Stability analysis of the drive-train of a wind turbine with quadratic torque control

This paper investigates the stability of a variable-speed wind turbine operating under low to medium wind speed. The turbine is controlled to capture as much wind energy as possible. We concentrate on the mechanical level of the turbine system, more precisely on the drive-train with the standard quadratic generator torque controller. We consider both the one-mass and the two-mass models for the drive-train, with the inputs being the deviation of the active torque from an arbitrary positive nominal value and the tracking error of the generator torque. We show that the turbine system is input-to-state stable for the one-mass model and integral input-to-state stable for the two-mass model.