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This paper proposes a robust controller for superconducting magnetic energy storage (SMES) unit to stabilize a grid connected wind generator system. In the proposed controller, both SMES active and reactive powers are controlled to decrease the fluctuations of output power and terminal voltage of the wind generator during abnormal conditions. In particular, the SMES controller is designed to enhance the system damping performance and robustness against transient disturbance. The power conversion system (PCS) of SMES unit used in this paper is composed of a sinusoidal PWM (Pulse Width Modulation) voltage source converter (VSC) and a two-quadrant DC-DC chopper using insulated-gate-bipolar-transistors (IGBT). Simulation results demonstrate that the proposed SMES controller is very effective for stabilizing wind generator as well as the entire power system. The effectiveness of the proposed system is verified by simulation analyses using PSCAD/EMTDC.