A method and device for determining a key node of a power system based on physical attack and defense parameters, an electronic device, and a storage medium

Abstract

This invention discloses a method, apparatus, electronic device, and storage medium for determining key nodes in a power system based on physical attack and defense parameters, belonging to the field of power system security assessment and defense. The method includes: acquiring real-time network topology data, real-time node load data, and physical attack and defense parameters under an attack and defense simulation scenario; calculating the attack success probability and defense success probability of each node based on the physical attack and defense parameters, and further obtaining the damage probability of each node; establishing an optimization model with the goal of maximizing system risk based on the damage probability of each node, the real-time network topology data, and the real-time node load data; and determining the combination of attack nodes that maximizes system risk as key nodes in the power system by solving the optimization model. By implementing this invention, the problem of accurately identifying real key nodes in complex physical attack and defense scenarios using existing technologies can be solved.

Description

Technical Field

[0001] This invention relates to the field of power system security assessment and defense technology, specifically to a method, device, electronic device, and storage medium for determining key nodes in a power system based on physical attack and defense parameters. Background Technology

[0002] With the continuous expansion of power system interconnection and its increasing importance in national security strategy, power grids have become key targets for physical attacks (such as precision-guided weapon strikes) in wartime or extreme confrontation environments. In such high-intensity physical confrontation scenarios, accurately identifying critical nodes in the power system is of paramount importance for guiding defenders in developing pre-deployment plans for interception resources, optimizing emergency defense strategies, and enhancing the overall survivability of the system.

[0003] However, existing methods for identifying critical nodes in power systems still have significant shortcomings when dealing with physical entity attack and defense scenarios. Most existing technologies focus on evaluating node importance from the perspective of network topology (such as degree centrality and betweenness centrality) or based on deterministic failure assumptions (such as the Nk principle). Even when some studies involve attack risk assessment, they often oversimplify the attack and defense interaction process. Specifically, existing technologies typically assume that an attacker's attack on a node is a deterministic event (i.e., attack equals destruction), or simply use fixed probability values ​​to replace complex attack and defense games, ignoring the inherent high degree of uncertainty in the physical attack process. In reality, the final probability of a node's destruction is constrained by complex physical ballistic characteristics and defense interception mechanisms, such as weapon accuracy, target size, radar detection performance, and the reaction speed of the interception system. Because existing technologies lack refined consideration of these key physical attack and defense parameters, they cannot accurately quantify the survival probability of nodes in a real physical confrontation environment. This leads to discrepancies between the calculated system risk distribution and the actual situation, making it difficult to accurately identify the truly critical nodes that require focused defense. Summary of the Invention

[0004] This invention provides a method, apparatus, electronic device, and storage medium for determining key nodes in a power system based on physical attack and defense parameters. This solves the problem in the prior art that, when determining key nodes, specific physical attack and defense parameters such as attack errors, radar cross-sections, and interception system effectiveness during physical attacks are ignored, leading to distorted calculations of node damage probability and making it difficult to accurately locate the real key nodes in complex physical attack and defense scenarios.

[0005] One embodiment of the present invention provides a method for determining critical nodes in a power system based on physical attack and defense parameters, comprising: The system acquires real-time network topology data, real-time load data of nodes, and physical attack and defense parameters in the attack and defense simulation scenario of the power system. The physical attack and defense parameters include attack error parameters of each node, target damage radius parameters, radar cross-section parameters, interceptor missile flight time parameters, fragment detonation parameters, and the number of interceptor missiles configured. Based on the attack error parameters and the target damage radius parameters, the attack success probability of each node in the attack and defense simulation scenario is calculated; based on the radar cross-section parameters, the interceptor missile flight time parameters, the fragment detonation parameters, and the number of interceptor missiles configured, the defense success probability of each node in the attack and defense simulation scenario is calculated; based on the attack success probability and the defense success probability, the damage probability of each node in the power system is calculated. Based on the damage probability of each node, the real-time network topology data, and the real-time load data of the nodes, an optimization model is established with the goal of maximizing system risk. Solving the optimization model will identify the combination of attack nodes that maximizes the system risk as the critical nodes of the power system.

[0006] Furthermore, the step of calculating the attack success probability of each node in the attack and defense simulation scenario based on the attack error parameter and the target damage radius parameter includes: Based on the preset diffusion Gaussian damage function, the target damage radius parameter is converted into a scaling factor, and the attack error parameter is converted into a standard error; Calculate the superposition value of the scaling factor and the standard error at a preset power; Calculate the ratio of the preset power value of the scaling factor to the superimposed value, and determine the ratio as the attack success probability of each node.

[0007] Furthermore, the step of calculating the success probability of defense for each node in the attack-defense simulation scenario based on the radar cross-section parameters, the interceptor missile flight time parameters, the fragment detonation parameters, and the number of interceptor missiles configured includes: Calculate the target detection probability for each node based on the radar cross-section parameters corresponding to each node; Based on the interceptor flight time parameters corresponding to each node, construct the interception time window constraints for each node; Based on the satisfaction of the interception time window constraints of each node, calculate the effective launch probability and the effective guidance probability of the interceptor missile at each node. Calculate the kill probability of the interceptor missile at each node based on the fragment detonation parameters corresponding to each node; Based on the target detection probability, effective launch probability of interceptor missile, effective guidance probability of interceptor missile, and kill probability of interceptor missile at each node, calculate the single-shot intercept success probability at each node. The success rate of defense for each node is calculated based on the number of interceptor missiles configured for each node and the single-shot interception success rate for each node.

[0008] Furthermore, the calculation of the defense success probability of each node based on the number of interceptor missiles configured for each node and the single-shot interception success probability of each node includes: Based on the single-shot interception success probability, calculate the single-shot failure probability of a single interceptor missile failing to intercept. The single-shot failure probability is powered based on the number of interceptor missiles configured to obtain the joint failure probability; The remaining probability after removing the joint failure probability from the preset full probability space is determined, and the remaining probability is determined as the defense success probability of each node.

[0009] Furthermore, the step of calculating the damage probability of each node in the power system based on the attack success probability and the defense success probability includes: Based on the success rate of defense at each node, determine the failure rate of defense at each node; Calculate the joint probability of the attack success probability and the defense failure probability of each node, and determine the joint probability as the damage probability of each node.

[0010] Furthermore, the step of establishing an optimization model aimed at maximizing system risk based on the damage probability of each node, the real-time network topology data, and the real-time load data of the nodes includes: Based on the damage probability of each node, determine the joint damage probability of the attack node combination composed of the nodes. Based on the real-time network topology data and the real-time load data of the nodes, power system operation constraints are constructed. Based on the power system operating constraints, determine the system load loss that is limited by the power system operating constraints; Based on the combined damage probability and the system load loss, a system risk assessment index is constructed to characterize the system risk assessment index of the attack node combination under attack. Using the selection state of the attack node combination as the decision variable and maximizing the system risk assessment index as the objective function, an optimization model constrained by the power system operation constraints is established.

[0011] Furthermore, the power system operating constraints include topology reconfiguration constraints, node power balance constraints, and line transmission power constraints: The topology reconstruction constraints are specifically as follows: in, Indicates the connection node and nodes The connection status of the line, 1 indicates connected, 0 indicates disconnected; and Representing nodes respectively and nodes The damage status is represented by 1 for normal and 0 for damaged. The node power balance constraint is specifically as follows: in, Represents a node The generator output, Represents a node The original load demand, Represents a node The shear load, Indicates the line Transmission power, Represents nodes The set of connected nodes; the load shedding amount The sum of these values ​​represents the system load loss. The line transmission power constraint is specifically as follows: in, and Representing nodes respectively and nodes voltage phase angle, Indicates the line Reactance, Indicates the line The upper limit of transmission capacity.

[0012] Based on the above method embodiments, the present invention provides corresponding apparatus embodiments.

[0013] An embodiment of the present invention provides a device for determining key nodes in a power system based on physical attack and defense parameters, comprising: a data acquisition module, a probability calculation module, a model building module, and a key node determination module; The data acquisition module is used to acquire real-time network topology data of the power system, real-time load data of nodes, and physical attack and defense parameters in the attack and defense simulation scenario; wherein, the physical attack and defense parameters include attack error parameters of each node, target damage radius parameters, radar cross-section parameters, interceptor missile flight time parameters, fragment detonation parameters, and the number of interceptor missiles configured. The probability calculation module is used to calculate the attack success probability of each node in the attack and defense simulation scenario based on the attack error parameter and the target damage radius parameter; to calculate the defense success probability of each node in the attack and defense simulation scenario based on the radar cross-section parameter, the interceptor missile flight time parameter, the fragment detonation parameter and the number of interceptor missiles configured; and to calculate the damage probability of each node in the power system based on the attack success probability and the defense success probability. The model building module is used to establish an optimization model with the goal of maximizing system risk based on the damage probability of each node, the real-time network topology data, and the real-time load data of the nodes. The critical node determination module is used to solve the optimization model and determine the combination of attack nodes that maximizes the system risk as the critical nodes of the power system.

[0014] Based on the above method embodiments, the present invention provides corresponding electronic device embodiments.

[0015] One embodiment of the present invention provides an electronic device, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the method for determining key nodes of a power system based on physical attack and defense parameters as described in any of the above-described method embodiments.

[0016] Based on the above method embodiments, the present invention provides corresponding storage medium embodiments.

[0017] One embodiment of the present invention provides a storage medium storing a computer program thereon, wherein, when the computer program is running, it controls the device where the storage medium is located to execute any of the above-described method embodiments of the method for determining key nodes of a power system based on physical attack and defense parameters.

[0018] Compared with the prior art, the present invention has the following beneficial effects: This invention provides a method, apparatus, electronic device, and storage medium for determining key nodes in a power system based on physical attack and defense parameters. The method acquires real-time network topology data, real-time node load data, and physical attack and defense parameters under an attack and defense simulation scenario for each power system. These physical attack and defense parameters include attack error parameters, target damage radius parameters, radar cross-section parameters, interceptor missile flight time parameters, fragment detonation parameters, and the number of interceptor missiles configured for each node. The method calculates the attack success probability of each node based on the attack error parameters and target damage radius parameters, and calculates the defense success probability of each node based on the radar cross-section parameters, interceptor missile flight time parameters, fragment detonation parameters, and the number of interceptor missiles configured for each node. The damage probability of each node is obtained from the attack success probability and defense success probability. Combining the node damage probability, real-time network topology data, and real-time node load data, an optimization model is constructed with the goal of maximizing system risk. By solving this optimization model, the combination of attack nodes that maximizes system risk is determined as the key nodes of the power system.

[0019] This invention obtains refined physical attack and defense parameters such as attack error, radar cross-section, interceptor flight time, and fragment detonation of each node, and calculates the attack success probability and defense success probability of each node in an attack and defense simulation scenario. This effectively solves the problem of distorted node survival status assessment caused by neglecting physical ballistic characteristics and defense interception details in existing technologies. On this basis, by embedding the node destruction probability, which can reflect the uncertainty of real physical confrontation, into an optimization model aimed at maximizing system risk, the invention achieves accurate identification of key nodes in power systems under complex physical attack and defense environments. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating a method for determining key nodes in a power system based on physical attack and defense parameters, provided by an embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram of a device for determining key nodes in a power system based on physical attack and defense parameters, provided in an embodiment of the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] like Figure 1As shown, to address the problem in existing technologies that neglect specific physical attack and defense parameters such as attack errors, radar cross-sections, and interception system effectiveness during the physical attack process when determining key nodes, leading to distorted calculations of node destruction probability and difficulty in accurately locating the true key nodes in complex physical attack and defense scenarios, an embodiment of the present invention provides a method for determining key nodes in a power system based on physical attack and defense parameters, comprising at least the following steps: Step S1: Obtain real-time network topology data of the power system, real-time load data of nodes, and physical attack and defense parameters in the attack and defense simulation scenario; wherein, the physical attack and defense parameters include attack error parameters of each node, target damage radius parameters, radar cross-section parameters, interceptor missile flight time parameters, fragment detonation parameters, and the number of interceptor missiles configured. Specifically, this step first requires building or connecting to a high-fidelity simulation environment that includes a power system operation model and a physical attack and defense model. For the power system portion, acquiring real-time network topology data refers to obtaining structured data characterizing the physical connections of the power network. This real-time network topology data includes the connection status between substation buses, transformers, transmission lines, and generator units, as well as electrical parameters such as resistance, reactance, susceptance, and transmission capacity limits of transmission lines. This data forms the physical basis for subsequent power flow calculations and constraint construction. Acquiring real-time node load data involves collecting the active power demand, reactive power demand, and active and reactive power output data of each node in the power system at the current moment. This real-time node load data reflects the current operating conditions of the power system and serves as the benchmark data for assessing the load loss after an attack.

[0024] In practical engineering implementation, to ensure the real-time nature and accuracy of the data, the real-time network topology data and node real-time load data can be collected through the real-time data interface of the power system's energy management system (EMS) or wide-area measurement system (WAMS). The topology data can be obtained by parsing CIM (Common Information Model) files, and the real-time load data can be derived from telemetry records of the SCADA system. For the physical attack and defense parameters in the attack and defense simulation scenario, they can be obtained by connecting to a military-grade attack and defense simulation platform or by loading a pre-set weapon and equipment database (containing parameters such as CEP and warhead yield of various missiles), thereby constructing a high-fidelity digital twin adversarial environment.

[0025] Based on the acquisition of power system data, this invention focuses on introducing physical attack and defense parameters in an attack and defense simulation scenario to quantify the uncertainties in the process of physical entity attack. The attack and defense simulation scenario is not a simple network attack simulation, but a digital simulation environment simulating the hard destruction of power facilities by physical weapons (such as precision-guided missiles) and the interception and countermeasure by defense systems (such as surface-to-air interceptor missiles). In the attack and defense simulation scenario, attack error parameters are acquired for each node. These parameters characterize the guidance accuracy of the attacking weapon system, typically manifested as the circular error probability (CEP) of the weapon's impact point relative to the predetermined target point. The attack error parameters determine the dispersion of the attack impact points. Target damage radius parameters are also acquired. These parameters characterize the effective coverage area that the attacking weapon's warhead can inflict on power facilities after explosion. The target damage radius parameters and attack error parameters together determine the single-shot hit probability in the absence of defensive interference.

[0026] Simultaneously, to assess the effectiveness of the defense, it is necessary to obtain the physical parameters related to defense and interception. This includes obtaining the radar cross section (RCS) parameters of each node. The RCS parameters characterize the electromagnetic wave reflection intensity of the target power node under radar illumination. The RCS parameters directly determine the distance at which the defense system's radar can detect incoming targets and are a key input for calculating the target detection probability. Finally, the interceptor missile's flight time parameters are obtained. These parameters characterize the dynamic flight time required for the interceptor missile launched by the defender to reach the predetermined interception point from the launch point. The interceptor missile's flight time parameters are constrained by its flight speed and interception distance. By comparing the interceptor missile's flight time parameters with the flight time of the incoming target, it can be determined whether the interception time window constraint is met.

[0027] Furthermore, obtaining fragmentation detonation parameters is crucial. These parameters characterize the effectiveness of the interceptor warhead in destroying incoming targets by detonating fragments, specifically reflecting the interceptor's lethality during the terminal guidance phase. Obtaining the number of interceptor missiles deployed refers to the total number of available interceptor missiles deployed by the defender around each protected node in the attack-defense simulation scenario. This number determines the number of interceptions or the density of multiple salvos that the defender can initiate. By acquiring the aforementioned real-time network topology data of the power system, real-time node load data, and six specific physical attack-defense parameters from the attack-defense simulation scenario, comprehensive and physically consistent data support can be provided for subsequent accurate calculations of node damage probabilities under complex adversarial environments and the construction of system risk optimization models.

[0028] Step S2: Calculate the attack success probability of each node in the attack and defense simulation scenario based on the attack error parameter and the target damage radius parameter; calculate the defense success probability of each node in the attack and defense simulation scenario based on the radar cross-section parameter, the interceptor missile flight time parameter, the fragment detonation parameter, and the number of interceptor missiles configured; calculate the damage probability of each node in the power system based on the attack success probability and the defense success probability. In a preferred embodiment, calculating the attack success probability of each node in the attack-defense simulation scenario based on the attack error parameter and the target damage radius parameter includes: Based on the preset diffusion Gaussian damage function, the target damage radius parameter is converted into a scaling factor, and the attack error parameter is converted into a standard error; Calculate the superposition value of the scaling factor and the standard error at a preset power; Calculate the ratio of the preset power value of the scaling factor to the superimposed value, and determine the ratio as the attack success probability of each node.

[0029] In a preferred embodiment, calculating the success probability of defense for each node in the attack-defense simulation scenario based on the radar cross-section parameters, the interceptor missile flight time parameters, the fragment detonation parameters, and the number of interceptor missiles configured includes: Calculate the target detection probability for each node based on the radar cross-section parameters corresponding to each node; Based on the interceptor flight time parameters corresponding to each node, construct the interception time window constraints for each node; Based on the satisfaction of the interception time window constraints of each node, calculate the effective launch probability and the effective guidance probability of the interceptor missile at each node. Calculate the kill probability of the interceptor missile at each node based on the fragment detonation parameters corresponding to each node; Based on the target detection probability, effective launch probability of interceptor missile, effective guidance probability of interceptor missile, and kill probability of interceptor missile at each node, calculate the single-shot intercept success probability at each node. The success rate of defense for each node is calculated based on the number of interceptor missiles configured for each node and the single-shot interception success rate for each node.

[0030] In a preferred embodiment, calculating the defense success probability of each node based on the number of interceptor missiles configured for each node and the single-shot interception success probability of each node includes: Based on the single-shot interception success probability, calculate the single-shot failure probability of a single interceptor missile failing to intercept. The single-shot failure probability is powered based on the number of interceptor missiles configured to obtain the joint failure probability; The remaining probability after removing the joint failure probability from the preset full probability space is determined, and the remaining probability is determined as the defense success probability of each node.

[0031] In a preferred embodiment, calculating the damage probability of each node in the power system based on the attack success probability and the defense success probability includes: Based on the success rate of defense at each node, determine the failure rate of defense at each node; Calculate the joint probability of the attack success probability and the defense failure probability of each node, and determine the joint probability as the damage probability of each node.

[0032] Specifically, the core task in this step is to transform the physical-level attack and defense parameters into probabilistic mathematical expressions, thereby providing a quantitative basis for subsequent risk assessment. First, regarding the calculation on the attack side, the attack and defense simulation scenario simulates the process of a ballistic missile or guided weapon striking a power node. The success probability of attacking each node in the attack and defense simulation scenario is calculated based on the attack error parameters and the target damage radius parameters. The specific execution process is as follows: A pre-defined Diffused Gaussian Damage Function is used to describe the relationship between weapon impact point distribution and damage effect. First, the obtained target damage radius parameter is defined as the effective coverage area capable of inflicting devastating damage on nodes, and this parameter is converted into a scaling factor. Simultaneously, the obtained attack error parameter (usually the circular error probable, CEP) is converted into a standard error characterizing the dispersion of impact points. Then, the scaling factor and the standard error are superimposed using a pre-defined power, typically 2, to simulate the area coverage effect on a two-dimensional plane. Specifically, the sum of the squares of the scaling factor and the standard error is calculated to obtain the superimposed value. Finally, the ratio of the pre-defined power of the scaling factor (i.e., the square of the scaling factor) to the superimposed value is calculated, and this ratio is determined as the attack success probability for each node. The formula for calculating the attack success probability is as follows: In the above formula, This indicates the probability of a successful attack on the node. This represents the scaling factor corresponding to the target damage radius parameter; This represents the standard error corresponding to the attack error parameter. It can be seen from the above formula that the higher the weapon accuracy (i.e., the more accurate the attack error parameter), the more accurate the attack error parameter becomes. The smaller the radius of attack (or the larger the radius of destruction), the higher the probability of a successful attack.

[0033] Secondly, regarding the calculations on the defensive side, the attack-defense simulation scenario considers the interception process of an incoming target by a surface-to-air missile defense system. The calculation of the successful defense probability at each node in the attack-defense simulation scenario, based on the radar cross-section parameters, the interceptor missile's flight time parameters, the fragment detonation parameters, and the number of interceptor missiles, is a phased probability accumulation process, specifically including the following steps: The first step is to calculate the target detection probability for each node based on the radar cross-section (RCS) parameters corresponding to each node. The RCS parameters determine the distance at which the defensive radar can detect incoming targets. When an incoming target enters the radar's detection range, the radar system locks onto the target with a certain probability, thus obtaining the target detection probability.

[0034] The second step is to construct the interception time window constraints for each node based on the interceptor missile's flight time parameters corresponding to each node. The interception operation must be completed before the incoming target hits the power node; therefore, it is necessary to compare the flight time required for the interceptor missile to reach the interception point with the remaining flight time of the incoming target. If the interceptor missile's flight time is less than the remaining flight time of the incoming target, then the interception time window constraints are satisfied.

[0035] The specific interception time window constraint can be expressed by the mathematical inequality as follows: in, For the dynamic flight time of the interceptor missile, This allows for the reaction and preparation time of the defense system (including radar lock confirmation and launch ignition delay). This represents the remaining flight time of the incoming target to the protected power node. The interception time window constraint is only considered "satisfied" when this inequality holds, at which point the effective launch probability of the interceptor missile can be non-zero; otherwise, physical interception is impossible, and the launch probability will be forcibly constrained to 0.

[0036] The third step is to calculate the effective launch probability and effective guidance probability of the interceptor missile at each node based on whether the interception time window constraints are met. If the interception time window is not met, the missile cannot be effectively launched or guided, and the corresponding probability approaches zero; if the time window is met, the specific launch probability and guidance probability are determined based on the fire control performance of the defense system.

[0037] The fourth step is to calculate the kill probability of the interceptor missile at each node based on the fragmentation detonation parameters corresponding to each node. The kill probability of the interceptor missile represents the likelihood that it will destroy the incoming target using a fragmentation cloud after detonation at the terminal stage.

[0038] Fifth, based on the target detection probability, effective launch probability, effective guidance probability, and kill probability of each node, the single-shot interception success probability of each node is calculated through multiplication. The formula for calculating the single-shot interception success probability is as follows: In the above formula, This indicates the probability of a single-shot interception being successful; This indicates the probability of the target being detected; This indicates the effective launch probability of the interceptor missile; This indicates the probability of the interceptor missile's guidance being effective; This indicates the kill probability of the interceptor missile.

[0039] Step 6: Considering that multiple interceptor missiles are usually deployed for salvo firing to improve the interception success rate, the defense success probability of each node is calculated based on the number of interceptor missiles configured for each node and the single-shot interception success probability of each node. Specifically, the probability complement method is used: First, based on the single-shot interception success probability, the single-shot failure probability (i.e., the total probability 1 minus the single-shot interception success probability) is calculated; then, the single-shot failure probability is exponentially calculated based on the number of interceptor missiles configured to obtain the joint failure probability. This joint failure probability physically represents the extreme case where all launched interceptor missiles simultaneously miss the target or fail to destroy it; finally, the remaining probability after removing the joint failure probability from a preset total probability space (value 1) is determined, and this remaining probability is used as the defense success probability of each node. The formula for calculating the defense success probability is as follows: In the above formula, This indicates the probability of successful defense for the node; This indicates the number of interceptor missiles configured.

[0040] Finally, considering the overall game results from both the attack and defense sides, the probability of the power node ultimately being physically destroyed is calculated. The calculation of the damage probability of each node in the power system based on the attack success probability and the defense success probability includes: determining the defense failure probability of each node (i.e., the probability that the defense system fails to intercept the incoming target) based on the defense success probability of each node; calculating the joint probability of the attack success probability and the defense failure probability of each node, and determining the joint probability as the damage probability of each node. The formula for calculating the damage probability is as follows: In the above formula, This represents the probability of damage to the node.

[0041] Through the above steps, this application can map complex physical attack and defense parameters into precise node destruction probabilities. It not only considers the accuracy and power of attack weapons, but also fully reflects the detection, guidance and multiple missile salvo effectiveness of the defense system. This provides high-confidence input data for the subsequent construction of a system risk optimization model that is more in line with the real battlefield environment, and effectively improves the accuracy and practicality of the determination results of key nodes in the power system in physical entity confrontation scenarios.

[0042] Step S3: Based on the damage probability of each node, the real-time network topology data, and the real-time load data of the nodes, establish an optimization model with the goal of maximizing system risk. In a preferred embodiment, establishing an optimization model aimed at maximizing system risk based on the failure probability of each node, the real-time network topology data, and the real-time load data of the nodes includes: Based on the damage probability of each node, determine the joint damage probability of the attack node combination composed of the nodes. Based on the real-time network topology data and the real-time load data of the nodes, power system operation constraints are constructed. Based on the power system operating constraints, determine the system load loss that is limited by the power system operating constraints; Based on the combined damage probability and the system load loss, a system risk assessment index is constructed to characterize the system risk assessment index of the attack node combination under attack. Using the selection state of the attack node combination as the decision variable and maximizing the system risk assessment index as the objective function, an optimization model constrained by the power system operation constraints is established.

[0043] In a preferred embodiment, the power system operating constraints include topology reconfiguration constraints, node power balance constraints, and line transmission power constraints: The topology reconstruction constraints are specifically as follows: in, Indicates the connection node and nodes The connection status of the line, 1 indicates connected, 0 indicates disconnected; and Representing nodes respectively and nodes The damage status is represented by 1 for normal and 0 for damaged. The node power balance constraint is specifically as follows: in, Represents a node The generator output, Represents a node The original load demand, Represents a node The shear load, Indicates the line Transmission power, Represents nodes The set of connected nodes; the load shedding amount The sum of these values ​​represents the system load loss. The line transmission power constraint is specifically as follows: in, and Representing nodes respectively and nodes voltage phase angle, Indicates the line Reactance, Indicates the line The upper limit of transmission capacity.

[0044] Specifically, the core logic in this step lies in combining the probability index calculated in step S2 with the physical operational consequences of the power system to construct a risk assessment model. The establishment of an optimization model aimed at maximizing system risk is not merely a mathematical calculation, but rather the construction of a planning problem with two layers of logic: the inner layer logic involves minimizing system losses through load shedding and other means under given equipment failure conditions; the outer layer logic seeks the combination of attack nodes that maximizes the product of the "probability of occurrence" and the "system loss" (i.e., risk).

[0045] In the specific implementation process, an optimization model is established based on the damage probability of each node, the real-time network topology data, and the real-time load data of the nodes, with the objective of maximizing system risk. The specific execution process is as follows: First, the input at the probabilistic level is processed. Based on the damage probability of each node, the joint damage probability of the attack node combination composed of these nodes is determined. In attack and defense simulation scenarios, the attacker typically selects a group of nodes as targets, forming an attack node combination. Assuming that the damage events of each node are physically independent, the joint damage probability can be obtained by multiplying the damage probabilities of each attacked node in the attack node combination. The joint damage probability characterizes the likelihood that a specific attack tactic will produce the expected physical damage consequences.

[0046] Secondly, physical constraints are constructed, which is a crucial link connecting the attack and defense scenario with power operation. Based on the real-time network topology data and the real-time load data of the nodes, power system operation constraints are constructed. Unlike conventional power system optimization and scheduling, the constraints in this application must include response logic to the discrete event of "component damage," that is, they need to describe how the network topology changes after a node is damaged, and how this change affects the power flow distribution. The power system operation constraints include topology reconfiguration constraints, node power balance constraints, and line transmission power constraints.

[0047] The topology reconfiguration constraint describes the logical relationship between node states and line states. Physically, damage to a substation or tower (node) inevitably leads to the disconnection of the transmission line connected to that node. Through this formula, if either node at either end of the line is damaged (state 0), the line state is forcibly changed to 0, thus achieving automatic network topology reconfiguration in the mathematical model.

[0048] The node power balance constraint is based on Kirchhoff's Current Law (KCL) to ensure energy conservation at each node. In emergency situations where an attack reduces network transmission capacity, partial load shedding must be allowed to maintain system balance. In this constraint, the amount of load shedding is... The sum (i.e.) The load loss of the system is defined as the physical quantity that directly reflects the severity of the consequences of the attack.

[0049] The line transmission power constraint is based on a DC-OPF model to describe the physical laws governing power flow and thermal stability limits on the line. This constraint formula cleverly incorporates state variables. When the line is disconnected ( At this time, regardless of the node phase angle difference, the line transmission power The limit will be forcibly constrained to 0, and the upper and lower limits of power will also be shrunk to 0, thus accurately simulating the effect of a physical wire break.

[0050] After completing the above physical constraint construction, the system load loss amount, which is subject to the power system operation constraints, is determined based on the power system operation constraints. This means that, under any given combination of attack nodes and damage state, by solving a linear programming problem that minimizes the load shedding, the minimum total load that the system must lose under the current residual topology can be calculated, i.e., the aforementioned system load loss amount.

[0051] Subsequently, based on the combined damage probability and the system load loss, a system risk assessment index characterizing the attack node combination under attack is constructed. Risk is defined as the product of probability and consequence. Therefore, multiplying the combined damage probability by the system load loss yields the system risk assessment index (Risk Metric). This index comprehensively considers both the ease of an attack (determined by physical attack and defense parameters) and the severity of the attack consequences (determined by power system topology and power flow).

[0052] Finally, using the selection state of the attack node combination as the decision variable and maximizing the system risk assessment index as the objective function, an optimization model constrained by the power system operation constraints is established. This is a mathematical programming model aimed at finding the weakest link. The model iterates or searches through different attack node combinations (i.e., changing the decision variables) to find the combination that maximizes the system risk assessment index while satisfying all physical operation constraints. By establishing and solving this optimization model, a deep integration of the complex physical attack and defense process with the power system operation mechanism is achieved, enabling the accurate identification of critical nodes from a massive number of nodes that, once attacked, would pose the greatest expected risk to the system.

[0053] Step S4: Solve the optimization model to determine the combination of attack nodes that maximizes the system risk as the key nodes of the power system.

[0054] Specifically, in this step, considering that the optimization model established in step S3 is a typical nonlinear bilevel programming problem, and that the decision variables (the selection state of the attack node combination) are discrete variables with characteristics of non-convexity, discontinuity, and combinatorial explosion, conventional analytical methods are difficult to solve directly. Therefore, an intelligent optimization algorithm is used to iteratively optimize the optimization model to efficiently approximate the global optimum. In specific implementation, a genetic algorithm (GA) is used as the solution engine, transforming the process of finding key nodes in the power system into a process of biological population evolution.

[0055] First, population initialization and encoding are performed. Each possible combination of attack nodes is mapped to a virtual biological individual, and a chromosome is constructed using binary encoding. In the chromosome, each gene bit corresponds to a node in the power system; a gene bit value of 1 indicates that the corresponding node has been selected as an attack target, and a gene bit value of 0 indicates that the corresponding node has not been selected. A certain number of initial individuals are generated using a random number generator to form the initial population, which covers a variety of potential attack node combinations.

[0056] Secondly, the core fitness evaluation process is executed. Fitness evaluation is the bridge connecting the optimization algorithm and the physical model. For each individual generated in the initial population or during the iteration process, the attack node combination state corresponding to that individual needs to be analyzed first. Based on the analyzed attack node combination state, the power system flow calculation program and linear programming solver are invoked. Under the premise of satisfying the topology reconfiguration constraints, node power balance constraints, and line transmission power constraints constructed in step S3, the minimum total load shedding of the system is calculated, thereby obtaining the system load loss. At the same time, using the node damage probabilities calculated in step S2, the joint damage probability corresponding to that individual is calculated. Subsequently, the joint damage probability is multiplied by the system load loss to obtain the value of the system risk assessment index. The value of the system risk assessment index is directly defined as the fitness function value of that individual. The larger the fitness function value, the higher the potential risk that the attack node combination poses to the power system.

[0057] Next, the population undergoes evolution and iterative updates. Based on the calculated fitness function values, selection, crossover, and mutation operations are performed on the population. A roulette wheel selection algorithm is used, giving individuals with higher fitness function values ​​a greater probability of being selected, thus preserving excellent attack node combination characteristics. Gene crossover is performed on selected individuals, generating new attack node combinations by exchanging partial gene segments. Gene positions of some individuals are flipped (i.e., 0 becomes 1 or 1 becomes 0) according to a preset mutation probability to increase population diversity and prevent the algorithm from getting trapped in local optima. The above fitness evaluation, selection, crossover, and mutation steps are repeated until a preset maximum number of iterations is reached or the fitness function value no longer increases significantly.

[0058] In practical calculations, to ensure the convergence speed and quality finding of the algorithm, and to avoid getting trapped in local optima, the relevant parameters of the genetic algorithm can be set according to the following strategy: the population size can be set according to the number of nodes N in the power system, for example, between 2N and 4N; the maximum number of iterations can be set to 100 to 500; the crossover probability is usually set between 0.6 and 0.9; and the mutation probability is usually set between 0.01 and 0.1. Furthermore, an elitism strategy can be introduced, that is, in each iteration, the individuals with the highest fitness are forcibly retained to directly enter the next generation.

[0059] Finally, the final result is output. After the iteration process terminates, the individual with the largest fitness function value is selected from the final population. This individual with the largest fitness function value is decoded to reconstruct a specific combination of attack nodes. This combination of attack nodes is identified as the critical nodes of the power system, that is, the set of targets that are most vulnerable and require the most focused defense under the current physical attack and defense parameters and power grid operating conditions. Through the above solution process, the set of nodes that would pose the greatest risk to the power system if attacked can be quickly and accurately identified from a massive number of possible combinations, providing a direct quantitative decision-making basis for the optimal allocation of defense resources.

[0060] Furthermore, after identifying the key nodes of the power system, this invention can also be directly applied to guide the optimized allocation of defense resources and the formulation of emergency plans for the power system. For example, for the identified key nodes, the defending party can prioritize the deployment of close-in weapon systems (CIWS) or increase electronic jamming equipment to reduce the probability of physical damage to the node; or at the power grid planning level, additional tie transformers can be added to the substations where these key nodes are located, or new transmission channels can be planned to improve the N-1 / Nk redundancy of the network topology, thereby comprehensively improving the survivability of the power system at the physical and cyber-physical integration level.

[0061] Based on the above method embodiments, the present invention provides corresponding apparatus embodiments.

[0062] like Figure 2 As shown, an embodiment of the present invention provides a device for determining key nodes in a power system based on physical attack and defense parameters, including: a data acquisition module, a probability calculation module, a model building module, and a key node determination module; The data acquisition module is used to acquire real-time network topology data of the power system, real-time load data of nodes, and physical attack and defense parameters in the attack and defense simulation scenario; wherein, the physical attack and defense parameters include attack error parameters of each node, target damage radius parameters, radar cross-section parameters, interceptor missile flight time parameters, fragment detonation parameters, and the number of interceptor missiles configured. The probability calculation module is used to calculate the attack success probability of each node in the attack and defense simulation scenario based on the attack error parameter and the target damage radius parameter; to calculate the defense success probability of each node in the attack and defense simulation scenario based on the radar cross-section parameter, the interceptor missile flight time parameter, the fragment detonation parameter and the number of interceptor missiles configured; and to calculate the damage probability of each node in the power system based on the attack success probability and the defense success probability. The model building module is used to establish an optimization model with the goal of maximizing system risk based on the damage probability of each node, the real-time network topology data, and the real-time load data of the nodes. The critical node determination module is used to solve the optimization model and determine the combination of attack nodes that maximizes the system risk as the critical nodes of the power system.

[0063] In a preferred embodiment, the probability calculation module calculates the attack success probability of each node in the attack and defense simulation scenario based on the attack error parameter and the target damage radius parameter, including: Based on the preset diffusion Gaussian damage function, the target damage radius parameter is converted into a scaling factor, and the attack error parameter is converted into a standard error; Calculate the superposition value of the scaling factor and the standard error at a preset power; Calculate the ratio of the preset power value of the scaling factor to the superimposed value, and determine the ratio as the attack success probability of each node.

[0064] In a preferred embodiment, the probability calculation module calculates the success probability of defense for each node in the attack-defense simulation scenario based on the radar cross-section parameters, the interceptor missile flight time parameters, the fragment detonation parameters, and the number of interceptor missiles configured, including: Calculate the target detection probability for each node based on the radar cross-section parameters corresponding to each node; Based on the interceptor flight time parameters corresponding to each node, construct the interception time window constraints for each node; Based on the satisfaction of the interception time window constraints of each node, calculate the effective launch probability and the effective guidance probability of the interceptor missile at each node. Calculate the kill probability of the interceptor missile at each node based on the fragment detonation parameters corresponding to each node; Based on the target detection probability, effective launch probability of interceptor missile, effective guidance probability of interceptor missile, and kill probability of interceptor missile at each node, calculate the single-shot intercept success probability at each node. The success rate of defense for each node is calculated based on the number of interceptor missiles configured for each node and the single-shot interception success rate for each node.

[0065] In a preferred embodiment, the probability calculation module calculates the defense success probability of each node based on the number of interceptor missiles configured for each node and the single-shot interception success probability of each node, including: Based on the single-shot interception success probability, calculate the single-shot failure probability of a single interceptor missile failing to intercept. The single-shot failure probability is powered based on the number of interceptor missiles configured to obtain the joint failure probability; The remaining probability after removing the joint failure probability from the preset full probability space is determined, and the remaining probability is determined as the defense success probability of each node.

[0066] In a preferred embodiment, the probability calculation module calculates the damage probability of each node in the power system based on the attack success probability and the defense success probability, including: Based on the success rate of defense at each node, determine the failure rate of defense at each node; Calculate the joint probability of the attack success probability and the defense failure probability of each node, and determine the joint probability as the damage probability of each node.

[0067] In a preferred embodiment, the model building module establishes an optimization model aimed at maximizing system risk based on the damage probability of each node, the real-time network topology data, and the real-time load data of the nodes, including: Based on the damage probability of each node, determine the joint damage probability of the attack node combination composed of the nodes. Based on the real-time network topology data and the real-time load data of the nodes, power system operation constraints are constructed. Based on the power system operating constraints, determine the system load loss that is limited by the power system operating constraints; Based on the combined damage probability and the system load loss, a system risk assessment index is constructed to characterize the system risk assessment index of the attack node combination under attack. Using the selection state of the attack node combination as the decision variable and maximizing the system risk assessment index as the objective function, an optimization model constrained by the power system operation constraints is established.

[0068] It should be noted that the embodiments of the device described above correspond to the embodiments of the present invention described above, and can realize the method for determining key nodes of a power system based on physical attack and defense parameters as described in any one of the present invention. Furthermore, the embodiments of the device described above are merely illustrative. The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Additionally, in the accompanying drawings of the device embodiments provided by the present invention, the connection relationship between modules indicates that they have a communication connection, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without creative effort.

[0069] Based on the above-described method embodiments of the present invention, a corresponding embodiment of an electronic device is provided.

[0070] An embodiment of the present invention provides an electronic device, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the method for determining key nodes of a power system based on physical attack and defense parameters as described in any one of the present invention, or the processor implements the functions of each module in the above-described device embodiments.

[0071] For example, the computer program may be divided into one or more modules, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules may be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program in the terminal device.

[0072] The terminal device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0073] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the terminal device, connecting all parts of the terminal device via various interfaces and lines.

[0074] The memory can be used to store the computer programs and / or modules. The processor implements various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory and by calling data stored in the memory. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, applications required for at least one function, etc.; the data storage area may store data created based on the use of the mobile phone, etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital card (SD card), flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0075] Based on the above method embodiments, the present invention provides corresponding storage medium embodiments; Another embodiment of the present invention provides a storage medium including a stored computer program, wherein, when the computer program is running, the device where the storage medium is located executes any of the above-described methods for determining key nodes of a power system based on physical attack and defense parameters.

[0076] The aforementioned storage medium is a computer-readable storage medium, and the computer program includes computer program code, which may be in the form of source code, object code, executable file, or certain intermediate forms. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0077] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0078] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for determining a critical node of a power system based on physical attack-defense parameters, characterized in that, include: The system acquires real-time network topology data, real-time load data of nodes, and physical attack and defense parameters in the attack and defense simulation scenario of the power system. The physical attack and defense parameters include attack error parameters of each node, target damage radius parameters, radar cross-section parameters, interceptor missile flight time parameters, fragment detonation parameters, and the number of interceptor missiles configured. Based on the attack error parameters and the target damage radius parameters, the attack success probability of each node in the attack and defense simulation scenario is calculated; based on the radar cross-section parameters, the interceptor missile flight time parameters, the fragment detonation parameters, and the number of interceptor missiles configured, the defense success probability of each node in the attack and defense simulation scenario is calculated; based on the attack success probability and the defense success probability, the damage probability of each node in the power system is calculated. Based on the damage probability of each node, the real-time network topology data, and the real-time load data of the nodes, an optimization model is established with the goal of maximizing system risk. Solving the optimization model will identify the combination of attack nodes that maximizes the system risk as the critical nodes of the power system.

2. The method for determining critical nodes of a power system based on physical attack-defense parameters according to claim 1, wherein, The step of calculating the attack success probability of each node in the attack and defense simulation scenario based on the attack error parameter and the target damage radius parameter includes: Based on the preset diffusion Gaussian damage function, the target damage radius parameter is converted into a scaling factor, and the attack error parameter is converted into a standard error; Calculate the superposition value of the scaling factor and the standard error at a preset power; Calculate the ratio of the preset power value of the scaling factor to the superimposed value, and determine the ratio as the attack success probability of each node. 3.The method for determining the critical nodes of a power system based on physical attack-defense parameters according to claim 2, wherein, The step of calculating the success probability of defense for each node in the attack-defense simulation scenario based on the radar cross-section parameters, the interceptor missile flight time parameters, the fragment detonation parameters, and the number of interceptor missiles configured includes: Calculate the target detection probability for each node based on the radar cross-section parameters corresponding to each node; Based on the interceptor flight time parameters corresponding to each node, construct the interception time window constraints for each node; Based on the satisfaction of the interception time window constraints of each node, calculate the effective launch probability and the effective guidance probability of the interceptor missile at each node. Calculate the kill probability of the interceptor missile at each node based on the fragment detonation parameters corresponding to each node; Based on the target detection probability, effective launch probability of interceptor missile, effective guidance probability of interceptor missile, and kill probability of interceptor missile at each node, calculate the single-shot intercept success probability at each node. The success rate of defense for each node is calculated based on the number of interceptor missiles configured for each node and the single-shot interception success rate for each node.

4. The method for determining critical nodes of a power system based on physical attack-defense parameters according to claim 3, wherein, The calculation of the defense success probability of each node based on the number of interceptor missiles configured for each node and the single-shot intercept success probability of each node includes: Based on the single-shot interception success probability, calculate the single-shot failure probability of a single interceptor missile failing to intercept. The single-shot failure probability is powered based on the number of interceptor missiles configured to obtain the joint failure probability; The remaining probability after removing the joint failure probability from the preset full probability space is determined, and the remaining probability is determined as the defense success probability of each node.

5. The method for determining key nodes in a power system based on physical attack and defense parameters as described in claim 4, characterized in that, The calculation of the damage probability of each node in the power system based on the attack success probability and the defense success probability includes: Based on the success rate of defense at each node, determine the failure rate of defense at each node; Calculate the joint probability of the attack success probability and the defense failure probability of each node, and determine the joint probability as the damage probability of each node.

6. The method for determining key nodes in a power system based on physical attack and defense parameters as described in claim 5, characterized in that, The step of establishing an optimization model based on the damage probability of each node, the real-time network topology data, and the real-time load data of the nodes, with the objective of maximizing system risk, includes: Based on the damage probability of each node, determine the joint damage probability of the attack node combination composed of the nodes. Based on the real-time network topology data and the real-time load data of the nodes, power system operation constraints are constructed. Based on the power system operating constraints, determine the system load loss that is limited by the power system operating constraints; Based on the combined damage probability and the system load loss, a system risk assessment index is constructed to characterize the system risk assessment index of the attack node combination under attack. Using the selection state of the attack node combination as the decision variable and maximizing the system risk assessment index as the objective function, an optimization model constrained by the power system operation constraints is established.

7. The method for determining key nodes in a power system based on physical attack and defense parameters as described in claim 6, characterized in that, The power system operation constraints include topology reconfiguration constraints, node power balance constraints, and line transmission power constraints: The topology reconstruction constraints are specifically as follows: in, Indicates the connection node and nodes The connection status of the line, 1 indicates connected, 0 indicates disconnected; and Representing nodes respectively and nodes The damage status is represented by 1 for normal and 0 for damaged. The node power balance constraint is specifically as follows: in, Represents a node The generator output, Represents a node The original load demand, Represents a node The shear load, Indicates the line Transmission power, Represents nodes The set of connected nodes; the load shedding amount The sum of these values ​​represents the system load loss. The line transmission power constraint is specifically as follows: in, and Representing nodes respectively and nodes voltage phase angle, Indicates the line Reactance, Indicates the line The upper limit of transmission capacity.

8. A device for determining key nodes in a power system based on physical attack and defense parameters, characterized in that, include: The module includes a data acquisition module, a probability calculation module, a model building module, and a key node determination module. The data acquisition module is used to acquire real-time network topology data of the power system, real-time load data of nodes, and physical attack and defense parameters in the attack and defense simulation scenario; wherein, the physical attack and defense parameters include attack error parameters of each node, target damage radius parameters, radar cross-section parameters, interceptor missile flight time parameters, fragment detonation parameters, and the number of interceptor missiles configured. The probability calculation module is used to calculate the attack success probability of each node in the attack and defense simulation scenario based on the attack error parameter and the target damage radius parameter; to calculate the defense success probability of each node in the attack and defense simulation scenario based on the radar cross-section parameter, the interceptor missile flight time parameter, the fragment detonation parameter and the number of interceptor missiles configured; and to calculate the damage probability of each node in the power system based on the attack success probability and the defense success probability. The model building module is used to establish an optimization model with the goal of maximizing system risk based on the damage probability of each node, the real-time network topology data, and the real-time load data of the nodes. The critical node determination module is used to solve the optimization model and determine the combination of attack nodes that maximizes the system risk as the critical nodes of the power system.

9. An electronic device, characterized in that, The system includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor executes the computer program to implement the method for determining critical nodes of a power system based on physical attack and defense parameters as described in any one of claims 1 to 7.

10. A storage medium, characterized in that, The storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device where the storage medium is located to perform the power system critical node determination method based on physical attack and defense parameters as described in any one of claims 1 to 7.

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