Method for assessing cyber-attack risk in power system networks

Abstract

A power system network attack risk assessment method based on residual covert attack space topology decomposition, comprising: acquiring the power system topology structure and the branch parameter matrix of each operation mode under multi-mode mobile target defense, and constructing a circulation basis matrix; establishing a branch power flow disturbance representation, converting the residual covert attack space into a multi-mode circulation consistency constraint based on the circulation basis matrix and the branch parameter matrix, forming a branch power flow disturbance space; identifying bridge branches and dividing circulation equivalent edge sets based on the column structure of the circulation basis matrix; constructing a reduced circulation graph and its associated matrix based on the circulation equivalent edge sets; based on the bridge branches, the circulation equivalent edge sets and the reduced circulation graph associated matrix, the structure of the branch power flow disturbance space is decomposed to obtain the bridge branch component, the circulation equivalent edge set local component and the coordinated cut set component; the degrees of freedom of the three components are calculated respectively, and the residual covert attack independent direction evaluation result is output.

Description

Technical Field

[0001] This invention relates to the fields of power system network security, state estimation, and mobile target defense, and in particular to a method for assessing the risk of power system network attacks based on residual covert attack space topology decomposition. Background Technology

[0002] With the rapid development of smart grids and power cyber-physical systems, power system operation increasingly relies on wide-area measurement, communication networks, and state estimation results. State estimation provides fundamental data for dispatch control, power flow analysis, fault diagnosis, and safety verification, and the integrity of its measurement data directly affects the correctness of power system operation decisions. Spoofed data injection attacks targeting state estimation measurement data can construct attack vectors consistent with the measurement model, making residual bad data detection difficult to identify, thus threatening the safe operation of the power grid.

[0003] Mobile target defense (MDP) makes it difficult for attackers to maintain a precise understanding of the system model over a long period by altering the power system measurement model or line parameters. Multimodal MDP further introduces multiple operating modes, requiring attack vectors to simultaneously satisfy concealment conditions under multiple modes, thus compressing the residual concealment attack space available to attackers. However, in existing technologies, the residual concealment attack space under multimodal MDP is typically represented as the intersection of multiple measurement Jacobian matrix column spaces. While this representation can provide the dimension of the residual space, the result is primarily in algebraic subspace form, making it difficult to explain which network topologies the residual concealment directions originate from, and also difficult to further distinguish the structural units and parameter information upon which different residual concealment directions depend.

[0004] Therefore, there is an urgent need for a method that can transform the residual covert attack space under multi-mode mobile target defense from an abstract algebraic representation to a topologically interpretable representation. This method can further identify the bridge branch structure, cyclic equivalent edge set structure, and cross-structure coordination relationship in the residual covert attack space, and calculate the number of independent residual covert attack directions that attackers can utilize, thereby providing a more refined basis for evaluating the effectiveness of mobile target defense in power systems. Summary of the Invention

[0005] The purpose of this invention is to provide a power system network attack risk assessment method based on residual covert attack space topology decomposition. This method enables the representation of branch power flow disturbances, topology decomposition, and degree of freedom calculation of the residual covert attack space that still exists after multi-mode mobile target defense, thereby obtaining the number of independent residual covert attack directions that attackers can utilize.

[0006] A method for assessing the risk of network attacks on power systems based on residual covert attack space topology decomposition includes: obtaining the power system topology and branch parameter matrices for each operating mode under multi-mode moving target defense. ,in And construct the cyclic basis matrix. C Establish a branch power flow perturbation representation to transform the residual covert attack space into a cyclic basis matrix-based representation. C and branch parameter matrix Multi-mode cyclic consistency constraints form branch power flow disturbance space. Based on cyclic basis matrix C The column structure is used to identify bridge branches and divide them into cyclic equivalent edge sets; based on the cyclic equivalent edge sets, a reduced cyclic graph and its correlation matrix are constructed. Based on the bridge branches, cyclic equivalent edge sets, and reduced cyclic graph correlation matrix. The branch power flow disturbance space Perform a three-structure decomposition to obtain the bridge branch component, the local component of the cyclic equivalent edge set, and the coordinated cut set component; calculate the degrees of freedom of the bridge branch component, the local component of the cyclic equivalent edge set, and the coordinated cut set component respectively, and output the evaluation results of the independent directions of residual covert attacks.

[0007] In some examples, the acquisition of the power system topology and branch parameter matrix for each operating mode under multi-mode moving target defense is described. This includes: obtaining the line topology of the power system and representing the power system as a connected graph. G =( V , E ),in V Represents a set of nodes. E Represents the branch set; obtains the measurement configuration, the measurements including node injection power measurement and branch power flow measurement; for the first... k The system operates in several modes, acquiring the corresponding line parameters for each branch to form a branch parameter matrix.

[0008] in, Indicates the first k The first operating mode e The equivalent susceptance of the branch circuit, Indicates the number of branches.

[0009] In some examples, the construction of the cyclic basis matrix... C This includes: constructing a cyclic basis matrix based on the power system topology. ,in This indicates the number of independent cycles in a power system diagram. Indicates the number of nodes. The cyclic basis matrix represents the number of branches. C Used to describe the relationship between branches and independent loops.

[0010] In some examples, the establishment of branch power flow perturbation representation transforms the residual covert attack space into a multi-mode cyclic consistency constraint, including: defining the measurement attack vector: ,in This indicates that the node is injected with measurement perturbation. Represents branch power flow measurement disturbances; based on node-branch correlation matrix Establish relationships The attack vector is uniformly represented by branch power flow perturbation variables. The form of the decision; transforming the condition for keeping the attack vector hidden in every operating mode into a multi-mode cyclic consistency constraint:

[0011] And this creates residual hidden spaces within the branch tidal current disturbance space: .

[0012] In some examples, the statement is based on a cyclic basis matrix. C The column structure identifies bridge branches, including: the cyclic basis matrix. C For each column, determine if the cyclic basis matrix corresponding to the e-th branch is... C Column vectors satisfy If the condition is met, then the branch is identified as a bridge branch; otherwise, it will be classified as a non-bridge branch. The branch roads were identified as non-bridge branch roads, forming a set of non-bridge branch roads. ,in, E Represents the set of branches. This represents a set of bridge branch roads.

[0013] In some examples, the partitioning of the cyclic equivalent edge set includes: for any two non-bridge branches , If there exist a sign coefficient η∈{+1,-1} such that Then the branch road and branch roads To partition them into the same cyclic equivalent edge set, the above partitioning is performed on all non-bridge branches to obtain the set of cyclic equivalent edges. ,in For the first i A set of cyclic equivalent edges is the number of cyclic equivalent edge sets.

[0014] In some examples, a reduced cyclic graph and its incidence matrix are constructed based on the cyclic equivalence edge set. This includes: setting each cyclic equivalent edge set Abstracted as a set of reduced cyclic edges in a reduced cyclic graph, the reduced cyclic graph is constructed based on the connectivity between the sets of cyclic equivalent edges in the power system topology. ,in Describes the reduced set of nodes. Represent the set of reduced edges; define a reference direction for each reduced edge in the reduced cyclic graph, and construct the node-edge incidence matrix of the reduced cyclic graph based on the reference direction. , in, Indicates the number of reduced nodes. The transpose of the matrix represents the number of reduced edges. The column space corresponds to the cut space of the reduced cyclic graph.

[0015] In some examples, the branch power flow disturbance space Perform a three-structure decomposition, including: The branch road tidal disturbance is only supported by the bridge branch road set. The part is defined as the bridge branch component. ; For each cyclic equivalent edge set A local matrix is ​​constructed based on the multi-mode line parameters and direction signs. , of which k Line number j The column elements are:

[0016] If cyclic equivalent edge set Internal branch power flow disturbance satisfaction Then the perturbation belongs to a local component of a cyclic equivalent edge set. ; For each cyclic equivalent edge set Define multimodal aggregation effect If the aggregation effect of all cyclic equivalent edge sets is in the th case... k Satisfy under each mode Then the disturbance belongs to the coordinated cut set component. ; The remaining covert attack space is decomposed into:

[0017] in, Indicates the component of the bridge branch road. Represents the local components of a cyclic equivalent edge set. This indicates the coordinated cut set components.

[0018] In some examples, the degrees of freedom of the bridge branch component, the local component of the cyclic equivalent edge set, and the coordinated cut set component are calculated, including: Degrees of freedom of bridge branch road components:

[0019] in, Indicates the number of bridge branch roads; Local component degrees of freedom of cyclic equivalent edge sets:

[0020] in, Indicates the first i The number of branches in a set of cyclic equivalent edges. Representing a local matrix rank; Coordinated cut set component degrees of freedom: } in, The dimension of the set represents the number of independent directions in the vector space of the aggregation effects that satisfy the conditions. Indicates the first k The aggregation effect vector of all cyclic equivalent edge sets in each operating mode.

[0021] In some examples, the total degrees of freedom of the residual covert attack space:

[0022] The total degrees of freedom represent the total number of independent directions from which an attacker can still construct a residual covert attack after a multi-mode moving target defense.

[0023] This invention transforms the problem of intersection of the column space of the multi-mode measurement Jacobian matrix into a multi-mode cyclic consistency constraint, transforming the residual covert attack space from an abstract algebraic subspace into a branch power flow disturbance space that can be explained by the power grid topology. By partitioning the cyclic equivalent edge set through the column structure of the cyclic basis matrix, it is possible to directly identify bridge branches, local equivalent structures, and cross-structure coordination relationships. Through the three-structure decomposition of bridge branch components, local components of cyclic equivalent edge sets, and coordination cut set components, it is possible to calculate the number of independent residual covert attack directions that attackers can utilize under different topological structures, avoiding the problem of only outputting the total dimension without being able to determine the structural source. This provides a quantitative basis for evaluating the effectiveness of multi-mode moving target defense and strengthening key structures. Attached Figure Description

[0024] Figure 1 This is a flowchart of a power system network attack risk assessment method based on residual covert attack space topology decomposition provided in an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of the bridge branch identification results of the IEEE 30-node system provided in an embodiment of the present invention.

[0026] Figure 3 This is a schematic diagram of the cyclic equivalent edge set partitioning result of the IEEE 30-node system provided in the embodiment of the present invention.

[0027] Figure 4 This is a schematic diagram of the reduced cycle diagram of the IEEE 30-node system provided in an embodiment of the present invention. Detailed Implementation

[0028] In this embodiment of the invention, a DC state estimation model is used as an example to illustrate the technical solution. However, the invention is not limited to a specific power grid size, a specific cyclic basis construction method, a specific matrix rank calculation method, or a specific form of moving target defense device. The technical solution of this invention can be adopted by any power system that can obtain multi-mode line parameters and perform residual concealment space analysis based on the state estimation model.

[0029] like Figure 1 As shown, a method for assessing the risk of network attacks on power systems based on residual covert attack space topology decomposition includes: obtaining the power system topology under multi-mode moving target defense and the branch parameter matrix of each operating mode. ,in And construct the cyclic basis matrix. C Establish a branch power flow perturbation representation to transform the residual covert attack space into a cyclic basis matrix-based representation. C and branch parameter matrix Multi-mode cyclic consistency constraints form branch power flow disturbance space. Based on cyclic basis matrix C The column structure is used to identify bridge branches and divide them into cyclic equivalent edge sets; based on the cyclic equivalent edge sets, a reduced cyclic graph and its correlation matrix are constructed. Based on the bridge branches, cyclic equivalent edge sets, and reduced cyclic graph correlation matrix. The branch power flow disturbance space A three-structure decomposition is performed to obtain the bridge branch component, the local component of the cyclic equivalent edge set, and the coordinated cut set component. The degrees of freedom of the bridge branch component, the local component of the cyclic equivalent edge set, and the coordinated cut set component are calculated respectively, and the evaluation results of the independent directions of residual covert attacks are output. The method is described in detail below.

[0030] Step 1: Obtain the power system topology, measurement configuration, and line parameters under multi-mode moving target defense.

[0031] S11. Obtain the power system's line topology, including node sets, branch sets, and branch connection relationships, and represent the power system as a connected graph: G=(V,E) Where V represents the set of nodes and E represents the set of branches.

[0032] S12. Obtain the measurement configuration of the power system, including the measurement type and measurement location in the state estimation, wherein the measurements include node injection power measurement and branch power flow measurement.

[0033] S13. Obtain line parameters under multi-mode moving target defense. Assume multi-mode moving target defense includes... K The operating mode, for the first k The system operates in several modes, acquiring the corresponding line parameters for each branch to form a branch parameter matrix.

[0034] in, Indicates the first k The first operating mode e The equivalent susceptance of the branch circuit, Indicates the number of branches.

[0035] S14. Construct the node-branch association matrix according to the branch direction convention. A This is used to describe the connection relationship between nodes and branches. After removing the reference node, the node-branch association matrix is:

[0036] in, Indicates the number of nodes.

[0037] S15. Construct the multi-mode measurement Jacobian matrix. For the first... k The operating modes are represented by the Jacobian matrix as follows:

[0038] The upper part Corresponding node injected power measurement, lower half Corresponding branch power flow measurement.

[0039] S16. Construct the cyclic basis matrix based on the power system topology:

[0040] in, This represents the number of independent cycles in the power system diagram, and the cycle basis matrix is ​​used to describe the relationship between branches and independent cycles.

[0041] Step 2: Establish branch flow perturbation representation and transform the residual covert attack space into multi-mode cyclic consistency constraints.

[0042] S21. Define the measurement attack vector. The measurement attack vector in state estimation is represented as a combination of node-injected measurement disturbances and branch power flow measurement disturbances:

[0043] in, This indicates that the node is injected with measurement perturbation. This indicates the disturbance in the branch power flow measurement.

[0044] S22, Based on node-branch association matrix Establish the relationship between node injection measurement disturbances and branch power flow measurement disturbances:

[0045] Therefore, the measurement attack vector is uniformly represented by the branch power flow disturbance variables. The form of the decision.

[0046] S23. Describe the traditional residual covert attack space. Under multi-modal moving target defense, if the attack vector... To remain hidden in every operating mode, it must satisfy the following:

[0047] in, Indicates the first k The column space of the Jacobian matrix is ​​measured under each operating mode.

[0048] S24. Transform the column space intersection condition into a branch power flow cyclic consistency constraint. Based on the branch power flow perturbation representation, the residual covert attack space is transformed from the intersection of the column spaces of the measured Jacobian matrix under multiple operating modes into the following multi-mode cyclic consistency constraint:

[0049] In the formula, Indicates the first k The diagonal matrix formed by the equivalent susceptance of the branches under each mode; It is a cyclic basis matrix; that is, if the branch power flow disturbance variables If the cyclic consistency constraint is satisfied in every moving target defense mode, then the corresponding measured attack vector belongs to the residual covert attack space under multi-mode moving target defense.

[0050] The inventors recognized that the attack vector remaining concealed in multiple modes is physically equivalent to the branch current perturbation it induces. This requires simultaneously satisfying Kirchhoff's voltage law imposed by the power grid topology under all defense modes. Therefore, this step creatively introduces a cyclic basis matrix. C， The abstract problem of "column space intersection" is reconstructed into a concrete problem of "multi-mode cycle consistency constraint": The key technical advantage of this transformation lies in its ability to break down the originally complex and integrated conditions for covert attacks into a matrix.C This allows us to analyze the source of attack constraints loop by loop, providing a structured analysis basis for accurately identifying independent residual attack directions originating from specific topologies (such as bridge branches and cyclic equivalent edge sets) in subsequent steps. This overcomes the limitation of existing technologies that can only derive an abstract spatial dimension but cannot locate specific weak structural units.

[0051] S25. Residual concealed space in the branch tidal current disturbance space:

[0052] This space serves as the foundation for subsequent topology identification, structural decomposition, and degree-of-freedom calculation. Compared to the traditional multi-mode measurement Jacobian matrix column space intersection description, the key technical advantage of this space lies in its direct establishment on branch power flow disturbance variables. Above, its constraints Explicitly includes a cyclic basis matrix C The contained topological information makes this residual hidden space not only a set in an algebraic sense, but also a topologically interpretable structured space. This allows subsequent steps to classify and trace the residual attack directions in a refined manner, step by step, and step by step, structural unit by unit.

[0053] Step 3: Identify bridge branches and divide cyclic equivalent edge sets based on the column structure of the cyclic basis matrix.

[0054] S31. Identifying bridge branches based on cyclic basis matrices. (This involves considering the cyclic basis matrix.) C Each column is evaluated. If the column vector of the cyclic basis matrix corresponding to the e-th branch satisfies:

[0055] This branch is then identified as a bridge branch. Bridge branches do not belong to any cycle and therefore do not participate in cycle consistency constraints.

[0056] This step physically identifies bridge branches that do not participate in any independent loops. Based on this, for the first time, bridge branches are isolated from the complex network topology. Power flow disturbances on bridge branches are naturally not subject to the loop constraints of Kirchhoff's voltage law; therefore, each bridge branch directly provides attackers with an independent, unconditionally covert degree of freedom for attack. This makes the assessment of bridge branch attack risks direct and explicit.

[0057] S32. Determine the set of non-bridge branches. Those that do not satisfy... The branch roads are identified as non-bridge branch roads, forming a set of non-bridge branch roads:

[0058] Where E represents the set of branches, This represents the set of non-bridge branch roads. This represents a set of bridge branch roads.

[0059] S33. Partitioning cyclic equivalent edge sets based on the column vector relationship of the cyclic basis matrix. For any two non-bridge branches... , If there exist a sign coefficient η∈{+1,-1} such that:

[0060] Then the branch road and branch roads They are assigned to the same cyclic equivalent edge set.

[0061] In the same independent loop, if two branches are topologically contained in the same set of loops (most typically serial connections), then they must carry synchronously changing power flow disturbances (or in opposite directions). This condition is the algebraic expression of this topological equivalence relation. By grouping branches that satisfy this relation into a group, this invention simplifies the original complex network into a series of basic structural units with the same function and moving in the same direction through clustering. This is the basis for subsequent "reduction" and "decomposition".

[0062] S34. By performing the above partitioning on all non-bridge branches, we obtain the set of cyclic equivalent edges:

[0063] in, Indicates the first i A set of cyclic equivalent edges This indicates the number of cyclic equivalent edge sets.

[0064] S35. Determine the reference column vector and direction sign for each cyclic equivalence edge set. For each cyclic equivalence edge set... Select the column vector of the cyclic basis matrix corresponding to one of the branches as the reference column vector. For any branch within the set Determine the sign coefficient , so that:

[0065] The symbol coefficient is used to construct the local matrix of the cyclic equivalent edge set.

[0066] Step 4: Based on bridge branches, cyclic equivalent edge sets, and reduced cyclic graphs, perform a three-structure decomposition of the remaining covert attack space.

[0067] This step is used to address remaining covert attack opportunities. Structural decomposition was performed. Based on the partitioning results of the bridge branch set and cyclic equivalent edge set identified in the preceding steps, the inventors discovered that... Any attack vector can be uniquely decomposed into the sum of the following three independent subspace components: The support set of the bridge branch component is completely contained in the bridge branch set and does not participate in any cyclic constraints. The local components of a cyclic equivalent edge set have non-zero elements that act only within a single cyclic equivalent edge set and satisfy the local hidden constraint conditions of that edge set, without spreading to external branches. The coordinated cut set component is formed through the coordinated relationship of the cut space between each cyclic equivalent edge set. It is manifested as the aggregation effect of multiple edge sets satisfying the global hidden condition on the reduced cyclic graph.

[0068] The three components mentioned above correspond to the residual covert attack directions provided by different topological structural units. The following steps, S41 to S47, sequentially present the construction methods, constraints, and mathematical expressions of spatial decomposition for each type of component.

[0069] S41. Construct the local matrix of the cyclic equivalent edge set. For the... i cyclic equivalent edge set Construct a local matrix based on multi-mode line parameters and direction signs:

[0070] Among them, the k Line number j The column elements are:

[0071] This matrix is ​​used to characterize the first i Local concealment constraints within a cyclic equivalent edge set under multi-mode moving target defense.

[0072] S42. Construct a reduced cycle graph. Equivalent edge set for each cycle. Abstracting this to a reduced cycle graph, and based on the connectivity between the sets of cyclic equivalent edges in the original power system topology, a reduced cycle graph is constructed:

[0073] in, Describes the reduced set of nodes. Let represent the reduced edge set.

[0074] S43. Construct the incidence matrix of the reduced cyclic graph to describe the coordination relationship between different cyclic equivalent edge sets.

[0075] The reduced cycle graph obtained in step S42 Each reduced edge in the equation specifies a reference direction, wherein each cyclic equivalent edge set... A corresponding reduced edge in a reduced cyclic graph Construct the node-edge association matrix of the reduced cyclic graph based on the reference direction. , in, Indicates the number of reduced nodes. This represents the number of reduced edges, which is equal to the number of cyclic equivalent edge sets.

[0076] For the reduced node and the i Treaty-based border Matrix elements are defined as

[0077] The reduced graph correlation matrix Used to characterize the topological connectivity between each cyclic equivalent edge set on the reduced cyclic graph, its transpose matrix The column space corresponds to the cut space of the reduced cyclic graph.

[0078] S44. Establish bridge branch components. Include only the bridge branch set in the branch power flow disturbance. The portion is defined as the bridge branch component:

[0079] Since the bridge branch does not belong to any cycle, this component is not subject to cycle consistency constraints.

[0080] S45. Establish local components of cyclic equivalent edge sets. For each cyclic equivalent edge set... If the power flow disturbance in its internal branches satisfies:

[0081] This perturbation belongs to a local component of a cyclic equivalent edge set. The local component of a global cyclic equivalent edge set is defined as:

[0082] This component represents the residual hidden direction formed by local cancellation within each cyclic equivalent edge set.

[0083] S46. Establish coordinated cut set components. For each cyclic equivalent edge set... Define its multimodal aggregation effect:

[0084] And the first k The aggregation effect of all cyclic equivalent edge sets under each pattern is denoted as . If it satisfies:

[0085] This formula represents the aggregation effect vector. The column space belonging to the transpose of the incidence matrix of the reduced cyclic graph is also the cut space of the reduced cyclic graph. Therefore, the aggregation effect satisfies the coordination cut set condition on the reduced cyclic graph. This yields the coordination cut set component, which represents the residual hidden direction formed by coordination between different cyclic equivalent edge sets through the cut space of the reduced cyclic graph.

[0086] Therefore, the space of coordinated cut set components is defined as:

[0087] The physical meaning of this component lies in its characterization of a cross-unit, macroscopically coordinated attack pattern. In this pattern, each cyclic equivalent edge set unit can be viewed as generating an outward "perturbation spillover." Furthermore, the overflow of all units, at a higher level of the reduced cyclic graph, collectively obeys the cut-set balance required by Kirchhoff's current law, thus achieving concealment at the global level.

[0088] S47. Three-Structure Decomposition of Residual Covert Attack Space. The residual covert attack space under multi-mode moving target defense is decomposed into:

[0089] in, Indicates the component of the bridge branch road. Represents the local components of a cyclic equivalent edge set. This indicates the coordinated cut set components.

[0090] The above decomposition will leave room for residual covert attacks. It is divided into three structural components. Compared with existing technologies that can only give the algebraic dimension of the space, this decomposition method directly establishes the correspondence between each component and specific topological structural units (bridge branches, cyclic equivalent edge sets, and reduced cyclic graph cut spaces), so that each type of residual covert attack direction can be located and quantified according to the structural features it depends on.

[0091] Step 5: Calculate the degrees of freedom of the three structural components respectively, and output the evaluation results of the independent directions of residual covert attacks.

[0092] S51. Based on the identified set of bridge branch roads Calculate the degrees of freedom of the bridge branch components:

[0093] in, This represents the number of bridge branch roads. This degree of freedom indicates the number of residual, hidden, independent directions that can be formed solely by the bridge branch road structure.

[0094] S52. Calculate the local component degrees of freedom of a cyclic equivalent edge set. For each cyclic equivalent edge set... According to its local matrix The local degrees of freedom corresponding to the null dimension are calculated as follows:

[0095] in, This represents the number of branches in the i-th cyclic equivalent edge set. Representing a local matrix rank, Let represent the local degrees of freedom of the i-th cyclic equivalent edge set.

[0096] The sum of the local degrees of freedom of all cyclic equivalent edge sets is:

[0097] This degree of freedom represents the number of residual hidden independent directions that an attacker can construct within each cyclic equivalent edge set.

[0098] S53. Calculate the degrees of freedom of the coordinated cut set components. Based on the column space realizability condition of the local matrix of the cyclic equivalence edge set and the coordination condition of the cut space of the reduced cyclic graph, calculate the degrees of freedom of the coordinated cut set components: } in, The dimension of the set is the number of independent directions in the vector space of the aggregation effect that satisfies the conditions. This represents the multimodal aggregation effect of the i-th cyclic equivalent edge set. This represents the aggregation effect vector of all cyclic equivalent edge sets in the k-th operating mode. This degree of freedom represents the number of residual covert independent directions that an attacker can construct through the coordination relationships between different cyclic equivalent edge sets.

[0099] S54. Calculate the total degrees of freedom of the residual covert attack space. Calculate the total degrees of freedom of the residual covert attack space based on the three structural component degrees of freedom:

[0100] The total degrees of freedom represent the total number of independent directions of residual covert attacks that an attacker can still construct after multi-mode moving target defense.

[0101] S55. Output the evaluation results of independent residual covert attack directions of the power system under multi-mode moving target defense. The results include the degrees of freedom of the bridge branch component, the degrees of freedom of the local component of the cyclic equivalent edge set, the degrees of freedom of the coordinated cut set component, and the total degrees of freedom of the residual covert attack space. Among them, the three structural component degrees of freedom correspond to the number of independent residual covert attack directions that the attacker can utilize under the bridge branch structure, the local structure of the cyclic equivalent edge set, and the coordinated structure of the reduced cyclic graph, respectively.

[0102] The higher the degree of freedom mentioned above, the greater the risk of residual covert attacks corresponding to the structural unit, which can provide a priority ranking basis for the reinforcement of key structures for the defense of moving targets.

[0103] The topological decomposition and degree-of-freedom calculation process of the method of this invention is illustrated using the IEEE 30-node system as an example. The IEEE 30-node system includes 30 nodes and 41 branches, with 12 independent cycles. After judgment based on the column structure of the cyclic basis matrix C, the set of bridge branches is obtained. Therefore, the degrees of freedom of the bridge branch components The bridge branch road identification results are as follows: Figure 2 As shown.

[0104] Furthermore, cyclic equivalent edge set partitioning is performed on non-bridge branches. That is, when the column vectors of the cyclic basis matrices corresponding to two non-bridge branches have the same or differ in overall sign, they are assigned to the same cyclic equivalent edge set. The cyclic equivalent edge set partitioning result of the IEEE 30-node system is as follows: Figure 3 As shown, the corresponding set partitions are shown in Table 1.

[0105] Table 1. Results of Cyclic Equivalent Edge Set Partitioning for the IEEE 30-Node System

[0106] Each cyclic equivalent edge set Abstracted into a reduced cycle graph A reduced edge in the equation is obtained by preserving the connectivity between different sets of cyclic equivalent edges. Figure 4 The reduced cyclic graph shown is used to characterize the coordination relationships between different cyclic equivalent edge sets formed by cut spaces.

[0107] In terms of degree of freedom calculation, the degrees of freedom of the bridge branch components are calculated separately. Local component degrees of freedom of cyclic equivalent edge sets and coordinate cut set component degrees of freedom And obtain the total degrees of freedom. In this embodiment, the degrees of freedom results of the IEEE 30-node system under different multi-mode moving target defense conditions are shown in Table 2.

[0108] Table 2. Calculation results of the three-structure degrees of freedom of the IEEE 30-node system

[0109] As shown in Table 2, the degree of freedom of the bridge branch component is always equal to the number of bridge branches (3) and does not disappear with changes in the moving target defense mode; the local component of the cyclic equivalent edge set and the coordinated cut set component decrease with the increase of the number of moving target defense modes. Therefore, the three structural degrees of freedom can respectively characterize the number of independent residual covert attack directions that an attacker can utilize under the bridge branch structure, the local structure of the cyclic equivalent edge set, and the coordinated structure of the reduced cyclic graph.

[0110] A computer system. The computer system includes a processor and memory. The memory and processor can be interconnected via a bus system and / or other forms of connection. The processor may include any one or more processors such as a central processing unit (CPU), a graphics processing unit (GPU), a microprocessor (MP), or a digital signal processor (DSP). The memory may include volatile memory, such as random access memory (RAM). The memory may also include non-volatile memory, such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid state drive (SSD). The memory stores executable program code, which the processor executes to implement the power system network attack risk assessment method based on residual covert attack space topology decomposition described in Embodiment 1.

[0111] A computer-readable storage medium. For example, the computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), or a compact disc read-only memory (CD). ROM, magnetic tape, floppy disk, and optical data storage devices, etc. This computer-readable storage medium is used to store computer-readable instructions, which, when executed by a computer, can implement one or more steps of the aforementioned method for simulating the cross-temporal and spatial social perception of historical figures.

Claims

1. A method for assessing the risk of network attacks on power systems based on residual covert attack space topology decomposition, characterized in that, include: Obtain the power system topology and branch parameter matrix for each operating mode under multi-mode moving target defense. ,in And construct the cyclic basis matrix. C ; By establishing a branch power flow perturbation representation, the residual covert attack space is transformed into a cyclic basis matrix-based representation. C and branch parameter matrix Multi-mode cyclic consistency constraints form branch power flow disturbance space. ; Based on cyclic basis matrix C The column structure identifies bridge branches and divides the cyclic equivalent edge set; Construct a reduced cyclic graph and its correlation matrix based on the cyclic equivalent edge set. ; Based on the bridge branches, cyclic equivalent edge sets, and reduced cyclic graph correlation matrix The branch power flow disturbance space Perform a three-structure decomposition to obtain the bridge branch component, the local component of the cyclic equivalent edge set, and the coordinated cut set component; Calculate the degrees of freedom of the bridge branch component, the local component of the cyclic equivalent edge set, and the coordinated cut set component, and output the evaluation results of the independent directions of the residual covert attack.

2. The method according to claim 1, characterized in that, The acquisition of the power system topology and branch parameter matrix for each operating mode under multi-mode moving target defense is described. ,include: Obtain the line topology of the power system and represent the power system as a connected graph. G =( V , E ),in V Represents a set of nodes. E Represents the set of branches; Obtain the measurement configuration, which includes node injection power measurement and branch power flow measurement; For the k The system operates in several modes, acquiring the corresponding line parameters for each branch to form a branch parameter matrix. in, Indicates the first k The first operating mode e The equivalent susceptance of the branch circuit, Indicates the number of branches.

3. The method according to claim 1, characterized in that, The construction of the cyclic basis matrix C ,include: Constructing a cyclic basis matrix based on the power system topology ,in This indicates the number of independent cycles in a power system diagram. Indicates the number of nodes. The cyclic basis matrix represents the number of branches. C Used to describe the relationship between branches and independent loops.

4. The method according to claim 1, characterized in that, The establishment of branch flow perturbation representation transforms the residual covert attack space into a multi-mode cyclic consistency constraint, including: Define the attack vector for measurement: ,in This indicates that the node is injected with measurement perturbation. Indicates branch power flow measurement disturbance; Based on node-branch association matrix Establish relationships The attack vector is uniformly represented by branch power flow perturbation variables. The form of the decision; The condition for keeping the attack vector hidden in every operating mode is transformed into a multi-mode cyclic consistency constraint: And this creates residual hidden spaces within the branch tidal current disturbance space: 。 5. The method according to claim 1, characterized in that, The cyclic basis matrix C The column structure identifies bridge branches, including: For cyclic basis matrices C For each column, determine if the cyclic basis matrix corresponding to the e-th branch is... C Column vectors satisfy If so, the branch road is identified as a bridge branch road; Will not be satisfied The branch roads were identified as non-bridge branch roads, forming a set of non-bridge branch roads. ,in, E Represents the set of branches. This represents a set of bridge branch roads.

6. The method according to claim 5, characterized in that, The partitioning of the cyclic equivalent edge set includes: For any two non-bridge branches , If there exist a sign coefficient η∈{+1,-1} such that Then the branch road and branch roads To partition them into the same cyclic equivalent edge set, the above partitioning is performed on all non-bridge branches to obtain the set of cyclic equivalent edges. ,in For the first i A set of cyclic equivalent edges is the number of cyclic equivalent edge sets.

7. The method according to claim 6, characterized in that, Construct a reduced cyclic graph and its correlation matrix based on the cyclic equivalent edge set. ,include: Each cyclic equivalent edge set Abstracted as a set of reduced cyclic edges in a reduced cyclic graph, the reduced cyclic graph is constructed based on the connectivity between the sets of cyclic equivalent edges in the power system topology. ,in Describes the reduced set of nodes. Denote the reduced edge set; Define a reference direction for each reduced edge in the reduced cyclic graph, and construct the node-edge incidence matrix of the reduced cyclic graph based on the reference direction. , in, Indicates the number of reduced nodes. The transpose of the matrix represents the number of reduced edges. The column space corresponds to the cut space of the reduced cyclic graph.

8. The method according to claim 7, characterized in that, The branch power flow disturbance space Perform a three-structure decomposition, including: The branch road tidal disturbance is only supported by the bridge branch road set. The part is defined as the bridge branch component. : For each cyclic equivalent edge set A local matrix is ​​constructed based on the multi-mode line parameters and direction signs. , of which k Line number j The column elements are: If cyclic equivalent edge set Internal branch power flow disturbance satisfaction Then the perturbation belongs to a local component of a cyclic equivalent edge set. ; For each cyclic equivalent edge set Define multimodal aggregation effect If the aggregation effect of all cyclic equivalent edge sets is in the th case... k Satisfy under each mode Then the disturbance belongs to the coordinated cut set component. ; The remaining covert attack space is decomposed into: in, Indicates the component of the bridge branch road. Represents the local components of a cyclic equivalent edge set. This indicates the coordinated cut set components.

9. The method according to claim 8, characterized in that, Calculate the degrees of freedom of the bridge branch component, the local component of the cyclic equivalent edge set, and the compatible cut set component, including: Degrees of freedom of bridge branch road components: in, Indicates the number of bridge branch roads; Local component degrees of freedom of cyclic equivalent edge sets: in, Indicates the first i The number of branches in a set of cyclic equivalent edges. Representing a local matrix rank; Coordinated cut set component degrees of freedom: } in, The dimension of the set represents the number of independent directions in the vector space of the aggregation effects that satisfy the conditions. Indicates the first k The aggregation effect vector of all cyclic equivalent edge sets in each operating mode.

10. The method according to claim 9, characterized in that, Total degrees of freedom in the residual covert attack space: The total degrees of freedom represent the total number of independent directions from which an attacker can still construct a residual covert attack after a multi-mode moving target defense.

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