Modelling the Wind Turbine by Using the Tip-Speed Ratio for Estimation and Control

The development of dynamic models for control purposes is characterised by the challenge of finding a compromise between the minimum necessary information about the system dynamics contained in the model and a model with a low level of complexity such that the model-based control system design becomes comfortable. To achieve this balance, a modified dynamic model for the drivetrain of a wind turbine is proposed in this contribution. The main idea is to introduce the tip-speed ratio as a state variable so that an interval observer can be designed in such a way that its estimates can be used in the torque control during the partial load operation as well as for the estimation of the effective wind speed. During the runtime, the observer's matrix gain is recalculated to adapt the behaviour to the current operational state, which changes all the time with the wind speed. Besides the theoretical formulation, a numerical example of a 20 MW reference wind turbine illustrates the utility of the method. The results show good control performance concerning the tip-speed ratio control loop and a satisfactory estimation of the effective wind speed.