This paper considers the design of linear parameter varying (LPV) controllers for wind turbines in order to obtain a multivariable control law that covers the entire nominal operating trajectory.



The paper first presents a controller structure for selecting a proper operating trajectory as a function of estimated wind speed. The dynamic control law is based on LPV controller synthesis with general parameter dependency by gridding the parameter space.



The controller construction can, for medium- to large-scale systems, be difficult from a numerical point of view, because the involved matrix operations tend to be ill-conditioned. The paper proposes a controller construction algorithm together with various remedies for improving the numerical conditioning the algorithm.



The proposed algorithm is applied to the design of a LPV controller for wind turbines, and a comparison is made with a controller designed using classical techniques to conclude that an improvement in performance is obtained for the entire operating envelope. Copyright © 2008 John Wiley & Sons, Ltd.

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Linear parameter varying control of wind turbines covering both partial load and full load conditions

The control of wind turbines is a very challenging task becau se it requires multi-objective control that needs to take into account effects like structu ral fatigue, power production/quality, and slip in the generator. In this thesis, a nu mber of linear parameter varying (LPV) design methods are investigated for use with medium to large scale systems and a method has been found to provide a numerically reliable comp utation of the controller. The thesis begins with an introduction to the control of wind turbines and provides an overview of the different methods that have been applied. Th is introduction is followed by a general introduction to LPV systems and the base for the a vailable design methods. The application of the LPV framework to the control of nonlin ear systems requires a method for describing the system by a LPV model. For doing th is there are two main directions: Jacobian-based linearisation or quasi-LPV mo dels through a substitution of nonlinearities by parameters. In the latter method the sche duling parameter is a function of the state vector which can introduce conservatism. This i ssue is investigated in the thesis leading to a proposed procedure with focus on frozen p arameter dynamics. The numerics in the design algorithms is one of the key issues for getting the methods working for medium to large scale systems. For the associate d optimisation problem, a grid-based method has been found promising and it has been fo und that the choice of state space realisation plays a very important role and a sim ulation based method has been developed for choosing a proper realisation for contro ller design. For closed loop analysis a Gramian-based method has been found promising. The construction of the LPV controller can be very challengi ng from a numerical point of view. Several algorithms have been investigated an d a method based on a classical result fromH∞ control has been found superior from a numerical point of vie w. This method does not directly produce a parameterised contr oller and another method (which can calculate a parameterised controller) has been m odified to enhance numerical performance. The numerical performance of this modifie controller is still not as strong as the first method, which makes the choice of construc tion algorithm a trade-off between numerical performance and calculating a parameter is d controller. A graphical design tool has been developed on the basis of the numerical findings for conditioning of algorithms for the design of LPV control lers. This tool provides an easy user interface which makes it possible for non-experts to design LPV controllers without worrying about matrix inequalities, construction algorithms, etc. The designer only needs to enter the model, weighting functions, tolerat ed rate of variation and basis functions for the storage (Lyapunov) functions. Then the co ntroller can be designed automatically by pressing a few buttons. Large scale design problems can be very difficult to solve fro m a numerical point of view. For these systems the tool provides a number of numeric al tuning handles with

/pdf/robust-gain-scheduled-control-of-wind-turbines-1tm53fss4n.pdf

Robust, Gain-Scheduled Control of Wind Turbines

Modelling and control of wind turbines

This paper proposes a MIMO linear quadratic regulator (LQR) controller designed for a horizontal variable speed wind turbine with focus on the operating range referring to the above rated wind speeds. The operating conditions of wind turbines make them subject to fluctuating loads that create fatigue and lead to damage. Alleviating these loads would reduce the needed materials, and increase the lifespan and the quality of the produced energy. The optimality of the entire system is defined in relation with the trade-off between the wind energy conversion maximization and the minimization of the fatigue in the mechanical structure. The solution of a control using an LQR regulator is presented. The performances of the optimal control are assessed and discussed by means of a set of simulations.

/pdf/optimal-control-of-variable-speed-wind-turbines-4s3aoxzr64.pdf

Optimal control of variable speed wind turbines

A fault-tolerant control system and method for variable-speed variable-pitch wind turbines with an inverter-fed generator. When generator faults are detected, the generator torque and/or flux is limited to prevent propagation of the faults and possible failure and shutdown of the generator. The control system and method improves on two-loop control methods for variable-speed variable-pitch wind turbines and provides improved power delivery under fault conditions.

Generator-fault-tolerant control for a variable-speed variable-pitch wind turbine

Wind turbines are constantly growing in size and power output level. This growth results in significant increase of structural loads and fatigue that have become limiting factors in wind turbine design. It introduces a need to control and limit structural loads and fatigue during wind turbine operation. This can be done by careful control system design. In this paper we focus on variable speed pitch controlled wind turbine that is today an industrial standard. A design procedure for three types of pitch controller is described and their performance is tested by simulations. Like first classic PID controller is described that aims only at achieving satisfactory rotor speed control. This classic pitch controller is then augmented and reduction of tower oscillations is used as additional demand during controller design. Two controller concepts used for this purpose are compared – SISO and full state feedback controller. Both controllers are designed by pole placement method that assures closed loop system to behave in desired manner. Desired closed loop system behavior is carefully chosen in such a way that controlled system behaves as if its structural damping has increased. It results in reduced tower motion what leads to loads and fatigue reduction. All controllers described in this paper are linear so an adaptation algorithm is needed to account for nonlinear nature of wind turbine. For this purpose we propose the use of Takagi-Sugeno fuzzy model that calculates process model output as a combination of "local" linear models identified in chosen operating points.

Design of a Wind Turbine Pitch Controller for Loads and Fatigue Reduction

U uvjetima kada vjetroelektrane postaju sve važniji cimbenici EES-a javlja se potreba za vrlo pouzdanim radom vjetroagregata. Zbog toga vjetroagregati moraju biti opremljeni sofisticiranim sustavom upravljanja koji je u stanju voditi vjetroagregat kroz vrlo razlicite pogonske uvjete određene vremenskim prilikama. U ovom su radu opisane glavne znacajke sustava upravljanja suvremenih komercijalnih vjetroagregata u klasi snage reda 1 MW. Poseban naglasak stavljen je na upravljanje brzinom vrtnje i snagom generatora. Također je istaknuta velika interakcija sustava upravljanja s konstrukcijom sustava te specificnosti projektiranja sustava vjetroagregata koje iz toga proizlaze.

Miroslav Mađerčić

Papers

Design of a Wind Turbine Pitch Controller for Loads and Fatigue Reduction

Wind turbine control system