Identification Method for Vulnerable Lines and Vulnerable Load Nodes in Gas-Electricity Interconnected Systems

Abstract

A method for identifying vulnerable lines and vulnerable load nodes for a gas-electricity interconnected system. According to the scheduling target requirements of the gas-electricity integrated energy system, a scheduling objective function that minimizes the sum of the power generation costs of traditional units, the cost of purchasing natural gas, and the load shedding cost is established; according to the attacker's intention, a multi-objective function that minimizes the network attack cost and maximizes the scheduling cost is established; according to the attacker's physical damage attacks on transmission lines and gas pipelines, a physical damage attack behavior model is established; according to the attack behavior constraints and operation constraints, a two-layer multi-objective programming model is established; the two-layer programming model is solved by a multi-objective particle swarm algorithm to calculate the optimal cyber-physical collaborative attack strategy; according to the optimal attack strategy, the transmission lines and gas pipelines that are vulnerable to physical attacks and the load nodes that are vulnerable to load redistribution network attacks are identified. This method can effectively ensure the safe and stable operation of the gas-electricity integrated energy system.

Description

Technical Field

[0001] The invention belongs to the technical field of cyber-physical security of integrated energy systems, and particularly relates to a method for identifying vulnerable lines and vulnerable load nodes for a gas-electricity interconnected system. Background Art

[0002] In the 21st century with an explosive growth in technology level, the security protection level of power systems has been greatly improved, and the harm that general non-human activities can cause to power systems is minimal. At the same time, the major power outage accident in Ukraine in 2015 sounded the alarm. The major power outage accident in Ukraine shows that compared with pure physical attacks or cyber attacks, deliberately coordinated cyber-physical attacks by humans have greater destructive power to power systems, deeper damage levels, and longer damage times. Since then, theoretical research on deliberately coordinated cyber-physical attacks has received extensive attention from domestic and foreign researchers.

[0003] In the context of the deep cyber-physical integration of gas-electricity interconnected integrated energy systems, whether it is a cyber attack on the information network or a physical attack on the natural gas network and power grid, it will pose a security threat to the safe and stable operation of the integrated energy system. At the same time, research on cyber-physical coordinated attacks on deeply integrated gas-electricity interconnected integrated energy systems is relatively scarce. Based on the perspective of attackers and combined with the actual situation, the multi-objective two-layer programming model established by the invention, on the one hand, considers the state of mutual restraint and mutual semi-transparency between attackers and dispatchers, and better simulates the real attack and defense scenarios. On the other hand, the multi-objective optimal frontier curve is used to identify the vulnerable lines and vulnerable load nodes of the integrated energy system. Through the attack strategy research method of the invention, it helps to more intuitively discover the loss level of the integrated energy system caused by attacks, can more timely identify the weak lines and load nodes in the integrated energy system, and lay a good foundation for better formulating corresponding defense strategies. Summary of the Invention

[0004] The technical problem to be solved by the invention is to overcome the deficiencies of the prior art and provide a method for identifying vulnerable lines and vulnerable load nodes for a gas-electricity interconnected system, construct a multi-objective two-layer programming model, and analyze the vulnerable lines and vulnerable load nodes of the gas-electricity interconnected integrated energy system to ensure the safe and stable operation of the gas-electricity interconnected integrated energy system.

[0005] The invention provides a method for identifying vulnerable lines and vulnerable load nodes for a gas-electricity interconnected system, including the following steps,

[0006] Step S1. According to the scheduling target requirements of the gas-electricity interconnected integrated energy system, establish a scheduling objective function that minimizes the sum of the power generation costs of traditional units, the cost of purchasing natural gas, and the load shedding cost;

[0007] Step S2. According to the attacker's intention, establish a multi-objective function with the minimum network attack cost and the maximum dispatching cost of the gas-electricity integrated energy system from the attacker's perspective;

[0008] Step S3. According to the attacker's physical damage attacks on the power transmission lines and gas pipelines of the gas-electricity integrated energy system, establish a physical damage attack behavior model;

[0009] Step S4. According to the attacker's attack behavior constraints and the operation constraints of the gas-electricity integrated energy system, establish a two-layer multi-objective programming model from the attacker's perspective;

[0010] Step S5. Solve the two-layer programming model through the multi-objective particle swarm algorithm to calculate the optimal cyber-physical collaborative attack strategy from the attacker's perspective;

[0011] Step S6. According to the attacker's optimal attack strategy, identify the power transmission lines and gas pipelines vulnerable to physical attacks and the load nodes vulnerable to load redistribution network attacks

[0012] As a further technical solution of the present invention, in Step S1, the dispatching objective function with the minimum sum of the traditional unit power generation cost, the natural gas purchase cost, and the load shedding cost is

[0013] f = min(C C + C W + C shed ),

[0014]

[0015]

[0016]

[0017] where C C is the power generation cost of the traditional power plant, C W is the natural gas purchase cost, C shed is the load shedding cost; P C，k is the active power output of the kth traditional unit; M w，w is the gas supply of the wth natural gas source; P shed，p , M shed，g are the load shedding amounts at the pth load node in the power grid and the gth load node in the gas network respectively; N C , N gw are the numbers of traditional units and natural gas sources respectively; N P , N G are the total numbers of nodes in the power grid and the gas network respectively; b 2，k , b 1k , b 0，kThey are the cost coefficients of the k-th traditional unit respectively; c 1，w and c 0，w are the cost coefficients of the w-th natural gas source respectively; d p is the cost coefficient for shedding the p-th electrical load; h g is the cost coefficient for shedding the g-th gas load.

[0018] Furthermore, in step S2, according to the attacker's intention, the specific method for establishing the multi-objective function with the minimum network attack cost and the maximum scheduling cost of the gas-electric interconnected integrated energy system from the attacker's perspective is as follows.

[0019] Step S21. The objective function for minimizing the attack cost from the attacker's perspective is expressed as

[0020]

[0021] where a P1,p and a P2，p are the coefficients of the attack cost for the electrical load respectively; a G1,g and a G2，g are the attack cost coefficients for the gas load respectively; ΔP LR，p is the false data of the electrical load injected at the power grid node p; P load，p is the load of the power grid node p; ΔM LR，g is the false data of the gas load injected at the gas network node g; M load，g is the load of the gas network node g;

[0022] Step S22. The objective function for maximizing the scheduling cost of the gas-electric interconnected integrated energy system from the attacker's perspective is expressed as F2 = max(C C + C W + C shed ).

[0023] Furthermore, in step S3, if a transmission line is attacked, the circuit breaker switch will immediately open, which is manifested as the admittance value of the line becoming zero; if a natural gas pipeline is attacked, the natural gas pipeline valve will immediately close, which is manifested as the gas transmission efficiency of the pipeline being zero. Then the models of the physical attacks on the transmission line and the natural gas pipeline are

[0024] Y e =(1 - α e )y e , e ∈ {0, 1, 2,..., E}

[0025] K l =(1 - β l )k l , l ∈ {0, 1, 2,..., L};

[0026] where E and L are the number of transmission lines and the number of pipelines in the natural gas network respectively; e and l are the numbers of the transmission lines and the pipelines in the natural gas network respectively; α e and β l are 0-1 logical vectors of physical attacks, 0 means no attack, and 1 means attack; y e is the admittance of the e-th transmission line; Y e is the actual admittance of the e-th transmission line; k l is the gas transmission performance coefficient of the l-th natural gas pipeline, and K l is the actual gas transmission performance coefficient of the l-th natural gas pipeline.

[0027] Furthermore, the bi-level multi-objective programming model established in step S4 is

[0028]

[0029] where and are two objective functions of the attacker, G(x, y) ≤ 0 is the constraint of the attacker, x is the decision variable of the attacker, is the scheduling objective function of the gas-electricity integrated energy system, g(x, y) ≤ 0 is the operation constraint of the gas-electricity integrated energy system, and y is the decision variable of the system dispatcher.

[0030] Furthermore, in step S5, the specific solution process is as follows.

[0031] Step S51. Use the particle x k to represent the physical attack vector and the load redistribution attack vector in the upper-level planning model, initialize the particle population X = [x1, x2,..., x n and the particle velocity vector V = [v1, v2,..., v n , and form the external archive set T0 with the population X;

[0032] Step S52. Use the particle x k to update the network topology parameter matrix and the load parameters in the lower-level planning model;

[0033] Step S53. The solver solves the lower-level planning model to obtain the scheduling strategy y k ;

[0034] Step S54. According to the upper-level particle x k and its corresponding lower-level scheduling strategy y k , calculate the fitness value and the degree of constraint violation z k ;

[0035] Step S55. The particle position vectors that satisfy the constraints form the elite solution set T1, the particle position vectors with a constraint violation degree less than the threshold ε form the alternative archive set T2, and the remaining particle position vectors form the inferior solution set T3;

[0036] Step S56. Select the particle position with the optimal fitness value in T1 as the global particle, select the distance to the particle position closest to the particle in T2 in T1 as the individual optimal particle of this particle, and select the distance to the particle position closest to the particle in T3 in T0 as the individual optimal particle of this particle;

[0037] Step S57. According to the multi-objective dominance relationship, compare the dominance relationships of all particles in T1, and retain the dominant particles to form the multi-objective front;

[0038] Step S58. If the number of iterations has not reached the maximum number, update the particle position X and velocity V, increment the number of iterations by 1, and go to Step S52; if the number of iterations has reached the maximum number, output the attacker's strategy x opt , and end the optimization.

[0039] Furthermore, in Step S6, the specific identification process is as follows

[0040] Step S61. If the optimal physical attack target of the attacker calculated according to Step S5 is the e-th transmission line and the l-th natural gas pipeline, then the e-th transmission line and the l-th natural gas pipeline are the vulnerable lines;

[0041] Step S62. If the optimal load reallocation attack strategy of the attacker calculated according to Step S5: <ΔP LR，p , p = {1, 2,..., N P}) and <ΔM LR，g , g = {1, 2,..., N G}>, then if the amplitude of the false load data injected into the p-th electrical load node exceeds the set threshold ε of the actual electrical load data P , that is then it is determined that the p-th electrical load node is a vulnerable load node; if the amplitude of the false load data injected into the g-th natural gas load node exceeds the set threshold ε of the actual natural gas load data G , that is then it is determined that the g-th natural gas load node is a vulnerable node.

[0042] The advantages of the present invention are as follows. On the one hand, the present invention establishes a multi-objective two-layer programming model to find the contradictory relationship between the attack cost and the system loss; on the other hand, the vulnerable lines and vulnerable load nodes of the integrated energy system are identified through the multi-objective optimal values.

[0043] The present invention is mainly completed by means of data modeling and data analysis. The method has a clear logical process and strong repeatability, and has certain reference significance. Users can also adjust the model details and specific operations in the method according to their actual application needs, and then apply the method of the present invention to various different integrated energy system optimization models. The overall application prospect of the method is broad and has good use value. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic flow chart of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0045] Please refer to Figure 1 , this embodiment provides a method for identifying vulnerable lines and vulnerable load nodes in a gas-electricity interconnected integrated energy system considering cyber-physical collaborative attacks. The method includes the following steps:

[0046] S1. According to the scheduling target requirements of the gas-electricity interconnected integrated energy system, establish a scheduling target function that minimizes the sum of the power generation costs of traditional units, the cost of purchasing natural gas, and the load shedding cost, expressed as:

[0047] f = min(C c + C W + C shed ) (1)

[0048] Wherein,

[0049] Wherein, C C represents the power generation cost of the traditional power plant, C W represents the cost of purchasing natural gas, C shed represents the load shedding cost; P C，k represents the active power output of the kth traditional unit; M w，w represents the gas supply volume of the wth natural gas source; P shed，p , M shed，g respectively represent the load shedding amounts at the pth load node in the power grid and the gth load node in the gas network; N C , N gw respectively represent the numbers of traditional units and natural gas sources; N P , N G respectively represent the total number of nodes in the power grid and the total number of nodes in the gas network; b 2，k , b 1k , b 0，k respectively represent the cost coefficients of the kth traditional unit; c 1，w , c 0，w respectively represent the cost coefficients of the wth natural gas source; d pDenote the cost coefficient for shedding the p-th electrical load; h g Denote the cost coefficient for shedding the g-th gas load.

[0050] S2. According to the attacker's intention, establish a multi-objective function that minimizes the cost of network attacks and maximizes the scheduling cost of the gas-electric interconnected integrated energy system from the attacker's perspective.

[0051] S21. The objective function for minimizing the attack cost from the attacker's perspective is expressed as:

[0052]

[0053] where, a p1，p , a p2，p are the coefficients of the attack cost for electrical loads respectively; a G1，g , a G2，g are the attack cost coefficients for gas loads respectively; ΔP LR，p represents the false data of the electrical load injected at the power grid node p; P load，p represents the load of the power grid node p; ΔM LR，g represents the false data of the gas load injected at the gas network node g; M load，g represents the load of the gas network node g.

[0054] S22. The objective function for maximizing the scheduling cost of the gas-electric interconnected integrated energy system from the attacker's perspective is expressed as:

[0055] F2 = max(C C + C W + C shed ) (3)

[0056] S3. Considering that the attacker physically damages the transmission lines and gas pipelines of the gas-electric interconnected integrated energy system, establish a corresponding physical damage attack behavior model. If a certain transmission line is attacked, the circuit breaker switch will immediately disconnect, manifested as the admittance value of the line becoming zero; if a certain natural gas pipeline is attacked, the natural gas pipeline valve will immediately close, manifested as the gas transmission efficiency of the pipeline becoming zero. Accordingly, the models of the transmission lines and natural gas pipelines under physical attacks are expressed as:

[0057] Y e = (1 - α e )y e , e ∈ {01, 2, …, E}

[0058] K l = (1 - β l )k l , l ∈ {0, 1, 2, …, L} (4)

[0059] Among them, E and L respectively represent the number of transmission lines and the number of pipelines in the natural gas network; e and l respectively represent the transmission line number and the pipeline number in the natural gas network; α e and β l represent the 0-1 logical vector of physical attacks (0 means no attack, 1 means attack); y e represents the admittance of the e-th transmission line; Y e represents the actual admittance of the e-th transmission line; k l represents the gas transmission performance coefficient of the l-th natural gas pipeline, K l represents the actual gas transmission performance coefficient of the l-th natural gas pipeline.

[0060] S4. Considering the attack behavior constraints of the attacker and the operation constraints of the gas-electricity integrated energy system, a two-layer multi-objective programming model from the perspective of the attacker is established.

[0061] S41. When the attacker conducts a load redistribution network attack, the network attack behavior constraints include:

[0062]

[0063]

[0064] Among them, Equation (5) means that the sum of all injected false load data is 0; Equation (6) means to constrain the amplitude of the injected false load data; τ p and τ G respectively represent the false attack intensity coefficients of electrical load and gas load.

[0065] S42. When the attacker implements a physical line attack, the physical attack behavior constraints are as follows:

[0066]

[0067] Among them, Equation (7) means that in order for the attacker to conceal his physical attack behavior, the maximum number of damaged transmission lines and natural gas pipelines is 1.

[0068] S43. The operation constraints of the gas-electricity integrated energy system include:

[0069] P E =A B A E θ (8)

[0070] θ ref =0 (9)

[0071] A C P C +A GT P GT =A load(P load +ΔP LR -P shed )+A PtG P PtG +A′ E P E (10)

[0072]

[0073] M CPi，j =K CPi，j M i，j (s i -s j ) (12)

[0074] B W M W +B PtG M PtG =B load (M load -M shed )+B CP M CP +B GT M GT +B′ L M L (13)

[0075] P GT，n =η GT，n M GT，n (14)

[0076]

[0077]

[0078]

[0079]

[0080] 0≤P shed ≤P load (20)

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] 0≤Mshed ≤M load (26)

[0087] Among them, Equation (8) represents the active power flow equation of the line, P E represents the active power vector of each line, θ is the node phase angle vector, and A E represents the node-branch incidence matrix; Equation (9) represents that the phase angle of the power grid balancing node is 0; Equation (10) represents the power grid node power balance equation, A C 、A GT 、A load 、A PtG 、A′ E respectively represent the node-conventional unit incidence matrix, node-gas turbine unit incidence matrix, node-load incidence matrix, node-PtG device incidence matrix, and node-branch incidence matrix when the transmission line is physically attacked. P C 、P GT 、P load 、P shed 、P PtG are respectively the active power vector of the conventional unit, the active power vector of the gas turbine unit, the active power load vector, the cut load vector, and the active power consumption vector of the PtG device; Equation (11) represents the Weymouth equation without a compressor, M l represents the flow rate on the l-th gas pipeline, and K l represents the actual gas transmission performance coefficient of the l-th natural gas pipeline, and s i 、s j respectively represent the gas pressure values at the starting node i and the ending node j of the l-th natural gas pipeline; Equation (12) represents the pipeline flow equation with a compressor, M CPi，j represents the gas consumption of the compressor working on the pipeline (i→j), and K CPi，j is the energy consumption coefficient of the compressor; Equation (13) represents the node flow balance equation of the gas network pipeline, B w 、B PtG 、B load 、B CP 、B GT 、B′ L respectively represent the incidence matrix between the gas network node and the gas source, the incidence matrix between the nodes of the PtG device, the incidence matrix between the node and the gas load, the incidence matrix between the node and the compressor, the incidence matrix between the node and the gas turbine unit, and the node-branch incidence matrix of the gas network after the gas pipeline is attacked; M w represents the gas production vector of each gas source; M PtG represents the gas production vector of the PtG device; M load is the gas load vector, and M shed represents the cut gas load vector, M CPDenote the compressor gas consumption vector as \(M\). GT Denote the gas turbine unit gas consumption vector as \(M\). L is the vector composed of all pipeline flows; Equation (14) represents the relationship equation between the power generation and gas consumption of the gas turbine unit, \(\eta\). GT，n Denote the power generation efficiency coefficient of the \(n\)th gas turbine unit as \(\eta\); Equation (15) represents the relationship equation between the gas production and power consumption of the PtG device, \(\eta\). PtG,m Denote the comprehensive efficiency of the \(m\)th PtG device in the process of power - to - hydrogen and hydrogen - to - methane conversion; \(H\) is the calorific value of natural gas; Equations (16) - (26) are the capacity limits of each device respectively; the superscripts min and max represent the minimum and maximum values of the corresponding variables respectively.

[0088] S44. Combine Equations (1) to (26) to establish a two - layer multi - objective programming model from the attacker's perspective. The structural form of this model is expressed as:

[0089]

[0090] where, min x \(F_1(x,y)\) and max x \(F_2(x,y)\) represent two objective functions of the attacker, \(G(x,y)\leq0\) represents the constraints of the attacker, \(x\) represents the decision variables of the attacker, min y \(f(x,y)\) represents the scheduling objective function of the gas - electricity interconnected integrated energy system, \(g(x,y)\leq0\) represents the operation constraints of the gas - electricity interconnected integrated energy system, and \(y\) represents the decision variables of the system scheduler.

[0091] S5. Use the two - layer programming model solved by the multi - objective particle swarm algorithm to calculate the optimal cyber - physical collaborative attack strategy from the attacker's perspective. The solution process includes:

[0092] S51. Use the particle \(x\). k to represent the physical attack vector and load re - distribution attack vector in the upper - layer programming model. Initialize the particle population \(X = [x_1,x_2,\cdots,x\). n and the particle velocity vector \(V = [v_1,v_2,\cdots,v\). n , and form the external archive set \(T_0\) with the population \(X\).

[0093] S52. Use the particle \(x\). k to update the network topology parameter matrix and load parameters in the lower - layer programming model.

[0094] S53. The solver solves the lower - layer programming model to obtain the scheduling strategy \(y\) of the integrated energy system. k ;

[0095] S54. According to the upper - layer particle \(x\). k and its corresponding lower - layer scheduling strategy \(y\).k , calculate the fitness value of the upper-level plan and the degree of constraint violation z k :

[0096] S55. Construct the elite solution set T1 with the particle position vectors that satisfy the constraints, construct the alternative archive set T2 with the particle position vectors whose degree of constraint violation is less than the threshold ε, and the remaining particle position vectors form the inferior solution set T3;

[0097] S56. Select the particle position with the optimal fitness value in T1 as the global particle, select the distance to the particle position closest to the particle in T2 in T1 as the individual optimal particle of this particle, and select the distance to the particle position closest to the particle in T3 in T0 as the individual optimal particle of this particle;

[0098] S57. According to the multi-objective domination relationship, compare the domination relationships of all particles in T1, and retain the dominating particles to form the multi-objective front;

[0099] S58. If the number of iterations has not reached the maximum number, update the particle position X and velocity V, increment the number of iterations by 1, and go to step S52;

[0100] S59. If the number of iterations has reached the maximum number, output the attacker's strategy x opt , and end the optimization program.

[0101] S6. According to the attacker's optimal attack strategy, identify the power transmission lines and gas pipelines that are vulnerable to physical attacks (i.e., vulnerable lines), and identify the load nodes that are vulnerable to load redistribution network attacks (i.e., vulnerable nodes). The identification process includes:

[0102] S61. If the optimal physical attack targets of the attacker calculated according to step S5 are the e-th power transmission line and the l-th natural gas pipeline, then the e-th power transmission line and the l-th natural gas pipeline are the vulnerable lines;

[0103] S62. If the optimal load redistribution attack strategy of the attacker calculated according to step S5 is: <ΔP LR，p , p = {1, 2,..., N p}> and <ΔM LR，g , g = {1, 2,..., N G}>, then: If the amplitude of the false load data injected into the p-th electrical load node exceeds the set threshold ε of the actual electrical load data P , that is then determine that the p-th electrical load node is a vulnerable load node; Similarly, if the amplitude of the false load data injected into the g-th natural gas load node exceeds the set threshold ε of the actual natural gas load data G , that is Then it is determined that the g-th natural gas load node is a vulnerable node.

[0104] In summary, for a method for identifying vulnerable lines and vulnerable load nodes in a gas-electricity interconnected system according to the present invention, on the one hand, it considers the state of mutual restraint and mutual semi-transparency between attackers and dispatchers, and better simulates the real attack and defense scenarios. On the other hand, a multi-objective optimal frontier curve is used to identify the vulnerable lines and vulnerable load nodes in the integrated energy system. Through the attack strategy research method of the present invention, it is helpful to more intuitively discover the loss level of the integrated energy system caused by attacks, and can more timely identify the weak lines and load nodes in the integrated energy system, laying a good foundation for better formulating corresponding defense strategies, which is of great significance for ensuring the overall safe and stable operation of the integrated energy system.

[0105] At the same time, the method flow of the present invention is mainly completed by means of data modeling and data analysis. The method logic flow is clear and highly repeatable, and has certain reference significance. Users can also adjust the model details and specific operations in the method according to their actual application needs, and then apply the method of the present invention to various different network attack detection methods. The overall application prospect of the method is broad and has good use value.

[0106] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and can be implemented in other specific forms without departing from the spirit and basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, it is intended to include all changes falling within the meaning and scope of the equivalent elements of the claims in the present invention. The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above specific embodiments, and the above specific embodiments and the description in the specification are only for further explaining the principle of the present invention. Without departing from the spirit scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the claims and their equivalents.

Claims

1. A method for identifying vulnerable lines and vulnerable load nodes in a gas-electricity interconnected system, characterized in that, It includes the following steps: Step S1. According to the scheduling objective requirements of the gas-electricity interconnected integrated energy system, establish a scheduling objective function that minimizes the sum of the power generation costs of traditional units, the cost of purchasing natural gas, and the load shedding cost. Step S2. According to the attacker's intention, establish a multi-objective function that minimizes the network attack cost and maximizes the scheduling cost of the gas-electricity interconnected integrated energy system from the attacker's perspective. Step S3. According to the attacker's physical damage attacks on the transmission lines and gas pipelines of the gas-electricity interconnected integrated energy system, establish a physical damage attack behavior model. Step S4. According to the attack behavior constraints of the attacker and the operation constraints of the gas-electricity interconnected integrated energy system, establish a two-layer multi-objective programming model from the attacker's perspective. Step S5. Solve the two-layer programming model through a multi-objective particle swarm algorithm to calculate the optimal cyber-physical collaborative attack strategy from the attacker's perspective. Step S6. According to the attacker's optimal attack strategy, identify the transmission lines and gas pipelines that are vulnerable to physical attacks and the load nodes that are vulnerable to load redistribution network attacks. In the above step S1, the scheduling objective function that minimizes the sum of the power generation costs of traditional units, the cost of purchasing natural gas, and the load shedding cost is f = min(C C + C W + C shed ) Among them, C C is the power generation cost of a traditional power plant, C W is the cost of purchasing natural gas, and C shed is the load shedding cost; P C，k is the active power output of the k-th traditional unit; M w，w is the gas supply volume of the w-th natural gas source; P shed，p and M shed，g are the load shedding amounts at the p-th load node in the power grid and the g-th load node in the gas grid respectively; N C and N gw are the numbers of traditional units and natural gas sources respectively; N P and N G are the total number of nodes in the power grid and the total number of nodes in the gas grid respectively; b 2，k and b 1k and b 0，k are the cost coefficients of the k-th traditional unit respectively; c 1，w and c 0，w are the cost coefficients of the w-th natural gas source respectively; d p is the cost coefficient for shedding the p-th electrical load; h g is the cost coefficient for shedding the g-th gas load; In the above step S2, the specific method for establishing a multi-objective function that minimizes the network attack cost and maximizes the scheduling cost of the gas-electricity interconnected integrated energy system from the attacker's perspective is as follows: Step S21. The objective function that minimizes the attack cost from the attacker's perspective is expressed as Among them, a P1，p and a P2，p are the coefficients of the attack cost against the electrical load respectively; a G1，g and a G2，g are the attack cost coefficients against the gas load respectively; ΔP LR，p is the false data of the electrical load injected at the power grid node p; P load，p is the load of the power grid node p; ΔM LR，g is the false data of the gas load injected at the gas network node g; M load，g is the load of the gas network node g; Step S22. The objective function for maximizing the scheduling cost of the gas-electricity interconnected integrated energy system from the attacker's perspective is expressed as F2 = max(C C + C W + C shed ); In the above step S3, if a transmission line is attacked, the circuit breaker switch will immediately open, which is manifested as the admittance value of the line becoming zero; if a natural gas pipeline is attacked, the natural gas pipeline valve will immediately close, which is manifested as the gas transmission efficiency of the pipeline being zero. Then the model of the physical attack on the transmission line and the natural gas pipeline is Y e = (1 - α e )y e , e ∈ {0, 1, 2, …, E} K l = (1 - β l )k l , l ∈ {0, 1, 2, …, L}; where E and L are the number of transmission lines and the number of pipelines in the natural gas network respectively; e and l are the numbers of the transmission lines and the pipelines in the natural gas network respectively; α e and β l are 0-1 logical vectors of physical attacks, 0 means no attack, and 1 means attack; y e is the admittance of the e-th transmission line; Y e is the actual admittance of the e-th transmission line; k l is the gas transmission performance coefficient of the l-th natural gas pipeline, K l is the actual gas transmission performance coefficient of the l-th natural gas pipeline; the bi-level multi-objective programming model established in step S4 is Among them, and are two objective functions of the attacker, G(x, y) ≤ 0 is the constraint of the attacker, x is the decision variable of the attacker, is the scheduling objective function of the gas-electricity integrated energy system, g(x, y) ≤ 0 is the operation constraint of the gas-electricity integrated energy system, and y is the decision variable of the system dispatcher.

2. The method for identifying vulnerable lines and vulnerable load nodes in a gas-electricity interconnected system according to claim 1, characterized in that, In the above step S5, the specific solution process is as follows: Step S51. Use particle x k to represent the physical attack vector and the load redistribution attack vector in the upper-layer planning model, initialize the particle population X = [x1, x2,..., x n and the particle velocity vector V = [v1, v2,..., v n , and form the external archive set T0 with the population X; Step S52. Use particle x k to update the network topology parameter matrix and load parameters in the lower-layer planning model; Step S53. The solver solves the lower-layer planning model to obtain the scheduling strategy y of the integrated energy system k ; Step S54. According to the upper-layer particle x k and its corresponding lower-layer scheduling strategy y k , calculate the fitness value and constraint violation degree z of the upper-layer plan k ; Step S55. The particle position vectors that satisfy the constraints form an elite solution set T1, the particle position vectors with a constraint violation degree less than the threshold ε form an alternative archive set T2, and the remaining particle position vectors form a non-dominated solution set T3. Step S56. Select the particle position with the optimal fitness value in T1 as the global particle, select the distance between the particle position closest to the particles in T2 in T1 as the individual optimal particle of this particle, and select the distance between the particle position closest to the particles in T3 in T0 as the individual optimal particle of this particle. Step S57. According to the multi-objective dominance relationship, compare the dominance relationships of all particles in T1, and retain the dominant particles to form a multi-objective front. Step S58. If the number of iterations has not reached the maximum number, update the particle positions X and velocities V, increment the iteration count by 1, and go to step S52; if the number of iterations has reached the maximum number, output the attacker's strategy x opt , and end the optimization.

3. The method for identifying vulnerable lines and vulnerable load nodes in a gas-electricity interconnected system according to claim 1, characterized in that, In the above step S6, the specific identification process is as follows: Step S61. If the optimal physical attack target of the attacker calculated according to Step S5 is the e-th transmission line and the l-th natural gas pipeline, then the e-th transmission line and the l-th natural gas pipeline are the vulnerable lines. Step S62. If the optimal load reallocation attack strategy of the attacker is calculated according to Step S5: <ΔP LR，p , p = {1, 2,..., N P}> and <ΔM LR，g , g = {1, 2,..., N G}>, then if the amplitude of the false load data injected into the p-th electrical load node exceeds the set threshold ε of the actual electrical load data P , that is then the p-th electrical load node is determined to be a vulnerable load node; if the amplitude of the false load data injected into the g-th natural gas load node exceeds the set threshold ε of the actual natural gas load data G , that is then the g-th natural gas load node is determined to be a vulnerable node.

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