Modeling and Linear Quadratic Optimal Control of Wind Turbines

Doktorsavhandling, 1997

Control can improve the performance of wind turbines by enhancing the energy capture and reducing dynamic, as well as static, loads. There are several possible configurations of the control system, depending on the available actuators. The control and optimal performance of two specific classes of plants are investigated in this thesis: fixed-pitch variable-speed plants and wind mills with two blades and active yaw regulation. The plant and its environment are structured as a system of interacting subsystems. The arrangement and contents of the subsystems are adapted to the specific problems. The subsystem models are gathered from the literature, derived from basic physical relationships or identified from experimental data. A specific problem arising when using a basic model-structure is that of finding a single scalar representation of the wind field over the rotor disc. It is suggested that the experienced wind speed should be defined as a weighted sum of the wind speeds in several points that are fixed in a revolving frame of reference. Models of the drive system and its two subsystems, the electrical and the mechanical parts, are identified from plant measurements. Physical parameters of a fundamental drive-train model are also identified. The estimated values are confirmed by plant data, although the uncertainties of the estimates are relatively large. The control of variable-speed plants is divided into three regions of operation: optimal, intermediate and stall region. In each of the regions, the optimal performance is determined in terms of some fundamental system parameters. These parameters characterize the turbulence, the plant and the criterion of optimality. Furthermore, a gain scheduled LQG controller is developed and compared with alternative schemes. Nonlinear simulations show that the differences in performance between the designs are comparatively small. The potential of continuous yaw-control is investigated. The idea is to actively attenuate structural-dynamic load-oscillations by means of the yaw servo. In three design examples various structural modes are studied. The tower lateral bending mode shows the best potential for active load reduction. The results also indicate the importance of considering the periodic dependence on time of the system in the controller design.