A study of periodic control for a variable speed wind turbine

An investigation of the performance of a model-based periodic gain controller is presented for a variable speed wind turbine. An attempt is made to quantify how periodic the chosen four degree of freedom linear system is, using modal properties. It was found that, while the system appears to be significantly periodic compared to other configurations, high gains were required for periodic control to outperform a fixed gain controller in speed regulation. INTRODUCTION Fixed gain control is a common technique used in performance regulation of wind turbines. Proportional- integral-derivative (FDD) control is one such method that has had widespread use because little knowledge of the plant dynamics is necessary prior to implementation. (If we assume a particular mode of turbine operation, gain-scheduling techniques are excluded from consideration.) As dynamics models of turbines are developed, more information can be incorporated into model-based controllers, with generally better performance. Optimal Control and Disturbance Accommodating Control (DAC) are two such methods of this type that have been investigated. If the controller model is assumed time-invariant as is invariably the case to take advantage of extensive control theory this method again involves constant gains. The periodic nature of wind turbine dynamics, both from aerodynamic loads and structural properties, suggests an improvement can be made to overall performance if a periodic control law, with periodic gains, is used. The goal of this paper is to make an assessment of how effective periodic control can be, compared to fixed gain control. Model-based linear control design requires a suitably accurate dynamics model of the system. For structural dynamics we may take advantage of SymDyn, a utility that derives the equations of motion of a simple wind Copyright © 2001 by the American Institute of Aeronautics and Astronautics Inc. and the American Society of Mechanical Engineers. All rights reserved turbine model explicitly. In SymDyn rigid bodies with single revolute joints and springs are used to model all flexible parts namely the tower, shaft, and blades. The result is a relatively simple set of discrete degrees of freedom. The equations of motion have been validated with ADAMS, a rigorously tested dynamics code, and have been exercised in applications such as operating modal analyses and preliminary control studies.*' For the analysis in this paper a simple four degree of freedom SymDyn model is used. An explicit set of governing equations for aerodynamic loads on turbine blades is currently not available. Instead, to complete the aeroelastic model we use aerodynamic subroutines from AeroDyn, developed at the University of Utah. AeroDyn has been coupled with many other structural dynamics models, including YawDyn, FAST_AD, and ADAMS. Details on how AeroDyn is used in this paper will be presented in a later section. Optimal periodic control has seen rigorous mathematical treatment in the last few decades and recently appeared in applications such as aircraft trajectory and spacecraft orbit optimization''. Hie application of this theory to wind turbines is straightforward provided familiar control issues such as stabilizability are addressed. The control objective in this paper is to regulate turbine speed in a fluctuating wind field near rated wind speed (region III or constant power turbine operation). We use a constant generator torque and control full-span blade pitch. The following section of this paper describes the structural and aerodynamic models in more detail and explains how the periodic linear model is derived. The remaining sections introduce methods for measuring how periodic a system is, describe the control system designs, and then present results comparing the fixed and periodic gain controllers. MODEL DESCRIPTION The turbine modeled is a downwind, free-yaw, variable speed machine with two blades and no hub teeter. Only (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. flap motion of each blade is considered, using a flap hinge and torsional spring to model the first flap bending mode. The tower, shaft, and blade sections were treated as rigid bodies. The result is four degrees of freedom: nacelle yaw (y), shaft rotation/azimuth position (vy), and flap of each blade (Pi, (J2). These degrees of freedom were chosen to give a periodic yet simple system to analyze. Properties were chosen to resemble the AWT-26 horizontal axis wind turbine. An accurate representation of a real turbine was not necessary in this study. See Figure 1 for an illustration and Table 1 for a list of the main geometric properties. The model may be recognized from previous papers by the authors as a reduced order SymDyn model.' SymDyn is a utility used to derive the equations of motion of a wind turbine symbolically. For the system described here the nonlinear equations of motion can be represented by the following vector equation. where f(q,q,q,L)=0, 0) Pi q= Pi IPJ and L is the vector of applied loads, described shortly. Description Hub height Blade length Yaw axis to flap hinge distance Shaft to flap hinge distance Precone angle Symbol - - d* 4 3o Value 25m 13m 2.8m 5.8m 7° Table 1: Geometric properties of the turbine model