Nonlinear Model Of Wind Turbine Research Articles

Design and Assessment of a LIDAR-Based Model Predictive Wind Turbine Control

The development of the Light Detection and Ranging (LIDAR) technology has enabled wider options for wind turbine control, in particular regarding disturbance rejection. The LIDAR measurements provide a spatial, preview wind information, based on which the controller has a better chance to cope with the wind disturbance before it affects the turbine operation. In this paper, a model predictive controller for above-rated wind turbine control was developed with the use of pseudo-LIDAR wind measurements data. A predictive control algorithm was developed based on a linearised wind turbine model, in which the disturbance from the incoming wind was computed by the LIDAR simulator. The optimal control action was applied to the nonlinear turbine model. The developed controller was compared with the baseline control and a previously developed LIDAR-assisted control combining a feedback-and-feedforward design. Our simulation studies on a 5 MW nonlinear wind turbine model, under different wind conditions, demonstrated that the developed LIDAR-based predictive control achieved improved performance in the presence of small variations in the out-of-plane rotor torque and fore-aft tower acceleration, as well as a smoother generator speed regulation and satisfied pitch activity control constraints.

A Set-Based Prognostics Approach for Wind Turbine Blade Health Monitoring

This paper presents a model-based prognostics procedure using a zonotopic Kalman filter in tandem with a zonotopic set-based propagation of degradation, aiding in the quantification of uncertainties associated with prognostics. The prognostics procedure is then applied to the degradation of a wind turbine blade material subjected to a forecasted bounded set description of wind profile. To facilitate an online condition based implementation, an otherwise nonlinear based Kalman filter from the nonlinear wind turbine model is presented in a pseudolinear form, a polytopic linear parameter varying representation, decreasing computational cost and easing in the propagation of the positive invariant zonotopic uncertainty sets to a reachable set that triggers an end of life. Using this information of health, the remaining useful life with its associated uncertainties can be predicted

Machine learning based model linearization of a wind turbine for power regulation

ABSTRACT Wind turbine systems exhibit highly nonlinear dynamics influenced by the aerodynamic torque induced in the wind turbine blades and thrust force on the turbine structure due to the wind flow. This paper presents a system identification approach to approximate the nonlinear wind turbine model. A clustering-based piecewise affine system identification technique is utilized to construct an affine multiple-model that is valid for the power regulation region of a wind turbine. A comprehensive study is performed to validate the accuracy and performance of the developed model. The piecewise affine model identified in this paper can be widely used for advanced control systems design and the security assessment of the power grid.

Look Ahead Based Control Strategy for Hydro-Static Drive Wind Turbine Using Dynamic Programming

This research paper presents a look-ahead optimal control strategy for a Hydro-static Drive Wind Turbine when look ahead wind speed information is available. The proposed predictive controller is a direct numerical optimizer based on the well established principles of Hamilton-Jacobi-Bellman (Dynamic Programming). Hydro-static transmission based, non-linear model of wind turbine is used in this optimization work. The optimal behavior of the turbine used the non-linearity of aerodynamic maps and hydro-static drive train by a convex combination of state space controller with measurable generator speed and hydraulic motor displacement as scheduling parameters. A comparative analysis between a optimal controller based on Maximum Power Point Tracking (MPPT) algorithm as published in literature and the proposed look ahead based predictive controller is presented. The simulation results show that proposed look ahead strategy offered optimal operation of the wind turbine by closely tracking the optimal tip-speed ratio to maximize capacity factor while also maintaining the hydraulic motor speed close to the desired value to ensure that the frequency of electrical output is constant. It is observed from the simulation results that the proposed predictive controller provided around 3.5% better performance in terms of improving total system losses and harvesting energy as compared to the MPPT algorithm.

New structure of sliding mode control for variable speed wind turbine

This article investigates a new sliding mode control structure for a variable speed wind turbine, in order to maximize the captured wind energy and to reduce the transient loads (shafts vibration) caused by the fast fluctuation of wind speed. The variable speed wind turbine control presents a difficult problem because of the nonlinearities of equivalent mathematical models and the effects of external disturbances (wind speed fluctuation). The sliding mode technique is a nonlinear control, widely used in this field; this is due to its robustness in terms of stability and performance against disturbances and modeling uncertainties, and its simplicity of implementation. However, this technique has a major problem which is the chattering phenomenon caused by the discontinuous portion of its control law. A new structure of sliding mode technique is developed in this paper to overcome this phenomenon and maintain the effectiveness of traditional approach. The performance of the developed control will be offered by numerical simulations and will be compared to the basic method of sliding mode control based on a strong nonlinear model of wind turbine.

Reinforcement-Based Robust Variable Pitch Control of Wind Turbines

Due to the influence of wind speed disturbance, there are some uncertain phenomena in the parameters of the nonlinear wind turbine model with time in an actual working environment. In order to mitigate the side effects of uncertainties in speed models of wind turbines, researchers have designed a variety of controllers in recent years. However, traditional control methods require more knowledge of dynamics. Therefore, based on reinforcement learning and system state data, a robust wind turbine controller that adopts adaptive dynamic programming (ADP) is proposed. The ADP algorithm is a combination of Temporal-Difference (TD) algorithm and actor-critic structure, which can guarantee the rotor speed is stable around the rated value to indirectly adjust the wind energy utilization coefficient by changing the pitch angle in the area of high wind speed and achieve online learning in real-time. In addition, the variation of the pitch angle command of the proposed controller is relatively gradual, which can reduce the energy consumption of the variable pitch actuator, and extend the service life of the equipment. Finally, the wind speed model is simulated by combined wind speed based on Weibull distribution, the comprehensive simulation results show that the proposed controller has better control effect than some existing ones.

Output Feedback Robust Siding Mode Controller Design for Wind Turbine

In this paper, by choosing a nonlinear model of wind turbine, we want to control the output power of a wind turbine by measuring the rotor speed. For this purpose, the robust sliding mode controller is used to improve the response and the observer is used to estimate system states, which ultimately the proposed controller will be able to limit the power by limiting the rotor speed. In this control system, the rotor speed is considered as output of the system and also input of the controller, blades angle is considered as output of the controller. Here, we use observer state, output feedback and robust sliding mode controller to get the desired response at speed faster than nominal wind speed. First, using rotor speed, system states are estimated while wind is considered as an exogenous state. Then, robust Disturbance Accommodation Controller (DAC) based on sliding mode (SM) is developed. Finally, the efficiency of the proposed DAC-SM approach is compared with existing Disturbance Accommodation Controller (DAC) method. At the end, after obtaining the data and analyze them, the simulation results verify the merits of the proposed controller.

Overcoming fundamental limitations of wind turbine individual blade pitch control with inflow sensors

AbstractIndividual pitch control (IPC) provides an important means of attenuating harmful fatigue and extreme loads upon the load bearing structures of a wind turbine. Conventional IPC architectures determine the additional pitch demand signals required for load mitigation in response to measurements of the flap‐wise blade‐root bending moments. However, the performance of such architectures is fundamentally limited by bandwidth constraints imposed by the blade dynamics. Seeking to overcome this problem, we present a simple solution based upon a local blade inflow measurement on each blade. Importantly, this extra measurement enables the implementation of an additional cascaded feedback controller that overcomes the existing IPC performance limitation and hence yields significantly improved load reductions. Numerical demonstration upon a high‐fidelity and nonlinear wind turbine model reveals (1) 60% reduction in the amplitude of the dominant 1P fatigue loads and (2) 59% reduction in the amplitude of extreme wind shear‐induced blade loads, compared with a conventional IPC controller with the same robust stability margin. This paper therefore represents a significant alternative to wind turbine IPC load mitigation as compared with light detection and ranging‐based feedforward control approaches.

Feedforward Control for Wind Turbine Load Reduction with Pseudo-LIDAR Measurement

A gain-scheduled feedforward controller, based on pseudo-LIDAR (light detection and ranging) wind speed measurement, is designed to augment the baseline feedback controller for wind turbine’s load reduction in above rated operation. The pseudo-LIDAR measurement data are generated from a commercial software – Bladed using a designed sampling strategy. The nonlinear wind turbine model has been simplified and linearised at a set of equilibrium operating points. The feedforward controller is firstly developed based on a linearised model at an above rated wind speed, and then expanded to the full above rated operational envelope by employing gain scheduling strategy. The combined feedforward and baseline feedback control is simulated on a 5 MW industrial wind turbine model. Simulation studies demonstrate that the proposed control strategy can improve the rotor and tower load reduction performance for large wind turbines.

Wind Turbine Multivariable Optimal Control Based on Incremental State Model

AbstractThe multivariable optimal control of a wind turbine by an approach based on incremental state model is proposed. The advantages of incremental state model in comparison with the non incremental one are that the control action cancels steady state errors and incremental state solves the problem of computing the target state, choosing zero as an objective. Linear Quadratic Regulator (LQR) and optimal state observer are applied. The effectiveness of the proposed control method, over the non incremental one, is examined by applying the linear controllers to the nonlinear wind turbine model. The results show that incremental LQR control presents good transient response and zero steady state errors, even in presence of disturbances, nonlinearities and modelling errors.

Adaptive State Feedback—Theory and Application for Wind Turbine Control

A class of adaptive disturbance tracking controllers (ADTCs) is augmented with disturbance and state estimation and adaptive state feedback, in which a controller and estimator, which are designed on the basis of a lower-order model, are used to control a higher-order nonlinear plant. The ADTC requires that the plant be almost strict positive real (ASPR) to ensure stability. In this paper, we show that the ASPR property of a plant is retained with the addition of disturbance and state estimation and state feedback, thereby ensuring the stability of the augmented system. The proposed adaptive controller with augmentation is presented in the context of maximum power extraction from a wind turbine in a low-wind-speed operation region. A simulation and comparative study on the National Renewable Energy Laboratory’s (NREL’s) 5 MW nonlinear wind turbine model with an existing baseline Proportional-Integral-Derivative(PID) controller shows that the proposed controller is more effective than the existing baseline PID controller.

Distributed Model Predictive Control of a Wind Farm for Optimal Active Power ControlPart I: Clustering-Based Wind Turbine Model Linearization

This paper presents a dynamic discrete-time piece-wise affine (PWA) model of a wind turbine for the optimal active power control of a wind farm. The control objectives include both the power reference tracking from the system operator and the wind turbine mechanical load minimization. Instead of partial linearization of the wind turbine model at selected operating points, the nonlinearities of the wind turbine model are represented by a piece-wise static function based on the wind turbine system inputs and state variables. The nonlinearity identification is based on the clustering-based algorithm, which combines the clustering, linear identification, and pattern recognition techniques. The developed model, consisting of 47 affine dynamics, is verified by the comparison with a widely used nonlinear wind turbine model. It can be used as a predictive model for the model predictive control (MPC) or other advanced optimal control applications of a wind farm.

Wind Turbine Model and Observer in Takagi-Sugeno Model Structure

Based on a reduced-order, dynamic nonlinear wind turbine model in Takagi- Sugeno (TS) model structure, a TS state observer is designed as a disturbance observer to estimate the unknown effective wind speed. The TS observer model is an exact representation of the underlying nonlinear model, obtained by means of the sector-nonlinearity approach. The observer gain matrices are obtained by means of a linear matrix inequality (LMI) design approach for optimal fuzzy control, where weighting matrices for the individual system states and outputs are included. The observer is tested in simulations with the aero-elastic code FAST for the NREL 5 MW reference turbine, where it shows a stable behaviour in turbulent wind simulations.

Derivation of 4 degrees of freedom nonlinear wind turbine model using effective mass and stiffness for simulation of control algorithm

As concern about limited energy is gradually growing and wind energy is regarded as one of the best solutions, research on the wind turbine system has been vigorously accomplished. The commercial tools to simulate the non-linear dynamic characteristics of the wind turbine system are various, but the tools take a significant amount of time to simulate the control algorithm and require many input variables. In this paper, the procedures to simulate and examine the controller of wind turbines at the initial design stage are proposed by a 4 degrees of freedom mathematical model of wind turbine, and methodology to make the turbine model is also proposed by effective mass and stiffness defined in the modal domain. The proposed method in this paper is simpler than other methods. The simulations by the three kinds of models for the 2-MW wind turbine are accomplished to discuss the simulation results: a 2 degrees of freedom wind turbine model without considering tower and blade behavior, a 4 degrees of freedom model considering tower and blade behavior modeled by mode shape function, and a 4 degrees of freedom model by the suggested method.

Intelligent Control of a Large Variable Speed Wind Turbine

We present two intelligent controllers for large and flexible wind turbines operating in high-speed winds, a Fuzzy-P + I and an adaptive neuro-fuzzy controller. The control objective is to regulate the rotor speed at the given rated power in region 3 (full load) via collective blade pitch angle. The modeled turbine is a three-bladed, upwind machine with a flexible blade and tower. We use the particle swarm optimization method in off-line training for our adaptive neuro-fuzzy controller. Numerical simulations are performed using wind inflow step change with a set of input–output data of a nonlinear wind turbine model. We compare the performance of the proposed controllers with the baseline PI-controller. Simulation results confirm successful performance of the proposed controllers.

Nonlinear Model Predictive Control of a Simplified Wind Turbine

AbstractThis paper discusses the implications of formulating a single control law governing the entire wind speed range of operation for a wind turbine. Furthermore, the knowledge of future wind speeds provided by e.g. LIDARs is included in the controller framework. This is possible as the presented controller is based on nonlinear model predictive control and includes the knowledge of the future wind speed in the prediction horizon of the controller. The potential benefits of exploiting the knowledge provided by LIDARs is demonstrated in simulations with a simplified 1 degree-of-freedom nonlinear wind turbine model.

Application of Constrained Stochastic Simulation to Determine the Extreme Loads of Wind Turbines

Via so-called constrained stochastic simulation, gusts can be generated, which satisfy some specified constraint. In this paper, it is used in order to generate specific wind gusts, which will lead to local maxima in the response of wind turbines. The advantage of constrained simulation is that any gust amplitude (no matter how large) can be chosen. By performing simulations for different gust amplitudes and mean wind speeds, the distribution of the response is obtained. This probabilistic method is demonstrated on the basis of a generic 1 MW stall regulated wind turbine. By considering a linearized dynamic model of the reference turbine, the proposed probabilistic method could be validated. The determined 50 year response value indeed corresponds to the theoretical value (based on the work of Rice on random noise). Next, both constrained and (conventional) unconstrained simulations have been performed for the nonlinear wind turbine model. For all wind speed bins, constrained simulation results in 50 year estimates closer to the real value. Furthermore, via constrained simulation a lower uncertainty range of the estimate is obtained. The involved computational effort for both methods is about the same.

Nonlinear Model Identification of Wind Turbine With a Neural Network

A nonlinear model of wind turbine based on a neural network (NN) is described for the estimation of wind turbine output power. The proposed nonlinear model uses the wind speed average, the standard deviation and the past output power as input data. An anemometer with a sampling rate of one second provides the wind speed data. The NN identification process uses a 10-min average speed with its standard deviation. The typical local data collected in September 2000 is used for the training, while those of October 2000 are used to validate the model. The optimal NN configuration is found to be 8-5-1 (8 inputs, 5 neurons on the hidden layer, one neuron on the output layer). The estimated mean square errors for the wind turbine output power are less than 1%. A comparison between the NN model and the stochastic model mostly used in the wind power prediction is done. This work is a basic tool to estimate wind turbine energy production from the average wind speed.