FDIA defense micro-grid multi-objective economic-reliable-toughness optimization method and system

Abstract

The invention discloses a micro-grid multi-target economy-reliability-toughness optimization method and system capable of defending FDIA (Foreign Discrete Identity Analysis). According to the method, the number of security defense components for defending FDIA, the active output and voltage amplitude of a generator, the transformation ratio of a transformer, the reactive input of a reactive compensation device, the estimated power output of a wind power plant and the estimated power output of a photovoltaic power station are taken as optimization variables; the total economic cost minimization, the load loss rate minimization and the system toughness index minimization which are used for defending FDIA and guaranteeing safe operation of the micro-grid are used as three optimization objective functions respectively, power balance, optimization variable limitation and economic cost limitation are used as constraint conditions, and an efficient constraint multi-objective optimization method is designed for optimization solution. The trade-off optimization among the system operation economy, the power supply reliability and the system toughness of the microgrid under the FDIA is realized, and an important technical guarantee is provided for the safe, reliable and economical operation of the microgrid under the network attack condition.

Description

Technical Field

[0001] The present invention relates to the field of operation optimization technology in the field of microgrid system information security, and particularly relates to a multi-objective economic-reliable-resilient optimization method and system for a microgrid to defend against FDIA (False Data Injection Attack). Background Art

[0002] A microgrid is a single controllable unit that integrates various distributed power sources, loads, energy storage, and control devices, etc., and can effectively optimize the energy allocation of the power grid. The large-scale access of distributed energy to the power grid brings new challenges to the safe and stable operation of the power grid. With the rapid development of information and communication technologies, network attacks such as FDIA pose a great threat to the microgrid, which can not only cause load losses or electricity price adjustments, but even lead to serious hazards such as large-scale power outages. Therefore, how to minimize the power generation cost and defense cost, balance the power, ensure the safe operation, and guarantee the reliability of power supply to users and the power quality of the microgrid under the condition of FDIA is one of the important problems that need to be solved urgently in the current research on microgrids.

[0003] The security defense ability of the microgrid system is closely related to the number of buses under attack and the security defense components inserted on the buses, etc. Therefore, in the planning, design, and operation optimization of the microgrid system, it is necessary to conduct a detailed analysis of the defense situation of the security defense components in the system, and the following factors should be comprehensively considered: (1) the total economic cost of the microgrid including the power generation cost and the cost of defense components; (2) the load loss rate; (3) the resilience index function. However, the current technical research mainly focuses on the single-objective optimization of the above problems. The common method of assigning weight coefficients is used to perform weighted processing on multiple objectives and convert them into single-objective optimization or directly single-objective optimization. This method has challenges such as difficult to accurately set the weight coefficients and difficult to compromise and optimize the comprehensive performance. In addition, the optimization planning problems of various systems under attack mainly focus on the optimization of power generation cost and load loss, but rarely consider the resilience index of the power system under network attack. Therefore, how to optimally plan and design variables such as the number of security defense components for defending against FDIA in the microgrid system, the active output of generators, the voltage amplitude of generators, the transformation ratio of voltage regulating transformers, the reactive power input of reactive power compensation devices, the estimated power output of wind power plants, the estimated power output of photovoltaic power plants, etc., so as to efficiently realize the multi-objective economic-reliable-resilient optimization of the microgrid system and obtain the Pareto optimal solution that takes into account the system economic cost, load loss, and system resilience index has become one of the key technical problems that need to be solved urgently in the field of safe operation optimization of microgrid systems. Summary of the Invention

[0004] The object of the present invention is to provide a multi-objective economic-reliable-resilient optimization method and system for a microgrid against FDIA in view of the deficiencies of the prior art.

[0005] The object of the present invention is achieved by the following technical solutions: In the first aspect of the embodiments of the present invention, a multi-objective economic-reliable-resilient optimization method for a microgrid against FDIA is provided, including the following steps:

[0006] S1: Construct a multi-objective economic-reliable-resilient optimization model for a microgrid against FDIA and its constraint conditions;

[0007] S2: Set a plurality of first parameters;

[0008] S3: According to the first parameters, initialize the optimization variables in the multi-objective economic-reliable-resilient optimization model of the microgrid against FDIA to be optimized, and randomly generate a first population P of size N. M ;

[0009] S4: Set the initial value of the iteration number t to 1, record the iteration number t, and for each individual in the first population P in the t-th iteration, perform a crossover operation using the simulated binary crossover method one by one, and then perform a mutation operation using the polynomial mutation method to obtain a second population P. M ; M+1 ;

[0010] S5: Combine the offspring individuals in the second population P M+1 with the parent individuals in the first population P M to form a third population P of size 2N. R , process the individual constraints in the third population P R according to the dominance theory of the constraint mechanism, judge the degree of constraint violation and the dominance relationship between individuals in the third population P R , and perform non-dominated ranking;

[0011] S6: According to the non-dominated ranking relationship, sort the individuals in the third population P R in descending order of rank, and sequentially store the rank sets of the lower ranks into the fourth population S T , until the number of individuals in the fourth population S T |S T |≥N. At this time, the last non-dominated rank set in the fourth population S T is F l ; If the number of individuals in the fourth population S T |S T | = N, then put all the individuals in the fourth population S T into the next-generation population P t+1 ; If the fourth population S TThe number of | S T | > N, then the first (l - 1) non - dominated rank sets in the fourth population S T are put into the next - generation population, and the following reference - point - based selection operation is performed to screen out some individuals from the last non - dominated rank set F T in the fourth population S l and put them into the next - generation population P t+1 ;

[0012] S7: Standardize the objective functions of each individual in the fourth population S T and create the corresponding reference set;

[0013] S8: Create the mapping relationship between each individual in the fourth population S T and the reference points, calculate the occurrence times of each reference point in the first (l - 1) non - dominated rank sets of the fourth population S T , select the reference points with fewer occurrence times, and screen out the remaining next - generation population individuals from the last non - dominated rank set F T in the fourth population S l and put them into the next - generation population P t+1 , so that the number of the population reaches N;

[0014] S9: Judge whether the iteration number t satisfies t≥G max , where G max represents the maximum number of iterations. If t≥G max , then all non - dominated individuals stored in the updated next - generation population P t+1 are output as the optimal Pareto solution set. According to the actual engineering requirements of the micro - grid operation, select the Pareto - optimal individuals and obtain the corresponding optimized objective - function values, including the total system economic cost, load loss rate, and resilience index function value of the micro - grid; otherwise, set t = t + 1 and repeat steps S4 to S8.

[0015] Furthermore, the micro - grid multi - objective economic - reliable - resilient optimization model for defending FDIA includes the optimization objective functions shown in formulas (1) - (12):

[0016]

[0017] Clund z = Crsj×f s (wm < P Vz )×[P Vz - E(wm < P Vz )] (6)

[0018] Clover z= Cpsj × f s (wm > P Vz ) × [E(wm > P Vz ) - P Vz (7)

[0019]

[0020]

[0021] Among them, f1, f2, and f3 respectively represent the first, second, and third optimization objective functions. f1 is the total economic cost describing the defense against FDIA and ensuring the safe operation of the microgrid. f2 is the load demand loss rate of the microgrid. f3 is the resilience index function value of the microgrid system under FDIA. Q1 and Q2 respectively represent the procurement costs of the first and second types of security defense components. c1 and c2 respectively represent the operation costs of the first and second types of security defense components. represents the number of the first type of security defense components inserted in the ath k busbar under the false data injection attack. a k = A1, A2, …, A h , where A1, A2, …, A h respectively represent the first serial number, the second serial number, …, the Ath h serial number of the attacked busbar. represents the number of the second type of security defense components inserted in the ath k busbar under the false data injection attack. B G represents the number of generators connected to the system. P Yi represents the active power output of the ith generator. h i , n i , y i represent the fuel cost curve coefficients corresponding to the ith generator. Wgencost and Sgencost respectively represent the wind power generation cost and the photovoltaic power generation cost. P Wr represents the estimated power output of the rth wind power plant. N w is the number of wind power plants. Wgr represents the cost coefficient of the wind power plant. Wovest r , Wundest r respectively represent the reserve cost and the penalty cost of the rth wind power plant. Crwj and Cpwj respectively represent the reserve cost coefficient and the penalty cost coefficient of the wind power plant. NT represents the number of wind turbines in the wind power plant. P ra represents the rated power of the wind turbines in the wind power plant. qf and k respectively represent the scale factor and the shape factor in the Weibull probability density function used to describe the wind speed distribution. v out , v rand v in represent the cut-out wind speed, rated wind speed, and cut-in wind speed of the wind turbine respectively, wp represents the actual power output of the wind power plant, P Vz represents the estimated power output of the z-th photovoltaic power station, N p is the number of photovoltaic power stations, Sgr represents the cost coefficient of the photovoltaic power station, Clund z and Clover z represent the reserve cost and penalty cost of the z-th photovoltaic power station respectively, Crsj and Cpsj represent the reserve cost coefficient and penalty cost coefficient of the photovoltaic power station respectively, wm represents the actual power output of the photovoltaic power station, f s (wm < P Vz ) represents the probability value that the actual power output of the z-th photovoltaic power station is lower than the estimated power output, E(wm < P Vz ) represents the expected value that the actual power output of the z-th photovoltaic power station is lower than the estimated power output, f s (wm > P Vz ) represents the probability value that the actual power output of the z-th photovoltaic power station is higher than the estimated power output, E(wm > P Vz ) represents the expected value that the actual power output of the z-th photovoltaic power station is higher than the estimated power output, G std represents the solar irradiance under standard conditions, R c represents a certain specific irradiance point, P sr represents the rated power of the photovoltaic modules of the photovoltaic power station, G s represents the solar irradiance, B Total represents the total number of buses in the system, B U represents the number of buses suffering from FDIA, represents the load demand of bus s, L s represents the probability value of a successful FDIA attack on the s-th bus, T sc represents the probability value of a successful defense of FDIA by the sc-class defense component, Q sc represents the procurement cost of the sc-class security defense component, b sc represents the reliability of the sc-class security defense component, c sc represents the operating cost of the sc-class security defense component, d sc represents the cost of attacking the sc-class security defense component, t r represents the start time of the effect period of FDIA in the microgrid, t ce represents the start time of the after-event state of FDIA in the microgrid, D(t) represents the system performance of the microgrid at time t, D p represents the system performance of the microgrid before the occurrence of FDIA, t f represents the start time of the recovery period of the microgrid, tcf Indicates the start time when the microgrid is in the post - restoration state, D ce Indicates the system performance after the occurrence of FDIA in the microgrid. T1 and T2 respectively represent the probability values of the successful defense of FDIA by the first - type and second - type defense components;

[0022] The constraint conditions include the constraint conditions shown in formulas (13) to (24):

[0023]

[0024] θ mn = θ m - θ n (15)

[0025]

[0026] Among them, θ m Represents the voltage angle of the m - th bus, θ n Represents the voltage angle of the n - th bus, θ mn Represents the voltage angle difference between the m - th bus and the n - th bus, B Total Represents the total number of buses in the system, and Respectively represent the active power and reactive power of the m - th generator, and Respectively represent the active power and reactive power of the load on the m - th bus, V m Represents the voltage of the m - th bus, V[[ID= forty - three]] n Represents the voltage of the n - th bus, S mn Represents the conductance between the m - th bus and the n - th bus, A mn Represents the susceptance between the m - th bus and the n - th bus, and Respectively represent the lower limit and upper limit of the estimated power output of the r - th wind power plant, N w Is the number of wind power plants, and Respectively represent the lower limit and upper limit of the estimated power output of the z - th photovoltaic power station, N p Is the number of photovoltaic power stations, and Respectively represent the lower limit and upper limit of the active power output of the i - th generator, B G Is the total number of generators in the system, and Respectively represent the lower limit and upper limit of the voltage amplitude of the i - th generator, O fe Represents the turns ratio of the e - th voltage regulating transformer on the branch, and respectively represent the lower and upper limits of the transformation ratio of the e-th voltage regulating transformer on the branch, N T is the total number of voltage regulating transformers, Q ml represents the reactive power input by the l-th reactive power compensation device, and respectively represent the lower and upper limits of the reactive power input by the l-th reactive power compensation device, N C is the total number of reactive power compensation devices, and respectively represent the lower and upper limits of the number of the first type of security defense components inserted in the a k th bus under false data injection attack, and respectively represent the lower and upper limits of the number of the second type of security defense components inserted in the a k th bus under false data injection attack, a k = A1, A2, …, A h , where A1, A2, …, A h respectively represent the first serial number, the second serial number, …, the A h th serial number of the attacked bus, and respectively represent the number of the first type and the second type of security defense components inserted in the a k th bus under false data injection attack, Q1 and Q2 respectively represent the procurement costs of the first type and the second type of security defense components, c1 and c2 respectively represent the operating costs of the first type and the second type of security defense components, Dcost max represents the upper limit of the FDIA security defense cost.

[0027] Furthermore, the first parameter includes the procurement cost Q1 of the first type of security defense component, the operating cost c1 of the first type of security defense component, the reliability b1 of the first type of security defense component, the cost d1 spent on attacking the first type of security defense component, the procurement cost Q2 of the second type of security defense component, the operating cost c2 of the second type of security defense component, the reliability b2 of the second type of security defense component, the cost d2 spent on attacking the second type of security defense component, the maximum number of iterations G max , the population size N, the cost coefficient Wgr of the wind power plant, the reserve cost coefficient Crwj of the wind power plant, the penalty cost coefficient Cpwj of the wind power plant, the number NT of wind turbines in the wind power plant, the rated power P of the wind turbines in the wind power plant ra , the scale factor qf in the Weibull probability density function used to describe the wind speed distribution, the shape factor k in the Weibull probability density function used to describe the wind speed distribution, the cut-out wind speed v of the wind turbine out , the rated wind speed v of the wind turbiner , the cut-in wind speed v of the wind turbine in , the cost coefficient Sgr of the photovoltaic power station, the reserve cost coefficient Crsj of the photovoltaic power station, the penalty cost coefficient Cpsj of the photovoltaic power station, the solar irradiance G under standard conditions std , a specific irradiance point R c , the rated power P of the photovoltaic modules of the photovoltaic power station sr , the distribution factor η in the binary crossover method, the polynomial mutation distribution index λ, the number of segments MF on each target, and the upper limit Dcost of the FDIA security defense cost max .

[0028] Furthermore, initialize the optimization variables in the microgrid multi-objective economic-reliable-resilient optimization model for the defense FDIA to be optimized, and randomly generate the first population P with a size of N M , specifically including:

[0029] Randomly generate the first population P with a size of N M = {P u , u = 1, 2, …, N}, where P M represents the initial population, P u represents the u-th individual, N represents the population size, and the u-th individual represents the estimated power output of the 1st, …, N-th w wind power plants corresponding to the u-th individual, N w is the number of wind power plants, represents the estimated power output of the 1st, …, N-th p photovoltaic power stations corresponding to the u-th individual, N p is the number of photovoltaic power stations, represents the active power output of the 2nd, …, B-th G generators corresponding to the u-th individual, B G is the total number of generators in the system, represents the voltage amplitude of the 1st, …, B-th G generators corresponding to the u-th individual, represents the transformation ratio of the 1st, …, N-th T voltage regulating transformers on the branch corresponding to the u-th individual, N T is the total number of voltage regulating transformers, represents the reactive power input by the 1st, …, N-th C reactive power compensation devices corresponding to the u-th individual, N C is the total number of reactive power compensation devices, represents the a-thk The insertion number of the first type of security defense components in the mth busbars, k representing the insertion number of the second type of security defense components in the k mth busbars, a h = A1, A2, …, A h respectively representing the first serial number, the second serial number, …, the h Ath serial number of the attacked busbars, and rounding it to the nearest integer.

[0030] Furthermore, the crossover operation is implemented by using the simulated binary crossover method, which specifically includes:

[0031] First, randomly generate a random number rn1 within the range of 0 to 1;

[0032] Then, implement the crossover operation by using the simulated binary crossover method, and its formula is specifically:

[0033]

[0034] where t represents the iteration number, P1(t) represents the first N / 2 individuals in the first population P M before crossover, P2(t) represents the last N / 2 individuals in the first population P M before crossover, P1(t + 1) represents the first N / 2 individuals in the first population P M after crossover, and P2(t + 1) represents the last N / 2 individuals in the first population P M after crossover, β represents the propagation factor in the binary crossover method, and η represents the distribution factor in the binary crossover method;

[0035] The mutation operation is performed by using the polynomial mutation method, which specifically includes:

[0036] First, randomly generate a random number rn2 within the range of 0 to 1;

[0037] Then, perform the mutation operation by using the polynomial mutation method, and its formula is specifically:

[0038]

[0039] where P em (t) represents the emth variable of the uth individual in the first population P M before mutation, and P em (t + 1) represents the emth variable of the uth individual in the second population P M+1 after mutation, and P em LKDenote the first population \(P\) M The allowable lower limit of the \(em\)-th variable of the \(u\)-th individual, \(P\) em LK Composed of , \(P\) em UK Denote the first population \(P\) M The allowable upper limit of the \(em\)-th variable of the \(u\)-th individual, \(P\) em UK Composed of , where \(\delta\) represents the polynomial mutation factor and \(\lambda\) represents the polynomial mutation distribution index.

[0040] Furthermore, the step S5 specifically includes the following sub-steps:

[0041] S51: Merge the offspring individuals in the second population \(P\) M+1 with the parent individuals in the first population \(P\) M to form a third population \(P\) R with a size of \(2N\), where the third population \(P\) R is composed of \(\{P\) u,R , \(u = 1, 2, \cdots, 2N\}\), and \(P\) u,R represents the \(u\)-th individual in the third population \(P\) R ; Determine whether all individuals in the third population \(P\) R violate the constraint conditions shown in formulas (13) to (24);

[0042] S52: Calculate the constraint violation amounts of all individuals \(\{P\) R , \(u = 1, 2, \cdots, 2N\}\) in the third population \(P\) u,R according to formulas (27) to (30) to obtain the corresponding constraint violation degree \(W(P\) u,R ):

[0043] \(W(P\) u,R ) = |L1(P\) u,R )| + |L2(P\) u,R )| + <L3(P\) u,R )> (27)

[0044]

[0045] Among them, represents the \(z1\)-th constraint corresponding to the case of individual \(P\) u,R , \(z1\) represents the serial number of the constraint, \(z1 = 1, 2, 3\), and \(W(P\) u,R ) represents the constraint violation degree index corresponding to individual \(P\) u,R , represents the absolute value of the \(z1\)-th constraint corresponding to the case of individual \(P\) u,R ​ Denote the negative of the z1-th constraint corresponding to the case of individual P u,R If then let

[0046] S53: According to the degree of constraint violation, use the first judgment method shown in formula (31) to judge the dominance relationship between any two individuals R in the third population P and :

[0047]

[0048] wherein, denotes the degree of constraint violation corresponding to the u1-th individual in the third population P R ; denotes the degree of constraint violation corresponding to the u2-th individual in the third population P R ; denotes the su1-th optimization objective function corresponding to the u1-th individual in the third population P R ; denotes the su1-th optimization objective function corresponding to the u2-th individual in the third population P R ; denotes the su2-th optimization objective function corresponding to the u1-th individual in the third population P R ; denotes the su2-th optimization objective function corresponding to the u2-th individual in the third population P R , su1 and su2 both represent the serial numbers of the optimization objective functions, su1 = 1, 2, 3, su2 = 1, 2, 3; denotes the existing mathematical symbol;

[0049] S54: Classify all individuals in the third population P R according to the first judgment method in step S53 for non-dominated ranking, specifically: classify all solutions that are not dominated by other solutions into the first front; from the remaining solutions, select those solutions that are not dominated by any solution in the first front and classify them into the second front; then from the remaining solutions, select those solutions that are not dominated by the solutions in the first and second fronts and classify them into the third front; and so on until all solutions are assigned to a certain front.

[0050] Furthermore, in step S7, normalizing the objective functions of each individual in the fourth population S T specifically includes:

[0051] First, traverse each objective of all individuals in the fourth population S T to find the minimum value of each objective, and form the ideal point ip, whose coordinates are Among them respectively represent the minimum values of the first, second, and third objective functions in the fourth population S T ;

[0052] Then, subtract the objective values of all individuals in the fourth population S T from the objective values of the ideal point to obtain the relative objective value coordinates i.e., (f1'(x), f2'(x), f3'(x)), where f1 fd , f2 fd , f3 fd respectively represent the first, second, and third objective function values of the fd-th individual in the fourth population S T , and x represents the individual in the fourth population S T after the objective function numerical transformation of the ideal point;

[0053] Then, find the extreme points of the fourth population S T according to formulas (32) - (33) whose coordinates are respectively denoted as (D1, G1, I1), (D2, G2, I2), (D3, G3, I3):

[0054]

[0055] Among them, f’ ms (x) represents the ms-th objective function value of the individual x in the fourth population S T after the objective function numerical transformation of the ideal point, ms represents the serial number of the objective, ms = 1, 2, 3, and w ms represents the standard vector of the ms-th objective;

[0056] Finally, substitute the coordinates (D1, G1, I1), (D2, G2, I2), (D3, G3, I3) into the intercept form plane formula (34) to obtain the plane equation formed and the intercepts a1, a2, a3 of the three objective axes x, y, z and the three extreme points forming a linear hyperplane, and normalize the relative objective values of all individuals in the fourth population S T according to formula (35) to obtain the normalized objective values:

[0057]

[0058] Among them, represents the normalized objective value obtained after normalizing the relative objective value of the fd-th individual in the fourth population S T , and ms represents the serial number of the objective.

[0059] Furthermore, in step S7, creating a corresponding reference set specifically includes:

[0060] First construct the two-dimensional x vj Combination of, get the initial point J x ,in j=1,2,J x =(x v1 , x v2 ), x v1 <x v2 , MF is the number of segments on each target, v is the number of reference set points;

[0061] Then, for the above initial points, operate according to formula (36) to formula (37) and obtain the target value s of each reference point vj , that is, the coordinates of the reference point (s v1 , s v2 , s v3 ):

[0062]

[0063]

[0064] Furthermore, the step S8 specifically includes the following sub-steps:

[0065] S81: Construct a ray reference line between each reference point and the origin, and divide the fourth group S T The mapping relationship between each individual and each reference point is constructed to obtain the distance between each individual and each reference point ray Get the reference point Cm with the minimum distance between individuals in each population sk , calculate the minimum distance Ce between each population individual and the reference point sk , where sk represents the fourth population S T The number of individuals in , v represents the number of reference points;

[0066] S82: Set the fourth population S T The last non-dominated level set F in l The initial value of km, the number of populations that have been selected into the next generation, is 1. It is determined whether km≤lc is satisfied, where lc is the fourth population S T The last non-dominated level set F in l The number of individuals that should be screened into the next generation population, if km≤lc is not satisfied, then execute step S9; if km≤lc is satisfied, then execute step S83;

[0067] S83: Calculate each reference point in the fourth group S TThe occurrence times ld in the first (l - 1) non - dominated rank sets v , take ld v The reference point corresponding to the minimum value is put into the set P qr , in the set P qr , randomly select a set point qr;

[0068] S84: Determine whether there is an individual in the last non - dominated rank set F T in the fourth population S l such that among the distances from all reference points, the distance from the set point qr is the shortest. If there is no such individual, delete the set point qr from the reference set, jump to step S83, and re - select the set P qr to screen the set points in it; if there is such an individual, put the above - mentioned individual that meets the conditions into the set P lj , at this time, judge the value ld corresponding to the set point qr v whether it is equal to 0. If ld v = 0, select the individual with the shortest distance from the set point qr in the set P lj and put it into the next - generation population P t+1 ; otherwise, randomly select an individual from the set P lj and put it into the next - generation population P t+1 ;

[0069] S85: Put the individual into the next - generation population P t+1 After that, delete the individual from the last non - dominated rank set F T in the fourth population S l , and it will no longer participate in the subsequent screening. km = km + 1, continue the screening, and repeat steps S82 to S84.

[0070] In the second aspect of the embodiments of the present invention, a micro - grid multi - objective economic - reliable - resilient optimization system for defending against FDIA is provided. It is built - in with the above - mentioned micro - grid multi - objective economic - reliable - resilient optimization method for defending against FDIA. The system includes:

[0071] A construction module for constructing a micro - grid multi - objective economic - reliable - resilient optimization model for defending against FDIA and its constraint conditions;

[0072] A setting module for setting multiple first parameters;

[0073] A first - population initialization module for initializing the optimization variables in the micro - grid multi - objective economic - reliable - resilient optimization model for defending against FDIA to be optimized according to the first parameters, and randomly generating a first population P with a size of N M ;

[0074] The second population generation module is used to set the initial value of the iteration number t to 1, record the iteration number t, and perform a crossover operation on each individual in the first population P M in the t-th iteration one by one using the simulated binary crossover method, and then perform a mutation operation using the polynomial mutation method to obtain the second population P M+1 ;

[0075] The dominance relationship judgment module is used to merge the offspring individuals in the second population P M+1 with the parent individuals in the first population P M to form a third population P R with a size of 2N, and process the individual constraints in the third population P R according to the dominance theory of the constraint mechanism, judge the degree of constraint violation and the dominance relationship between individuals in the third population P R to perform non-dominated ranking;

[0076] The individual screening module is used to sort the individuals in the third population P R according to the non-dominated ranking relationship, store the low-level rank sets in the fourth population S T in sequence until the number of individuals in the fourth population S T |S T |≥N. At this time, the last non-dominated rank set in the fourth population S T is F l ; if the number of individuals in the fourth population S T |S T | = N, then all individuals in the fourth population S T are put into the next-generation population P t+1 ; if the number of individuals in the fourth population S T |S T | > N, then the first (l - 1) non-dominated rank sets in the fourth population S T are put into the next-generation population, and the following reference-point-based selection operation is performed to screen out some individuals in the last non-dominated rank set F T in the fourth population S l and put them into the next-generation population P t+1 ;

[0077] The normalization module is used to normalize the objective functions of each individual in the fourth population S T and create a corresponding reference set;

[0078] The mapping relationship screening module is used to create the mapping relationship between each individual in the fourth population S T and the reference points, and calculate each reference point in the fourth population S TThe number of occurrences in the first (l - 1) non - dominated rank sets, select the reference point with fewer occurrences, and from the fourth population S T select the remaining individuals of the next - generation population from the last non - dominated rank set F l in it, and put them into the next - generation population P t+1 to make the number of the population reach N; and

[0079] An iteration judgment module, used to judge whether the iteration number t satisfies t≥G max where G max represents the maximum number of iterations. If t≥G max is satisfied, then all non - dominated individuals stored in the updated next - generation population P t+1 are output as the optimal Pareto solution set. Select the Pareto - optimal individuals according to the actual engineering requirements of the micro - grid operation, and obtain the values of the optimization objective functions corresponding to the Pareto - optimal individuals, including the total economic cost of the micro - grid system, the load loss rate, and the resilience index function value; otherwise, set t = t + 1, and repeat the execution from the second - population generation module to the mapping - relationship screening module.

[0080] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention comprehensively considers three objective functions of defending against FDIA and ensuring the total economic cost, load loss rate, and resilience index function of the safe operation of the micro - grid, designs a multi - objective economic - reliable - resilient optimization method for the micro - grid to defend against FDIA, and realizes the trade - off optimization among the system operation economy, power supply reliability, and system resilience of the micro - grid under FDIA; the present invention has more satisfactory optimization performance in the optimal trade - off among system resilience, load loss, and economic indicators, and provides an important technical guarantee for the safe, reliable, and economic operation of the micro - grid in the case of being attacked by a cyber - attack. Brief Description of the Drawings

[0081] Figure 1 is a schematic diagram of the topological structure of a 30 - node micro - grid system in an embodiment of the present invention;

[0082] Figure 2 is a flowchart of the multi - objective economic - reliable - resilient optimization method for the micro - grid to defend against FDIA of the present invention;

[0083] Figure 3 is the optimal Pareto - front graph obtained after iterative optimization of the present invention;

[0084] Figure 4 is a schematic structural diagram of a multi - objective economic - reliable - resilient optimization system for the micro - grid to defend against FDIA of the present invention. Detailed Embodiment

[0085] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0086] This embodiment will be specifically described in combination with a 30-node microgrid system. Figure 1 It is a schematic diagram of the topological structure of a 30-node microgrid system, including 1 wind power plant, 1 photovoltaic power station, and 3 thermal generators.

[0087] In this embodiment, false data injection attacks are simulated. The goal of the implemented attacks is to bypass bad data detection and maximize the load loss and generation cost of the microgrid through false scheduling information, thereby causing safety problems or physical damage. In this embodiment, it is assumed that in the 30-node microgrid system, the 2nd, 5th, 7th, 8th, and 21st buses are subject to false data injection attacks, and the attack locations are the voltages, angles, and load demands of the 2nd, 5th, 7th, 8th, and 21st buses.

[0088] See Figure 2 , the multi-objective economic-reliable-resilient optimization method for a microgrid to defend against FDIA specifically includes the following steps:

[0089] S1: Construct a multi-objective economic-reliable-resilient optimization model for a microgrid to defend against FDIA and its constraint conditions.

[0090] Furthermore, the multi-objective economic-reliable-resilient optimization model for a microgrid to defend against FDIA includes optimization objective functions as shown in formulas (1) to (12):

[0091]

[0092]

[0093] Clund z = Crsj × f s (wm < P Vz ) × [P Vz - E(wm < P Vz )] (6)

[0094] Clover z = Cpsj × f s (wm > P Vz ) × [E(wm > P Vz ) - P Vz (7)

[0095]

[0096] Among them, f1, f2, and f3 respectively represent the first, second, and third optimization objective functions. f1 is the total economic cost describing the defense against FDIA and ensuring the safe operation of the microgrid. f2 is the load demand loss rate of the microgrid. f3 is the resilience index function value of the microgrid system under FDIA. Q1 and Q2 respectively represent the procurement costs of the first and second types of security defense components. c1 and c2 respectively represent the operating costs of the first and second types of security defense components. represents the number of the first type of security defense components inserted in the ath k busbars under false data injection attack, where a k = A1, A2, …, A h and among them, A1, A2, …, A h respectively represent the first serial number, the second serial number, …, the Ath h serial number of the attacked busbars. represents the number of the second type of security defense components inserted in the ath k busbars under false data injection attack, B G represents the number of generators connected to the system, P Yi represents the active power output of the ith generator, h i , n i , y i represent the fuel cost curve coefficients corresponding to the ith generator. Wgencost and Sgencost respectively represent the wind power generation cost and the photovoltaic power generation cost. P Wr represents the estimated power output of the rth wind power plant, N w is the number of wind power plants. Wgr represents the cost coefficient of the wind power plant. Wovest r , Wundest r respectively represent the reserve cost and the penalty cost of the rth wind power plant. Crwj and Cpwj respectively represent the reserve cost coefficient and the penalty cost coefficient of the wind power plant. NT represents the number of wind turbines in the wind power plant. P ra represents the rated power of the wind turbines in the wind power plant. qf and k respectively represent the scale factor and the shape factor in the Weibull probability density function used to describe the wind speed distribution. v out , v r , and v in respectively represent the cut-out wind speed, the rated wind speed, and the cut-in wind speed of the wind turbine. wp represents the actual power output of the wind power plant. P Vz represents the estimated power output of the zth photovoltaic power station, N p is the number of photovoltaic power stations. Sgr represents the cost coefficient of the photovoltaic power station. Clund zand Clover z respectively represent the reserve cost and penalty cost of the z-th photovoltaic power station. Crsj and Cpsj respectively represent the reserve cost coefficient and penalty cost coefficient of the photovoltaic power station. wm represents the actual power output of the photovoltaic power station, f s (wm < P Vz ) represents the probability value that the actual power output of the z-th photovoltaic power station is lower than the estimated power output. E(wm < P Vz ) represents the expected value that the actual power output of the z-th photovoltaic power station is lower than the estimated power output. f s (wm > P Vz ) represents the probability value that the actual power output of the z-th photovoltaic power station is higher than the estimated power output. E(wm > P Vz ) represents the expected value that the actual power output of the z-th photovoltaic power station is higher than the estimated power output. G std represents the solar irradiance under standard conditions. R c represents a specific irradiance point. P sr represents the rated power of the photovoltaic modules of the photovoltaic power station. G s represents the solar irradiance. B Total represents the total number of buses in the system. B U represents the number of buses suffering from FDIA. represents the load demand of bus s. L s represents the probability value of a successful FDIA attack on the s-th bus. T sc represents the probability value of the sc-class defense component successfully defending against FDIA. Q sc represents the procurement cost of the sc-class security defense component. b sc represents the reliability of the sc-class security defense component. c sc represents the operating cost of the sc-class security defense component. d sc represents the cost of attacking the sc-class security defense component. t r represents the start time of the effect period of FDIA in the microgrid. t ce represents the start time of the after-event state of FDIA in the microgrid. D(t) represents the system performance of the microgrid at time t. D p represents the system performance of the microgrid before the occurrence of FDIA. t f represents the start time of the recovery period of the microgrid. t cf represents the start time of the post-recovery state of the microgrid. D ce represents the system performance of the microgrid after the occurrence of FDIA. T1 and T2 respectively represent the probability values of the first-class and second-class defense components successfully defending against FDIA.

[0097] Furthermore, the constraint conditions include the constraint conditions shown in Formulas (13) to (24):

[0098]

[0099] θ mn = θ m - θ n (15)

[0100]

[0101] where θ m represents the voltage angle of the m-th bus, θ n represents the voltage angle of the n-th bus, and θ mn represents the voltage angle difference between the m-th bus and the n-th bus. B Total represents the total number of buses in the system, and respectively represent the active power and reactive power of the m-th generator, and respectively represent the active power and reactive power of the load on the m-th bus. V m represents the voltage of the m-th bus, and V n represents the voltage of the n-th bus. S mn represents the conductance between the m-th bus and the n-th bus. A mn represents the susceptance between the m-th bus and the n-th bus, and respectively represent the lower limit and upper limit of the estimated power output of the r-th wind power plant. N w is the number of wind power plants, and respectively represent the lower limit and upper limit of the estimated power output of the z-th photovoltaic power station. N p is the number of photovoltaic power stations, and respectively represent the lower limit and upper limit of the active power output of the i-th generator. B G is the total number of generators in the system, and respectively represent the lower limit and upper limit of the voltage amplitude of the i-th generator. O fe represents the turns ratio of the e-th voltage regulating transformer on the branch, and respectively represent the lower limit and upper limit of the turns ratio of the e-th voltage regulating transformer on the branch. N T is the total number of voltage regulating transformers. Q ml represents the reactive power input by the l-th reactive power compensation device, and Respectively represent the lower limit and upper limit of the reactive power input by the first reactive compensation device, N C is the total number of reactive power compensation devices, and They represent the number of attacks by false data injection k The lower and upper limits of the number of Class 1 security defense components installed in a bus, and They represent the number of attacks by false data injection k The lower and upper limits of the number of Class 2 security defense components installed in a busbar, a k =A1,A2,…,A h , where A1, A2, …, A h They represent the first serial number, the second serial number, ..., the A serial number of the attacked busbar respectively. h Serial number, and They represent the number of attacks by false data injection k The number of Class 1 and Class 2 security defense components installed in the bus, Q1 and Q2 represent the purchase cost of Class 1 and Class 2 security defense components, c1 and c2 represent the operating cost of Class 1 and Class 2 security defense components, Dcost max Indicates the upper limit of FDIA security defense costs.

[0102] S2: Set multiple first parameters.

[0103] In this embodiment, the first parameter includes the purchase cost Q1 of the first type of security defense component, the operating cost c1 of the first type of security defense component, the reliability b1 of the first type of security defense component, the cost d1 of attacking the first type of security defense component, the purchase cost Q2 of the second type of security defense component, the operating cost c2 of the second type of security defense component, the reliability b2 of the second type of security defense component, the cost d2 of attacking the second type of security defense component, and the maximum number of iterations G. max , population size N, wind power plant cost coefficient Wgr, wind power plant reserve cost coefficient Crwj, wind power plant penalty cost coefficient Cpwj, the number of wind turbines in the wind power plant NT, the rated power of wind turbines in the wind power plant P ra , describing the wind speed distribution using the scale factor qf in the Weibull probability density function, describing the wind speed distribution using the shape factor k in the Weibull probability density function, and the cut-out wind speed v of the wind turbine out , rated wind speed v of the wind turbine r , wind turbine cut-in wind speed v in, the cost coefficient Sgr of the photovoltaic power station, the reserve cost coefficient Crsj of the photovoltaic power station, the penalty cost coefficient Cpsj of the photovoltaic power station, the solar irradiance G under standard conditions std , a specific irradiance point R c , the rated power P of the photovoltaic modules of the photovoltaic power station sr , the distribution factor η in the binary crossover method, the polynomial mutation distribution index λ, the number of segments MF on each target, and the upper limit Dcost of the FDIA security defense cost max .

[0104] It should be noted that the first parameter can be set according to the actual situation. For example, in this embodiment, the above first parameter is set as Q1 = 239.52, c1 = 143.71, b1 = 0.75, d1 = 209.58, Q2 = 958.08, c2 = 86.23, b2 = 0.90, d2 = 838.32, G max = 500, N = 200, Wgr = 1.7, Crwj = 3, Cpwj = 1.5, NT = 25, P ra = 3, qf = 9, k = 2, v out = 25, v r = 16, v in = 3, Sgr = 1.6, Crsj = 3, Cpsj = 1.5, G std = 1000, R c = 120, P sr = 50, η = 20, λ = 20, MF = 18, Dcost max = 6947.

[0105] S3: According to the first parameter, initialize the optimization variables in the microgrid multi-objective economic-reliable-resilient optimization model of the defense FDIA to be optimized, and randomly generate the first population P with a size of N M .

[0106] Specifically, randomly generate the first population P with a size of N M = {P u , u = 1, 2,..., N}, where P M represents the initial population, P u represents the u-th individual, N represents the population size, and the u-th individual represents the estimated power output of the 1st,..., Nth w wind power plants corresponding to the u-th individual, N w is the number of wind power plants, represents the 1st,..., Nth pEstimated power output of a photovoltaic power station, N p is the number of photovoltaic power stations, denotes the active power output of the 2nd, …, Bth G generators corresponding to the uth individual, B G is the total number of generators in the system, denotes the voltage amplitudes of the 1st, …, Bth G generators corresponding to the uth individual, denotes the transformation ratios of the 1st, …, Nth T voltage regulating transformers on the branch corresponding to the uth individual, N T is the total number of voltage regulating transformers, denotes the reactive power input by the 1st, …, Nth C reactive power compensation devices corresponding to the uth individual, N C is the total number of reactive power compensation devices, denotes the number of inserted 1st type security defense components in the ath k busbars attacked by false data injection corresponding to the uth individual, denotes the number of inserted 2nd type security defense components in the ath k busbars attacked by false data injection corresponding to the uth individual, a k = A1, A2, …, A h , where A1, A2, …, A h respectively denote the 1st serial number, 2nd serial number, …, Ath h serial number of the attacked busbars, and round to the nearest integer.

[0107] S4: Set the initial value of the iteration number t to 1, record the iteration number t, and for each individual in the first population P M in the tth iteration, perform crossover operations one by one using the simulated binary crossover method, and then perform mutation operations using the polynomial mutation method to obtain the second population P M+1 .

[0108] Furthermore, performing crossover operations using the simulated binary crossover method specifically includes:

[0109] First, randomly generate a random number rn1 within the range of 0 to 1;

[0110] Then perform crossover operations using the simulated binary crossover method, and its formula is specifically:

[0111]

[0112] where t represents the iteration number, and P1(t) represents the first population P before crossover MThe first N / 2 individuals in the population, and P2(t) represents the first population P before crossover. M The last N / 2 individuals in the population, and P1(t + 1) represents the first population P after crossover. M The first N / 2 individuals in the population, and P2(t + 1) represents the first population P after crossover. M The last N / 2 individuals in the population, β represents the propagation factor in the binary crossover method, and η represents the distribution factor in the binary crossover method.

[0113] Furthermore, the polynomial mutation method is adopted for the mutation operation, which specifically includes:

[0114] First, randomly generate a random number rn2 within the range of 0 to 1.

[0115] Then, adopt the polynomial mutation method for the mutation operation, and its formula is specifically:

[0116]

[0117] Among them, P em (t) represents the first population P before mutation M The em-th variable of the u-th individual in the population, and P em (t + 1) represents the second population P after mutation M+1 The em-th variable of the u-th individual in the population, and P em LK Represents the first population P M The lower limit allowed for the em-th variable of the u-th individual in the population, and P em LK Consists of P em UK Represents the first population P M The upper limit allowed for the em-th variable of the u-th individual in the population, and P em UK Consists of δ represents the polynomial mutation factor, and λ represents the polynomial mutation distribution index.

[0118] S5: Merge the offspring individuals in the second population P M+1 with the parent individuals in the first population P M to form a third population P with a size of 2N R , and process the individual constraints in the third population P R according to the domination theory of the constraint mechanism, judge the degree of constraint violation and the domination relationship between individuals in the third population P R to perform non-dominated ranking.

[0119] Specifically, step S5 includes the following sub-steps:

[0120] S51: Combine the offspring individuals in the second population P M+1 with the parent individuals in the first population P M to form a third population P with a size of 2N R , where the third population P R consists of {P u,R , u = 1, 2, …, 2N}, and P u,R represents the u-th individual in the third population P R ; determine whether all individuals in the third population P R violate the constraint conditions shown in formulas (13) to (24).

[0121] S52: Calculate the constraint violation amounts for all individuals {P R , u = 1, 2, …, 2N} in the third population P u,R according to formulas (27) to (30) to obtain the corresponding constraint violation degree W(P u,R ):

[0122] W(P u,R ) = |L1(P u,R )| + |L2(P u,R )| + <L3(P u,R )> (27)

[0123]

[0124]

[0125] where represents the z1-th constraint corresponding to the case of individual P u,R , z1 represents the serial number of the constraint, z1 = 1, 2, 3, and W(P u,R ) represents the constraint violation degree index corresponding to individual P u,R , represents the absolute value of the z1-th constraint corresponding to the case of individual P u,R , represents the opposite number of the z1-th constraint corresponding to the case of individual P u,R , if then let

[0126] S53: According to the constraint violation degree, use the first judgment method shown in formula (31) to judge the dominance relationship between any two individuals R in the third population P and :

[0127]

[0128] Among them, represents the degree of constraint violation corresponding to the u1-th individual in the third population P R ; represents the degree of constraint violation corresponding to the u2-th individual in the third population P R ; represents the su1-th optimization objective function corresponding to the u1-th individual in the third population P R ; represents the su1-th optimization objective function corresponding to the u2-th individual in the third population P R ; represents the su2-th optimization objective function corresponding to the u1-th individual in the third population P R ; represents the su2-th optimization objective function corresponding to the u2-th individual in the third population P, where su1 and su2 both represent the serial numbers of the optimization objective functions, su1 = 1, 2, 3, and su2 = 1, 2, 3; R represents the existing mathematical symbol.

[0129] S54: Perform non-dominated ranking on all individuals in the third population P R according to the first judgment method in step S53, specifically: classify all solutions that are not dominated by other solutions into the first front; from the remaining solutions, select those solutions that are not dominated by any solution in the first front and classify them into the second front; then from the remaining solutions, select those solutions that are not dominated by the solutions in the first and second fronts and classify them into the third front; and so on until all solutions are assigned to a certain front.

[0130] S6: According to the non-dominated ranking relationship, sort the individuals in the third population P R in ascending order of their ranks, and sequentially store the rank sets of lower ranks into the fourth population S T , until the number of individuals in the fourth population S T |S T | ≥ N. At this time, the last non-dominated rank set in the fourth population S T is F l ; if the number of individuals in the fourth population S T |S T | = N, then put all individuals in the fourth population S T into the next-generation population P t+1 ; if the number of individuals in the fourth population S T |S T | > N, then put the first (l - 1) non-dominated rank sets in the fourth population S T into the next-generation population and perform the following reference-point-based selection operation to screen out the last non-dominated rank set F in the fourth population S T ​l Put some individuals in the next-generation population P t+1 .

[0131] S7: Standardize each individual's objective function in the fourth population S T and create a corresponding reference set.

[0132] Furthermore, standardize each individual's objective function in the fourth population S T , specifically including:

[0133] First, traverse each objective of all individuals in the fourth population S T to find the minimum value of each objective, and form the ideal point ip, whose coordinates are where represent the minimum values of the 1st, 2nd, and 3rd objective functions in the fourth population S T respectively.

[0134] Then subtract the objective value of the ideal point from each objective value of all individuals in the fourth population S T to obtain the relative objective value coordinates , that is, (f1'(x), f2'(x), f3'(x)), where f1<( fd , f2 fd , f3 fd represent the 1st, 2nd, and 3rd objective function values of the fd-th individual in the fourth population S T respectively, and x represents the individual in the fourth population S T after the objective function value transformation of the ideal point.

[0135] Then, according to formulas (32) - (33), find the extreme points T of the fourth population S whose coordinates are denoted as (D1, G1, I1), (D2, G2, I2), (D3, G3, I3) respectively:[[]]

[0136]

[0137] where, f’ ms (x) represents the ms-th objective function value of the individual x in the fourth population S T after the objective function value transformation of the ideal point, ms represents the serial number of the objective, ms = 1, 2, 3, and w ms represents the standard vector of the ms-th objective. In this embodiment, w1 = (1, 10 -6 , 10 -6 ), w2 = (10 -6 , 1, 10 -6 ), w3 = (10 -6 , 10 -6, 1).

[0138] Finally, substitute the coordinates (D1, G1, I1), (D2, G2, I2), (D3, G3, I3) of into the intercept form plane formula (34) to obtain the plane equation formed and the intercepts a1, a2, a3 of the linear hyperplane formed by the three objective axes x, y, z and the three extreme points And normalize the relative objective values of all individuals in the fourth population S T according to formula (35) to obtain the normalized objective values:

[0139]

[0140] where represents the normalized objective value obtained after normalizing the relative objective value of the fd-th individual in the fourth population S T , and ms represents the serial number of the objective.

[0141] Furthermore, create the corresponding reference set, specifically including:

[0142] First, construct the combination of two-dimensional x vj to obtain the initial point J x , where j = 1, 2, J x = (x v1 , x v2 ), x v1 < x v2 , MF is the number of segments on each objective, and v is the number of reference set points.

[0143] Then, for the above initial points, perform operations according to formulas (36) to (37) and obtain the objective value s vj of each reference point, that is, obtain the coordinates of the reference point (s v1 , s v2 , s v3 ):

[0144]

[0145] S8: Create the mapping relationship between each individual in the fourth population S T and the reference points, calculate the number of occurrences of each reference point in the first (l - 1) non-dominated rank sets in the fourth population S T , select the reference points with fewer occurrences, and filter the remaining next-generation population individuals from the last non-dominated rank set F T in the fourth population S l and put them into the next-generation population P t+1 to make the population size reach N.

[0146] Specifically, step S8 includes the following sub-steps:

[0147] S81: Construct the ray reference lines between each reference point and the origin, and establish the mapping relationship between each individual in the fourth population S T and each reference point, and obtain the distance between each individual and each reference point ray Obtain the reference point Cm with the smallest distance for each individual in each population sk , and calculate the minimum distance Ce between each individual in each population and the reference point sk , where sk represents the number of individuals in the fourth population S T , and v represents the number of reference points

[0148] S82: Set the initial value of the number km of individuals in the last non-dominated rank set F T in the fourth population S l that have been screened into the next generation population to be 1, and determine whether km ≤ lc is satisfied, where lc is the number of individuals in the last non-dominated rank set F T in the fourth population S l that should be screened into the next generation population. If km ≤ lc is not satisfied, then execute step S9; if km ≤ lc is satisfied, then execute step S83

[0149] S83: Calculate the number of occurrences ld of each reference point in the first (l - 1) non-dominated rank sets in the fourth population S T , and put the reference point corresponding to the minimum ld v into the set P v , and randomly select a set point qr from the set P qr qr

[0150] S84: Determine whether there is an individual in the last non-dominated rank set F T in the fourth population S l whose distance to all reference points is the shortest to the set point qr. If there is no such individual, then delete the set point qr from the reference set, and jump to step S83 to re-select the set points in the set P qr for screening; if there is such an individual, then put the above-mentioned individuals that meet the conditions into the set P lj , and at this time, determine whether the value ld v corresponding to the set point qr is equal to 0. If ld v = 0, select the individual with the shortest distance to the set point qr from the set P lj and put it into the next generation population P t+1 ; otherwise, randomly select an individual from the set P lj and put it into the next generation population P​​t+1 .

[0151] S85: The individual is placed into the next-generation population P t+1 After that, the individual is removed from the last non-dominated rank set F T in the fourth population S l and will no longer participate in the subsequent screening. km = km + 1, and the screening continues. Steps S82 to S84 are repeatedly executed.

[0152] S9: Determine whether the iteration number t satisfies t ≥ G max , where G max represents the maximum number of iterations. If t ≥ G max is satisfied, then all non-dominated individuals stored in the updated next-generation population P t+1 are output as the optimal Pareto solution set. According to the actual engineering requirements of the microgrid operation, the Pareto-optimal individuals are selected, and the corresponding optimized objective function values are obtained, including the total system economic cost, load loss rate, and resilience index function value of the microgrid; otherwise, set t = t + 1, and repeatedly execute steps S4 to S8.

[0153] In this embodiment, after 500 iterations, the obtained Pareto front is as Figure 3 shown. The real number coding corresponding to the selected optimal compromise solution is p best = [45.9124, 41.9965, 34.8097, 16.5344, 15.5873, 1.0768, 1.0618, 1.0361, 1.0384, 1.0429, 1.0469, 1.0026, 1.2054, 1.0016, 1, 6, 3.4275, 4.3183, 5.5622, 4.3667, 4.7701, 2.0186, 5.9981, 3.5064, 8, 1, 10, 1, 9, 1, 6, 1, 4, 1], and the specific values of the three optimization objectives are: [20332.23, 0.37, 0.5786].[[]]

[0154] In the real - number encoding corresponding to the optimal compromise individual, 45.9124 represents the estimated power output of the wind power plant on the first bus, 41.9965 represents the estimated power output of the photovoltaic power station on the second bus, 34.8097, 16.5344, 15.5873 respectively represent the active power outputs of the generators on the 8th, 11th, and 13th buses, 1.0768, 1.0618, 1.0361, 1.0384, 1.0429, 1.0469 respectively represent the voltage amplitudes of the generators on the 1st, 2nd, 5th, 8th, 11th, and 13th buses, 1.0026, 1.2054, 1.0016, 1 respectively represent the transformation ratios of the voltage - regulating transformers on the 11th, 12th, 15th, and 36th branches, 6, 3.4275, 4.3183, 5.5622, 4.3667, 4.7701, 2.0186, 5.9981, 3.5064 respectively represent the reactive powers input by the reactive - power compensation devices on the 10th, 12th, 15th, 17th, 20th, 21st, 23rd, 24th, and 29th buses, 8, 10, 9, 6, 4 respectively represent the installation numbers of the first - type security defense components in the 2nd, 5th, 7th, 8th, and 21st buses, and 1, 1, 1, 1, 1 respectively represent the installation numbers of the second - type security defense components in the 2nd, 5th, 7th, 8th, and 21st buses; among the three objective values corresponding to the optimal compromise individual, the total system economic cost of the micro - grid is 20332.23 US dollars, the load loss rate is 0.37%, and the resilience index function is 0.5786.

[0155] In summary, the present invention comprehensively considers three objective functions: the total system economic cost, the load loss rate, and the resilience index function of the micro - grid, designs a multi - objective economic - reliable - resilient optimization method for the micro - grid to defend against FDIA, thus efficiently integrating the resilience function and economic indicators in the micro - grid simultaneously, achieving the best trade - off between attack risk and cost; through formulas (1) - (37) combined with steps S1 - S9 of the present invention, finally, the resilient and economic operation of the micro - grid with multi - performance index compromise optimization is efficiently realized. Compared with the prior art, the present invention has more satisfactory optimization performance in the optimal trade - off among system resilience, load loss, and economic indicators.

[0156] It is worth mentioning that the present invention also provides a multi - objective economic - reliable - resilient optimization for the micro - grid to defend against FDIA, which is used to implement the multi - objective economic - reliable - resilient optimization method for the micro - grid to defend against FDIA in the above - mentioned embodiment.

[0157] See Figure 4 , this system includes a construction module 10, a setting module 20, a first - population initialization module 30, a second - population generation module 40, a dominance - relation judgment module 50, a screening - individual module 60, a normalization module 70, a mapping - relation screening module 80, and an iteration - judgment module 90.

[0158] In this embodiment, the construction module 10 is used to construct a multi-objective economic-reliable-resilient optimization model for a microgrid against FDIA and its constraint conditions.

[0159] In this embodiment, the setting module 20 is used to set a plurality of first parameters.

[0160] In this embodiment, the first population initialization module 30 is used to initialize the optimization variables in the multi-objective economic-reliable-resilient optimization model of the microgrid against FDIA to be optimized according to the first parameters, and randomly generate a first population P with a size of N. M .

[0161] In this embodiment, the second population generation module 40 is used to set the initial value of the iteration number t to 1, record the iteration number t, and perform a crossover operation on each individual in the first population P for the t-th iteration one by one using the simulated binary crossover method, and then perform a mutation operation using the polynomial mutation method to obtain a second population P. In this embodiment, the second population generation module 40 is used to set the initial value of the iteration number t to 1, record the iteration number t, and perform a crossover operation on each individual in the first population P for the t-th iteration one by one using the simulated binary crossover method, and then perform a mutation operation using the polynomial mutation method to obtain a second population P. M For each individual in the first population P for the t-th iteration, perform a crossover operation using the simulated binary crossover method, and then perform a mutation operation using the polynomial mutation method to obtain a second population P. M+1 .

[0162] In this embodiment, the dominance relationship judgment module 50 is used to merge the offspring individuals in the second population P with the parent individuals in the first population P into a third population P with a size of 2N, process the individual constraints in the third population P according to the dominance theory of the constraint mechanism, judge the degree of constraint violation and the dominance relationship between the individuals in the third population P, and perform non-dominated ranking. M+1 The offspring individuals in the second population P are merged with the parent individuals in the first population P into a third population P with a size of 2N. M Process the individual constraints in the third population P according to the dominance theory of the constraint mechanism, judge the degree of constraint violation and the dominance relationship between the individuals in the third population P, and perform non-dominated ranking. R According to the dominance theory of the constraint mechanism, process the individual constraints in the third population P. R Judge the degree of constraint violation and the dominance relationship between the individuals in the third population P. R Perform non-dominated ranking.

[0163] In this embodiment, the individual screening module 60 is used to sort the individuals in the third population P according to the non-dominated ranking relationship, store the low-level rank sets in the fourth population S in turn until the number of individuals in the fourth population S, |S|, is greater than or equal to N. At this time, the last non-dominated rank set in the fourth population S is F; if the number of individuals in the fourth population S, |S|, is equal to N, all individuals in the fourth population S are put into the next generation population P; if the number of individuals in the fourth population S, |S|, is greater than N, the first (l - 1) non-dominated rank sets in the fourth population S are put into the next generation population and the following reference point-based selection operation is performed to screen out the fourth population S. R Sort the individuals in the third population P according to the non-dominated ranking relationship, and store the low-level rank sets in the fourth population S in turn. T Until the number of individuals in the fourth population S, |S|, is greater than or equal to N. T At this time, the last non-dominated rank set in the fourth population S is F. T | T If the number of individuals in the fourth population S, |S|, is equal to N, all individuals in the fourth population S are put into the next generation population P. l ; if the number of individuals in the fourth population S, |S|, is equal to N, all individuals in the fourth population S are put into the next generation population P. T If the number of individuals in the fourth population S, |S|, is equal to N, all individuals in the fourth population S are put into the next generation population P. T | T All individuals in the fourth population S are put into the next generation population P. t+1 ; if the number of individuals in the fourth population S, |S|, is equal to N, all individuals in the fourth population S are put into the next generation population P. T If the number of individuals in the fourth population S, |S|, is equal to N, all individuals in the fourth population S are put into the next generation population P. T | T If the number of individuals in the fourth population S, |S|, is greater than N, the first (l - 1) non-dominated rank sets in the fourth population S are put into the next generation population and the following reference point-based selection operation is performed to screen out the fourth population S.T the last non-dominated rank set F in l put some individuals in it into the next-generation population P t+1 .

[0164] In this embodiment, the standardization module 70 is used to standardize the objective function of each individual in the fourth population S T and create a corresponding reference set.

[0165] In this embodiment, the mapping relationship screening module 80 is used to create the mapping relationship between each individual in the fourth population S T and the reference point, calculate the number of occurrences of each reference point in the first (l - 1) non-dominated rank sets in the fourth population S T , select the reference points with fewer occurrences, and screen the remaining next-generation population individuals from the last non-dominated rank set F T in l and put them into the next-generation population P t+1 to make the number of populations reach N.

[0166] In this embodiment, the iteration judgment module 90 is used to judge whether the iteration number t satisfies t ≥ G max , where G max represents the maximum number of iterations. If t ≥ G max is satisfied, then all non-dominated individuals stored in the updated next-generation population P t+1 are output as the optimal Pareto solution set. Select the Pareto-optimal individuals according to the actual engineering requirements of the microgrid operation, and obtain the values of the optimization objective functions corresponding to the Pareto-optimal individuals, including the total system economic cost, load loss rate, and resilience index function value of the microgrid; otherwise, set t = t + 1 and repeat steps S4 to S8.

[0167] Those of ordinary skill in the art can understand that all or part of the steps of implementing the above embodiments can be completed by hardware related to program instructions. The foregoing program can be stored in a computer-readable storage medium. When the program is executed, it executes the steps including the above method embodiments; and the foregoing storage medium includes: various media such as ROM, RAM, magnetic disk, or optical disc that can store program codes.

[0168] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective economic-reliable-resilient optimization method for microgrids to defend against FDIA, characterized in that, Including the following steps: S1: Construct a multi-objective economic-reliable-resilient optimization model for a microgrid to defend against FDIA and its constraints; S2: Set multiple first parameters; S3: Initialize the optimization variables in the microgrid multi-objective economic-reliable-resilient optimization model for defending against FDIA to be optimized according to the first parameter, and randomly generate the first population \(P\) with a size of \(N\). M ; S4: Set the initial value of the iteration number t to 1, record the iteration number t, and perform the crossover operation on each individual in the first population P for the t-th iteration one by one using the simulated binary crossover method, and then perform the mutation operation using the polynomial mutation method to obtain the second population P M ; M+1 ; S5: Combine the offspring individuals in the second population P M+1 with the parent individuals in the first population P M to form a third population P with a size of 2N R , and process the individual constraints in the third population P according to the domination theory of the constraint mechanism R , judge the degree of constraint violation and the domination relationship between individuals in the third population P R , and perform non-dominated ranking; S6: According to the non-dominated rank division relationship, sort the individuals in the third population P R in descending order of rank, and sequentially store the rank sets of the lower ranks into the fourth population S T , until the number of individuals in the fourth population S T |S T |≥N. At this time, the last non-dominated rank set in the fourth population S T is F l ; if the number of individuals in the fourth population S T |S T | = N, then put all the individuals in the fourth population S T into the next-generation population P t+1 ; if the number of individuals in the fourth population S T |S T |>N, then put the first (l - 1) non-dominated rank sets in the fourth population S T into the next-generation population, and perform the following reference point-based selection operation to screen out some individuals in the last non-dominated rank set F T in the fourth population S l and put them into the next-generation population P t+1 ; S7: Standardize the objective function of each individual in the fourth population S and create the corresponding reference set; T ​ S8: Create the fourth population S T The mapping relationship between each individual and the reference points, and calculate the number of occurrences of each reference point in the first (l - 1) non-dominated rank sets of the fourth population S T Select the reference point with fewer occurrences among them, and filter the remaining individuals of the next generation population from the last non-dominated rank set F T in the fourth population S l and put them into the next generation population P t+1 to make the number of populations reach N; S9: Determine whether the iteration number t satisfies t ≥ G max , where G max represents the maximum number of iterations. If t ≥ G max is satisfied, then all non-dominated individuals stored in the updated next-generation population P t+1 are output as the optimal Pareto solution set. Select Pareto-optimal individuals according to the actual engineering requirements of microgrid operation, and obtain the optimized objective function values corresponding to the Pareto-optimal individuals, including the total system economic cost, load loss rate, and resilience index function value of the microgrid; otherwise, set t = t + 1 and repeat steps S4 to S8.

2. The multi-objective economic-reliable-resilient optimization method for a microgrid to defend against FDIA according to claim 1, characterized in that, The multi-objective economic-reliable-resilient optimization model for the microgrid to defend against FDIA includes optimization objective functions shown in formulas (1) to (12): Clund z = Crsj × f s (wm < P Vz ) × [P Vz - E(wm < P Vz )] (6) Clover z = Cpsj × f s (wm > P Vz ) × [E(wm > P Vz ) - P Vz (7) Among them, f1, f2, and f3 respectively represent the first, second, and third optimization objective functions. f1 is the total economic cost describing the defense against FDIA and ensuring the safe operation of the microgrid. f2 is the load demand loss rate of the microgrid. f3 is the resilience index function value of the microgrid system under FDIA. Q1 and Q2 respectively represent the procurement costs of the first and second types of security defense components. c1 and c2 respectively represent the operating costs of the first and second types of security defense components. represents the number of the first type of security defense components inserted in the ath k busbars under false data injection attack, and a k = A1, A2, …, A h , where A1, A2, …, A h respectively represent the first serial number, the second serial number, …, the Ath h serial number of the attacked busbars. represents the number of the second type of security defense components inserted in the ath k busbars under false data injection attack, B G represents the number of generators connected to the system, P Yi represents the active power output of the ith generator, h i , n i , y i represent the fuel cost curve coefficients corresponding to the ith generator. Wgencost and Sgencost respectively represent the wind power generation cost and the photovoltaic power generation cost. P Wr represents the estimated power output of the rth wind power plant, N w is the number of wind power plants, Wgr represents the wind power plant cost coefficient, Wovest r , Wundest r respectively represent the reserve cost and the penalty cost of the rth wind power plant. Crwj and Cpwj respectively represent the reserve cost coefficient and the penalty cost coefficient of the wind power plant. NT represents the number of wind turbines in the wind power plant, P ra represents the rated power of the wind turbines in the wind power plant. qf and k respectively represent the scale factor and the shape factor in the Weibull probability density function used to describe the wind speed distribution. v out , v r and v in respectively represent the cut-out wind speed, the rated wind speed, and the cut-in wind speed of the wind turbine. wp represents the actual power output of the wind power plant, P Vz represents the estimated power output of the zth photovoltaic power station, N p is the number of photovoltaic power stations, Sgr represents the photovoltaic power station cost coefficient, Clund z and Clover z respectively represent the reserve cost and penalty cost of the z-th photovoltaic power station, Crsj and Cpsj respectively represent the reserve cost coefficient and penalty cost coefficient of the photovoltaic power station, wm represents the actual power output of the photovoltaic power station, f s (wm < P Vz ) represents the probability value that the actual power output of the z-th photovoltaic power station is lower than the estimated power output, E(wm < P Vz ) represents the expected value that the actual power output of the z-th photovoltaic power station is lower than the estimated power output, f s (wm > P Vz ) represents the probability value that the actual power output of the z-th photovoltaic power station is higher than the estimated power output, E(wm > P Vz ) represents the expected value that the actual power output of the z-th photovoltaic power station is higher than the estimated power output, G std represents the solar irradiance under standard conditions, R c represents a certain specific irradiance point, P sr represents the rated power of the photovoltaic modules of the photovoltaic power station, G s represents the solar irradiance, B Total represents the total number of buses in the system, B U represents the number of buses suffering from FDIA, represents the load demand of bus s, L s represents the probability value of a successful FDIA attack on the s-th bus, T sc represents the probability value of a successful defense of FDIA by the sc-class defense component, Q sc represents the procurement cost of the sc-class security defense component, b sc represents the reliability of the sc-class security defense component, c sc represents the operating cost of the sc-class security defense component, d sc represents the cost of attacking the sc-class security defense component, t r represents the start time of the effective period of FDIA in the microgrid, t ce represents the start time of the post-event state of FDIA in the microgrid, D(t) represents the system performance of the microgrid at time t, D p represents the system performance of the microgrid before the occurrence of FDIA, t f represents the start time of the recovery period of the microgrid, t cf represents the start time of the post-recovery state of the microgrid, D ce represents the system performance of the microgrid after the occurrence of FDIA in the microgrid, T1 and T2 respectively represent the probability values of successful defense of FDIA by the first-class and second-class defense components; The constraints include constraints shown in formulas (13) to (24): θ mn = θ m - θ n (15) Among them, θ m represents the voltage angle of the m-th bus, θ n represents the voltage angle of the n-th bus, θ mn represents the voltage angle difference between the m-th bus and the n-th bus, B Total represents the total number of buses in the system, and respectively represent the active power and reactive power of the m-th generator, and respectively represent the active power and reactive power of the load on the m-th bus, V m represents the voltage of the m-th bus, V n represents the voltage of the n-th bus, S mn represents the conductance between the m-th bus and the n-th bus, A mn represents the susceptance between the m-th bus and the n-th bus, and respectively represent the lower limit and upper limit of the estimated power output of the r-th wind power plant, N w is the number of wind power plants, and respectively represent the lower limit and upper limit of the estimated power output of the z-th photovoltaic power station, N p is the number of photovoltaic power stations, and respectively represent the lower limit and upper limit of the active power output of the i-th generator, B G is the total number of generators in the system, and respectively represent the lower limit and upper limit of the voltage amplitude of the i-th generator, O fe represents the turns ratio of the e-th voltage regulating transformer on the branch, and respectively represent the lower limit and upper limit of the turns ratio of the e-th voltage regulating transformer on the branch, N T is the total number of voltage regulating transformers, Q ml represents the reactive power input by the l-th reactive power compensation device, and respectively represent the lower limit and upper limit of the reactive power input by the l-th reactive power compensation device, N C is the total number of reactive power compensation devices, and respectively represent the lower limit and upper limit of the number of insertions of the first type of security defense component in the a k th bus under false data injection attack, and respectively represent the lower limit and upper limit of the number of insertions of the second type of security defense component in the a k th bus under false data injection attack, a k =A1,A2,…,A h , where A1, A2, …, A h They represent the first serial number, the second serial number, ..., the A serial number of the attacked busbar respectively. h Serial number, and They represent the number of attacks by false data injection k The number of Class 1 and Class 2 security defense components installed in the bus, Q1 and Q2 represent the purchase cost of Class 1 and Class 2 security defense components, c1 and c2 represent the operating cost of Class 1 and Class 2 security defense components, Dcost max Indicates the upper limit of FDIA security defense costs.

3. The microgrid multi-objective economic-reliable-resilient optimization method for defending against FDIA according to claim 1, characterized in that The first parameter includes the procurement cost Q1 of the first - type security defense component, the operation cost c1 of the first - type security defense component, the reliability b1 of the first - type security defense component, the cost d1 spent on attacking the first - type security defense component, the procurement cost Q2 of the second - type security defense component, the operation cost c2 of the second - type security defense component, the reliability b2 of the second - type security defense component, the cost d2 spent on attacking the second - type security defense component, and the maximum number of iterations G max , the population size N, the cost coefficient Wgr of the wind power plant, the reserve cost coefficient Crwj of the wind power plant, the penalty cost coefficient Cpwj of the wind power plant, the number NT of wind turbines in the wind power plant, and the rated power P of the wind turbines in the wind power plant ra , the scale factor qf in the Weibull probability density function used to describe the wind speed distribution, the shape factor k in the Weibull probability density function used to describe the wind speed distribution, and the cut - out wind speed v of the wind turbine out , the rated wind speed v of the wind turbine r , the cut - in wind speed v of the wind turbine in , the cost coefficient Sgr of the photovoltaic power station, the reserve cost coefficient Crsj of the photovoltaic power station, the penalty cost coefficient Cpsj of the photovoltaic power station, the solar irradiance G under standard conditions std , a specific irradiance point R c , the rated power P of the photovoltaic modules of the photovoltaic power station sr , the distribution factor η in the binary crossover method, the polynomial mutation distribution index λ, the number of segments MF on each target, and the upper limit Dcost of the FDIA security defense cost max .

4. The microgrid multi-objective economic-reliable-resilient optimization method for defending against FDIA according to claim 1, characterized in that, Initialize the optimization variables in the microgrid multi-objective economic-reliable-resilient optimization model for defending against FDIA to be optimized, and randomly generate the first population $P$ with a size of $N$. M , which specifically includes: Randomly generate the first population \(P\) of size \(N\). M \(=\{P_u, u = 1, 2, \ldots, N\}\), where \(P\) M represents the initial population, \(P\) u represents the \(u\)-th individual, \(N\) represents the population size, and the \(u\)-th individual represents the predicted power outputs of the 1st, \(\ldots\), \(N\) w wind power plants corresponding to the \(u\)-th individual, \(N\) w is the number of wind power plants, represents the predicted power outputs of the 1st, \(\ldots\), \(N\) p photovoltaic power stations corresponding to the \(u\)-th individual, \(N\) p is the number of photovoltaic power stations, represents the active power outputs of the 2nd, \(\ldots\), \(B\) G generators corresponding to the \(u\)-th individual, \(B\) G is the total number of generators in the system, represents the voltage amplitudes of the 1st, \(\ldots\), \(B\) G generators corresponding to the \(u\)-th individual, represents the turns ratios of the 1st, \(\ldots\), \(N\) T tap-changing transformers on the branches corresponding to the \(u\)-th individual, \(N\) T is the total number of tap-changing transformers, represents the reactive powers input by the 1st, \(\ldots\), \(N\) C reactive power compensation devices corresponding to the \(u\)-th individual, \(N\) C is the total number of reactive power compensation devices, represents the number of insertions of the 1st type of security defense components in the \(a\) k busbars attacked by false data injection corresponding to the \(u\)-th individual, represents the number of insertions of the 2nd type of security defense components in the \(a\) k busbars attacked by false data injection corresponding to the \(u\)-th individual, \(a\) k \(= A_1, A_2, \ldots, A\) h , where \(A_1, A_2, \ldots, A\) h respectively represent the 1st serial number, 2nd serial number, \(\ldots\), \(A\) h serial number of the attacked busbars, and round to the nearest integer.

5. The multi-objective economic-reliable-resilient optimization method for a microgrid to defend against FDIA according to claim 1, characterized in that The implementation of the crossover operation using the simulated binary crossover method specifically includes: First, randomly generate a random number rn1 within the range of 0 to 1; Then, implement the crossover operation using the simulated binary crossover method, and its formula is specifically: Among them, t represents the number of iterations, P1(t) represents the first N / 2 individuals in the first population P before crossover, M P2(t) represents the last N / 2 individuals in the first population P before crossover, M P1(t + 1) represents the first N / 2 individuals in the first population P after crossover, M P2(t + 1) represents the last N / 2 individuals in the first population P after crossover, M β represents the propagation factor in the binary crossover method, and η represents the distribution factor in the binary crossover method; The implementation of the mutation operation using the polynomial mutation method specifically includes: First, randomly generate a random number rn2 within the range of 0 to 1; Then, implement the mutation operation using the polynomial mutation method, and its formula is specifically: P em (t + 1)=P em (t)+δ×(P em UK -P em LK ) Among them, P em (t) represents the first population P before mutation M The emth variable of the uth individual in em (t+1) represents the second population P after mutation M+1 The emth variable of the uth individual in em LK Represents the first population P M The lower limit allowed for the emth variable of the uth individual, P em LK Depend on Composition, P em UK Represents the first population P M The upper limit allowed for the emth variable of the uth individual, P em UK Depend on composition, δ represents the polynomial variation factor, and λ represents the polynomial variation distribution index.

6. The multi-objective economic-reliable-resilient optimization method for a microgrid to defend against FDIA according to claim 1, characterized in that Step S5 specifically includes the following sub-steps: S51: Combine the offspring individuals in the second population P M+1 with the parent individuals in the first population P M to form a third population P R with a size of 2N, where the third population P R consists of {P u,R , u = 1, 2, …, 2N}, and P u,R represents the u-th individual in the third population P R ; determine whether all individuals in the third population P R violate the constraint conditions shown in formulas (13) to (24). S52: Calculate the constraint violation amounts of all individuals {P u,R , u = 1, 2, …, 2N} within the third population P according to formulas (27) to (30), and obtain the corresponding constraint violation degrees W(P u,R ): R within all individuals {P u,R , u = 1, 2, …, 2N} u,R , u = 1, 2, …, 2N} to obtain the corresponding constraint violation degree W(P u,R ): u,R ): W(P u,R ) = |L1(P u,R )| + |L2(P u,R )| + <L3(P u,R )> (27) Among them, represents the z1-th constraint corresponding to the case of individual P u,R , where z1 represents the serial number of the constraint, z1 = 1, 2, 3, and W(P u,R ) represents the constraint violation degree index corresponding to individual P u,R . represents the absolute value of the z1-th constraint corresponding to the case of individual P u,R . represents the opposite number of the z1-th constraint corresponding to the case of individual P u,R . If , then let S53: According to the degree of constraint violation, use the first judgment method shown in formula (31) to judge the dominance relationship between any two individuals in the third population P R among and : Among them, represents the degree of constraint violation corresponding to the u1-th individual in the third population P R ; represents the degree of constraint violation corresponding to the u2-th individual in the third population P R ; represents the su1-th optimization objective function corresponding to the u1-th individual in the third population P R ; represents the su1-th optimization objective function corresponding to the u2-th individual in the third population P R ; represents the su2-th optimization objective function corresponding to the u1-th individual in the third population P R ; represents the su2-th optimization objective function corresponding to the u2-th individual in the third population P, where both su1 and su2 represent the serial numbers of the optimization objective functions, su1 = 1, 2, 3, and su2 = 1, 2, 3; R ; represents the existing mathematical symbol; S54: Rank all individuals in the third population P R using the first judgment method in step S53. Specifically, classify all solutions that are not dominated by other solutions into the first front; from the remaining solutions, select those that are not dominated by any solution in the first front and classify them into the second front; then from the remaining solutions, select those that are not dominated by the solutions in the first and second fronts and classify them into the third front; and so on until all solutions are assigned to a certain front.

7. The multi-objective economic-reliable-resilient optimization method of the microgrid for defending against FDIA according to claim 1, characterized in that In the step S7, the objective function of each individual in the standardized fourth population S T specifically includes: First, traverse each objective of all individuals in the fourth population S T to find the minimum value of each objective, and form the ideal point ip, whose coordinates are where respectively represent the minimum values of the first, second, and third objective functions in the fourth population S T ; Then subtract the objective value of the ideal point from the objective value of each individual in the fourth population S T to obtain the relative objective value coordinates i.e., (f1'(x), f2'(x), f3'(x)), where f1 fd , f2 fd , f3 fd respectively represent the 1st, 2nd, and 3rd objective function values of the fd-th individual in the fourth population S T , and x represents the individual in the fourth population S T after the objective function value transformation of the ideal point; Then, find the fourth population S according to formulas (32) to (33). T extreme points whose coordinates are respectively denoted as (D1, G1, I1), (D2, G2, I2), (D3, G3, I3): Among them, f m ' s (x) represents the ms-th objective function value of the individual x after the numerical transformation of the ideal point objective function in the fourth population S T . Here, ms represents the serial number of the objective, ms = 1, 2, 3, and w ms represents the standard vector of the ms-th objective; Finally, substitute the coordinates (D1, G1, I1), (D2, G2, I2), (D3, G3, I3) into the intercept form plane formula (34) to obtain the plane equation formed and the intercepts a1, a2, a3 of the linear hyperplane formed by the three target axes x, y, z and the three extreme points and normalize the relative objective values of all individuals in the fourth population S according to formula (35) to obtain the normalized objective values: T ​ Among them, represents the normalized objective value obtained by normalizing the relative objective value of the fd-th individual in the fourth population S T , and ms represents the serial number of the objective.

8. The multi-objective economic-reliable-resilient optimization method for a microgrid to defend against FDIA according to claim 1, characterized in that In step S7, the creation of the corresponding reference set specifically includes: First, construct a combination of two-dimensional x vj to obtain the initial point J x , where j = 1, 2, J x =(x v1 , x v2 ), x v1 < x v2 , MF is the number of segments on each target, and v is the number of reference set points; Then, for the above initial points, perform operations according to formulas (36) to (37) and obtain the target value s of each reference point vj , that is, obtain the coordinates of the reference point (s v1 , s v2 , s v3 ):

9. The microgrid multi-objective economic-reliable-resilient optimization method for defending against FDIA according to claim 1, wherein Step S8 specifically includes the following sub-steps: S81: Construct ray reference lines between each reference point and the origin, and establish mapping relationships between each individual in the fourth population S T and each reference point, and obtain the distances between each individual and the rays of each reference point Obtain the reference point Cm with the smallest distance for each individual in each population sk , and calculate the minimum distance Ce between each individual in each population and the reference point sk , where sk represents the number of individuals in the fourth population S T , and v represents the number of reference points; S82: Set the fourth population S T The number km of the individuals that have been screened into the next-generation population in the last non-dominated rank set F l in T is initialized to 1, and it is judged whether km ≤ lc is satisfied, where lc is the number of individuals that should be screened into the next-generation population in the last non-dominated rank set F T in l . If km ≤ lc is not satisfied, step S9 is executed; if km ≤ lc is satisfied, step S83 is executed; l in T S83: Calculate the occurrence times ld of each reference point in the first (l - 1) non - dominated rank sets in the fourth population S T of the first (l - 1) non - dominated rank sets v , and take ld v when it is the smallest, and put the corresponding reference point into the set P qr , and randomly select a set point qr from the set P qr ; S84: Determine the fourth population S T in the last non-dominated rank set F l whether there is an individual whose distance to the set point qr is the shortest among the distances to all reference points. If there is no such individual, delete the set point qr from the reference set, jump to step S83, and reselect the set P qr to screen the set points in it; if there is such an individual, put the above individuals that meet the conditions into the set P lj , and at this time, judge the value ld v corresponding to the set point qr v whether it is equal to 0. If ld lj = 0, select the individual with the shortest distance to the set point qr in the set P t+1 and put it into the next-generation population P lj ; otherwise, randomly select an individual from the set P t+1 and put it into the next-generation population P ; S85: The individual is placed into the next-generation population P t+1 After that, the individual is removed from the last non-dominated rank set F T in the fourth population S l and will no longer participate in the subsequent screening. km = km + 1, and the screening continues. Steps S82 to S84 are repeatedly executed.

10. A microgrid multi-objective economic-reliable-resilient optimization system for defending against FDIA, characterized in that, Built-in with the multi-objective economic-reliable-resilient optimization method for a microgrid to defend against FDIA according to any one of claims 1-9, the system includes: A construction module for constructing a multi-objective economic-reliable-resilient optimization model for a microgrid to defend against FDIA and its constraints; A setting module for setting multiple first parameters; The first population initialization module is used to initialize the optimization variables in the microgrid multi-objective economic-reliable-resilient optimization model for defending FDIA to be optimized according to the first parameter, and randomly generate the first population P with a size of N M ; The second population generation module is used to set the initial value of the iteration number t to 1, record the iteration number t, and perform the crossover operation on each individual in the first population P M in the t-th iteration one by one using the simulated binary crossover method, and then perform the mutation operation using the polynomial mutation method to obtain the second population P M+1 ; The dominance relationship judgment module is used to combine the offspring individuals in the second population P M+1 with the parent individuals in the first population P M to form a third population P with a size of 2N R . According to the dominance theory of the constraint mechanism, the constraints of the individuals in the third population P R are processed, the degree of constraint violation and the dominance relationship between the individuals in the third population P R are judged, and the non-dominated ranking is carried out; A screening individual module, which is used to sort the individuals of the third population P according to the non-dominated rank division relationship, and store the rank sets of the lower ranks into the fourth population S in turn R until the number of individuals in the fourth population S T |S T |≥N. At this time, the last non-dominated rank set in the fourth population S T is F T ; if the number of individuals in the fourth population S l |S T | = N, then all individuals in the fourth population S T are put into the next-generation population P T ; if the number of individuals in the fourth population S t+1 |S T |>N, then the first (l - 1) non-dominated rank sets in the fourth population S T are put into the next-generation population, and the following reference point-based selection operation is performed to screen out some individuals in the last non-dominated rank set F T in the fourth population S T and put them into the next-generation population P l ; t+1 ​ A normalization module for normalizing the objective functions of each individual in the fourth population S and creating a corresponding reference set; T and creating a corresponding reference set; The mapping relationship screening module is used to create the fourth population S T The mapping relationship between each individual and the reference point, and calculate the occurrence times of each reference point in the first (l - 1) non-dominated rank sets of the fourth population S T Select the reference point with fewer occurrence times, and screen the remaining individuals of the next generation population from the last non-dominated rank set F T in the fourth population S, and put them into the next generation population P l to make the number of populations reach N; and t+1 ​ An iterative judgment module for judging whether the iteration number t satisfies t≥G max , where G max represents the maximum number of iterations. If t≥G max is satisfied, then all non-dominated individuals stored in the updated next-generation population P t+1 are output as the optimal Pareto solution set. According to the actual engineering requirements of the microgrid operation, Pareto optimal individuals are selected, and the optimal objective function values corresponding to the Pareto optimal individuals are obtained, including the total system economic cost, load loss rate, and resilience index function value of the microgrid; otherwise, set t = t + 1 and repeat the execution from the second population generation module to the mapping relationship screening module.

Images