A method and device for analyzing vulnerable links in a power transmission system considering attack success rate

Abstract

A method and device for analyzing vulnerable links of a power transmission system considering the success rate of an attack, the method constructs a power system logic diagram according to the actual wiring diagram of the power system; sets up corresponding variables; represents the coordinated attack scheme and the impact on the power system through the corresponding variables; constructs a correlation analysis model to perform correlation analysis on the selection of attack targets, attack success and failure scenarios, and the probability of occurrence of attack success and failure scenarios; converts the proposed problem into a mixed integer linear programming and solves it through a linearization strategy; simulates and generates attack success rate distribution scenarios through a Monte Carlo model and solves them to obtain the vulnerable links of the power system under the current sampling batch; obtains a list of vulnerable links in the power system by performing batch sampling calculations. The present invention can fully reflect the impact of the attack success rate on the attack decision, can more comprehensively and accurately evaluate the attack effect of the coordinated attack, thereby predicting the behavior of the attacker, and then guiding the formulation of defense measures.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system security, and in particular relates to a method and a device for analyzing vulnerable links of a power transmission system taking attack success rate into consideration. Background Art

[0002] In recent years, the risk of malicious attacks faced by power systems has been increasing. As modern power systems are increasingly dependent on communications and automatic control systems, cyber-physical coordinated attacks will have a more severe impact on reliable power supply than traditional malicious attacks. It is urgent to improve the ability of power systems to resist coordinated attacks.

[0003] At present, there are certain defects in the existing technology when analyzing the vulnerable links of the power system. First, the uncertainty of the knowledge of the diverse attackers about the success rate of the attack is not considered enough, which may lead to the misalignment of the attack and defense positions, making the defense measures effective only for some attackers; second, related studies often use a fixed success probability to represent the uncertainty of the attack effect, that is, it is believed that the success probability of the attack is irrelevant to the selection of the attack location; in addition, the existing technology often only considers the most serious fault scenario when evaluating the attack loss and ignores the impact of other incomplete attack plans, which makes the estimated attack plan lack of accuracy.

[0004] Therefore, after introducing the attack success rate parameter, how to reflect the vulnerability of power components and the impact of diversified attackers on attack decisions in the attack and defense game problem, and comprehensively search for the list of vulnerable links in the power system under coordinated attacks, have become issues to be solved. Summary of the invention

[0005] To this end, the present invention provides a method and device for analyzing vulnerable links in a power transmission system taking into account the attack success rate, introduces the attack success rate into the attack and defense decision-making process, and establishes an analytical model that describes the selection of attack targets, attack success and failure scenarios, and their corresponding probabilities. In addition, a two-layer optimization framework that considers the full-scenario loss under a coordinated attack is established, and a solution method for converting a two-layer nonlinear optimization problem into a single-layer mixed integer linear programming problem is designed. It can fully reflect the impact of the attack success rate on the attack decision, and can more comprehensively and accurately evaluate the attack effect of the coordinated attack to predict the behavior of the attacker, thereby guiding the formulation of defense measures.

[0006] In order to achieve the above object, the present invention provides the following technical solution: a method for analyzing vulnerable links of a power transmission system considering the attack success rate, comprising:

[0007] Construct a power system logic diagram based on the actual wiring diagram of the power system; establish corresponding variables based on the attack principle and impact mechanism of the cyber-physical coordinated attack; and represent the coordinated attack scheme and the impact on the power system through the corresponding variables;

[0008] Constructing a correlation analysis model, and performing correlation analysis on attack target selection, attack success and failure scenarios, and the probability of occurrence of attack success and failure scenarios through the correlation analysis model;

[0009] According to the attack success or failure scenarios, in the power system logic diagram, fault evolution constraints under multiple scenarios are constructed; in the power system wiring diagram, power flow constraints under multiple scenarios are constructed; and the objective function of the power system full-scenario fault loss is calculated;

[0010] Through the linearization strategy, the two-layer nonlinear optimization problem of the power grid vulnerable link analysis is transformed into a single-layer mixed integer linear programming and solved; through the Monte Carlo model, the attack success rate distribution scenario is simulated and generated; by solving the Monte Carlo model, the vulnerable links of the power system under the current sampling batch are obtained; by performing batch sampling calculations, a list of vulnerable links in the power system is obtained.

[0011] As a preferred scheme for a power transmission system vulnerable link analysis method taking into account the attack success rate, the cyber-physical coordinated attack includes a physical attack targeting a power transmission line and a denial-of-operation network attack targeting a relay protection device;

[0012] The construction principle of the power system logic diagram is:

[0013] The power system is divided into several regions according to the circuit breakers; the vertices in the logic graph are obtained according to the one-to-one correspondence between the regions and the vertices; the edges in the logic graph are obtained according to the one-to-one correspondence between the circuit breakers and the edges of the regions;

[0014] The fault state of the region represents the state of all components inside the region; the on-off state of the edge in the logic graph represents the switch state of the corresponding circuit breaker.

[0015] As a preferred method for analyzing the vulnerable links of a power transmission system taking into account the attack success rate, the correlation analysis model is constructed through formulas (1)-(5):

[0016]

[0017]

[0018]

[0019] In the formula, Indicates whether the actual area corresponding to vertex i in the logical graph has been physically attacked, 0 means no attack, 1 means attack; E is the set of edges in the logical graph; V is the set of vertices in the logical graph; λ ij is the weight constant corresponding to edge ij; A p A is the number of physical attack resources; cr The number of network attack resources to be denied; Indicates whether the network attack numbered d occurs on the relay protection device corresponding to edge ij, 0 means no attack, 1 means attack; Indicates whether the network attack numbered d+1 occurs on the relay protection device corresponding to edge ij, 0 means no attack, 1 means attack;

[0020]

[0021]

[0022] In the formula, Indicates whether the relay protection device configured on the circuit breaker corresponding to edge ij in scenario s is affected by the denial-of-operation network attack, 1 for yes and 0 for no;

[0023] Indicates whether the dth denial-of-service network attack in scenario s is successful, 1 for yes and 0 for no;

[0024] P(s) is the occurrence probability of scene s; ρ ij is the success rate of network attacks on the relay protection device corresponding to edge ij.

[0025] As a preferred method for analyzing the vulnerable links of a power transmission system taking into account the attack success rate, the fault evolution process of multiple scenarios is constructed in the power system logic diagram through formulas (6)-(12):

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] In the formula, Ω S For scene collection;

[0034] Indicates the on-off status of edge ij in scene s, 1 for on and 0 for off;

[0035] Indicates whether the area corresponding to the vertex numbered i in scene s is affected by the fault, 1 for yes and 0 for no;

[0036] Indicates whether the area corresponding to the vertex numbered j in scene s is affected by the fault, 1 for yes and 0 for no;

[0037] M is a positive number; is the commodity flow flowing on edge ij in scenario s; is the commodity flow flowing on edge ji in scene s; is the commodity flow flowing on edge ik in scene s;

[0038] Through formulas (13)-(15), the fault evolution process in the power system logic diagram is mapped to the power system wiring diagram:

[0039]

[0040]

[0041]

[0042] In the formula, c m,s Indicates the fault status of node m in scenario s, 1 means the node is affected by the short circuit fault, and 0 means the node is not affected; is the actual power system node set corresponding to vertex i in the logical graph; Indicates the switch status of the circuit breaker mn on the left side of the line in scenario s, 1 means the circuit breaker is closed, and 0 means the circuit breaker is open; Ω T is a set of transmission lines indexed by (m,n); is the set of edges corresponding to the circuit breaker at the left end of the transmission line mn; is the switch state of the circuit breaker mn on the right side of the line in scenario s, 1 means the circuit breaker is closed, and 0 means the circuit breaker is open; is the set of edges corresponding to the circuit breaker at the right end of the transmission line mn;

[0043] Through formulas (16)-(22), the generation redispatch process is constructed in the power system wiring diagram according to the fault situation:

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] The objective function for calculating the fault loss of the power system in all scenarios is:

[0052]

[0053] In the formula, Ω N represents a node set indexed by m; Ω T represents the set of transmission lines indexed by (m,n); Ω G represents a collection of generators; represents the set of generators on node m; Ω D represents the load set indexed by l; represents the load set on node m; represents the set of transmission lines indexed by (m,n) with the left end node being m; represents the set of transmission lines indexed by (m,n) with n as the right end node; represents the active output of generator g in scenario s; P l L represents the active load demand of load l; represents the active load reduction of load l in scenario s; represents the active power flow on branch mn in scenario s; represents the active power flow on branch hm in scenario s; represents the maximum active power transmitted by the transmission line mn; x mn represents the reactance of the transmission line mn; θ m represents the voltage phase angle of node m; θ n represents the voltage phase angle of node n; Indicates the maximum active output of generator g; represents the active output of the generator g beforehand; Indicates the ramp rate of active output of generator g.

[0054] As a preferred scheme for the vulnerable link analysis method of the transmission system taking into account the attack success rate, the linearization strategy is to transform the nonlinear two-layer problem into a single-layer mixed integer programming problem through the probability generation constraint piecewise linearization strategy of the second special order set and the equivalent transformation strategy of the optimization problem according to variable transformation.

[0055] The present invention also provides a power transmission system vulnerable link analysis device considering the attack success rate, which adopts the above-mentioned power transmission system vulnerable link analysis method considering the attack success rate, comprising:

[0056] The basic information data conversion module is used to construct a power system logic diagram based on the actual wiring diagram of the power system; to set up corresponding variables according to the attack principle and impact mechanism of the cyber-physical coordinated attack; and to represent the coordinated attack scheme and the impact on the power system through the corresponding variables;

[0057] A correlation analysis model building module, used to build a correlation analysis model, through which the correlation analysis model is used to perform correlation analysis on attack target selection, attack success or failure scenarios, and the probability of occurrence of attack success or failure scenarios;

[0058] A fault evolution constraint and power flow constraint construction module is used to construct fault evolution constraints under multiple scenarios in the power system logic diagram according to the attack success or failure scenarios; construct power flow constraints under multiple scenarios in the power system wiring diagram; and calculate the fault loss objective function of the power system in all scenarios;

[0059] The module for acquiring the list of vulnerable links in the power system is used to transform the double-layer nonlinear optimization problem of the vulnerable link analysis of the power grid into a single-layer mixed integer linear programming and solve it through a linearization strategy; simulate and generate the attack success rate distribution scenario through a Monte Carlo model; obtain the vulnerable links of the power system under the current sampling batch by solving the Monte Carlo model; and obtain the list of vulnerable links in the power system by performing batch sampling calculations.

[0060] As a preferred solution of a power transmission system vulnerable link analysis device taking into account the attack success rate, in the basic information data conversion module, the cyber-physical coordinated attack includes a physical attack targeting the transmission line and a denial-of-operation network attack targeting the relay protection device;

[0061] The construction principle of the power system logic diagram is:

[0062] The power system is divided into several regions according to the circuit breakers; the vertices in the logic graph are obtained according to the one-to-one correspondence between the regions and the vertices; the edges in the logic graph are obtained according to the one-to-one correspondence between the circuit breakers and the edges of the regions;

[0063] The fault state of the region represents the state of all components inside the region; the on-off state of the edge in the logic graph represents the switch state of the corresponding circuit breaker.

[0064] As a preferred solution of a power transmission system vulnerable link analysis device taking into account the attack success rate, in the correlation analysis model construction module, the correlation analysis model is constructed by formulas (1)-(5):

[0065]

[0066]

[0067]

[0068] In the formula, Indicates whether the actual area corresponding to vertex i in the logical graph has been physically attacked, 0 means no attack, 1 means attack; E is the set of edges in the logical graph; V is the set of vertices in the logical graph; λ ij is the weight constant corresponding to edge ij; A p A is the number of physical attack resources; cr The number of network attack resources to be denied; Indicates whether the network attack numbered d occurs on the relay protection device corresponding to edge ij, 0 means no attack, 1 means attack; Indicates whether the network attack numbered d+1 occurs on the relay protection device corresponding to edge ij, 0 means no attack, 1 means attack;

[0069]

[0070]

[0071] In the formula, Indicates whether the relay protection device configured on the circuit breaker corresponding to edge ij in scenario s is affected by the denial-of-operation network attack, 1 for yes and 0 for no;

[0072] Indicates whether the dth denial-of-service network attack in scenario s is successful, 1 for yes and 0 for no;

[0073] P(s) is the occurrence probability of scene s; ρ ij is the success rate of network attacks on the relay protection device corresponding to edge ij.

[0074] As a preferred solution for a power transmission system vulnerable link analysis device taking into account the attack success rate, in the fault evolution constraint and power flow constraint construction module, a multi-scenario fault evolution process is constructed in the power system logic diagram through formulas (6)-(12):

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082] In the formula, Ω S For scene collection;

[0083] Indicates the on-off status of edge ij in scene s, 1 for on and 0 for off;

[0084] Indicates whether the area corresponding to the vertex numbered i in scene s is affected by the fault, 1 for yes and 0 for no;

[0085] Indicates whether the area corresponding to the vertex numbered j in scene s is affected by the fault, 1 for yes and 0 for no;

[0086] M is a positive number; is the commodity flow flowing on edge ij in scenario s; is the commodity flow flowing on edge ji in scene s; is the commodity flow flowing on edge ik in scene s;

[0087] Through formulas (13)-(15), the fault evolution process in the power system logic diagram is mapped to the power system wiring diagram:

[0088]

[0089]

[0090]

[0091] In the formula, c m,s Indicates the fault status of node m in scenario s, 1 means the node is affected by the short circuit fault, and 0 means the node is not affected; is the actual power system node set corresponding to vertex i in the logical graph; Indicates the switch status of the circuit breaker mn on the left side of the line in scenario s, 1 means the circuit breaker is closed, and 0 means the circuit breaker is open; Ω T is a set of transmission lines indexed by (m,n); is the set of edges corresponding to the circuit breaker at the left end of the transmission line mn; is the switch state of the circuit breaker mn on the right side of the line in scenario s, 1 means the circuit breaker is closed, and 0 means the circuit breaker is open; is the set of edges corresponding to the circuit breaker at the right end of the transmission line mn;

[0092] Through formulas (16)-(22), the generation redispatch process is constructed in the power system wiring diagram according to the fault situation:

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] The objective function for calculating the fault loss of the power system in all scenarios is:

[0101]

[0102] In the formula, Ω N represents a node set indexed by m; Ω T represents the set of transmission lines indexed by (m,n); Ω G represents a collection of generators; represents the set of generators on node m; Ω D represents the load set indexed by l; represents the load set on node m; represents the set of transmission lines indexed by (m,n) with the left end node being m; represents the set of transmission lines indexed by (m,n) with n as the right end node; represents the active output of generator g in scenario s; P l L represents the active load demand of load l; represents the active load reduction of load l in scenario s; represents the active power flow on branch mn in scenario s; represents the active power flow on branch hm in scenario s; represents the maximum active power transmitted by the transmission line mn; x mn represents the reactance of the transmission line mn; θ m represents the voltage phase angle of node m; θ n represents the voltage phase angle of node n; Indicates the maximum active output of generator g; represents the active output of the generator g beforehand; Indicates the ramp rate of active output of generator g.

[0103] As a preferred solution for a power transmission system vulnerable link analysis device taking into account the attack success rate, in the power system vulnerable link list acquisition module, the linearization strategy is to convert the nonlinear two-layer problem into a single-layer mixed integer programming problem through the probability generation constraint piecewise linearization strategy of the second type of special order set and the equivalent transformation strategy of the optimization problem based on variable transformation.

[0104] The present invention has the following advantages: constructing a power system logic diagram according to an actual power system wiring diagram; establishing corresponding variables according to the attack principle and influencing mechanism of information-physical collaborative attack; representing the collaborative attack scheme and the impact on the power system through the corresponding variables; constructing a correlation analysis model, and performing correlation analysis on attack target selection, attack success or failure scenarios, and the probability of occurrence of attack success or failure scenarios through the correlation analysis model; constructing fault evolution constraints under multiple scenarios in the power system logic diagram according to the attack success or failure scenarios; constructing flow constraints under multiple scenarios in the power system wiring diagram; calculating the full-scenario fault loss objective function of the power system; converting the double-layer nonlinear optimization problem of the power grid vulnerable link analysis into a single-layer mixed integer linear programming through a linearization strategy and solving it; simulating and generating attack success rate distribution scenarios through a Monte Carlo model; obtaining the vulnerable links of the power system under the current sampling batch by solving the Monte Carlo model; and obtaining a list of vulnerable links of the power system by performing batch sampling calculations. The present invention constructs an analytical model that describes the selection of attack targets, attack success and failure scenarios and their corresponding probabilities. The model can analyze and describe different complete situations of the implementation of the coordinated attack scheme, and describe all possible success and failure scenarios caused by the coordinated attack scheme; on this basis, according to the success probability, the probability of occurrence of each success and failure scenario is calculated, so as to obtain the corresponding fault evolution scenario weight setting. The model can more accurately and comprehensively evaluate the impact of information-physical coordinated attacks on the reliable power supply of power systems. A two-layer optimization framework considering the full-scenario loss under the coordinated attack is also proposed. In the two-layer model, the scenario probability and the scenario load loss are comprehensively considered to evaluate the attack effect and generate the optimal coordinated attack scheme from the perspective of a specific attacker. At the same time, a linearization method that converts the two-layer nonlinear optimization problem into a single-layer mixed integer linear programming problem is designed. By converting the problem, the model can be solved by an existing commercial solver, and the solution efficiency is improved. The present invention uses an analytical model of the correlation between the selection of attack targets, the success and failure scenarios of the attack and their corresponding probabilities to describe the actual attack effect of the information-physical coordinated attack considering all attack success and failure scenarios, and simulates the decision-making process of the attacker based on a two-layer optimization framework considering the attack success rate and the full-scenario loss. Through the designed linearization method, a comprehensive and accurate list of vulnerable links is obtained by analyzing the changes in the success rates of various attacks, guiding the formulation of defense measures for the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] In order to more clearly illustrate the implementation methods of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the implementation methods or the description of the prior art. Obviously, the drawings in the following description are only exemplary, and for ordinary technicians in this field, other implementation drawings can be derived from the provided drawings without creative work.

[0106] Figure 1 A schematic flow chart of a method for analyzing vulnerable links in a power transmission system taking into account attack success rate provided in Embodiment 1 of the present invention;

[0107] Figure 2 A schematic diagram of a wiring diagram of an IEEE RTS24 node system in a possible embodiment provided in Embodiment 1 of the present invention;

[0108] Figure 3 A schematic diagram of probability distribution of an optimal attack scheme in a possible embodiment provided in Embodiment 1 of the present invention;

[0109] Figure 4 A schematic diagram of a specific implementation effect of the optimal attack scheme 3 in a possible embodiment provided in Embodiment 1 of the present invention;

[0110] Figure 5 This is an architecture diagram of a power transmission system vulnerable link analysis device taking into account attack success rate provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0111] The following is a description of the implementation of the present invention by specific embodiments. People familiar with the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0112] Example 1

[0113] See also Figure 1 Embodiment 1 of the present invention provides a method for analyzing vulnerable links of a power transmission system taking into account attack success rate, comprising the following steps:

[0114] S1. Construct a power system logic diagram based on the actual wiring diagram of the power system; set up corresponding variables based on the attack principle and impact mechanism of the cyber-physical coordinated attack; and represent the coordinated attack scheme and the impact on the power system through the corresponding variables;

[0115] S2. Constructing a correlation analysis model, and performing correlation analysis on attack target selection, attack success or failure scenarios, and the probability of occurrence of attack success or failure scenarios through the correlation analysis model;

[0116] S3. According to the attack success or failure scenarios, in the power system logic diagram, construct fault evolution constraints under multiple scenarios; in the power system wiring diagram, construct power flow constraints under multiple scenarios; calculate the fault loss objective function of the power system in all scenarios;

[0117] S4. The two-layer nonlinear optimization problem of the power grid vulnerable link analysis is converted into a single-layer mixed integer linear programming and solved through a linearization strategy; the attack success rate distribution scenario is simulated and generated through a Monte Carlo model; the vulnerable links of the power system under the current sampling batch are obtained by solving the Monte Carlo model; and a list of vulnerable links of the power system is obtained by performing batch sampling calculations.

[0118] In this embodiment, in step S1, the cyber-physical coordinated attack includes a physical attack targeting a power transmission line and a denial-of-operation network attack targeting a relay protection device;

[0119] The construction principle of the power system logic diagram is:

[0120] The power system is divided into several regions according to the circuit breakers; the vertices in the logic graph are obtained according to the one-to-one correspondence between the regions and the vertices; the edges in the logic graph are obtained according to the one-to-one correspondence between the circuit breakers and the edges of the regions;

[0121] The fault state of the region represents the state of all components inside the region; the on-off state of the edge in the logic graph represents the switch state of the corresponding circuit breaker.

[0122] Specifically, for each system component, a binary variable is used to represent the selection of the coordinated attack target and the impact on the power system;

[0123] In the power system logic diagram, the attack variables include: Indicates whether any of the transmission lines contained in vertex i has been subjected to physical attack, which is 1 if yes and 0 if no; Indicates whether the relay protection device configured on the circuit breaker corresponding to edge ij is subjected to the dth refusal-to-operate network attack, which is 1 if yes and 0 if no;

[0124] Variables affecting actual components of the power system include: Represents the switch status of the circuit breaker at the left end of the transmission line mn. If the circuit breaker is open, it is represented as 1, otherwise it is 0; Represents the switch status of the circuit breaker at the right end of the transmission line mn. If the circuit breaker is open, it is represented as 1, otherwise it is 0; c m,sIndicates the impact of the fault on node m. If the node is affected by the fault, it is 1, otherwise it is 0.

[0125] In this embodiment, in step S2, the correlation analysis model is constructed by formulas (1)-(5):

[0126]

[0127]

[0128]

[0129] In the formula, Indicates whether the actual area corresponding to vertex i in the logical graph has been physically attacked, 0 means no attack, 1 means attack; E is the set of edges in the logical graph; V is the set of vertices in the logical graph; λ ij is the weight constant corresponding to edge ij; A p A is the number of physical attack resources; cr The number of network attack resources to be denied; Indicates whether the network attack numbered d occurs on the relay protection device corresponding to edge ij, 0 means no attack, 1 means attack; Indicates whether the network attack numbered d+1 occurs on the relay protection device corresponding to edge ij, 0 means no attack, 1 means attack;

[0130] Formula (1) and Formula (2) limit the maximum number of components that can be affected by physical attacks and network attacks respectively. Formula (3) sorts the network attack positions by the weight constant corresponding to the edge ij. The sorting achieved by this constraint can greatly reduce the possible values ​​of the variables. For the case of Acr network attack resources, this method can represent Acr! variable groups with one variable group, effectively improving the efficiency of problem solving.

[0131]

[0132]

[0133] In the formula, Indicates whether the relay protection device configured on the circuit breaker corresponding to edge ij in scenario s is affected by the denial-of-operation network attack, 1 for yes and 0 for no;

[0134] Indicates whether the dth denial-of-service network attack in scenario s is successful, 1 for yes and 0 for no;

[0135] P(s) is the occurrence probability of scene s; ρ ij is the success rate of network attacks on the relay protection device corresponding to edge ij.

[0136] After the attack location is determined, it is necessary to generate corresponding success and failure scenarios based on the success or failure of the attack plan and calculate the probability of occurrence of each scenario.

[0137] Formula (4) indicates that only when a network attack occurs on edge ij and the network attack succeeds in scenario s, edge ij in scenario s will be affected by the rejected network attack. Formula (5) indicates that for different network attack success situations in each scenario, the probability of occurrence of the success or failure scenario is calculated based on the success or failure probability of the network attack of all components.

[0138] In this embodiment, in step S3, the fault evolution process of multiple scenarios is constructed in the power system logic diagram through formulas (6)-(12):

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146] In the formula, Ω S For scene collection;

[0147] Indicates the on-off status of edge ij in scene s, 1 for on and 0 for off;

[0148] Indicates whether the area corresponding to the vertex numbered i in scene s is affected by the fault, 1 for yes and 0 for no;

[0149] Indicates whether the area corresponding to the vertex numbered j in scene s is affected by the fault, 1 for yes and 0 for no;

[0150] M is a positive number; is the commodity flow flowing on edge ij in scenario s; is the commodity flow flowing on edge ji in scene s; is the commodity flow flowing on edge ik in scene s;

[0151] Formula (6) indicates that the fault states of two areas connected by a closed edge are the same; Formula (7) indicates that commodity flow can only flow on the closed edge; Formula (8) takes the short-circuit fault point as the source point, each vertex as the sink point, and the edge as the flow path of the commodity flow, which constrains the conservation of commodity flow on each vertex. Formulas (9)-(12) simulate the action logic of the protection device under the influence of network attacks in the logic diagram; Formulas (9) and (10) indicate that the circuit breaker that is not affected by the refusal network attack can trip and isolate the fault; Formula (11) indicates that the circuit breaker with no faults at both ends will not trip; Formula (12) indicates that the circuit breaker that is affected by the refusal network attack will not trip.

[0152] Through formulas (13)-(15), the fault evolution process in the power system logic diagram is mapped to the power system wiring diagram:

[0153]

[0154]

[0155]

[0156] In the formula, c m,s Indicates the fault status of node m in scenario s, 1 means the node is affected by the short circuit fault, and 0 means the node is not affected; is the actual power system node set corresponding to vertex i in the logical graph; Indicates the switch status of the circuit breaker mn on the left side of the line in scenario s, 1 means the circuit breaker is closed, and 0 means the circuit breaker is open; Ω T is a set of transmission lines indexed by (m,n); is the set of edges corresponding to the circuit breaker at the left end of the transmission line mn; is the switch state of the circuit breaker mn on the right side of the line in scenario s, 1 means the circuit breaker is closed, and 0 means the circuit breaker is open; is the set of edges corresponding to the circuit breaker at the right end of the transmission line mn;

[0157] Formula (13) indicates that the fault state of the vertex in the logic graph is the same as the corresponding fault state of all power components; Formula (14) and Formula (15) respectively indicate that the on-off state of the edge in the logic graph is consistent with the switch state of the circuit breaker at the left and right ends of the corresponding line.

[0158] Through formulas (16)-(22), the generation redispatch process is constructed in the power system wiring diagram according to the fault situation:

[0159]

[0160]

[0161]

[0162]

[0163]

[0164]

[0165]

[0166] The objective function for calculating the fault loss of the power system in all scenarios is:

[0167]

[0168] In the formula, Ω N represents a node set indexed by m; Ω T represents the set of transmission lines indexed by (m,n); Ω G represents a collection of generators; represents the set of generators on node m; Ω D represents the load set indexed by l; represents the load set on node m; represents the set of transmission lines indexed by (m,n) with the left end node being m; represents the set of transmission lines indexed by (m,n) with n as the right end node; represents the active output of generator g in scenario s; P l L represents the active load demand of load l; represents the active load reduction of load l in scenario s; represents the active power flow on branch mn in scenario s; represents the active power flow on branch hm in scenario s; represents the maximum active power transmitted by the transmission line mn; x mn represents the reactance of the transmission line mn; θ m represents the voltage phase angle of node m; θ n represents the voltage phase angle of node n; Indicates the maximum active output of generator g; represents the active output of the generator g beforehand; Indicates the ramp rate of active output of generator g.

[0169] Formula (16) represents the power balance equation of the node in the actual power system; Formula (17) and Formula (18) indicate that the line with any circuit breaker disconnected at both ends cannot transmit power flow; Formula (19) indicates that the power flow of the non-fault line satisfies the DC power flow equation, while the fault line does not need to satisfy this constraint; Formula (20) represents the maximum output constraint of the generator, and the output of the generator at the fault node is 0; Formula (21) represents the ramp constraint of the generator output; Formula (22) represents the load reduction constraint, and the load at the fault node is completely lost.

[0170] Formula (23) represents the objective function of the two-layer optimization framework, which takes into account multiple scenarios caused by the success or failure of the attack, and comprehensively evaluates the load loss that may be caused by the complete attack scheme and the incomplete attack scheme by means of probability weighting.

[0171] In this embodiment, in step S4, the linearization strategy is to transform the nonlinear two-level problem into a single-level mixed integer programming problem through the probability generation constraint piecewise linearization strategy of the second type of special order set and the equivalent transformation strategy of the optimization problem according to variable transformation.

[0172] Specifically, in the proposed two-level optimization framework, since the constraints introduce the scenario probability calculation and consider the impact of the scenario probability on the total loss in the objective function, the product terms corresponding to the scenario probability and the product terms corresponding to the scenario loss expectation appear. For this type of nonlinear problem, the present invention uses a probability generation constraint piecewise linearization strategy based on the second special order set and an optimization problem equivalent transformation strategy based on variable transformation to transform the nonlinear two-level problem into a single-level mixed integer programming problem.

[0173] A piecewise linearization strategy for generating constraints based on the probability of the second type of special ordered sets:

[0174] First, the product of the variables is converted into the sum of the variables by taking the logarithm, as shown in formula (24). In this way, the probability calculation becomes an exponential function with the independent variable as a linear term.

[0175]

[0176] Next, the exponential function needs to be piecewise linearized. The specific implementation method is as follows: for the function y=ex, take m points (xi,yi) on the interval of interest in the problem within the domain of definition, and make x1 and xm the left and right endpoints of the interval of interest.

[0177] Finally, the linear relationship between variables x and y can be expressed as shown in equations (25)-(32).

[0178]

[0179]

[0180]

[0181] z i ≥μ i ≥0 , i=1,2,…,m (28)

[0182] z i +z j ≤1, i=1,2,…,m-2; j=i+2,…,m (29)

[0183] z i ∈{0,1} , i=1,2,…,m (30)

[0184]

[0185] y=P(s) (32)

[0186] Equivalent transformation strategy for optimization problems based on variable transformation:

[0187] Taking scenario s as an example, the two-layer problem is expressed in matrix form as shown in formula (33), showing the transformation process of the equivalent problem.

[0188]

[0189]

[0190]

[0191] sA T Y'≤P(s)C

[0192] Y'≥0

[0193] P(s)=f(Z) (35)

[0194] Where A, B, C, and D are constant matrices representing constraint coefficients; X is a continuous variable column vector, including all continuous variables such as power generation output, load, and branch flow of the aforementioned model; Z is a 0-1 variable column vector, including all 0-1 variables such as the fault evolution of the aforementioned model and the switch status of the circuit breaker; the value of the scenario probability P(s) depends entirely on the value of Z, that is, it depends entirely on the attack location and the success or failure of the attack.

[0195] Formula (33) is the original two-layer problem expressed in matrix, considering only the loss of scene s. Formula (34) is the max-max problem after dualization. Formula (35) is the equivalent single-layer problem obtained. Let Y' = P(s)Y to transform Formula (33) into Formula (35).

[0196] In a possible embodiment, an example of analyzing vulnerable links of the IEEE RTS24 node system is provided as follows:

[0197] T1. The wiring diagram of the system is as follows Figure 2 As shown in the figure, there are 24 nodes and 38 transmission lines in the system. A logic diagram is generated based on the actual wiring diagram of the power system, and corresponding variables are set up to represent the coordinated attack scheme and the impact on the power system according to the attack principle and impact mechanism of the cyber-physical coordinated attack.

[0198] T2. Considering the various attack success and failure situations brought about by the introduction of attack success rate, an analytical model is constructed that utilizes the correlation between attack target selection, attack success and failure scenarios and their corresponding probabilities.

[0199] T3. For each success or failure scenario, establish the fault evolution constraints and power flow constraints under multiple scenarios in the logic diagram and power system wiring diagram, and calculate the fault loss objective function of the power system in all scenarios;

[0200] T4. Use the linearization method to transform the proposed problem into a mixed integer linear programming and solve it. Generate the attack success rate distribution scenario through Monte Carlo simulation, and solve the model to obtain the vulnerable links of the power system under the current sampling. Through a large number of sampling, a more comprehensive list of vulnerable links in the power system is finally obtained to support the formulation of defense measures for the power system.

[0201] The number of physical attack resources is 2, the number of denial network attack resources is 2, and the baseline success rate of denial network attack is 75%, and the uniform distribution range is [65%, 85%]. The Monte Carlo method is used to sample 200 times and solve the optimal attack plan, which is divided into 3 types. The specific distribution is as follows: Figure 3 As shown; the specific implementation effect of the optimal attack plan 3 is as follows Figure 4 As shown;

[0202]

[0203] Table 1 Loss statistics of each scenario of the optimal attack scheme 3

[0204] The loss statistics of each scenario of the optimal attack scheme 3 are shown in Table 1.

[0205] In summary, the present invention constructs a power system logic diagram according to the actual wiring diagram of the power system; establishes corresponding variables according to the attack principle and impact mechanism of the information-physical collaborative attack; represents the collaborative attack plan and the impact on the power system through the corresponding variables; constructs a correlation analysis model, and performs correlation analysis on the attack target selection, attack success or failure scenarios, and the probability of occurrence of attack success or failure scenarios through the correlation analysis model; according to the attack success or failure scenarios, in the power system logic diagram, fault evolution constraints under multiple scenarios are constructed; in the power system wiring diagram, flow constraints under multiple scenarios are constructed; the full-scenario fault loss objective function of the power system is calculated; the two-layer nonlinear optimization problem of the power grid vulnerable link analysis is converted into a single-layer mixed integer linear programming through a linearization strategy and solved; through a Monte Carlo model, an attack success rate distribution scenario is simulated and generated; by solving the Monte Carlo model, the vulnerable links of the power system under the current sampling batch are obtained; and a list of vulnerable links of the power system is obtained by performing batch sampling calculations. The present invention constructs an analytical model that describes the selection of attack targets, attack success and failure scenarios and their corresponding probabilities. The model can analyze and describe different complete situations of the implementation of the coordinated attack scheme, and describe all possible success and failure scenarios caused by the coordinated attack scheme; on this basis, according to the success probability, the probability of occurrence of each success and failure scenario is calculated, so as to obtain the corresponding fault evolution scenario weight setting. The model can more accurately and comprehensively evaluate the impact of information-physical coordinated attacks on the reliable power supply of power systems. A two-layer optimization framework considering the full-scenario loss under the coordinated attack is also proposed. In the two-layer model, the scenario probability and the scenario load loss are comprehensively considered to evaluate the attack effect and generate the optimal coordinated attack scheme from the perspective of a specific attacker. At the same time, a linearization method that converts the two-layer nonlinear optimization problem into a single-layer mixed integer linear programming problem is designed. By converting the problem, the model can be solved by an existing commercial solver, and the solution efficiency is improved. The present invention uses an analytical model of the correlation between the selection of attack targets, the success and failure scenarios of the attack and their corresponding probabilities to describe the actual attack effect of the information-physical coordinated attack considering all attack success and failure scenarios, and simulates the decision-making process of the attacker based on a two-layer optimization framework considering the attack success rate and the full-scenario loss. Through the designed linearization method, a comprehensive and accurate list of vulnerable links is obtained by analyzing the changes in the success rates of various attacks, guiding the formulation of defense measures for the power system.

[0206] It should be noted that the method of the embodiment of the present disclosure can be performed by a single device, such as a computer or a server. The method of the present embodiment can also be applied in a distributed scenario and completed by multiple devices cooperating with each other. In the case of such a distributed scenario, one of the multiple devices can only perform one or more steps in the method of the embodiment of the present disclosure, and the multiple devices will interact with each other to complete the described method.

[0207] It should be noted that the above describes some embodiments of the present disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the above embodiments and still achieve the desired results. 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.

[0208] Example 2

[0209] See also Figure 5 Embodiment 2 of the present invention further provides a power transmission system vulnerable link analysis device taking into account the attack success rate, adopting a power transmission system vulnerable link analysis method taking into account the attack success rate of the above embodiment 1, comprising:

[0210] The basic information data conversion module 001 is used to construct a power system logic diagram according to the actual wiring diagram of the power system; set up corresponding variables according to the attack principle and impact mechanism of the cyber-physical coordinated attack; and represent the coordinated attack scheme and the impact on the power system through the corresponding variables;

[0211] A correlation analysis model construction module 002 is used to construct a correlation analysis model, and to perform correlation analysis on attack target selection, attack success or failure scenarios, and the probability of occurrence of attack success or failure scenarios through the correlation analysis model;

[0212] The fault evolution constraint and power flow constraint construction module 003 is used to construct the fault evolution constraint under multiple scenarios in the power system logic diagram according to the attack success or failure scenario; construct the power flow constraint under multiple scenarios in the power system wiring diagram; and calculate the fault loss objective function of the power system in all scenarios;

[0213] The power system vulnerable link list acquisition module 004 is used to convert the double-layer nonlinear optimization problem of power grid vulnerable link analysis into a single-layer mixed integer linear programming and solve it through a linearization strategy; simulate and generate attack success rate distribution scenarios through a Monte Carlo model; obtain the vulnerable links of the power system under the current sampling batch by solving the Monte Carlo model; and obtain the power system vulnerable link list by performing batch sampling calculations.

[0214] In this embodiment, in the basic information data conversion module 001, the cyber-physical coordinated attack includes a physical attack targeting a power transmission line and a denial-of-operation network attack targeting a relay protection device;

[0215] The construction principle of the power system logic diagram is:

[0216] The power system is divided into several regions according to the circuit breakers; the vertices in the logic graph are obtained according to the one-to-one correspondence between the regions and the vertices; the edges in the logic graph are obtained according to the one-to-one correspondence between the circuit breakers and the edges of the regions;

[0217] The fault state of the region represents the state of all components inside the region; the on-off state of the edge in the logic graph represents the switch state of the corresponding circuit breaker.

[0218] In this embodiment, in the correlation analysis model construction module 002, the correlation analysis model is constructed by formulas (1)-(5):

[0219]

[0220]

[0221]

[0222] In the formula, Indicates whether the actual area corresponding to vertex i in the logical graph has been physically attacked, 0 means no attack, 1 means attack; E is the set of edges in the logical graph; V is the set of vertices in the logical graph; λ ij is the weight constant corresponding to edge ij; A p A is the number of physical attack resources; cr The number of network attack resources to be denied; Indicates whether the network attack numbered d occurs on the relay protection device corresponding to edge ij, 0 means no attack, 1 means attack; Indicates whether the network attack numbered d+1 occurs on the relay protection device corresponding to edge ij, 0 means no attack, 1 means attack;

[0223]

[0224]

[0225] In the formula, Indicates whether the relay protection device configured on the circuit breaker corresponding to edge ij in scenario s is affected by the denial-of-operation network attack, 1 for yes and 0 for no;

[0226] Indicates whether the dth denial-of-service network attack in scenario s is successful, 1 for yes and 0 for no;

[0227] P(s) is the occurrence probability of scene s; ρ ij is the success rate of network attacks on the relay protection device corresponding to edge ij.

[0228] In this embodiment, in the fault evolution constraint and power flow constraint construction module 003, the fault evolution process of multiple scenarios is constructed in the power system logic diagram through formulas (6)-(12):

[0229]

[0230]

[0231]

[0232]

[0233]

[0234]

[0235]

[0236] In the formula, Ω S For scene collection;

[0237] Indicates the on-off status of edge ij in scene s, 1 for on and 0 for off;

[0238] Indicates whether the area corresponding to the vertex numbered i in scene s is affected by the fault, 1 for yes and 0 for no;

[0239] Indicates whether the area corresponding to the vertex numbered j in scene s is affected by the fault, 1 for yes and 0 for no;

[0240] M is a positive number; is the commodity flow flowing on edge ij in scenario s; is the commodity flow flowing on edge ji in scene s; is the commodity flow flowing on edge ik in scene s;

[0241] Through formulas (13)-(15), the fault evolution process in the power system logic diagram is mapped to the power system wiring diagram:

[0242]

[0243]

[0244]

[0245] In the formula, c m,s Indicates the fault status of node m in scenario s, 1 means the node is affected by the short circuit fault, and 0 means the node is not affected; is the actual power system node set corresponding to vertex i in the logical graph; Indicates the switch status of the circuit breaker mn on the left side of the line in scenario s, 1 means the circuit breaker is closed, and 0 means the circuit breaker is open; Ω T is a set of transmission lines indexed by (m,n); is the set of edges corresponding to the circuit breaker at the left end of the transmission line mn; is the switch state of the circuit breaker mn on the right side of the line in scenario s, 1 means the circuit breaker is closed, and 0 means the circuit breaker is open; is the set of edges corresponding to the circuit breaker at the right end of the transmission line mn;

[0246] Through formulas (16)-(22), the generation redispatch process is constructed in the power system wiring diagram according to the fault situation:

[0247]

[0248]

[0249]

[0250]

[0251]

[0252]

[0253]

[0254] The objective function for calculating the fault loss of the power system in all scenarios is:

[0255]

[0256] In the formula, Ω N represents a node set indexed by m; Ω T represents the set of transmission lines indexed by (m,n); Ω G represents a collection of generators; represents the set of generators on node m; Ω D represents the load set indexed by l; represents the load set on node m; represents the set of transmission lines indexed by (m,n) with the left end node being m; represents the set of transmission lines indexed by (m,n) with n as the right end node; represents the active output of generator g in scenario s; P l L represents the active load demand of load l; represents the active load reduction of load l in scenario s; represents the active power flow on branch mn in scenario s; represents the active power flow on branch hm in scenario s; represents the maximum active power transmitted by the transmission line mn; x mn represents the reactance of the transmission line mn; θ m represents the voltage phase angle of node m; θ n represents the voltage phase angle of node n; Indicates the maximum active output of generator g; represents the active output of the generator g beforehand; Indicates the ramp rate of active output of generator g.

[0257] In this embodiment, in the power system vulnerable link list acquisition module 004, the linearization strategy is to transform the nonlinear two-layer problem into a single-layer mixed integer programming problem through the probability generation constraint piecewise linearization strategy of the second type of special order set and the equivalent transformation strategy of the optimization problem according to variable transformation.

[0258] It should be noted that the information interaction, execution process and other contents between the modules of the above-mentioned device are based on the same concept as the method embodiment in Example 1 of the present application, and the technical effects they bring are the same as those of the method embodiment of the present application. For specific contents, please refer to the description in the method embodiment shown in the previous part of the present application, and will not be repeated here.

[0259] Example 3

[0260] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium, in which a program code for a method for analyzing vulnerable links in a power transmission system taking into account the attack success rate is stored. The program code includes instructions for executing embodiment 1 or any possible implementation method of a method for analyzing vulnerable links in a power transmission system taking into account the attack success rate.

[0261] The computer-readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that includes one or more available media. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0262] Example 4

[0263] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0264] The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute a method for analyzing vulnerable links in a power transmission system that takes into account attack success rate, which is embodiment 1 or any possible implementation thereof.

[0265] Specifically, the processor can be implemented by hardware or by software. When implemented by hardware, the processor can be a logic circuit, an integrated circuit, etc.; when implemented by software, the processor can be a general-purpose processor implemented by reading software codes stored in a memory. The memory can be integrated in the processor or can be located outside the processor and exist independently.

[0266] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions can be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center.

[0267] Obviously, those skilled in the art should understand that the above modules or steps of the present invention can be implemented by a general computing device, they can be concentrated on a single computing device, or distributed on a network composed of multiple computing devices, and optionally, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, and in some cases, the steps shown or described can be executed in a different order than here, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. Thus, the present invention is not limited to any specific combination of hardware and software.

[0268] Although the present invention has been described in detail above by general description and specific embodiments, it is obvious to those skilled in the art that some modifications or improvements can be made to the present invention. Therefore, these modifications or improvements made without departing from the spirit of the present invention all belong to the scope of protection claimed by the present invention.

Claims

1. A method for analyzing vulnerable links in a power transmission system considering attack success rate, characterized in that: include: Construct the power system logic diagram based on the actual wiring diagram of the power system; set up corresponding variables based on the attack principle and impact mechanism of cyber-physical coordinated attack; The coordinated attack scheme and the impact on the power system are represented by the corresponding variables; Constructing a correlation analysis model, and performing correlation analysis on attack target selection, attack success and failure scenarios, and the probability of occurrence of attack success and failure scenarios through the correlation analysis model; According to the attack success or failure scenarios, constructing fault evolution constraints under multiple scenarios in the power system logic diagram; In the power system wiring diagram, build power flow constraints for multiple scenarios; Calculate the objective function of power system failure losses in all scenarios; The two-layer nonlinear optimization problem of the power grid vulnerable link analysis is converted into a single-layer mixed integer linear programming and solved through a linearization strategy; the attack success rate distribution scenario is simulated and generated through a Monte Carlo model; the vulnerable links of the power system under the current sampling batch are obtained by solving the Monte Carlo model; and a list of vulnerable links of the power system is obtained by performing batch sampling calculations; The cyber-physical coordinated attacks include physical attacks targeting transmission lines and denial-of-operation cyber attacks targeting relay protection devices; The construction principle of the power system logic diagram is: The power system is divided into several regions according to the circuit breakers; the vertices in the logic graph are obtained according to the one-to-one correspondence between the regions and the vertices; the edges in the logic graph are obtained according to the one-to-one correspondence between the circuit breakers and the edges of the regions; The fault state of the region represents the state of all components within the region; the on-off state of the edge in the logic diagram represents the switch state of the corresponding circuit breaker; The correlation analysis model is constructed by formulas (1)-(5): In the formula, Indicates whether the actual area corresponding to vertex i in the logical graph has been physically attacked, 0 means no attack, 1 means attack; E is the set of edges in the logical graph; V is the set of vertices in the logical graph; λ ij is the weight constant corresponding to edge ij; A p A is the number of physical attack resources; cr The number of network attack resources to be denied; Indicates whether the network attack numbered d occurs on the relay protection device corresponding to edge ij, 0 means no attack, 1 means attack; Indicates whether the network attack numbered d+1 occurs on the relay protection device corresponding to edge ij, 0 means no attack, 1 means attack; In the formula, Indicates whether the relay protection device configured on the circuit breaker corresponding to edge ij in scenario s is affected by the denial-of-operation network attack, 1 for yes and 0 for no; Indicates whether the dth denial-of-service network attack in scenario s is successful, 1 for yes and 0 for no; P(s) is the occurrence probability of scene s; ρ ij is the success rate of network attacks on the relay protection device corresponding to edge ij; Through formulas (6)-(12), the fault evolution process of multiple scenarios is constructed in the power system logic diagram: In the formula, Ω S For scene collection; Indicates the on-off status of edge ij in scene s, 1 for on and 0 for off; Indicates whether the area corresponding to the vertex numbered i in scene s is affected by the fault, 1 for yes and 0 for no; Indicates whether the area corresponding to the vertex numbered j in scene s is affected by the fault, 1 for yes and 0 for no; M is a positive number; is the commodity flow flowing on edge ij in scenario s; is the commodity flow flowing on edge ji in scene s; is the commodity flow flowing on edge ik in scene s; Through formulas (13)-(15), the fault evolution process in the power system logic diagram is mapped to the power system wiring diagram: In the formula, c m,s Indicates the fault status of node m in scenario s, 1 means the node is affected by the short circuit fault, and 0 means the node is not affected; is the actual power system node set corresponding to vertex i in the logical graph; Indicates the switch status of the circuit breaker mn on the left side of the line in scenario s, 1 means the circuit breaker is closed, and 0 means the circuit breaker is open; Ω T is a set of transmission lines indexed by (m,n); is the set of edges corresponding to the circuit breaker at the left end of the transmission line mn; is the switch state of the circuit breaker mn on the right side of the line in scenario s, 1 means the circuit breaker is closed, and 0 means the circuit breaker is open; is the set of edges corresponding to the circuit breaker at the right end of the transmission line mn; Through formulas (16)-(22), the generation redispatch process is constructed in the power system wiring diagram according to the fault situation: The objective function for calculating the fault loss of the power system in all scenarios is: In the formula, Ω N represents a node set indexed by m; Ω T represents the set of transmission lines indexed by (m,n); Ω G represents a collection of generators; represents the set of generators on node m; Ω D represents the load set indexed by l; represents the load set on node m; represents the set of transmission lines indexed by (m,n) with the left end node being m; represents the set of transmission lines indexed by (m,n) with n as the right end node; represents the active output of generator g in scenario s; P l L represents the active load demand of load l; represents the active load reduction of load l in scenario s; represents the active power flow on branch mn in scenario s; represents the active power flow on branch hm in scenario s; represents the maximum active power transmitted by the transmission line mn; x mn represents the reactance of the transmission line mn; θ m represents the voltage phase angle of node m; θ n represents the voltage phase angle of node n; Indicates the maximum active output of generator g; represents the active output of the generator g beforehand; Indicates the ramp rate of active output of generator g.

2. A method for analyzing vulnerable links in a power transmission system considering attack success rate according to claim 1, characterized in that: The linearization strategy converts the nonlinear double-layer problem into a single-layer mixed integer programming problem through a probability generation constraint piecewise linearization strategy of the second type of special order sets and an equivalent transformation strategy of the optimization problem according to variable transformation.

3. A power transmission system vulnerable link analysis device considering attack success rate, adopting any one of claims 1 to 2 power transmission system vulnerable link analysis method considering attack success rate, characterized in that: include: The basic information data conversion module is used to construct a power system logic diagram based on the actual wiring diagram of the power system; set up corresponding variables according to the attack principle and impact mechanism of the cyber-physical coordinated attack; and represent the coordinated attack scheme and the impact on the power system through the corresponding variables; A correlation analysis model building module, used to build a correlation analysis model, through which the correlation analysis model is used to perform correlation analysis on attack target selection, attack success or failure scenarios, and the probability of occurrence of attack success or failure scenarios; A fault evolution constraint and power flow constraint construction module, used to construct fault evolution constraints under multiple scenarios in the power system logic diagram according to the attack success or failure scenarios; In the power system wiring diagram, build power flow constraints for multiple scenarios; Calculate the objective function of power system failure losses in all scenarios; The module for obtaining the list of vulnerable links in the power system is used to convert the double-layer nonlinear optimization problem of the vulnerable link analysis of the power grid into a single-layer mixed integer linear programming and solve it through a linearization strategy; simulate and generate the attack success rate distribution scenario through a Monte Carlo model; obtain the vulnerable links of the power system under the current sampling batch by solving the Monte Carlo model; obtain the list of vulnerable links in the power system by performing batch sampling calculations; In the basic information data conversion module, the cyber-physical coordinated attack includes a physical attack targeting a power transmission line and a denial-of-operation network attack targeting a relay protection device; The construction principle of the power system logic diagram is: The power system is divided into several regions according to the circuit breakers; the vertices in the logic graph are obtained according to the one-to-one correspondence between the regions and the vertices; the edges in the logic graph are obtained according to the one-to-one correspondence between the circuit breakers and the edges of the regions; The fault state of the region represents the state of all components within the region; the on-off state of the edge in the logic diagram represents the switch state of the corresponding circuit breaker; In the correlation analysis model construction module, the correlation analysis model is constructed by formulas (1)-(5): In the formula, Indicates whether the actual area corresponding to vertex i in the logical graph has been physically attacked, 0 means no attack, 1 means attack; E is the set of edges in the logical graph; V is the set of vertices in the logical graph; λ ij is the weight constant corresponding to edge ij; A p A is the number of physical attack resources; cr The number of network attack resources to be denied; Indicates whether the network attack numbered d occurs on the relay protection device corresponding to edge ij, 0 means no attack, 1 means attack; Indicates whether the network attack numbered d+1 occurs on the relay protection device corresponding to edge ij, 0 means no attack, 1 means attack; In the formula, Indicates whether the relay protection device configured on the circuit breaker corresponding to edge ij in scenario s is affected by the denial-of-operation network attack, 1 for yes and 0 for no; Indicates whether the dth denial-of-service network attack in scenario s is successful, 1 for yes and 0 for no; P(s) is the occurrence probability of scene s; ρ ij is the success rate of network attacks on the relay protection device corresponding to edge ij; In the fault evolution constraint and power flow constraint construction module, the fault evolution process of multiple scenarios is constructed in the power system logic diagram through formulas (6)-(12): In the formula, Ω S For scene collection; Indicates the on-off status of edge ij in scene s, 1 for on and 0 for off; Indicates whether the area corresponding to the vertex numbered i in scene s is affected by the fault, 1 for yes and 0 for no; Indicates whether the area corresponding to the vertex numbered j in scene s is affected by the fault, 1 for yes and 0 for no; M is a positive number; is the commodity flow flowing on edge ij in scenario s; is the commodity flow flowing on edge ji in scene s; is the commodity flow flowing on edge ik in scene s; Through formulas (13)-(15), the fault evolution process in the power system logic diagram is mapped to the power system wiring diagram: In the formula, c m,s Indicates the fault status of node m in scenario s, 1 means the node is affected by the short circuit fault, and 0 means the node is not affected; is the actual power system node set corresponding to vertex i in the logical graph; Indicates the switch status of the circuit breaker mn on the left side of the line in scenario s, 1 means the circuit breaker is closed, and 0 means the circuit breaker is open; Ω T is a set of transmission lines indexed by (m,n); is the set of edges corresponding to the circuit breaker at the left end of the transmission line mn; is the switch state of the circuit breaker mn on the right side of the line in scenario s, 1 means the circuit breaker is closed, and 0 means the circuit breaker is open; is the set of edges corresponding to the circuit breaker at the right end of the transmission line mn; Through formulas (16)-(22), the generation redispatch process is constructed in the power system wiring diagram according to the fault situation: The objective function for calculating the fault loss of the power system in all scenarios is: In the formula, Ω N represents a node set indexed by m; Ω T represents the set of transmission lines indexed by (m,n); Ω G represents a collection of generators; represents the set of generators on node m; Ω D represents the load set indexed by l; represents the load set on node m; represents the set of transmission lines indexed by (m,n) with the left end node being m; represents the set of transmission lines indexed by (m,n) with n as the right end node; represents the active output of generator g in scenario s; P l L represents the active load demand of load l; represents the active load reduction of load l in scenario s; represents the active power flow on branch mn in scenario s; represents the active power flow on branch hm in scenario s; represents the maximum active power transmitted by the transmission line mn; x mn represents the reactance of the transmission line mn; θ m represents the voltage phase angle of node m; θ n represents the voltage phase angle of node n; Indicates the maximum active output of generator g; represents the active output of the generator g beforehand; Indicates the ramp rate of active output of generator g.

4. The device for analyzing vulnerable links of a power transmission system taking into account attack success rate according to claim 3, characterized in that: In the power system vulnerable link list acquisition module, the linearization strategy is to transform the nonlinear double-layer problem into a single-layer mixed integer programming problem through the probability generation constraint piecewise linearization strategy of the second type special order set and the equivalent transformation strategy of the optimization problem according to variable transformation.

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