Nonlinear Pitch Control Method for Offshore Wind Turbines Based on Time Disturbance Observer

Abstract

The invention discloses a non-linear pitch control method for an offshore wind turbine based on a time disturbance observer. First, the invention considers the platform negative damping effect of a floating wind turbine and designs the rated generator speed according to the platform pitching motion; then, a pitch dynamics model of the floating wind turbine is established; by using the feedback linearization theory, the established pitch dynamics model is linearized in terms of input and output; the pole placement method is used to complete the design of the linearized model controller; an adaptive preset-time sliding mode disturbance observer is designed to compensate for the external uncertainty disturbances in the system. Compared with the traditional control method, the invention can better stabilize the power generation of the wind turbine under time-varying wind speeds and has better dynamic performance.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent control for pitch regulation of wind power generation, and particularly to a non-linear pitch control method for offshore wind turbines based on a time disturbance observer. Background Art

[0002] Floating wind turbines are more vulnerable to environmental influences such as wind and waves, generating more platform motions. This causes the wind turbines to bear more fatigue loads, and also leads to instability in the output power, resulting in a decline in power generation performance and a reduction in the service life of the wind turbine system. The dynamic system of floating wind turbines is very complex, with strong non-linearity and strong coupling, and is affected by uncertainties such as system parameter perturbations and wind and wave disturbances. The change in the operating working point makes the performance of the linearized model controller deteriorate. Therefore, it is particularly important to construct a non-linear robust control scheme. Summary of the Invention

[0003] Object of the Invention: To overcome the defects of the above-mentioned linear control, the present invention provides a non-linear pitch control method for floating wind turbines based on a time disturbance observer, which can achieve power stability under time-varying wind speeds and better meet the pitch requirements of floating wind turbines.

[0004] Technical Solution: The non-linear pitch control method for floating wind turbines based on a time disturbance observer according to the present invention includes the following steps:

[0005] S1: Considering the platform negative damping effect of the floating wind turbine, design the rated generator speed based on the platform pitching motion;

[0006] S2: Establish a pitch dynamics model of the floating wind turbine;

[0007] S3: Using the feedback linearization theory, linearize the input and output of the pitch dynamics model established in step S2;

[0008] S4: Use the pole placement method to complete the design of the model controller for the linearized model in step S3;

[0009] S5: Design an adaptive preset-time sliding mode disturbance observer to compensate for the external uncertainty disturbances in the system.

[0010] Further, the consideration of the platform negative damping effect in step S1, and the design of the rated generator speed based on the platform pitching motion , and its expression is:

[0011] ,

[0012] where 1173.7 is the rated set value of the generator speed, with the unit of , i.e., the rated generator speed of the unified pitch controller; is the platform pitch rate, is the gear ratio; the positive direction of the platform pitch rate is defined as the downwind platform pitch, so the slope in the equation is negative.

[0013] Furthermore, the pitch dynamics model of the floating wind turbine established in step S2 is as follows:

[0014] Select the rotor speed , the high-speed shaft speed , the slip ratio and the pitch angle as the system state vector, then the state vector is written as:

[0015] ,

[0016] In the formula, the superscript represents the transpose operation;

[0017] Taking the pitch angle reference input as the input, the state equation of the wind turbine is:

[0018] ,

[0019] In the formula, represents the vector representation of the rotor speed, represents the derivative of with respect to, represents the vector representation of the high-speed shaft speed, represents the derivative of with respect to, represents the vector representation of the slip ratio, represents the derivative of with respect to, represents the vector representation of the pitch angle, represents the derivative of with respect to, represents the mechanical power output by the wind turbine, represents the torsional damping of the drive train, represents the torsional stiffness of the drive train, represents the rotor inertia, represents the gear ratio, represents the generator inertia, represents the generator torque, represents the control variable, represents the output variable, represents the pitch time constant.

[0020] Furthermore, the specific method of step S3 is as follows:

[0021] First, transform the pitch dynamics model established in step S2 into the standard form of an affine nonlinear system:

[0022] ,

[0023] where and are state - space n - dimensional vector fields, represents a scalar function of x;

[0024] The specific steps for input - output linearization of the affine nonlinear system are as follows:

[0025] S2.1. Relative - degree determination: For the affine nonlinear system model, calculate the Lie derivative until the relative degree is found such that where represents the Lie derivative of the vector field , represents the Lie derivative of the vector field ;

[0026] S2.2. Dynamic separation: Decompose the system into a linear subsystem and internal dynamics through a coordinate transformation;

[0027] ,

[0028] represents the coordinate - transformation function of the wind - turbine system; z represents the new state variables of the wind - turbine system after coordinate transformation; the subscript represents the external state variables, whose dimension is equal to the relative degree of the system; the subscript represents the internal state variables, whose dimension is equal to the dimension of the system minus the relative degree of the system;

[0029] S2.3. Feedback - linearization control - law design: Design the control quantity to cancel the nonlinear terms, and then realize the linearization relationship through the virtual input , represents the r - th derivative of the output quantity y;

[0030] ,

[0031] where represents the Lie derivative of the vector fields and , represents the second - order Lie derivative of the vector field ;

[0032] S2.4. Zero dynamic stability analysis: Select the following Lyapunov function to prove the zero dynamic stability of the system;

[0033] ,

[0034] where, represents the internal state 1, represents the derivative of, represents the internal state 2, represents the derivative of.

[0035] Furthermore, under the specific method of step S4:

[0036] Obtain a linear controller through pole placement:

[0037] ,

[0038] where, represents the control gain 1, represents the external state 1, represents the reference value of, represents the control gain 2, represents the external state 2, represents the reference value of;

[0039] Substitute the linear controller obtained by pole placement into to obtain the nonlinear control law:

[0040] .

[0041] Furthermore, the specific steps of step S5 are as follows:

[0042] S5.1. Assume that the nonlinear term and the system input gain in the controller are both unknown, and when the input wind is a time-varying wind, define a disturbance quantity to represent the nonlinear term and the time-varying disturbance in the system:

[0043] ,

[0044] where, represents the constant gain;

[0045] Introduce an auxiliary variable defined as follows:

[0046] ,

[0047] where is the disturbance observation value, so the following equation exists:

[0048] ,

[0049] where represents the disturbance observation error, represents the second derivative of;

[0050] S5.2. The designed preset-time integral sliding mode surface is as follows:

[0051] ,

[0052] where, is the adaptive gain, satisfying , is the preset-time parameter, , represents the sliding mode surface, represents the constant 3.14;

[0053] S5.3. Based on the sliding mode surface, construct the differential form of the adaptive preset-time disturbance observer as follows:

[0054] ,

[0055] where, is the adaptive parameter, satisfying , is the preset-time parameter, a positive number satisfies ; represents the reciprocal of the disturbance observation value, represents the sign function;

[0056] Through the sliding mode disturbance observer, the disturbance in the wind turbine system can be accurately observed within the preset time .

[0057] The present invention discloses a non-linear pitch control method for a wind turbine based on a time disturbance observer, and the specific beneficial effects are as follows:

[0058] Traditional pitch control methods for wind turbines are often based on onshore wind turbines and do not take into account the impact of platform motion on the operation of the wind turbines. At the same time, traditional control methods are often based on linear control methods. The dynamic system of a floating wind turbine is very complex, with strong nonlinearity and strong coupling, and is affected by uncertainties such as system parameter perturbation and wind and wave disturbance. The change of the operating point makes the performance of the linearized model controller deteriorate. The nonlinear pitch control method for wind turbines based on a time disturbance observer provided by the present invention takes into account the platform motion to correct the rated speed of the wind turbine and can effectively suppress the platform motion. The feedback linearization theory is used to linearize the nonlinear part in the system, and at the same time, an adaptive preset time disturbance observer is designed to compensate for the external disturbance uncertainty in the system. The proposed control strategy does not require an accurate system model and can achieve power stability under time-varying wind speeds, which better meets the pitch requirements of floating wind turbines. Description of the Drawings

[0059] Figure 1 It is a flowchart of the method of the present invention;

[0060] Figure 2 It is a wind speed and wave height curve graph;

[0061] Figure 3 It is a pitch angle change curve graph of the wind turbine;

[0062] Figure 4 It is a wind turbine rotor speed curve graph;

[0063] Figure 5 It is an engine power curve graph of the wind turbine;

[0064] Figure 6 It is the standard deviation of the platform motion of the wind turbine;

[0065] Figure 7 It is the maximum absolute value of the platform motion of the wind turbine. Detailed Embodiment

[0066] This detailed embodiment discloses a nonlinear pitch method for a wind turbine based on a time disturbance observer, as Figure 1 , and the specific implementation method is as follows:

[0067] S1: Considering the platform negative damping effect of the floating wind turbine, design the rated generator speed based on the platform pitching motion;

[0068] S2: Establish a pitch dynamics model of the floating wind turbine;

[0069] S3: Using the feedback linearization theory, linearize the input and output of the pitch dynamics model established in step S2;

[0070] S4: Complete the design of the model controller for the linearization in step S3 using the pole placement method;

[0071] S5: Design an adaptive preset-time sliding mode disturbance observer for compensation of external uncertainty disturbances in the system.

[0072] In step S1, consider the platform motion to correct the rated generator speed of the wind turbine. To solve the platform negative damping effect,

[0073] Design the rated generator speed based on the platform pitch motion , and its expression is:

[0074] ,

[0075] where 1173.7 is the rated generator speed setting value, with the unit of , that is, the rated generator speed of the unified pitch controller; is the platform pitch speed, is the gear ratio. Define the positive direction of the platform pitch speed as the upwind platform pitch, so the slope in the equation is negative. When the wind turbine tilts upward, obtain more energy from the wind by increasing the rated speed of the wind turbine, thereby suppressing the platform motion; when the wind turbine pitches downwind, less energy is extracted because the rated speed of the wind turbine is reduced and the motion is suppressed again. Therefore, achieve the effect of suppressing the platform motion by tracking the rated wind turbine speed with the actual wind turbine speed.

[0076] The pitch dynamics model of the floating wind turbine established in step S2 is as follows:

[0077] Select the rotor speed , the high-speed shaft speed , the slip ratio and the pitch angle as the system state vector, then the state vector is written as:

[0078] ,

[0079] where the superscript represents the transpose operation;

[0080] Take the pitch angle reference input as the input, then the state equation of the wind turbine is:

[0081] ,

[0082] where represents the vector representation of the rotor speed, represents the derivative of with respect to The vector representation of the high-speed shaft speed Denote the derivative with respect to Derivation The vector representation of the slip ratio Denote the derivative with respect to Derivation The vector representation of the pitch angle Denote the derivative with respect to Derivation Denote the mechanical power output by the wind turbine Denote the torsional damping of the drive train Denote the torsional stiffness of the drive train Denote the rotor inertia Denote the gear ratio Denote the generator inertia Denote the generator torque Denote the control quantity Denote the output quantity Denote the pitch time constant

[0083] The input-output linearization in step S3 is a method in control theory for transforming a nonlinear system into a linear system through state feedback, thus simplifying the control design. Its core idea is to make the relationship between the input and output of the system linear through appropriate coordinate transformation and feedback control. The present invention considers using feedback linearization to transform the nonlinear floating wind turbine model into a linear model. The specific method of step S3 is as follows:

[0084] First, transform the pitch dynamics model established in step S2 into the standard form of an affine nonlinear system:

[0085] ,

[0086] Wherein, And Are state-space n-dimensional vector fields, Denote the scalar function of x;

[0087] Next, the specific steps for input-output linearization of the affine nonlinear system are as follows:

[0088] S2.1. Relative degree determination: For the affine nonlinear system model, calculate the Lie derivative until the relative degree Is found such that , where Denote The Lie derivative of the vector field And Denote The Lie derivative of the vector field ;

[0089] S2.2. Dynamic decoupling: The system is decomposed into a linear subsystem and internal dynamics through coordinate transformation;

[0090] ,

[0091] represents the coordinate transformation function of the fan system; z represents the new state variables of the fan system after coordinate transformation; the subscript represents the external state variables, and the dimension is equal to the relative order of the system; the subscript represents the internal state variables, and the dimension is equal to the system dimension minus the relative order of the system;

[0092] S2.3. Feedback linearization control law design: Design the control quantity to cancel the non-linear terms, and then through the virtual input to achieve the linearization relationship , represents the rth derivative of the output quantity y;

[0093] ,

[0094] where represents the Lie derivative of the vector field and ; represents the second-order Lie derivative of the vector field ;

[0095] S2.4. Zero dynamics stability analysis: Select the following Lyapunov function to prove the zero dynamics stability of the system.

[0096] ,

[0097] In the formula, represents the internal state 1, represents the derivative of, represents the internal state 2, represents the derivative of.

[0098] Feedback linearization eliminates non-linear coupling through global feedback, transforms the non-linear system into a linear system, simplifies the controller design, and improves the stability of the system at the same time.

[0099] In step S4, the pole placement method realizes stability optimization and precise adjustment of dynamic response by dynamically adjusting the positions of the closed-loop poles of the system and combining feedback control, and is applicable to the robust design of the system. The specific method of step S4 is as follows:

[0100] Obtain a linear controller through pole placement:

[0101] ,

[0102] In the formula, represents the control gain 1, represents the external state 1, represents the reference value of represents the control gain 2, represents the external state 2, represents the reference value of ;

[0103] Substitute the linear controller obtained by pole placement into , and the following non - linear control law is obtained:

[0104] .

[0105] The present invention uses an adaptive preset - time sliding - mode disturbance observer to compensate for external unknown disturbances. Its advantages are as follows: The upper bound of the convergence time of the adaptive preset - time sliding - mode disturbance observer is used as an independent observer parameter, which is convenient for direct design, more intuitive, and at the same time avoids the problem of excessive dependence on parameters in the traditional fixed - time sliding - mode disturbance observer. An adaptive gain is introduced in the sliding - mode disturbance observer to replace the fixed gain in the traditional sliding - mode control to achieve preset - time convergence, further improving the robustness of the observer to the disturbance initial value. The specific steps of step S5 are as follows:

[0106] S5.1. Assume that the non - linear term and the system input gain in the controller are both unknown, and when the input wind is time - varying wind, define a disturbance quantity to represent the non - linear term and the time - varying disturbance in the system:

[0107] ,

[0108] In the formula, represents the constant gain;

[0109] Introduce an auxiliary variable defined as follows:

[0110] ,

[0111] In the formula is the disturbance observation value, so there is the following formula:

[0112] ,

[0113] In the formula represents the disturbance observation error, denotes the second derivative of;

[0114] S5.2. The preset time integral sliding mode surface of the design is as follows:

[0115] ,

[0116] wherein, is the adaptive gain, satisfying , is the preset time parameter, , denotes the sliding mode surface, denotes the constant 3.14;

[0117] S5.3. Based on the sliding mode surface, construct the differential form of the adaptive preset time disturbance observer as follows:

[0118] ,

[0119] wherein, is the adaptive parameter, satisfying , is the preset time parameter, a positive number satisfies ; denotes the reciprocal of the disturbance observation value, denotes the sign function;

[0120] Through the sliding mode disturbance observer, the disturbance in the wind turbine system can be accurately observed within the preset time .

[0121] Simulation example and calculation parameters

[0122] Based on the pitch control system of the FAST and Matlab / Simulink platforms, verify the effectiveness of the present invention. Use the NREL 5MW floating offshore wind turbine, with a fixed step size of 0.0125s and a simulation running time of 600s. Considering the actual physical application of the wind turbine, set the operating range of the blade pitch angle to ( ), and the pitch rate limit is . The simulation environment is set to the constant power stage, that is, the operating stage between the rated wind speed and the cut-out wind speed. The rated wind speed and cut-out wind speed of the NREL-5MW wind turbine are 11.4m / s and 25m / s respectively. According to the IEC standard, such as Figure 2As shown, the wind speed model adopts the turbulent wind with an average wind speed of 18 m / s generated by Turbsim, and the significant wave height is 3 m. To verify the superiority of the control method (SMDOF) of the present invention, a simulation is carried out by comparing with the variable gain PI controller (GSPI) of FAST. The parameters of the control scheme are set according to experience as , , , and the control parameters of the disturbance observer are set according to experience as , , . By analyzing the simulation results, the performance and effectiveness of this application are evaluated.

[0123] As Figure 3 stated, compared with the traditional GSPI control, under the action of the nonlinear pitch control strategy of the floating wind turbine based on the time disturbance observer proposed in the present invention, the pitch angle of the blade of the offshore floating wind turbine fluctuates greatly. However, due to the addition of pitch angle rate and angle limits in the control, the fluctuation change of the pitch actuator is acceptable at this time.

[0124] Figure 4 And Figure 5 are respectively the comparisons of the wind turbine speed and output power under the two controls. It can be seen that under the nonlinear control strategy, the response to the change of wind speed is faster, the overshoot is smaller, the change range and fluctuation of the wind turbine speed under the nonlinear control are also smaller, and the generated power of the variable gain PI controller and the nonlinear control can both be stabilized at about 5 MW. Compared with the variable gain PI control, the output power under the nonlinear control is more stable.

[0125] The detailed data comparison of the wind turbine speed and the generated power is shown in Table 1:

[0126] Table 1: Control effect parameters under different controllers

[0127]

[0128] It can be seen from Table 1 that the fluctuations of the wind turbine speed and the engine power under the nonlinear control are smaller.

[0129] The floating wind turbine will generate six-degree-of-freedom motions under the combined action of wind and wave loads, including translational and rotational motions. The translational motions include surge, sway, and heave; the rotational motions include pitch, roll, and yaw. Suppressing the motion of the platform can effectively improve the stability of the floating wind turbine.

[0130] As Figure 6 and Figure 7It can be seen that, compared with the traditional GSPI controller, the present invention has less influence on the pitch and surge of the platform, and has a certain degree of deterioration on the roll motion, but the amplitude is relatively low. The standard deviations of the yaw, sway, and heave of the platform are reduced by 7.6%, 38%, and 5.1% respectively, and the maximum values of the platform motion are significantly suppressed.

[0131] In summary, the present invention proposes a nonlinear pitch control method for a floating wind turbine based on a time disturbance observer. A wind turbine generator model is established according to the relevant models and parameters of the wind turbine generator set; secondly, based on the feedback linearization theory, a feedback linearization pitch controller is designed in this paper, and a time disturbance observer is used to compensate the uncertain terms in the controller. The nonlinear pitch control method for a floating wind turbine based on a time disturbance observer proposed by the present invention provides a nonlinear pitch method that is more in line with the operating mechanism of the wind turbine, and can provide a reference for the study of wind turbine pitch control.

[0132] The above embodiments are only used to illustrate the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any modifications made on the basis of the technical solution according to the technical idea proposed by the present invention fall within the protection scope of the present invention; the technologies not involved in the present invention can all be realized through the prior art.

Claims

1. A nonlinear variable pitch control method for offshore wind turbines based on a time disturbance observer, characterized in that: The method comprises the following steps: S1: Considering the negative damping effect of the floating wind turbine platform, the design is based on the rated generator speed of the platform pitch motion; S2: Establish the variable pitch dynamics model of floating wind turbines; S3: using feedback linearization theory, the pitch dynamics model established in step S2 is linearized in terms of input and output; S4: Complete the model controller design of step S3 linearization using the pole placement method; S5: Design an adaptive preset time sliding mode disturbance observer to compensate for the external uncertainty interference in the system.

2. The nonlinear variable pitch control method for offshore wind turbines based on a time disturbance observer according to claim 1 is characterized in that: Considering the negative damping effect of the floating wind turbine platform described in step S1, the rated generator speed w of the platform pitch motion is designed. ref , whose expression is: Where 1173.7 is the rated setting value of the generator speed in r / min, i.e. the rated generator speed of the unified pitch controller; is the platform pitch velocity, N g is the gear ratio; the positive platform pitch velocity is defined as the downwind platform pitch, so the slope K in the equation is negative.

3. The nonlinear variable pitch control method for offshore wind turbines based on a time disturbance observer according to claim 2 is characterized in that: The variable pitch dynamics model of the floating wind turbine generator set is established in step S2 as follows: Select the rotor speed w r , high speed shaft speed w g , the slip rate δ and the pitch angle β are used as the system state vector, and the state vector x is written as: x=[x1 x2 x3 x4]=[w r w g δ β] T In the formula, the superscript T represents the transposition operation; Take the pitch angle reference input β r As input, the state equation of the wind turbine is: Where x1 is the vector representation of the rotor speed, represents the derivative of x1, x2 represents the vector representation of the high-speed shaft speed, represents the derivative of x2, x3 represents the vector representation of the slip rate, represents the derivative of x3, x4 represents the vector representation of the pitch angle, represents the derivative of x4, P m Indicates the mechanical power output of the wind turbine, D s represents the torsional damping of the transmission chain, K s Indicates the torsional stiffness of the transmission chain, J r Indicates the rotor inertia, N g Indicates the gear ratio, J g represents the generator inertia, T g represents the generator torque, u represents the control quantity, y represents the output quantity, and τ represents the pitch time constant.

4. The nonlinear variable pitch control method for offshore wind turbines based on a time disturbance observer according to claim 3 is characterized in that: The specific method of step S3 is as follows: First, the variable pitch dynamics model established in step S2 is converted into the standard form of an affine nonlinear system: Where f(x) and g(x) are n-dimensional vector fields in the state space, and h(x) represents a scalar function of x; The specific steps to linearize the input and output of the affine nonlinear system are as follows: S2.

1. Relative order determination: For the affine nonlinear system model, calculate the Lie derivative until the relative order r is found such that Where L g represents the Lie derivative of h(x) with respect to the vector field g(x), L f represents the Lie derivative of h(x) with respect to the vector field f(x); S2.

2. Dynamic separation: decomposing the system into linear subsystems and internal dynamics by coordinate transformation; represents the coordinate transformation function of the fan system; z represents the new state variable of the fan system after the coordinate transformation; subscript o represents the external state variable, and its dimension is equal to the relative order of the system; subscript i represents the internal state variable, and its dimension is equal to the system dimension minus the relative order of the system; S2.

3. Feedback linearization control rate design: Design the control quantity u to offset the nonlinear term, and then realize the linearization relationship y through the virtual input v (r) =v,y (r) It means to find the r-order derivative of the output y; Where L g L f h(x) represents the Lie derivative of h(x) with respect to the vector fields g(x) and f(x), represents the second-order Lie derivative of h(x) with respect to the vector field f(x); S2.4.Zero dynamic stability analysis: Select the following Lyapunov function to prove the zero dynamic stability of the system; In the formula, z i1 Indicates internal state 1, Indicates z i1 The derivative of i2 Indicates internal state 2, Indicates z i2 The derivative of .

5. The nonlinear variable pitch control method for offshore wind turbines based on a time disturbance observer according to claim 4 is characterized in that: The specific method of step S4 is as follows: The linear controller is obtained by pole placement: v=-k1(z o1 -With o1ref )-k2(z o2 -With o2ref ) In the formula, k1 represents the control gain 1, z o1 Represents the external state 1, z o1ref Indicates z o1 The reference value, k2 represents the control gain 2, z o2 Represents external state 2, z o2ref Indicates z o2 Reference value of Substitute the linear controller v obtained by pole configuration into The nonlinear control rate is obtained:

6. The nonlinear variable pitch control method for offshore wind turbines based on a time disturbance observer according to claim 5 is characterized in that: The specific steps of step S5 are as follows: S5.

1. Assume nonlinear terms in the controller System input gain L g L f When both h(x) and h(x) are unknown and the input wind is time-varying, a disturbance ψ(x) is defined to represent the nonlinear terms and time-varying disturbances in the system: Where b0 represents constant gain; Introducing auxiliary variables The definition is as follows: In the formula is the perturbed observation value, so there exists the following formula: In the formula represents the perturbation observation error, Indicates w r The second derivative of S5.

2. The designed preset time-integrated sliding surface is as follows: Where η is the adaptive gain, satisfying η(0)=0, T1 is the preset time parameter, 0<α1<1, s di represents the sliding surface, π represents a constant of 3.14; S5.

3. Based on the sliding surface, the differential form of the adaptive preset time disturbance observer is constructed as follows: Where φ is an adaptive parameter, satisfying φ(0)=0, T2 is a preset time parameter, and the positive number Δ satisfies ψ(x)≤Δ<∞; represents the inverse of the perturbed observation value, sgn(·) represents the sign function; Through the sliding mode disturbance observer, the disturbance ψ in the wind turbine system can be accurately observed within the preset time T=T1+T2.

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