In this paper, we present a design of a 2DOF (Degree Of Freedom) RHC/FB (FeedBack) control method for the pitch system of wind turbines based on the preview wind speed measurement by a Lidar system

Beuth, Thorsten

Shinohara, Leilei

Stork, Wilhelm

Xu, Shenyao

English

KITopen

  KIT SCIENTIFIC WORKING PAPERS Receding horizon control (RHC) on a Lidar based preview controller design for the active wind turbine pitch system    by Leilei Shinohara1, Shenyao Xu2, Thorsten Beuth1, Wilhelm Stork1    facultative (1) Information on affiliation as follows: 1 Institute of Information Processing Technologies (ITIV), Karlsruhe Institute of Technology (KIT) 2 Institute of Sensor Systems Technology, Karlsruhe University of Applied Sciences (HSKA) (2) Information on parallel publications in conference “Jahrestagung KIT-Zentrum Energie – Tagungsband 2014” (3) Details of projects, clients, sponsors, URLs, numbers and other project-related information is not entitled  Impressum Karlsruher Institut für Technologie (KIT) www.kit.edu    Diese Veröffentlichung ist im Internet unter folgender Creative Commons-Lizenz  publiziert: http://creativecommons.org/licenses/by-nc-nd/3.0/de  2014  ISSN: 2194-1629 facultative Institute of Information Processing Technologies (ITIV) Engesserstr. 5 76131, Karlsruhe www.itiv.kit.edu 1  Receding horizon control (RHC) on a Lidar based preview controller design for the active wind turbine pitch system Leilei Shinohara*a, Shenyao Xub, Thorsten Beutha, Wilhelm Storka a Karlsruhe Institute of Technology, Kaiserstr. 12, 76131 Karlsruhe, Germany b Hochschule Karlsruhe – Technik und Wirtschaft, Moltkestr. 30, 76133 Karlsruhe In this paper, we present a design of a 2DOF (Degree Of Freedom) RHC/FB (FeedBack) control method for the pitch system of wind turbines based on the preview wind speed measurement by a Lidar system. This approach has higher industrial feasibilities without losing the control performance in comparison to state of the art control methods. The RHC controller is designed with the Multi-Parametric Toolbox (MPT) 3 and tested with a nonline-ar wind turbine model designed via the aeroelastic simulation tool FAST (Fatigue, Aerodynamics, Structures, and Turbulence) by NREL (National Renewable Energy Laboratory) in a Simulink simulation enviroment. As a result we figure out that the new RHC control is maintaining a stable rotation speed for reducing the operational dynamic loads of the driver train especially on gust wind conditions. Keywords: Wind Turbine, Model Predictive Control, Receding Horizon Control, FAST, Linearized Wind Turbine Model, Pitch Control 1. Introduction  With the replacement of the stall regulated wind turbine by variable pitch systems in the 1990s, the pitch control, torque control, and power quality control of wind turbine systems have become industry standard. In general the main purpose of the wind turbine control is minimizing the cost of energy (COE) [1]. The operation of wind turbine systems can be divided into two regions, below and above the rated wind speed [2]. The control strate-gies are depending on those operational regions. If the wind speed is below the rated speed, generator torque control provides the input to vary the rotor speed and keeps the blade pitch angle and tip speed ratio to maximize the power capturing. If the wind speed is over the rated speed, the primary objective is to maintain a constant power output by keeping the generator torque constant with the pitch control to vary the blade pitch angle [3]. The active pitch control has been proved to be an efficient way of reducing fatigue load and increasing the power capturing [4]. Since the rotor sizes increases very fast recently, the wind shear is having a stronger aerodynam-ical impact [5]. Therefore, there is a need for more advanced pitch control systems, as well as new designs of blades and their materials to reduce the fatigue and extreme loads. In [6] a preview based control is presented on a spline interpolation method to process the wind data and improve blade load regulation via the blade pitch angle control. The method guarantees a hard upper bound on the flap wise bending moment. In [7] an extra input is added to the control system by using an accelerometer to measure the acceleration of the tower. This new measurement is used to calculate the extra pitch contribution to the original pitch which helps to damp the tower motion in the control system. In the here presented article, a preview control based on the 2DOF FF/FB control                                                           * Shinohara@kit.edu; phone:+49 721 608 41972; fax:+49 721 608 42511; www.itiv.kit.edu 2  is proposed for the active pitch system of wind turbines. The proposed controller is based on the 2DOF FF/FB controller, however, the FF term is designed with the RHC methods. Figure 1shows the basic idea of this concept which we called a 2DOF RHC/FB control in this article.   Figure 1. System diagram of the 2DOF RHC/FB controller for the active pitch control of wind turbines, green represent the control signal, yellow represents the wind signal The system consists of a normative model of a wind turbine (WT Model) to generate a full states output, then a RHC controller to calculate the pitch commands for the normative model. The wind field is generated by the TurbSim and reprocessed by a Lidar model for the WT Model and controller. The RHC controller takes the Lidar data for predicting the future pitch commands. The feedback controller takes the states error to generate the correcting pitch commands and add into the RHC commands for the real nonlinear wind turbine model (Wind Turbine) created by the FAST tool. Reference signal can be the states at the linearization setting point or the output from the normative model. This concept is first introduced by T. Hatanaka et. al. for the control of an electrodynamics shaker (Figure 2) [8], where Pm is the nominal model of plant, Pr is the real plant, Kf is disturb-ance-force compensator, d̂f is the estimated disturbance force, GE is the disturbance estimator.   Figure 2. Block diagram of the 2DOF electrodynamics shaker controller [8] 2. Modeling of the wind turbine  A FAST nonlinear model for the simulation of a 5 MW offshore reference turbine from NREL is used [3]. However, the FAST model is too complex and so it is not possible to integrate into the control loop. Therefore, a reduced linear model is designed based on the study by C. L. Bottasso et. al [9]. The simple model can be divid-ed into an aerodynamic model and a servo-elastic model. The aerodynamic model simulates the forces affected 3  by the airflow around the wind turbine body. The servo-elastic dynamic model can be further separated into different sub-models: drivetrain model, generator model, tower model, blades model, pitch actuator model, and torque actuator model. In this article, we only consider the drivetrain and the generator.  The aerodynamics torque and thrust force on the turbine rotor are given as a nonlinear function τRotor =12ρπRRotor3 U∞2 CQ(λTSR, βPitch), fT =12ρπRRotor2 UREWS2 CT(λTSR, βPitch). Where ρ is the air density, AD is the rotor swept area, Rrotor is the rotor radius, U∞ =UREWS(1−a) is the wind speed at the far upstream side and CP is the power coefficient.  λTSR =ΩRotor∙RRotorUwind is the tip-speed ratio, CQ =CPλTSR is the torque coefficient, CT is the thrust force coefficient. The servo-elastic dynamic model of the rotor and the drive train are represented with the equation of motion (EoM) as 𝐽totΩ̇Rotor = 𝜏Rotor − 𝑁Gear(𝜏Gen + Δ𝜏EM), Ω̇DT =𝜏Rotor𝐽Rotor− (1𝐽Rotor+1𝑁Gear2 𝐽Gen) (𝑘DT ∙ 𝜃DT + 𝑐DT ∙ ΩDT) +𝜏Gen−Δ𝜏EM𝑁Gear𝐽Gen. where, Jtot = JRotor + NGear2 JGen is the overall rotational inertia of the drivetrain system, θDT and ΩDT denotes the drive train shaft torsion angle and rates, θDT = θRotor −θGenNGear, ΩDT = ΩRotor −ΩGenNGear, with θ̇ = Ω. A linear time-invariant (LTI) model is used to derive the RHC controller from the MPT toolbox. Therefore, a lineariza-tion process is applied with FAST. The model in state space is reprenseted as ∆?̇? = 𝐴∆𝑥 + 𝐵∆𝑢 + Γ∆𝑣,   ∆𝑦 = C ∙ ∆𝑥 + 𝐷 ∙ ∆𝑢 + 𝐷𝑑 ∙ ∆𝑣 where, ∆𝑥, ∆?̇?, ∆𝑢, ∆𝑣 are the system states and its first order deliverable, system control input and wind dis-turbance input which are defined as ∆𝑥 = [δΩRotor 𝛿𝜃DT δΩDT]T,  ∆𝑢 = [Δ𝜏EM 𝛿βPitch]T. Parameters A, B, C, D, Γ, and 𝐷𝑑 are the parameter matrices which are  𝐴 =[    𝛿𝜏Rotor 𝛿ΩRotor⁄𝐽Rotor−𝑘DT𝐽Rotor−𝑐DT𝐽Rotor0 0 1−𝛿𝜏Rotor 𝛿ΩRotor⁄𝐽Rotor−(𝑘DT𝐽Rotor+𝑘DT𝑁Gear2 𝐽Gen) − (𝑐DT𝐽Rotor+𝑐DT𝑁Gear2 𝐽Gen)]    , 𝐵 =[   0 −𝛿𝜏Rotor 𝛿βPitch⁄𝐽Rotor0 0−1𝑁Gear𝐽Gen𝛿𝜏Rotor 𝛿βPitch⁄𝐽Rotor ]   ,    Γ = [𝛿𝜏Rotor 𝛿𝑈⁄𝐽Rotor0𝛿𝜏Rotor 𝛿𝑈⁄𝐽Rotor]T. We linearize the system at the operation point in the middle of the above rated speed region with UREW =18 m/s, βPitch = 14.9°, ΩRotor = 12.1 rpm. Therefore, the linearized LTI system parameters are given as 𝐴|𝑈REW=18 = [3.32 × 10−4 172.83 1.23820 0 1−0.2742 −195.21 −1.6724], 4  𝐵|𝑈REW=18 = [0 −1.93 × 10−50 0−1.3364 1.93 × 10−5],   Γ|𝑈REW=18 = [0 0 0.0313]T. Figure 3 shows the bode diagram of the drivetrain open loop response. The input and outputs are defined as: In(1) contralable electrical magnatic torque of generator, In(2) collective blade pitch angle, In(3) wind speed disturbance, Out(1) rotor speed, Out(2) drivetrain torsion angle, Out(3) drivetrain torsion angular rates. Since the control objective is to keep the rotor speed stable, the responses from inputs to the output 1 are most important.  Figure 3. Bode diagram of the drivetrain open loop response 3. RHC controller design  Figure 4. Illustration of the receding horizon of RHC methods [10] RHC is based on iterative, finite horizon optimization of a plant model. At time k the current plant state is sampled and an optimal predicted output is calculated for a fixed time horizon in the future: [k, k+p]. Then a corresponding control input for the plant is calculated by the controller. Only the selected steps of the control output are implemented, then the plant is sampled again and the calculations are repeated from the current states, yielding a new control and prediction. The prediction horizon is continously shifted forward and for this reason MPC is called receding horizon control. Figure 4 illustrates the working principle of the RHC methods. 5  RHC controller performs an optimization on the predicted output of the plant. Assume now the time is k, ∆u(k + j|k) denotes the input of ∆u at time (k + j) in the future, so the same expressed of x(k + j|k), z(k + j|k). For the optimization, a cost function is defined where the different outputs and control inputs can be weighted to decide the objectives of the controller. The cost function is given as a quadratic equation: Jk[x(k), u] = ∑ ‖z(k + j|k) − zr(k + j|k)‖Q(j)2Nj=1 + ∑ ‖∆u(k + j|k)‖R(j)2Nc−1j=0 . System constraints are given as zmin ≤ z(k + j|k) ≤ zmax, j = 1,⋯ , N,    ∆umin ≤ ∆u(k + j|k) ≤ ∆umax, j = 0,⋯, Nc − 1. Here z(k + j|k) is the predicted output from the plant, zr(k + j|k) is the reference for the output and ∆u(k + j|k) is the predicted control input. [z(k + j|k) − zr(k + j|k)] is the tracking error which is weighted and minimized in the optimization. The weight of the tracking error is determined by the matrix Q. The last part of the cost func-tion is the calculation of the cost for the control input, which is weighted by the matrix R. 4. Controller validation via simulation The controller is tested with the simulation setup in Simulink as shown on Figure 1. The RHC controller is designed with a full state model output. Assuming a perfect model of the real wind turbine, the calculated turbine control input for the norminal model is exactly the same which can be used for the real turbine model. However due to the simplified norminal model, error occurs in between the norminal and real turbine model. To evaluate the controller performance, a gust wind profile for testing of the extreme load and an IEC turbulence wind profile for testing the operational fatigue load is applied. For the comparison, a standard industrial PI (Propor-tional Integral) FB controller and a 2DOF FF/FB controller are used.  Figure 5. Simulation result with (left) gust wind (right) turbulent wind 6   Gust wind an extreme operating gust (EOG) wind profile of 18 m/s on the hub height is disturbed to the wind turbine rotor without vertical share. Figure 5 left shows the gust wind profile, the rotor rotation speed, and pitch command input from the simulation. Comparing to the PI FB controller, RHC keeps the rotor ro-tation speed more constant.   Turbulence wind Operational turbulent wind interacts with wind turbine continuesly.  Figure 5 right shows the result with an operational turbulent wind with mean wind speed of 18 m/s and turbulent intensity of 16%. Comparing to the PI FB controller, the RHC shows slightly better result on reducing of the fluctua-tions of the rotor speed, but not better than the FF/FB controller. This is mainly due to uncertainty on the linearized norminal model of the wind turbine. Since within this article, only 2 DOFs out of 18 on the FAST model are used for the linear norminal model.  5. Conculusion In this article we proposed a new control approach, 2DOF RHC/FB method with Lidar assisted wind preview measurements. Based on the simulation veladition, a significant improvement is shown on extreme operating gust wind condition in comparison to the standard PI FB control. However, due to the model uncertainty, it does not show much improvement in the turbulent wind conditions. Further development is needed for the RHC gain tunning as well as the norminal model improvement. 6. Acknowledgement This work is supported by "BMWi" (No. 0325386A). We also thank the KSOP for their support. 7. Reference [1] A. Stotsky, and B. Egardt, “Model-based control of wind turbines: look-ahead approach,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 226(8), 1029-1038 (2012). [2] F. D. Bianchi, H. de Battista, and R. J. Mantz, [Wind Turbine Control Systems: Principles, Modelling and Gain Scheduling Design] Springer, (2007). [3] J. Jonkman, S. Butterfield, W. Musial et al., [Definition of a 5-MW Reference Wind Turbine for Offshore System Development], (2009). [4] T. S. Ackermann, Lennart, “Wind energy technology and current status: a review,” Renewable and Sustainable Energy Reviews, 4(4). [5] E. W. E. Association, [UpWind - Design limits and solutions for very large turbines] Ewea, (2011). [6] B. E. Alexander Stotsky, “Model-based control of wind turbines: look-ahead approach,” Journal of Systems and Control Engineering, vol. 226, (September 2012). [7] E. A. Bossanyi, “The Design of closed loop controllers for wind turbines,” Wind Energy, 3(3), 149-163 (2000). [8] Y. Uchiyama, T. Hatanaka, and M. Fujita, "2DOF control of an electrodynamic shaker using explicit receding horizon control for feedforward term." 596-601. [9] C. Bottasso, A. Croce, B. Savini et al., “Aero-servo-elastic modeling and control of wind turbines using finite-element multibody procedures,” Multibody System Dynamics, 16(3), 291-308 (2006). [10] M. Soliman, O. P. Malik, and D. T. Westwick, “Multiple Model Predictive Control for Wind Turbines With Doubly Fed Induction Generators,” IEEE Trans. on Sustainable Energy,, 2(3), 215-225 (2011). KIT – University of the State of Baden-Wuerttemberg andNational Research Center of the Helmholtz AssociationReceding horizon control (RHC) on a Lidar based previewcontroller design for the active wind turbine pitch systemNeed of Renewable Energysources growing stronglyWind turbine and Wind farmconstruction on the riseHigh Stress level, significantWear and TearPredictive control systemwith Lidar wind forecastingLeilei Shinohara, Shenyao Xu, Thorsten Beuth, Wilhelm StorkIntroductionInstitut für Technik der InformationsverarbeitungEngesserstr. 5, 76131 Karlsruhewww.itiv.kit.edushinohara@kit.eduWind speed measured100m awayWind speedwill be ‘uvw’Pitch angleshould be ‘βγ’Our approach A combination of 2DOF control & RHC Wind turbine linear model1 ∆ ΓΔ··Cost function, | |∆ |Constraints | , 1,⋯ ,∆ ∆ | ∆ , 0,⋯ , 1Tracking errorsControl inputs[differential pitch angles]Simulation resultsGust windTurbulent windConclusionBetter performance comparing toindustrial PI-Feedback controller ✓Effects on reducing fluctuation ✓Need more optimization to reach ✓Feedforward-Feedback performanceRHCWinddisturbancesControlinputsWinddisturbancesSystem states KIT Scientific Working Papers ISSN 2194-1629www.kit.eduKIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association

Receding horizon control (RHC) on a Lidar based preview controller design for the active wind turbine pitch system

https://publikationen.bibliothek.kit.edu/1000043016/3196140

Receding horizon control (RHC) on a Lidar based preview controller design for the active wind turbine pitch system

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