Robust Model Predictive Control of a Wind Turbine

In this work the problem of robust model predictive control (robust MPC) of a wind turbine in the full load region is considered. A minimax robust MPC approach is used to tackle the problem. Nonlinear dynamics of the wind turbine are derived by combining blade element momentum (BEM) theory and first principle modeling of the turbine flexible structure.

Thereafter the nonlinear model is linearized using Taylor series expansion around system operating points. Operating points are determined by effective wind speed and an extended Kalman filter (EKF) is employed to estimate this. In addition, a new sensor is introduced in the EKF to give faster estimations.

Wind speed estimation error is used to assess uncertainties in the linearized model. Significant uncertainties are considered to be in the gain of the system (B matrix of the state space model). Therefore this special structure of the uncertain system is employed and a norm-bounded uncertainty model is used to formulate a minimax model predictive control.

The resulting optimization problem is simplified by semidefinite relaxation and the controller obtained is applied on a full complexity, high fidelity wind turbine model. Finally simulation results are presented. First a comparison between PI and robust MPC is given. Afterwards simulations are done for a realization of turbulent wind with uniform profile based on the IEC standard.