Power system state feedback period MPC control method under spoofing attack

Abstract

The invention requests to protect a state feedback period MPC control method of a power system under spoofing attack. The method comprises the following steps: firstly, establishing an LFC system model comprising a doubly-fed induction generator DFIG; potential spoofing attacks are modeled as Bernoulli processes with known conditional probabilities. A dynamic event triggering mechanism is adopted, and based on internal dynamic variables, the system can flexibly deal with an abnormal state, and the real-time defense capability for hostile attacks is enhanced. Secondly, describing external interference by using a quadratic bounded QB theorem, and designing a state feedback PMPC controller on this basis; the PMPC adjusts the control input according to the real-time feedback of the system state, optimizes the performance, and ensures that the system state is kept in a periodic invariant set, thereby maintaining the stability of the system under the uncertain interference. Finally, a simulation result shows that the designed PMPC controller can quickly respond to wind power generation fluctuation, and the dynamic performance of the frequency of a power system is remarkably improved.

Description

Technical Field

[0001] The invention relates to the field of power systems, and mainly to a state feedback periodic MPC control method for power systems under deception attacks. Background Art

[0002] The three major stability factors of power systems include frequency stability, voltage stability and power angle stability. Among them, frequency stability reflects the active power balance of the power system. Load frequency control (LFC) is the main functional module to achieve active power balance (Literature: Yang J, Sun X, Liao K, He Z, Cai L. Model predictive control-based load frequency control for power systems with wind-turbine generators. IET Renewable Power Generation. 2019 Nov; 13 (15): 2871-2879.). However, when wind power is connected to the power system, the intermittent, volatile and high penetration characteristics of wind power will affect the frequency balance (Literature: Gulzar MM, Iqbal M, Shahzad S, Muqeet HA, Shahzad M, Hussain MM. Load frequency control (LFC) strategies in renewable energy-based hybrid power systems: A review. Energies. 2022 May 10; 15 (10): 3488.). Doubly-fed induction generators (DFIGs), as a type of variable-speed wind turbine generator, can achieve frequency regulation by modulating the torque set point of the rotor-side converter (Reference: Ekanayake JB, Jenkins N, Strbac G. Frequency response from wind turbines. Wind Engineering. 2008 Dec; 32 (6): 573-586.). This control scheme has shown good results in interconnected systems with potential high penetration of wind power in the eastern and western United States (Reference: Vittal V, Ayyanar R. Grid Integration and Dynamic Impact of Wind Energy. Springer New York. 2013 Oct.). Although the academic community has provided many solutions to solve the frequency fluctuation of doubly-fed induction wind turbines in LFC system applications, some other issues, such as communication efficiency and cyber attacks, may also significantly affect the frequency quality of LFC systems.

[0003] Modern power systems usually adopt open communication infrastructure, which reduces costs and increases flexibility, but also brings network security issues (Reference: Peng C, Sun H, Yang M, Wang YL. A survey on security communication and control for smart grids under malicious cyber attacks. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2019 Jan 1; 49 (8): 1554-1569.). More importantly, due to the addition of new energy, control requirements are increased, control objects are complicated, and limited communication and computing resources are squeezed by higher load data transmission (Reference: Mohan AM, Meskin N, Mehrjerdi H. A comprehensive review of the cyber-attacks and cyber-security on load frequency control of power systems. Energies. 2020 Jul 28; 13 (15): 3860.). Network communication has become an important part that must be considered in control system design. In order to save network bandwidth and minimize the frequency of data transmission, event-triggered schemes have become a key research area in modern network power systems (Reference: Ge X, Han QL, Ding L, Wang YL, Zhang XM. Dynamic event-triggered distributed coordination control and its applications: A survey of trends and techniques. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2020 Jul 29; 50 (9): 3112-3125.). The combination of event-triggered mechanism and LFC can effectively solve the increasingly complex power grid control problems while reducing the network communication load and pressure caused by the complexity of control.

[0004] Model predictive control (MPC) is another solution for LFC and has been widely concerned. The advantage of the MPC controller is that the system state and response of the next prediction cycle can be predicted in advance. After obtaining the prediction information, the control signal of the system is optimized to improve the frequency response of the system. (Literature: Hu Z, Su R, Ling KV, Guo Y, MaR. Resilient event-triggered MPC for load frequency regulation with windturbines under false data injection attacks. IEEE Transactions on AutomationScience and Engineering. 2023Nov 29.). MPC has fast response characteristics and robustness to wind and load changes. Based on this, when studying the LFC problem of power system, it is of great research significance and value to consider how to design MPC controller to reduce computing resource consumption under the premise of ensuring global control performance (Literature: Liu Y, Chen Y, LiM. Dynamic event-based model predictive load frequency control for powersystems under cyber attacks. IEEE Transactions on Smart Grid. 2020Sep 7; 12(1): 715-725.). For interconnected power systems with DFIG, it is difficult to accurately predict wind speed. In the context of renewable energy grid connection, this is a problem that the LFC system needs to solve.

[0005] CN117913988A solves the problem of load frequency control of multi-regional power systems based on a flexible dynamic event triggering scheme under DoS attacks. The following research is conducted: a dynamic model of a multi-regional LFC system with a communication network under different system parameters is established; a model is built for energy-constrained DoS attacks; a flexible dynamic event triggering scheme is constructed: when the impact of DoS attacks is not considered in the system, the event triggering condition introduces an internal variable ρ(t), ρ(t) = 1-tanh(∈·e T(t)e(t)); When considering DoS attacks in the system, if the current state meets the triggering conditions and is in the attack sleep interval, it is the triggering moment. The triggering moment will also appear at the switching point between the end of the attack interval of the current attack cycle and the beginning of the sleep interval in the next attack cycle; according to the constructed elastic dynamic event triggering scheme, the load frequency of the multi-regional power system is controlled considering DoS attacks. It can further alleviate the pressure on communication bandwidth while improving the system control performance.

[0006] CN 116365509 A relates to a distributed model predictive control of load frequency tube of power system, including: establishing several regional interconnected power system load frequency control simulation models; setting a power system load frequency control nominal model describing the dynamic characteristics of the interconnected power system under the condition of ignoring uncertain interference and inter-regional coupling; determining the objective function and constraint conditions according to the power system load frequency control nominal model; establishing a distributed feedback control law for compensating the trajectory difference between the power system nominal model and the simulation model due to disturbance; adding the feedback control amount to the nominal control amount to obtain the final control amount and applying it to the actual system. Aiming at the wind speed disturbance problem caused by wind power grid connection, a distributed model predictive control method for power system with stronger robustness and capable of effectively handling uncertain interference is proposed, thereby ensuring the safe and stable operation of the power system. Summary of the invention

[0007] The present invention aims to solve the above problems of the prior art. A state feedback periodic MPC control method for a power system under a deception attack is proposed. The technical solution of the present invention is as follows:

[0008] A state feedback periodic MPC control method for a power system under a deception attack comprises the following steps:

[0009] Step a, establishing a mathematical model of load frequency control of a power system including a DFIG (doubly fed induction generator);

[0010] Step b, introducing a dynamic event trigger mechanism and setting trigger conditions;

[0011] Step c, introducing a deception attack and modeling the deception attack as a Bernoulli process with known conditional probabilities;

[0012] Step d, combining the state feedback moving horizon model predictive control (PMPC) method with the quadratic bounded QB theorem and constructing a closed-loop system;

[0013] Step e, solve the LMI optimization problem to perform system stability analysis and process system constraints. Further, in step a, a mathematical model of load frequency control of the power system including DFIG (doubly fed induction generator) is established as follows:

[0014] A simplified frequency response model of a wind turbine based on DFIG is established. This simplified model can be described by the following formula:

[0015]

[0016] P ω =ω n X3i qr (3)

[0017] After linearization, formula (3) can be rewritten as:

[0018] P w =ω opt X3i qr (4)

[0019]

[0020] Among them, i qr 、V qr ,ω n , H t , T m They represent the q-axis component of the rotor current, the q-axis component of the rotor voltage, the synchronous speed, the equivalent inertia constant of the wind turbine, and the mechanical torque. ω , T e 、i qs , L m , L ss They represent the regulating valve power, electric torque, s-axis component of the rotor current, magnetizing inductance, and stator self-inductance respectively. X2, X3, and T1 are known constants. ω opt is the angular velocity actuation point of the wind turbine. On the assumption that wind power is the load, the fluctuation caused by wind power in the control model is given by ΔP w capture.

[0021] Furthermore, the mathematical model of the system is established as follows:

[0022] The overall generator-load dynamic relationship can be expressed as:

[0023]

[0024] Δf, D, M, ΔP m , ΔP ω , ΔP l They respectively represent the system frequency deviation, load-damping constant, generator rotation inertia, mechanical power change, control valve position change, and load disturbance change.

[0025] The dynamics of the prime mover can be described as:

[0026]

[0027] T ch , ΔP v They represent the turbine time constant and the change in governor valve position respectively.

[0028] The dynamic equation of the speed regulator can be expressed as:

[0029]

[0030] T g , u represent the speed regulator time constant and control input respectively.

[0031] Define ΔΓ t Indicates the degree of deviation of the system frequency:

[0032] ΔΓ t =∫ACE τ dτ (9)

[0033] ACE τ Represents the regional control error.

[0034] Through the inverse Laplace transform, the state space model of the LFC system can be obtained as follows:

[0035]

[0036] Among them, x t =[Δf,ΔP m ,ΔΓ t ,ΔP υ ,Δi qr ,Δω n ] T represents the state vector, u t =[u,ΔV qr ] T is the system input, w t =[w1,w2] T =[ΔP ι ,ΔT m ] T is a bounded disturbance; represents the system matrix and can be obtained indirectly from the given values.

[0037]

[0038]

[0039] Furthermore, in step b, the dynamic event triggering mechanism is as follows:

[0040] At each moment k, the sensor obtains the system state x k,Considering the limited network bandwidth, it is necessary to determine the current measurement state value x k Whether the trigger condition is met and transmitted to the controller, assuming k ET is the next trigger moment, the trigger condition can be described as:

[0041]

[0042] λ k , x k They represent internal dynamic variables, latest trigger data, and system status respectively.

[0043] Let the measurement error The expression of the scalar function λ is:

[0044]

[0045] Among them, ε,δ∈R + ,ρ∈(0,1),λ0≥0,P>0 is the matrix to be determined. ε,δ,ρ are given coefficients.

[0046] Furthermore, in step c, the deception attack model is as follows:

[0047] Published data The data packets may be attacked maliciously when transmitted on the communication channel. There are spoofing attacks.

[0048]

[0049] Among them, ξ k is the energy signal constant, belonging to L2=[0,+∞) and satisfying θ k represents a Bernoulli variable with a value of 0 or 1, θ k =0 means is successfully transmitted to the controller; otherwise, θ k =1 indicates a spoofing attack. In addition,

[0050]

[0051] in, yes The constants in .

[0052] Furthermore, in step d, the state feedback controller is designed as follows:

[0053]

[0054] Among them, K [t] =K [mod(t,v+1)],K [t] is the feedback gain matrix to be designed; K [mod(t,v+1)] Represents the modulo operation.

[0055] make It can be concluded that the augmented closed-loop system is:

[0056]

[0057] in, A, B, and F represent the system matrices after discretization. represents the matrix to be determined. Θ, θ k , m represents the attack probability.

[0058] Furthermore, the disturbance process is handled using quadratic boundedness as follows:

[0059] Consider bounded interference and finite attack energy:

[0060]

[0061] For all allowed perturbations if Equivalent to The system is quadratically bounded. d. They represent the size of bounded interference and finite attack energy respectively.

[0062] Furthermore, in step e, the LMI optimization problem is solved to perform system stability analysis:

[0063] Define the Lyapunov function as

[0064]

[0065] Among them, P [t] =P [mod(t,v+1)] For the convenience of writing, V is used in the subsequent calculation process. t|k Instead of V(x t|k ,λ t|k ), in order to ensure the stability of the system, the condition ΔV t|k ≤0;

[0066] Assume that the system satisfies the following constraints at each time k:

[0067]

[0068] Through mathematical transformation, the above inequality is transformed into the following LMI form:

[0069]

[0070] Among them, N [t] =K [t] Q [t] ,

[0071]

[0072] * indicates a symmetrical structure. [t] , K [t] , Q [t] , H [t] is the matrix to be determined. η, I, is a constant and is given in the simulation.

[0073] Furthermore, the process of processing system constraints is as follows:

[0074] Guarantee x ∞|k =0, V ∞|k = 0, sum (19) from t = 0 to ∞, considering the performance index function in and represents a weighting matrix with appropriate dimensions, γ k is a positive variable, representing the upper limit of the performance index function; the upper limit of the cost function can be expressed as

[0075]

[0076] P [0] Represents the first calculated value of the required matrix.

[0077] Applying Shur's complement theorem, we can get:

[0078]

[0079] Define z ι For the ιth row of the ι-ordered identity matrix, we can obtain:

[0080]

[0081] Ω1,Ψ t|k , Ω2, Φ are the matrices to be determined.

[0082] If there is a matrix Ω2=[-K [t] ,-K [t] ,[0,K [t] ]], Φ=[P [t] ,P [t] ,Q w ].

[0083] Assume that there exists a matrix U that satisfies the inequality

[0084]

[0085] Applying Shur's complement theorem, we can get:

[0086]

[0087] In the case that the above LMI has a solution, ensuring the stability of the system, we can find Q [t] ,N [t] ,H [t] ,

[0088] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, a state feedback periodic MPC control method for a power system under a deception attack as described in any one of the items is implemented.

[0089] A non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements a state feedback periodic MPC control method for a power system under a deception attack as claimed in any one of claims 1 to 8.

[0090] The advantages and beneficial effects of the present invention are as follows:

[0091] The present invention proposes a state feedback periodic model predictive control method for a load frequency control system for dealing with deception attacks and external interference. Taking deception attacks and external interference into consideration at the same time, a state feedback PMPC controller is designed to significantly improve the dynamic performance of the power system frequency. Claims 2 and 3 establish a mathematical model of load frequency control of a power system including DFIG; according to claim 4, a dynamic event trigger mechanism is introduced; claim 5 introduces deception attacks and models deception attacks as Bernoulli processes with known conditional probabilities; on the basis of claim 6, combined with claim 7, the state feedback rolling time domain model predictive control (PMPC) method is combined with the quadratic bounded (QB) theorem and a closed-loop system is constructed; claims 8 and 9 solve the LMI optimization problem to perform system stability analysis and process system constraints; finally, in order to achieve the indicators in claims 8 and 9, a simulation study is conducted on the proposed wind power grid-connected power system to verify the effectiveness of the control method proposed in this study. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 The present invention provides a simplified frequency response model of a wind turbine generator based on DFIG in a preferred embodiment;

[0093] Figure 2It is a simplified model of the DFIG of the present invention;

[0094] Figure 3 This is the energy-limited non-periodic deception attack signal diagram;

[0095] Figure 4 It is the change diagram of system state frequency deviation;

[0096] Figure 5 This is a graph showing the change of the dynamic variable λ under different violation thresholds. DETAILED DESCRIPTION

[0097] The following will describe the technical solutions in the embodiments of the present invention in detail in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention.

[0098] The technical solution of the present invention to solve the above technical problems is:

[0099] The following will describe the technical solutions in the embodiments of the present invention in detail in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention.

[0100] The technical solution of the present invention to solve the above technical problems is:

[0101] first, Figure 1 and Figure 2 A simplified frequency response model of a DFIG-based wind turbine and a simplified model of the DFIG itself are provided. Figure 3 Aperiodic spoofing attack signals are described, showing the characteristics of randomness and energy limitation. Figure 4 The change of system state frequency deviation is shown: under non-periodic spoofing attack, the system frequency deviation increases significantly, showing an unstable trend. Through the MPC method, the control frequency deviation gradually tends to zero. Figure 5 The changes of dynamic variables under different trigger thresholds are shown. By adjusting the trigger threshold, the control strategy has stronger anti-interference performance under attack signals. The specific implementation includes the following steps:

[0102] Step a, establishing a mathematical model of load frequency control of a power system including DFIG;

[0103] Step b, introduce a dynamic event trigger mechanism and give the trigger conditions;

[0104] Step c, introducing a deception attack and modeling the deception attack as a Bernoulli process with known conditional probabilities;

[0105] Step d, combining the state feedback moving horizon model predictive control (PMPC) method with the quadratic bounded (QB) theorem and constructing a closed-loop system;

[0106] Step e, solving the LMI optimization problem to analyze system stability and process system constraints;

[0107] Step f, conduct simulation study on the proposed wind power grid-connected power system to verify the effectiveness of the control method proposed in this study.

[0108] In step a, the simplified DFIG mathematical model established is as follows:

[0109] Figure 1 The simplified frequency response model of a wind turbine based on DFIG is shown. This simplified model can be described by the following formula:

[0110]

[0111] P ω =ω n X3i qr (27)

[0112] After linearization, formula (3) can be rewritten as:

[0113] P w =ω opt X3i qr (28)

[0114]

[0115] Among them, ω opt is the speed actuation point. Based on the assumption that wind power is the load, the fluctuation caused by wind power in the control model is given by ΔP w capture.

[0116] Furthermore, the load frequency control system model including DFIG is as follows: Figure 2 As shown. The system mathematical model is established as follows:

[0117] The overall generator-load dynamic relationship can be expressed as:

[0118]

[0119] The dynamics of the prime mover can be described as:

[0120]

[0121] The dynamic equation of the speed regulator can be expressed as:

[0122]

[0123] Define ΔΓ t Indicates the degree of deviation of the system frequency:

[0124] ΔΓ t =∫ACE τ dτ (33)

[0125] Through the inverse Laplace transform, the state space model of the LFC system can be obtained as follows:

[0126]

[0127] Among them, x t =[Δf,ΔP m ,ΔΓ t ,ΔP υ ,Δi qr ,Δω n ] T represents the state vector, u t =[u,ΔV qr ] T is the system input, w t =[w1,w2] T =[ΔP ι ,ΔT m ] T is a bounded disturbance.

[0128]

[0129] In step b, the dynamic event triggering mechanism is as follows:

[0130] At each moment k, the sensor obtains the system state x k ,Considering the limited network bandwidth, it is necessary to determine the current measurement state value x k Whether the trigger condition is met and transmitted to the controller. ET is the next trigger moment, the trigger condition can be described as:

[0131]

[0132] Let the measurement error The expression of the scalar function λ is:

[0133]

[0134] Among them, ε,δ∈R + ,ρ∈(0,1),λ0≥0,P>0 is the matrix to be determined.

[0135] In step c, the deception attack model is as follows:

[0136] Published data When transmitting on the communication channel, it may be subject to malicious attacks. A spoofing attack can be

[0137]

[0138] Among them, ξ k is the energy signal constant, belonging to L2=[0,+∞) and satisfying θ k represents a Bernoulli variable with a value of 0 or 1, θ k =0 means is successfully transmitted to the controller; otherwise, θ k =1 indicates a spoofing attack has occurred.

[0139] also,

[0140]

[0141] in, yes The constants in .

[0142] In step d, the state feedback controller is designed as follows:

[0143]

[0144] Among them, K [t] =K [mod(t,v+1)] ,K [t] is the feedback gain matrix to be designed.

[0145] make It can be concluded that the augmented closed-loop system is:

[0146]

[0147] in,

[0148]

[0149] Furthermore, the disturbance process is handled using quadratic boundedness as follows:

[0150] Consider bounded interference and finite attack energy:

[0151]

[0152] For all allowed perturbations if Equivalent to The system is quadratically bounded.

[0153] In step e, the LMI optimization problem is solved to perform system stability analysis:

[0154] Define the Lyapunov function as

[0155]

[0156] Among them, P [t] =P [mod(t,v+1)] For the convenience of writing, V is used in the subsequent calculation process. t|k Instead of V(x t|k ,λ t|k ). In order to ensure the stability of the system, the condition ΔV needs to be met t|k ≤0

[0157] Assume that the system satisfies the following constraints at each time k:

[0158]

[0159] Through mathematical transformation and applying the above results, the above inequality is transformed into the following LMI form:

[0160]

[0161] Among them, N [t] =K [t] Q [t] ,

[0162]

[0163]

[0164] Furthermore, the process of processing system constraints is as follows:

[0165] Guarantee x ∞|k =0, V ∞|k = 0, sum (19) from t = 0 to ∞. Consider the performance indicator function in and denotes a weighting matrix with appropriate dimension. Let γ k Becomes a suitable positive variable, representing the upper limit of the performance indicator function. The upper limit of the cost function can be expressed as

[0166]

[0167] Applying Shur's complement theorem, we can get:

[0168]

[0169] Define z ι For the ιth row of the ι-ordered identity matrix, we can obtain:

[0170]

[0171] If there is a matrix Ω2=[-K [t] ,-K [t] ,[0,K [t] ]], Φ=[P [t] ,P [t] ,Q w ].

[0172] Assume that there exists a matrix U that satisfies the inequality

[0173]

[0174] Applying Shur's complement theorem, we can get:

[0175]

[0176] In the case that the above LMI has a solution, ensuring the stability of the system, we can find Q [t] ,N [t] ,H [t] ,

[0177] In the step f, a mathematical model of a doubly fed induction generator (DFIG) is established to simulate a deception attack signal model. A state feedback controller is implemented in MATLAB / Simulink, combined with a model predictive control (MPC) algorithm. The response of system dynamic variables and frequency deviations under different control trigger thresholds is studied to verify the robustness and adaptability of the control method. The changes in system frequency deviation before and after the attack are compared to verify the attack suppression effect of the proposed control method. Through the simulation results, it can be seen that the proposed control method is effective and has advantages in resisting non-periodic deception attacks and maintaining system frequency stability.

[0178] The systems, devices, modules or units described in the above embodiments may be implemented by computer chips or entities, or by products with certain functions.

[0179] Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0180] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0181] The above embodiments should be understood to be only used to illustrate the present invention and not to limit the protection scope of the present invention. After reading the contents of the present invention, technicians can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A state feedback periodic MPC control method for a power system under a deception attack, characterized by: The following steps are involved: Step a, establishing a mathematical model of load frequency control of a power system including a DFIG double-fed induction generator; Step b, introduce a dynamic event trigger mechanism and set the trigger conditions; Step c, introducing a deception attack and modeling the deception attack as a Bernoulli process with known conditional probabilities; Step d, combining the state feedback moving horizon model predictive control PMPC method with the quadratic bounded QB theorem and constructing a closed-loop system; Step e: Solve the LMI optimization problem to analyze the system stability and process the system constraints.

2. The state feedback periodic MPC control method for a power system under a deception attack according to claim 1 is characterized in that: In the step a, a mathematical model of load frequency control of a power system including a DFIG double-fed induction generator is established as follows: A simplified frequency response model of a wind turbine based on DFIG is established. This simplified model can be described by the following formula: P ω =ω n X3i qr (3) After linearization, formula (3) can be rewritten as: P w =ω opt X3i qr (4) Among them, i qr 、V qr ,ω n , H t , T m They represent the q-axis component of the rotor current, the q-axis component of the rotor voltage, the synchronous speed, the equivalent inertia constant of the wind turbine, and the mechanical torque, respectively. ω , T e 、i qs , L m , L ss They represent the regulating valve power, electric torque, s-axis component of the rotor current, magnetizing inductance, and stator self-inductance respectively. X2, X3, and T1 are known constants. ω opt is the angular velocity actuation point of the wind turbine. On the assumption that wind power is the load, the fluctuation caused by wind power in the control model is given by ΔP w capture.

3. The state feedback periodic MPC control method for a power system under a deception attack according to claim 2 is characterized in that: The mathematical model of the system is established as follows: The overall generator-load dynamic relationship can be expressed as: Δf, D, M, ΔP m , ΔP ω , ΔP l They represent system frequency deviation, load-damping constant, generator moment of inertia, mechanical power change, control valve position change, and load disturbance change respectively; The dynamics of the prime mover can be described as: T ch , ΔP v They represent the turbine time constant and the governor valve position change respectively; The dynamic equation of the speed regulator can be expressed as: T g , u represent the governor time constant and control input respectively; Define ΔΓ t Indicates the degree of deviation of the system frequency: DG t =∫ACE τ dt (9) ACE τ represents the regional control error; Through the inverse Laplace transform, the state space model of the LFC system can be obtained as follows: Among them, x t =[Δf,ΔP m ,ΔΓ t ,ΔP υ ,Δi qr ,Δω n ] T represents the state vector, u t =[u,ΔV qr ] T is the system input, w t =[w1,w2] T =[ΔP ι ,ΔT m ] T is a bounded disturbance; represents the system matrix, which can be obtained indirectly from the given values; 4. The state feedback periodic MPC control method for a power system under a deception attack according to claim 3 is characterized in that: In step b, the dynamic event triggering mechanism is as follows: At each moment k, the sensor obtains the system state x k ,Considering the limited network bandwidth, it is necessary to determine the current measurement state value x k Whether the trigger condition is met and transmitted to the controller, assuming k ET is the next trigger moment, the trigger condition can be described as: λ k , x k Respectively represent internal dynamic variables, latest trigger data, and system status; Let the measurement error The expression of the scalar function λ is: Among them, ε,δ∈R + ,ρ∈(0,1),λ0≥0,P>0 is the matrix to be determined, ε, δ, ρ are given coefficients.

5. The state feedback periodic MPC control method for a power system under a deception attack according to claim 4 is characterized in that: In step c, the deception attack model is as follows: Published data The data packets may be attacked maliciously when transmitted on the communication channel. There are spoofing attacks. Among them, ξ k is the energy signal constant, belonging to L2=[0,+∞) and satisfying θ k represents a Bernoulli variable with a value of 0 or 1, θ k =0 means is successfully transmitted to the controller; otherwise, θ k =1 indicates a spoofing attack. In addition, in, yes The constants in .

6. The state feedback periodic MPC control method for a power system under a deception attack according to claim 5 is characterized in that: In step d, the state feedback controller is designed as follows: Among them, K [t] =K [mod(t,v+1)] ,K [t] is the feedback gain matrix to be designed; K [mod(t,v+1)] Represents modular operation; make It can be concluded that the augmented closed-loop system is: in, A, B, and F represent the system matrices after discretization. represents the matrix to be determined, Θ, θ k , m represents the attack probability.

7. The state feedback periodic MPC control method for a power system under a spoofing attack according to claim 6 is characterized in that: The perturbation process using quadratic boundedness is as follows: Consider bounded interference and finite attack energy: For all allowed perturbations if Equivalent to The system is quadratically bounded, d. They represent the size of bounded interference and finite attack energy respectively.

8. The state feedback periodic MPC control method for a power system under a spoofing attack according to claim 7 is characterized in that: In step e, the LMI optimization problem is solved to perform system stability analysis: Define the Lyapunov function as Among them, P [t] =P [mod(t,v+1)] For the convenience of writing, V is used in the subsequent calculation process. t|k Instead of V(x t|k ,λ t|k ), in order to ensure the stability of the system, the condition ΔV t|k ≤0; Assume that the system satisfies the following constraints at each time k: Through mathematical transformation, the above inequality is transformed into the following LMI form: in, * indicates symmetrical structure, N [t] , K [t] , Q [t] , H [t] is the matrix to be determined, η, I, is a constant and is given in the simulation.

9. The state feedback periodic MPC control method for a power system under a spoofing attack according to claim 8, characterized in that: The process of handling system constraints is as follows: Guarantee x ∞|k =0, V ∞|k = 0, sum (19) from t = 0 to ∞, considering the performance index function in and represents a weighting matrix with appropriate dimensions, γ k is a positive variable, representing the upper limit of the performance index function; The upper limit of the cost function can be expressed as P [0] Represents the first calculated value of the required matrix; Applying Shur's complement theorem, we can get: Define z ι For the ιth row of the ι-ordered identity matrix, we can obtain: Ω1,Ψ t|k ,Ω2,Φ are the matrices to be determined; If there is a matrix Ω2=[-K [t] ,-K [t] ,[0,K [t] ]] Φ=[P [t] ,P [t] ,Q w ]. Assume that there exists a matrix U that satisfies the inequality Applying Shur's complement theorem, we can get: In the case that the above LMI has a solution, ensuring the stability of the system, we can find Q [t] ,N [t] ,H [t] , 10. An electronic device, characterized in that: It comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, a state feedback periodic MPC control method for a power system under a deception attack as claimed in any one of claims 1 to 9 is implemented.

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