Stability analysis of a wind turbine active power control system

Wind penetration levels have increased dramatically in recent years. This has motivated the need for wind turbines and wind plants to provide grid frequency regulation services. Wind turbines do not inherently provide frequency regulation services in the same manner as conventional synchronous generators because modern wind turbines are decoupled from the grid via their power electronics. Consequently, active power control (APC) must be performed to allow wind turbines to participate in grid frequency regulation. In this paper, we consider a wind turbine APC system, which uses a generator torque controller to operate in a derated manner, allowing the turbine to maintain overhead power. Derated operation is achieved by operating the turbine at a higher-than-optimal tip-speed ratio. We show the stability of the APC torque controller and the asymptotic stability of the derated operating points for a constant input. Further, the control system is shown to be input-to-state stable for time-varying inputs.