1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Department of Electrical Engineering, Technical University of Denmark4 Automation and Control, Department of Electrical Engineering, Technical University of Denmark
In the 1970s the oil price crisis encouraged investigation of non-petroleum energy sources of which wind energy was the most promising one. Lately global warming concerns have even intensified the demand for green and sustainable energy resources and opened up several lines of research in this area. Wind turbines are the most common wind energy conversion systems and are hoped to be able to compete economically with fossil fuel power plants in near future. However this demands better technology to reduce the price of electricity production. Control can play an essential part in this context. This is because, on the one hand, control methods can decrease the cost of energy by keeping the turbine close to its maximum efficiency. On the other hand, they can reduce structural fatigue and therefore increase the lifetime of the wind turbine. The power produced by a wind turbine is proportional to the square of its rotor radius, therefore it seems reasonable to increase the size of the wind turbine in order to capture more power. However as the size increases, the mass of the blades increases by cube of the rotor size. This means in order to keep structural feasibility and mass of the whole structure reasonable, the ratio of mass to size should be reduced. This trend results in more flexible structures. Control of the flexible structure of a wind turbine in a wind field with stochastic nature is very challenging. In this thesis we are examining a number of robust model based methods for wind turbine control. Firstly we examine potentials of -synthesis methods and use -tools to analyze robustness of the resulting controllers both in terms of robust stability and robust performance. Afterwards we employ model predictive control (MPC) and show that the way MPC solves control problems suits wind turbine control problems very well, especially when we have preview measurements of wind speed using LIDARs. For the control problem with LIDAR measurements we have proposed a new MPC approach which gives better results than linear MPC while it has almost the same computational complexity. We have also tackled wind turbine control using robust MPC. In general, robust MPC problems are very computationally demanding, however we have shown that with some approximations the resulting robust MPC problem can be specialized with reduced computational complexity. After a short introduction on wind energy and wind turbines in chapter 1, we briefly explain wind turbine modeling in chapter 2. Introductions to different control design methods are given in chapter 3. The goal of this chapter is to show how different control methods are chosen. The next eight chapters comprise the body of the thesis and are scientific papers that are published or going to be published. Control methods which were briefly introduced in chapter 3 are explained in these chapters in details.