Linear Parameter Varying Approach to Wind Turbine Control Vedran Bobanac University of Zagreb Faculty of Electrical Engineering and Computing Unska 3, HR-10000 Zagreb, Croatia E-mail: vedran.bobanac@fer.hr Abstract—Design of linear parameter varying control (LPV) for wind turbines is considered in this paper. Multivariable, robust control law, which can guarantee stability and desired performance in the whole operating region of the wind turbine, is obtained. LPV controller is compared with a classical controller. Keywords—wind turbine, linear parameter varying control, robust control. I. INTRODUCTION Modern wind turbines are complex systems which are expected to operate autonomously and produce energy in a variety of operating conditions specified in the first place by the wind speed. Designing control system of a wind turbine is a challenging task as there are many conflicting requirements which should be taken into account. Foremost there is highly nonlinear relation between power in the wind and the wind speed. Wind power is proportional to the third power of the wind speed [8] and this nonlinearity reflects directly to the control system. Interaction of the wind and of the turbine blades causes torque which drives the rotor, but it also causes thrust on the rotor which is undesirable, as thrust causes structural loads and vibrations of tower and blades. Thrust on the rotor is very dependent on the pitching control strategy. Inadequately designed control may cause large tower oscillations and in the worst case can lead to the destruction of the turbine. On the other hand, by using advanced control techniques tower vibrations can be damped and the lifetime of the wind turbine can be extended. Moreover, the starting investment can be reduced because the construction of the turbine can be made lighter (lesser consumption of material) owing to the reduced structural vibrations. There are many other problems that make the design of the control system more demanding. Some of this problems are: stochastic nature of the wind, wind shear effect, tower shadow effect, wake effect in wind parks, the fact that it is impossible to measure the wind speed precisely enough to include the measured signal in the control system and so on. Wind energy industry is growing rapidly and new wind turbines are built larger and larger. As dimensions of wind turbines increase problems like tower and blade oscillations become more pronounced and designing the control system becomes more challenging. Therefore, it makes sense to explore applicability of the advanced control algorithms to the wind turbines. In recent years there has been a lot of research activity in this field. One of the advanced control methods, called Linear Parameter Varying (LPV) control is the topic of this paper. The paper is organized as follows. In section II control objectives for modern wind turbines are given and in section III wind turbine mathematical model is described. Linear parameter varying control basics are given in section IV, while the algorithm for controller synthesis is described in section V. This section is followed by a presentation of simulation results in section VI. Conclusions are given in section VII. II. CONTROL OBJECTIVES Nonlinear relation between power in the wind and the wind speed has resulted in modern wind turbines having two main operating regions: below rated wind speed and above rated wind speed. Rated wind speed is defined as the lowest wind speed at which wind turbine may operate continuously at its rated power. Below rated wind speed, power that can be extracted from the wind is smaller than the rated power of the wind turbine and the control objective in this region is to maximize the energy conversion efficiency. Control is performed by adjusting the generator torque, while the pitch angle is kept around minimal value of 0 o so that system is operating along maximum power coefficient curve [8]. Controlling the generator torque is possible because modern generators are not connected to the grid directly, but over the AC-DC-AC converter which allows generator speed to be varied in a wide range. Wind turbines, with synchronous generator that is connected to the frequency converter of rated generator power, are particularly suitable for such control strategy. Control of such wind turbines is considered in this paper. Above rated wind speed, power that can be extracted from the wind grows rapidly with the wind speed and it is greater than the rated power of the wind turbine. Control objective in this region is limitation of the turbine rotational speed to its rated value which implies that the wind turbine is operating at the rated power. This is the case because generator torque is kept at the rated value above rated wind speed, and it is well known that the electrical power is a product of generator torque and rotational speed. Control in this region is performed by pitching the turbine blades around their longitudinal axis which changes aerodynamic characteristic of the blades and therefore lowers energy conversion efficiency. This degradation in energy conversion efficiency is necessary as the wind turbine generator cannot operate continuously above its rated power.