Power distribution network survivability evaluation method considering false data injection attack

Abstract

The invention relates to the technical field of power system security, and discloses a power distribution network survivability evaluation method considering false data injection attacks, which comprises the following steps: establishing an information physical coupling system (CPS) model of a power distribution network; based on a preset node criticality evaluation index system, performing criticality evaluation on the power nodes in the power distribution network; constructing a false data injection attack (FDIA) model based on the criticality value of the power node; constructing an survivability evaluation index system comprising indexes of a physical layer, an information layer and a coupling layer; and calculating and outputting the survivability comprehensive evaluation index of the power distribution network CPS under the FDIA in combination with the survivability evaluation index system. According to the power distribution network survivability evaluation method, the accuracy, comprehensiveness and credibility of power distribution network survivability evaluation are remarkably improved by constructing a more real CPS model and an attack scene and adopting a more scientific evaluation system and an empowerment method, and effective decision support is provided for power grid safety planning and defense.

Description

Technical Field

[0001] This invention relates to the field of power system security technology, specifically to a method for evaluating the resilience of distribution networks that takes into account spoofing data injection attacks. Background Technology

[0002] Traditional distribution networks, primarily based on unidirectional power supply, are ill-suited to the complex scenarios of modern smart grids. In contrast, under a Cyber-Physical Systems (CPS) architecture, information flow becomes an indispensable part of the closed-loop energy flow within the power grid. Through the deep integration and interaction of energy and information flows, the functional and behavioral characteristics of the power grid are jointly determined. Introducing CPS allows for a more effective study and utilization of the coupling relationship between energy and information flows in distribution networks, breaking away from the isolated analysis of physical faults and information risks, and facilitating further research.

[0003] In recent years, there have been many large-scale power outages caused by sudden events worldwide. Research on the resilience assessment of power distribution networks is not only of theoretical significance, but also a key factor in ensuring the reliability and security of power supply.

[0004] With the deep integration of power distribution network cybersecurity systems (CPS) physical and information systems, cyberattacks not only disrupt the functionality of information systems but may also further threaten the secure operation of physical systems, highlighting the increasing importance of cybersecurity in distribution network CPS. Numerous malicious incidents involving cyberattacks have occurred internationally, threatening power grid operations and causing widespread and prolonged grid outages. FDIA (Distribution Data Interference) attacks, as a typical cyberattack method, pose a significant threat to the safe and reliable operation of distribution networks. Therefore, assessing the resilience of FDIA attacks is crucial for the safe, stable, and efficient operation of distribution networks.

[0005] Current research on FDIA in power systems mostly focuses on attack point detection and optimization strategies, with very little integration of such network attacks with distribution network resilience, analysis of the damage caused by FDIA to the distribution network, and resilience research focusing on node importance assessment, lacking research on cyber-physical joint considerations under CPS and resilience evaluation methods for specific attack scenarios. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for evaluating the resilience of distribution networks that takes into account spoofing data injection attacks. This method solves the problem that existing methods for evaluating the resilience of distribution networks, when considering spoofing data injection attacks, fail to fully integrate the coupling characteristics of cyber-physical systems (CPS) and the attacker's strategies, resulting in evaluation results that are not objective and accurate enough.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for evaluating the resilience of a distribution network considering spoofing data injection attacks, comprising the following steps: Step 1: Establish a cyber-physical system (CPS) model for the power distribution network, which includes a coupled information layer and a physical layer; Step 2: Based on the preset node criticality evaluation index system, the criticality of the power nodes in the power distribution network is evaluated to obtain the criticality value of each power node. Step 3: Based on the criticality value of the power node, construct a False Data Injection (FDIA) attack model to simulate an attack on the distribution network CPS; Step 4: Construct a resilience evaluation index system that includes physical layer, information layer and coupling layer indicators, and assign weights to each indicator using a subjective and objective weighting method. Step 5: Combining the FDIA attack model and the weighted resilience evaluation index system, calculate and output the comprehensive resilience evaluation index of the distribution network CPS under FDIA.

[0008] Preferably, the node criticality evaluation index system includes a composite index that combines traditional network topology indexes and power system characteristics, specifically including: degree centrality, node betweenness centrality, proximity centrality, electrical betweenness centrality, and voltage sensitivity index.

[0009] Preferably, the step of assessing the criticality of power nodes specifically includes: Construct an initial decision matrix based on the index values ​​of each node; The decision matrix is ​​normalized. The Gini coefficient is used to objectively weight each indicator, resulting in a weighting matrix; Determine the ideal optimal solution and the worst solution, and calculate the distance of each node to the ideal optimal solution and the worst solution. Finally, use the relative proximity as the criticality value of the node.

[0010] Preferably, the step of constructing the fake data injection attack model includes: determining the probability and intensity of an attacker attacking nodes with different criticality values ​​based on the criticality values ​​of the power nodes, wherein the higher the criticality value of a node, the higher the probability of it being attacked and the intensity of the attack.

[0011] Preferably, the subjective-objective fusion weighting method specifically includes: The best-worst method (BWM) was used as the subjective weighting method to determine the subjective weights of each dreadability index. The CRITIC method was used as an objective weighting method to determine the objective weights of each dreadability index; The subjective and objective weights are combined and optimized to obtain the final combined weights.

[0012] Preferably, the physical layer indicators in the resilience evaluation index system include at least: load loss rate and network connectivity rate.

[0013] Preferably, the information layer indicators in the resilience evaluation index system include at least: communication survival rate.

[0014] Preferably, the coupling layer indicators in the resilience evaluation index system include at least: cross-layer fault propagation speed and system resilience index.

[0015] Preferably, the step of calculating the comprehensive evaluation index of survivability specifically includes: multiplying the standardized index values ​​of each layer with the combined weights to obtain a weighted evaluation value, and calculating a comprehensive index representing the survivability level of the system based on the evaluation value.

[0016] This invention provides a method for evaluating the resilience of a distribution network that takes into account spoofing data injection attacks. It has the following beneficial effects: 1. This invention takes a cyber-physical system (CPS) perspective, analyzing the information nodes and physical devices of the distribution network as a tightly coupled whole, accurately depicting their interdependence and influence mechanisms. This overcomes the limitations of traditional methods that separate the information and physical layers, making the evaluation model more reflective of the actual operation of modern distribution networks.

[0017] 2. This invention determines the criticality of different nodes by quantitatively analyzing important nodes and weak links in the power grid, and uses this as a basis to set the target and intensity of False Data Injection (FDIA) attacks. This criticality-based attack strategy can effectively simulate the targeted attack behavior of advanced attackers in pursuit of maximum destructive effect, thereby more accurately predicting the actual damage to the distribution network when facing such intelligent threats.

[0018] 3. This invention is based on the distribution network CPS model and constructs resilience evaluation indicators from three dimensions: physical layer, information layer, and coupling layer. It combines the security status of the information system with the stable operation of the physical system and incorporates the direct impact of FDIA. This multi-level, multi-dimensional indicator system can comprehensively and three-dimensionally measure the system state after an attack, avoiding the one-sidedness of single-dimensional evaluation.

[0019] 4. This invention comprehensively employs both subjective and objective weighting methods, and optimizes the weight coefficients obtained from both methods. This effectively avoids the subjective bias or data distortion problems that may arise from a single weighting method, ensuring the scientific and reasonable nature of the weights for each indicator. The resulting comprehensive resilience index provides a reliable basis for quantitatively assessing the resilience of the distribution network, thus improving the overall authenticity and accuracy of the evaluation results. Attached Figure Description

[0020] Figure 1 This is the power CPS coupled network model of the present invention; Figure 2 This is a schematic diagram of the weighted construction of power grid nodes according to the present invention; Figure 3 This is a flowchart of the survivability evaluation process of the present invention; Figure 4 This is a schematic diagram of the overall method for assessing the resilience of power distribution networks according to the present invention; Figure 5 The diagram illustrates the effects of three different scenarios and the resilience index attack of this invention. Detailed Implementation

[0021] The technical solutions in 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.

[0022] Please see the appendix Figure 1 This invention provides a method for evaluating the resilience of a distribution network considering spoofing data injection attacks, comprising: The following steps: Step 1: Establish a cyber-physical system (CPS) model for the power distribution network, which includes a coupled information layer and a physical layer; Distribution network CPS deeply integrates physical devices and information networks in new power systems. Through the coupling of the information layer and the physical layer, it realizes the coordinated optimization of power flow and information flow, providing core support for the safe and stable operation and intelligent construction of distribution networks. It is the key technological foundation for promoting the transformation of traditional distribution networks into highly reliable smart distribution networks.

[0023] The distribution network CPS mainly consists of an information layer and a physical layer. The adjacency matrix J can be used to represent the connection relationships between different nodes in the distribution network. Therefore: (1); In the formula, J It is an adjacency matrix; m This refers to the number of nodes in the information layer. n This refers to the number of nodes in the physical layer. This is the information layer connection matrix, representing the connection relationships within the information layer; This is the physical layer connectivity matrix, representing the internal connectivity relationships of the physical layer. This is an information-physical coupling connection matrix, representing the corresponding links for data acquisition and command issuance; and Both are information-physical coupling connection matrices, but they have different functions, representing the power supply links of information nodes.

[0024] In this architecture, the physical layer forms the physical foundation, while the information layer is responsible for data acquisition, transmission, and the generation of decision-making instructions. The corresponding distribution network CPS architecture is as follows: Figure 1 Show.

[0025] Physical Layer: This layer represents the actual physical infrastructure of the distribution network. Specifically, graph theory is used to model the topology of the distribution network, where electrical equipment such as generators, substations, and load points are abstracted as power nodes, while transmission and distribution lines, transformers, etc., are abstracted as edges connecting nodes. This physical layer model reflects the network's connectivity and power flow distribution, among other physical characteristics.

[0026] Information Layer: This layer represents the communication and computing network supporting the monitoring, protection, and control of the power distribution network. Nodes in the information layer can include sensors, remote terminal units (RTUs), intelligent electronic devices (IEDs), and control center servers, while edges represent communication links between them. This information layer model is responsible for data acquisition, transmission, and processing. The physical layer and information layer are closely linked through coupling. For example, sensors on the power nodes in the physical layer (belonging to the information layer) collect data such as voltage and current, which are transmitted to the control center through the information layer's communication network; the control center's decision commands are then issued through the information layer, and the actuators (such as circuit breakers) in the physical layer complete the operation. The model in this invention accurately depicts this bidirectional coupling dependency.

[0027] The two operate in a closed-loop linkage of "perception-decision-execution": the physical layer's operational status is monitored and analyzed in real time by the information layer, and the information layer's optimization commands react on the physical layer's equipment control, jointly achieving the safe and efficient operation of the distribution network. In such a CPS, if any part fails or malfunctions, the connection may be disrupted, leading to interruptions in information or energy transmission, or even directly causing system malfunctions or failures. Therefore, it is urgent to construct the resource configuration of the physical layer, information layer, and coupling layer of the distribution network CPS, and to conduct research on the resilience assessment of the distribution network based on this.

[0028] Step 2: Based on the preset node criticality evaluation index system, the criticality of the power nodes in the power distribution network is evaluated to obtain the criticality value of each power node. Determination of node importance evaluation parameters: This invention abstracts the power grid structure and constructs a topology model, namely The set of power grid nodes is as follows: Let i represent the power grid node with ID i, and N be the total number of power grid nodes; the set of edges connecting nodes is... In the formula Let be the edge connecting nodes i and j.

[0029] The ratio of the load of node i to the total load per unit time is set as the weight of the power grid node, forming a weight set. In the formula Let be the weight of node i. The load of node i per unit time is the sum of the incoming load and outgoing load per unit time. This is achieved using an adjacency matrix. This indicates the connection status between nodes in the power grid: (2); If power grid nodes i and j are directly connected, then ;otherwise .

[0030] Power grid node load weighted construction such as Figure 2 As shown, the size of the node is positively correlated with the load.

[0031] To identify weaknesses in the network and simulate attacker preferences, it is necessary to assess the criticality of power nodes at the physical layer. First, a composite node criticality evaluation index system is established. This system considers not only the network topology but also the operational characteristics of the power system. Specifically, this index system includes the following five indicators: 1) Degree centrality Node degree generally refers to the number of neighboring nodes with direct connections to a given node, i.e., the number of edges connecting node i to other nodes. Node degree centrality, based on node degree, represents the degree to which a node in a network is directly connected to all other nodes. The higher the degree centrality value, the more important the node. Degree centrality reflects a node's ability to be directly connected to its neighbors, and its expression is: (3); (4); In the formula, This represents the degree of node i, where i = 1, 2, ,N; Indicate the degree centrality of node i, i=1,2, ,N.

[0032] 2) Node betweenness centrality Node betweenness centrality generally refers to the proportion of shortest paths passing through a given node. The more shortest paths that pass through the same node, the higher its importance. Node betweenness centrality characterizes a node's control over network flows transmitted along the shortest paths. Its expression is: (5); In the formula, Let i be the betweenness centrality of node i, i=1,2, ,N; The number of all shortest paths from node s to node t; Let i be the number of paths that pass through node i in these shortest paths.

[0033] 3) Proximity centrality Proximity centrality describes a node's overall influence in a network. It calculates the average shortest distance from a node to other nodes. A higher proximity centrality means a shorter average distance from that node to all other nodes, resulting in faster propagation within the network. Its expression is: (6); In the formula, Let i be the proximity centrality of node i; Let i be the average shortest distance from node i to all other nodes; Let j be the average shortest distance from node i to node j, where j = 1, 2, ,N.

[0034] 4) Electrical betweenness centrality Electrical betweenness centrality measures the pivotal role of a node in the power flow transmission path of a distribution network, representing the degree to which a node acts as an intermediary for energy transmission. Unlike nodal betweenness, electrical betweenness incorporates the physical characteristics of active power flow in a power system, better reflecting the nature of power transmission in a distribution network that follows Ohm's law. Its expression is: (7); In the formula, N is the total number of nodes; Let i be the total active power flow from node i to j; This refers to the portion of the active power flow from node i to j that is transmitted through node k. The electrical betweenness centrality of the node.

[0035] 5) Voltage sensitivity index Voltage sensitivity measures how easily a node's voltage is affected by power disturbances, reflecting the node's crucial role in maintaining system voltage stability. A higher node sensitivity means its voltage is more susceptible to power fluctuations, increasing the likelihood of voltage overshoot and threatening safe system operation. Its expression is: (8); In the formula This represents the voltage magnitude at node i; This represents the injected reactive power at node i; This represents the voltage sensitivity of node i.

[0036] The research approach for evaluating the criticality of power grid nodes is as follows: each power node is regarded as a decision-making scheme, and the evaluation index of node criticality is one of the attributes of the scheme. Multiple evaluation indicators correspond to multiple different attributes. Multi-attribute decision-making is carried out on the node criticality. The larger the final value, the more critical the node is.

[0037] Then, based on the above indicator system, the final criticality value of each power node is calculated through the following process: 1) Construct the decision matrix. If the total number of nodes in the network is n, then there are n decision schemes. If the number of node importance evaluation indicators is m, then there are m attributes for each scheme. The indicator value for each node in the network is... (i=1,2,…,n; j=1,2,…,m), the initial decision matrix X constructed is as follows: (9); 2) For the index values ​​in the decision matrix Normalization is performed: (10); In the formula For indicator value Normalization result. The normalized matrix R obtained after normalization is as follows: (11); 3) The indicators for assessing the importance of network nodes are generally of different importance; therefore, it is necessary to assign weights to each indicator. The Gini coefficient is introduced to objectively weight each indicator. Assume that the group income is arranged in ascending order and divided into n equal groups, where the ratio of the cumulative income from group 1 to group i to the total income of the entire population is... The formula for calculating the Gini coefficient is: (12); The resulting weighted matrix Z is: (13); In the formula, This represents the weight of the j-th indicator.

[0038] 4) Determine the ideal optimal solution and the worst-case solution. The ideal optimal solution represents the combination of the maximum values ​​among all indicators, while the ideal worst-case solution represents the combination of the minimum values ​​among all indicators. Let the optimal solution be... The worst solution is ,but: (14); (15); 5) Calculate the distance from each solution to the ideal optimal solution and the worst solution. and : (16); (17); 6) Calculate the degree of closeness of each scheme to the ideal optimal solution and the worst solution. : (18); In the formula, Based on proximity The size of the value is used to sort the different schemes represented by different nodes. The larger the value, the more important the scheme, and thus the key nodes are identified.

[0039] Step 3: Based on the criticality value of the power node, construct a False Data Injection (FDIA) attack model to simulate an attack on the distribution network CPS; Based on the criticality values ​​of the power nodes obtained in the previous step, an FDIA model capable of simulating intelligent and targeted attacks is constructed. The core idea of ​​this model is that attackers will prioritize attacking nodes they deem more critical in order to cause the greatest destructive effect.

[0040] The specific construction method is as follows: the criticality value of a node is directly correlated with its probability of being attacked and the intensity of the attack. The higher the criticality value of a node, the greater the probability that it will be selected as an attack target in this attack model, and the greater the extent of tampering with the injected fake data (i.e., the attack intensity). For example, a probability function and an intensity function can be set, with the criticality value of the node as input and the corresponding attack probability and intensity as output.

[0041] Attack vectors built upon a complete power grid topology possess high stealth, targeting, and destructive power. From a security defense perspective, research on FDIA (Fixed-Fault Attack Analysis) is of great significance. Once attackers obtain power grid network topology information, they can acquire crucial information such as the Jacobian matrix. Assuming the injection attack vector is Then the measured value after FDIA It can be represented as: (19); (20); In the formula, Measurements after an attack. For state Measurement estimates without injection attacks For the injected attack vector, This is the Jacobian matrix. To satisfy the concealment condition and avoid residual detection: (twenty one); (twenty two); In the formula Let r be the state estimation bias, i.e., the amount of alteration caused by the FDIA attack. Equation (22) can ensure that the residual after the attack still conforms to the noise distribution, where r is the measurement error. At this time, the residual after the attack can be expressed as: (twenty three); Simultaneously satisfy , The threshold is set at 1. After an attacker has a complete grasp of the network topology, the residual of the injected attack vector, under certain conditions, will be equal to the residual before the attack. In this case, FDI can bypass state estimation detection and has strong stealth capabilities.

[0042] Nodes with different criticalities have different probabilities of being subjected to FDIA from attackers, and these probabilities are relatively close to those obtained in the node criticality assessment. The value is related to the criticality; higher criticality corresponds to higher attack strength.

[0043] (twenty four); (25); In the formula, Let be the probability that node i is attacked. This is the attack strength coefficient; This represents the maximum permissible threshold for tampering with the state variable.

[0044] For FDIA attack modeling, with concealment as a constraint and maximizing state estimation bias as the optimization objective, the mathematical expression of the model can be obtained as follows: (26); Step 4: Construct a resilience evaluation index system that includes physical layer, information layer and coupling layer indicators, and assign weights to each indicator using a subjective and objective weighting method. Damage assessment should be based on relevant industry standards and is mainly related to multiple factors such as power grid physical equipment, information nodes, and extreme conditions. Integrating subjective judgment with objective data can greatly reduce errors caused by a single weighting method and increase the credibility of the final results. The overall process of damage assessment is as follows: 1. Establish a system of factors affecting the resilience of distribution networks based on relevant standards published by the power grid, and select resilience assessment indicators for each level, namely the information layer, physical layer, and coupling layer; 2. For the massive amounts of data from internal and external sources, process and summarize them, calculate the corresponding resilience index values, and perform index standardization. 3. Combining subjective and objective weighting methods, different resilience indicators are weighted; 4. Conduct a comprehensive evaluation and output a comprehensive damage resistance index.

[0045] Overall damage assessment flowchart as follows Figure 3 Show.

[0046] (1) Damage resistance evaluation indicators: To comprehensively evaluate the system status of the distribution network after suffering a FDIA (Distribution Fault Injury Assessment), a resilience evaluation index system comprising three dimensions—physical layer, information layer, and coupling layer—is constructed.

[0047] 1) Physical layer Normal power supply to the load is a fundamental requirement for the normal operation of the power grid. Therefore, the load loss rate is an important physical layer indicator for evaluating the resilience of the distribution network. The higher the load loss rate caused by a network attack, the lower the overall resilience. (Definition of Load Loss Rate) for: ; In the formula, This represents the set of load points that cannot be powered after a fault. Represents the set of all load points in the system; This represents the active load of node i.

[0048] Network connectivity It can reflect the integrity of the physical layer topology; the higher the connectivity, the higher the network integrity.

[0049] ; In the formula This indicates the number of physical nodes that remain connected after a failure. This represents the total number of nodes in the physical layer.

[0050] 2) Information layer Communication Survival Rate This value reflects the integrity of the information layer's communication functions; it decreases significantly when the communication network is severely damaged.

[0051] ; In the formula This refers to the number of information nodes that can still transmit data normally after a failure. This indicates the total number of nodes in the information layer.

[0052] 3) Coupling layer Cross-layer fault propagation speed This indicates the speed at which cross-layer faults propagate, and is negatively correlated with system resilience.

[0053] ; In the formula Indicates the time interval for fault propagation; Indicates time interval The number of newly added cross-layer fault nodes.

[0054] The system resilience index is It is a core indicator that can assess the system's ability to maintain and restore normal operation after being disturbed.

[0055] ; In the formula This is the time required for the system to return to normal operation. Let be the power supplied at time t; This represents the total system load power.

[0056] (2) BRM method The Brown-Wood Method (BWM) is a multi-criteria decision-making method that primarily determines the relative importance of different indicators through expert scoring. Its main steps are: 1) Establish an indicator set for the three-level indicators. The optimal indicator is selected based on expert opinions. With worst indicators One of each; 2) Compare the best (worst) indicator with other indicators. Perform importance comparisons and establish comparison vectors. , ,in ( The sign indicates the relative importance of the best (worst) indicator compared to indicator j. , ; 3) Solve according to equation (27) to calculate the subjective weights corresponding to each indicator. ; (27); 4) Perform a consistency check to ensure that the following conditions are met. If the consistency check is passed, it will pass; otherwise, it will fail.

[0057] (3) CRITIC method The CRITIC method measures the objective weight of evaluation indicators based on their comparative strength and the conflict between them, comprehensively considering the differences and relationships between different indicators to reduce the influence of subjective factors on the evaluation results. Its main steps are as follows: 1) Establish a standardized evaluation matrix. Given n evaluation objects and m indicators, establish a standardized evaluation matrix X' with consistent quantitative units: (28); If we use the min-max normalization method to perform dimensionless processing on each index, then we have: Positive indicators (29); contrarian indicators (30); In the formula ; .

[0058] 2) Construct a correlation sparse matrix and correlation coefficients. This indicates the correlation between different evaluation indicators. As the value increases, the correlation between indicators becomes stronger, and the correlation coefficient matrix... .

[0059] (31); 3) Calculate objective weights The conflict quantification value of the evaluation index is solved using the correlation coefficient. : (32); By combining the conflict quantification value of the indicator with the contrast intensity, the amount of information contained in the indicator can be determined. : (33); In the formula To evaluate the mean square error of the j-th column vector in the matrix. The size of the objective weight is positively correlated with the amount of information it contains, hence the objective weight. : (34); (4) Evaluation combining subjective and objective factors Since neither a single subjective nor objective evaluation method can comprehensively reflect the importance of indicators, a combined subjective and objective evaluation method is used.

[0060] Construct weight vector ,in , Weighting coefficients: (35); Optimize the weighting coefficients to minimize the deviation between the combined weight vector and the subjective and objective weight vectors: (36); The optimal first derivative condition for the objective function to reach its minimum value is: (37); Solving for coefficients , And perform normalization: (38); Combined weights : (39); (5) Derive the comprehensive index of the distribution network's resilience. Multiply the standardized index by the combined weights to obtain the weighted matrix. In the formula Then, following the node criticality evaluation steps in Step 2, calculate the distances of each solution to the ideal optimal solution and the worst solution. and Relative similarity to the overall resilience index. ,in It is directly proportional to its survivability.

[0061] Overall methodology for assessing the resilience of power distribution networks, such as Figure 4 As shown.

[0062] Step 5: Combining the FDIA attack model and the weighted resilience evaluation index system, calculate and output the comprehensive resilience evaluation index of the distribution network CPS under FDIA.

[0063] This is the final step in the evaluation.

[0064] First, the FDIA model from step three is used to simulate an attack on the CPS model from step one, and the specific values ​​of each resilience index (such as load loss rate, communication survival rate, etc.) in step four are calculated based on the simulation results.

[0065] Then, these indicator values ​​are standardized.

[0066] Next, the standardized values ​​of each indicator are multiplied by the final combined weights obtained in step four to obtain the weighted evaluation value of each indicator.

[0067] Finally, the weighted evaluation values ​​of all indicators are summed or other aggregation functions are used to calculate a unique comprehensive resilience evaluation index. The value range of this index can be set between [0, 1], and the higher the value, the stronger the resilience of the distribution network when FDIA is taken into account.

[0068] Example verification: The method proposed in this invention is used to simulate the IEEE 14-node power distribution system. The criticality of the relevant nodes is shown in Table 1.

[0069] Table 1 Node Criticality: Table 2 System resilience index under three conditions: FDIA was performed at nodes ranked 1st and 7th (nodes 9 and 14), 7th and 8th (nodes 14 and 3), and 8th and 14th (nodes 14 and 8) in terms of criticality. Then, the overall resilience index was calculated according to the method proposed in this invention. The three different cases and their resilience indices are as follows: Figure 5 Table 2 shows the results. This demonstrates that the higher the criticality of a node, the lower the system's resilience after an attack. This method can effectively evaluate the resilience of distribution network CPS under FDIA.

[0070] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for evaluating the invulnerability of a power distribution network against false data injection attacks, characterized in that, The method comprises the following steps: Step 1: establishing a CPS model of the power distribution network, wherein the model comprises an information layer and a physical layer which are coupled with each other; Step 2: evaluating the criticality of power nodes in the power distribution network based on a preset criticality evaluation index system of nodes, to obtain criticality values of the power nodes; Step 3: constructing a FDIA model based on the criticality values of the power nodes, to simulate an attack on the CPS of the power distribution network; Step 4: constructing a survivability evaluation index system comprising physical layer, information layer and coupling layer indexes, and adopting a subjective and objective fusion weighting method to weight the indexes; Step 5: combining the FDIA attack model and the weighted survivability evaluation index system, to calculate and output a survivability comprehensive evaluation index of the CPS of the power distribution network under the FDIA.

2. The method of claim 1, wherein, The criticality evaluation index system of nodes comprises composite indexes combining traditional network topology indexes and power system characteristics, and specifically comprises degree centrality, node betweenness centrality, closeness centrality, electrical betweenness centrality and voltage sensitivity index.

3. The method of claim 2, wherein, The step of evaluating the criticality of power nodes specifically comprises: constructing an initial decision matrix based on index values of the nodes; normalizing the decision matrix; adopting Gini coefficient to objectively weight the indexes, to obtain a weighted matrix; determining an ideal optimal solution and a worst solution, and calculating distances of the nodes to the ideal optimal solution and the worst solution, and finally taking the relative closeness as the criticality value of the node.

4. The method of claim 1, wherein, The step of constructing the FDIA model comprises: determining probabilities and attack intensities of attacks on different criticality nodes by an attacker according to the criticality values of the power nodes, wherein the higher the criticality value of a node is, the higher the probability and attack intensity of the node are.

5. The method of claim 1, wherein, The subjective and objective fusion weighting method specifically comprises: adopting BWM as a subjective weighting method to determine subjective weights of the survivability indexes; adopting CRITIC method as an objective weighting method to determine objective weights of the survivability indexes; optimizing the subjective weights and the objective weights to obtain final combined weights.

6. The method of claim 4, wherein, The physical layer indexes in the survivability evaluation index system at least comprise load loss rate and network connectivity rate.

7. The method of claim 4, wherein, The information layer indexes in the survivability evaluation index system at least comprise communication survival rate.

8. The method of claim 4, wherein, The coupling layer indexes in the survivability evaluation index system at least comprise cross-layer fault propagation speed and system resilience index.

9. The method of claim 1, wherein, The step of calculating the survivability comprehensive evaluation index specifically comprises: multiplying the standardized index values of each layer with the combined weights to obtain weighted evaluation values, and calculating a comprehensive index representing the survivability level of the system according to the evaluation values.

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