Robust control of wind turbines to reduce wind power fluctuation

The wind power generation system of a 5 MW horizontal axis wind turbine has a high wind energy conversion efficiency. The proportion of installed capacity in practical production applications is increasing year on year, so that the stability of its operation becomes a central factor in determining the productivity of the wind farm in question. This paper takes a 5 MW wind turbine as the research object and proposes a parameter‐adaptive robust model predictive control method to achieve self‐optimization of controller parameters through a Bayesian optimization approach. A robust model predictive control strategy, aiming to reduce the power fluctuation while maximizing the power output, is developed in this paper to enhance the dynamic economic performance under uncertain wind speed variation. A Bayesian algorithm is used in this paper to optimize the parameters of the controller. Moreover, wind speeds are simulated using TurbSim for different turbulence intensities of 5%, 10%, and 15% turbulence. Finally, the robust model predictive control toolbox in MATLAB is designed and simulated. The results show that the operational instability of the wind energy system is overcome. Meanwhile, the robustness of the wind energy system operation is improved compared to the traditional model predictive control approach.


| INTRODUCTION
Renewable energy has become an integral part of the global energy system as global energy demand has increased and greenhouse gas emissions have decreased in recent years.Wind power technology is a viable renewable energy technology that offers the advantages of being low cost, environmentally friendly, and renewable. 1Therefore, the technology for the configuration, control, and scheduling of wind power generation system (WPGS) is particularly important.As an increasingly critical source of renewable energy, the operational quality and construction costs of WPGS are currently the focus of research. 2The greatest challenges to its operation are the complex meteorological parameters, the disorderly variability, and the dynamic properties of the system, which make it problematic to be reliable, predictable, and controllable.Thus, improving the stability of wind power systems is extremely valuable to solve the problem of stable control of the WPGS. 3,4odern megawatt-class wind turbines are in need of strong and powerful controlling approach, taking into account some controlling goals and process constraints simultaneously.Many different solutions have been employed to control WPGS to improve system efficiency. 5Model predictive control (MPC) is a promising research scheme for wind turbines that not only deals with multivariate control problems but also with process constraints.The uncertainty caused by fluctuating wind speeds is currently the biggest challenge to the stable operation of the WPGS. 6Finite control set MPC was used for the control of doubly fed asynchronous generators, showing superior results in terms of both steady-state ripple and dynamic performance. 7An iterative neurofuzzy Hammerstein model-based MPC was proposed to control wind turbine, and it had a superior control effect. 8A multiple adaptive model predictive controller is proposed for the wind farm frequency regulation problem.The results show that this not only improves the frequency response but also reduces machine fatigue. 9An innovative reinforcement learning-based control method was developed for wind turbine applications.The proposed control strategy was data-driven, adapted to real-time changes in system dynamics, and improved control performance. 10A new application of terminal integral sliding mode control for variable-speed wind turbines was presented and stability was also demonstrated. 11n response to the uncertainty and randomness of the WPGS, many scholars have conducted relevant studies.Van et al. proposed a fuzzy logic-based pitch control scheme using a variable-speed wind power system as the research object.The practicality of the proposed method was verified with a 2 MW synchronous generator, reducing the output power and speed fluctuations. 12Xu et al. improved the stability and operational efficiency of the wind power generator by detecting and locating multiple open-circuit faults in PMSG wind turbine converters. 13To tackle the issue of pitch and torque control of wind turbines, Koerber et al.'s study is based on an MPC approach by means of state constraints to improve the smooth operation of wind turbines in high wind speed situations. 14 Mosaad et al. proposed a new control theory for direct-drive PMG wind turbines to obtain greater and more smoother power. 15An adaptive multi-MPC scheme is used for WPGS, which significantly eliminates uncertainty in the generation of wind power. 16Various control strategies for the three main control systems of a wind turbine were compared for different operating regions, taking into account multiobjective control techniques. 17A multivariate control strategy based on MPC is proposed for variable pitch control of WPGSs.The proposed method improves the quality of power and extends the lifetime of the wind turbine components. 18Moreover, various driving and induced loads in wind turbines were discussed, and vibration control methods to mitigate fatigue loads were introduced. 19In fact, the ideal linear time-invariant model in practical control is almost nonexistent.In addition, WPGS always encounters wind speed disturbances with uncertainty.In summary, the uncertainty of wind speed needs to be allowed for in the control of the WPGS.Consequently, the MPC algorithm needs to be improved to enhance the operational reliability of the WPGS.
Robust model predictive control (RMPC) is an approach for controlling complex motions, capable of predicting and controlling multiple future steps in pursuit of optimal control.][22] A robust EMPC strategy was proposed to achieve maximizing power output while reducing damage to the turbine, improving the dynamic economic performance under uncertain wind speed variation conditions. 23Li et al. proposed an RMPC controller that takes into account the uncertainty and nonlinearity, which improves the stability of the control system. 24Wintermeyer-Kallen et al. extended the design approach of RMPC to uncertain linear systems, which provides new ideas for the control of uncertain systems. 25A tube-based RMPC control strategy was proposed to WPGS, which is a nontrivial reference for the control of linear time-varying models. 26The robustness of MPC is considered in research, mainly with respect to parameter uncertainty, static time-varying uncertainty in the system variables, and bounded disturbances. 27MPC was developed for the wind turbine system.This achieved a smooth power output and reduced dynamic loads. 28Xu et al. enhanced the reliability of WPGS through importance gradient assessment, which is essential for the safe operation of the entire grid network. 29Falugi and Mayne optimized the operational reliability of WPGS based on the real-time state of wind turbines. 30Guntur et al. described the efficiency of the FAST v8 code, an aeroelastic engineering simulation tool for wind turbines.A 2.3 MW wind turbine was simulated using FAST and BHawC, and the results from FAST were compared with those from BHawC as well as experimental measurements.It shows good agreement between predictions using FAST, BHawC, and experimental measurements. 31Zhu et al. optimized the operational reliability of WPGS based on the real-time state of wind turbines.A blade of a 1.5 MW wind turbine was used for the study target and a vortex generator was installed in the blade transit region. 32The aerodynamic properties of the blade transition region were modified to suppress surface flow segregation of the blades and increase the torque. 33All of the above methods have been successful in addressing the overall operational performance of wind power systems, structural uncertainty, or uncertainty in external disturbances.However, wind speed is a random and discontinuous perturbation input and is difficult to predict.Minimizing wind speed uncertainty is a prerequisite to ensure that wind power system control can proceed smoothly.At the same time, the robust boundaries of stochastic disturbances are not easily determined, and too small or too large boundaries can cause problems of insufficient robustness and excessive conservatism of the control system.Therefore, the integrated consideration of different random wind speed disturbance inputs and the optimization of the robust boundaries are important issues to be addressed in the control of wind power systems.
According to the above analysis, this paper designs a robust model predictive controller with self-optimizing parameters to improve the performance of wind power systems.The robust boundaries are optimized based on Bayesian optimization methods to ensure robustness and low conservativeness of the controller.Wind speeds of different turbulence intensities are also simulated, and finally, the reliability of the proposed method is verified by simulation experiments.The experimental results show that it has the advantage of high-speed response, high accuracy, and robust performance against external noise and internal disturbances, thus better meeting the system's requirements for stability and efficacy.In overview, the application of RMPC is of great importance in the control and scheduling of WPGS, helping to enhance the stability and robustness of systems.Additionally, to apply RMPC technology effectively, factors such as the selection of control parameters, noise interference in the wind power application environment, and the application of model prediction techniques must be considered.A flow diagram of RMPC for WPGS is shown in Figure 1.
The sections of this paper are structured as follows.Section 2 develops a wind speed model and a mathematical model of the WPGS, as well as simulating wind speeds for different turbulence intensities using TurbSim.Section 3 introduces two control strategies, MPC and RMPC, designs an RMPC controller, and models a F I G U R E 1 Flow diagram of robust model predictive control for wind power generation system.LMI, linear matrix inequality.control strategy for wind power systems based on RMPC.Furthermore, the parameters of the robust model predictive controller are optimized using Bayesian.Section 4 designs the controllers using MPC and RMPC methods, respectively, compares and analyses the operational performance and control effects of the WPGS under the two different control strategies, and analyses the validity of the proposed model.Finally, Section 5 presents the conclusions.

| SYSTEM MODEL
In recent years, China's installed capacity of new energy generation has set several new records.WPGS is a new technology for generating electricity from wind energy in a low cost-effective and environmentally friendly manner.When the incoming flow meets the cut-in speed, the wind turbine will be turning, thus causing the converter to operate and convert the energy emitted into electrical energy for output to the grid to generate electricity.WPGS usually consists of three components, as shown in Figure 2.With a combination of low-speed shafts, gearboxes, and high-speed shaft cascades, the drive system turns the aerodynamic torque gained from the wind energy into generator torque.Detailed wind speed and system modellings are therefore essential to achieve effective WPGS control.

| Wind speed model
Due to the considerable range of variability in wind energy, it is crucial to take into account the various wind speeds that can occur in modelling WPGS so that a more realistic wind speed model can be obtained.Therefore, the unsteady stochastic effective wind speed can be decomposed into two separate components, as shown in Equation (1) 34 In Equation (1), v is the effective wind speed and v m represents the average wind speed, following a Weibull distribution with two parameters, which is shown in Equation (2).Two of the parameters are: s 1 is the scale parameter and s 2 is the shape parameter, and v t is the turbulent speed 35


(2) At the same time, turbulent wind speeds are wind models with random and rapidly varying wind speeds that obey the Gaussian distribution in Equation ( 3) where σ is the standard deviation.
According to Equation (1), it is clear that v m and v t are independent components of wind speed.Therefore, the average value of the wind speed disturbance v ¯= v − v* is calculated to be equal to zero.Equation ( 4) shows the variance calculation where v* is the average value of the wind speed over the measuring horizon T , σ v is the variance, and Γ(*) is the gamma function where f v ( ) is the frequency function, which is calculated by the convection method, as shown in Equation ( 5).The upper limit of the actual wind speed disturbance is shown in Equation ( 6) where γ 1 is a nonnegative scalar.Accordingly, as long as there is a sufficiently small normal number ε, it has In practical wind power system control, the cut-out wind speed v _ cut off will limit the real value v reaching the WPGS, so the upper limit should conform The components of the wind energy system.
TANG ET AL.

| WPGS model
A mathematical model of the dynamics of the WPGS was developed as Here, T r is the rotor's aerodynamic torque, so it is presented as Equation ( 9) 36 where C P is the wind energy utilization factor and it is correlated with β and λ Rω /v = r .β is the collective blade pitch angle, and λ is the tip speed ratio 37 It is determined using the method in Equation ( 11) The state variable is defined as g , and the input variable is g .Based on Equations ( 8), (9), and (10), the kinetic structure of WPGS can be given the form of Equation ( 12) In Equation ( 12), f x u v ( , , ) denotes a Lipschitz function, and it is a nonlinear function.
To track the stability target for optimal turbine performance.The operation of the WPGS is regulated according to changes in wind speed v.Under v v v < < _ in cut off , the entire working area of the WPGS is divided into four sections, which are presented in Figure 3.In the control of power generation systems, the controlling goals for the lower level value areas (v < v < v in 3 ) are usually to maximize the capture of wind energy by varying the ratio of the blade tip speed to the wind speed of the wind turbine and fixing the pitch moment angle to attain the highest aerodynamic efficiency C p,max . 38In the high wind speed region ), the control task of the WPGS is to adjust the blade pitch angle, ensuring that both the output power and the generator speed are stabilized at their rated values.This ensures the safe operation of the wind turbine at high wind speeds and also ensures the stability of the back-end system. 39Therefore, the optimal steady-state targets for WPGS are as follows 40 :

| Simulation of wind speeds with different turbulence intensities
Due to the abundance of wind energy resources in the northwest of the country, the wind is highly concentrated at high altitudes and the quality of wind energy is good.In general the higher the altitude, the higher the wind speed.Due to the large difference in altitude, the wind speed varies greatly, with the annual average wind speed at 70 m high ranging from about 6 to 10 m/s.Highaltitude areas have a variety of wind speed types suitable for the establishment and operation of wind farms.Therefore, the wind speed at an altitude in the northwestern part of the country is used as the simulated wind speed so that a more realistic wind speed model can be obtained.
In this paper, we provide an in-depth study of a 5 MW horizontal axis wind power system. 41The turbulent speeds of wind turbines in three directionslongitudinal, lateral, and vertical-are simulated using the Vonkarm model in TurbSim.The scale size of the simulated two-dimensional (2D) wind field created by TurbSim is Y × Z = 145 m × 145 m, and the whole simulated 2D wind field includes the projection region and the tower in the Y × Z plane. 42The procedure is shown in Figure 4.
Based on the values of the parameters of the simulated turbulent wind field defined in Table 1 and how the description of simulated turbulent winds in a 2D rectangular region of space is created, 43 turbulent wind fields with different turbulence intensities are created in TurbSim with wind speed data present in a 2D spatial grid (41 × 41), simulating the turbulent wind speed wind power spectrum along the horizontal and vertical directions at hub height.

| RMPC
RMPC is a nonlinear controlled scheme for dealing with model uncertainty and unknown effects in unobservable future time steps 40.In RMPC, the optimal control efficiency of the nonlinear control network is minimized with regard to model uncertainty and unobservability.To achieve this, RMPC uses a technique called multiobjective optimization to maximize control performance in the presence of different unknown variables.
The advantage of RMPC is that a high degree of robustness can be achieved and the ability to adapt to the changing environment that may exist in many industrial and transport applications, as the model varies according to unknown factors.If systems have high levels of uncertainty, RMPC can estimate them more accurately, resulting in improved control performance, increased effectiveness, reduced energy consumption, less risk of system failure, and shorter histories.The main difference between an RMPC and an MPC is that the former takes into account possible differences between the system and the model and uses multistep control measures to reduce and offset these errors, and is therefore more flexible and reliable.For the MPC, only the model of the system is considered and one-step control is used to reduce and eliminate errors.As a result, RMPC is more robust than MPC and better able to meet the requirements of a changing environment.When the system encounters anomalies, RMPC is able to find the best control strategy in a limited amount of time.Figure 5 shows a comparison of MPC and RMPC for the operational control of WPGS.

| RMPC scheme for WPGS
RMPC inherits the control idea of MPC and effectively extends the model predictive control technique to the field of nonlinear control by means of adjustment of algorithm parameters and online correction of the reference model.For the control targets in the different modes of operation, the RMPC achieves this control through the adjustment of the algorithm parameters.The use of robust control algorithms for WPGS-related reference trajectory tracking takes the uncertainty of the system into account at an early stage of the algorithm design, allowing the entire control system to still exhibit the stability it should in the face of object uncertainty in actual control.Within the sampling time t k , the RMPC-based WPGS controlling issues are described in Equation ( 18) Equations ( 21), ( 22), ( 23), (24), and ( 25) are the constraints: x ˜t x t F I G U R E 5 Model predictive control (MPC) versus robust MPC in the wind power generation system control.FIR, finite impluse response; LMI, linear matrix inequality.
g,min g g,max Here, S t (Δ ) is the segmentation function, N is the prediction range, t Δ is the sampling time, x ˜τ ( ) is the predictive status trace of the control system, and τ is the time parameter.Equation ( 19) is the WPGS nonlinear status model based on Equation ( 12).x t ( ) k is the original qualification for time in Equation (20).Equation ( 21) is a constraint on the power to ensure the safety of the system, which is a prerequisite for the WPGS to operate by suppressing the damage caused by extreme loads.The constraints are given in Equations ( 22), ( 23), (24), and (25).The objective function is shown in Equation ( 26) The first and second terms of the objective function Equation ( 26) describe the fatigues of the system's structure, while the last item illustrates the case of wind power generation.As wind power systems are nonlinear control systems, there is no clear linear relationship between u and x.Furthermore, the predicted output of the wind power system depends on future control actions.To facilitate the solution of the nonlinear optimization problem in Equation (18), model (12) needs to be linearized for the purpose of online optimization near the working point.Accordingly, the WPGS control optimal question that is based on RMPC can be represented by Equation (27) when the constraints are being fulfilled  J x ˜τ u τ dτ min max ( ( ), ( )) .
Equations ( 28), ( 29), ( 30), (31), and (32) are the constraints: x ¯t x t − x ( ) = ( ) *, k k (32)   where Equation ( 27) represents the predictive model.ω denotes an external bounded disturbance, located in the set derived from the Lipschitz condition. 44It consists of two components, the linearized higher ordering period and the random instability resulting from wind speed disturbances.A ¯l and B ¯l are the matrix of coefficients, obtained by linearizing Equation ( 12) about the best reference points x u ( *, *), as shown in Equations ( 33) and ( 34) Unfortunately, there is a huge computational burden in finding the perfect address for all points in the forecasting horizon W by enumeration.Therefore, the min-max optimization problem in Equation ( 27) is solved by a dynamic output feedback robust model predictive control method based on quasi-minimunmaximum robust optimization to reduce the computational burden. 41For unknown system states in constrained linear parameter varying systems with bounded disturbances, a dynamic output feedback robust model predictive control approach via quasi-min-max robust optimization is used.In the optimization problem, the dynamic output feedback controller takes a parameterdependent form, and the optimization control problem can be formulated as convex optimization by the techniques of linear matrix inequalities.In the quasimin-max robust optimization control problem, by constraining the current and predicted closed-loop system states to be within different robust positively invariant sets, and considering the exactly known model parameters at the current sampling time, the conservativeness of the dynamic output feedback controller parameters is reduced.Furthermore, the updates on real-time estimation error sets are performed by considering the invariance of the predicted closed-loop system states in the robust positively invariant set, which avoids the requirement of an auxiliary optimization to update estimation error sets in common output feedback robust model predictive control algorithms.The controller is calculated at the time of dispersion.t 0 is the origin moment.In case the optimized solve of the optimizing issue in Equation ( 18  ) .
RMPC can effectively overcome the effects of model errors and external disturbances on the control system by TANG ET AL.
| 1825 optimizing WPGS control through robust modelling, predictive control, consideration of constraints, and adaptive control.In summary, the WPGS optimization scheme includes both offline and online calculations.A major advantage of this algorithm is that it can separate the deterministic and uncertain parts of the system, allowing the controller to do much of the work offline, a feature that has led to the widespread development and application of the tube-based RMPC algorithm.Figure 6 shows the simulation environment for a 5 MW wind turbine power generation system.First, a reference turbulence intensity level is determined based on the basic classification parameters of the wind turbine.The wind profile selected for this paper is the IEC Vonkarm.Second, the choice of selecting the type of turbulence and the wind speed power profile model is chosen.Then, the power profile in the frequency domain is transformed into a wind speed-time profile in the time domain.Finally, running the MATLAB code and outputting the results.

| Bayesian algorithm
Bayesian optimization algorithms have a wide range of applications in parameter tuning.The global optimal solution can be found quickly with a small number of samples.A wind turbine output power prediction model is constructed based on Bayesian optimized robust model predictive control.The model uses a Bayesian optimization algorithm to optimize the parameters of the robust model predictive controller on the basis of robust model predictive control to improve the accuracy and robustness of the prediction.
Bayesian optimization algorithm is a sequential model optimization method for global optimization.This algorithm optimizes by constructing a Gaussian process for the objective function on a given input space, combined with a Bayesian formulation.In simple terms, it is to gradually approach the global optimal solution in each iteration by utilizing the already observed optimal results to adjust the search direction and select better candidate points in the next step.
In summary, the Bayesian optimization algorithm has been widely used in various fields as an efficient and accurate parameter tuning strategy.The algorithm approximates the global optimal solution step by step by modeling the Gaussian process, and it can select better candidate points by sampling and calculating the expected improvement.In the future, the Bayesian optimization algorithm will have a wider range of application scenarios with the continuous progress and development of technology, bringing us more intelligent innovation and progress.

| Bayesian optimization of controller parameters
The robust boundary deflation coefficients in the RMPC controller and the rotor speed, drive train torsion angle, and generator speed weighting coefficients are to be optimally adjusted.The above parameters are optimized using Bayesian.Considering the need for maximum power tracking and constant power maintaining in wind power system control tasks, the following global objective function is established:  ( ) where where Ω is the bounded domain of parameters that guarantee the stability of the controller.Since the gradient and concavity properties of the global objective function are unknown, it is assumed that the global objective function is a Gaussian process, as shown in Equation ( 28) where μ W ( ) Bo is the posterior mean and ( ) The global target values are calculated as well as the Gaussian process regression on the collected sample data set to obtain μ W ( ) Bo and ( ) Bo Bo of the Gaussian process of the alternative model, which is obtained from the upper confidence boundary collection function to suggest sampling optimization parameters, W Bo , for the next iteration.The minimum global objective value corresponding to the controller optimization parameter value output by the Bayesian optimization algorithm is used as the final RMPC controller parameter.

| SIMULATION STUDY
To simulate a more realistic wind speed, the values of turbulence intensity are changed in the TurbSim input file and are set to 5%, 10%, and 15%.The incoming wind conditions in FAST are used to establish turbulent wind conditions in TurbSim, thus studying the characteristics of the 5 MW wind power system, where the effective simulation calculation time is 300 s.The data from 0 to 300 s is chosen for the analysis of the operational characteristics of the 5 MW wind turbine.

| Simulation settings
6][47] The simulations are carried out using the FAST software.FAST software is a comprehensive software for wind turbine performance and load calculations that adequately reflects the characteristics of two or three blade horizontal axis wind turbines. 48The WPGS parameter values for 5 MW wind turbines are listed in Table 2. 49 NREL 5 MW wind turbine is a numerical wind turbine model. 50In the simulation experiment, the weighting values of the objective function (25)

| Robust MPC control results
Figure 7 gives the controlling effect of a 5 MW horizontal axis wind turbine based on RMPC.The RMPC control method can be seen in Figure 7 in allowing the actual system to operate around the nominal system.The analysis shows that the RMPC is the control model that will provide linear state feedback on the control input based on the differential values to achieve a calming effect.As a result, its generator speed is stable.
As can be seen from the above figures, under wind conditions with different turbulence intensities, the RMPC control method can significantly mitigate the influence of wind speed changes on the wind power system, reduce fluctuations in generator output power, and increase aerodynamic power, thus improving power generation efficiency.In the area of wind power mechanical systems, the RMPC in the wind power sector improves the dynamic response performance of the operation of wind power mechanical systems.The RMPC technology can significantly minimize the dynamic feedback errors of wind turbine systems due to changes in meteorological parameters, and reduce the operational noise and vibration of wind turbines, improving their reliability and extending their service life.Figure 8 presents a comparison of the control results for RMPC and MPC. Figure 8 shows that the RMPC and MPC of the WPGS are not obviously distinct from each other in terms of essentially the same power tracking and rotor torque.This is because the output power is always lower than the rated power when the WPGS is working in areas where the wind speed is lower than the rated wind speed.In this case, the constraints in the MPC approach are not being violated, which leads to essentially similar results as in the RMPC. Figure 9 shows the control results for output power and rotor torque and speed and aerodynamic power for 10% turbulence intensity wind speed conditions.It can be seen from Figure 9B that the control result of WPGS is essentially indistinguishable from that of the mild turbulence case under RMPC and MPC.This is because the MPC control method achieves control of the system by predicting the dynamic model of the system and calculating the optimal control input for a future period.The effects of model errors and external perturbations on the control system are not considered.Moreover, the MPC rolling optimization is used to execute only the optimization process for current optimal control amount.As can be seen from the MPC scheme, this control strategy does not have major influence on the control efficiency of the WPGS.However, it can be seen from the curves in Figure 9A,D that the output power under the RMPC control strategy is higher than that of the MPC, which improves the power generation efficiency.Furthermore, it can be seen from Figure 9C that RMPC reduces the generator torque, saving wind energy and achieving efficient wind energy conversion at lower turbulent wind speeds.
Figure 10 depicts the controlled outcomes of the various parameters for 15% turbulence intensity wind speed conditions.Modify the turbulence intensity parameter to 15% in the TurbSim input file to emulate serious turbulent wind conditions.Turbulent wind speeds provide a more realistic simulation of actual wind speeds.The simulated turbulent wind speeds are attached to the mean wind speed series to obtain a more realistic wind speed.According to Equation (6), the boundary parameter γ = 3.572 1 is obtained.It is clear from Figure 10 that the MPC fluctuates relatively widely during transient moments.As the MPC scheme considers wind speed at the boundary instead of the random information, it may produce less optimization and higher conservatism in dominating the WPGS.Nevertheless, the RMPC can adapt the control strategy based on real-time data, thus improving the adaptability and robustness of the wind power system.RMPC performs relatively better than MPC at transient moments.The stability of the method is significantly improved compared to the RMPC control results.The outcome suggests that RMPC is superior in wind power system control and has higher robustness.In the meantime, the reasonableness and precision of the claimed method were verified.
Taking the turbulence intensity of 15% as an example, the paper calculates the average parameter values for two different control results as shown in Table 3.
It can intuitively be obtained that the output power of the wind power system is higher under RMPC control than under MPC control, so the approach proposed in this article is preferred over the MPC control method.When the wind speed is below the rated wind speed, the rotor speed of the generator is adjusted to capture the maximum possible wind energy.When the wind speed is higher than the rated wind speed, the output power of the generator is expected to be stable at around the rated power due to the limitations of the wind power's own mechanical and electrical strength, as well as the grid's requirements for power supply quality.Depending on the wind speed value, the controller has to constantly switch between the set optimal reference value, switching back and forth between the two control tasks of maximum wind tracking and constant power operation.Tracking the optimal wind turbine rotor speed at low wind speeds and adjusting the pitch angle at high wind speeds.The generator output power value, rotor speed, and aerodynamic power value have increased.The most significant reduction in rotor torque is particularly noticeable, with a drop of 201.01 kN m, which results in significant savings in wind drive power.At high turbulence intensity wind speeds, RMPC allows better control of wind turbine operation around the optimal point, significantly reducing the disturbance to wind turbine operation caused by wind speed fluctuations.In summary, RMPC not only improves control performance but also increases output power and thus the efficiency of the WPGS.

| Industrial field verification
To further validate the efficacy of the Bayesian optimization Robust MPC method in tackling power control of wind turbine, this study uses a large wind farm in north-western China to validate the proposed method in the field for a month.Field tests are run at wind farms to evaluate the performance of the RMPC algorithm relative to conventional MPC controllers.Figure 11 shows the field application.
From  axis wind turbines and all units in the wind farm are of controlled power.The individual wind farms contain 134, 25, 66, 55, 32, and 91 turbines, respectively, for a total of 403 turbines.The approach presented in this paper provides robust control of individual wind farms within this wind farm.The comparative control outcome of the wind farm's output power is shown in Figure 12.
In this study, a robust model predictive controller with self-optimizing parameters is developed for the power fluctuation problem of wind power systems, which ensures robust stability of the control under perturbations.Meanwhile, in contrast to the MPC controller, the research resulting in this paper indicates that RMPC realizes the optimal control strategy of WPGS and increases the output power.The specific conclusions from the simulation analysis are as follows.
1. RMPC can help to achieve optimal control of rotor speed and torque in wind power systems and to achieve full optimization of mechanical characteristics.It provides greater immunity to unknown external disturbances or internal parameter changes, reduces system output turbulence, increases control accuracy and stability, and improves wind turbine energy efficiency.The results show that under the parameter adaptive RMPC control strategy, the output power obtained by the wind turbine is increased and the power generation efficiency is improved by 1.93%.2. In this paper, a parameter self-optimization method is proposed to further optimize the parameters of the RMPC controller by Bayesian algorithm to perform parameter self-optimization on the robustness boundary deflation coefficients and cost function weighting coefficients.RMPC effectively improves the reliability of the WPGS, optimizes the power generation operation of the wind farm, and enhances the wind power generation capacity, thus improving the wind power generation efficiency.3. The comparative results of the MPC and RMPC show that there is essentially no difference in the control of WPGS between the RMPC and MPC in the presence of slight turbulence.At high turbulence intensity, the turbine output increased by 2.0%.RMPC control results are better than MPC.RMPC technology effectively improves the reliable operation of wind power systems, optimizes the power generation operation of wind farms, enhances wind power generation capacity, and thus improves the efficiency of wind power generation.4. When optimizing the control input, the RMPC is used to dynamically optimize the classical MPC controller error, so that when the error between the real data and the rated data of the input is large, the tracking error can be quickly reduced to ensure that the system is more operationally stable as required.Compared with the MPC strategy, the Bayesian optimization RMPC strategy further utilizes the feedback from the control system to mitigate the uncertainty of the model parameters.It can reduce the rotational torque by about 4.6%.The simulation results show that the method used in this paper achieves fast stability control of the WPGS and enhances the reliability of the system.Moreover, it provides a feasible method for the stability control of wind power systems affected by continuous bounded disturbances.Future work is directed toward mitigating the conservatism of the controller and improving the optimization of the control parameters.minimum pitch angle rate β ̇max maximum pitch angle rate T ̇g,min minimum generator torque rate T ̇g,max maximum generator torque rate ω r,rated rated rotor speed θ rated rated shaft torsion ω g,rated rated generator speed λ opt optimal tip speed ratio

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I G U R E 3 Optimal steady-state targets for different operating regions.

F 1 4 Roughness
I G U R E 4 FAST simulation flowchart.T A B L E 1 Parameter values for simulating turbulent wind farms.Average wind speed at reference height (m/s) 11.

6
w β bo, is the global objective function pitch angle deviation factor and β Δ k is the pitch angle deviation.w P bo, is the global objective function output power deviation coefficient and P Δ g k , is the output power deviation value.The global objective value is minimized by adjusting the optimization parameter matrix W ω θ ω α = [ , , , ] Dynamic simulation environment of the wind power generation system.

1 ,
are set to r = 7

F I G U R E 7
Robust model predictive control results.(A) Generator output power.(B) Rotor speed.(C) Rotor torque.(D) Aerodynamic power.F I G U R E 8 Comparison of control results at 5% turbulence intensity.(A) Output power.(B) Rotor speed.(C) Rotor torque.(D) Aerodynamic power.MPC, model predicitve control; RMPC, robust MPC.F I G U R E 9 Comparison of control results at 10% turbulence intensity.(A) Output power.(B) Rotor speed.(C) Rotor torque.(D) Aerodynamic power.

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I G U R E 10 Comparison of control results at 15% turbulence intensity.(A) Output power.(B) Rotor speed.(C) Rotor torque.(D) Aerodynamic power.T A B L E 3 Comparison of MPC and RMPC results at high turbulent wind speeds.

F I G U R E 11
Wind farm field applications.

Figure 11
it can be seen that the wind farm is located in the north-western part of China and is very rich in wind energy resources.The wind farm has an annual average wind speed of 7.89 m/s at 70 m height and an annual average wind power density of 427.5 W/m 2 for the representative year.The current installed capacity has reached 638.8 MW.The wind energy development and utilization of this wind power base is mainly concentrated in four areas, A, B, C, and D. The areas A and D have two wind farms and areas B and C have one wind farm, respectively.Each wind farm is equipped with horizontal

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I G U R E 12 Comparison of output power.
T A B L E 2 The parameters from a 5 MW WPGS.