MPPT non-singular fast terminal sliding mode control method for permanent magnet direct drive wind power system based on improved sparrow search algorithm

Abstract

The invention discloses a permanent magnet direct drive wind power system MPPT nonsingular fast terminal sliding mode control method based on a sparrow search algorithm, and the method comprises the steps: building a fan mathematical model, and building a permanent magnet synchronous generator stator voltage equation based on a synchronous rotating coordinate system dq; designing a nonsingular fast terminal sliding mode controller for a rotating speed ring, wherein a state error e = omega * m-omega m is taken as a control target; designing a nonlinear function of a variable boundary layer in combination with a Softsign function; designing a fixed time sliding-mode observer, performing estimation and active compensation on internal and external disturbance uncertain factors of the system, and performing feedforward compensation on an observation value to a non-singular fast terminal sliding-mode controller to offset interference; the to-be-designed parameters in the nonsingular fast terminal sliding mode controller are optimized based on the improved sparrow search algorithm, and the parameters are obtained more accurately. According to the method, the chattering phenomenon existing in sliding mode control is effectively reduced, the improved sparrow search algorithm is used for optimizing controller parameters, a wind power system has the better response speed, the wind energy utilization efficiency is improved, and maximum power tracking is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of wind power generation system control, and relates to a permanent magnet direct-drive wind power system MPPT non-singular fast terminal sliding mode control method based on an improved sparrow search algorithm. Background Art

[0002] Wind energy is becoming one of the most promising clean energy sources for sustainable development. Permanent magnet direct-drive wind turbines (PMSG) have been widely used in wind power generation due to their small structure, high power density, and high torque-to-inertia ratio. Compared with the doubly-fed induction generator (DFIG), the internal structure of PMSG is simpler. Therefore, the wind energy conversion system based on PMSG has become a research hotspot in the field of wind power generation. However, due to the randomness and unpredictability of wind speed, wind turbines often cannot achieve their full power output, which reduces the efficiency of wind energy utilization. For this reason, it is more important to improve the control method of maximum power point tracking (MPPT) of wind power generation systems. PI control has the advantages of simple control algorithm, high reliability, and simple implementation, and has been widely used in wind power systems. However, PI control is a linear control method and is not robust to the nonlinearity of PMSG wind turbine systems, changes in wind speed and wind turbine parameters. Sliding mode control, as a nonlinear control, has been developed and applied to wind turbine systems due to its high robustness and insensitivity to changes in system parameters. However, due to the characteristics of sliding mode control, the control system has high-frequency chattering, which reduces the control accuracy of the system. Therefore, in order to ensure the maximum power tracking performance of permanent magnet direct-drive wind turbines under wind speed changes and external disturbances, it is necessary to seek new control methods to achieve efficient and reliable operation of wind turbines. Summary of the invention

[0003] The purpose of the present invention is to provide a permanent magnet direct-drive wind power system MPPT non-singular fast terminal sliding mode control method based on a sparrow search algorithm in view of the shortcomings and defects of the prior art, effectively reduce the chattering phenomenon existing in the sliding mode control, and use the improved sparrow search algorithm to optimize the controller parameters, so that the wind power system has a better response speed, improves the efficiency of wind energy utilization, and realizes maximum power tracking.

[0004] The technical solution adopted by the present invention is:

[0005] A non-singular fast terminal sliding mode control method for MPPT of a permanent magnet direct-drive wind power system based on a sparrow search algorithm is characterized by comprising the following steps:

[0006] Step 1: Establish a mathematical model of the fan based on the principle of aerodynamics, and establish the stator voltage equation of the permanent magnet synchronous generator based on the synchronous rotating coordinate system dq;

[0007] Step 2: Design a non-singular fast terminal sliding mode controller for the speed loop, state error For the control target, For a given mechanical angular velocity, ω m is the speed of the fan; in order to reduce the inherent chattering phenomenon in the non-singular fast terminal sliding mode control process, a nonlinear function of a variable boundary layer is designed by combining the Softsign function with continuous smooth characteristics and its convergence characteristics to improve the convergence speed of the reaching law function and effectively reduce the chattering;

[0008] Step 3: Design a fixed-time sliding mode observer to estimate and actively compensate for the uncertainties such as the internal and external disturbances of the system, and feed forward the observed values ​​to the non-singular fast terminal sliding mode controller to offset the disturbance;

[0009] Step 4: Based on the improved sparrow search algorithm, the parameters to be designed in the non-singular fast terminal sliding mode controller are optimized to obtain the parameters more accurately.

[0010] In step 1, according to aerodynamic theory, the aerodynamic mechanical power captured by the fan is:

[0011]

[0012] Where: ρ is air density; v is wind speed; R is blade radius; λ is tip speed ratio; β is pitch angle; P m is the aeromechanical power captured by the fan.

[0013] The tip speed ratio is the ratio of the fan impeller speed to the wind speed, that is:

[0014]

[0015] Where: m is the speed of the fan; R is the radius of the blade.

[0016] C p (λ,β) is the wind energy utilization coefficient. When the pitch angle β is constant, C p (λ,β) changes with the change of λ. By adjusting the speed at different wind speeds, there is an optimal tip speed ratio λ opt Make C p When (λ, β) reaches the maximum value, the maximum output power can be obtained. This process is the maximum power tracking process of the wind power generation system. Therefore, the essence of maximum power tracking is the control of the speed.

[0017] The aerodynamic torque of the fan is T m The mechanical power it captures satisfies:

[0018]

[0019] Where:ω m is the speed of the fan.

[0020] Assuming that the motor operates under ideal conditions and its internal parameters remain unchanged, the mathematical model of the permanent magnet synchronous generator PMSG in the dq synchronous rotating coordinate system can be obtained as follows:

[0021]

[0022] Where: i d 、i q are the d-axis and q-axis current components of the generator respectively; L is the equivalent inductance of the generator; u d 、u q are the d-axis and q-axis voltage components of the generator respectively; R s is the stator resistance; ψ f is the flux linkage of the permanent magnet; n p is the number of pole pairs of the generator rotor; ω g is the speed of the generator rotor.

[0023] For a permanent magnet synchronous motor, if the d-axis component of the stator current is always 0 during operation, the electromagnetic torque can be expressed as:

[0024] T e =1.5n p ψ f i q (5);

[0025] In the permanent magnet direct drive wind power generation system, the fan shaft is directly connected to the permanent magnet synchronous generator, and the generator rotor speed is consistent with the wind wheel speed, so the dynamic state equation of the wind power generation system transmission shaft system is:

[0026]

[0027] Where: J is the moment of inertia of the wind power generation system; B m is the viscous friction coefficient.

[0028] Taking into account the parameter mismatch, the dynamic equation above can be rewritten as:

[0029]

[0030] Where d is the unknown total disturbance including parameter mismatch and external load torque.

[0031] The stator voltage equation of the permanent magnet synchronous generator is equation (4).

[0032] In step 2, the speed error equation of the system is:

[0033]

[0034] In the formula, is the given speed of the generator; e is the error between the given speed and the actual speed of the generator.

[0035] The designed non-singular fast terminal sliding surface is:

[0036] s=e+p∫(e)+q∫|e| λ sgn(e) (9);

[0037] Where, e is the speed error; sgn is the sign function; p and q are the sliding mode coefficients; λ is the parameter to be designed, and p>0, q>0, 0<λ<1.

[0038] By taking the derivative of formula (9), we can get:

[0039]

[0040] In the formula, is the first-order derivative of the non-singular fast terminal sliding surface; is the first-order derivative of the actual speed of the generator; sgn(e) is the sign function of the speed error;

[0041] Substituting formula (7) into formula (10) we can obtain:

[0042]

[0043] The traditional exponential convergence rate is:

[0044]

[0045] Where: μ, n are constants greater than 0, s is the sliding surface, and sgn is the sign function.

[0046] make i q =u, select the traditional exponential approach rate, and the control rate of the speed controller can be obtained from formula (11):

[0047]

[0048] From formula (13), we can see that there is a discontinuous term μsgn(s) in the control rate, which will cause the system to produce high-frequency jitter and affect the system performance. Therefore, a new improved exponential approach rate is designed as:

[0049]

[0050] Where ε and k are constants greater than 0; H(s) is the Softsign activation function; h(s) is the variable boundary layer nonlinear function.

[0051]

[0052] Where: η is a positive constant.

[0053] The activation function Softsign with continuous smooth characteristics is used to replace the sign function sgn in the traditional exponential reaching law, which effectively reduces the chattering phenomenon caused by the sign function in the process of the traditional exponential reaching law moving along the sliding surface to the equilibrium point.

[0054]

[0055] Where: m is a positive constant.

[0056] In the improved reaching law, selecting the appropriate exponential reaching term kh(s) according to the absolute value of s can better control the change of the controller output and improve the speed of global convergence in the process of approaching the sliding surface.

[0057] Therefore, the control rate of the speed controller can be obtained from equations (11) and (14):

[0058]

[0059] Where: u is the control rate of the speed controller; D is the constant term, and J is the moment of inertia of the wind power generation system.

[0060] In step 3, it can be seen from equation (17) that there is an unknown disturbance d in the system control input, which will affect the performance of the control system. In order to further enhance the robustness of the system, a fixed-time sliding mode observer is introduced to efficiently identify and estimate the unknown disturbance d, thereby ensuring accurate identification of the unmodeled dynamics and external complex disturbances in the wind power generation system within a fixed time.

[0061] In an actual wind power generation system, in each sampling period of the speed loop, the system disturbance changes very slowly compared with the system state. Therefore, the derivative of the total unknown disturbance d in formula (17) with respect to time t can be regarded as therefore,

[0062] According to formula (6), the dynamic system of PMSG can be expressed as:

[0063]

[0064] Then, the mechanical rotor angular velocity ω m and the unknown total disturbance d are state variables; the q-axis current i q is the control input; ω m is the system output, then the fixed-time convergence observer can be designed as:

[0065]

[0066] Where: and are the observed values ​​of the mechanical rotor angular velocity ω and the unknown total disturbance d respectively; is the speed observation error; is the sliding mode function; and ρ<0 is the observer gain.

[0067] According to equations (18) and (19), the observation error differential equation can be obtained as follows:

[0068]

[0069] Where: is the disturbance observation error.

[0070] The sliding surface of the fixed-time convergence observer is designed as:

[0071]

[0072] Where: k1>0 is the integral coefficient, λ1>0, 0 <a1<1、b1> 1 is the design parameter; An estimate of the speed error; is the function term of the estimated speed error; Function of the speed error estimate.

[0073] The sliding mode reaching law of the fixed-time convergence observer is defined as:

[0074]

[0075] Where: k2>0 sliding mode coefficient, sig a2 (s)=|s| a2 sign(s), sig b2 (s)=|s| b2 sign(s),λ2>0,0 <a2<1、b2> 1. ζ0>0 is the switching gain of the observer.

[0076] consider As a disturbance term, substituting equation (20) and equation (21) into equation (22), we can obtain equation (23):

[0077]

[0078] The fixed-time convergent observer does not depend on the observer's initial conditions, and the observation error It can converge to the origin in a fixed time.

[0079] Proof: Select the Lyapunov function as V = s2 , and its derivative is obtained as follows:

[0080]

[0081] Lemma 1: Consider the following system of differential equations:

[0082]

[0083] where: α, β, a, b are system parameters satisfying the differential equation, α > 0, β > 0, 0 < a < 1, b > 1, sig a (z) = |x| a sign(z), sign(z) is the sign function, z(0) is the initial state of z(x), and z0 is the initial value.

[0084] It can be obtained that the system (25) is a fixed-time stable system, and the upper bound of its stable time is:

[0085]

[0086] According to Equation (24) and Lemma 1, the fixed-time convergent sliding mode observer can make the observation error converge to the sliding mode surface s = 0 within the upper limit time, and its upper limit time is:

[0087]

[0088] where: T1 is the stable time of the sliding mode reaching process; a2 is a parameter to be designed and 0 < a2 < 1; b2 is a parameter to be designed and b2 > 1; λ2 is a parameter to be designed and λ2 > 0; k2 is the sliding mode coefficient and k2 > 0.

[0089] When reaching the sliding mode surface s = 0, taking the derivative of both sides of Equation (21) gives:

[0090]

[0091] where: The first derivative of the estimated value of the rotational speed error; λ1 is a parameter to be designed and λ1 > 0; k1 is the integral coefficient and k1 > 0; is the function term of the estimated value of the rotational speed error; is the function term of the estimated value of the rotational speed error.

[0092] Therefore, according to Lemma 1, the convergence time of the speed observation error can be bounded, and its upper bound is:

[0093]

[0094] Where: T2 is the stable time of the sliding process; b1 is the parameter to be designed and b1>1;

[0095] According to the above analysis, the total stable time of the fixed-time convergent sliding mode observer is T=T1+T2.

[0096] In step 4, since some unknown parameters are introduced in the design of the non-singular fast terminal sliding mode controller, the values ​​of these parameters affect the system performance. In order to accurately determine these parameters, an improved sparrow search algorithm is designed to optimize the unknown parameters p, q, λ, ε, and k, so that the wind power system reaches the optimal state when performing MPPT tracking;

[0097] The traditional sparrow search algorithm consists of a discoverer, a joiner, and a scout, and each sparrow position corresponds to a solution. The update formula for each position is as follows:

[0098] The discoverer's position update formula is:

[0099]

[0100] Where t is the current iteration number; iter max is the maximum number of iterations, which is a constant; represents the location information of the i-th sparrow in the t+1 generation; ξ∈(0,1) is a random number; R2(R2∈[0,1]) and ST(ST∈[0.5,1]) are the warning value and safety value; Q is a random number of normal distribution; L is a 1×d matrix; represents the position information of the i-th sparrow in generation t.

[0101] The position update formula of the joiner is as follows:

[0102]

[0103] In the formula, is the global optimal position; is the global worst position; A is a 1×d matrix with each element randomly assigned to 1 or -1, A + =A T (AA T ) -1 , A + is the right inverse matrix of matrix A; A T is the transposed matrix of matrix A.

[0104] When the population is foraging, a small number of sparrows will act as guards. The description of their position update is as follows:

[0105]

[0106] In the formula, is the global optimal position; δ is the step size control parameter; f i is the individual fitness value of the sparrow; f g is the optimal fitness value; f w is the worst fitness value; σ is a constant; r is the parameter for controlling the step length; is the global worst position.

[0107] Since the sparrow search algorithm adopts the strategy of randomly generating the initial position of the population, the algorithm lacks traversal, thereby reducing the search breadth of the algorithm. Therefore, in order to improve the global search ability of the algorithm, the strategy of Piecewise chaotic mapping is adopted to generate chaotic sequences in a mapping manner and convert them into new population initial positions. The new initial population is:

[0108] X new =lb+X i *(ub-lb) (33);

[0109] Where, X new represents the new initial population; X i is the location information of the i-th sparrow; lb and ub represent the lower and upper bounds of the population respectively.

[0110] In order to solve the problem that the sparrow search algorithm falls into the local search optimum, when the individual fitness f i Less than the average fitness of the group f avg , then Cauchy mutation is applied to the sparrow individual. On the contrary, if f i Greater than or equal to f avg , use Circle chaos perturbation on individuals to increase the diversity of the population and prevent it from falling into the local optimum.

[0111] The Cauchy variation formula is:

[0112] CauchyX i =X i ×(1+tan(π(v-0.5))),v∈[0,1] (34);

[0113] Where CauchyX i is the position after Cauchy mutation; X i is the original position; v is a random number.

[0114] The iteration method of Circle chaos perturbation is:

[0115]

[0116] In the formula, CircleX i is the individual after disturbance; X i to the original position.

[0117] Compared with the prior art, the MPPT non-singular fast terminal sliding mode control method of a permanent magnet direct-drive wind power system based on an improved sparrow search algorithm of the present invention has the following advantages and technical effects:

[0118] In view of the shortcomings of traditional PI control in permanent magnet direct-drive wind power generation systems, such as large overshoot and poor robustness, a new non-singular fast terminal control algorithm is adopted in the outer loop of the speed, and an improved exponential approach rate is proposed, which effectively reduces the jitter phenomenon in the control process and improves the convergence speed. At the same time, a fixed-time convergence sliding mode observer is introduced to observe and compensate for the unknown disturbances of the system in real time, ensuring accurate identification of unmodeled dynamics and external complex interferences in the wind power generation system within a fixed time. Finally, in order to accurately obtain the parameters of the sliding mode controller, an improved sparrow search algorithm is proposed to optimize the parameters of the controller. The control method of the present invention has fast response speed and high control accuracy, and can achieve maximum power tracking of the wind power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0119] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0120] Figure 1 This is a control block diagram of the maximum power tracking control method for wind power generation according to the present invention.

[0121] Figure 2 The figure is a flow chart of the improved sparrow search algorithm in the present invention.

[0122] Figure 3 This is the waveform diagram of generator speed tracking under the action of gradually changing wind.

[0123] Figure 4 This is the waveform diagram of wind energy utilization coefficient under the action of gradually changing wind.

[0124] Figure 5 This is the waveform diagram of generator speed tracking under the action of natural wind.

[0125] Figure 6 This is a partial enlarged view of the generator speed tracking under the action of natural wind.

[0126] Figure 7 This is the waveform diagram of wind energy utilization coefficient under the action of natural wind.

[0127] Figure 8 This is a partial enlarged diagram of the wind energy utilization coefficient under the action of natural wind. DETAILED DESCRIPTION

[0128] A non-singular fast terminal sliding mode control method for MPPT of permanent magnet direct-drive wind power system based on sparrow search algorithm. Aiming at the shortcomings of traditional PI control in wind power system, such as large overshoot and poor robustness, a new non-singular fast terminal control algorithm is adopted in the outer loop of speed, and an improved exponential approach rate is proposed, which effectively reduces the jitter phenomenon in the control process and improves the convergence speed. At the same time, a fixed-time convergence sliding mode observer is introduced to observe and compensate the unknown disturbance of the system in real time, so as to ensure the accurate identification of the unmodeled dynamics and external complex interference in the wind power generation system within a fixed time. Finally, in order to accurately obtain the parameters of the sliding mode controller, an improved sparrow search algorithm is proposed to optimize the parameters of the controller. The control method of the present invention has fast response speed and high control accuracy, and can realize the maximum power tracking of the wind power system.

[0129] The specific steps are:

[0130] (I) Establish a mathematical model of the fan based on the principle of aerodynamics and establish the stator voltage equation of the permanent magnet synchronous generator based on the synchronous rotating coordinate system dq;

[0131] According to aerodynamic theory, the aerodynamic mechanical power captured by the fan is:

[0132]

[0133] Where: ρ is air density; v is wind speed; R is the radius of the blade; λ is the tip speed ratio; β is the pitch angle. m is the aeromechanical power captured by the fan.

[0134] The tip speed ratio is the ratio of the fan impeller speed to the wind speed, that is:

[0135]

[0136] Where: m is the speed of the fan; R is the radius of the blade;

[0137] C p (λ,β) is the wind energy utilization coefficient. When the pitch angle β is constant, C p (λ,β) changes with the change of λ. By adjusting the speed at different wind speeds, there is an optimal tip speed ratio λ opt Make C p When (λ, β) reaches the maximum value, the maximum output power can be obtained. This process is the maximum power tracking process of the wind power generation system. Therefore, the essence of maximum power tracking is the control of the speed.

[0138] The aerodynamic torque of the fan is T m The mechanical power it captures meets

[0139]

[0140] Assuming that the motor operates under ideal conditions and its internal parameters remain unchanged, the mathematical model of PMSG in the dq synchronous rotating coordinate system can be obtained as follows:

[0141]

[0142] Where: i d 、i q are the d-axis and q-axis current components of the generator respectively; L is the equivalent inductance of the generator; u d 、u q are the d-axis and q-axis voltage components of the generator respectively; R s is the stator resistance; ψ f is the flux linkage of the permanent magnet; n p is the number of pole pairs of the generator rotor; ω m is the speed of the generator rotor.

[0143] For a permanent magnet synchronous motor, if the d-axis component of the stator current is always 0 during operation, the electromagnetic torque can be expressed as:

[0144] T e =1.5n p ψ f i q (5);

[0145] In the permanent magnet direct drive wind power generation system, the fan shaft is directly connected to the permanent magnet synchronous generator, and the generator rotor speed is consistent with the wind wheel speed, so the dynamic state equation of the wind power generation system transmission shaft system is:

[0146]

[0147] Where: J is the moment of inertia of the wind power generation system; B m is the viscous friction coefficient.

[0148] Taking into account the parameter mismatch, the dynamic equation above can be rewritten as:

[0149]

[0150] Where d is the unknown total disturbance including parameter mismatch and external load torque.

[0151] (II) Design of non-singular fast terminal sliding mode controller:

[0152] The speed error equation of the system is:

[0153]

[0154] In the formula, is the given speed of the generator, and e is the error between the given speed and the actual speed of the generator.

[0155] The designed non-singular fast terminal sliding surface is:

[0156] s=e+p∫(e)+q∫|e| λ sgn(e) (9);

[0157] Where e is the speed error, sgn is the sign function, p and q are the sliding mode coefficients, λ is the parameter to be designed, and p>0, q>0, 0<λ<1.

[0158] By taking the derivative of formula (9), we can get:

[0159]

[0160] In the formula, is the first-order derivative of the non-singular fast terminal sliding surface; is the first-order derivative of the actual speed of the generator; sgn(e) is the sign function of the speed error.

[0161] Substituting formula (7) into formula (10) we can obtain:

[0162]

[0163] The traditional exponential convergence rate is:

[0164]

[0165] Where: μ, n are constants greater than 0, s is the sliding surface, and sgn is the sign function.

[0166] make i q =u, select the traditional exponential approach rate, and the control rate of the speed controller can be obtained from formula (11):

[0167]

[0168] Where: u is the control rate of the speed controller; D is a constant term and J is the moment of inertia of the wind power generation system.

[0169] From formula (13), we can see that there is a discontinuous term μsgn(s) in the control rate, which will cause the system to produce high-frequency jitter and affect the system performance. Therefore, a new improved exponential approach rate is designed as:

[0170]

[0171] Where ε and k are constants greater than 0, H(s) is the Softsign activation function, and h(s) is the variable boundary layer nonlinear function.

[0172]

[0173] Where: η is a positive constant.

[0174] The activation function Softsign with continuous smooth characteristics is used to replace the sign function sgn in the traditional exponential reaching law, which effectively reduces the chattering phenomenon caused by the sign function in the process of the traditional exponential reaching law moving along the sliding surface to the equilibrium point.

[0175]

[0176] Where: m is a positive constant.

[0177] In the improved reaching law, selecting the appropriate exponential reaching term kh(s) according to the absolute value of s can better control the change of the controller output and improve the speed of global convergence in the process of approaching the sliding surface.

[0178] Therefore, the control rate of the speed controller can be obtained from equations (11) and (14):

[0179]

[0180] (III) Design of fixed time convergence sliding mode observer:

[0181] According to formula (6), the dynamic system of PMSG can be expressed as:

[0182]

[0183] Then, the mechanical rotor angular velocity ω m and the unknown total disturbance d as state variables, the q-axis current i q is the control input, ω m is the system output, then the fixed-time convergence observer can be designed as:

[0184]

[0185] In the formula and are the observed values ​​of the mechanical rotor angular velocity ω and the unknown total disturbance d respectively; is the speed observation error; is the sliding mode function; and ρ<0 is the observer gain.

[0186] According to equations (18) and (19), the observation error differential equation can be obtained as follows:

[0187]

[0188] Where: is the disturbance observation error.

[0189] The sliding surface of the fixed-time convergence observer is designed as:

[0190]

[0191] Where k1>0 is the integral coefficient, λ1>0, 0 <a1<1、b1> 1 is the design parameter of the generation. An estimate of the speed error; is the function term of the estimated speed error; Function of the speed error estimate.

[0192] The sliding mode reaching law of the fixed-time convergence observer is defined as:

[0193]

[0194] Where k2>0, sig a2 (s)=|s| a2 sign(s), sig b2 (s)=|s| b2 sign(s),λ2>0,0 <a2<1、b2> 1. ζ0>0 is the switching gain of the observer.

[0195] consider As a disturbance term, substituting equation (20) and equation (21) into equation (22) yields equation (23):

[0196]

[0197] Fixed time convergence observer, independent of observer initial conditions, observation error It can converge to the origin in a fixed time.

[0198] Proof: Select the Lyapunov function as V = s 2 , and taking its derivative we get:

[0199]

[0200] Lemma 1 Consider the following system of differential equations:

[0201]

[0202] Where: α, β, a, b are system parameters that satisfy the differential equation, α>0, β>0, 0 <a<1,b> 1, sig a (z)=|x|a sign(z), where sign(z) is the sign function, z(0) is the initial state of z(x), and z0 is the initial value.

[0203] It can be obtained that the system (25) is a fixed-time stable system, and the upper bound of its stable time is:

[0204]

[0205] According to Equation (24) and Lemma 1, the fixed-time convergent sliding mode observer can make the observation error converge to the sliding mode surface s = 0 within the upper bounded time, and its upper bounded time is:

[0206]

[0207] In the formula: T1 is the stable time of the sliding mode reaching process; a2 is a parameter to be designed and 0 < a2 < 1; b2 is a parameter to be designed and b2 > 1; λ2 is a parameter to be designed and λ2 > 0; k2 is the sliding mode coefficient and k2 > 0.

[0208] When reaching the sliding mode surface s = 0, taking the derivative of both sides of Equation (21) gives:

[0209]

[0210] In the formula: The first derivative of the estimated value of the rotational speed error; λ1 is a parameter to be designed and λ1 > 0; k1 is the integral coefficient and k1 > 0; is the function term of the estimated value of the rotational speed error; is the function term of the estimated value of the rotational speed error.

[0211] Therefore, according to Lemma 1, the convergence time of the speed observation error can be bounded, and its upper bound is:

[0212]

[0213] In the formula: T2 is the stable time of the sliding mode sliding process; b1 is a parameter to be designed and b1 > 1.

[0214] According to the above analysis, the total stable time of the fixed-time convergent sliding mode observer is T = T1 + T2.

[0215] (IV). Design of the improved sparrow search algorithm:

[0216] The traditional sparrow search algorithm consists of discoverers, joiners, and scouts, and each sparrow position corresponds to a solution. The update formulas for their respective positions are as follows:

[0217] Update formula for the position of the discoverer:

[0218]

[0219] Where t is the current iteration number; iter max is the maximum number of iterations, which is a constant; represents the location information of the i-th sparrow in the t+1 generation; ξ∈(0,1) is a random number; R2(R2∈[0,1]) and ST(ST∈[0.5,1]) are the warning value and safety value; Q is a random number of normal distribution; L is a 1×d matrix; represents the position information of the i-th sparrow in generation t.

[0220] The position update formula of the joiner is as follows:

[0221]

[0222] In the formula, is the global optimal position; is the global worst position; A is a 1×d matrix with each element randomly assigned to 1 or -1, A + =A T (AA T ) -1 , A + is the right inverse matrix of matrix A, A T is the transposed matrix of matrix A.

[0223] When the population is foraging, a small number of sparrows will act as guards. The description of their position update is as follows:

[0224]

[0225] In the formula, is the global optimal position; δ is the step size control parameter; f i is the individual fitness value of the sparrow; f g is the optimal fitness value; σ is a constant; r is the parameter for controlling the step size.

[0226] Since the sparrow search algorithm adopts the strategy of randomly generating the initial position of the population, the algorithm lacks traversal, thereby reducing the search breadth of the algorithm. Therefore, in order to improve the global search ability of the algorithm, the strategy of Piecewise chaotic mapping is adopted to generate chaotic sequences in a mapping manner and convert them into new population initial positions. The new initial population is:

[0227] X new =lb+X i *(ub-lb) (33);

[0228] Where, X newDenote the new initial population; X i is the position information of the i-th sparrow; lb and ub represent the lower and upper bounds of the population respectively.

[0229] To solve the problem that the sparrow search algorithm falls into local search for the optimal solution, when the fitness f of an individual i is less than the average fitness f of the population avg , at this time, Cauchy mutation is applied to this sparrow individual. On the contrary, if f i is greater than or equal to f avg , Circle chaotic perturbation is adopted for the individual. Increase the diversity of the population and prevent falling into local optimum.

[0230] The Cauchy mutation formula is:

[0231] CauchyX i = X i ×(1 + tan(π(v - 0.5))), v ∈ [0, 1] (34);

[0232] In the formula, CauchyX i is the position after Cauchy mutation; X i is the original position; v is a random number.

[0233] The iterative method of Circle chaotic perturbation is:

[0234]

[0235] In the formula, CircleX i is the individual after perturbation; X i is the original position.

[0236] Next, a permanent magnet direct drive wind power generation system is modeled and simulated. The system model is as Figure 1 . The speed loop controller of the control system is controlled by a non-singular fast terminal sliding mode controller (NFTSMC). Observe the speed tracking situation under two wind speeds of gradual wind and natural wind, and compare and analyze traditional PI control and sliding mode control (SMC).

[0237] From Figure 3 , it can be seen that when the wind speed changes slowly, that is, 2s < t < 4s, compared with the PI controller and the SMC controller, the NFTSMC control method adopted in this design has better control performance for the speed. When the wind speed suddenly drops at the 6th second, the NFTSMC can track the sudden change speed of the system without overshoot, while the SMC has a slight overshoot and large chattering, and the PI control has a large overshoot.

[0238] Figure 4It is a comparison of wind energy utilization coefficients. It is obvious that NFTSMC can make the system converge quickly in a very short time, making the wind energy utilization coefficient quickly reach about 0.48, and remain stable during the subsequent tracking process.

[0239] Depend on Figure 5 , Figure 6 It can be seen that the tracking effects of SMC and PI control in natural wind are both insufficient, while NFTSMC, whether in terms of response speed or overshoot, can well meet the system requirements and improve the system's anti-interference ability.

[0240] Depend on Figure 7 , Figure 8 It can be seen that NFTSMC can maximize the wind energy utilization coefficient more quickly and keep it stable, thereby improving the utilization efficiency of wind energy.

Claims

1. A non-singular fast terminal sliding mode control method for MPPT of permanent magnet direct-drive wind power system based on sparrow search algorithm, characterized by It includes the following steps: Step 1: Establish a mathematical model of the wind turbine, and establish the stator voltage equation of the permanent magnet synchronous generator based on the synchronous rotating coordinate system dq; Step 2: Design a nonsingular fast terminal sliding mode controller for the speed loop, with the state error e as the control objective, and design a nonlinear function with a variable boundary layer in combination with the Softsign function; Step 3: Design a fixed-time sliding mode observer to estimate and actively compensate for the uncertainties of the internal and external disturbances of the system, and feed forward the observed value to the nonsingular fast terminal sliding mode controller to cancel the interference; Step 4: Optimize the parameters to be designed in the nonsingular fast terminal sliding mode controller based on the improved sparrow search algorithm to obtain the parameters more accurately.

2. According to the sparrow search algorithm-based permanent magnet direct-drive wind power system MPPT non-singular fast terminal sliding mode control method of claim 1, it is characterized by: In the above Step 1, the aerodynamic mechanical power captured by the wind turbine is: Where: ρ is air density; v is wind speed; R is blade radius; λ is tip speed ratio; β is pitch angle; P m aeromechanical power captured for the fan; The tip speed ratio is the ratio of the speed of the wind turbine impeller to the wind speed, that is: Where: m is the speed of the fan; R is the radius of the blade; C p (λ,β) is the wind energy utilization coefficient. When the pitch angle β is constant, C p (λ,β) changes with the change of λ. By adjusting the speed at different wind speeds, there is an optimal tip speed ratio λ opt Make C p (λ, β) reaches the maximum value, and the maximum output power can be obtained. This process is the maximum power tracking process of the wind power generation system; The aerodynamic torque of the fan is T m The mechanical power it captures satisfies: Where:ω m is the speed of the fan; Assume that the motor operates under ideal conditions, and its internal parameters remain unchanged at this time. The mathematical model of the permanent magnet synchronous generator PMSG in the d-q synchronous rotating coordinate system can be obtained as: Where: i d 、i q are the d-axis and q-axis current components of the generator respectively; L is the equivalent inductance of the generator; u d 、u q are the d-axis and q-axis voltage components of the generator respectively; R s is the stator resistance; ψ f is the flux linkage of the permanent magnet; n p is the number of pole pairs of the generator rotor; ω g is the speed of the generator rotor.

3. According to claim 2, the MPPT non-singular fast terminal sliding mode control method of a permanent magnet direct-drive wind power system based on a sparrow search algorithm is characterized in that: For a permanent magnet synchronous motor, during operation, the d-axis component of the stator current is always 0, then the electromagnetic torque is expressed as: T e =1.5n p ψ f I q (5); In a permanent magnet direct drive wind power generation system, the shaft of the wind turbine is directly connected to the permanent magnet synchronous generator, and the rotor speed of the generator is the same as the wind turbine speed. Therefore, the dynamic state equation of the drive shaft system of the wind power generation system is: Where: J is the moment of inertia of the wind power generation system; B m is the viscous friction coefficient; Considering parameter mismatch, the dynamic equation of the above formula is rewritten as: In the formula, d is the unknown total disturbance including parameter mismatch and external load torque.

4. According to claim 1, the MPPT non-singular fast terminal sliding mode control method of a permanent magnet direct-drive wind power system based on a sparrow search algorithm is characterized by: In the above Step 2, the speed error equation of the system is: In the formula, is the given speed of the generator; e is the error between the given speed of the generator and the actual speed; The designed nonsingular fast terminal sliding mode surface is: s=e+p∫(e)+q∫|e| λ sgn(e) (9); In the formula, e is the speed error; sgn is the sign function; p, q are sliding mode coefficients; λ is the parameter to be designed, and p>0, q>0, 0<λ<1; Taking the derivative of Equation (9) gives: Where s is the first-order derivative of the non-singular fast terminal sliding surface; is the first-order derivative of the actual speed of the generator; sgn(e) is the sign function of the speed error; Substituting Equation (7) into Equation (10) gives: The traditional exponential reaching law is: In the formula: μ, n are constants greater than 0, s is the sliding mode surface, sgn is the sign function; make i q =u, select the traditional exponential approach rate, and the control rate of the speed controller can be obtained from formula (11): From Equation (13), it can be seen that there is a discontinuous term μsgn(s) in the control law, which will cause high-frequency chattering of the system and affect the system performance; therefore, an improved exponential reaching law is designed as: In the formula, ε, k are constants greater than 0; H(s) is the Softsign activation function; h(s) is the variable boundary layer nonlinear function; In the formula: η is a positive constant; Use the activation function Softsign with continuous and smooth characteristics to replace the sign function sgn in the traditional exponential reaching law; In the formula: m is a positive constant; In the improved reaching law, the appropriate exponential reaching term kh(s) is selected according to the magnitude of the absolute value of s; Therefore, from Equation (11) and Equation (14), the control law of the speed controller is: Where: u is the control rate of the speed controller; D is the constant term, and J is the moment of inertia of the wind power generation system.

5. According to claim 4, the MPPT non-singular fast terminal sliding mode control method of permanent magnet direct-drive wind power system based on sparrow search algorithm is characterized by: In step 3, a fixed-time sliding mode observer is introduced to efficiently identify and estimate the unknown disturbance d. The derivative of the total unknown disturbance d in equation (17) with respect to time t can be regarded as Therefore, the dynamic system of PMSG according to equation (6) is expressed as: Then, the mechanical rotor angular velocity ω m and the unknown total disturbance d are state variables; the q-axis current i q is the control input; ω m is the system output, then the fixed-time convergence observer is designed as: Where: and are the observed values ​​of the mechanical rotor angular velocity ω and the unknown total disturbance d respectively; is the speed observation error; is the sliding mode function; and ρ<0 is the observer gain; According to Equations (18) and (19), the following observation error differential equation is obtained: Where: is the disturbance observation error.

6. The MPPT non-singular fast terminal sliding mode control method for a permanent magnet direct-drive wind power system based on a sparrow search algorithm according to claim 5 is characterized in that: The sliding mode surface for designing a fixed-time convergent observer is: Where: k1>0 is the integral coefficient, λ1>0, 0 <a1<1、b1> 1 is the design parameter; An estimate of the speed error; is the function term of the estimated speed error; Function term of the speed error estimate; Define the sliding mode reaching law of the fixed-time convergent observer as: Where: k2>0 sliding mode coefficient, sig a2 (s)=|s| a2 sign(s), sig b2 (s)=|s| b2 sign(s),λ2>0,0 <a2<1、b2> 1. ζ0>0 is the switching gain of the observer; consider As a disturbance term, substituting equation (20) and equation (21) into equation (22), we can obtain equation (23): The fixed-time convergent observer does not depend on the observer's initial conditions, and the observation error It can converge to the origin within a fixed time; the fixed time convergence sliding mode observer can make the observation error Converges to the sliding surface s = 0, where the time limit is: In the formula: T1 is the stable time of the sliding mode reaching process; a2 is the parameter to be designed and 0<a2<1; b2 is the parameter to be designed and b2>1; λ2 is the parameter to be designed and λ2>0; k2 is the sliding mode coefficient and k2>0; When the sliding surface s = 0 is reached, taking the derivatives on both sides of equation (21) yields: Where: The first-order derivative of the speed error estimate; λ1 is the parameter to be designed and λ1>0; k1 is the integral coefficient and k1>0; is the function term of the estimated speed error; is the function term of the estimated speed error; Therefore, the velocity observation error The convergence time of is bounded, and its upper bound is: Where: T2 is the stabilization time of the sliding process; b1 is the parameter to be designed and b1>1; According to the above analysis, the total stable time of the fixed-time convergent sliding mode observer is T=T1+T2.

7. The MPPT non-singular fast terminal sliding mode control method for a permanent magnet direct-drive wind power system based on a sparrow search algorithm according to claim 6 is characterized in that: In step 4, since some unknown parameters are introduced in the design of the non-singular fast terminal sliding mode controller, the values ​​of these parameters affect the system performance. In order to accurately determine these parameters, an improved sparrow search algorithm is designed to optimize the unknown parameters p, q, λ, ε, and k, so that the wind power system reaches the optimal state when performing MPPT tracking; The sparrow search algorithm consists of discoverers, joiners, and scouts, and each sparrow position corresponds to a solution. The update formula for each position is as follows: The discoverer's position update formula is: Where t is the current iteration number; iter max is the maximum number of iterations, which is a constant; represents the location information of the i-th sparrow in the t+1 generation; ξ∈(0,1) is a random number; R2(R2∈[0,1]) and ST(ST∈[0.5,1]) are the warning value and safety value; Q is a random number of normal distribution; L is a 1×d matrix; represents the position information of the i-th sparrow in generation t; The position update formula of the joiner is as follows: In the formula, is the global optimal position; is the global worst position; A is a 1×d matrix with each element randomly assigned to 1 or -1, A + =A T (AA T ) -1 , A + is the right inverse matrix of matrix A; A T is the transposed matrix of matrix A; When the population is foraging, a small number of sparrows will act as guards; their position updates are described as follows: In the formula, is the global optimal position; δ is the step size control parameter; f i is the individual fitness value of the sparrow; f g is the optimal fitness value; f w is the worst fitness value; σ is a constant; r is the parameter for controlling the step length; is the global worst position; The strategy of piecewise chaotic mapping is adopted to generate chaotic sequences in a mapping manner and transform them into new population initial positions; the new initial population is: X new =lb+X i *(ub-lb) (33); Where, X new represents the new initial population; X i is the location information of the i-th sparrow; lb and ub represent the lower and upper bounds of the population respectively; In order to solve the problem that the sparrow search algorithm falls into the local search optimum, when the individual fitness f i Less than the average fitness of the group f avg , then the Cauchy mutation is applied to the sparrow individual; on the contrary, if f i Greater than or equal to f avg , Circle chaos perturbation is used for individuals; The Cauchy variation formula is: CauchyX i =X i ×(1+tan(π(v-0.5))),v∈[0,1] (34); Where CauchyX i is the position after Cauchy mutation; X i is the original position; v is a random number; the iteration method of Circle chaos perturbation is: In the formula, CircleX i is the individual after disturbance; X i to the original position.

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