Delay dependent H ∞ control of wind energy conversion systems via singular perturbation theory

In this paper, the maximum power point tracking problem of variable-speed wind turbine systems is studied. Both mechanical part and electromagnetic part of the wind energy conversion system are taken into consideration. In view of the different time scales between the mechanical part and electromagnetic part, singular perturbation theory is applied to model the system in order to cope with the stiffness caused by the two-time-scale characteristic. Then, linear parameter varying (LPV) model is developed to approximate the nonlinear singularly perturbed model. In consideration of data detection time of the state variables, in practice, the control inputs are dependent on the states with a small time delay. Therefore, a novel delay dependent H ∞ controller is designed to make the rotor speed track the reference rotor speed. Furthermore, it is proved that the closed-loop system under control is asymptotically robust stable using Lyapunov theory. In the end, an example simulation verifies the effectiveness and advantages of the developed method by means of comparison with optimal torque control.