Defense method for zero dynamic attack of wind power generation system

Abstract

The invention belongs to the field of network security, and discloses a defense method for zero dynamic attacks of a wind power generation system, which comprises the following steps: constructing a mathematical model of the wind power generation system; a gain scheduling PI controller and electronic adjustable passive elements are introduced into the wind power generation system, and the electronic adjustable passive elements are a controllable inductance module and a controllable capacitance module and are used for adjusting inductance and capacitance of the system; designing a zero-dynamic attack signal, injecting the zero-dynamic attack signal into the system, and analyzing destructive factors of the zero-dynamic attack; defending the designed zero-dynamic attack signal, dynamically adjusting and optimizing the parameter value of the element adjustment coefficient so as to adjust the inductance and capacitance, converting an unstable zero point into a stable zero point, weakening the destructiveness of the zero-dynamic attack, and realizing defending. According to the method, the system can keep stable operation in a complex environment, the dependence limitation in the prior art is overcome, and the defense robustness is enhanced.

Description

Technical Field

[0001] The invention belongs to the field of network security, and in particular relates to a defense method for zero-dynamic attacks on a wind power generation system. Background Art

[0002] Zero-Dynamics Attack (ZDA), as a new attack method in the field of network security, has brought huge losses to wind power generation systems due to its unpredictability and concealment.

[0003] For these attacks, existing defense measures can be divided into two categories: one is to change the system model to make it difficult for attackers to obtain accurate system parameters; the other is to introduce external disturbances or modify the control quantity to interfere with the implementation of the attack. However, the application of these methods in multi-input multi-output systems still has limitations.

[0004] The generalized hold device (GH) is proposed to deal with zero-dynamics attack (ZDA). It controls the zero point of the system by designing a specific holding function so that all zero points are within the unit circle, thereby weakening or eliminating the impact of ZDA on the system.

[0005] A generalized sampler (GS) is a sampling device that can flexibly adjust the zero-point characteristics of a sampling system, aiming to increase the degree of freedom of zero-point configuration of a sampled data system. The purpose is to place the zero point of the sampled data system within the unit circle, thereby making the zero dynamically stable and avoiding the internal state divergence caused by ZDA.

[0006] However, the implementation of generalized keepers and generalized samplers depends on the precise control of the system zero point, which usually requires complex numerical optimization algorithms and high-precision modeling. However, in actual control systems, due to the uncertainty of system parameters such as equipment aging and environmental changes, the design of GH and GS may fail, especially in dynamic environments where the parameters of the keepers or samplers need to be frequently adjusted to ensure zero point stability, which greatly increases the difficulty and cost of system implementation.

[0007] In addition, most existing GH and GS methods assume that system parameters are constant or change slowly, but in some industrial scenarios, system parameters may fluctuate significantly due to changes in operating conditions. For example, in a wind power generation system, changes in wind speed will directly affect the dynamic characteristics of the system, and GH and GS cannot adapt to these changes in real time. In this case, the generalized holder and sampler in the prior art need to be carefully designed for the holding function or accurately calculate the sampling weights, which will greatly increase the design difficulty. Summary of the invention

[0008] In order to solve this technical problem, the present invention provides a defense method against zero dynamic attacks on wind power generation systems, which effectively reduces the destructive effects of zero dynamic attacks, effectively reduces costs and improves reliability, enables the system to maintain stable operation in complex environments, overcomes the dependence limitations of existing technologies, and enhances the robustness of defense.

[0009] In order to achieve the above object, the present invention is achieved through the following technical solutions:

[0010] The present invention is a defense method for zero-dynamic attacks on a wind power generation system, and the method specifically comprises the following steps:

[0011] Step 1: construct a mathematical model of the wind power generation system and obtain the transfer function of the power generation system;

[0012] Step 2: Introduce a gain-scheduled PI controller and electronically adjustable passive components into the wind power generation system obtained in step 1, wherein the gain-scheduled PI controller gain scheduling includes a proportional gain k p and integral gain k i The electronically adjustable passive components are specifically controllable inductance modules and controllable capacitance modules, and the controllable inductance modules and controllable capacitance modules are used to adjust the inductance L and capacitance C of the wind power generation system;

[0013] Step 3: design a zero dynamic attack signal, inject the designed zero dynamic attack signal into the wind power generation system, and analyze the destructive factors of the zero dynamic attack;

[0014] Step 4: Implement defense against the zero dynamic attack signal designed in step 3, dynamically adjust and optimize the component adjustment coefficient k and the component to capacitance adjustment coefficient k c The parameter values ​​are adjusted to adjust the inductance L and the capacitance C, converting the unstable zero point into a stable zero point, weakening the destructiveness of the zero dynamic attack and achieving defense.

[0015] A further improvement of the present invention is that the step 1 specifically comprises the following steps:

[0016] Step 1.1, assuming that the electromotive force of the wind power generation system is E, expressed as:

[0017] E=K g ω g

[0018] Among them, K g is the electromagnetic torque coefficient, ω g is the generator speed;

[0019] The voltage balance equation in the entire wind power generation system is:

[0020]

[0021] Where U is the motor terminal voltage, is the voltage drop across the resistor, U L is the voltage drop across the inductor, i L is the current through the inductor, I is the motor armature current, R 1 , R 2 is the resistance in the system, the torque balance equation is:

[0022]

[0023] Among them, K t is the potential constant, the total moment of inertia J = J d +J m +J h , J d is the moment of inertia of the wind turbine, J m is the moment of inertia of the direct-drive permanent magnet synchronous generator (D-PMSG), J h Combining the characteristics of capacitance and inductance for the gearbox with equivalent rotational inertia, the above formula is obtained

[0024]

[0025] in,

[0026]

[0027] Perform a Laplace transform,

[0028] U(s)=K g ((a 0 s 3 +a 1 s 2 +a 2 s+1)ω g (s));

[0029] Wherein, L and C are the inductance and capacitance of the wind power generation system before the controllable elements are deployed;

[0030] Step 1.2: The transfer function G of the wind power generation system 1 (s);

[0031]

[0032] make Then we have:

[0033]

[0034] A further improvement of the present invention is that in step 2, a gain-scheduled PI controller is introduced into the power generation system obtained in step 1, specifically:

[0035] Step 2.1: Set the proportional gain k p and integral gain k i The values ​​of are dynamically associated with the real-time inductance L(t) and the real-time capacitance C(t), respectively, so that the gain-scheduled PI controller can adapt to the changes in the parameters of the wind power generation system. The association relationship is defined as follows:

[0036] K p (t) = αL(t) + βC(t)

[0037] K i (t) = γL(t) + δC(t)

[0038] Among them, the sampling time t = kT, T is the sampling period, α, β, γ, δ are the internal adjustment parameters of the gain-scheduled PI controller, which is designed and adjusted according to the needs of the wind power generation system, and flexibly responds to the real-time changes of the real-time inductance L(t) and the real-time capacitance C(t). The gain-scheduled PI controller automatically adjusts K according to the changes in the system state. p (t) and K i (t).

[0039] The internal adjustment parameters α, β, γ, and δ of the gain-scheduled PI controller are set to fixed values. The transfer function of the wind power generation system becomes:

[0040]

[0041] Among them, G 1 is the transfer function of the wind power generation system, G 2 is the transfer function of the gain-scheduled PI controller;

[0042] Step 2.2: Convert the wind power system transfer function from the frequency domain to the state space table in the time domain and select the state variable Among them, ω g is the angular velocity of the generator, and the high-order derivative represents the corresponding rate of change. The state variables are used to describe the dynamic behavior of the wind power generation system. The state space expression is:

[0043]

[0044] y(t)=Cx(t)

[0045] The system matrix is ​​expressed as:

[0046]

[0047] B=[Kk i K p 0 0] T

[0048] C=[1 0 0 0]

[0049] Step 2.3: To remotely operate the continuous-time system, a gain-scheduled PI controller is used to perform the task, that is, to remotely operate the continuous-time wind power generation system. The input and output of the gain-scheduled PI controller are processed at discrete time points. The discretized state equation is expressed as:

[0050]

[0051] For ease of expression, the above formula is simplified to:

[0052] x(k+1)=Gx(k)+Hu(tk)

[0053] y(k)=Cx(k)

[0054] Wherein, sampling time t=kT, where T is the sampling period;

[0055] In the discretization process, the zero-order hold method (ZOH) is used for discretization, and the discretization matrix of the wind power generation system is:

[0056]

[0057]

[0058] A further improvement of the present invention is that in step 2, the electronically adjustable passive components are introduced into the wind power generation system obtained in step 1, specifically:

[0059] The controllable inductance module realizes real-time dynamic adjustment of the total inductance by connecting the adjustable inductance array in parallel with the original inductance L of the wind power generation system. The adjustment formula is:

[0060] L′=Lk l

[0061] Among them, L′ is the equivalent inductance after adjustment by the controllable inductance module, L is the original inductance of the wind power generation system, k l is the adjustment coefficient of the component to the inductance, by adjusting k l , effectively controlling the inductance to ensure that its regulation meets the actual needs of the power system;

[0062] The controllable capacitor module is connected in parallel with the original capacitance of the wind power generation system to realize the real-time dynamic adjustment of the total capacitance. The adjustment formula is:

[0063] C′=Ck

[0064] Among them, C′ is the equivalent capacitance after adjustment by the controllable capacitor module, C is the original capacitance of the wind power generation system, k cis the adjustment coefficient of the component to the capacitance;

[0065] In order to prevent the parameter adjustment from affecting the normal operation of the original wind power generation system, the adjustment coefficient k of the component to the inductance is l And the adjustment coefficient k of the element to the capacitance c Configure as a continuously adjustable value within the specified parameter range, defining the parameter adjustment range:

[0066] k l，min ≤k l ≤k l，max

[0067] k c，min ≤k c ≤k c，max

[0068] The equivalent inductance L′ after adjustment by the controllable inductance module and the equivalent capacitance C′ after adjustment by the controllable capacitance module are linear functions of the inductance L and the capacitance C. As long as the boundary values ​​meet the required conditions, all intermediate values ​​meet the same criteria.

[0069] A further improvement of the present invention is that in step 3, the zero dynamic attack signal is specifically designed as follows:

[0070] Step 3.1: Based on the Euclidean algorithm, the transfer function of the wind power generation system in step 2.2 is rewritten to represent the transfer function of the feedback loop:

[0071]

[0072] Among them, Q(s) is the quotient and R(s) is the remainder;

[0073] Step 3.2: Convert the wind power system into Byrnes-Isidori form

[0074] η(t+1)=G 0 η(t)+H 0 C c ξ(t)

[0075] ξ(t+1)=(G c +H c λ T )ξ(t)+H c b m (u(t)-C 0 η(t))

[0076] y(t)=C c ξ(t)

[0077] in,

[0078]

[0079] λ T ξ(t)=y(t)+b m C 0 η(t)-b m u(t)

[0080]

[0081] C c =[1 0 0]

[0082] Among them, b m is the maximum power numerator coefficient of the Byrnes-Isidori form transfer function; η(t) and ξ(t) represent the internal and external states of the wind power generation system, G 0 , H 0 and C 0 is the minimum realization of the feedback path R(s) / E(s) transfer function. Applying the Euclidean algorithm, the transfer function of the equation in step 3.2 is derived and expressed as

[0083] η[k+1]=G d η[k]+H d C c ξ[k]

[0084] ξ[k+1]=(G c +H c λ T )ξ[k]+H c b m (u[k]-C d η[k])

[0085] y[k]=C c ξ[k]

[0086] Step 3.3: The goal of the zero dynamic attack signal is to cut off the connection between the internal and external states of the wind power generation system. Assume that the attacker injects an attack signal a[k] into the wind power generation system that introduces a gain-scheduled PI controller, i.e., a closed-loop system. The attack signal is designed as:

[0087] z[k+1]=G d z[k]

[0088] a[k]=C d z[k]

[0089] After the attack is launched, the sampling is converted into

[0090] z[k+1]=G d z[k]

[0091] ξ[k+1]=(G c +Hc λ T )ξ[k]+H c b m u[k]

[0092] y[k]=C c ξ[k]

[0093] A further improvement of the present invention is that in step 3, the destructive factors of the zero dynamic attack are analyzed, specifically:

[0094] Design zero dynamic attack z[k+1]=G for the discretized wind power generation x[k+1]=Gx[k]+Hu[k]; y[k]=Cx[k] d z[k], the impact of zero dynamic attack on the internal state of the wind power generation system depends on G d , assuming G d is an n×n matrix with eigenvalue λ 1 ,λ 2 , ..., λ n , replace the initial state z[0] with G d The eigenvector of is represented as follows:

[0095] z[0]=c 1 v 1 +c 2 v 2 +…+c n v n

[0096] Among them, v i is the eigenvalue λ i The corresponding eigenvector, c i Yes i Coefficient, according to the state equation of the open-loop system, that is, the wind power generation system without the introduction of the gain scheduling PI controller, is:

[0097]

[0098] Due to G d Decompose into G d =VΛV -1 , where Λ is the diagonal matrix of eigenvalues ​​and V is the matrix of eigenvectors, we get:

[0099] z[k]=VΛ k V -1 z[0]

[0100] Substituting z[0] into the above equation, we can obtain and satisfy the following conditions:

[0101]

[0102] Analyzing the eigenvalue λ i The modulus of i |The impact on the state vector z[k] is as follows:

[0103] If there exists an eigenvalue λ i So that |λ i |>1, then It grows exponentially with k, so the state vector z[k] will also become unbounded, causing z[k] to be unstable;

[0104] If all eigenvalues ​​satisfy |λ i |≤1, then It does not grow unbounded with k, but remains bounded or converges to zero as k increases, thus ensuring that z[k] remains bounded or converges to a stable value;

[0105] The impact of zero dynamic attack on the internal state of the wind power system depends on G d , and meet the following conditions:

[0106]

[0107] in, For existence, Indicates any one.

[0108] A further improvement of the present invention is that: in step 4, the defense method for the zero dynamic attack signal designed in step 3 is to offset the unstable zero point of the wind power generation system after sampling. There are two types of unstable zero points of the wind power generation system after sampling. One is the unstable zero point of the original system after sampling mapping, and the other is additionally introduced due to sampling. By adjusting k l and k c , converting unstable zero points into stable zero points, including:

[0109] Step 4.1. Considering the designed gain-scheduled PI controller, the expression of the zero point is:

[0110]

[0111] Due to the deployment of electronically tunable passive components, the above expression is transformed into:

[0112]

[0113] It can be seen that the adjustment of the zero point mainly depends on k l and k c The choice of k l and k c The choice of is constrained to ensure that the primary functionality of the system is not compromised. Therefore, not all systems can implement defenses against zero-dynamic attacks.

[0114] Step 4.2: Under the condition that the sampling period of the continuous-time system is T, the obtained discrete system is expressed by the transfer function

[0115]

[0116] Among them, D d (z) is the characteristic polynomial of the discrete system. For a wind power generation system with a relative degree greater than 2, the degree of the characteristic polynomial of the discrete system increases after sampling, thereby introducing additional zeros, which are the sampling-induced zeros;

[0117] The degree of discretization of the characteristic polynomial increases, which is expressed as

[0118] D d (z) = b 0 +b 1 z -1 +b 2 z -2 +…+b n z -n

[0119] Among them, the coefficient b i is the continuous system coefficient a 0 , a 1 , a 2 The function is defined according to the parameters in the system, a 0 , a 1 , a 2 It is directly related to inductance L and capacitance C, so b i It is also a function of L and C, recorded as:

[0120] b i =f(a 0 , a 1 , a 2 , ...) = g(L,C)

[0121] Changes in the values ​​of inductance L and capacitance C will affect the position of the roots of the characteristic polynomial Dd(z) of the discrete system. The characteristic polynomial D d The (z) roots correspond to the zeros in the discrete system.

[0122] After sampling the system, the composition of the zero point becomes more complicated. In order to deal with the unstable zero introduced by sampling, it is necessary to choose a suitable value within the parameter range.

[0123] A further improvement of the present invention is that in step 4, the parameter k l and k c The optimization is achieved through the particle swarm optimization (PSO) algorithm, which includes the following steps:

[0124] Step 4.1.1, initialize the position and velocity of the particles in the wind power generation system, each particle represents a candidate solution;

[0125] Step 4.1.2: In each iteration, the transfer characteristics of the wind power generation system are evaluated by calculating the inductance and capacitance corresponding to each particle to determine whether the wind power generation system meets the stability condition, that is, |P|<1;

[0126] Step 4.1.3: Update the historical best position p of the particle according to its performance best and the global optimal position g best ;

[0127] Step 4.1.4: By adjusting the speed and position of the particles, the optimal solution is found through continuous iteration, and the optimal inductance k is finally output. l and capacitance k c parameter.

[0128] The beneficial effects of the present invention are:

[0129] 1. Reduce implementation difficulty and cost

[0130] The present invention replaces the complex design and numerical optimization requirements of the traditional GH and GS in zero point configuration by using electronically adjustable passive components. Electronically adjustable passive components stabilize the system zero point position by automatically and in real time adjusting the inductance and capacitance values ​​of the system, without the need for precise numerical optimization and high-precision models. In this way, frequent parameter adjustments and high-cost numerical calculations are eliminated, a simpler control method is achieved, and the difficulty and cost of implementing the system are greatly reduced.

[0131] Because they no longer rely on complex numerical calculations and high-precision modeling, electronically adjustable passive components effectively reduce costs and improve reliability by simplifying the implementation process, allowing the system to maintain stable operation in complex environments.

[0132] 2. Enhance robustness in dynamic environments

[0133] The electronically adjustable passive components designed in the present invention are combined with a gain-scheduled PI controller to automatically adapt to real-time changes in environmental conditions by monitoring the system's operating status, effectively coping with uncertainties in dynamic environments. In application scenarios such as wind power generation, the electronically adjustable passive components can adjust the system zero point in real time according to changes in external factors such as wind speed, thereby ensuring system stability and improving defense capabilities against ZDA.

[0134] Since the present invention can dynamically adjust key parameters, it can automatically adapt to changes in system characteristics even in industrial scenarios such as wind speed fluctuations, ensuring the stability of the system zero point, thereby improving the defense effect and the overall robustness of the system.

[0135] 3. Overcoming the limitation of system zero point configuration’s reliance on feedback

[0136] In the traditional method, the system zero point configuration depends on the system state or output feedback. If the system state information is incomplete or the feedback information is invalid, the control effect of GH and GS will be limited. The present invention enhances the adaptability of the system by directly adjusting the physical parameters, avoids feedback dependence, and ensures that the system can still maintain stable operation in the case of feedback failure or incomplete information.

[0137] Since the present invention is designed based on physical parameter adjustment, it can work effectively under the condition of incomplete system status feedback, ensuring the continuous stability of the system in complex environments such as network attacks, overcoming the dependence limitations of existing technologies, and enhancing the robustness of defense. BRIEF DESCRIPTION OF THE DRAWINGS

[0138] Figure 1 It is a structural diagram of the wind power generation system of the present invention.

[0139] Figure 2 It is an equivalent circuit diagram of the power generation link of the present invention.

[0140] Figure 3 It is a schematic diagram of the wind power generation system of the present invention being attacked by zero power.

[0141] Figure 4 It is a schematic diagram of the changes in the internal and external states of the system in which the unstable zero point introduced after sampling is attacked by the present invention.

[0142] Figure 5 It is a schematic diagram of the changes in the state variables of the system in which the unstable zero point introduced after sampling is attacked by the present invention.

[0143] Figure 6 It is a schematic diagram of the changes in the internal and external states of the system after the defense method of the present invention is deployed.

[0144] Figure 7 It is a schematic diagram of the changes in system state variables after the defense method of the present invention is deployed. DETAILED DESCRIPTION

[0145] The following will disclose the embodiments of the present invention with drawings. For the purpose of clear description, many practical details will be described together in the following description. However, it should be understood that these practical details should not be used to limit the present invention. That is to say, in some embodiments of the present invention, these practical details are not necessary.

[0146] The present invention proposes a defense method for zero dynamic attack on wind power generation system. Compared with the complex design of zero point configuration and complex numerical optimization algorithm and high-precision system modeling of GH and GS, the introduction of electronic adjustable passive components simplifies the zero point adjustment process. By real-time monitoring of system parameter changes, the values ​​of inductance and capacitance are automatically adjusted to maintain the stability of the system zero point, and complex numerical optimization and high-precision modeling are no longer required, thereby reducing the difficulty and cost of system implementation. In addition, the electronic adjustable passive components can dynamically adjust key parameters according to real-time changes in system operating conditions (such as load, environmental conditions, etc.). This ability enables the system to effectively combat ZDA when facing uncertain factors. In addition, combined with a gain-scheduled PI controller, the present invention can achieve real-time adjustment of the PI control gain, ensuring the zero point stability of the system under different conditions, thereby improving the robustness of the system.

[0147] Specifically, the defense method of the present invention comprises the following steps:

[0148] Step 1: construct a mathematical model of the wind power generation system and obtain the transfer function of the power generation system;

[0149] The wind power generation system of the present invention is composed as follows: 1. Wind turbine: including blades, hub and rotor; 2. Transmission system: including main shaft and gearbox; 3. Generator: mainly permanent magnet synchronous generator (PMSG); 4. Power conversion system: including rectifier, inverter and filter.

[0150] Wind turbines capture the kinetic energy of wind and convert it into mechanical energy using blades, hubs and rotors; the mechanical energy is transmitted to the generator through the main shaft and gearbox of the transmission system; the generator converts the mechanical energy into electrical energy; finally, the power conversion system adjusts the AC power output by the generator into stable DC power or AC power that meets grid connection requirements through rectifiers, inverters and filters, thereby achieving efficient conversion and output of wind energy into electrical energy.

[0151] The power generated by the generator is adjusted by the converter to meet the needs of the power grid, stabilize the voltage and frequency, and ensure the reliable grid-connected operation of the system. The monitoring and data acquisition system tracks the operating status and key parameters in real time, and ensures the efficient operation of the equipment and timely problem handling through data analysis, extending the service life and improving the power generation efficiency. Figure 1 shown.

[0152] From the system structure, it can be seen that the power generation link of the wind power generation system is at risk of being attacked through input signals. Interference with the input signal may damage the power generation link, affecting power generation efficiency and system stability. Zero dynamic attack destroys the power generation link by manipulating the input signal to achieve the attack purpose and affect the normal operation of the system. The circuits involved are as follows Figure 2 shown.

[0153] Assume that the electromotive force of the wind power generation system is E, which can be expressed as:

[0154] E=K g ω g

[0155] Among them, K g is the electromagnetic torque coefficient, ω g is the speed of the generator.

[0156] According to Kirchhoff's voltage law, the voltage balance equation in the entire wind power generation system can be derived as follows:

[0157]

[0158] Where U is the motor terminal voltage, is the voltage drop across the resistor, U L is the voltage drop across the inductor, i L is the current through the inductor, I is the motor armature current, R 1 , R 2 is the resistance in the system, the torque balance equation is:

[0159]

[0160] Among them, K t is the potential constant, the total moment of inertia J = J d +J m +J h , J d is the moment of inertia of the wind turbine, J m is the moment of inertia of the direct-drive permanent magnet synchronous generator (D-PMSG), J h Combining the characteristics of capacitance and inductance for the gearbox with equivalent rotational inertia, the above formula is obtained

[0161]

[0162] in,

[0163]

[0164] Perform a Laplace transform,

[0165] U(s)=K g ((a 0 s 3 +a 1 s 2 +a 2 s+1)ω g (s));

[0166] Wherein, L and C are the inductance and capacitance of the wind power generation system before the controllable elements are deployed;

[0167] The transfer function G of the wind power generation system 1 (s):

[0168]

[0169] make Then we have:

[0170]

[0171] Step 2: Introduce a gain-scheduled PI controller and electronically adjustable passive components into the wind power generation system obtained in step 1, wherein the gain scheduling includes a proportional gain k p and integral gain k i The electronically adjustable passive components are specifically controllable inductance modules and controllable capacitance modules. The controllable inductance modules and controllable capacitance modules are used to adjust the inductance L and capacitance C of the wind power generation system.

[0172] A common PI controller is:

[0173]

[0174] To further optimize the performance of the controller and ensure its stability and robustness under various operating conditions, the proportional gain k p and integral gain k i The values ​​of are dynamically associated with the real-time inductance L(t) and the real-time capacitance C(t), respectively, so that the gain-scheduled PI controller can adapt to the changes in the parameters of the wind power generation system. The association relationship is defined as follows:

[0175] K p (t) = αL(t) + βC(t)

[0176] K i (t) = γL(t) + δC(t)

[0177] Among them, the sampling time t = kT, T is the sampling period, α, β, γ, δ are the internal adjustment parameters of the gain-scheduled PI controller, which are designed and adjusted according to the needs of the wind power generation system, and flexibly respond to the real-time changes of the real-time inductance L(t) and the real-time capacitance C(t), ensuring the efficient and stable operation of the control system under different working conditions. The gain-scheduled PI controller automatically adjusts K according to the changes in the system state. p (t) and K i (t). This mechanism improves the system's adaptability in complex environments and makes the controller design more versatile and practical.

[0178] To simplify the system, the internal adjustment parameters α, β, γ, and δ of the gain-scheduled PI controller are set to fixed values. At this time, the transfer function of the wind power generation system becomes:

[0179]

[0180] Among them, G 1 is the transfer function of the wind power generation system, G 2 is the transfer function of the gain-scheduled PI controller.

[0181] To facilitate subsequent system analysis, the system is converted from the transfer function form in the frequency domain to the state space expression in the time domain. Select the state variable Among them, ω g is the angular velocity of the generator, and the high-order derivatives represent the corresponding rate of change. The state variables are used to describe the dynamic behavior of the wind power generation system. Based on this choice, the state space expression is:

[0182]

[0183] y(t)=Cx(t)

[0184] The system matrix is ​​expressed as:

[0185]

[0186] B=[Kk i K p 0 0] T

[0187] C=[1 0 0 0]

[0188] To remotely operate a continuous-time system, assume that a gain-scheduled PI controller is used to perform this task. The gain-scheduled PI controller can implement a variety of control strategies. The discretization process is to process continuous-time signals in the gain-scheduled PI controller so that it can adapt to discrete sampling periods. Set the sampling time t = kT, where T is the sampling period. At this time, the input and output of the gain-scheduled PI controller are processed at discrete time points. The discretized state equation is expressed as:

[0189]

[0190] For ease of expression, the above formula is simplified to:

[0191] x(k+1)=Gx(k)+Hu(tk)

[0192] y(k)=Cx(k)

[0193] In the discretization process, the zero-order hold (ZOH) method is used to adjust the system's state equation to reflect the dynamic characteristic changes brought about by discretization while keeping the static output equation of the system unchanged. Specifically, using ZOH for discretization, the discretization matrix of the wind power generation system is:

[0194]

[0195] Electronically adjustable passive components are a type of dynamically adjustable passive components, specially designed for use in the fields of power electronics and automatic control, providing flexible and dynamic response capabilities in circuits.

[0196] The controllable inductor module is connected in parallel with the existing inductor to form an adjustable inductor array or use an adjustable inductor module based on power electronics. By using power electronic switches, these small inductors can be quickly controlled to be engaged or disconnected, thereby achieving real-time dynamic adjustment of the total inductance.

[0197] In order to facilitate analysis and application, a simplified adjustment formula is introduced, which is expressed as:

[0198] L′=Lk l

[0199] Among them, L′ is the equivalent inductance after adjustment by the controllable inductance module, L is the original inductance of the wind power generation system, k l is the adjustment coefficient of the component to the inductance, by adjusting k l , effectively controlling the inductance to ensure that its regulation meets the actual needs of the power system;

[0200] Similarly, the controllable capacitor module is connected in parallel with the original capacitance of the wind power generation system to the adjustable capacitor array to achieve real-time dynamic adjustment of the total capacitance. The adjustment formula is:

[0201] C′=Ck c

[0202] Among them, C′ is the equivalent capacitance after adjustment by the controllable capacitor module, C is the original capacitance of the wind power generation system, k c is the adjustment coefficient of the component to the capacitance;

[0203] In order to prevent the parameter adjustment from affecting the normal operation of the original wind power generation system, the adjustment coefficient k of the component to the inductance is l And the adjustment coefficient k of the element to the capacitance c Configure as a continuously adjustable value within the specified parameter range, defining the parameter adjustment range:

[0204] k l，min ≤k l ≤k l，max

[0205] k c，min ≤kc ≤k c，max

[0206] The equivalent inductance L′ after adjustment by the controllable inductance module and the equivalent capacitance C′ after adjustment by the controllable capacitance module are linear functions of the inductance L and the capacitance C. As long as the boundary values ​​meet the required conditions, all intermediate values ​​meet the same criteria.

[0207] Step 3: Design a zero dynamic attack signal, inject the designed zero dynamic attack signal into the wind power generation system, and analyze the destructive factors of the zero dynamic attack.

[0208] Based on the Euclidean algorithm, the transfer function of the wind power system is rewritten to represent the transfer function of the feedback loop:

[0209]

[0210] Where Q(s) is the quotient and R(s) is the remainder; this form can be interpreted as a transfer function representation of the feedback loop.

[0211] Converting wind power systems to Byrnes-Isidori form

[0212] η(t+1)=G 0 η(t)+H 0 C c ξ(t)

[0213] ξ(t+1)=(G c +H c λ T )ξ(t)+H c b m (u(t)-C 0 η(t))

[0214] y(t)=C c ξ(t)

[0215] in,

[0216]

[0217] λ T ξ(t)=y(t)+b m C 0 η(t)-b m u(t)

[0218]

[0219] C c =[1 0 0]

[0220] Among them, b mis the maximum power numerator coefficient of the Byrnes-Isidori form transfer function; η(t) and ξ(t) represent the internal and external states of the wind power generation system, G 0 , H 0 and C 0 is the minimum realization of the feedback path R(s) / E(s) transfer function. Applying the Euclidean algorithm, the transfer function of the above equation is derived and expressed as

[0221] η[k+1]=G d η[k]+H d C c ξ[k]

[0222] ξ[k+1]=(G c +H c λ T )ξ[k]+H c b m (u[k]-C d η[k])

[0223] y[k]=C c ξ[k]

[0224] The construction of the system matrix can refer to the discretization matrix of the wind power generation system:

[0225]

[0226] The zero dynamic characteristic is described by a transfer function or state space model, which is manifested as a situation where the output of the system remains unchanged under certain inputs, but its internal state deviates significantly. The attacker uses this characteristic to design signals so that the output of the system appears normal, while its internal state gradually deviates from the expected trajectory, eventually leading to system failure. The goal of the zero dynamic attack signal is to cut off the connection between the internal and external states of the wind power generation system. Assume that the attacker injects an attack signal a[k] into the wind power generation system that introduces a gain-scheduled PI controller, i.e., a closed-loop system, such as Figure 3 To achieve this goal, the attack signal is designed as follows:

[0227] z[k+1]=G d z[k]

[0228] a[k]=C d z[k]

[0229] After the attack is launched, the sampling expression formula is transformed into

[0230] z[k+1]=G d z[k]

[0231] ξ[k+1]=(G c +Hc λ T )ξ[k]+H c b m u[k]

[0232] y[k]=C c ξ[k]

[0233] From the above formula, we can see that the internal state of the system is replaced by z[k], and the state space expression of the system is And y(t) = Cx(t), constructing the attack signal needs to meet the following conditions:

[0234]

[0235] When the state after the attack converges locally, the zero-power attack is invalid, indicating that the attack has failed. Therefore, to construct a more effective attack, the condition ∥G must be satisfied. 0 ∥>1. In this case, the state will continue to diverge, which can be considered a successful and effective attack.

[0236] Design zero dynamic attack z[k+1]=G for the discretized wind power generation x[k+1]=Gx[k]+Hu[k]; y[k]=Cx[k] d z[k], the impact of zero dynamic attack on the internal state of the wind power generation system depends on G d , assuming G d is an n×n matrix with eigenvalue λ 1 ,λ 2 , ..., λ n , replace the initial state z[0] with G d The eigenvector of is represented as follows:

[0237] z[0]=c 1 v 1 +c 2 v 2 +…+c n v n

[0238] Among them, v i is the eigenvalue λ i The corresponding eigenvector, c i Yes i Coefficient, according to the state equation of the open-loop system, that is, the wind power generation system without the introduction of the gain scheduling PI controller, is:

[0239]

[0240] Due to G d Decompose into G d =VΛV -1, where Λ is the diagonal matrix of eigenvalues ​​and V is the matrix of eigenvectors, we get:

[0241] z[k]=VΛ k V -1 z[0]

[0242] Substituting z[0] into the above equation, we can obtain and satisfy the following conditions:

[0243]

[0244] Analyzing the eigenvalue λ i The modulus of i |The impact on the state vector z[k] is as follows:

[0245] If there exists an eigenvalue λ i So that |λ i |>1, then It grows exponentially with k, so the state vector z[k] will also become unbounded, causing z[k] to be unstable;

[0246] If all eigenvalues ​​satisfy |λ i |≤1, then It does not grow unbounded with k, but remains bounded or converges to zero as k increases, thus ensuring that z[k] remains bounded or converges to a stable value;

[0247] The impact of zero dynamic attack on the internal state of the wind power system depends on G d , and meet the following conditions:

[0248]

[0249] in, For existence, Indicates any one.

[0250] Step 4: Implement defense against the zero dynamic attack signal designed in step 3, dynamically adjust and optimize the component adjustment coefficient k and the component to capacitance adjustment coefficient k c The parameter values ​​are adjusted to adjust the inductance L and the capacitance C, converting the unstable zero point into a stable zero point, weakening the destructiveness of the zero dynamic attack and achieving defense.

[0251] The defense method for the zero dynamic attack signal designed in step 3 is to offset the unstable zero point of the wind power generation system after sampling. There are two types of unstable zero points of the wind power generation system after sampling. One is the unstable zero point of the original system after sampling mapping, and the other is additionally introduced due to sampling. By adjusting k l and k c , converting unstable zeros into stable zeros.

[0252] Considering the designed gain-scheduled PI controller, the expression of the zero point is:

[0253]

[0254] Due to the deployment of electronically tunable passive components, the above expression is transformed into:

[0255]

[0256] It can be seen that the adjustment of the zero point mainly depends on k l and k c The choice of k l and k c The choice of is constrained to ensure that the primary functionality of the system is not compromised. Therefore, not all systems can implement defenses against zero-dynamic attacks.

[0257] Under the condition that the sampling period of the continuous-time system is T, the obtained discrete system is expressed by the transfer function

[0258]

[0259] Among them, D d (z) is the characteristic polynomial of the discrete system. For a wind power generation system with a relative degree greater than 2, the degree of the characteristic polynomial of the discrete system increases after sampling, thereby introducing additional zeros, which are the sampling-induced zeros;

[0260] The characteristic polynomial Dd(z) of the sampled discrete system is derived from the characteristic polynomial D(s) of the continuous system. The degree of discretization of the characteristic polynomial increases, which is expressed as

[0261] D d (z) = b 0 +b 1 z -1 +b 2 z -2 +…+b n z -n

[0262] Among them, the coefficient b i is the continuous system coefficient a 0 , a 1 , a 2 The function is defined according to the parameters in the system, a 0 , a 1 , a 2 It is directly related to inductance L and capacitance C, so b i It is also a function of L and C, recorded as:

[0263] b i =f(a 0 , a1 , a 2 , ...) = g(L,C)

[0264] Changes in the values ​​of inductance L and capacitance C will affect the position of the roots of the characteristic polynomial Dd(z) of the discrete system. The characteristic polynomial D d The (z) roots correspond to the zeros in the discrete system.

[0265] After sampling the system, the composition of zeros becomes more complicated. In order to deal with the unstable zeros introduced by sampling, it is necessary to choose appropriate values ​​within the parameter range. In order to successfully implement the defense strategy, a particle algorithm based on k is designed to select the appropriate l and k c The value of .

[0266]

[0267] The main function of the algorithm is to l and k c Optimize and find the combination that minimizes the maximum zero of the system. When complete defense cannot be achieved, the destructive impact of zero-power attacks can be weakened.

[0268] In order to verify the present invention, an attack is injected and defense is deployed to perform performance verification, as follows:

[0269] Table 1 System parameters

[0270] parameter Numeric <![CDATA[Rotor inertia (J d )]]> <![CDATA[2.13×10 -5 kg·m]]> <![CDATA[Generator inertia (J m )]]> <![CDATA[4×10 -6 kg·m]]> <![CDATA[Gearbox inertia (J h )]]> <![CDATA[6.5×10 -7 kg·m]]> Resistor R 21Ω Resistor R 1.2Ω Inductance L 0.7H Capacitor C 5F Gearbox ratio n 2 <![CDATA[Tip speed ratio λ o > 1.38

[0271] The simulation parameters are set as shown in Table 1, which reasonably demonstrates the destruction process of zero-dynamic attack and the effectiveness of the designed defense strategy.

[0272]

[0273] Assume constant wind speed V = 15m / s, sampling period T = 1.5s. According to the information in Table 1, the complete system model can be derived, where λ 0 represents the tip speed ratio, n g represents the gearbox speed ratio, which determines the system input w g is (35).

[0274] Figure 4-5 As shown in Figure 2, when the parameters are α=1,β=-0.041,γ=0.87,δ=-0.022, the original system is no longer a minimum phase system. Similarly, the attack signal is injected after the system is running. After 100 seconds of injection of the attack signal, Figure 4 The internal state of the system oscillates, while the output remains almost unchanged, indicating that the attack is successful. Figure 5Further inspection shows that the system’s state variables also exhibit divergent oscillations after the attack, effectively demonstrating the destructive nature of the attack. Figure 5 As shown, a defense method is deployed in the designed system. Figure 6 It shows that after the attack signal is injected, the internal state η oscillates but gradually stabilizes. The results show that the proposed defense method effectively mitigates the destructive impact of zero-dynamic attacks. Figure 7 The changes in the system state variables are shown, indicating that although small oscillations occur after the attack, they eventually stabilize, further supporting the effectiveness of the proposed defense method.

[0275] The above description is only an embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A defense method against zero-dynamic attacks on a wind power generation system, characterized by: The defense method specifically includes the following steps: Step 1: construct a mathematical model of the wind power generation system and obtain the transfer function of the power generation system; Step 2: Introduce a gain-scheduled PI controller and electronically adjustable passive components into the wind power generation system obtained in step 1, wherein the gain-scheduled PI controller includes a proportional gain k p and integral gain k i The electronically adjustable passive components are specifically controllable inductance modules and controllable capacitance modules, and the controllable inductance modules and controllable capacitance modules are used to adjust the inductance L and capacitance C of the wind power generation system; Step 3: design a zero dynamic attack signal, inject the designed zero dynamic attack signal into the wind power generation system, and analyze the destructive factors of the zero dynamic attack; Step 4: Implement defense against the zero dynamic attack signal designed in step 3, dynamically adjust and optimize the component adjustment coefficient k l And the adjustment coefficient k of the element to the capacitance c The parameter values ​​are adjusted to adjust the inductance L and the capacitance C, converting the unstable zero point into a stable zero point, weakening the destructiveness of the zero dynamic attack and achieving defense.

2. A method for defending against zero-dynamic attacks on a wind power generation system according to claim 1, characterized in that: The step 1 specifically includes the following steps: Step 1.1, assuming that the electromotive force of the wind power generation system is E, expressed as: E=K g oh g Among them, K g is the electromagnetic torque coefficient, ω g is the angular velocity of the generator; The voltage balance equation in the entire wind power generation system is: Where U is the motor terminal voltage, is the voltage drop across the resistor, U L is the voltage drop across the inductor, i L is the current through the inductor, I is the motor armature current, R1 and R2 are the resistances in the system, and the torque balance equation is: Among them, K t is the potential constant, the total moment of inertia J = J d +J m +J h , J d is the moment of inertia of the wind turbine, J m is the moment of inertia of the permanent magnet direct-drive synchronous generator, J h In order to obtain the equivalent moment of inertia of the gearbox, the characteristics of capacitance and inductance are combined to obtain the voltage balance equation and torque balance equation: in, Perform a Laplace transform, U(s)=K g ((a0s 3 +a1s 2 +a2s+1)ω g (s)); Wherein, L and C are the inductance and capacitance of the wind power generation system before the controllable elements are deployed; Step 1.2, the transfer function G1(s) of the wind power generation system: make Then we have:

3. A defense method against zero-dynamic attacks on a wind power generation system according to claim 1, characterized in that: In step 2, a gain-scheduled PI controller is introduced into the power generation system obtained in step 1, specifically: Step 2.1: Set the proportional gain k p and integral gain k i The values ​​of are dynamically associated with the real-time inductance L(t) and the real-time capacitance C(t), respectively, so that the gain-scheduled PI controller can adapt to the changes in the parameters of the wind power generation system. The association relationship is defined as follows: K p (t)=αL(t)+βC(t) K i (t)=γL(t)+δC(t) Among them, the sampling time t = kT, T is the sampling period, α, β, γ, δ are the internal adjustment parameters of the gain-scheduled PI controller, which is designed and adjusted according to the needs of the wind power generation system, and flexibly responds to the real-time changes of the real-time inductance L(t) and the real-time capacitance C(t). The gain-scheduled PI controller automatically adjusts K according to the changes in the system state. p (t) and K i (t); The internal adjustment parameters α, β, γ, and δ of the gain-scheduled PI controller are set to fixed values. The transfer function of the wind power generation system becomes: Where G1 is the transfer function of the wind power generation system, and G2 is the transfer function of the gain-scheduled PI controller; Step 2.2: Convert the wind power system transfer function from the frequency domain to the state space table in the time domain and select the state variable Among them, ω g is the angular velocity of the generator, and the high-order derivative represents the corresponding rate of change. The state variables are used to describe the dynamic behavior of the wind power generation system. The state space expression is: y(t)=Cx(t) The wind power generation system matrix is ​​expressed as: B=[Kk i lol p 0 0] T C＝[1 0 0 0]； Step 2.3: To remotely operate the continuous-time wind power generation system, a gain-scheduled PI controller is used to perform the task. The input and output of the gain-scheduled PI controller are processed at discrete time points. The discretized state equation is expressed as: For ease of expression, the above formula is simplified to: x(k+1)=Gx(k)+Hu(tk) y(k)=Cx(k) Wherein, sampling time t=kT, where T is the sampling period; In the discretization process, the zero-order hold method is used for discretization, and the discretization matrix of the wind power generation system is:

4. A method for defending against zero-dynamic attacks on a wind power generation system according to claim 3, characterized in that: In step 2, the electronically adjustable passive components are introduced into the wind power generation system obtained in step 1 as follows: The controllable inductance module realizes real-time dynamic adjustment of the total inductance by connecting the adjustable inductance array in parallel with the original inductance L of the wind power generation system. The adjustment formula is: L′=Lk l Among them, L′ is the equivalent inductance after adjustment by the controllable inductance module, L is the original inductance of the wind power generation system, k l is the adjustment coefficient of the component to the inductance, by adjusting k l Control the inductance to ensure that its regulation meets the actual needs of the power system; The controllable capacitor module is connected in parallel with the original capacitor C of the wind power generation system to realize the real-time dynamic adjustment of the total capacitance. The adjustment formula is: C′=Ck c Among them, C′ is the equivalent capacitance after adjustment by the controllable capacitor module, C is the original capacitance of the wind power generation system, k c is the adjustment coefficient of the component to the capacitance; In order to prevent the parameter adjustment from affecting the normal operation of the original wind power generation system, the adjustment coefficient k of the component to the inductance is l And the adjustment coefficient k of the element to the capacitance c Configured as a continuously adjustable value within the specified parameter range, define k l and k c Adjustment range: k l，min ≤k l ≤k l，max k c，min ≤k c ≤k c，max The equivalent inductance L′ after adjustment by the controllable inductance module and the equivalent capacitance C′ after adjustment by the controllable capacitance module are linear functions of the inductance L and the capacitance C. As long as the boundary values ​​meet the required conditions, all intermediate values ​​meet the same criteria.

5. A defense method against zero-dynamic attack on a wind power generation system according to claim 3, characterized in that: In step 3, the zero dynamic attack signal design is specifically as follows: Step 3.1: Based on the Euclidean algorithm, the transfer function of the wind power generation system in step 2.2 is rewritten to represent the transfer function of the feedback loop: Among them, Q(s) is the quotient and R(s) is the remainder; Step 3.2: Convert the wind power system into Bymes-Isidori form: η(t+1)=G0η(t)+H0C c ξ(t) ξ(t+1)=(G c +H c λ T )ξ(t)+H c b m (u(t)-C0η(t)) y(t)=C c ξ(t) in, ξ(t)=[y(t),y(t+1),y(t+2)] T λ T ξ(t)=y(t)+b m C0η(t)-b m u(t) H c ＝[0 0 1] T C c ＝[1 0 0] Among them, b m is the maximum power numerator coefficient of the transfer function; η(t) and ξ(t) represent the internal and external states of the wind power generation system. G0, H0 and C0 are the minimum realizations of the transfer function of the feedback path R(s) / E(s). Applying the Euclidean algorithm, the transfer function of the equation in step 3.2 is derived and expressed as η[k+1]=Gdη[k]+H after sampling. d C c ξ[k] ξ[k+1]=(G c +H c l T )ξ[k]+H c b m (u[k]-C d the[k]) y[k]=C c ξ[k]; Step 3.3: The goal of the zero dynamic attack signal is to cut off the connection between the internal and external states of the wind power generation system. Assume that the attacker injects an attack signal a[k] into the wind power generation system that introduces a gain-scheduled PI controller, i.e., a closed-loop system. The attack signal is designed as: z[k+1]=G d z[k] a[k]=C d z[k] After the attack is launched, the sampled representation is converted to z[k+1]=G d z[k] ξ[k+1]=(G c +H c l T )ξ[k]+H c b m u[k] y[k]=C c ξ[k] Among them, z[k] is the state vector.

6. A method for defending against zero-dynamic attacks on a wind power generation system according to claim 5, characterized in that: In step 3, the destructive factors of zero-dynamic attacks are analyzed, specifically: For the discretized wind power generation system x[k+1]=Gx[k]+Hu[k];y[k]=Cx[k], a zero dynamic attack z[k+1]=G d z[k], the impact of zero dynamic attack on the internal state of the wind power generation system depends on G d , assuming G d is an n×n matrix with eigenvalues ​​λ1,λ2,..., λ n, the initial state z[0] is replaced by G d The eigenvector of is represented as follows: z[0]=c1v1+c2v2+…+c n v n Among them, v i is the eigenvalue λ i The corresponding eigenvector, c i Yes i Coefficient, according to the state equation of the open-loop system, that is, the wind power generation system without the introduction of the gain scheduling PI controller, is: Due to G d Decompose into G d =VΛV -1 , where Λ is the diagonal matrix of eigenvalues ​​and V is the matrix of eigenvectors, we get: z[k]=VΛ k IN -1 from[0] Substituting z[0] into the above equation, we can obtain and satisfy the following conditions: Analyzing the eigenvalue λ i The modulus of i |The impact on the state vector z[k] is as follows: If there exists an eigenvalue λ i So that |λ i |>1, then It grows exponentially with k, so the state vector z[k] will also become unbounded, resulting in the instability of the state vector z[k]; If all eigenvalues ​​satisfy |λ i |≤1, then It does not grow unbounded with k, but remains bounded or converges to zero as k increases, thus ensuring that z[k] remains bounded or converges to a stable value; The impact of zero dynamic attack on the internal state of the wind power system depends on G d , and meet the following conditions: in, For existence, Indicates any one.

7. A method for defending against zero-dynamic attacks on a wind power generation system according to claim 1, characterized in that: In step 4, the defense method for the zero dynamic attack signal designed in step 3 is to offset the unstable zero point of the wind power generation system after sampling. There are two types of unstable zero points of the wind power generation system after sampling. One is the unstable zero point of the original system mapped by sampling, and the other is additionally introduced due to sampling. By adjusting the component adjustment coefficient k and the component adjustment coefficient k for capacitance c , converting unstable zero points into stable zero points, including: Step 4.

1. Considering the designed gain-scheduled PI controller, the expression of the zero point is: Since electronically tunable passive components are deployed, the expression for the above zero point is transformed into: It can be seen that the adjustment of the zero point mainly depends on k l and k c Choice; Step 4.2: Under the condition that the sampling period of the continuous-time system is T, the obtained discrete system is expressed by the transfer function Among them, D d (z) is the characteristic polynomial of the discrete system; The degree of discretization of the characteristic polynomial increases, denoted as D d (z) = b0 + b1z -1 +b2z -2 +…+b n z -n Among them, the coefficient b i It is a function of the continuous system coefficients a0, a1, a2. According to the parameter definition in the wind power generation system, a0, a1, a2 are directly related to the inductance L and the capacitance C, so b i Denoted as: b i =f(a0,a1,a2,...)=g(L,C) Changes in the values ​​of inductance L and capacitance C will affect the position of the roots of the characteristic polynomial Dd(z) of the discrete system. The characteristic polynomial D d The (z) roots correspond to the zeros in the discrete system.

8. A method for defending against zero-dynamic attacks on a wind power generation system according to claim 7, characterized in that: In step 4, the parameter k l and k c The optimization is achieved through the particle swarm optimization (PSO) algorithm, which includes the following steps: Step 4.1.1, initialize the position and velocity of the particles in the wind power generation system, each particle represents a candidate solution; Step 4.1.2, in each iteration, by calculating the inductance and capacitance corresponding to each particle, the transfer characteristics of the wind power generation system are evaluated to determine whether the wind power generation system meets the stability conditions; Step 4.1.3: Update the historical best position p of the particle according to its performance best and the global optimal position p best ; Step 4.1.4: By adjusting the speed and position of the particles, the optimal solution is found through continuous iteration, and the optimal inductance k is finally output. l and the optimal capacitance k c parameter.

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