A graph-based power CPS vulnerability assessment method and system

Abstract

The present application relates to the field of power system application technology, and specifically to a graph-theory-based power CPS vulnerability assessment method and system, the method comprising: constructing an unweighted network topology model of a power CPS network, obtaining each node of the power CPS network, the edges between nodes, and the load voltage data of each node; obtaining the load anomaly of each node of the power CPS network; obtaining the voltage recovery responsiveness of each node of the power CPS network; obtaining the operation robustness of each node of the power CPS network; obtaining each community in the power CPS network and the associated communities of each community; obtaining the voltage mutation time sequence of each node in the power CPS network; obtaining the degree of cascading failure of each community in the power CPS network; obtaining the cascading criticality of each community in the power CPS network; obtaining the power CPS network vulnerability factor, and evaluating the power CPS vulnerability. The present application reduces the risk of damage to the safety of the power system.

Description

Technical Field

[0001] The present application relates to the field of power system application technology, and specifically to a graph-theory-based power CPS vulnerability assessment method and system. Background Art

[0002] Power CPS (Cyber-Physical Systems) refers to a system that closely integrates physical components with computing resources and communication networks. It changes the planning and control methods of traditional power grids, highly integrates physical systems with information systems, and integrates traditional energy systems with new energy. It has the advantages of safe, efficient and accurate autonomy and collaboration. The power CPS vulnerability assessment method can effectively monitor possible security vulnerabilities and risks in the power system, providing important guarantees for taking preventive measures in advance and improving system security.

[0003] The power CPS vulnerability assessment method based on graph theory can more intuitively characterize the structure of the power network and facilitate the analysis of the stability and fault risks of the power network. However, in the existing technology, when using graph theory to assess the power CPS vulnerability, there is a lack of analysis of the fault recovery response of the power system, and it is difficult to fully consider the cascading fault conditions of the power system, resulting in the inability to accurately assess the power CPS vulnerability, which may cause risks such as damage to the security of the power system. Summary of the invention

[0004] In order to solve the above technical problems, the present application provides a graph theory-based power CPS vulnerability assessment method to solve the existing problems.

[0005] The graph-theory-based power CPS vulnerability assessment method of this application adopts the following technical solution:

[0006] In a first aspect, an embodiment of the present application provides a graph-theory-based power CPS vulnerability assessment method, the method comprising the following steps:

[0007] Construct an unweighted network topology model of the power CPS network, and obtain the data of each node, the edges between nodes, and the load voltage of each node in the power CPS network;

[0008] Based on the difference between the load voltage data at the mutation point and the non-mutation point, and the difference between the load voltage data between the mutation points, the load abnormality of each node in the power CPS network is obtained; based on the time interval between the mutation point and the adjacent mutation point, and the mutation probability of the mutation point, the voltage recovery responsiveness of each node in the power CPS network is obtained; the load abnormality and voltage recovery responsiveness are reversely integrated to obtain the operation robustness of each node in the power CPS network;

[0009] Use overlapping community discovery algorithm to obtain each community and associated communities in the power CPS network;

[0010] Based on the moment of the mutation of load voltage data, the voltage mutation time sequence of each node in the power CPS network is obtained; based on the similarity between the voltage mutation time sequences of nodes in the operation robustness and associated communities, the degree of cascading failure of each community in the power CPS network is obtained;

[0011] Based on the number of edges between nodes in the communities, the cascade criticality of each community in the power CPS network is obtained; based on the degree of cascade failure and the value of cascade criticality, the power CPS network vulnerability factor is obtained, and the power CPS vulnerability is evaluated based on the power CPS network vulnerability factor.

[0012] Furthermore, the method for obtaining the load abnormality is:

[0013] For each node of the power CPS network, the load voltage data is arranged in time order to obtain the load voltage data sequence of each node;

[0014] A mutation point detection algorithm is used to obtain the mutation point and mutation probability of the load voltage data sequence of each node;

[0015] The calculation formula of the load abnormality is: ; In the formula, is the load anomaly of the i-th node in the power CPS network; It is the cumulative result of the absolute value of the difference between the load voltage of all mutation points and non-mutation points in the load voltage data sequence of the i-th node in the power CPS network; It is the cumulative result of the absolute value of the difference in load voltage between all mutation points in the load voltage data sequence of the i-th node in the power CPS network.

[0016] Furthermore, the calculation formula of the voltage recovery responsiveness is: ; In the formula, is the voltage recovery responsiveness of the i-th node in the power CPS network; is the total number of mutation points in the load voltage data sequence of the i-th node in the power CPS network; is the time interval between the jth mutation point and the next mutation point in the load voltage data sequence of the i-th node in the power CPS network. If the jth mutation point is the last mutation point, is the time interval between it and the previous mutation point; is the mutation probability of the jth mutation point in the load voltage data sequence corresponding to the i-th node in the power CPS network.

[0017] Furthermore, the method for obtaining the operation robustness is:

[0018] For each node in the power CPS network, the sum of the node's load abnormality and a preset adjustment parameter is calculated, and the normalized value of the ratio of the node's voltage recovery responsiveness to the sum is calculated as the operation robustness of each node in the power CPS network.

[0019] Furthermore, the method for obtaining each community and its associated communities is as follows:

[0020] The unweighted network topology model of the power CPS network is taken as input, and the overlapping community discovery algorithm is used to obtain the communities in the unweighted network topology model of the power CPS network, and the overlapping communities are recorded as associated communities.

[0021] Furthermore, the method for obtaining the voltage mutation time sequence is as follows:

[0022] The sequences composed of all the mutation points in the load voltage data sequence of each node in the power CPS network in time sequence are recorded as the voltage mutation time sequence of each node.

[0023] Further, the method for obtaining the degree of cascading failure is:

[0024] For each community in the power CPS network, the minimum value of the operating robustness of all nodes in the community is obtained, the cumulative result of the similarity between the voltage mutation time series of all nodes in the community and the voltage mutation time series of all nodes in its associated community is calculated, and the ratio of the cumulative result to the minimum value is used as the cascading failure degree of each community in the power CPS network.

[0025] Furthermore, the calculation formula of the cascade criticality is: ; In the formula, is the cascade criticality of the pth community in the power CPS network; is the total number of nodes in the power CPS network that have edges connected to the pth community; is the maximum number of edges possessed by all nodes in the power CPS network that have edges connected to the pth community.

[0026] Further, the obtaining of the power CPS network vulnerability factor and the evaluation of the power CPS vulnerability based on the power CPS network vulnerability factor include: calculating the product of the cascading failure degree and the cascading criticality of each community in the power CPS network, and accumulating the normalized values ​​of the product of all communities as the power CPS network vulnerability factor;

[0027] When the power CPS network vulnerability factor is less than or equal to the preset power CPS vulnerability threshold, the power CPS network area to be evaluated has high operational robustness; when the power CPS network vulnerability factor obtained in real time is greater than the preset power CPS vulnerability threshold, the power CPS network area to be evaluated is vulnerable.

[0028] In the second aspect, an embodiment of the present application also provides a graph theory-based power CPS vulnerability assessment system, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor implements the steps of any one of the above-mentioned methods when executing the computer program.

[0029] This application has at least the following beneficial effects:

[0030] The present application obtains operational robustness through the load change status and voltage recovery characteristics of nodes in the power CPS network, and adds consideration of voltage recovery response characteristics on the basis of load voltage mutation analysis of power CPS network nodes, which more accurately reflects the operational robustness of each node in the power CPS network; the power CPS vulnerability factor is obtained according to the cascading failure characteristics and cascading criticality of each community in the power CPS network, and is used as a basis for evaluating the vulnerability of the power CPS network, and the cascading failure status and impact range of the power system are comprehensively analyzed. When new transmission lines are built between the nodes of the power CPS network, the vulnerability status of the power CPS network can also be accurately quantified and evaluated, providing scientific data support for relevant personnel to evaluate the robust characteristics of the power CPS, reducing the risk of damage to the safety of the power system, and realizing a graph-theory-based power CPS vulnerability assessment method. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions and advantages in the embodiments of the present application or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0032] Figure 1 A flowchart of a graph-theory-based power CPS vulnerability assessment method provided for this application;

[0033] Figure 2 This is a schematic diagram of the power CPS network model;

[0034] Figure 3 Schematic diagram of community division in the unweighted network topology model. DETAILED DESCRIPTION

[0035] In order to further explain the technical means and effects adopted by this application to achieve the predetermined invention purpose, the following is a detailed description of the graph-based power CPS vulnerability assessment method proposed in this application, its specific implementation method, structure, characteristics and effects, in combination with the accompanying drawings and preferred embodiments. In the following description, different "one embodiment" or "another embodiment" does not necessarily refer to the same embodiment. In addition, specific features, structures or characteristics in one or more embodiments may be combined in any suitable form.

[0036] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0037] The following is a detailed description of a specific scheme of a graph theory-based power CPS vulnerability assessment method provided by the present application in conjunction with the accompanying drawings.

[0038] An embodiment of the present application provides a graph-based power CPS vulnerability assessment method. Specifically, the following graph-based power CPS vulnerability assessment method is provided. Figure 1 , the method comprises the following steps:

[0039] Step S1, constructing an unweighted network topology model of the power CPS network, obtaining each node of the power CPS network, the edges between nodes, and the load voltage data of each node.

[0040] The specific method of constructing the physical layer model of the power CPS network is as follows: deploy sensors in the power system whose power CPS vulnerability is to be evaluated, and the power system includes but is not limited to: power stations, substations, distribution stations, and load areas. The above areas are respectively used as a node in the physical layer model of the power CPS network, and an unweighted network topology model is constructed. When there is a transmission line between the corresponding areas of two nodes, an edge is generated in the unweighted network topology model; the information layer model of the power CPS network is also an unweighted network topology model, and the information system for data transmission and processing corresponding to the physical layer model of the power CPS network is used as an information node, and the communication lines between the information nodes are used as the edges between the information nodes in the unweighted network topology model. All information nodes correspond one-to-one to the nodes in the physical layer model of the power CPS network according to the coupling strategy.

[0041] like Figure 2 As shown, Figure 2 This is a schematic diagram of the power CPS network model. Figure 2In the figure, it includes the power CPS network physical layer model 1 and the power CPS network information layer model 2. The black solid circles and black solid squares in the figure are the nodes in the power CPS network physical layer model and the information nodes in the information layer model respectively; the solid lines are the transmission lines between the corresponding areas of the nodes, the dotted lines indicate that the nodes and the information nodes are one-to-one coupled, and the bold dotted lines represent the communication lines between the information nodes, including wired communication and wireless communication.

[0042] The load voltage data of each node in the physical layer model of the power CPS network is obtained through the deployed voltage sensors. The sensor data collection time interval is 1s. In order to prevent the transmission data from being missing due to the transmission fluctuation of the power CPS system network, the mean filling method is used to fill the missing values ​​of the load voltage time series data of each node in the power CPS network. Since the power CPS network and the mean filling method are both well-known technologies, the specific process will not be repeated here.

[0043] Step S2, based on the difference between the load voltage data at the mutation point and the non-mutation point, and the difference between the load voltage data between the mutation points, obtain the load abnormality of each node in the power CPS network; based on the time interval between the mutation point and the adjacent mutation point, and the mutation probability of the mutation point, obtain the voltage recovery responsiveness of each node in the power CPS network; reversely fuse the load abnormality and voltage recovery responsiveness to obtain the operation robustness of each node in the power CPS network.

[0044] In the power CPS network, voltage control network attacks and natural disasters may cause power equipment failures, resulting in changes and abnormal fluctuations in the load voltage of regional nodes. The more significant the abnormal load voltage condition is, the more serious the failure of the regional power equipment in the power CPS network is, and the more serious the impact on the normal operation of the power CPS network is.

[0045] Based on the above analysis, the load voltage data of each node in the power CPS network is sequenced in time order as the load voltage data sequence of each node, and the load voltage data sequences of all nodes are taken as input respectively. The Bayesian mutation point detection algorithm is used to obtain all mutation points and the mutation probability of the mutation points in the load voltage data sequence corresponding to each node. Since the Bayesian mutation point detection algorithm is a well-known technology, the specific acquisition process will not be described in detail.

[0046] Furthermore, for the load anomaly of each node in the power CPS network, the calculation formula is: ; In the formula, is the load anomaly of the i-th node in the power CPS network; It is the cumulative result of the absolute value of the difference between the load voltage of all mutation points and non-mutation points in the load voltage data sequence corresponding to the i-th node in the power CPS network; It is the cumulative result of the absolute value of the load voltage difference between all mutation points in the load voltage data sequence corresponding to the i-th node in the power CPS network.

[0047] When the fault of the power equipment in the area corresponding to the node in the power CPS network is more serious, the abnormal condition of the load voltage of the node corresponding to the area is more significant, the difference between the mutation point and the non-mutation point of the load voltage data is greater, the difference between the mutation points of the load voltage data is greater, and the load abnormality is higher. That is, the greater the cumulative result of the absolute value of the difference between the load voltage of all mutation points and non-mutation points in the load voltage data sequence corresponding to the node, the greater the cumulative result of the absolute value of the difference between the load voltage of all mutation points in the load voltage data sequence corresponding to the node.

[0048] Normally, when the load voltage of the power CPS network changes abnormally due to network attacks or natural disasters, a voltage control strategy will be adopted to adjust the load voltage back to normal. The stronger the load voltage recovery response effect, that is, the shorter the time interval for the load voltage to recover to normal, the smaller the impact on the normal operation of the power CPS network, and the stronger the robustness of the power CPS network.

[0049] Based on the above analysis, the voltage recovery responsiveness of each node in the power CPS network is calculated using the following formula: ; In the formula, is the voltage recovery responsiveness of the i-th node in the power CPS network; is the total number of mutation points in the load voltage data sequence corresponding to the i-th node in the power CPS network; is the time interval between the jth mutation point and the next mutation point in the load voltage data sequence corresponding to the i-th node in the power CPS network (for the last mutation point in the load voltage data sequence corresponding to any node in the power CPS network, is the time interval between it and the previous mutation point); is the mutation probability of the jth mutation point in the load voltage data sequence corresponding to the i-th node in the power CPS network;

[0050] When the robustness in the power CPS network is stronger, the time interval for the nodes in the power CPS network to restore the load voltage to a normal state through voltage control is shorter, the time interval between the load voltage data mutation moments is longer, and the voltage recovery responsiveness is stronger, that is, the time interval between all mutation points in the load voltage data sequence corresponding to the node in the power CPS network and the next mutation point is longer; the beneficial effect of using the mutation probability of the mutation point as the weight is: when the mutation probability of the mutation point is greater, it means that the degree of change of the load voltage at the mutation point is greater, and the time interval between the mutation point and the next mutation point can more reflect the voltage recovery response characteristics of the node.

[0051] In the power CPS network, the more significant the abnormal load voltage of the power equipment in the area corresponding to the node is, and the longer the time interval for the load voltage to recover to the normal state through voltage control is, the worse the resistance of the area corresponding to the node to network attacks or natural disasters is, which in turn affects the stability and reliability of the operation of the entire power CPS network.

[0052] Therefore, the operation robustness of each node in the power CPS network can be calculated as follows: ; In the formula, is the operation robustness of the i-th node in the power CPS network; is the voltage recovery responsiveness of the i-th node in the power CPS network; is the load anomaly of the i-th node in the power CPS network; It is a preset adjustment parameter. In this embodiment, its value is 1 to prevent the denominator from being 0, which causes calculation failure. Norm is a normalized value.

[0053] The stronger the robustness in the power CPS network, the more vague the load abnormality of the power equipment in the area corresponding to each node in the power CPS network, the shorter the time interval for the load voltage in the area corresponding to each node to recover to the normal state through voltage control, and the stronger the operation robustness of the node, that is, the stronger the voltage recovery responsiveness of the node, and the weaker the load abnormality of the node.

[0054] At this point, the operational robustness of any node in the power CPS network can be obtained through the above method.

[0055] Step S3, using the overlapping community discovery algorithm to obtain each community in the power CPS network and the associated communities of each community; obtaining the voltage mutation time sequence of each node in the power CPS network based on the moment of the mutation of the load voltage data; obtaining the cascading failure degree of each community in the power CPS network based on the similarity between the voltage mutation time sequences of the nodes in the associated communities and the operation robustness; obtaining the cascading criticality of each community in the power CPS network based on the number of edges connecting the nodes between the communities; obtaining the power CPS network vulnerability factor based on the value of the cascading failure degree and the cascading criticality.

[0056] When the vulnerability of power CPS is evaluated only by the operational robustness of each node in the power CPS network, there is a lack of analysis of the spatial topological relationship of the power CPS network, and the cascading failure conditions of the power system are not considered, making it impossible to accurately evaluate the vulnerability of power CPS.

[0057] Therefore, the unweighted network topology model corresponding to the physical layer of the power CPS network is taken as input, and the CPM (Clique Percolation Method) faction filtering algorithm is used to obtain the various communities in the unweighted network topology model corresponding to the power CPS network. In this embodiment, the K value in the CPM faction filtering algorithm is 4. It should be noted that the smaller the K value, the more accurate the division of the unweighted network topology model, but it will cause excessive division of the community, affecting the correlation of each node in the subsequent unweighted network topology model and increasing the amount of calculation. The implementer can set the K value according to the actual situation. If there is overlap between communities, the overlapping communities will be recorded as associated communities.

[0058] The beneficial effect of using the CPM faction filtering algorithm to obtain each community of the unweighted network topology model is that the CPM algorithm can divide the unweighted network topology model into several factions, namely communities, which facilitates the subsequent quantitative analysis of the association status between nodes in the power CPS network, while reducing the impact of abnormal nodes on the results and improving the robustness of community division. Since the CPM faction filtering algorithm is a well-known technology, the specific acquisition process will not be described in detail.

[0059] Figure 3 This is a schematic diagram of community division in the unweighted network topology model. Figure 3 6, 7, and 8 are communities R1, R2, and R3 respectively. R1, R2, and R3 are related communities. 3 and 4 are overlapping nodes between communities R1 and R2. 5 and 4 are overlapping nodes between communities R3 and R2. 4 is an overlapping node between communities R1, R2, and R3.

[0060] Because the CPM faction filtering algorithm only considers the connection relationship between nodes in the power CPS network, that is, the transmission line relationship, when dividing the communities in the unweighted network topology model, and does not consider the properties of the nodes themselves. Under normal circumstances, the more fragile the power CPS network is, the more significant the cascading failure conditions in the power CPS network are, that is, when the power equipment in the corresponding area of ​​the community fails, it will interact with other communities, resulting in more similar load voltage abnormalities between communities.

[0061] Based on the above analysis, the sequences composed of the moments of all mutation points in the load voltage data sequence corresponding to each node in the power CPS network in chronological order are recorded as the voltage mutation moment sequence of each node.

[0062] The degree of cascading failure of any community in the power CPS network can be calculated as follows: ; In the formula, is the cascading failure degree of the pth community in the power CPS network; It is the cumulative result of the cosine similarity between the voltage mutation time series of all nodes in the pth community in the power CPS network and the voltage mutation time series of all nodes in its associated community; It is the minimum value of the operation robustness of all nodes in the pth community in the power CPS network.

[0063] When the power CPS network is more fragile, the power equipment in the corresponding area of ​​the community in the power CPS network is more likely to be affected by other communities and cause cascading failures, the weaker the operating robustness of the nodes in the community, the more similar the load voltage abnormalities between the associated communities, and the higher the degree of cascading failures in the community, that is, the greater the cumulative cosine similarity between the voltage mutation time series corresponding to the community and all nodes in its associated communities, the smaller the minimum value of the corresponding operating robustness of all nodes in the community.

[0064] Generally speaking, the more fragile the power CPS network is, the higher the degree of cascading failures in the network, the higher the criticality of the area. When a community in the power CPS network fails, it is more likely to cause its associated communities to fail one after another, seriously affecting the stability of the power CPS network.

[0065] Therefore, the cascade criticality of any community in the power CPS network can be calculated as follows: ; In the formula, is the cascade criticality of the pth community in the power CPS network; is the total number of nodes in the power CPS network that have edges connected to the pth community; is the maximum number of edges possessed by all nodes in the power CPS network that have edges connected to the pth community;

[0066] The stronger the cascade criticality of a community in the power CPS network, the more likely it is that when the power equipment in the corresponding area of ​​the community fails, it will cause a cascading failure of the power equipment in the surrounding areas. At this time, the more nodes the community is associated with in the power CPS network, the more remaining nodes in the power CPS network can be affected, that is, the greater the ratio between the total number of nodes connected to the pth community and the maximum number of edges owned by all nodes connected to the pth community.

[0067] When the area with a higher degree of cascading failure in the power CPS network is more critical in the network, it is more likely to cause large-scale cascading failures when a failure occurs in the power CPS network, reducing the robustness of the power CPS network.

[0068] Furthermore, the power CPS network vulnerability factor is calculated by calculating the product of the cascading failure degree and the cascading criticality of each community in the power CPS network, and the accumulated result of the normalized values ​​of the product of all communities is used as the power CPS network vulnerability factor.

[0069] The more fragile the power CPS network is, the more significant the regional load voltage fault condition in the power CPS network, which is more likely to cause large-scale cascading failures, is, the greater the cumulative result of the product of the cascading failure degree and the cascading criticality of each community.

[0070] At this point, the network vulnerability factor of each power CPS can be obtained through the above method.

[0071] Step S4, evaluating the power CPS vulnerability based on the power CPS network vulnerability factor.

[0072] A preset power CPS vulnerability threshold H is set. When the power CPS network vulnerability factor obtained in real time is less than or equal to the preset power CPS vulnerability threshold, it is considered that the power CPS network area to be evaluated has a high operational robustness; conversely, when the power CPS network vulnerability factor obtained in real time is greater than the preset power CPS vulnerability threshold, it is considered that the power CPS network area to be evaluated has a relatively significant vulnerability. When a failure occurs in the corresponding area of ​​each node in the power CPS network, it is easy to cause a chain failure in the remaining areas of the power CPS network, which may cause damage to the safety of the power system. The preset power CPS vulnerability threshold H has a value range of [0,1]. The value of this embodiment is 0.5. The larger H is, the stricter the vulnerability assessment requirements for the power CPS network. The implementer can set other preset power CPS vulnerability thresholds according to actual conditions.

[0073] Based on the same inventive concept as the above method, an embodiment of the present application also provides a graph theory-based power CPS vulnerability assessment system, including a memory, a processor, and a computer program stored in the memory and running on the processor, and when the processor executes the computer program, it implements the steps of any one of the above-mentioned graph theory-based power CPS vulnerability assessment methods.

[0074] It should be noted that the above-mentioned sequence of the embodiments of the present application is only for description and does not represent the advantages and disadvantages of the embodiments. The above-mentioned specific embodiments of the present application are described. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0075] The various embodiments in the present application are described in a progressive manner, and the same or similar parts between the various embodiments can be referenced to each other, and each embodiment focuses on the differences from other embodiments.

[0076] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Modifications to the technical solutions recorded in the aforementioned embodiments, or equivalent replacement of some of the technical features therein, do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A graph-theory-based power CPS vulnerability assessment method, characterized in that: The method comprises the following steps: Construct an unweighted network topology model of the power CPS network, and obtain the data of each node, the edges between nodes, and the load voltage of each node in the power CPS network; For each node of the power CPS network, the load voltage data is sorted in chronological order to obtain its load voltage data sequence; and the mutation point and the corresponding mutation probability are obtained through the mutation point detection algorithm; the product of the cumulative result of the absolute value of the difference between the load voltage of all mutation points and non-mutation points in the load voltage data sequence of each node and the cumulative result of the absolute value of the difference between the load voltage of all mutation points is taken as the load abnormality of each node; based on the time interval between the mutation point and the adjacent mutation point and the mutation probability of the mutation point, the voltage recovery responsiveness of each node of the power CPS network is obtained; the load abnormality and voltage recovery responsiveness are reversely fused to obtain the operation robustness of each node of the power CPS network; Use overlapping community discovery algorithm to obtain each community and associated communities in the power CPS network; Based on the moment of the mutation of load voltage data, the voltage mutation time sequence of each node in the power CPS network is obtained; based on the similarity between the voltage mutation time sequences of nodes in the operation robustness and associated communities, the degree of cascading failure of each community in the power CPS network is obtained; Based on the number of edges between nodes in the community, the cascade criticality of each community in the power CPS network is obtained; based on the cascade failure degree and the value of the cascade criticality, the power CPS network vulnerability factor is obtained, and the power CPS vulnerability is evaluated based on the power CPS network vulnerability factor; The calculation formula of the voltage recovery responsiveness is: ; In the formula, is the voltage recovery responsiveness of the i-th node in the power CPS network; is the total number of mutation points in the load voltage data sequence of the i-th node in the power CPS network; is the time interval between the jth mutation point and the next mutation point in the load voltage data sequence of the i-th node in the power CPS network. If the jth mutation point is the last mutation point, is the time interval between it and the previous mutation point; is the mutation probability of the jth mutation point in the load voltage data sequence corresponding to the i-th node in the power CPS network.

2. The graph-theory-based power CPS vulnerability assessment method according to claim 1, characterized in that: The method for obtaining the operation robustness is: For each node in the power CPS network, the sum of the node's load abnormality and a preset adjustment parameter is calculated, and the normalized value of the ratio of the node's voltage recovery responsiveness to the sum is calculated as the operation robustness of each node in the power CPS network.

3. The graph-theory-based power CPS vulnerability assessment method according to claim 1, characterized in that: The method for obtaining each community and its associated communities is as follows: The unweighted network topology model of the power CPS network is taken as input, and the overlapping community discovery algorithm is used to obtain the communities in the unweighted network topology model of the power CPS network, and the overlapping communities are recorded as associated communities.

4. The graph-theory-based power CPS vulnerability assessment method according to claim 1, characterized in that: The method for obtaining the voltage mutation time sequence is as follows: The sequences composed of all the mutation points in the load voltage data sequence of each node in the power CPS network in time sequence are recorded as the voltage mutation time sequence of each node.

5. The graph-theory-based power CPS vulnerability assessment method according to claim 1, characterized in that: The method for obtaining the degree of cascading failure is: For each community in the power CPS network, the minimum value of the operating robustness of all nodes in the community is obtained, the cumulative result of the similarity between the voltage mutation time series of all nodes in the community and the voltage mutation time series of all nodes in its associated community is calculated, and the ratio of the cumulative result to the minimum value is used as the cascading failure degree of each community in the power CPS network.

6. The graph-theory-based power CPS vulnerability assessment method according to claim 1, characterized in that: The calculation formula of the cascade criticality is: ; In the formula, is the cascade criticality of the pth community in the power CPS network; is the total number of nodes in the power CPS network that have edges connected to the pth community; is the maximum number of edges possessed by all nodes in the power CPS network that have edges connected to the pth community.

7. The graph-theory-based power CPS vulnerability assessment method according to claim 1, characterized in that: The obtaining of the power CPS network vulnerability factor and the evaluation of the power CPS vulnerability based on the power CPS network vulnerability factor include: calculating the product of the cascading failure degree and the cascading criticality of each community in the power CPS network, and accumulating the normalized values ​​of the product of all communities as the power CPS network vulnerability factor; When the power CPS network vulnerability factor is less than or equal to the preset power CPS vulnerability threshold, the power CPS network area to be evaluated has high operational robustness; when the power CPS network vulnerability factor obtained in real time is greater than the preset power CPS vulnerability threshold, the power CPS network area to be evaluated is vulnerable.

8. A graph-theory-based power CPS vulnerability assessment system, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the computer program, the processor implements the steps of a graph theory-based power CPS vulnerability assessment method as described in any one of claims 1 to 7.

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