similar to that of removing an application node: the elimination process involves removing the target node and its associated intra-layer connections in the physical layer. Changes in cross-layer dependencies require a more complex process. Since a transition node in the physical layer does not have a direct corresponding node in the logical layer, removing the transition node does not lead to the elimination of the logical node, but rather affects the connectivity between pairs of logical nodes. When performing specific logical network connectivity disruption operations, i.e., selecting logical edges for elimination, the algorithm is as follows: From the characteristics of this multi-layer network structure, it is known that for connected node pairs in the logical layer, the corresponding application node pairs in the physical layer must be connected.

[0084] Furthermore, before removing transition nodes, Dijkstra's algorithm is first used to identify all node pairs in the original graph that maintain connections between both layers. These node pairs are then systematically filtered to identify those whose physical layer paths are interrupted due to the absence of transition nodes.

[0085] For simplicity, Algorithm 1 is presented, considering the impact of removing a single target transition node. In actual network node removal, each node in the target transition node set will cyclically follow this process. The target transition node that should be deleted is... The mapping relationship between logical nodes and their application nodes is ,in, This represents the set of nodes in the logical layer.

[0086] Algorithm 1 Node Pair Selection

[0087] Input: Physical layer diagram Logic layer diagram Target transition node Mapping ;

[0088] Output: Disrupted physical node pairs Disrupted logical node pairs ;

[0089] 1. Initialization , ;

[0090] 2. Calculate the logical connectivity matrix. ,if and If connected, then ,otherwise ;

[0091] 3. For each ,in, Nodes representing the physical layer:

[0092] 4. Order , ;

[0093] 5. If :

[0094] 6. Add to In the middle, Add to middle;

[0095] 7. Update ;

[0096] 8. For each with or Connected logical nodes ,renew and ;

[0097] 9. Return , .

[0098] The cascading impact of removing physical layer transition nodes on logical connectivity requires targeted edge elimination at the logical layer, such as... Figure 4 As shown. In the logical layer, the affected node pairs present two connection configurations: the first is direct association, where the node pairs contain a direct logical edge, and the second is indirect association, where the connection is maintained through a multi-hop path mediated by an intermediate node.

[0099] During the process of logical network connectivity disruption, since the number of hops between affected node pairs is uncertain, the proposition of "path failure guarantee" is formulated and used when selecting specific edges to be severed. In terms of topology, logical node pairs have two possible connectivity methods at the logical level: direct edge connection and multi-hop path connection. Therefore, in the logical network, node pairs... The system should be disconnected in the following ways: Process 1, direct edge deletion, i.e., explicitly removing all adjacent edges between logically co-located node pairs. Process 2, indirect path invalidation, i.e., the path dependency indicates that for... Through multi-hop path set Each connected node pair In the physical layer of the original diagram and There is at least one path between them. It is represented as:

[0100] ;

[0101] In the above formula, , , Each is represented as a line and The physical layer path with endpoints, the physical nodes along the path, and the physical layer path with endpoints. and The set of physical layer paths for endpoints.

[0102] For indirect path failure, let It is the set of deleted edges after direct edge deletion. Crucially, the proposition "path failure guarantee" indicates that the removal of adjacent edges in the previous step essentially guarantees the interruption of all indirect paths:

[0103] ;

[0104] In the above formula, Indicates a path. , These are represented as the path set and the adjacent edge set, respectively.

[0105] Furthermore, it is necessary to prove the proposition "path failure guarantee". Let... It is a pair of interrupt logic nodes The logical layer. In explicitly removing adjacent edges. Then, for all node pairs connected only by multi-hop paths... ,have:

[0106] ;

[0107] In the above formula, Representing a path edge set, This represents the set of all directly adjacent edges in the logical layer to be removed in process 1.

[0108] Specifically, a recursive path compression proof is performed: the proof method is consistent for any logical node pairs that need to be disconnected after potentially removing adjacent edges in step 1 while maintaining multi-hop connections. This is achieved through node pairs... Representative case studies are used to demonstrate this: at the logical level, Represents node pairs The set of paths between them, for each path The set of nodes in the path is . This represents the corresponding co-location application node pair in the physical layer. The set of paths between them.

[0109] Step 1: Prove the path set Every path in the path must be a multi-hop path: assuming there is an edge ( and (Adjacent edges exist between them). The target transition node is deleted. After that, physical layer Become If the target is deleted back, and If the adjacent edges between nodes still exist, then the node pair... It will not be included in the set of disturbed physical node pairs in the first place. Therefore, Each path in the path must be a multi-hop path.

[0110] Step 2: Proof is needed in and Each physical path between There must be at least one intermediate application node: Let The set of nodes in the path is If there exists a ,in (i.e., no intermediate nodes), then according to the "edge-centric one-to-many coupling paradigm", there exists a path in the logical layer. Mapped to this And along this path There are no intermediate logical nodes because each intermediate logical node should be co-located with an application node in the physical layer. In this case, this path... that is The adjacent edges between them, which is This contradicts the precondition that the connection is solely via a multi-hop path. Therefore, in and Each physical path between There must be at least one intermediate application node.

[0111] Step 3: It is necessary to prove that for node pairs Each path between Due to the transition node The shortest subpath break caused by the removal of [the element] has been completed in "Process 1. Direct Edge Deletion": [The path will be deleted]. Split into two sub-paths and , ,in connect and a specific logical intermediate node , connect and To interrupt the path At least the sub-path needs to be interrupted. or One of them. Since the two sub-paths are equivalent in terms of disruptive impact, a simplified proof can be made: assume that interruption is required. To meet this requirement, application nodes... Should be in Therefore, The logical path between them should also be interrupted, and it is more than The paths between them are shorter. The iterative decomposition process continues until the path reaches the minimum generated configuration. The recursive decomposition converges to the adjacent edges.

[0112] Through the logical layer dependency propagation mechanism, the strategic removal of all direct logical connections between these node pairs essentially disables their indirect connection paths. This cascading failure phenomenon is consistent with the established principles of interdependent network failure models, where local physical layer perturbations lead to nonlinear logical topology deterioration.

[0113] By analyzing the coupling relationships between network layers in logical-physical coupled networks, a more practical and operable Critical Edge-to-Node Removal (CENS) strategy was further developed. This strategy addresses the reality that logical layer nodes are difficult to remove directly by physical means, establishing a damage mechanism that targets only physical layer nodes, indirectly causing the logical network layer to fail due to coupling relationships. Furthermore, analyzing the specific process by which physical layer node removal affects logical network connectivity reveals that removing physical layer application nodes causes intra-layer connectivity loss and the elimination of cross-layer logical nodes and links; removing physical layer transition nodes reduces physical layer connectivity, while the disruption of connectivity caused by affected logical layer nodes requires specific algorithms. To address this, we further strengthened the Critical Edge-to-Node Removal (CENS) strategy by developing and using a "node ablation mechanism" algorithm for pre-processing the logical network, enabling more precise identification of the logical edges to be disrupted when using the CENS strategy. These analyses clarify the essential impact of physical node removal on network connectivity: removing the set of adjacent edges of the corresponding logical node pair. This provides insights for the CENS strategy to select target physical nodes, enabling it to disrupt logical network functionality by attacking the critical physical nodes corresponding to high-value logical edges.

[0114] Given the characteristics of the coupled networks analyzed above, this embodiment proposes a novel node removal strategy and an enhanced version thereof. In reality, only the physical layer can be subjected to actual node removal; therefore, the connectivity of the logical network can be indirectly affected by removing physical nodes. In other words, the attack only requires selecting physical nodes.

[0115] When the target node is a transition node At that time, as mentioned above, remove Essentially equivalent to removing the affected node pair in the logic layer. Adjacent edges. From a mathematical perspective, let... For the transition node Remove the set of adjacent edges in the affected logical layer. Then, remove... The impact on logical network connectivity, and the removal The changes that edges in the logical network structure cause are equivalent.

[0116] When the target node is an application node At that time, the corresponding logical node in the logical network Its associated edges will be removed, which is equivalent to making the network connectivity... Isolated. Assume For logical nodes in a logical network The set of associated edges.

[0117] In general, regardless of whether the target physical node is a transition node or an application node, its essence is to affect network connectivity by removing the set of adjacent edges of the logical node pairs corresponding to that physical node. Selecting a target physical node is actually about sorting and filtering these sets of logical edges.

[0118] In this embodiment, the proposed Critical Edge to Node Removal (CENS) strategy is a cross-layer attack method designed to disrupt the functionality of a logical network by attacking critical physical nodes originating from high-value logical edges. This strategy operates sequentially through four stages: step S120, which identifies critical logical edges and prioritizes them using centrality based on random walks; step S130, which maps physical nodes using path dependency analysis; and step S140, which iteratively removes nodes until the network damage reaches a preset threshold, thereby achieving the identification of critical nodes.

[0119] In step S120, the centrality score of each logical edge in the logical layer network is calculated using the following formula:

[0120] ;

[0121] In the above formula, This represents the corresponding logical edge under an infinite number of random walks. The steady-state access probability, Represents the corresponding logical edge Intermediation centrality in logical networks Represents the corresponding logical edge Degree centrality, , , This represents the weighting coefficient.

[0122] Specifically, calculation Use the following formula:

[0123] ;

[0124] In the above formula, Indicates the first Step random walk path, Indicates the probability of restarting. This represents the initial edge from which the journey begins.

[0125] In one embodiment, ,and .

[0126] In step S130, the two corresponding application nodes are determined in the physical layer network according to the target logical edge, and multiple shortest paths between the two nodes are calculated to construct the total path set. This includes: firstly, using the K-shortest path method, multiple shortest paths are calculated between the two nodes to construct the first path set; then, starting from one of the two nodes, the breadth-first search algorithm is used to explore the physical layer network layer by layer until the other node is reached, resulting in multiple paths and constructing the second path set; finally, the union of the first path set and the second path set is taken as the total path set.

[0127] Specifically, for each selected target logical edge ,in, This list represents the criticality of logical edges and identifies the corresponding physical application nodes. and According to the mapping relationship ,have Using the K-shortest path algorithm, calculate the physical network layers. middle and Between The shortest paths are denoted as the first path set. To ensure the comprehensiveness of path finding, from Starting from the beginning, a breadth-first search (BFS) approach is used to explore the physical layer network until the destination is reached. All paths found by BFS constitute the second path set. .examine Does it exist in the middle? If any of the paths in the path set exist, add them to the total path set. In, that is .set up , The nodes in the list are considered as candidate nodes for removal. This represents the set of all physical nodes in the physical layer that meet the removal criteria.

[0128] Next, in step S140, candidate nodes corresponding to each target logical edge are removed from the logical edge criticality list in sequence, and the damage rate of the logical layer network after the removal of nodes is calculated and updated. If the damage rate does not meet the preset value, the candidate nodes corresponding to the next target logical edge in the logical edge criticality list are removed until the damage rate of the logical layer network meets the preset value. Then, all the removed nodes are critical nodes.

[0129] Specifically, first initialize the remaining physical layer network. and logic layer network damage rate Determine the iteration loop (let the maximum number of iterations be...). After that, from the current list of logical edge criticality Select the logical edge with the highest priority. and its related physical layer network nodes This includes application nodes and transition nodes. Extract the path set. All physical nodes on all paths. After removing these nodes, update the physical layer to... .

[0130] Furthermore, after removing a physical node, due to the deletion of paths in the physical layer network, logical edges that are no longer supported will also be removed from the logical layer network. Remove from the middle. At this point, the logic layer network can be calculated based on the change in the maximum connected component. damage rate The calculation formula is:

[0131] ;

[0132] In the above formula, and These represent the maximum connected component size of the logical network before and after the update, respectively.

[0133] In this embodiment, the criticality level of logical edges is listed. After removing the logical edges and their corresponding nodes, calculate the size of the maximum connected component. Then the attack will stop. The specific actions taken can be adjusted according to the actual situation. Make adjustments; otherwise, proceed to the next iteration. After node removal stops, all removed nodes are considered critical nodes, thus enabling the identification of critical nodes in the power grid system.

[0134] In this embodiment, a specific algorithm flow for implementing the above-mentioned node removal method, i.e., the key node identification method, is also provided, as shown below:

[0135]

[0136] In this paper, the effectiveness of the proposed method is demonstrated through simulation experiments. Comparative experiments were conducted on an IEEE 118-node power system and three synthetic networks (random networks, small-world networks, and scale-free networks). Performance metrics included logical network impairment rate (ρ), attack efficiency (the number of nodes removed to achieve the target impairment), and robustness variations under different network topologies. All results are averages of 200 independent trials with 95% confidence intervals.

[0137] First, a logical-physical coupled network was constructed using the IEEE 118-node power system. The physical layer consisted of application nodes (power plants) and transition nodes (communication relays). The logical layer network employed three different connection modes: (1) control relationships defined by the dataset; (2) uniform random connections; and (3) Watts-Strogatz small-world network (reconnection probability = 0.15, average degree = 6). The CENS strategy was compared with random attacks, degree-centrality-based attacks, and betweenness-centrality-based attacks, such as... Figure 5 As shown.

[0138] like Figure 5 (a) to Figure 5 As shown in (c), CENS consistently outperforms the baseline method across all logical layer configurations. When removing a certain proportion of physical nodes, CENS achieves a significantly higher damage rate compared to degree centrality and betweenness centrality strategies. CENS exhibits a much faster damage growth rate in the initial stages of node removal, indicating its ability to quickly identify critical nodes across layers. In contrast, random node removal performs the worst because it cannot prioritize critical infrastructure, resulting in a relatively low damage rate even when removing a large number of nodes.

[0139] Network topology has a profound impact on attack effectiveness. In the logical layer defined by the dataset, CENS targets transition nodes connecting high-between-number logical edges, exploiting pre-existing control dependencies. Removing these nodes typically triggers a cascading logical failure. For the stochastic logical layer without a hub structure, CENS maintains a high damage growth rate through adaptive path enumeration, while damage accumulation based on degree centrality is much slower. In the small-world logical layer, the short-path characteristic further amplifies the advantages of CENS. Removing a small subset of transition nodes disrupts a large proportion of critical logical paths.

[0140] The vulnerability of the IEEE 118-node power system stems primarily from the presence of centralized hubs at the physical layer and their tight coupling with logical control relationships. CENS can dynamically prioritize physical nodes supporting multiple logical paths. These findings underscore the importance of reinforcing transition nodes (such as communication relays) and deploying redundant physical paths to mitigate the risk of single points of failure.

[0141] Furthermore, to verify the scalability and topology adaptability of the Critical Edge-to-Node Attack (CENS) strategy, a coupled network model was constructed, containing 1000 physical nodes (800 transition nodes and 200 application nodes), 200 logical nodes, and 1200 logical edges. Three representative logical topologies were tested: Watts-Strogatz small-world network, Scale-free networks and Randomized network. The experiment involved 200 independent trials to calculate 95% confidence intervals for damage rate (ρ) and attack efficiency, such as... Figure 6 As shown.

[0142] like Figure 6 As shown in (a), the CENS strategy demonstrates superior efficiency in leveraging the short-path characteristics of small-world networks. Furthermore, it can be observed that CENS maintains its leading performance compared to traditional algorithms as the size of the logical network increases. By removing a small subset of physical nodes, CENS inflicts significant logical damage, clearly outperforming betweenness-based and degree-based strategies. CENS exhibits a significantly faster damage growth rate, attributed to its ability to disrupt critical bridging paths between logical hubs. For example, removing specific transition nodes can sever multiple short paths in the logical layer, triggering a significant damage leap. Compared to random attacks, CENS demonstrates higher accuracy, reflected in its narrower confidence interval.

[0143] like Figure 6As shown in (b), in scale-free networks, CENS attacks cross-layer paths that depend on hubs, effectively triggering an avalanche-like collapse. In the early stages of the attack, removing a small number of physical hub nodes with a high degree of density causes a significant spike in the damage rate. Removing a single hub node can invalidate multiple logical edges, highlighting the strategy's sensitivity to power-law degree distributions. Compared to traditional methods, CENS requires fewer nodes to achieve a high damage rate, highlighting the limitations of single-layer centrality metrics in heterogeneous networks.

[0144] like Figure 6 As shown in (c), even in random networks with uniform topology, CENS maintains a significant damage advantage over the baseline strategy. By adaptively prioritizing dispersed critical paths, CENS achieves a higher damage rate and lower variability compared to degree-based methods, which struggle to identify dispersed high-influence nodes.

[0145] Furthermore, the advantages of the CENS strategy become more pronounced as the number of network nodes and edges increases. This is likely because larger network scales lead to more complex network structures. Traditional methods for calculating metrics tend to overlook more details in complex structures. In contrast, the CENS strategy focuses on logical edges. Regardless of changes in connections and topology, it always focuses on the ultimate target of the attack. This characteristic allows CENS to better adapt to the complexity of large-scale networks, thus highlighting its superior attack capabilities.

[0146] The experiment was further expanded by introducing an enhanced version of the CENS strategy with a node ablation mechanism (denoted as the CENS (Node-ablation) strategy), and a newly added k-core attack algorithm was used as a comparison algorithm. Tests were conducted on random networks and small-world networks, based on a network consisting of 1000 physical nodes and 200 logical nodes, to comprehensively evaluate the attack performance of each strategy.

[0147] like Figure 7 As shown, in random networks, the CENS-N strategy (dark red curve) exhibits a more rapid increase in damage rate compared to the CENS strategy (blue curve). This is because node dependencies are relatively dispersed in such networks. The CENS algorithm with node ablation can more accurately capture the potential dependencies of the logical network on physical layer connectivity. By performing node ablation, this strategy avoids interference from reference nodes and focuses more on the key physical layer nodes that truly support the connectivity of the logical network. As a result, it improves attack efficiency and leads to a more significant increase in damage rate. In contrast, the traditional CENS strategy, due to its retention of reference nodes, has limitations in identifying key nodes in the dispersed structure of random networks, resulting in a slower increase in damage rate compared to the node ablation strategy.

[0148] The damage rate growth trend of the newly added k-core attack algorithm (purple curve) falls between that of the CENS strategy and the traditional betweenness centrality (orange curve) and degree centrality (green curve) strategies. While it possesses some attack capability, its efficiency in exploring potential dependencies in random network structures remains lower than that of the CENS (Node-ablation) strategy. An improved CENS strategy (CENS-N) using node ablation mechanisms for pre-processing of logical networks was also added to the experiments. Figure 7 As shown by the dark red line, it can be seen that the CENS strategy and its improved version (CENS-N) both outperform the traditional algorithm, and the CENS-N strategy is more efficient than the CENS strategy. The damage rate of the random attack strategy (assuming the corresponding color) increases the slowest, which further highlights the advantages of targeted attack strategies in random networks.

[0149] like Figure 8 As shown, when observing experimental results in small-world networks, the damage rate growth trends of the CENS-N (Node-ablation) strategy (dark red curve) and the CENS strategy (blue curve) are almost identical. This is mainly due to the significant "80 / 20 rule" effect of logical edges in small-world networks. A few key edges bear most of the network's connectivity function. The high clustering and short path characteristics of small-world networks make the distribution of key edges relatively concentrated and predictable. Regardless of whether node ablation is introduced, most CENS-related strategies can locate the physical layer nodes on which these key edges depend. Since node ablation has little impact on capturing key edges, the two strategies identify roughly the same key edges, resulting in similar damage rate growth effects.

[0150] The k-core attack algorithm (purple curve) can achieve some damage growth in small-world networks, but its efficiency in utilizing network structure characteristics is still lower than that of CENS-related strategies. The damage growth rates of betweenness centrality (orange curve) and degree centrality (degree curve) strategies are relatively slow, while the random attack strategy (red curve) remains the weakest.

[0151] In summary, in random networks, the CENS strategy with node ablation exhibits better attack performance by more effectively capturing the potential dependencies of the logical network on the physical layer connectivity. In small-world networks, the "80 / 20 rule" of logical edges makes the impact of node ablation on key edge capture negligible, thus the two CENS-related strategies have similar effects. While the newly added k-core attack algorithm shows some performance, it is less efficient at utilizing key nodes or edges in different network structures compared to CENS-related strategies.

[0152] The simulation experiments and results further reveal the characteristics of the proposed method and its variants in different network structures, providing more detailed directions for network security protection. In random networks, special attention should be paid to protecting the potential dependencies of the logical network on the physical layer. In small-world networks, defenses can be enhanced based on the concentrated characteristics of critical edges to improve the overall network's resistance to attacks. When constructing the logical network layer using a random network model, special attention should be paid to the scale ratio of the logical network to the physical network. The more independent the logical network nodes are on their corresponding physical layer paths—that is, the larger the scale ratio of the logical network to the physical network—the easier it is to protect the connectivity of the logical network. When constructing small-world logical networks, special attention needs to be paid to the selection of application nodes corresponding to the physical network layer. Due to the high clustering and long-connection characteristics of small-world networks, more physical network paths are needed to protect highly connected logical nodes. Therefore, it is best to select physical nodes with high centrality as application nodes and connect them to highly central nodes in the logical network. These findings provide important basis for formulating subsequent network security strategies.

[0153] In the aforementioned method for identifying key nodes in a power coupled network, the method, apparatus, equipment, and medium for identifying key nodes in a power coupled network construct a physical layer network based on relevant information of the power system. Power plants and power relays are respectively designated as application nodes and transition nodes in the physical layer network. Corresponding logical nodes are constructed based on the application nodes in the physical layer network, and a logical layer network representing communication capabilities is constructed based on each logical node. The logical layer network is an undirected, unweighted graph structure. Based on the physical and logical layer networks, the power system is modeled as a physical-logical coupled network. A hybrid centrality metric is used to calculate the centrality score of each logical edge in the logical layer network. Logical edges are sorted in descending order based on their scores to obtain a list of criticality levels. Logical edges are selected from this list as target logical edges. Two corresponding transition nodes are identified in the physical layer network based on the target logical edge. Multiple shortest paths between these two nodes are calculated to construct a total path set. All nodes in the total path set are considered candidate nodes to be removed. Simultaneously, the candidate nodes are removed from the physical layer network, and the corresponding logical edges in the logical layer network are deleted. The maximum change in the connected components of the logical layer network after edge removal is used as the damage rate. When the damage rate meets a preset value, all removed nodes are considered critical nodes.

[0154] In this method, the proposed CENS strategy (centrality-based node selection strategy) fully considers the correlation characteristics of power-communication coupled networks (such as the coupling between the dispatch communication network and the power transmission network in the power system), as well as the functional attributes of nodes such as substations, converter stations, and control centers. It creates a key node screening and attack strategy that fits the actual operation of the power network and accurately anchors the nodes that play a core role in the security and stability of the power network and the functions of power transmission and distribution. It can be directly used for power communication network optimization, quickly identifying data interaction hub nodes (such as the corresponding nodes of core switches in the dispatch data network), optimizing power system communication routing planning, and ensuring reliable transmission of business data such as relay protection and automation control; or it can be used for power network operation and maintenance, locking high-load and high-importance key nodes (such as ultra-high voltage transmission nodes and regional power supply hub substations), and deploying maintenance strategies such as equipment inspection and status monitoring in advance to prevent large-scale power outages caused by faults; it is also suitable for power network security protection, by locating the power information transmission and control command interaction hubs (such as the master station nodes of the power monitoring system), implementing targeted security supervision, significantly improving the efficiency of power network resource allocation (such as power allocation of transmission channels and communication bandwidth allocation) and the targeting of security protection, and resisting threats such as network attacks and malicious intrusions.

[0155] The CENS strategy with node ablation mechanism introduces node ablation simulation on the basis of CENS, which can more accurately identify the key hubs in the power network where communication and power connections are integrated. This mechanism can be used to verify the resilience of the Internet of Things in Power (IoT in Power) network design. By simulating attacks on sensor interaction nodes such as key smart meters and distribution automation terminals, or changes in the connectivity and power transmission stability of the power-communication coupled network after failures of substation communication gateways and intelligent inspection robot control nodes, it can optimize redundant node deployment schemes (such as adding equipment-useful communication relay nodes near key transmission nodes and configuring backup automation control units in important substations). Alternatively, it can be used in smart distribution networks with distributed power sources to analyze the impact of power supply hub node failures (such as distributed power source grid connection points and regional distribution network interconnection switch nodes) on the overall power flow and power quality, and assist in the formulation of emergency dispatch strategies (such as rapid islanding of distributed power sources / Grid connection control strategies and load transfer plans are developed. At the same time, ablation test data is used to back-infer weak links in the power network (such as key transmission corridor nodes that are prone to cascading power outages due to single node failures, and nodes that are highly coupled with communication and power functions and lack redundancy). This provides quantitative basis for adaptive power network reconfiguration algorithms (such as fast grid topology self-healing algorithms after faults and automatic rerouting algorithms for communication links), enhances the survivability of the power network in dynamic threat environments such as equipment failures and network attacks, and ensures reliable power supply.

[0156] The combination of these two technologies constructs a complete technical chain of "identification of key nodes in the power network - fault simulation verification - generation of operation and maintenance optimization strategies," which is suitable for business scenarios such as power network security protection, operation optimization, and communication assurance. It creates a network management solution with advanced technology and practical deployment value for the power industry, helps improve the resilience and intelligent operation level of the power system, and can highlight the innovative support for the safe and stable operation of the power-communication coupled system in the power network-related patent layout, thus possessing significant industrial application value.

[0157] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0158] In one embodiment, such as Figure 9 As shown, a key node identification device for a power coupled network is provided, comprising: an information acquisition module 200, a physical-logical coupled network construction module 210, a logical edge criticality list construction module 220, a candidate node to be removed generation module 230, and a key node identification module 240, wherein:

[0159] The relevant information acquisition module 200 is used to acquire relevant information of the power system, which includes multiple interconnected power stations and power relays;

[0160] The physical-logical coupled network construction module 210 is used to construct a physical layer network based on relevant information of the power system, taking power plants and power relays as application nodes and transition nodes in the physical layer network, respectively, constructing corresponding logical nodes based on the application nodes in the physical layer network, and constructing a logical layer network representing communication capabilities based on each logical node. The logical layer network is an undirected and unweighted graph structure. Based on the physical layer network and the logical layer network, the power system is modeled as a physical-logical coupled network.

[0161] The logical edge criticality list construction module 220 is used to calculate the centrality score of each logical edge in the logical layer network using a mixed centrality metric, and to sort the logical edges in descending order according to the scores to obtain a logical edge criticality list.

[0162] The candidate node to be removed generation module 230 is used to select logical edges as target logical edges in the logical edge criticality list in order, determine two corresponding application nodes in the physical layer network according to the target logical edges, calculate multiple shortest paths between the two nodes, construct a total path set, and use all nodes in the total path set as candidate nodes to be removed.

[0163] The critical node identification module 240 is used to remove the candidate nodes to be removed in the physical layer network and delete the corresponding logical edges in the logical layer network. The maximum connected component change of the logical layer network after the logical edge deletion is used as the damage rate. When the damage rate meets a preset value, all the removed nodes are critical nodes.

[0164] Specific limitations regarding the critical node identification device for power coupled networks can be found in the limitations of the critical node identification method for power coupled networks described above, and will not be repeated here. Each module in the aforementioned critical node identification device for power coupled networks can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0165] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 10 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements a method for identifying key nodes in a power-coupled network. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0166] Those skilled in the art will understand that Figure 10The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0167] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0168] Obtain relevant information about a power system, which includes multiple interconnected power plants and power relays;

[0169] A physical layer network is constructed based on the relevant information of the power system. Power plants and power relays are respectively used as application nodes and transition nodes in the physical layer network. Corresponding logical nodes are constructed based on the application nodes in the physical layer network. A logical layer network representing communication capabilities is constructed based on each logical node. The logical layer network is an undirected and unweighted graph structure. Based on the physical layer network and the logical layer network, the power system is modeled as a physical-logical coupled network.

[0170] The centrality score of each logical edge in the logical layer network is calculated using a mixed centrality metric, and the logical edges are arranged in descending order according to the scores to obtain a list of the criticality of logical edges;

[0171] Select logical edges as target logical edges in the logical edge criticality list in order, determine two corresponding application nodes in the physical layer network based on the target logical edges, calculate multiple shortest paths between these two nodes, construct a total path set, and take all nodes in the total path set as candidate nodes to be removed.

[0172] While removing the candidate nodes to be removed in the physical layer network, the corresponding logical edges in the logical layer network are deleted. The maximum change in the connected components of the logical layer network after the logical edge deletion is used as the damage rate. When the damage rate meets a preset value, all the nodes removed are critical nodes.

[0173] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0174] Obtain relevant information about a power system, which includes multiple interconnected power plants and power relays;

[0175] A physical layer network is constructed based on the relevant information of the power system. Power plants and power relays are respectively used as application nodes and transition nodes in the physical layer network. Corresponding logical nodes are constructed based on the application nodes in the physical layer network. A logical layer network representing communication capabilities is constructed based on each logical node. The logical layer network is an undirected and unweighted graph structure. Based on the physical layer network and the logical layer network, the power system is modeled as a physical-logical coupled network.

[0176] The centrality score of each logical edge in the logical layer network is calculated using a mixed centrality metric, and the logical edges are arranged in descending order according to the scores to obtain a list of the criticality of logical edges;

[0177] Select logical edges as target logical edges in the logical edge criticality list in order, determine two corresponding application nodes in the physical layer network based on the target logical edges, calculate multiple shortest paths between these two nodes, construct a total path set, and take all nodes in the total path set as candidate nodes to be removed.

[0178] While removing the candidate nodes to be removed in the physical layer network, the corresponding logical edges in the logical layer network are deleted. The maximum change in the connected components of the logical layer network after the logical edge deletion is used as the damage rate. When the damage rate meets a preset value, all the nodes removed are critical nodes.

[0179] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0180] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0181] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for identifying key nodes in a power coupling network, characterized in that, The method includes: Obtain relevant information about a power system, which includes multiple interconnected power plants and power relays; A physical layer network is constructed based on the relevant information of the power system. Power plants and power relays are respectively used as application nodes and transition nodes in the physical layer network. Corresponding logical nodes are constructed based on the application nodes in the physical layer network. A logical layer network representing communication capabilities is constructed based on each logical node. The logical layer network is an undirected and unweighted graph structure. Based on the physical layer network and the logical layer network, the power system is modeled as a physical-logical coupled network. The centrality score of each logical edge in the logical layer network is calculated using a mixed centrality metric, and the logical edges are arranged in descending order according to the scores to obtain a list of the criticality of logical edges; Select logical edges as target logical edges in the logical edge criticality list in order, determine two corresponding application nodes in the physical layer network based on the target logical edges, calculate multiple shortest paths between the two application nodes, construct a total path set, and take all nodes in the total path set as candidate nodes to be removed. While removing the candidate nodes to be removed in the physical layer network, the corresponding logical edges in the logical layer network are deleted. The maximum change in the connected components of the logical layer network after the logical edge deletion is used as the damage rate. When the damage rate meets a preset value, all the nodes removed are critical nodes.

2. The method for identifying key nodes in a power coupling network according to claim 1, characterized in that, In the physical layer network, the attributes of each node are represented as follows: In the above formula, The two-dimensional coordinates of the node represent the location of the corresponding power station or power relay. Indicate whether the node is an application node or a transition node.

3. The method for identifying key nodes in a power coupling network according to claim 2, characterized in that, In the logical layer network, the attributes of each logical node are represented as two-dimensional coordinates of the corresponding application node, and the relationship between the corresponding logical nodes is constructed based on the power transmission and communication requirements between each power station.

4. The method for identifying key nodes in a power coupling network according to claim 3, characterized in that, The centrality score of each logical edge in the logical layer network is calculated using the following formula: In the above formula, This represents the corresponding logical edge under an infinite number of random walks. The steady-state access probability, Represents the corresponding logical edge Intermediation centrality in logical networks Represents the corresponding logical edge Degree centrality, , , This represents the weighting coefficient.

5. The method for identifying key nodes in a power coupling network according to claim 4, characterized in that, calculate Use the following formula: In the above formula, Indicates the first Step random walk path, Indicates the probability of restarting. This represents the initial edge from which the journey begins.

6. The method for identifying key nodes in a power coupling network according to claim 5, characterized in that, Based on the target logical edge, determine the corresponding two application nodes in the physical layer network, calculate multiple shortest paths between these two nodes, and construct the total path set including: Using the K-shortest path method, multiple shortest paths are calculated between two nodes, and a first set of paths is constructed. Starting from one of the two nodes, the breadth-first search algorithm is used to explore the physical layer network layer by layer until the other node is reached, resulting in multiple paths, and a second path set is constructed. The union of the first path set and the second path set is taken as the total path set.

7. A key node identification device for a power coupling network, characterized in that, The device includes: The relevant information acquisition module is used to acquire relevant information about the power system, which includes multiple interconnected power plants and power relays; The physical-logical coupled network construction module is used to construct a physical layer network based on relevant information of the power system. Power plants and power relays are respectively used as application nodes and transition nodes in the physical layer network. Corresponding logical nodes are constructed based on the application nodes in the physical layer network, and a logical layer network representing communication capabilities is constructed based on each logical node. The logical layer network is an undirected and unweighted graph structure. Based on the physical layer network and the logical layer network, the power system is modeled as a physical-logical coupled network. The logical edge criticality list construction module is used to calculate the centrality score of each logical edge in the logical layer network using a mixed centrality metric, and to sort the logical edges in descending order according to the scores to obtain the logical edge criticality list. The module for generating candidate nodes to be removed is used to select logical edges as target logical edges in the list of logical edge criticality in order, determine two corresponding application nodes in the physical layer network according to the target logical edges, calculate multiple shortest paths between the two application nodes, construct a total path set, and take all nodes in the total path set as candidate nodes to be removed. The critical node identification module is used to remove the candidate nodes to be removed in the physical layer network and delete the corresponding logical edges in the logical layer network. The maximum connected component change of the logical layer network after the logical edge deletion is used as the damage rate. When the damage rate meets a preset value, all the removed nodes are critical nodes.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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