Nonlinear model predictive control method based on equivalent wind speed prediction of GRU

Abstract

This invention proposes a nonlinear model predictive control method based on GRU equivalent wind speed prediction. First, an objective function is established to achieve multiple control objectives, including maximizing wind energy capture, reducing power output fluctuations, and minimizing fatigue damage to the transmission system; this is the proposed nonlinear model predictive control method. Then, the GRU method is used to predict the equivalent wind speed on the impeller surface in advance, and this wind speed information is used as the control input for the nonlinear model predictive control. Finally, since traditional numerical solution methods are not suitable for solving nonlinear optimization problems, an efficient search algorithm based on iterative optimization and an efficient search solver is employed to solve for the nonlinear optimal solution. This nonlinear model predictive control method captures more wind energy than the classical optimal torque control method and exhibits better performance in suppressing fluctuations, while also extending the service life of unit components. This method demonstrates strong robustness and good control performance, providing a new approach and method for improving maximum power point tracking performance.

Description

Technical Field

[0001] This invention belongs to the field of wind power generation control technology, specifically a nonlinear model predictive control method based on GRU equivalent wind speed prediction. Background Technology

[0002] Due to its high environmental friendliness and moderate cost per kilowatt-hour, wind power has become the renewable energy technology with the most potential for large-scale development and commercialization. As the capacity of individual wind turbine units continues to increase and turbine development deepens, the requirements for control technology are also becoming increasingly stringent. Employing appropriate control technologies to improve wind turbine performance has always been a research hotspot in both the wind energy industry and academia.

[0003] The primary objective of wind turbine control is to maximize power generation, reduce fatigue loads on dynamic and static turbine components, and ensure a smooth power supply. Therefore, designing a control algorithm that achieves maximum wind energy capture while minimizing output fluctuations and fatigue damage to the transmission system is of significant importance for improving the system performance of wind turbines in practical applications. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a nonlinear model predictive control method based on GRU equivalent wind speed prediction. This method can capture more wind energy than the classical optimal torque control method, and it is more effective in suppressing fluctuations while also extending the service life of unit components.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] The nonlinear model predictive control method based on GRU equivalent wind speed prediction has the following specific steps:

[0007] S1, Establishment of the objective function for the nonlinear model predictive control (NMPC) method;

[0008] S2 uses the GRU method to predict the equivalent wind speed on the impeller surface in advance, providing the control input for NMPC;

[0009] S3 employs an efficient search algorithm to solve nonlinear multi-objective optimization problems.

[0010] As a further improvement to the present invention, the establishment of the objective function of the NMPC method described in S1 is specifically carried out as follows:

[0011] The control objective of a wind turbine in the sub-rated wind speed range is to capture wind energy to the maximum extent. This control objective can be expressed as an objective function, namely:

[0012]

[0013] In the formula, E represents the wind energy captured by the wind turbine within time T, while E max Indicates that the power factor is C pmax The maximum wind energy captured by a wind turbine within time T, where ρ represents air density, R represents rotor radius, and the tip speed ratio λ = ω. r R / υ e ω r Indicates the impeller speed, υ e Represents the equivalent wind speed at the impeller surface, and the power coefficient C. p (λ,β) is a nonlinear function of the tip speed ratio λ and the pitch angle β. In the maximum wind energy capture area, the control of the pitch angle is not considered, and the pitch angle is fixed at the optimal value of 0°. p (λ) depends only on the tip speed ratio λ, C p The expression for the (λ) curve fitting function is as follows:

[0014]

[0015] Where C0~C4 are fitting parameters, C0=-1.621, C1=0.6582, C2=-0.07541, C3=0.003813, C4=-7.539e-5. From equation (2), it can be seen that when the tip speed ratio reaches the optimal value λ opt At that time, the power coefficient reaches its maximum value C. pmax ;

[0016] Due to the large inertia of wind turbines, the rotor speed response cannot keep up with the rapid changes in wind speed, and the optimal speed cannot be maintained indefinitely. As a compromise, instead of extracting the maximum wind energy over a longer period, the long period T is divided into n short periods, and E is re-expressed as...

[0017]

[0018] In the formula, Δt represents the length of the short period, and C pk (k = 1, 2, ..., n) and υ ek (k=1,2,…,n) represent the power coefficient and the average value of the predicted equivalent wind speed in the short period Δt, respectively. Therefore, the control objective of capturing wind energy to the greatest extent can be optimized into the problem of extracting more wind energy in the short period Δt.

[0019] The tip speed ratio λ = ω r R / υ e Substituting C into equation (2), p The expression for the (λ) curve fitting function is rewritten as follows:

[0020]

[0021] Based on equations (3) and (4), equation (1) is restated as follows:

[0022]

[0023] In the formula, ω rk (k = 1, 2, ..., n) represents the average impeller speed over a short period Δt;

[0024] The impeller speed must meet hardware limitations, and its allowable range can be expressed as follows:

[0025]

[0026] In addition to the primary objective, there is a second objective: to minimize the generator's electrical torque fluctuation. This control objective of minimizing the generator's electrical torque fluctuation can be expressed as an objective function, as follows:

[0027]

[0028] In the formula, the generator electrical torque rate ΔT g =T gk -T gk–1 To indicate the action of the torque control actuator, the generator's electrical torque rate must meet hardware limitations, and its allowable range is expressed as follows:

[0029] ΔT g ∈[ΔT g min ,ΔT g max (8) Wherein, ΔT g min and ΔT g max These are the generator's minimum and maximum torque rates, respectively. Simultaneously, the permissible range of the generator's electrical torque value meets the following requirements.

[0030] T gk ∈[T g min ,T g rated (9) Here, T g min It is the minimum torque of the generator, T g rated This is the generator's rated torque;

[0031] Considering fatigue damage in wind turbine drive systems, some scholars have pointed out that the fatigue load on the drive system can be calculated using the fluctuations in generator electrical torque and tower bending moment. Furthermore, reducing the standard deviation of both generator electrical torque and tower bending moment can decrease the fatigue load on the drive system. Reducing generator electrical torque fluctuation aligns perfectly with the second control objective: minimizing tower bending moment fluctuation. This control objective is expressed as an objective function, as follows:

[0032]

[0033] In the formula, the bending moment M t =hF a h is a constant, F a It is the thrust of the blades, ΔM t =M tk -M tk–1 The bending moment ratio is expressed as the allowable range of its values.

[0034] ΔM t ∈[0,ΔM t max (11) Wherein, ΔM t max It is the maximum bending moment ratio of the tower;

[0035] The three objectives are normalized, and then weighted together using a weighting factor. These three objectives are formulated as an optimization problem under certain constraints. The final objective function and constraints are designed as follows:

[0036]

[0037] stEq.(6),(8),(9),(11).

[0038] As a further improvement to the present invention, the GRU method described in S2 is used to predict the equivalent wind speed on the impeller surface in advance, providing the control input for NMPC. The specific process is as follows:

[0039] The external structure of the GRU gated recurrent unit network is the same as that of a regular recurrent neural network, while its internal structure is similar to that of an LSTM (Long Short-Term Memory) network. GRU contains two gates: an update gate, which combines the input and forget gates of an LSTM network, and a reset gate. The update gate z... t The previous state information h is controlled by a σ neural network layer. t-1 The degree of participation in the current state, reset gate r. t h is selected through a σ neural network layer. t-1 Written into the candidate set The degree of;

[0040] First, reset gate r t and h t-1 Perform a dot product, then add it to the current input x. t The data is concatenated and scaled to between -1 and 1 using a tanh layer to obtain the candidate set. Secondly, through (1-z t ) and h t-1 To forget h by performing dot product t-1 Unimportant memories, and z t and candidate set Perform a dot product to obtain information containing the current state. To achieve selective memorization, the specific expression is as follows:

[0041]

[0042] Among them, W xr W xz and Representing x t The weight matrix W to be multiplied hr W hz and They represent the relationship with h respectively t-1 The weight matrix of the product; b r and b z These represent the bias terms for resetting the gate and updating the gate, respectively;

[0043] Because the sigmoid function, i.e., σ, will z t The data is transformed into values ​​in the range of 0 to 1, therefore (1-z) t ) is equivalent to z t The complement of memory means that forgotten memory and selective memory are complementary, thus maintaining the constant state of memory.

[0044] Compared to LSTM networks, GRU has one less gate, resulting in a smaller total number of parameters and consequently fewer matrix multiplications. This leads to faster overall training speed, especially when dealing with large amounts of data, which can significantly save time.

[0045] The steps for GRU-based equivalent wind speed prediction are as follows:

[0046] Step 1: Preprocess the raw time series wind speed data, including data grouping, data standardization, and dataset partitioning;

[0047] Step 2: Input the processed data into the GRU model, iterate through training and testing, and finally determine the ideal model parameters;

[0048] Step 3: Use the constructed GRU model to predict wind speed in advance and output the prediction results.

[0049] As a further improvement to the present invention, the efficient search algorithm used in S3 to solve the nonlinear multi-objective optimization problem is as follows:

[0050] According to equation (12), the input variable wind speed sequence is variable. Given the nonlinear aerodynamic characteristics of the wind turbine height, the above optimization problem is nonlinear. The key to solving this real-time global optimization problem is to find the solution to the generator electrical torque sequence. Traditional numerical methods are not suitable for solving nonlinear optimization problems. Therefore, an efficient search algorithm based on iterative optimization and an efficient search solver is used to solve the generator electrical torque sequence.

[0051] Divide the constraint range in equation (12) into small subsets, defining it as a finite set with s candidate solutions, as shown in the following expression T. gk ∈{T g min ,T g min +(T g max -T g min ) / (s-1),...,T g max} (14)

[0052] Solving the generator electrical torque sequence using only iterative optimization algorithms has s n The computational complexity and cost are high. Therefore, an efficient search solver is proposed, which includes a constrained dynamic region and a neighborhood search technique.

[0053] According to equation (14), the dynamic zone constraining the generator's electrical torque requirement is expressed as follows:

[0054]

[0055] In the formula, c1 and c2 are constants, and ω r m It is the measured rotational speed, K. opt =0.5ρπR 5 C pmax / N(λ opt ) 3 This represents the optimal gain, where N is the gearbox ratio and ω is the finite gain. r min =min{υ e1 ,υ e2 ,…,υ en}λ opt / R,ω r max =max{υ e1 ,υ e2,…,υ en}λ opt / R;

[0056] For defining s T gk The candidate solutions are obtained by using the neighborhood search technique, which only provides T with the following options. gk+1 (k = 1, ..., n-1) Define s p There are candidate neighborhoods, and T gk The number of candidate solutions for (k=1) is (ss p );

[0057] Assume T gk (k=1)=T g min So T gk+1 The candidate set of (k = 1, ..., n-1) is

[0058] T gk+1 ∈{T g min +(T g max -T g min )j / (s-1),j=0,1,...,s p -1} (16)

[0059] The two-mass model of the wind turbine during steady-state operation is as follows

[0060]

[0061] In the formula, J r and J g T represents the moment of inertia of the impeller rotor and the generator, respectively. a and T g These represent the aerodynamic torque of the wind turbine and the electrical torque of the generator, respectively. The combined inertia of the impeller rotor and the generator, i.e., the equivalent rotational inertia, is given by J. R In the substitution formula (J) r +N 2 J g ), and the aerodynamic torque T a =0.5ρπR 2 υ e 3 C p (λ) / ω r Substituting into equation (17), ω rk Approximate expression

[0062] ω rk =[0.5ρπR 2 υ ek 3 C pk (λ k) / (ω rk-1 )-NT gk ]Δt / J R +ω rk-1 (18)

[0063] Here, λ k ≈ω rk R / υ ek T gk It is the generator electrical torque in the kth control cycle;

[0064] When applying the NMPC strategy to wind turbines, the steps are as follows:

[0065] Step 1: Initialize parameters c1, c2, T, Δt, s, and s p ;

[0066] Step 2: Take the average wind speed over the 1-second prediction interval and convert it into a wind speed sequence υ. ek (k = 1, 2, ..., n);

[0067] Step 3: Define T using equations (14) and (15) gk The candidate solution set of (k=1) is defined by Equations (15) to (16) to define T. gk The candidate solution set (k = 2, ..., n) is used to obtain the generator electrical torque sequence T. gk (k = 1, 2, ..., n);

[0068] Step 4, place υ ek (k = 1, 2, ..., n), T gk (k = 1, 2, ..., n) and ω rk–1 Substituting into equation (18), the predicted rotational speed sequence ω rk (k = 1, 2, ..., n);

[0069] Step 5: When the maximum number of iterations is reached, output the optimal sequence T corresponding to the maximum fitness of equation (12). gk * Otherwise, update the iteration count, go to step 3, and continue the loop;

[0070] Step 6: Extract the first element T of the generator's optimal torque sequence. gk * (k=1) is the NMPC output of the wind turbine model.

[0071] The NMPC method based on GRU equivalent wind speed prediction proposed in this invention captures more wind energy than the classical optimal torque control method, and has better performance in suppressing fluctuations while extending the service life of unit components. This method is robust and has good control performance, providing a new approach and method for improving maximum power point tracking performance. Attached Figure Description

[0072] Figure 1 A schematic diagram illustrating the construction of the wind speed prediction model based on GRU in this invention;

[0073] Figure 2 NMPC algorithm block diagram of this invention embodiment;

[0074] Figure 3 Simulation waveform of step wind speed predicted by the wind speed prediction model based on GRU in this embodiment of the invention;

[0075] Figure 4 Comparison of energy capture curves of the NMPC algorithm under step wind speeds according to embodiments of the present invention;

[0076] Figure 5 Comparison of vibration acceleration curves before and after a step wind speed using the NMPC algorithm in this embodiment of the invention;

[0077] Figure 6 Maximum power coefficient curve tracking diagram of the NMPC algorithm under step wind speed in this embodiment of the invention;

[0078] Figure 7 Comparison of output power curves of the NMPC algorithm under step wind speed in this invention embodiment;

[0079] Figure 8 A comparison of the electrical torque curves of the NMPC algorithm under step wind speeds in this embodiment of the invention. Detailed Implementation

[0080] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0081] This invention provides an NMPC method based on GRU equivalent wind speed prediction, which can capture more wind energy than the classic optimal torque control method, and has better performance in suppressing fluctuations, while also extending the service life of unit components. The core of this control strategy lies in constructing an objective function that satisfies the requirements of increasing wind energy capture, reducing output fluctuations, and minimizing fatigue damage to the transmission system. By selecting a suitable wind speed prediction model to predict the equivalent wind speed at the impeller surface in advance, and using an efficient search algorithm to search for the optimal solution to this nonlinear multi-objective optimization problem, a robust and effective control algorithm is obtained.

[0082] like Figure 1 As shown, the steps for applying the NMPC strategy to a wind turbine are as follows:

[0083] Step 1: Initialize parameters c1, c2, T, Δt, s, and s p ;

[0084] Step 2: Take the average wind speed over the 1-second prediction interval and convert it into a wind speed sequence υ. ek (k = 1, 2, ..., n);

[0085] Step 3: Define T using equations (14) and (15) gk The candidate solution set of (k=1) is defined by Equations (15) to (16) to define T. gk The candidate solution set (k = 2, ..., n) is used to obtain the generator electrical torque sequence T. gk (k = 1, 2, ..., n);

[0086] Step 4, place υ ek (k = 1, 2, ..., n), T gk (k = 1, 2, ..., n) and ω rk–1 Substituting into equation (18), the predicted rotational speed sequence ω rk (k = 1, 2, ..., n);

[0087] Step 5: When the maximum number of iterations is reached, output the optimal sequence T corresponding to the maximum fitness of equation (12). gk * Otherwise, update the iteration count, go to step 3, and continue the loop;

[0088] Step 6: Extract the first element T of the generator's optimal torque sequence. gk * (k=1) is the NMPC output of the wind turbine model.

[0089] Figure 2 This diagram illustrates the construction of the GRU-based wind speed prediction model of this invention. First, the original time-series wind speed data is preprocessed, including data grouping, data standardization, and dataset partitioning. Then, the processed data is input into the GRU model, and the model is iteratively trained, tested, and the ideal model parameters are finally determined. Finally, the constructed GRU model is used to predict wind speed in advance and the prediction results are output.

[0090] Figure 3 This is a simulation waveform of the step wind speed predicted by the GRU model in this invention. Experimental results confirm that the step wind speed predicted by the model 1 second ahead of the ideal wind speed is almost identical and can be used as the control input for NMPC.

[0091] Figure 4 This is a comparison chart of the energy capture curves of the NMPC algorithm under step wind speeds according to an embodiment of the present invention. Figure 4It can be seen that under a step wind speed input, the wind turbine using the classical optimal torque control (OTC) method captures an average energy of 26.41449 kWh, while the wind turbine using the NMPC method captures an average energy of 26.46873 kWh. The wind turbine captures more energy under the NMPC mode than under the OTC mode.

[0092] Figure 5 This presents the simulation results of the NMPC method in this invention for the front and rear vibration acceleration of a wind turbine tower under a step wind speed. The vibration amplitude in the OTC mode is larger than that in the NMPC mode, resulting in greater fatigue damage.

[0093] Figure 6 , Figure 7 and Figure 8 The graphs show the power factor, output power, and electrical torque in NMPC mode when a step wind speed is input. Figure 6 It can be seen that the power factor in NMPC mode is closer to the maximum power factor of 0.483 than that in OTC mode. Figure 7 It can be seen that the output power fluctuation in NMPC mode is smaller than that in OTC. Figure 8 It can be seen that the electrical torque fluctuation in the NMPC mode is smaller than that in the OTC mode, and both meet the hardware limitations. Under the simulation conditions of this invention, when the step wind speed reaches 8 m / s and 9 m / s, the generator output power and electrical torque in the OTC mode exhibit vibration phenomena, indicating that the OTC method has stability issues. In other words, the NMPC method proposed in this invention has good stability and robustness.

[0094] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A nonlinear model predictive control method based on GRU equivalent wind speed prediction, characterized in that, The specific steps are as follows: S1, establishment of the NMPC method target function; The establishment of the NMPC method target function in S1 has the following specific process: The control objective of the wind turbine in the sub-rating wind speed section is to capture wind energy to the greatest extent, and this control objective is expressed as a target function, that is, max OF(1) = max E / E max (1) wherein represents the wind energy captured by the wind turbine in time T, and E max represents the maximum wind energy captured by the wind turbine in time T when the power coefficient takes C pmax , wherein p represents the air density, R represents the rotor radius, the tip speed ratio λ = ω r R / u e , ω r represents the rotor speed, u e represents the rotor face equivalent wind speed, the power coefficient C p (λ, β) is a nonlinear function of the tip speed ratio λ and the pitch angle β, in the maximum wind energy capture region, without considering the control of the pitch angle, the pitch angle is fixed at the optimal value 0°, C p (λ) is only related to the tip speed ratio λ, C p (λ) curve fitting function is expressed as follows: wherein Co to C4 are fitting parameters, Co = -1.621, C1 = 0.6582, C2 = -0.07541, C3 = 0.003813, C4 = -7.539e-5, and from equation (2) it is known that the power coefficient reaches its maximum value C opt when the tip speed ratio reaches the optimum value λ pmax ; In order to extract more wind energy in a longer period of time, instead of extracting the maximum wind energy at any time, the long period T is divided into n short periods, and E is re-expressed as where Δt represents the length of the divided short period, C pk (k = 1, 2,..., n) and u ek (k = 1, 2,..., n) represent the power coefficient and the average value of the predicted equivalent wind speed in the short period Δt, respectively; The tip speed ratio λ = ωR / V r R / υ e Substituting into equation (2), C p The expression of the curve fitting function of (λ) is changed to According to formula (3) and (4), formula (1) is re-expressed as In the formula, ω rk (k = 1, 2, …, n) represents the average value of the impeller rotating speed in the short period Δt; The impeller speed must meet the hardware limit condition, and the allowable range of its value can be expressed as In addition to the main objective, there is a second objective, that is, to minimize the generator electrical torque fluctuation, and this control objective is expressed as a target function, and the expression is as follows wherein the generator electrical torque ratio ΔT g = T gk - T gk–1 represents the action of the torque control actuator, the generator electrical torque ratio must satisfy the hardware limits, the allowed range of values of which is indicated as ΔT g ∈ [ΔT g min , ΔT g max ](8) wherein ΔT g min and ΔT g max are the minimum and maximum torque ratios of the generator, respectively, and the allowed range of values of the generator electrical torque satisfies the condition Here, T g min is the minimum torque of the generator, T g rated is the rated torque of the generator; Considering the fatigue damage of the wind turbine transmission system, the fluctuation of the tower bending moment is considered to be reduced, that is, the fluctuation of the tower bending moment is minimized, and this control objective is expressed as a target function, and the expression is as follows where the bending moment M t = hF a , h is a constant, F a is the thrust of the blade, ΔM t = M tk - M tk–1 represents the bending moment ratio, the allowable range of the value is represented as ΔM t ∈ [0, ΔM t max ](11) where ΔM t max is the maximum bending moment ratio of the tower The above three objectives are normalized, and then the three control objectives are combined using a weighting factor, and the three control objectives are expressed as an optimization problem under certain constraints, and the final target function and constraint conditions are designed as S2, using GRU method to predict the impeller surface equivalent wind speed in advance to provide the control input of NMPC; S3, using an efficient search algorithm to solve the nonlinear multi-objective optimization problem.

2. The GRU equivalent wind speed prediction based nonlinear model predictive control method of claim 1, wherein: The specific process of using the GRU method to predict the impeller surface equivalent wind speed in advance to provide the control input of NMPC in S2 is as follows: The GRU contains two gating units, one is the update gate which combines the input gate and the forget gate of the LSTM network, and the other is the reset gate, the update gate z t The state information h of the previous moment is controlled by a σ neural network layer t-1 The degree of participation in the current state, the reset gate r t h is selected by a σ neural network layer t-1 The degree of being written into the candidate set ​ First, reset gate r t is performed, then multiplied by current input x t-1 , and then concatenated with h t , and a tanh layer is used to scale the data to -1 to 1 to get the candidate set Second, the unimportant memory in h t is forgotten by multiplying (1-z t-1 ) and h t-1 , and z t is multiplied by the candidate set to achieve selective memory containing current state information , the specific expression is as follows Among them, W xr W xz and They represent the relationship with x respectively t The weight matrix W to be multiplied hr W hz and They represent the relationship with h respectively t-1 The weight matrices of the product; b r and b z These represent the bias terms for resetting the gate and updating the gate, respectively. Since the sigmoid function, σ, transforms the data z t into values in the range 0 to 1, (1 - z t ) is equivalent to the complement of z t ; The steps of equivalent wind speed prediction based on GRU are as follows: Step 1, pre-process the original time series wind speed data, including data grouping, data standardization and data set division; Step 2, input the processed data into the GRU model, and finally determine the ideal model parameters through cyclic training and testing; Step 3, use the constructed GRU model to perform wind speed prediction in advance and output the prediction results.

3. The GRU equivalent wind speed prediction based nonlinear model predictive control method of claim 2, wherein: The specific process of using an efficient search algorithm to solve the nonlinear multi-objective optimization problem in S3 is as follows: According to formula (12), the input variable wind speed sequence is changing, and according to the nonlinear aerodynamic characteristics of the wind turbine height, the above optimization problem is nonlinear, and the key to solving this real-time global optimization problem is to solve the generator electrical torque sequence. An efficient search algorithm based on iterative optimization algorithm and efficient search solver is used to solve the generator electrical torque sequence; The constraint range in formula (12) is divided into small subsets, and is defined as a finite set with s candidate solutions, and the expression is as follows According to formula (14), the dynamic region of the constraint generator electrical torque requirement is represented as where c1, c2 are constants, ω r m is the measured rotational speed, K opt = 0.5 p R 5 C pmax / N(λ opt ) 3 denotes the optimal gain, N is the gear box ratio, ω r min = min{υ e1 ,υ e2 ,…,υ en} λ opt / R, ω r max = max{υ e1 ,υ e2 ,…,υ en} λ opt / R; For defining s candidate solutions of T gk , neighborhood search technique is employed to define s gk+1 candidate neighborhoods for T p (k = 1,..., n - 1) and (s - s gk ) candidate solutions for T p (k = 1). Assume T gk (k = 1) = T g min Then T gk+1 (k = 1,..., n - 1) is a candidate set for The two-mass model of the wind turbine in steady state operation is where J r and J g represent the impeller rotor and generator moment of inertia, respectively, T a and T g represent the fan aerodynamic torque and generator electrical torque, respectively, and the combined inertia of the impeller rotor and generator, i.e., the equivalent moment of inertia, J R is substituted for (J r + N 2 ) in equation (15), and the aerodynamic torque T g is replaced by T a = 0.5 p p R 2 v e 3 C p (λ) / ω r in equation (17), and ω rk is approximated as ω rk = [0.5 p π R 2 υ ek 3 C pk (λ k ) / (ω rk-1 )-NT gk ]Δt / J R +ω rk-1 (18) Here, λ k ≈ω rk R / υ ek , T gk is the electrical torque of the generator in the kth control period. When the NMPC strategy is applied to the wind turbine, the steps are as follows: Step 1, parameter initialization c1, c2, T, At, s and s p ; Step 2, average the wind speed over the 1 s prediction interval, converted to a wind speed sequence u ek (k = 1, 2,..., n); Step 3, define T using equations (14) and (15) gk (k = 1) using equations (15) - (16) gk (k = 2,..., n) to obtain the sequence of generator electrical torques T gk (k = 1, 2,..., n); Step 4, υ ek (k = 1, 2,..., n), T gk (k = 1, 2,..., n) and ω rk–1 Substituting equation (18) into the predicted speed sequence ω rk (k = 1, 2,..., n); Step 5, output the optimal sequence T corresponding to the maximum fitness of formula (12) when the maximum number of iterations is reached gk * Otherwise, update the number of iterations, go to step 3, and continue the loop; Step 6, the first element T of the optimal torque sequence of the generator is set as the NMPC output of the wind turbine model (k = 1). gk * (k = 1) as the NMPC output of the wind turbine model.

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