Power load re-allocation attack defense method and system based on phase-shift transformer

Abstract

The application provides a power system load redistribution attack defense method and system, and the method comprises the following steps: a load redistribution attack defense framework based on a phase-shifting transformer is designed, a three-layer game model containing a defender-attacker-system is constructed, and the three-layer game model is used for decision-making of key positions and quantities of phase-shifting transformer deployment; the three-layer game model of attack influence elimination based on the phase-shifting transformer is decomposed into a solvable optimization problem, and an iterative algorithm capable of obtaining a global optimal solution is designed; the solution of the attack influence elimination optimization problem is simplified, and a high-efficiency simplified algorithm is designed to realize fast solution. The application solves the technical problems of poor attack influence elimination effect, high economic loss caused by load redistribution attack and poor load redistribution attack influence elimination effect.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of false data injection attack defense of new power grid cyber-physical system, and in particular to a power system load redistribution attack defense method and system based on phase shift transformer. BACKGROUND

[0002] With the continuous development of power system, more and more information technology is introduced into the power grid, and the deep coupling between the information layer and the physical layer makes the traditional power system gradually intelligent. However, this also brings new security challenges to the power system: because of the lack of security protection means between the communication of the data acquisition and monitoring control system (SCADA, Supervisory Control And Data Acquisition) and the remote terminal unit (RTU, remote terminal unit), attackers can easily tamper with legitimate measurement data, causing serious damage to the power system, and even causing major security incidents such as cascading power outages. Therefore, the new power system faces serious security challenges, and the field of power system network attack defense needs to be studied.

[0003] Load redistribution (LR, load redistribution) attack is one of the most common false data injection attacks in power system. The attack misleads the optimal power flow (OPF, Optimal Power Flow) application in the real-time power market by secretly tampering with load measurement, and seriously affects the economic efficiency of power grid operation. Its characteristics are that it does not change the total load, but only tampers with the load distribution and the corresponding line flow. These characteristics make the attack have strong stealthiness, and system operators often have difficulty in detecting it, which increases the difficulty of attack defense. Therefore, it is of great significance to study effective load redistribution attack defense methods to eliminate the impact of attacks and ensure the safe and stable operation of the power system.

[0004] There is already some work on defending against false data injection attacks, such as the existing invention patent application document CN114221343A, "A Method for Solving Optimal Power Flow Considering Random Wind Farm Output Based on the Collocation Method." This existing method includes: by accounting for the impact of random variations in wind farm output on the system's optimal power flow solution, adjusting the requirements for power system security analysis and control, and reflecting the impact of renewable energy output such as wind farms on the system's steady-state optimal power flow. It solves the optimal power flow under various complex operating conditions of the power system. And the existing invention patent application document with publication number CN118229012A, "A method for resilient scheduling of multi-integrated energy systems under collaborative attacks considering comprehensive demand response based on state-adversarial multi-agent deep reinforcement learning", the existing method includes: constructing a multi-integrated energy system (MIES) scheduling model with the maximum operating net profit of each IES as the goal; then, a model is constructed for the information attacks that may be suffered during the scheduling process of the integrated energy system; secondly, taking the information attack as the opponent, a multi-agent state-adversarial Markov decision process model is proposed; in addition, adversarial learning and deep reinforcement learning are combined to propose a state-adversarial multi-agent soft actor-critic (SA-MASAC) algorithm that integrates authentication defense training; finally, the proposed algorithm is used to solve the model to obtain the MIES resilient scheduling strategy. Determine the electric thermal system including thermal power units, wind power units, photovoltaic equipment, electric thermal storage system and electric energy storage device, and build an energy management system model; determine the electric thermal storage system and model; compare the operation process of the electric energy storage device with that of the thermal power units, and build an electric energy storage device operation cost model; with the goal of minimizing the system operation cost, divide the system optimization scheduling problem into unit combination sub-problem and optimal power flow sub-problem, considering the thermal power units, electric energy storage devices, electric thermal storage system and network power flow, system balance and rotating reserve constraints, and determine the output of each distributed power source; use differential evolution algorithm and genetic algorithm to solve the two sub-problem models respectively. And the existing invention patent application document "Distribution network risk assessment method based on random game network under network attack" with publication number CN112819300A, the existing method includes: constructing a distribution network information-physical system model based on random game theory and Petri net as the architecture; refining the attack and intrusion situation and defense measures through hierarchical analysis of network risks; considering the change probability of network risk under different states based on the calculation of the attack and defense game profit matrix and the analysis of Nash equilibrium strategy value; summarizing the risk formula calculation method to obtain the risk value under the state and formulate a defense decision-making plan of "resource allocation-attack and defense analysis-risk assessment" to obtain a better defense strategy.However, most of the aforementioned existing technologies focus on attack detection, vulnerability analysis, and optimal power flow solution. There is little research on attack impact elimination strategies, and there are shortcomings such as instability and being greatly affected by environmental factors. For example, the robust correction scheduling strategy based on dynamic line evaluation dynamically adjusts the capacity of the transmission line in the form of real-time scheduling, which plays a role in partially eliminating the economic impact caused by load redistribution attacks. However, its performance depends on the additional transmission capacity of the transmission line and is greatly affected by factors such as weather. Therefore, in view of the shortcomings of existing false data injection attack defense methods in eliminating attack effects, designing an effective attack impact elimination method to reduce the losses caused by load redistribution attacks on the power grid is a problem that technicians in this field urgently need to solve.

[0005] Phase-shifting transformers (PSTs), as specialized regulators, have been widely deployed in power systems as part of optimal power flow scheduling due to their ability to regulate active power and optimize power flow distribution. However, a framework that leverages the characteristics of PSTs and deploys them in optimal locations to proactively defend against load redistribution attacks remains lacking.

[0006] The existing public document "Optimal Defense Strategy for Load Redistribution Attacks Based on Game Theory" describes a defense strategy that focuses on protecting certain measuring instruments, assuming that they will not be attacked after being protected. This is highly hypothetical, and if the attacker has the means to bypass the instrument protection, the impact of the load redistribution attack cannot be eliminated. The model in the aforementioned existing document only models the game between the system and the attacker, and does not model the interaction between the defender, attacker, and system, making it impossible to accurately grasp the game process among the three. Finally, the method disclosed in the aforementioned document is based on measurement protection, and does not fully consider the characteristics of the components in the existing power system, namely the phase-shifting transformer, in the defense operation.

[0007] In summary, the existing technology has technical problems such as poor effect in eliminating the impact of attacks, high economic losses caused by load redistribution attacks, and poor effect in eliminating the impact of load redistribution attacks. Summary of the Invention

[0008] The technical problem to be solved by the present invention is: how to solve the technical problems in the prior art of poor attack impact elimination effect, high economic losses caused by load redistribution attacks, and poor load redistribution attack impact elimination effect.

[0009] The present invention solves the above technical problems by adopting the following technical solutions: A method for defending against power load redistribution attacks based on a phase-shifting transformer includes:

[0010] S1. Use the Stackelberg game model to describe the attacker's impact on the system, and build a load redistribution attack impact elimination model based on phase-shifting transformers;

[0011] S2. Based on the preset defender constraints, the defender is introduced into the Stackelberg game model corresponding to the attacker and the preset system to construct a three-layer defender-attacker-system game model. The defender is used as the top layer of the game, and the minimized operating cost and phase-shifting transformer cost are obtained and used as the objective function to make decisions on the deployment location and number of phase-shifting transformers. This describes the three-layer optimization problem of eliminating the attack impact of phase-shifting transformer load redistribution.

[0012] S3. Eliminate the three-layer optimization problem of attack impact. Use the C&CG algorithm to decompose the problem into a main problem and sub-problems. Set the global optimal solution algorithm based on the main problem and sub-problems to optimize the defender-attacker-system three-layer game model.

[0013] S4. Based on the defender-attacker-system three-layer game model, analyze the inherent mechanism of load redistribution attacks and simplify the attack vector generation process based on pre-set load redistribution attack characteristics.

[0014] S5. Construct and design a simplified solution algorithm for the three-layer optimization problem of attack impact elimination to address the problem that is difficult to apply to large-scale systems due to the complexity of the model. This algorithm is used to optimize the defender-attacker-system three-layer game model and obtain the phase-shifting transformer deployment set.

[0015] S6. Define evaluation indicators for different load values ​​to determine the optimal phase-shifting transformer deployment location in the planning phase. In the operation phase, obtain and determine the value of the phase shift angle based on the optimal power flow scheduling information to eliminate the impact of load redistribution attacks.

[0016] This invention uses phase-shifting transformers to defend against load redistribution attacks in power systems, addressing the shortcomings of existing load redistribution attack defense methods in mitigating the impact of attacks. This invention models the defense framework as a three-layer optimization problem and, through the design of an efficient iterative algorithm, determines the optimal deployment location and number of phase-shifting transformers. This method significantly reduces the economic losses from load redistribution attacks and eliminates their impact. This invention demonstrates effective protection across a wide load range and demonstrates strong applicability.

[0017] In a more specific technical solution, S1 includes:

[0018] S11 uses the following logic to constrain the attacker’s load redistribution attack vector:

[0019]

[0020] Where N d is the number of load measurements in the system, ΔD k is the tampered value measured by the attacker for the kth load;

[0021] S12. Tampering with the attacker's power flow measurement in response, wherein the attack vector ΔF for the power flow measurement is expressed using the following logic:

[0022] ΔF=-L·A D ΔD (2)

[0024] Where L is the power transfer distribution factor, A D is the topological correlation matrix between busbar and load;

[0025] S13. Use the following logic to set the true value range of the attack vector:

[0026]

[0027] Where D k is the true value of the kth load measurement, is the amplitude coefficient of the attack, which represents the attack vector at the true value of the load within times;

[0028] S14. Use the following logic to set an upper limit on the number of meters that an attacker can tamper with:

[0029]

[0030] Where N l is the number of transmission lines in the system, ω D,k and ω F,l are binary variables representing whether load measurement and line flow measurement are attacked, l is the line flow number, R a The maximum number of measurements that an attacker can attack;

[0031] S15. Describe a load redistribution attack impact elimination model based on setting load redistribution attack vector constraints, attack vectors, true value range of attack vectors, and an upper limit on the number of tampered meters.

[0032] In a more specific technical solution, in S15, the Stackelberg game model is used to describe the following logic:

[0033]

[0034] st(1)-(4)

[0035]

[0036] stF=L·A P ·PL·A D ·(D+ΔD * )+(X -1 ·N LB ·L T -X -1 )·σ (9)

[0038]

[0039] Where N g is the number of generators in the system, α i and β i is the power generation cost coefficient, is the upper limit of the transmission line capacity, and are the upper and lower bounds of the generator output, and is the upper and lower bounds of the phase shift angle, A P is the topological correlation matrix between busbar and generator, N LB is the topological correlation matrix of the busbar and the branch, X is a diagonal matrix whose diagonal elements are the impedances on each transmission line, Φ is the set of lines with phase-shifting transformers deployed; P is the output of the generator, F is the power flow on the transmission line, σ l is the phase shift angle of the phase-shifting transformer on the lth line; the attacker's objective function (5) is to maximize the operating cost of the system, and equations (6) and (7) are the attack vectors ΔD k , ΔF l With the binary variable ω D,k ,ω F,l The logical constraints of the relationship; Equations (8) to (14) are the optimal power flow scheduling optimization problems of the system, where Equation (8) is the objective function of the system - minimizing the operating cost, constraint (9) is the power flow equation in the form of power distribution transfer factor, constraint (10) is the supply and demand balance equation, and Equations (11) to (13) are the upper and lower limit constraints of the variables.

[0040] In a more specific technical solution, in S2, the following logic is used to describe the three-layer optimization problem of attack impact elimination:

[0041]

[0042] std l ∈{0,1},l=1,…,N l (16)

[0044]

[0045] s.t.

[0046] (1)-(7)

[0047]

[0048] s.t.

[0049] (9)-(12)

[0050]

[0051] where c l is the cost of deploying phase-shifting transformers on line l, d l is a binary variable representing whether line l is deployed with phase-shifting transformers; equation (15) is the objective function of the defender, equation (16) is the value constraint of d l , equation (17) is the objective function of the attacker, equation (18) is the objective function of the system optimal power flow, and equation (19) represents the value range of the phase shift angle of the phase-shifting transformer on line l.

[0052] The application constructs a three-layer optimization problem for eliminating the attack influence based on load redistribution attack of phase-shifting transformers, designs an algorithm based on the C&CG method for solving, and designs a simplified algorithm which greatly reduces the computational complexity under the premise of not significantly reducing the optimality, and gives the optimal phase-shifting transformer deployment set under the load.

[0053] In a more specific technical solution, step S3 comprises:

[0054] S31, according to the C&CG algorithm, the upper and lower problems of the attack influence elimination three-layer optimization problem are combined, and gradually added constraints are added as the main problem with the iteration; wherein the main problem is described by the following logic:

[0055]

[0056] where subscript I is the iteration count, N I is the upper limit of the number of iterations, and η is an auxiliary variable in the C&CG algorithm; equation (20) is the objective function of the main problem, constraint (21) represents the relationship between the auxiliary variable η and the objective function of the original three-layer optimization problem, and equations (22) to (25) are the iteration forms of the power grid constraints (9) to (12) and the power grid constraint (19);

[0057] S32, the middle layer and the lower layer of the attack influence elimination three-layer optimization problem are combined as a sub-problem; wherein the sub-problem is described by the following logic:

[0058]

[0059] st(1)-(7)

[0060]

[0061] st

[0062] (9)-(12), (19)

[0063] S33. Based on the main problem and sub-problems, a three-level optimization problem for attack impact elimination is proposed, and a global optimal solution algorithm is given.

[0064] In a more specific technical solution, S33 includes:

[0065] S331, solve the sub-problem for the preset initial value d0 and obtain the attack vector ΔD * , use the following logic to obtain the optimal value as the upper bound of the global optimal value:

[0066]

[0067] S332. Obtain and use ΔD * Solve the main problem and obtain the phase-shifting transformer deployment set d and the optimal value η * As the lower bound of the global optimal value;

[0068] S333, iterate S331 to S332 in a loop until the upper bound of the global optimal value and the lower bound of the global optimal value converge.

[0069] In a more specific technical solution, S4 analyzes the internal mechanism information and uses the following logic to perform an approximate optimization problem operation to obtain the load redistribution attack vector and obtain an approximate result of the original attack vector optimization problem:

[0070]

[0071] st(1),(3)

[0072] Where, ρ l is the coefficient that characterizes the direction of the power flow, and Ψ is the target line set selected by the attacker.

[0073] In more specific technical solutions, S5 includes:

[0074] S51. Given the initial phase-shifting transformer deployment set d0, calculate the optimal power flow scheduling problem of the preset system. If the power flow of line l satisfies the condition with γ as the threshold:

[0075]

[0076] Add the line γ to the attacker's target set Ψ and use the following logic to update the global optimal value upper bound UB:

[0077]

[0078]

[0079] in, is the optimal value of the optimal power flow scheduling problem;

[0080] S52. Solve the optimization problem described in formula (28) based on the current target set Ψ to obtain the attack vector ΔD * ;

[0081] S53, according to the attack vector ΔD * , solve the main problem to obtain the optimal solution d * ,η * , use the following logic to update the global optimal lower bound LB:

[0082] LB=η * (31)

[0084] S54, iterate S51 to S53 until the upper bound of the global optimal value and the lower bound of the global optimal value meet the following conditions, and take the optimal solution d obtained in the current iteration as * As a collection deployed using a PhaseShifter transformer:

[0085]

[0086] Where ε is the threshold;

[0087] S55. The target set Ψ, the global optimal value upper bound UB, and the global optimal value lower bound LB satisfy the following conditions:

[0088] Ψ * =Ψ I-1 ,UB I >UB I-1 ,LB I <LB I-1

[0089] Exit the loop and use the optimal solution d obtained in the previous iteration * Deploy the collection as a phase-shifting transformer.

[0090] Aiming at the problem that the three-layer model is difficult to apply to large-scale systems due to its complexity, the present invention designs an efficient attack impact elimination simplified solution algorithm for the three-layer optimization problem, thereby shortening the calculation time without significantly reducing the optimality.

[0091] In more specific technical solutions, S6 includes:

[0092] S61. In the pre-planning stage, use the following logic to define different load value evaluation indicators A D,D′ :

[0093]

[0094] Among them, when the load value is D, the phase-shift transformer deployment set d is calculated by the three-layer optimization problem of attack impact elimination. * After installation on the line, when the load value changes to D′, the operating cost is f D,D′ ;

[0095] S62. If, according to load forecast, there is a deployment set of phase-shifting transformers d * Evaluation index A for different load values ​​under multiple D′ D,D′ All satisfy the following threshold τ:

[0096] A D,D′ ≤τ (34)

[0098] According to the deployment set d * Deploy phase-shifting transformers on transmission lines;

[0099] S63. Construct and determine the phase shift angle of the phase-shifting transformer based on the optimal power flow scheduling problem using the following logic:

[0100]

[0101] st(9)-(12)

[0102]

[0103] Where, d * Deploy a collection for the phase-shifting transformer mentioned above.

[0104] The present invention designs a method for determining the deployment set of phase-shifting transformers according to load forecasting in the planning stage, which can significantly reduce the economic losses caused by load redistribution attacks and eliminate the impact of load redistribution attacks.

[0105] In a more specific technical solution, the power system load redistribution attack defense system based on phase-shifting transformers includes:

[0106] An impact elimination model construction module is used to describe the attacker's impact on the system using the Stackelberg game model, so as to build a load redistribution attack impact elimination model based on phase-shifting transformers;

[0107] A three-layer game model construction module is used to introduce the defender into the Stackelberg game model corresponding to the attacker and the preset system based on the preset defender constraints, so as to construct a three-layer defender-attacker-system game model. In this module, the defender is used as the top layer of the game, and the minimized operating cost and phase-shifting transformer cost are obtained and used as the objective function to make decisions on the deployment location and number of phase-shifting transformers. This describes the three-layer optimization problem of eliminating the attack impact of phase-shifting transformer load redistribution. The three-layer game model construction module is connected to the impact elimination model construction module.

[0108] The problem decomposition module is used to eliminate the three-layer optimization problem of attack impact. It uses the C&CG algorithm to decompose the problem to convert it into a main problem and sub-problems. The global optimal solution algorithm is set based on the main problem and sub-problems to optimize the three-layer game model of defender-attacker-system. The problem decomposition module is connected to the three-layer game model construction module.

[0109] A vector generation process simplification module is used to analyze the inherent mechanism of the load redistribution attack based on the defender-attacker-system three-layer game model and simplify the attack vector generation process based on the preset load redistribution attack characteristics. The vector generation process simplification module is connected to the first optimization module of the three-layer game model;

[0110] The simplified solution module is used to construct and design a simplified solution algorithm for the three-layer optimization problem of attack impact elimination, which is difficult to apply to large-scale systems due to the complexity of the model. This algorithm optimizes the defender-attacker-system three-layer game model and processes the obtained phase-shifting transformer deployment set. The simplified solution module is connected to the three-layer game model construction module.

[0111] The attack impact elimination module is used to define evaluation indicators for different load values. Based on the phase-shifting transformer deployment set, it determines the optimal phase-shifting transformer deployment location in the preset planning stage. It obtains and determines the value of the phase shift angle based on the optimal power flow scheduling information to eliminate the impact of the load redistribution attack. The attack impact elimination module is connected to the simplification solution module.

[0112] Compared with the prior art, the present invention has the following advantages:

[0113] This invention uses phase-shifting transformers to defend against load redistribution attacks in power systems, addressing the shortcomings of existing load redistribution attack defense methods in mitigating the impact of attacks. This invention models the defense framework as a three-layer optimization problem and, through the design of an efficient iterative algorithm, determines the optimal deployment location and number of phase-shifting transformers. This method significantly reduces the economic losses from load redistribution attacks and eliminates their impact. This invention demonstrates effective protection across a wide load range and demonstrates strong applicability.

[0114] The application constructs a three-layer optimization problem for eliminating the influence of load redistribution attacks based on phase shift transformers, designs an algorithm based on the C&CG method for solving, and designs a simplified algorithm which greatly reduces the computational complexity without significantly reducing the optimality, and gives the optimal phase shift transformer deployment set under the load.

[0115] The application designs an efficient attack influence elimination three-layer optimization problem simplification solving algorithm to shorten the calculation time without significantly reducing the optimality.

[0116] The application designs a method for determining the phase shift transformer deployment set according to the load prediction in the planning stage, which can significantly reduce the economic loss suffered by the load redistribution attack and eliminate the influence of the load redistribution attack.

[0117] The defense method involved in the application is aimed at the case of load redistribution attack, and the influence caused by the attack is greatly eliminated by using the callable resources in the deployment system, i.e., phase shift transformers (PST). The defense method provided by the application models the interaction between the defender, the attacker and the system, can more accurately grasp the game process among the three, and designs an efficient calculation method to apply the defense method to large-scale systems. The application realizes effective defense against load redistribution attacks based on the characteristics of phase shift transformers.

[0118] The application solves the technical problems of poor attack influence elimination effect, high economic loss suffered by load redistribution attacks and poor load redistribution attack influence elimination effect in the prior art. BRIEF DESCRIPTION OF DRAWINGS

[0119] Figure 1 It is a basic step schematic diagram of the power system load redistribution attack defense method based on phase shift transformers of the embodiment 1 of the application;

[0120] Figure 2 It is a data flow processing schematic diagram of the power system load redistribution attack defense method based on phase shift transformers of the embodiment 1 of the application;

[0121] Figure 3 It is a protection effect diagram of the power system load redistribution attack defense method based on phase shift transformers of the embodiment 2 of the application in a 14-node test system;

[0122] Figure 4 It is a protection effect diagram of the power system load redistribution attack defense method based on phase shift transformers of the embodiment 2 of the application in a 30-node test system;

[0123] Figure 5Figure of protection effect of the power system load re-allocation attack defense method based on phase-shift transformer of embodiment 2 of the present application in the 118-node test system. DETAILED DESCRIPTION

[0124] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below in combination with the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0125] Embodiment 1

[0126] As shown in Figure 1 and Figure 2 , the power system load re-allocation attack defense method based on phase-shift transformer provided by the present application comprises the following basic steps:

[0127] S1, using a Stackelberg game model to describe the influence of an attacker on a system, so as to construct an influence elimination model of load re-allocation attack based on phase-shift transformer;

[0128] In this embodiment, in order to ensure concealment, the load re-allocation attack vector needs to satisfy:

[0129]

[0130] Wherein, N d is the number of load measurements in the system, ΔD k is the tampering value of the attacker on the kth load measurement;

[0131] In this embodiment, since the load and the line flow satisfy an equation relationship, in order to ensure concealment, the attacker needs to tamper with the load measurement at the same time, and the attack vector ΔF for the flow measurement can be expressed as the following formula:

[0132] ΔF=-L·A D ·ΔD (2)

[0134] Wherein, L is a power transfer distribution factor, and A D is a topological correlation matrix of buses and loads;

[0135] In this embodiment, since abnormal measurements exceeding the true value too much are easy to be detected by the control center, in order to ensure concealment, the true value of the attack vector generally does not exceed a certain range of the true value, and the attack vector needs to satisfy the following formula:

[0136]

[0137] where D k is the true value of the kth load measurement, is the amplitude coefficient of the attack, representing that the attack vector is within ζ times of the true value of the load;

[0138] In this embodiment, since the resources mastered by the attacker are often limited, there is an upper limit to the number of meters that the attacker can tamper with, so the attacker needs to satisfy:

[0139]

[0140] where N l is the number of transmission lines in the system, ω D,k and ω F,l are binary variables representing whether the load measurement and the line power flow measurement are attacked, that is, when the kth load measurement is attacked, ω D,k = 1, otherwise ω D,k = 0; when the lth line power flow is attacked, ω F,l = 1, otherwise ω F,l = 0, R a is the maximum number of measurements that can be attacked by the attacker;

[0141] In this embodiment, under the constraints (1)-(4) of the attacker, the influence of the attacker on the system can be described using the Stackelberg game model:

[0142]

[0143] s.t.(1)-(4)

[0144]

[0145] s.t.F = L·A P ·P - L·A D ·(D + ΔD * ) + (X -1 ·N LB ·L T - X -1 )·σ (9)

[0147]

[0148] where N g is the number of generators in the system, α i and β i are the generation cost coefficients, is the upper limit of the capacity of the transmission line, and upper and lower bounds of generator output, and upper and lower bounds of phase shift angle, A P topology incidence matrix of bus and generator, N lB topology incidence matrix of bus and branch, X is a diagonal matrix whose diagonal elements are the impedance on each transmission line, Φ is the set of lines equipped with phase shift transformers; P is the output of the generator, F is the power flow on the transmission line, σ l is the phase shift angle of the phase shift transformer on the lth line; the attacker's objective function (5) maximizes the operating cost of the system, (6) and (7) are the logical constraints of the relationship between the attack vectors ΔD k , ΔF l and the binary variable ω D,k , ω F,l ; (8)-(14) are the optimal power flow scheduling optimization problems of the system, where (8) is the objective function of the system-minimize operating cost, constraint (9) is the power flow equation in the form of power flow distribution transfer factor, constraint (10) is the supply and demand balance equation, (11)-(13) are the upper and lower bound constraints of the variables, and constraint (14) represents that the phase shift angle on the line without phase shift transformer should be 0.

[0149] S2, give the constraint conditions of the defender, introduce the role of the defender into the Stackelberg game model of the attacker and the system, and construct a three-layer game model of the defender-attacker-system;

[0150] In this embodiment, the defender is the top layer of the game, and the objective function is to minimize the operating cost and the cost of the phase shift transformer, and the deployment position and the number of the phase shift transformer are decided to minimize the influence of the load redistribution attack on the power grid; the three-layer optimization problem based on the influence of the load redistribution attack of the phase shift transformer can be described as follows:

[0151]

[0152] s.t.d l ∈{0, 1}, l = 1,..., N l (16)

[0154]

[0155] s.t.

[0156] (1)-(7)

[0157]

[0158] s.t.

[0159] (9)-(12)

[0160]

[0161] Among them, c l is the cost of deploying a phase-shifting transformer on line l, d l is a binary variable, representing whether the line l is equipped with a phase-shifting transformer; (15) is the defender's objective function, and (16) is d l The value constraint of , (17) is the attacker's objective function, (18) is the objective function of the system's optimal power flow, (19) represents the value range of the phase shift angle of the phase-shift transformer on line l, when d l =0 indicates that there is no phase-shifting transformer on the line.

[0162] S3. Decompose the three-level optimization problem of eliminating the impact of load redistribution attacks based on phase-shifting transformers into a main problem and sub-problems, and provide a solution algorithm for the global optimal solution;

[0163] In this embodiment, the three-layer optimization problem of eliminating the impact of load redistribution attacks based on phase-shifting transformers can be decomposed into a main problem and sub-problems according to the C&CG algorithm. The main problem can be described as follows:

[0164]

[0165]

[0166] Where, the subscript I is the iteration count, N I is the upper limit of the number of iterations, η is the auxiliary variable in the C&CG algorithm; (20) is the objective function of the main problem, constraint (21) represents the relationship between the auxiliary variable η and the objective function of the original three-layer optimization problem, and (22)-(25) are the iterative forms of the aforementioned power grid constraints (9)-(12) and (19).

[0167] In this embodiment, the sub-problems are the middle and lower two layers of the original three-layer optimization problem, which can be described as follows:

[0168]

[0169] st

[0170] (1)-(7)

[0171]

[0172] st

[0173] (9)-(12), (19)

[0174] In this embodiment, based on the above main problem and sub-problems, a global optimal solution algorithm is given: for a given initial value d0, the sub-problem is solved to obtain the attack vector ΔD * , the optimal value As the upper bound of the global optimal value; for the obtained ΔD * Solve the main problem and obtain the phase-shifting transformer deployment set d. The optimal value is used as the lower bound of the global optimal value; iterate until the upper and lower bounds converge.

[0175] S4. Analyze the inherent mechanism of load redistribution attacks and simplify the attack vector design problem based on the characteristics of load redistribution attacks;

[0176] In this embodiment, by analyzing the principle of load redistribution attacks, the following conclusions are drawn:

[0177] The load redistribution attack vector can be approximated by the following optimization problem, which has similar results to the original attack vector optimization problem:

[0178]

[0179] st(1),(3)

[0180] Among them, ρ l is the coefficient that characterizes the direction of the power flow, Ψ is the target line set selected by the attacker;

[0181] The above conclusions can be used to simplify the process of generating attack vectors to reduce the computational complexity of the three-layer optimization problem.

[0182] S5. Design an efficient attack impact elimination simplified solution algorithm for the three-layer optimization problem that is difficult to apply to large-scale systems due to the complexity of the model, shortening the computation time without significantly reducing optimality;

[0183] In this embodiment, a fast calculation method for the three-layer optimization problem of attack impact elimination is provided:

[0184] Given the initial phase-shifting transformer deployment set d0, calculate the optimal power flow scheduling problem of the system. If the power flow of line l satisfies the condition with γ as the threshold:

[0185]

[0186] Add the line γ to the attacker's target set Ψ and update the upper bound UB to:

[0187]

[0188] in, is the optimal value of the optimal power flow scheduling problem;

[0189] Solve the optimization problem (28) based on the current attack target Ψ to obtain the attack vector ΔD * ; According to the attack vector ΔD * Solve the main problem to obtain the optimal solution d * and η * , then update the lower bound LB to:

[0190] LB=η * (31)

[0192] Enter the iterative loop until the upper and lower bounds meet the threshold ε:

[0193]

[0194] Exit the loop, the optimal phase-shift transformer deployment set is the d of the current iteration * ; or satisfy Ψ * =Ψ I-1 ,UB I >UB I-1 ,LB I <LB I-1 One of them is to exit the loop, and the optimal phase-shift transformer deployment set is the d of the previous iteration. * .

[0195] S6. Define evaluation indicators and provide a method to determine the optimal phase-shifting transformer deployment location during the planning phase. Optimal power flow scheduling will determine the phase shift angle in real time to eliminate the impact of load redistribution attacks.

[0196] In this embodiment, the indicator A is defined in the planning stage. D,D′ To evaluate suitability for different load values:

[0197]

[0198] Among them, when the load value is D, the phase-shift transformer deployment set d calculated by the attack impact elimination three-layer optimization problem is * After installation on the line, when the load value changes to D′, the operating cost is f D,D′ ;

[0199] In this embodiment, if there is a phase-shifting transformer deployment set d according to load forecast * Index A under multiple D′ D,D′ All satisfy the threshold τ:

[0200] A D,D′ ≤τ (34)

[0202] Then according to the phase-shifting transformer deployment set d * Deploy phase-shifting transformers on actual transmission lines;

[0203] In this embodiment, the phase shift angle value of the phase-shifting transformer is determined in real time by the optimal power flow scheduling problem during the real-time operation of the power grid to maximize the elimination of the impact of the load redistribution attack:

[0204]

[0205] st(9)-(12)

[0206]

[0207] Among them, d * Deploy a collection for the phase-shifting transformer mentioned above.

[0208] Example 2

[0209] like Figure 3 、 Figure 4 and Figure 5 As shown in this embodiment, to verify the protection capability of the power system load redistribution attack defense method and device based on phase-shifting transformers proposed in this application, we compared the system operating costs when subjected to load redistribution attacks in three cases: when no phase-shifting transformers are deployed, when a phase-shifting transformer deployment set is deployed based on the C&CG method, and when a phase-shifting transformer deployment set is deployed based on the simplified method. The protection effect of IEEE 14-node, IEEE 30-node, and IEEE 118-node systems under load redistribution attacks can be found in [1]. Figure 3 、 Figure 4 and Figure 5 As shown in the preceding figure, the proposed attack impact elimination method can significantly reduce the operating cost under load redistribution attacks across a wide range of load values. For example, in the IEEE-14-node, 30-node, and 118-node test systems, the operating cost reduction under load redistribution attacks ranges from $308.7 / h to $1213.2 / h, $835.93 / h to $953.63 / h, and $2259.61 / h to $2494.86 / h, respectively. This verifies the effectiveness of the attack impact elimination method in reducing the economic losses after a load redistribution attack and eliminating the impact of load redistribution attacks. Furthermore, in the IEEE-14-node, IEEE-30-node, and IEEE-118-node test systems, the operating cost of the simplified method is almost identical to that of the C&CG-based method, confirming the optimality of the simplified method in solving the three-layer optimization of attack impact elimination.

[0210] In summary, the present application carries out power system load redistribution attack defense based on phase-shifting transformers, and solves the defects of the existing load redistribution attack defense methods in attack influence elimination. The present application models the defense framework as a three-layer optimization problem, and gives the optimal deployment location and quantity of phase-shifting transformers through designing an efficient iterative algorithm, which can significantly reduce the economic loss suffered by load redistribution attacks and eliminate the influence of load redistribution attacks. The present application has good protection effect in a wide range of loads and has strong applicability.

[0211] The present application constructs a three-layer optimization problem for load redistribution attack influence elimination based on phase-shifting transformers, designs an algorithm based on C&CG method for solving, and designs a simplified algorithm to significantly reduce the computational complexity without significantly reducing the optimality, and gives the optimal phase-shifting transformer deployment set under the load.

[0212] The present application designs an efficient attack influence elimination three-layer optimization problem simplification algorithm to solve the problem that the model is difficult to apply to large-scale systems due to the complexity of the model, and shortens the calculation time without significantly reducing the optimality.

[0213] The present application designs a method for determining the phase-shifting transformer deployment set according to the load prediction in the planning stage, which can significantly reduce the economic loss suffered by load redistribution attacks and eliminate the influence of load redistribution attacks.

[0214] The present application solves the technical problems of poor attack influence elimination effect, high economic loss suffered by load redistribution attacks, and poor load redistribution attack influence elimination effect in the prior art.

[0215] The above examples are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacement for part 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 application.

Claims

1. A method for defending against load redistribution attacks in a power system, characterized in that: The method comprises: S1. Use the Stackelberg game model to describe the attacker's impact on the system, and build a load redistribution attack impact elimination model based on phase-shifting transformers; S1 includes: S11 uses the following logic to constrain the attacker’s load redistribution attack vector: Where N d is the number of load measurements in the system, ΔD k is the tampered value measured by the attacker for the kth load; S12. Tampering with the attacker's power flow measurement in response, wherein the attack vector ΔF for the power flow measurement is expressed using the following logic: ΔF=-L·A D ·ΔD (2) Where L is the power transfer distribution factor, A D is the topological correlation matrix between busbar and load; S13. Use the following logic to set the true value range of the attack vector: -ζ·D k ≤ΔD k ≤ζ·D k k=1,…,N d (3) Where D k is the true value of the kth load measurement, ζ is the attack amplitude coefficient, which indicates that the attack vector is within ζ times the true value of the load; S14. Use the following logic to set an upper limit on the number of meters that an attacker can tamper with: Where, is the number of transmission lines in the system, ω D,k and are binary variables representing whether load measurement and line flow measurement are attacked, is the line flow number, R a The maximum number of measurements that an attacker can attack; S15. Describing a load redistribution attack impact elimination model based on setting load redistribution attack vector constraints, attack vectors, a true value range of the attack vectors, and an upper limit on the number of tampered meters; S2. Based on the preset defender constraints, the defender is introduced into the Stackelberg game model corresponding to the attacker and the preset system to construct a three-layer defender-attacker-system game model. The defender is used as the top layer of the game, and the minimization of operating costs and phase-shifting transformer costs is obtained and used as the objective function to make decisions on the deployment location and number of phase-shifting transformers, thereby describing a three-layer optimization problem for eliminating the attack impact of load redistribution on the phase-shifting transformers. S3. Decomposing the three-layer optimization problem of attack impact elimination using the C&CG algorithm to convert it into a main problem and sub-problems, setting a global optimal solution algorithm based on the main problem and the sub-problems, and optimizing the defender-attacker-system three-layer game model accordingly; S4. Analyze the inherent mechanism of the load redistribution attack based on the defender-attacker-system three-layer game model, and simplify the attack vector generation process based on preset load redistribution attack characteristics; S5. Construct and design a simplified solution algorithm for the three-layer optimization problem of attack impact elimination to address the problem that the model is difficult to apply to large-scale systems due to its complexity, so as to optimize the defender-attacker-system three-layer game model and obtain a phase-shifting transformer deployment set; S6. Define evaluation indicators for different load values ​​to determine the optimal phase-shifting transformer deployment location in the planning phase. In the operation phase, obtain and determine the value of the phase shift angle based on the optimal power flow scheduling information to eliminate the impact of load redistribution attacks.

2. The method for defending against load redistribution attacks in a power system according to claim 1, characterized in that: In S15, the Stackelberg game model is used to describe the following logic: st(1)-(4) s.t. F=L·A P ·P-L·A D ·(D+ΔD * )+(X -1 ·N LB ·L T -X -1 )·σ (9) Where N g is the number of generators in the system, α i and β i is the power generation cost coefficient, is the upper limit of the transmission line capacity, and are the upper and lower bounds of the generator output, and is the upper and lower bounds of the phase shift angle, A P is the topological correlation matrix between busbar and generator, N LB is the topological correlation matrix of the busbar and the branch, X is a diagonal matrix whose diagonal elements are the impedances on each transmission line, Φ is the set of lines with phase-shifting transformers deployed; P is the output of the generator, F is the power flow on the transmission line, For the The phase shift angle of the phase-shifting transformer on the line; the attacker's objective function (5) is to maximize the operating cost of the system, and the formula (6) and the formula (7) are used to characterize the attack vector ΔD k 、 With the binary variable ω D,k , The logical constraints of the relationship; the equations (8) to (14) are the system optimal power flow scheduling optimization problem, wherein the equation (8) is the objective function of the system - minimizing the operating cost, the constraint (9) is the power flow equation in the form of the power flow distribution transfer factor, the constraint (10) is the supply and demand balance equation, and the equations (11) to (13) are the upper and lower limit constraints of the variables.

3. The method for defending against load redistribution attacks in a power system according to claim 1, characterized in that: In S2, the following logic is used to describe the three-layer optimization problem of attack impact elimination: st(1)-(7) st(9)-(12) Where, For online The cost of deploying a phase-shifting transformer, is a binary variable representing the line Whether to deploy a phase-shifting transformer; Formula (15) is the defender's objective function, and Formula (16) is The value constraint of , the formula (17) is the attacker's objective function, the formula (18) is the objective function of the system's optimal power flow, and the formula (19) represents the line The range of phase shift angle of the upper phase shift transformer.

4. The method for defending against load redistribution attacks in a power system according to claim 1, characterized in that: The step S3 comprises: S31. According to the C&CG algorithm, the upper-level problem and the lower-level problem of the three-level optimization problem of attack impact elimination are merged, and constraints are gradually added as the iteration proceeds, to form the main problem. The main problem is described using the following logic: Where, subscript I is the iteration count, N I is the upper limit of the number of iterations, η is the auxiliary variable in the C&CG algorithm; the formula (20) is the objective function of the main problem, the constraint (21) characterizes the relationship between the auxiliary variable η and the objective function of the original three-layer optimization problem, and the formulas (22) to (25) are the iterative forms of the power grid constraint (9) to the power grid constraint (12) and the power grid constraint (19); S32: Merge the middle layer and the lower layer of the three-layer optimization problem of attack impact elimination as the sub-problem; wherein the sub-problem is described using the following logic: st(1)-(7) st(9)-(12), (19) S33. Based on the main problem and the sub-problems, the three-layer optimization problem of eliminating the attack impact is solved, and the global optimal solution algorithm is given.

5. The power system load redistribution attack defense method according to claim 4, characterized in that: The S33 includes: S331, solve the sub-problem for the preset initial value d0 to obtain the attack vector ΔD * , use the following logic to obtain the optimal value as the upper bound of the global optimal value: S332. Obtain and use ΔD * Solve the main problem and get the phase-shifting transformer deployment set d and the optimal value η * As the lower bound of the global optimal value; S333, looping and iterating from S331 to S332 until the upper bound of the global optimal value and the lower bound of the global optimal value converge.

6. The method for defending against load redistribution attacks in a power system according to claim 1, characterized in that: In S4, by analyzing the intrinsic mechanism information, the following logic is used to perform an optimization problem approximation operation to obtain a load redistribution attack vector and obtain an approximate result of the original attack vector optimization problem: st(1),(3) Where, is the coefficient that characterizes the direction of the power flow, and Ψ is the target line set selected by the attacker.

7. The method for defending against load redistribution attacks in a power system according to claim 1, characterized in that: The S5 includes: S51. Given the initial phase-shifting transformer deployment set d0, calculate the optimal power flow scheduling problem of the preset system. If the line The power flow satisfies the condition with γ as the threshold: Add the line l to the attacker's target set Ψ and use the following logic to update the global optimal value upper bound UB: in, is the optimal value of the optimal power flow scheduling problem; S52: Solve the optimization problem described in equation (28) based on the current target set Ψ to obtain the attack vector ΔD * ; S53, according to the attack vector ΔD * , solve the main problem to obtain the optimal solution d * ,η * , use the following logic to update the global optimal value lower bound LB: LB=η * (31) S54, iterate and loop the steps S51 to S53 until the upper bound of the global optimal value and the lower bound of the global optimal value meet the following conditions, and use the optimal solution d obtained in the current iteration as the optimal solution. * As a collection deployed using a PhaseShifter transformer: Where ε is the threshold; S55: The target set Ψ, the global optimal value upper bound UB, and the global optimal value lower bound LB satisfy the following conditions: Ψ * =Ψ I-1 ,UB I >UB I-1 ,LB I <LB I-1 Exit the loop and use the optimal solution d obtained in the previous iteration * As the phase-shifting transformer deployment set.

8. The method for defending against load redistribution attacks in a power system according to claim 1, characterized in that: The S6 includes: S61. In the pre-set planning stage, the following logic is used to define the different load value evaluation indicators A: D,D′ : Among them, when the load value is D, the phase-shifting transformer deployment set d calculated by the attack impact elimination three-layer optimization problem is * After installation on the line, when the load value changes to D′, the operating cost is f D,D′ ; S62. If, according to load forecast, there is a deployment set d of the phase-shifting transformers * The different load value evaluation index A under multiple D′ D,D′ All satisfy the following threshold τ: A D,D′ ≤τ (34) Then according to the deployment set d * Deploy phase-shifting transformers on transmission lines; S63. Construct and determine the phase shift angle of the phase-shifting transformer based on the optimal power flow scheduling problem using the following logic: st(9)-(12) Where, d * A set is deployed for the phase-shifting transformer.

9. A power system load redistribution attack defense system, configured to execute the power system load redistribution attack defense method according to any one of claims 1 to 8, characterized in that: The system comprises: An impact elimination model construction module is used to describe the attacker's impact on the system using the Stackelberg game model, so as to build a load redistribution attack impact elimination model based on phase-shifting transformers; A three-layer game model construction module is used to introduce the defender into the Stackelberg game model corresponding to the attacker and the preset system according to the preset defender constraints, so as to construct a three-layer defender-attacker-system game model; wherein, the defender is used as the top layer of the game, and the minimization of operating cost and phase-shifting transformer cost is obtained and used as the objective function to make decisions on the deployment location and number of phase-shifting transformers, describing the three-layer optimization problem of eliminating the attack impact of the phase-shifting transformer load redistribution. The three-layer game model construction module is connected to the impact elimination model construction module; A problem decomposition module is used to eliminate the three-layer optimization problem of the attack impact, using the C&CG algorithm to perform decomposition operations to convert into a main problem and sub-problems, and setting a global optimal solution algorithm based on the main problem and the sub-problems to optimize the defender-attacker-system three-layer game model. The problem decomposition module is connected to the three-layer game model construction module; a vector generation process simplification module, configured to analyze the inherent mechanism of the load redistribution attack based on the defender-attacker-system three-layer game model and simplify the attack vector generation process based on preset load redistribution attack characteristics; the vector generation process simplification module is connected to the first optimization module of the three-layer game model; A simplified solution module is used to construct and design a simplified solution algorithm for the three-layer optimization problem of attack impact elimination, which is difficult to apply to large-scale systems due to the complexity of the model, to optimize the defender-attacker-system three-layer game model and obtain a phase-shifting transformer deployment set. The simplified solution module is connected to the three-layer game model construction module; The attack impact elimination module is used to define evaluation indicators for different load values ​​to determine the optimal phase-shifting transformer deployment location in the planning stage, and to obtain and decide the value of the phase shift angle based on the optimal power flow scheduling information in the operation stage to eliminate the impact of the load redistribution attack. The attack impact elimination module is connected to the simplification solution module.

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