A smart grid multi-objective operation optimization method and system for defending network attacks

Abstract

The application discloses a kind of smart grid multi-objective operation optimization method and system of network attack defense, the number of security defense components of this method will defend network attack, generator active output vector, generator voltage vector, transformer decomposition ratio vector, reactive power generation vector, transformer tapping number and reactive power unit number as optimization variable, the load demand loss minimization of smart grid, the procurement and operation cost minimization of security defense components, the total fuel cost minimization of power generation is respectively as three optimization targets, realizes the multi-objective adaptive operation optimization process of smart grid of network attack defense.This application can efficiently realize the high safety and reliability and economic operation of the compromise optimization of multiple performance indicators of smart grid, with higher power supply reliability, higher security defense and lower operating cost.

Description

Technical Field

[0001] The present invention relates to the field of operation optimization technology in the field of smart grid system information security, and in particular to a smart grid multi-objective operation optimization method and system for defending against network attacks. Background Art

[0002] As electricity consumption continues to rise, infrastructure is becoming more susceptible to failures and reliability issues. Traditional power systems are being replaced by smart grids. The emergence of smart grids provides energy providers with greater transparency and accessibility, enabling efficient real-time monitoring and management. However, as smart grids become increasingly dependent on communication networks, they are also increasingly vulnerable to cyberattacks. Cyberattacks such as denial of service and false data injection pose significant challenges to smart grid security monitoring technology in terms of detection accuracy, computational complexity, and reliability. Therefore, ensuring that smart grids can defend against external cyberattacks while maintaining economical system operation remains a pressing technical challenge.

[0003] Since the security defense capability of the smart grid system is closely related to the number of attacked buses and the security defense components installed on the buses, a systematic analysis of the defense status of the smart grid system security defense components should be conducted during the planning, design, and operation optimization of the smart grid system, and the following factors should be comprehensively considered: (1) the load demand loss of the smart grid; (2) the procurement and operation costs of the security defense components; and (3) the total fuel cost of power generation. However, current technical research is limited to optimizing a single objective for the above situations. The common method of assigning weight coefficients to multi-objective scaling to form a single objective optimization or direct single objective optimization has the problem that the weight coefficients are difficult to accurately set and the comprehensive performance is difficult to optimize. In addition, there are a few studies that start from the perspective of multi-objective optimization, but they often start from the aspects of economy, system power supply loss probability, etc., and only optimize the number of components in the smart grid system. The multi-objective optimization algorithm used is also relatively complex. Therefore, how to optimize the planning and design of the number of security defense components, generator active output vector, generator voltage vector, transformer decomposition ratio vector, reactive power generation vector, number of transformer taps and number of reactive units in the smart grid system to ultimately achieve high security, reliability and economic operation of the smart grid with compromise optimization of multiple performance indicators has become one of the key technical problems that need to be solved urgently in the field of smart grid system defense against cyber attacks. Summary of the Invention

[0004] The purpose of the present invention is to address the deficiencies of the existing technology and provide a smart grid multi-objective operation optimization method and system for defending against network attacks.

[0005] The object of the present invention is achieved through the following technical solutions: In a first aspect, an embodiment of the present invention provides a multi-objective operation optimization method for a smart grid for defending against network attacks, comprising the following steps:

[0006] S1: Constructing a multi-objective operation optimization model for smart grids to defend against cyber attacks and its constraints;

[0007] S2: setting multiple first parameters;

[0008] S3: Based on the first parameter, the optimization variables in the multi-objective operation optimization model of the smart grid to be optimized for defense against network attacks are encoded using a real number encoding method. After iterating the initial population, the first population P is generated. I ;

[0009] S4: Set the initial value of the iteration number t to 1, record the iteration number t, and for the first population P of the tth iteration I Each individual in the mutates one by one to obtain the second population P I+1 ;

[0010] S5: For the second population P I+1 The offspring individuals in the second population P are processed according to the control method of the constraint mechanism I+1 The offspring individual constraints within the group are used to determine the degree of constraint violation and the second group P I+1 Dominance relationships among offspring individuals within a species;

[0011] S6: According to the dominance relationship determined in step S5, I+1 A non-dominated individual is randomly selected from the individuals, and the non-dominated individual is named P d , stored in the third population P n Used to update individuals in the next iteration, and at the same time, the second population P I+1 All non-dominated individuals are stored in the external archive A;

[0012] S7: Based on the maximum number of archives L of the external archive A max And the crowding distance sorting results, determine whether to use the second population P I+1 All non-dominated individuals in update the external archive A;

[0013] S8: In the external archive A, sort in ascending order according to the crowding distance sorting results described in step S7, and select the top individuals, replacing the third population P n Randomly selected from individuals, forming the fourth population; where |A| represents the number of individuals stored in the external archive A, Indicates that Round up;

[0014] S9: determining whether the iteration number t satisfies t≥G max , if yes, outputting all non-dominated individuals stored in the external archive A as the optimal Pareto solution set, selecting a Pareto optimal individual according to the actual engineering demand of the smart grid operation, obtaining the optimization objective function value corresponding to the Pareto optimal individual, including the procurement and operation cost of the security defense component, the total fuel cost of power generation, and the load demand loss of the smart grid; otherwise, setting t=t+1, unconditionally replacing the next generation population with the fourth population, and repeating steps S4 to S8; wherein, G max represents the maximum iteration number.

[0015] Further, the smart grid multi-objective operation model for defending network attacks comprises:

[0016] f1=(K1+b1)×(W1+W2+W3+W4+W5)+(K2+b2)×(W6+W7+W8+W9+W 10 10) (1)

[0017]

[0018]

[0019] wherein, f1, f2, f3 represent the 1st, 2nd, and 3rd optimization objective functions respectively, f1 describes the procurement and operation cost of the security defense component, f2 describes the total fuel cost of power generation, and f3 describes the load demand loss of the smart grid, K1 and K2 represent the procurement costs of the 1st and 2nd security defense components respectively, b1 and b2 represent the operation costs of the 1st and 2nd security defense components respectively, e1 and e2 represent the reliabilities of the 1st and 2nd security defense components respectively, z1 and z2 represent the costs of attacking the 1st and 2nd security defense components respectively, W1, W2, W3, W4, and W5 represent the numbers of the 1st security defense component installed in the 2nd, 5th, 7th, 8th, and 21st buses respectively, W6, W7, W8, W9, and W 10 10 represent the numbers of the 2nd security defense component installed in the 2nd, 5th, 7th, 8th, and 21st buses respectively, H G represents the number of generators connected to the grid, P Gv represents the actual output power of the vth generator, r v , s v , t v represent the fuel cost curve coefficients of the vth generator respectively, H Loss represents the number of buses related to load loss, represents the load demand of bus m, D mN represents the probability of a successful network attack on bus m. re Indicates the probability that the re-type defense component successfully defends against network attacks.

[0020] Furthermore, the constraints include instantaneous power balance and attack defense funding limits, and their specific expressions include:

[0021]

[0022] δ ij =δ i -δ j (8)

[0023] (K1+b1)×W m +(K2+b2)×W m+5 <6947 m=1,2,…,5 (9)

[0024]

[0025] Among them, δ i represents the voltage angle at busbar i, δ j represents the voltage angle at busbar j, δ ij represents the voltage angle difference between busbar i and busbar j, NB represents the number of buses, and They represent the active load demand and reactive load demand at bus i, respectively. and They represent the active power generation and reactive power generation of the power source connected to bus i, V i Represents the voltage at busbar i, V j represents the voltage at busbar j, G ij represents the transmission conductance between bus i and bus j, B ij represents the susceptance between bus i and bus j, K1 and K2 represent the purchase cost of the first and second category security defense components respectively, b1 and b2 represent the operating cost of the first and second category security defense components respectively, W1, W2, W3, W4, W5 represent the number of first category security defense components installed in the 2nd, 5th, 7th, 8th, 21st bus respectively, W6, W7, W8, W9, W 10 Respectively represents the number of type 2 security defense components installed in the 2nd, 5th, 7th, 8th, and 21st buses, P Gk represents the active power of the generator of the kth bus, and They represent the lower and upper limits of the active power of the generator of the kth bus, Q Cn represents the parallel compensation of the nth busbar, and They represent the lower and upper limits of the parallel compensation of the nth busbar, T td represents the tap ratio vector of the voltage regulating transformer on the d-th branch, and They represent the lower and upper limits of the tap ratio vector of the voltage regulating transformer on the dth branch, V Gf represents the generator voltage amplitude of the f-th bus, and They represent the lower and upper limits of the generator voltage amplitude of the f-th bus, W a Indicates the number of installed defense components. and They represent the lower and upper limits of the number of installed defense components, a=1, 2,…, 10.

[0026] Furthermore, the first parameter includes the purchase cost K1 of the first type of security defense component, the operating cost b1 of the first type of security defense component, the reliability e1 of the first type of security defense component, the cost z1 of attacking the first type of security defense component, the purchase cost K2 of the second type of security defense component, the operating cost b2 of the second type of security defense component, the reliability e2 of the second type of security defense component, the cost z2 of attacking the second type of security defense component, the maximum number of iterations G max , population size NP, external archive size L max , multi-point non-uniform variation parameter bc, and polynomial variation parameter q.

[0027] Furthermore, the real number coding method is used to encode the optimization variables in the multi-objective operation optimization model of the smart grid to be optimized for defense against network attacks, and after iterating the initial population, the first population P is generated. I , specifically including:

[0028] The first population P with uniform distribution is randomly generated using real number coding method I ={P s ,s=1,2,…,NP}, where P I represents the initial first population, P s represents the sth individual, NP represents the population size, and the sth individual P s =(P G1s ,P G2s ,P G3s ,P G4s ,P G5s ,V G1s ,V G2s ,V G5s ,V G8s ,V G11s ,V G13s ,T 11s ,T 12s,T 15s ,T 36s ,Q C10s ,Q C12s ,Q C15s ,Q C17s ,Q C20s ,Q C21s ,Q C23s ,Q C24s ,Q C29s ,W 1s ,W 2s ,W 3s ,W 4s ,W 5s ,W 6s ,W 7s ,W 8s ,W 9s ,W 10s ), P G1s ,P G2s ,P G3s ,P G4s ,P G5s Respectively represent the generator active power of the 2nd, 5th, 8th, 11th, and 13th buses corresponding to the sth individual, V G1s ,V G2s ,V G5s ,V G8s ,V G11s ,V G13s Respectively represent the generator voltage amplitudes of the 1st, 2nd, 5th, 8th, 11th, and 13th buses corresponding to the sth individual, T 11s ,T 12s ,T 15s ,T 36s The sth individual corresponds to the tap ratio vector of the voltage regulating transformer on the 11th, 12th, 15th, and 36th branches, Q C10s ,Q C12s ,Q C15s ,Q C17s ,Q C20s ,Q C21s ,Q C23s ,Q C24s ,Q C29s Respectively represent the parallel reactive compensation of the 10th, 12th, 15th, 17th, 20th, 21st, 23rd, 24th, and 29th buses corresponding to the sth individual, W 1s ,W 2s ,W 3s ,W 4s ,W 5s W represents the number of installed Class 1 security defense components in the 2nd, 5th, 7th, 8th, and 21st buses corresponding to the sth individual, respectively. 6s ,W 7s ,W 8s ,W9s ,W 10s Respectively represent the number of second-class security defense components installed in the 2nd, 5th, 7th, 8th, and 21st buses corresponding to the sth individual, and W 1s ,W 2s ,W 3s ,W 4s ,W 5s ,W 6s ,W 7s ,W 8s ,W 9s ,W 10s Round to the nearest integer.

[0029] Furthermore, the mutation operation specifically includes:

[0030] Generate 6 random numbers between 0 and 1, labeled rn1, rn2, rn3, rn4, rn5, rn6;

[0031] If rn1 is greater than rn4, a multi-point non-uniform mutation operation is performed. The formula of the multi-point non-uniform mutation operation is specifically:

[0032]

[0033] If rn1 is less than or equal to rn4, a polynomial mutation operation is performed. The specific formula of the polynomial mutation operation is:

[0034]

[0035] Among them, t represents the number of iterations, G max represents the maximum number of iterations, bc represents the multi-point non-uniform variation parameter, P cd (t) represents the first population P before mutation I The cdth variable of the sth individual, P cd (t+1) represents the second population P after mutation I+1 The cdth variable of the sth individual, P cd LB Represents the first population P I The lower limit allowed, P cd UB Represents the first population P I The upper limit of the allowable cd LB Depend on Composition, P cd UB Depend on Composition, q represents the polynomial variation parameter, represents the intensity coefficient of random variation, δ maxIt represents the farthest distance of the individual from the boundary, and B(t) represents the mutation intensity under the remaining number of iterations.

[0036] Furthermore, step S5 includes the following sub-steps:

[0037] S51: The second population P I+1 By {P s,I+1 ,s=1,2,…,NP}, P s,I+1 Represents the population P I+1 The sth individual in the second population P I+1 Whether all individuals in the group violate the constraints described in formula (6) to formula (14), and then calculate the cost performance according to formula (17);

[0038]

[0039] in, Indicates price / performance ratio, PF indicates the second population P I+1 The number of feasible solutions, NP represents the population size;

[0040] S52: If the second population P I+1 All individuals in the are infeasible solutions. For the second population P I+1 The constraint violation amount of all individuals in the group is normalized, and the normalized constraint violation degree is calculated according to formula (18) to formula (25), and the corresponding constraint violation degree index is marked as H(P s,I+1 ); According to the degree of constraint violation, the first judgment method corresponding to formula (23) is used to judge the second population P I+1 The dominant relationship between any two individuals in the Marked as the first non-dominated individual P d,I+1 ;

[0041]

[0042] in, Indicates that in individual P s,I+1 The corresponding o1th constraint in the case is, Indicates that in individual P s,I+1 The corresponding constraint violation degree index of o1 in the case, o1 represents the sequence number of the constraint, δ represents the tolerance of constraint violation, s1 and s2 both represent P I+1 The number of individuals in the function, s1 = 1, 2, ..., NP, s2 = 1, 2, ..., NP, but s1 ≠ s2, d1 represents the number of the optimization objective function, d1 = 1, 2, 3, Indicates P I+1 The d1th optimization objective function corresponding to the s1th individual in , Indicates P I+1 The d1th optimization objective function corresponding to the s2th individual in , Indicates P I+1 The normalized index of the constraint violation degree corresponding to the s1th individual in , Indicates P I+1 The constraint violation degree normalized index corresponding to the s2th individual in , ε represents the maximum tolerance value of the constraint violation degree normalized index, ≤ ε represents the ε constraint dominance, Represents an individual For individuals Satisfy the ε constraint, represents any mathematical symbol, It means that when d1 takes any value among 1, 2, and 3, the corresponding relationship in formula (23) must be established, cp is the feedback coefficient, is the price / performance ratio, t is the current number of iterations, G max is the maximum number of iterations, rn7 is a randomly generated number in the range of 0 to 1;

[0043] S53: If the second group P I+1 There are some feasible solutions in the memory. The evaluation method corresponding to formula (26) to formula (28) is used to evaluate all individual P s,I+1 ,s=1,2,…,NP corresponding optimization objective function Perform an evaluation to obtain a first evaluation result; based on the first evaluation result, use the first judgment method corresponding to formula (23) to determine the second population P I+1 The dominant relationship between any two individuals in the Marked as the second non-dominated individual P d,I+1 ;

[0044]

[0045] in, Represents individual P s,I+1 The corresponding d1th new optimization objective function, H(P s,I+1 ) represents individual P s,I+1 The corresponding normalized constraint violation degree, Represents individual P s,I+1 The corresponding d1th normalized optimization objective function, P fea,I+1 represents a feasible solution, Represents the population P I+1 The minimum function value of the d1th optimization objective function corresponding to the feasible solution, P mvol,I+1 Represents the population P I+1 The individual corresponding to the maximum value of the normalized index of constraint violation degree, representing individual P mvol,I+1 corresponding d1th optimization objective function value, for individual P s,I+1 corresponding d1th optimization objective function value, ε represents the maximum tolerance value of constraint violation degree normalization index, mk is a penalty coefficient, for cost performance ratio;

[0046] S54: If the second population P I+1 are all feasible solutions, using the evaluation method corresponding to formula (29), evaluating all individuals in the second population P I+1 Satisfy the evaluation method corresponding to formula (29), mark the individuals as third non-dominated individuals P d,I+1 ;

[0047]

[0048] wherein, representing the d1th optimization objective function corresponding to the s1th individual in P I+1 ; representing the d1th optimization objective function corresponding to the s2th individual in P I+1 ; representing the d2th optimization objective function corresponding to the s1th individual in P I+1 ; representing the d2th optimization objective function corresponding to the s2th individual in P I+1 ; d1 and d2 represent the serial numbers of optimization objective functions, d1=1, 2, 3, d2=1, 2, 3; representing the mathematical symbol.

[0049] Further, according to the maximum number L max of the external archive A and the crowding distance sorting result, it is judged whether to update the external archive A with all non-dominated individuals in the second population P I+1 , specifically including:

[0050] If the maximum number L max of the external archive A is greater than the number of all non-dominated individuals in the second population P I+1 , then all non-dominated individuals in the second population P I+1 are used to update the external archive A;

[0051] If the maximum number L max of the external archive A is less than or equal to the number of all non-dominated individuals in the second population P I+1 , then all non-dominated individuals in the second population P I+1 ​In the embodiment, all the non-dominated individuals are sorted according to the crowding distance, and the first L individuals in the most crowded position are left, and the external archive A is updated. max

[0052] Further, the process of sorting according to the crowding distance specifically comprises:

[0053]

[0054] Let the current size of the external archive be |A|, and A(s) represent the s-th individual in the external archive. The three new optimization objective functions corresponding to all the individuals {A(s), s=1, 2, …, |A|} in the external archive are sorted in ascending order, so that wherein, d1, d2, and d|A| represent the 1st, 2nd, and |A|th serial numbers of the sorting index of the d1-th optimization objective function respectively, A(d1) represents the individual in the external archive corresponding to the d1-th optimization objective function value sorted as A(d2) represents the individual in the external archive corresponding to the d2-th optimization objective function value sorted as and the crowding distances of d1 and d2 are respectively marked as and For s=2, L, |A|-1, the crowding distance of d1 is calculated according to formula (30)

[0055] The second aspect of the embodiment provides an intelligent power grid multi-objective operation optimization system for defending network attacks, which is used to implement the intelligent power grid multi-objective operation optimization method for defending network attacks. The system comprises:

[0056] A construction module for constructing an intelligent power grid multi-objective operation optimization model for defending network attacks and constraint conditions thereof;

[0057] A setting module for setting a plurality of first parameters;

[0058] A first population initialization module for encoding optimization variables in an intelligent power grid multi-objective operation optimization model for defending network attacks to be optimized by using a real number coding method according to the first parameters, and generating a first population P I after iterating the initial population;

[0059] A second population generation module for recording the iteration number t, and implementing a mutation operation on each individual in the first population P I of the t-th iteration one by one to generate a second population P I+1 ; ​​

[0060] A dominance relationship judgment module is used to determine the dominance relationship of the second population P I+1 The offspring individuals in the second population P are processed according to the control method of the constraint mechanism I+1 The offspring individual constraints within the group are used to determine the degree of constraint violation and the second group P I+1 Dominance relationships among offspring individuals within a species;

[0061] The archive module is used to extract the data from the second population P according to the dominance relationship. I+1 A non-dominated individual is randomly selected from the individuals, and the non-dominated individual is named P d , stored in the third population P n Used to update individuals in the next iteration, and at the same time, the second population P I+1 All non-dominated individuals are stored in the external archive A;

[0062] Archive update module, for updating the data according to the second population P I+1 All non-dominated individuals and crowding distances in the external archive A are updated;

[0063] The fourth group generation module is used to sort the external archive A in ascending order according to the crowding distance and select the top individuals, replacing the third population P n Randomly selected from individuals, forming a fourth population; and

[0064] Iteration judgment module, used to judge whether the number of iterations t satisfies t≥G max If it is satisfied, all non-dominated individuals stored in the external archive A are output as the optimal Pareto solution set, and the Pareto optimal individual is selected according to the actual engineering requirements of the smart grid operation to obtain the optimization objective function value corresponding to the Pareto optimal individual; otherwise, set t = t + 1, unconditionally replace the next generation population with the fourth population, and return to the second population generation module to re-execute the iterative process.

[0065] Compared with the existing technology, the beneficial effects of the present invention are as follows: the present invention comprehensively considers three important indicators of the load demand loss of the smart grid, the procurement and operation costs of security defense components, and the total fuel cost of power generation, and designs a multi-objective adaptive operation optimization method for the smart grid to defend against network attacks, which efficiently realizes the high safety, reliability and economic operation of the smart grid through compromise optimization of multiple performance indicators; the present invention can efficiently realize the high safety, reliability and economic operation of the smart grid through compromise optimization of multiple performance indicators, and has higher power supply reliability, higher security defense and lower operating costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1is a schematic diagram of the topology of the IEEE 30-node power system in an embodiment of the present application;

[0067] Figure 2 is a flow chart of the intelligent power grid multi-objective adaptive operation optimization method for defending network attacks in the present application;

[0068] Figure 3 is an optimal Pareto front graph obtained after iteration optimization in the present application;

[0069] Figure 4 is a schematic diagram of the structure of the intelligent power grid multi-objective adaptive operation optimization system for defending network attacks in the present application. DETAILED DESCRIPTION

[0070] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0071] This embodiment is specifically described in combination with the IEEE 30-node power system, Figure 1 is a schematic diagram of the topology of the IEEE 30-node power system, which contains 5 thermal power generators.

[0072] In this embodiment, the network attack simulated is a false data injection attack, and the target of the implemented network attack is to bypass bad data detection and maximize the load demand loss of the smart grid through false scheduling information, thereby causing safety problems or physical damage. In this embodiment, it is assumed that the 2nd, 5th, 7th, 8th and 21st bus bars in the IEEE 30-node power system are subjected to false data injection attacks.

[0073] Referring to Figure 2 The intelligent power grid multi-objective adaptive operation optimization method for defending network attacks specifically includes the following steps:

[0074] S1: Constructing an intelligent power grid multi-objective operation optimization model for defending network attacks and its constraint conditions.

[0075] Further, the intelligent power grid multi-objective operation model for defending network attacks includes:

[0076] f1=(K1+b1)×(W1+W2+W3+W4+W5)+(K2+b2)×(W6+W7+W8+W9+W 10 ) (1)

[0077]

[0078]

[0079] Among them, f1, f2, and f3 represent the first, second, and third optimization objective functions respectively, f1 describes the procurement and operation costs of security defense components, f2 describes the total fuel cost of power generation, f3 describes the load demand loss of the smart grid, K1 and K2 represent the procurement costs of the first and second category security defense components respectively, b1 and b2 represent the operating costs of the first and second category security defense components respectively, e1 and e2 represent the reliability of the first and second category security defense components respectively, z1 and z2 represent the cost of attacking the first and second category security defense components respectively, W1, W2, W3, W4, and W5 are the number of first category security defense components installed in the 2nd, 5th, 7th, 8th, and 21st buses respectively, and W6, W7, W8, W9, and W 10 The number of Class 2 security defense components installed in the 2nd, 5th, 7th, 8th, and 21st buses, respectively. G Indicates the number of generators connected to the grid, P Gv represents the actual output power of the vth generator, r v 、s v , t v They represent the fuel cost curve coefficients corresponding to the vth generator, H Loss represents the number of buses associated with the load loss, Denotes the load demand of busbar m, D m N represents the probability of a successful network attack on bus m. re Indicates the probability that the re-type defense component successfully defends against network attacks.

[0080] Furthermore, the constraints include instantaneous power balance and attack defense budget constraints, and their specific expressions include:

[0081]

[0082] δ ij =δ i -δ j (8)

[0083] (K1+b1)×W m +(K2+b2)×W m+5 <6947 m=1,2,…,5 (9)

[0084]

[0085] Among them, δ i represents the voltage angle at busbar i, δ j represents the voltage angle at busbar j, δ ijrepresents the voltage angle difference between busbar i and busbar j, NB represents the number of buses, and They represent the active load demand and reactive load demand at bus i, respectively. and They represent the active power generation and reactive power generation of the power source connected to bus i, V i Represents the voltage at bus i, V j represents the voltage at busbar j, G ij represents the transmission conductance between bus i and bus j, B ij represents the susceptance between bus i and bus j, K1 and K2 represent the purchase cost of the first and second category security defense components respectively, b1 and b2 represent the operating cost of the first and second category security defense components respectively, W1, W2, W3, W4, W5 represent the number of first category security defense components installed in the 2nd, 5th, 7th, 8th, 21st bus respectively, W6, W7, W8, W9, W 10 Respectively represents the number of type 2 security defense components installed in the 2nd, 5th, 7th, 8th, and 21st buses, P Gk represents the active power of the generator of the kth bus, and They represent the lower and upper limits of the active power of the generator of the kth bus, Q Cn represents the parallel compensation of the nth busbar, and They represent the lower and upper limits of the parallel compensation of the nth busbar, T td represents the tap ratio vector of the voltage regulating transformer on the d-th branch, and They represent the lower and upper limits of the tap ratio vector of the voltage regulating transformer on the d-th branch, V Gf represents the generator voltage amplitude of the f-th bus, and They represent the lower and upper limits of the generator voltage amplitude of the f-th bus, W a Indicates the number of installed defense components. and They represent the lower and upper limits of the number of installed defense components, a=1, 2,…, 10.

[0086] S2: Set multiple first parameters.

[0087] In this embodiment, the first parameter includes the purchase cost K1 of the first type of security defense component, the operating cost b1 of the first type of security defense component, the reliability e1 of the first type of security defense component, the cost z1 of attacking the first type of security defense component, the purchase cost K2 of the second type of security defense component, the operating cost b2 of the second type of security defense component, the reliability e2 of the second type of security defense component, the cost z2 of attacking the second type of security defense component, and the maximum number of iterations G max , population size NP, external archive size L max , multi-point non-uniform variation parameter bc, and polynomial variation parameter q.

[0088] It should be noted that the first parameter can be set according to actual conditions. For example, in this embodiment, the first parameter is set to: K1 = 239.52, b1 = 143.71, e1 = 0.75, z1 = 209.58, K2 = 958.08, b2 = 86.23, e2 = 0.90, z2 = 838.32, G max =1000,NP=500,L max =100, bc=3, q=0.1.

[0089] S3: Based on the first parameter, the optimization variables in the multi-objective operation optimization model of the smart grid to be optimized for defense against network attacks are encoded using the real number encoding method. After iterating the initial population, the first population P is generated. I .

[0090] Specifically, the real number coding method is used to randomly generate the uniformly distributed first population P I ={P s ,s=1,2,…,NP}, where P I represents the initial first population, P s represents the sth individual, NP represents the population size, and the sth individual P s =(P G1s ,P G2s ,P G3s ,P G4s ,P G5s ,V G1s ,V G2s ,V G5s ,V G8s ,V G11s ,V G13s ,T 11s ,T 12s ,T 15s ,T 36s ,Q C10s ,Q C12s ,Q C15s ,Q C17s ,QC20s ,Q C21s ,Q C23s ,Q C24s ,Q C29s ,W 1s ,W 2s ,W 3s ,W 4s ,W 5s ,W 6s ,W 7s ,W 8s ,W 9s ,W 10s ), P G1s ,P G2s ,P G3s ,P G4s ,P G5s Respectively represent the generator active power of the 2nd, 5th, 8th, 11th, and 13th buses corresponding to the sth individual, V G1s ,V G2s ,V G5s ,V G8s ,V G11s ,V G13s Respectively represent the generator voltage amplitudes of the 1st, 2nd, 5th, 8th, 11th, and 13th buses corresponding to the sth individual, T 11s ,T 12s ,T 15s ,T 36s The sth individual corresponds to the tap ratio vector of the voltage regulating transformer on the 11th, 12th, 15th, and 36th branches, Q C10s ,Q C12s ,Q C15s ,Q C17s ,Q C20s ,Q C21s ,Q C23s ,Q C24s ,Q C29s Respectively represent the parallel reactive compensation of the 10th, 12th, 15th, 17th, 20th, 21st, 23rd, 24th, and 29th buses corresponding to the sth individual, W 1s ,W 2s ,W 3s ,W 4s ,W 5s W represents the number of installed Class 1 security defense components in the 2nd, 5th, 7th, 8th, and 21st buses corresponding to the sth individual, respectively. 6s ,W 7s ,W 8s ,W 9s ,W 10s Respectively represent the number of second-class security defense components installed in the 2nd, 5th, 7th, 8th, and 21st buses corresponding to the sth individual, and W 1s ,W 2s ,W3s ,W 4s ,W 5s ,W 6s ,W 7s ,W 8s ,W 9s ,W 10s Round to the nearest integer.

[0091] S4: Set the initial value of the iteration number t to 1, record the iteration number t, and for the first population P of the tth iteration I Each individual in the mutates one by one to obtain the second population P I+1 .

[0092] Furthermore, the mutation operation specifically includes:

[0093] Generate 6 random numbers between 0 and 1, labeled rn1, rn2, rn3, rn4, rn5, rn6;

[0094] If rn1 is greater than rn4, a multi-point non-uniform mutation operation is performed. The formula for the multi-point non-uniform mutation operation is as follows:

[0095]

[0096] If rn1 is less than or equal to rn4, perform the polynomial mutation operation. The formula for the polynomial mutation operation is:

[0097]

[0098] Among them, t represents the number of iterations, G max represents the maximum number of iterations, bc represents the multi-point non-uniform variation parameter, P cd (t) represents the first population P before mutation I The cdth variable of the sth individual, P cd (t+1) represents the second population P after mutation I+1 The cdth variable of the sth individual, P cd LB Represents the first population P I The lower limit allowed, P cd UB Represents the first population P I The upper limit of the allowable cd LB Depend on Composition, P cd UB Depend on Composition, q represents the polynomial variation parameter, represents the intensity coefficient of random variation, δ maxIt represents the farthest distance of the individual from the boundary, and B(t) represents the mutation intensity under the remaining number of iterations.

[0099] S5: For the second population P I+1 The offspring individuals in the second population P are processed according to the control method of the constraint mechanism. I+1 The offspring individual constraints within the group are used to determine the degree of constraint violation and the second group P I+1 The dominance relationship between offspring individuals within a species.

[0100] Specifically, step S5 includes the following sub-steps:

[0101] S51: The second population P I+1 By {P s,I+1 ,s=1,2,…,NP}, P s,I+1 Represents the population P I+1 The sth individual in the second population P I+1 Whether all individuals in the group violate the constraints described in formulas (6) to (14); then calculate the cost performance according to formula (17):

[0102]

[0103] in, Indicates price / performance ratio, PF indicates the second population P I+1 NP represents the number of feasible solutions in the population.

[0104] It should be understood that each individual in the second population is composed of the generator active power of its corresponding bus, the generator voltage amplitude of the bus, the tap ratio vector of the voltage-regulating transformer on the branch, the parallel reactive compensation of the bus, and the number of Class 1 and Class 2 safety defense components installed in the bus. Based on formulas (6) to (14), calculations are performed according to the composition of the individual to determine whether the individual violates the constraints described in formulas (6) to (14).

[0105] It should be noted that the second population P I+1 The individual that does not violate the constraints described in formulas (6) to (14) is a feasible solution.

[0106] S52: If the second population P I+1 All individuals in the are infeasible solutions. For the second population P I+1 The constraint violation amount of all individuals in the group is normalized, and the normalized constraint violation degree is calculated according to formula (18) to formula (25), and the corresponding constraint violation degree index is marked as H(P s,I+1 ); According to the degree of constraint violation, the first judgment method corresponding to formula (23) is used to judge the second population P I+1The dominant relationship between any two individuals in the equation (23) will satisfy the individual of the first judgment method. Marked as the first non-dominated individual P d,I+1 .

[0107]

[0108]

[0109] in, Indicates that in individual P s,I+1 The corresponding o1th constraint in the case is, Indicates that in individual P s,I+1 The corresponding constraint violation degree index in the case of o1, o1 represents the sequence number of the constraint, δ represents the tolerance of constraint violation, s1 and s2 both represent P I+1 The number of individuals in the function, s1 = 1, 2, ..., NP, s2 = 1, 2, ..., NP, but s1 ≠ s2, d1 represents the number of the optimization objective function, d1 = 1, 2, 3, Indicates P I+1 The d1th optimization objective function corresponding to the s1th individual in , Indicates P I+1 The d1th optimization objective function corresponding to the s2th individual in , Indicates P I+1 The normalized index of the constraint violation degree corresponding to the s1th individual in , Indicates P I+1 The constraint violation degree normalized index corresponding to the s2th individual in , ε represents the maximum tolerance value of the constraint violation degree normalized index, ≤ ε represents the ε constraint dominance, Represents an individual For individuals Satisfy the ε constraint, represents any mathematical symbol, It means that when d1 takes any value among 1, 2, and 3, the corresponding relationship in formula (23) must be established, cp is the feedback coefficient, is the price / performance ratio, t is the current number of iterations, G max is the maximum number of iterations, and rn7 is a randomly generated number in the range of 0 to 1.

[0110] S53: If the second group P I+1 There are some feasible solutions in the memory. The evaluation method corresponding to formula (26) to formula (28) is used to evaluate all individual P s,I+1 ,s=1,2,…,NP corresponding optimization objective function Perform an evaluation to obtain a first evaluation result; based on the first evaluation result, use the first judgment method corresponding to formula (23) to judge the second population P I+1 The dominant relationship between any two individuals in the equation (23) will satisfy the individual of the first judgment method. Marked as the second non-dominated individual P d,I+1 .

[0111]

[0112] in, Represents individual P s,I+1 The corresponding d1th new optimization objective function, H(P s,I+1 ) represents individual P s,I+1 The corresponding normalized constraint violation degree, Represents individual P s,I+1 The corresponding d1th normalized optimization objective function, P fea,I+1 represents a feasible solution, Represents the population P I+1 The minimum function value of the d1th optimization objective function corresponding to the feasible solution, P mvol,I+1 Represents the population P I+1 The individual corresponding to the maximum value of the normalized index of constraint violation degree, Represents individual P mvol,I+1 The corresponding d1th optimization objective function value, For individual P s,I+1 The corresponding d1th optimization objective function value, ε represents the maximum tolerance value of the normalized constraint violation index, mk is the penalty coefficient, For cost-effectiveness.

[0113] S54: If the second population P I+1 All are feasible solutions. The evaluation method corresponding to formula (29) is used to evaluate the second population P. I+1 The dominant relationship of all individuals in the Labeled as the third non-dominated individual P d,I+1 .

[0114]

[0115] in, Indicates P I+1 The d1th optimization objective function corresponding to the s1th individual in , Indicates P I+1 The d1th optimization objective function corresponding to the s2th individual in , Indicates P I+1 The d2th optimization objective function corresponding to the s1th individual in , Indicates P I+1 The d2th optimization objective function corresponding to the s2th individual, d1 and d2 both represent the sequence numbers of the optimization objective functions, d1 = 1, 2, 3, d2 = 1, 2, 3; A mathematical symbol that indicates existence.

[0116] S6: According to the dominance relationship determined in step S5, from the second population P I+1 A non-dominated individual is randomly selected from the individuals, and the non-dominated individual is named P d , stored in the third population P n Used to update individuals in the next iteration, and at the same time, the second population P I+1 All non-dominated individuals in are stored in the external archive A.

[0117] S7: Maximum number of archives L according to external archive A max And the crowding distance sorting results, determine whether to use the second population P I+1 All non-dominated individuals in update the external archive A.

[0118] Furthermore, according to the maximum number of archives L of the external archive A max And the crowding distance sorting results, determine whether to use the second population P I+1 All non-dominated individuals in update the external archive A, including:

[0119] If the maximum number of archives in external archive A is L max Greater than the second population P I+1 The number of all non-dominated individuals in the second population P I+1 All non-dominated individuals in update the external archive A;

[0120] If the maximum number of archives in external archive A is L max Less than or equal to the second population P I+1 The number of all non-dominated individuals in the second population P I+1 In the above example, all non-dominated individuals are sorted by crowding distance, and the top L individuals in the most crowded position are left. max Individuals update external archive A.

[0121] Furthermore, the process of crowding distance sorting specifically includes: marking the current size of the external archive as |A|, A(s) represents the sth individual in the external archive, and for all individuals in the external archive {A(s), s=1,2,…,|A|} corresponding to three new optimization objective functions Sort in ascending order so that in, They represent the first, second and |A|th order numbers of the sorted index of the d1th optimization objective function, respectively. Indicates that the d1th optimization objective function value is sorted as The corresponding external archive individual; and The congestion distances are marked as and For s=2,L,|A|-1, calculate according to formula (30) crowding distance

[0122]

[0123] S8: Sort in ascending order according to the crowding distance sorting results in step S7 in the external archive A, and select the top individuals, replacing the third population P n Randomly selected from individuals, forming the fourth population; where |A| represents the number of individuals stored in the external archive A, Indicates that Round up.

[0124] S9: Determine whether the number of iterations t satisfies t≥G max If it is satisfied, all non-dominated individuals stored in the external archive A are output as the optimal Pareto solution set, and the Pareto optimal individual is selected according to the actual engineering requirements of the smart grid operation to obtain the optimization objective function value corresponding to the Pareto optimal individual, including the procurement and operation cost of security defense components, the total fuel cost of power generation, and the load demand loss of the smart grid; otherwise, set t = t + 1, unconditionally replace the next generation population with the fourth population, and repeat steps S4 to S8; where G max Indicates the maximum number of iterations.

[0125] In this embodiment, after 1000 iterations, the Pareto frontier is obtained as follows: Figure 3 As shown, the real number code corresponding to the optimal compromise solution is p best =[58.7383,20.9685,35,18.2862,17.3430,1.0744,1.0599,1.0310,1.0398,1.0644,1.0526,1,1,1,1,4.7048,6,4.0534,6,4.3517,6,2.8310,6,3.8047,5,1,6,1,4,1,5,1,7,1]. The specific values ​​of the three optimization objectives are: [15568.76,972.3013,2.709421].

[0126] In the real number coding corresponding to the optimal compromise individual, 58.7383, 20.9685, 35, 18.2862, 17.3430 represent the generator active power of the 2nd, 5th, 8th, 11th and 13th bus respectively, 1.0744, 1.0599, 1.0310, 1.0398, 1.0644, 1.0526 represent the generator voltage amplitude of the 1st, 2nd, 5th, 8th, 11th and 13th bus respectively, 1, 1, 1, 1 represent the tap ratio vector of the voltage regulating transformer on the 11th, 12th, 15th and 36th branch respectively, 4.7048, 6, 4.0534, 6, 4.3517, 6, 2.8310, 6, 3.8047 represent the parallel reactive power compensation of the 10th, 12th, 15th, 17th, 20th, 21st, 23rd, 24th and 29th bus respectively, 5, 6, 4, 5, 7 represent the number of the first type of security defense components installed in the 2nd, 5th, 7th, 8th and 21st bus respectively, 1, 1, 1, 1, 1 represent the number of the second type of security defense components installed in the 2nd, 5th, 7th, 8th and 21st bus respectively; among the three target values corresponding to the optimal compromise individual, the load demand loss of the smart grid is 2.709421 MW, the procurement and operation cost of the security defense components is 15568.76 dollars, and the total fuel cost of power generation is 972.3013 dollars.

[0127] In summary, by the above technical scheme, the present application comprehensively considers the three important performance indicators of the load demand loss of the smart grid, the procurement and operation cost of the security defense components, and the total fuel cost of power generation, designs a smart grid multi-objective operation optimization adaptive method for defending network attacks, and through the smart grid system for defending network attacks, not only the defense time of the smart grid system in response to network attacks is shortened, but also the defense cost and fuel cost are minimized while ensuring the safe operation of the smart grid system against network attacks, effectively balancing the safety and reliability and the economy of the smart grid system; through formula (1) to formula (29) combined with steps S1-S9 of the present application, the high safety and reliability and economic operation of the smart grid multi-performance indicator compromise optimization are finally efficiently realized. Compared with the prior art, the present application has higher power supply reliability, higher security defense and lower operation cost.

[0128] It is worth mentioning that the present application also provides a smart grid multi-objective operation optimization system for defending network attacks, which is used to realize the smart grid multi-objective adaptive operation optimization method for defending network attacks in the above-mentioned embodiments.

[0129] Referring to Figure 4 , the system comprises a construction module 10, a setting module 20, a first population initialization module 30, a second population generation module 40, a dominance relationship judgment module 50, an archive module 60, an archive update module 70, a fourth population generation module 80 and an iteration judgment module 90.

[0130] In this embodiment, the construction module 10 is used to construct a smart grid multi-objective operation optimization model and its constraint conditions for defending against network attacks.

[0131] In this embodiment, the setting module 20 is used to set a plurality of first parameters.

[0132] In this embodiment, the first population initialization module 30 is used to encode the optimization variables in the multi-objective operation optimization model of the smart grid to be optimized for defending against network attacks according to the first parameter using a real number encoding method, and after iterating the initial population, generate the first population P. I .

[0133] In this embodiment, the second population generation module 40 is used to record the number of iterations t. For the first population P of the tth iteration, I Each individual in the mutates one by one to generate the second population P I+1 .

[0134] In this embodiment, the dominance relationship judgment module 50 is used to determine the dominance relationship of the second group P. I+1 The offspring individuals in the second population P are processed according to the control method of the constraint mechanism. I+1 The offspring individual constraints within the group are used to determine the degree of constraint violation and the second group P I+1 The dominance relationship between offspring individuals within a species.

[0135] In this embodiment, the archiving module 60 is used to obtain the second population P according to the dominance relationship. I+1 A non-dominated individual is randomly selected from the individuals, and the non-dominated individual is named P d , stored in the third population P n Used to update individuals in the next iteration, and at the same time, the second population P I+1 All non-dominated individuals in are stored in the external archive A.

[0136] In this embodiment, the archive update module 70 is used to update the archive according to the second population P I+1 Update the external archive A with all non-dominated individuals and crowding distances.

[0137] In this embodiment, the fourth population generation module 80 is used to sort the external archive A in ascending order according to the congestion distance, and select the top individuals, replacing the third population P n Randomly selected from individuals, forming the fourth population.

[0138] In this embodiment, the iteration judgment module 90 is used to judge whether the number of iterations t satisfies t≥G maxIf it is satisfied, all non-dominated individuals stored in the external archive A are output as the optimal Pareto solution set, and the Pareto optimal individual is selected according to the actual engineering requirements of the smart grid operation to obtain the optimization objective function value corresponding to the Pareto optimal individual; otherwise, set t = t + 1, unconditionally replace the next generation population with the fourth population, and return to the second population generation module to re-execute the iterative process.

[0139] Those skilled in the art will understand that all or part of the steps of implementing the above-mentioned embodiments can be completed by hardware related to program instructions, and the aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it executes the steps of the above-mentioned method embodiment; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk, etc. Various media that can store program codes.

[0140] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A multi-objective operation optimization method for smart grids to defend against network attacks, characterized in that: The following steps are involved: S1: Construct a multi-objective operation optimization model for smart grids to defend against cyber attacks and its constraints. The constraints include instantaneous power balance and budget constraints for defending against attacks. The specific expressions include: d ij =d i -d j (8) (K1+b1)×W m +(K2+b2)×W m+5 <6947 m=1,2,…,5 (9) Among them, δ i represents the voltage angle at busbar i, δ j represents the voltage angle at busbar j, δ ij represents the voltage angle difference between busbar i and busbar j, NB represents the number of buses, and They represent the active load demand and reactive load demand at bus i, respectively. and They represent the active power generation and reactive power generation of the power source connected to bus i, V i Represents the voltage at bus i, V j represents the voltage at busbar j, G ij represents the transmission conductance between bus i and bus j, B ij represents the susceptance between bus i and bus j, K1 and K2 represent the purchase cost of the first and second category security defense components respectively, b1 and b2 represent the operating cost of the first and second category security defense components respectively, W1, W2, W3, W4, W5 represent the number of first category security defense components installed in the 2nd, 5th, 7th, 8th, 21st bus respectively, W6, W7, W8, W9, W 10 Respectively represents the number of type 2 security defense components installed in the 2nd, 5th, 7th, 8th, and 21st buses, P Gk represents the active power of the generator of the kth bus, and They represent the lower and upper limits of the active power of the generator of the kth bus, Q Cn represents the parallel compensation of the nth busbar, and They represent the lower and upper limits of the parallel compensation of the nth busbar, T td represents the tap ratio vector of the voltage regulating transformer on the d-th branch, and They represent the lower and upper limits of the tap ratio vector of the voltage regulating transformer on the dth branch, V Gf represents the generator voltage amplitude of the f-th bus, and They represent the lower and upper limits of the generator voltage amplitude of the f-th bus, W a Indicates the number of installed defense components. and Respectively represent the lower and upper limits of the number of defense components installed, a=1,2,…,10; S2: setting multiple first parameters; S3: Based on the first parameter, the optimization variables in the multi-objective operation optimization model of the smart grid to be optimized for defense against network attacks are encoded using a real number encoding method. After iterating the initial population, the first population P is generated. I ; S4: Set the initial value of the iteration number t to 1, record the iteration number t, and for the first population P of the tth iteration I Each individual in the mutates one by one to obtain the second population P I+1 ; S5: For the second population P I+1 The offspring individuals in the second population P are processed according to the control method of the constraint mechanism. I+1 The offspring individual constraints within the group are used to determine the degree of constraint violation and the second group P I+1 Dominance relationships among offspring individuals within a species; S6: According to the dominance relationship determined in step S5, from the second population P I+1 A non-dominated individual is randomly selected from the individuals, and the non-dominated individual is named P d , stored in the third population P n Used to update individuals in the next iteration, and at the same time, the second population P I+1 All non-dominated individuals are stored in the external archive A; S7: Based on the maximum number of archives L of the external archive A max And the crowding distance sorting results, determine whether to use the second population P I+1 All non-dominated individuals in update the external archive A; S8: Sort in ascending order according to the crowding distance sorting results in step S7 in the external archive A, and select the top individuals, replacing the third population P n Randomly selected from individuals, forming the fourth population; where |A| represents the number of individuals stored in the external archive A, Indicates that Round up; S9: Determine whether the number of iterations t satisfies t≥G max If it is satisfied, all non-dominated individuals stored in the external archive A are output as the optimal Pareto solution set, and the Pareto optimal individual is selected according to the actual engineering requirements of the smart grid operation to obtain the optimization objective function value corresponding to the Pareto optimal individual, including the procurement and operation cost of security defense components, the total fuel cost of power generation, and the load demand loss of the smart grid; otherwise, set t = t + 1, unconditionally replace the next generation population with the fourth population, and repeat steps S4 to S8; where G max Indicates the maximum number of iterations.

2. The multi-objective operation optimization method for smart grids for defending against network attacks according to claim 1 is characterized in that: The multi-objective operation model of the smart grid for defending against network attacks includes: f1=(K1+b1)×(W1+W2+W3+W4+W5)+(K2+b2)×(W6+W7+W8+W9+W 10 ) (1) Among them, f1, f2, and f3 represent the first, second, and third optimization objective functions respectively, f1 describes the procurement and operation costs of security defense components, f2 describes the total fuel cost of power generation, f3 describes the load demand loss of the smart grid, K1 and K2 represent the procurement costs of the first and second category security defense components respectively, b1 and b2 represent the operating costs of the first and second category security defense components respectively, e1 and e2 represent the reliability of the first and second category security defense components respectively, z1 and z2 represent the cost of attacking the first and second category security defense components respectively, W1, W2, W3, W4, and W5 are the number of first category security defense components installed in the 2nd, 5th, 7th, 8th, and 21st buses respectively, and W6, W7, W8, W9, and W 10 The number of Class 2 security defense components installed in the 2nd, 5th, 7th, 8th, and 21st buses, respectively. G Indicates the number of generators connected to the grid, P Gv represents the actual output power of the vth generator, r v 、s v , t v They represent the fuel cost curve coefficients corresponding to the vth generator, H Loss represents the number of buses associated with the load loss, Denotes the load demand of busbar m, D m N represents the probability of a successful network attack on bus m. re Indicates the probability that the re-type defense component successfully defends against network attacks.

3. The multi-objective operation optimization method for smart grids to defend against network attacks according to claim 1 is characterized in that: The first parameters include the purchase cost K1 of the first type of security defense component, the operating cost b1 of the first type of security defense component, the reliability e1 of the first type of security defense component, the cost z1 of attacking the first type of security defense component, the purchase cost K2 of the second type of security defense component, the operating cost b2 of the second type of security defense component, the reliability e2 of the second type of security defense component, the cost z2 of attacking the second type of security defense component, and the maximum number of iterations G max , population size NP, external archive size L max , multi-point non-uniform variation parameter bc, and polynomial variation parameter q.

4. The multi-objective operation optimization method for smart grids for defending against network attacks according to claim 1 is characterized in that: The real number coding method is used to encode the optimization variables in the multi-objective operation optimization model of the smart grid to be optimized for defense against network attacks, and after iterating the initial population, the first population P is generated. I , specifically including: The first population P with uniform distribution is randomly generated using real number coding method I ={P s ,s=1,2,…,NP}, where P I represents the initial first population, P s represents the sth individual, NP represents the population size, and the sth individual P s =(P G1s ,P G2s ,P G3s ,P G4s ,P G5s ,V G1s ,V G2s ,V G5s ,V G8s ,V G11s ,V G13s ,T 11s ,T 12s ,T 15s ,T 36s ,Q C10s ,Q C12s ,Q C15s ,Q C17s ,Q C20s ,Q C21s ,Q C23s ,Q C24s ,Q C29s ,W 1s ,W 2s ,W 3s ,W 4s ,W 5s ,W 6s ,W 7s ,W 8s ,W 9s ,W 10s ), P G1s ,P G2s ,P G3s ,P G4s ,P G5s Respectively represent the generator active power of the 2nd, 5th, 8th, 11th, and 13th buses corresponding to the sth individual, V G1s ,V G2s ,V G5s ,V G8s ,V G11s ,V G13s Respectively represent the generator voltage amplitudes of the 1st, 2nd, 5th, 8th, 11th, and 13th buses corresponding to the sth individual, T 11s ,T 12s ,T 15s ,T 36s The sth individual corresponds to the tap ratio vector of the voltage regulating transformer on the 11th, 12th, 15th, and 36th branches, Q C10s ,Q C12s ,Q C15s ,Q C17s ,Q C20s ,Q C21s ,Q C23s ,Q C24s ,Q C29s Respectively represent the parallel reactive compensation of the 10th, 12th, 15th, 17th, 20th, 21st, 23rd, 24th, and 29th buses corresponding to the sth individual, W 1s ,W 2s ,W 3s ,W 4s ,W 5s W represents the number of installed Class 1 security defense components in the 2nd, 5th, 7th, 8th, and 21st buses corresponding to the sth individual, respectively. 6s ,W 7s ,W 8s ,W 9s ,W 10s Respectively represent the number of second-class security defense components installed in the 2nd, 5th, 7th, 8th, and 21st buses corresponding to the sth individual, and W 1s ,W 2s ,W 3s ,W 4s ,W 5s ,W 6s ,W 7s ,W 8s ,W 9s ,W 10s Round to the nearest integer.

5. The multi-objective operation optimization method for smart grids for defending against network attacks according to claim 1 is characterized in that: The mutation operation specifically includes: Generate 6 random numbers between 0 and 1, labeled rn1, rn2, rn3, rn4, rn5, rn6; If rn1 is greater than rn4, a multi-point non-uniform mutation operation is performed. The formula of the multi-point non-uniform mutation operation is specifically: If rn1 is less than or equal to rn4, a polynomial mutation operation is performed. The specific formula of the polynomial mutation operation is: Among them, t represents the number of iterations, G max represents the maximum number of iterations, bc represents the multi-point non-uniform variation parameter, P cd (t) represents the first population P before mutation I The cdth variable of the sth individual, P cd (t+1) represents the second population P after mutation I+1 The cdth variable of the sth individual, P cd LB Represents the first population P I The lower limit allowed, P cd UB Represents the first population P I The upper limit of the allowable cd LB Depend on Composition, P cd UB Depend on Composition, q represents the polynomial variation parameter, represents the intensity coefficient of random variation, δ max It represents the farthest distance of the individual from the boundary, and B(t) represents the mutation intensity under the remaining number of iterations.

6. The multi-objective operation optimization method for smart grids to defend against network attacks according to claim 1 is characterized in that: The step S5 includes the following sub-steps: S51: The second population P I+1 By {P s,I+1 ,s=1,2,…,NP}, P s,I+1 Represents the population P I+1 The sth individual in the second population P I+1 Whether all individuals in the group violate the constraints described in formula (6) to formula (14), and then calculate the cost performance according to formula (17); in, Indicates price / performance ratio, PF indicates the second population P I+1 The number of feasible solutions, NP represents the population size; S52: If the second population P I+1 All individuals in the are infeasible solutions. For the second population P I+1 The constraint violation amount of all individuals in the group is normalized, and the normalized constraint violation degree is calculated according to formula (18) to formula (25), and the corresponding constraint violation degree index is marked as H(P s,I+1 ); According to the degree of constraint violation, the first judgment method corresponding to formula (23) is used to judge the second population P I+1 The dominant relationship between any two individuals in the Marked as the first non-dominated individual P d,I+1 ; in, Indicates that in individual P s,I+1 The corresponding o1th constraint in the case is, Indicates that in individual P s,I+1 The corresponding constraint violation degree index of o1 in the case, o1 represents the sequence number of the constraint, δ represents the tolerance of constraint violation, s1 and s2 both represent P I+1 The number of individuals in the function, s1 = 1, 2, ..., NP, s2 = 1, 2, ..., NP, but s1 ≠ s2, d1 represents the number of the optimization objective function, d1 = 1, 2, 3, Indicates P I+1 The d1th optimization objective function corresponding to the s1th individual in , Indicates P I+1 The d1th optimization objective function corresponding to the s2th individual in , Indicates P I+1 The normalized index of the constraint violation degree corresponding to the s1th individual in , Indicates P I+1 The constraint violation degree normalized index corresponding to the s2th individual in , ε represents the maximum tolerance value of the constraint violation degree normalized index, ≤ ε represents the ε constraint dominance, Represents an individual For individuals Satisfy the ε constraint, represents any mathematical symbol, It means that when d1 takes any value among 1, 2, and 3, the corresponding relationship in formula (23) must be established, cp is the feedback coefficient, is the price / performance ratio, t is the current number of iterations, G max is the maximum number of iterations, rn7 is a randomly generated number in the range of 0 to 1; S53: If the second population P I+1 There are some feasible solutions in the memory. The evaluation method corresponding to formula (26) to formula (28) is used to evaluate all individual P s,I+1 ,s=1,2,…,NP corresponding optimization objective function Perform an evaluation to obtain a first evaluation result; based on the first evaluation result, use the first judgment method corresponding to formula (23) to determine the second population P I+1 The dominant relationship between any two individuals in the Marked as the second non-dominated individual P d,I+1 ; in, Represents individual P s,I+1 The corresponding d1th new optimization objective function, H(P s,I+1 ) represents individual P s,I+1 The corresponding normalized constraint violation degree, Represents individual P s,I+1 The corresponding d1th normalized optimization objective function, P fea,I+1 represents a feasible solution, Represents the population P I+1 The minimum function value of the d1th optimization objective function corresponding to the feasible solution, P mvol,I+1 Represents the population P I+1 The individual corresponding to the maximum value of the normalized index of constraint violation degree, Represents individual P mvol,I+1 The corresponding d1th optimization objective function value, For individual P s,I+1 The corresponding d1th optimization objective function value, ε represents the maximum tolerance value of the normalized constraint violation index, mk is the penalty coefficient, For cost-effectiveness; S54: If the second population P I+1 All are feasible solutions. The evaluation method corresponding to formula (29) is used to evaluate the second population P I+1 The dominant relationship of all individuals in the Labeled as the third non-dominated individual P d,I+1 ; in, Indicates P I+1 The d1th optimization objective function corresponding to the s1th individual in , Indicates P I+1 The d1th optimization objective function corresponding to the s2th individual in , Indicates P I+1 The d2th optimization objective function corresponding to the s1th individual in , Indicates P I+1 The d2th optimization objective function corresponding to the s2th individual, d1 and d2 both represent the sequence numbers of the optimization objective functions, d1 = 1, 2, 3, d2 = 1, 2, 3; A mathematical symbol that indicates existence.

7. The multi-objective operation optimization method for smart grids to defend against network attacks according to claim 1 is characterized in that: According to the maximum number of archives L of the external archive A max And the crowding distance sorting results, determine whether to use the second population P I+1 All non-dominated individuals in update the external archive A, including: If the maximum number of archives in the external archive A is L max Greater than the second population P I+1 The number of all non-dominated individuals in the second population P I+1 All non-dominated individuals in update the external archive A; If the maximum number of archives in the external archive A is L max Less than or equal to the second population P I+1 The number of all non-dominated individuals in the second population P I+1 In the above example, all non-dominated individuals are sorted by crowding distance, and the top L individuals in the most crowded position are left. max Individuals update external archive A.

8. The multi-objective operation optimization method for smart grids for defending against network attacks according to claim 7 is characterized in that: The process of the congestion distance sorting specifically includes: The current size of the external archive is marked as |A|, A(s) represents the sth individual in the external archive, and the three new optimization objective functions corresponding to all individuals in the external archive {A(s), s=1,2,…,|A|} are Sort in ascending order so that in, They represent the first, second and |A|th order numbers of the sorted index of the d1th optimization objective function, respectively. Indicates that the d1th optimization objective function value is sorted as The corresponding external archive individual; and The congestion distances are marked as and For s=2,…,|A|-1, calculate according to formula (30) crowding distance 9. A multi-objective operation optimization system for a smart grid for defending against network attacks, used to implement the multi-objective operation optimization method for a smart grid for defending against network attacks according to any one of claims 1 to 8, characterized in that: The system comprises: A building block for constructing a multi-objective operation optimization model of a smart grid that defends against cyber attacks and its constraints; A setting module, used for setting a plurality of first parameters; The first population initialization module is used to encode the optimization variables in the multi-objective operation optimization model of the smart grid to be optimized for defense against network attacks using a real number encoding method according to the first parameter, and to generate the first population P after iterating the initial population. I ; The second population generation module is used to record the number of iterations t. For the first population P of the tth iteration, I Each individual in the mutates one by one to generate the second population P I+1 ; A dominance relationship judgment module is used to determine the dominance relationship of the second population P I+1 The offspring individuals in the second population P are processed according to the control method of the constraint mechanism. I+1 The offspring individual constraints within the group are used to determine the degree of constraint violation and the second group P I+1 Dominance relationships among offspring individuals within a species; The archive module is used to extract the data from the second population P according to the dominance relationship. I+1 A non-dominated individual is randomly selected from the individuals, and the non-dominated individual is named P d , stored in the third population P n Used to update individuals in the next iteration, and at the same time, the second population P I+1 All non-dominated individuals are stored in the external archive A; Archive update module, for updating the data according to the second population P I+1 All non-dominated individuals and crowding distances in the external archive A are updated; The fourth group generation module is used to sort the external archive A in ascending order according to the crowding distance and select the top individuals, replacing the third population P n Randomly selected from individuals, forming a fourth population; and Iteration judgment module, used to judge whether the number of iterations t satisfies t≥G max If it is satisfied, all non-dominated individuals stored in the external archive A are output as the optimal Pareto solution set, and the Pareto optimal individual is selected according to the actual engineering requirements of the smart grid operation to obtain the optimization objective function value corresponding to the Pareto optimal individual; otherwise, set t = t + 1, unconditionally replace the next generation population with the fourth population, and return to the second population generation module to re-execute the iterative process.

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