CN111963372B - An optimal speed tracking control method for wind turbines - Google Patents

Abstract

An optimal rotational speed tracking control method of a wind turbine belongs to the technical field of control. The invention aims to solve the problem that the wind power generator has a low wind energy capture efficiency in a low wind speed area. The method of the present invention firstly establishes the dynamic equation of the wind power generation system for the wind power generation system; then the error variable e=ω _r ‑ω _ref of the wheel speed tracking the expected wind wheel speed is constrained to P _l (t)<e(t )<P _r (t), then convert the error variable, and finally select the Lyapunov function, and derive the Lyapunov function V with respect to time t based on the converted error ε and the corresponding derivative, and finally get the wind turbine’s The preset performance controller is controlled according to the preset performance controller of the wind turbine. Mainly used for wind turbine optimal speed tracking control.

Description

An optimal speed tracking control method for wind turbines

technical field

The invention relates to a method for tracking and controlling the rotational speed of a wind generator. It belongs to the field of control technology.

Background technique

Wind power has received a lot of attention in recent years due to energy shortages and the harmful effects of fossil fuels. Wind turbines can usually be divided into fixed-speed type and variable-speed type. Under various wind speeds, the variable-speed type has the advantages of high efficiency and low conversion cost compared with the fixed-speed type. However, these advantages must rely on advanced control methods, and maximum power point tracking (MPPT) control is one of the important topics, which aims to control the rotor speed to track the optimal speed under the rated wind speed, so as to capture more of wind energy.

At present, the commonly used control methods for maximum power tracking include optimal torque method, power curve method, and tip speed ratio method, among which the tip speed ratio method is widely used in theoretical research. This method maintains the maximum wind energy capture rate mainly by maintaining the tip speed ratio of the wind turbine at an optimum value when the wind speed changes. However, due to the highly nonlinear and cross-coupled system dynamics, as well as the dynamic changes of natural wind speed, grid demand and system operating conditions, large model uncertainties and external disturbances are introduced to the wind power generation system model, which in turn increases The difficulty of controller design. Conventional control methods often have problems such as serious wind wheel buffeting and low wind energy capture efficiency, which reduce the safety, reliability and economy of wind power generation systems.

SUMMARY OF THE INVENTION

In order to solve the problem that the wind power generator has a low wind energy capture efficiency in the low wind speed region, the present invention further proposes an optimal rotational speed tracking control method of the wind power generator, which is a preset performance tracking control method based on an improved performance function , the tracking error of the optimal speed of the fan can be converged within a specified time, and the overshoot is small.

A wind turbine optimal rotational speed tracking control method, comprising the following steps:

s1. Establish the dynamic equation of the wind power generation system for the wind power generation system;

s2. Constrain the error variable that the wheel speed ω _r tracks the desired wind wheel speed ω _ref as e=ω _r -ω _ref :

P _l (t)<e(t)<P _r (t) (1)

The upper bound P _r (t) and lower bound P _l (t) of the error are as follows

where 0≤δ ₁ ≤1, 0≤δ ₂ ≤1, δ ₁ and δ ₂ are design parameters, sign( ) is the sign function; ρ(t) is the performance function;

Convert the error variable, and the converted error ε(t) is

s3. Select the Lyapunov function, derive the Lyapunov function V with respect to time t based on the converted error ε and the corresponding derivative, and finally obtain the preset performance controller of the wind turbine. According to the preset performance of the wind turbine controller to control.

Further, the desired rotor speed ω _ref is

ω _ref =λ _opt v/R (4)

Among them, v is the wind speed, λ _opt is the optimal tip speed ratio, and R is the radius of the rotor.

Further, the dynamic equation of the wind power generation system established in the step s1 is as follows:

In the formula, ω _r is the rotational angular velocity of the wind rotor, J _r is the rotational inertia of the low-speed shaft, B _r is the damping coefficient of the low-speed shaft, J _g is the rotational inertia of the high-speed shaft, B _g is the damping coefficient of the high-speed shaft, and T _a is the aerodynamic torque, T _g is the electromagnetic torque of the generator, n _g is the transmission ratio of the gearbox, and F is the system uncertainty and disturbance.

Further, the system uncertainty and interference F are bounded, and can be expressed as:

为系统不确定性，d为未知干扰，δ为不确定性的上界。In the formula,

is the system uncertainty, d is the unknown disturbance, and δ is the upper bound of the uncertainty.

Further, the aerodynamic torque T _a is as follows:

In the formula, ρ is the air density, R is the radius of the rotor, v is the wind speed, and the wind energy utilization coefficient C _p is a nonlinear function of the tip speed ratio λ and the blade pitch angle β.

Further, the performance function ρ(t) is as follows

Where ρ ₀ =ρ(0) is the initial value; ρ _∞ is the maximum allowable value of the tracking error in steady state; T ₀ is the preset convergence time.

Further, the preset performance controller of the wind turbine is

B_r为低速轴的阻尼系数，B_g为高速轴阻尼系数，ω_r为风轮旋转角速度，ω_ref为期望风轮转速，δ为不确定性的上界，

J_r为低速轴的转动惯量，J_g为高速轴的转动惯量，为转换后的误差。Among them, T _g is the electromagnetic torque of the generator, T _a is the aerodynamic torque, n _g is the transmission ratio of the gearbox,

B _r is the damping coefficient of the low-speed shaft, B _g is the damping coefficient of the high-speed shaft, ω _r is the rotational angular velocity of the rotor, ω _ref is the expected rotor speed, δ is the upper bound of uncertainty,

J _r is the moment of inertia of the low-speed shaft, J _g is the moment of inertia of the high-speed shaft, and is the converted error.

Further, the Lyapunov function is selected as described in step s3, and the Lyapunov function V is derived with respect to time t based on the converted error ε and the corresponding derivative, and the process of obtaining the preset performance controller of the wind turbine includes the following steps:

Without considering uncertainty and interference, the transformed error ε is derived with respect to time t to get

in

When considering uncertainty and disturbance F, the derivative of Lyapunov function V with respect to time t has

where δ represents the upper bound of uncertainty;

Finally, the preset performance controller of the wind turbine is obtained as

Further, in the process of derivation of the converted error ε with respect to time t without considering uncertainty and interference, first, the tracking error e is derived without considering uncertainty and interference.

Then the transformed error ε is derived with respect to time t

Arranging the above formula, we get

in

Beneficial effects:

The invention can well solve the problem of low wind energy capture efficiency of the existing wind generators in the low wind speed area, and even in the low wind speed area, the wind energy capture has a high capture efficiency.

Compared with the existing control methods, the existing control methods do not consider the overshoot of the control, and it is difficult to establish a clear mathematical relationship between the parameters of the designed performance function and the actual error convergence rate. The invention improves the traditional preset performance control method, adopts an improved performance function and a new error transformation method, can limit the system overshoot, and can obtain the required steady-state accuracy within a specified time. It can be seen from the examples that the preset performance control method for improving the performance function of the present invention can obtain the required steady-state accuracy within a specified time, and has good robustness.

Description of drawings

Fig. 1 is the wind speed curve that simulation uses in the embodiment;

FIG. 2 is a rotational speed tracking error curve in the embodiment.

Detailed ways

Specific implementation one:

Before describing this embodiment, first describe the parameters involved in this embodiment:

ω _r ——rotational angular velocity of wind wheel; J _r —— rotational inertia of low-speed shaft; B _r —— damping coefficient of low-speed shaft; J _g —— rotational inertia of high-speed shaft; B _g —— damping coefficient of high-speed shaft; T _a —— aerodynamic torque; T _g —— electromagnetic torque of generator; n _g —— transmission ratio of gear box; F —— system uncertainty and disturbance; ω _ref —— expected value of rotor rotational angular velocity; e=ω _r -ω _ref — tracking error; ρ — air density; R — rotor radius; v — wind speed; C _p — wind energy utilization coefficient; λ — tip speed ratio; λ _opt — optimal blade Tip speed ratio; β - blade pitch angle; δ - upper bound of uncertainty.

A method for tracking and controlling the optimum rotational speed of a wind turbine according to this embodiment includes the following steps:

1. Establish the dynamic equation of the wind power generation system:

Introducing the system disturbance force F, assuming that the low-speed shaft is completely rigid, the dynamic model of a wind power system can be expressed as:

In the formula, ω _r is the rotational angular velocity of the wind rotor, J _r is the rotational inertia of the low-speed shaft, B _r is the damping coefficient of the low-speed shaft, J _g is the rotational inertia of the high-speed shaft, B _g is the damping coefficient of the high-speed shaft, and T _a is the aerodynamic Torque, T _g is the electromagnetic torque of the generator, n _g is the transmission ratio of the gearbox, and F is the system uncertainty and disturbance, which are usually unknown.

Aerodynamic torque T _a :

In the formula, ρ is the air density, R is the radius of the rotor, v is the wind speed, and the wind energy utilization coefficient C _p is the nonlinear function of the tip speed ratio λ and the blade pitch angle β;

Assuming that F is bounded, it can be expressed as:

为系统不确定性，d为未知干扰，δ为不确定性的上界。In the formula,

is the system uncertainty, d is the unknown disturbance, and δ is the upper bound of the uncertainty.

The control objective of the wind turbine below the rated wind speed is to capture the wind energy to the maximum extent. To maximize the output power of the wind power system, C _p (λ, β) needs to be at the maximum value. Since C _p (λ, β) is a function of λ and β as variables, in the case of keeping the pitch angle β constant (usually around 0°), the rotor can be indirectly changed by adjusting the generator torque T _g speed ω _r so that it better tracks the optimum tip speed ratio λ _opt .

The expected rotor speed _ωref is

ω _ref =λ _opt v/R (14)

where v is the wind speed.

Using tip speed ratios to achieve maximum power tracking typically requires an estimate of wind speed. Commonly used estimation methods include observation by observer, Kalman filter and Newton-Raphson algorithm, etc., all of which have good estimation results. The present invention assumes that the estimated value of the wind speed is equal to the true value.

The objective of the present invention can thus be expressed as: designing a preset performance controller that improves the performance function to control the generator torque T _g so that the rotor speed ω _r tracks the desired rotor speed ω _ref more quickly. The error variable is defined as e = ω _r - ω _ref .

2. Improved performance function and error transformation:

In order to achieve the expected control objective, a performance function is introduced as a preset performance boundary. The performance function is defined as follows:

Definition 1: For a smooth function ρ(t): R ₊ →R, if it satisfies

(1) ρ(t) is a monotonically decreasing positive function.

(2) lim _t→∞ ρ(t)=ρ _∞ >0.

Then this function is called the performance function.

Traditional performance functions are usually designed in exponential form.

ρ(t)=(ρ ₀ -ρ _∞ )e ^-kt +ρ _∞ (15)

where ρ ₀ , ρ _∞ and k are preset constants.

Obviously, the convergence speed of the conventional performance function depends on the exponential term e ^-kt . However, it is very difficult to establish a clear mathematical relationship between the parameter k and the convergence rate, and it is difficult to determine the specific error convergence time. In addition, the choice of parameter k is not clear. Therefore, the present invention improves upon the conventional performance function. The improved performance function is

where ρ ₀ , ρ _∞ , T ₀ are predefined design parameters. ρ ₀ =ρ(0), which is the initial value; ρ _∞ is the maximum allowable value of tracking error in steady state; T ₀ is the preset convergence time.

Through the improved performance function, we can preset the convergence time T ₀ , and it can be intuitively concluded that the smaller the preset convergence time T ₀ is, the faster the convergence speed is when the error accuracy reaches ρ _∞ under the same performance requirements.

Next, the wind turbine preset performance controller is derived based on the proposed improved performance function. The constraint inequality used is

P _l (t) < e (t) < P _r (t) (17)

The upper bound P _r (t) and the lower bound P _l (t) of the error are defined as follows

Among them, 0≤δ ₁ ≤1, 0≤δ ₂ ≤1, are design parameters. sign(·) is a sign function.

It is difficult to directly solve the tracking control problem under constraints, so an error transformation method is needed to convert the constrained problem into an unconstrained stable control problem. The traditional error transformation function S _i (ε _i ) is defined as follows:

Definition 2: If there is a function S _i (ε _i ) that satisfies the following properties:

(1) S _i (ε _i ) is smooth and strictly monotonically increasing

(2)

(3)

Then this function is called the error transformation function.

Since the present invention improves the traditional performance function, the traditional error transformation function cannot be used, so a corresponding new error transformation method needs to be designed. The converted error ε(t) used in the present invention is

The following theorem can be obtained:

Theorem 1: If the transformed error ε(t) is bounded, then the tracking error e(t) can be constrained between an upper bound Pr( _t ) and a lower bound _Pl (t).

Prove: The inverse transformation of Equation (19)ε(t) is

Equation (20), it can be further obtained

Since ε(t) is bounded, there exists a constant ε _M ∈R ⁺ such that |ε(t)|≤ε _M , ie -ε _M ≤ε(t)≤ε _M ; therefore, the above equation (21) can be turn into

可以得到notice

can get

eventually have

P _l (t) < e (t) < P _r (t) (24)

Certificate completed.

Next, we will use the transformed error ε(t) instead of the tracking error e(t) for the derivation of the controller. Theorem 1 states that when the transformed error ε(t) is bounded, the tracking error e(t) is bounded within a preset performance bound (17). By choosing appropriate design parameters for P _l (t) and P _r (t), both transient and steady-state performance of the tracking error e(t) can be guaranteed.

3. Preset performance controller design

Without considering the uncertainty and interference, the derivative of the tracking error e obtained from equation (11) is

The transformed error ε is derived with respect to time t

in

Arranging the above formula, we can get

in,

For convenience of description and expression, all time variables t are omitted. The following e(t), ε(t), θ(t) and ρ(t) are abbreviated as e, ε, θ, ρ.

The Lyapunov function is chosen as

Then the derivative of the Lyapunov function V with respect to time t has

So far, the preset performance controller of the wind turbine is designed as

是负定的，因此系统渐近稳定。where c ₁ is a positive definite constant. The derivative of the Lyapunov function V with respect to time t at this time

is negative definite, so the system is asymptotically stable.

When considering uncertainty and disturbance F, the derivative of Lyapunov function V with respect to time t has

In the formula, δ represents the upper bound of uncertainty.

Therefore, the preset performance controller of the wind turbine is designed as

Example

In order to verify the effectiveness of the control method designed in the present invention, it is applied to a wind turbine model for simulation verification, and the influence caused by model uncertainty and disturbance is considered. The parameters of the 5MW wind turbine used are shown in Table 1.

Table 1 Wind turbine parameters

The present invention superimposes two sinusoidal signals of different frequencies as the input wind speed. The wind speed curve used in the simulation is shown in Figure 1.

In order to verify the effectiveness of the designed controller, white noise is added as the random disturbance of the system, and the parameters of the improved performance function controller are shown in Table 2.

Table 2 Improved performance function controller parameters

Simulation analysis: The speed tracking error curve is shown in Figure 2.

It can be seen from Figure 2 that the tracking error can obtain the required steady-state accuracy at the 4th second of the preset convergence time. The random disturbance of the system will cause slight fluctuations in the tracking error curve, but it can still be controlled within the preset value. within the performance function. It is proved that the preset performance control method with improved performance function can obtain the required steady-state accuracy within the specified time and has good robustness.

Comparison with existing technical solutions

If you want to achieve the control requirements of wind turbine speed tracking under the influence of rated wind speed, model uncertainty and unknown interference, in addition to the algorithm of the present invention, there are also schemes based on neural network control, traditional preset performance control and other schemes. The following two schemes are briefly introduced and compared with the algorithm of the present invention.

a, neural network-based scheme

The neural network is mostly used to deal with the uncertainty or unknown external disturbance of the wind turbine model. The neural network is used to estimate the above disturbance, and some common control methods are used, such as PID control, sliding mode control, backstep control, adaptive control, etc. , so as to obtain a relatively good control scheme. For example, "Non-Singular Fast Terminal Sliding Mode Control of Manipulator Neural Network" uses radial basis function neural network (RBFNN) to approximate unknown dynamic characteristics.

However, compared with the algorithm of the present invention, the above scheme cannot meet the requirement of rapidity of the system because the calculation amount is too large. By introducing the preset performance method and the error transformation, the algorithm of the invention can preset the convergence speed and the convergence time, which is closer to the actual engineering requirements.

b. Scheme based on traditional preset performance control

"Adaptive neural network based prescribed performance control forteleoperation system under input saturation" In the presence of system uncertainty and external interference, a preset performance control scheme based on the combination of corresponding adaptive control and neural network control is designed, and The scheme is simulated and compared with PD (proportional plus derivative) controller, which proves the effectiveness of the preset performance control method. "Quasi fixed-time fault-tolerant control for nonlinear mechanical systems with enhanced performance" studies a very novel method of preset performance control using quasi-timing, and finds that it has the outstanding advantage that a fixed convergence time can be specified in advance. "A low-complexityglobal approximation-free control scheme with prescribed performance forunknown pure feedback systems" for unknown pure feedback systems, uses the preset performance control method to design the controller, and proposes a general feedback control scheme without approximation state . This scheme can make the output error converge to a preset arbitrary small value, and avoid the complexity problem brought by the traditional backstepping method.

However, compared with the algorithm of the present invention, the above scheme does not consider the overshoot of the control, and it is difficult to establish a clear mathematical relationship between the parameters of the designed performance function and the actual error convergence rate. The algorithm of the invention improves the traditional preset performance control method, adopts an improved performance function and a new error transformation method, can limit the overshoot of the system, and can obtain the required steady-state accuracy within a specified time.

It should be noted that the specific embodiments are only explanations and descriptions of the technical solutions of the present invention, and cannot be used to limit the protection scope of the rights. Any changes made according to the claims and description of the present invention are only partial changes, which should still fall within the protection scope of the present invention.

Claims (8)

1. The optimal rotating speed tracking control method of the wind driven generator is characterized by comprising the following steps of:

s1, establishing a dynamic equation of the wind power generation system aiming at the wind power generation system;

s2 wheel speed omega_rTracking desired rotor speed omega_refThe error variable of (2) is e ═ ω_r-ω_refAnd (4) carrying out constraint:

P_l(t)＜e(t)＜P_r(t) (1)

upper bound of error P_r(t) and lower bound P_l(t) is as follows

Wherein 0 is not less than delta₁≤1，0≤δ₂≤1，δ₁And delta₂Sign () is a sign function for a design parameter; ρ (t) is a performance function; the performance function ρ (t) is as follows

Where ρ is₀ρ (0) is an initial value; rho_∞The maximum allowable value of the tracking error at the steady state; t is₀Is a preset convergence time;

converting the error variable to obtain a converted error epsilon (t)

s3, selecting a Lyapunov function, deriving the Lyapunov function V for time t based on the converted error epsilon and the corresponding derivative, finally obtaining a preset performance controller of the wind driven generator, and controlling according to the preset performance controller of the wind driven generator.

2. Method for optimal speed tracking control of wind turbines according to claim 1, wherein said desired rotor speed ω_refIs composed of

ω_ref＝λ_optv/R (4)

Wherein v is wind speed, λ_optFor optimal tip speed ratio, R is the wind wheel radius.

3. The method for tracking and controlling the optimal rotating speed of the wind turbine generator as claimed in claim 1, wherein the step s1 is implemented by establishing the following dynamic equations of the wind turbine generator system:

in the formula, ω_rIs the rotational angular velocity of the wind wheel, J_rMoment of inertia of low-speed shaft, B_rDamping coefficient for low-speed shaft, J_gMoment of inertia of high-speed shaft, B_gIs a high-speed shaft damping coefficient, T_aFor pneumatic torque, T_gFor the electromagnetic torque of the generator, n_gIs the gear ratio of the gearbox, and F is the system uncertainty and disturbance.

4. A method according to claim 3, wherein the system uncertainty and disturbance F are bounded and can be expressed as:

in the formula,

for system uncertainty, d is the unknown interference and δ is the upper bound of uncertainty.

5. The method as claimed in claim 4, wherein the aerodynamic torque T is a torque value of a rotor of the wind turbine_aThe following were used:

wherein rho is air density, R is wind wheel radius, v is wind speed, and wind energy utilization coefficient C_pIs a non-linear function of the tip speed ratio λ and the blade pitch angle β.

6. The method as claimed in claim 1, wherein the predetermined performance controller of the wind turbine is a predetermined performance controller

Wherein, T_gFor generator electromagnetic torque, T_aFor pneumatic torque, n_gIs the transmission ratio of the gear box,

B_rdamping coefficient for low-speed shafts, B_gIs a high-speed shaft damping coefficient, omega_rIs the angular velocity, omega, of the wind wheel rotation_refTo expect a rotor speed, delta is an upper bound of uncertainty,

J_rmoment of inertia of low-speed shaft, J_gIs the moment of inertia of the high-speed axis, ε is the error after conversion, c₁Is a positive constant.

7. The method as claimed in claim 6, wherein the step s3 of selecting the lyapunov function, deriving the lyapunov function V with respect to time t based on the converted error e and the corresponding derivative to obtain the preset performance controller of the wind turbine comprises the steps of:

under the condition of not considering uncertainty and interference, the error epsilon after conversion is obtained by derivation of time t

Wherein

When uncertainty and interference F are considered, the Lyapunov function V is derived over time t

Where δ represents the upper bound of uncertainty;

finally obtaining a preset performance controller of the wind driven generator as

8. The method as claimed in claim 7, wherein the derivation of the post-conversion error e with respect to time t without considering uncertainty and disturbance is performed by first deriving the tracking error e without considering uncertainty and disturbance

The post-conversion error epsilon is then derived over time t

The above formula is arranged to obtain

Wherein

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