Wind power is the most fast growing energy source in the world while its intermittency and uncertainty generate stability, reliability and power quality problems in the electric grid. A battery/supercapacitor Hybrid Energy Storage System (HESS) is integrated to the directly driven Wind Turbine Generation (WTG) system to achieve a better wind power output characteristic. When integrated to a grid connected WTG, the supercapacitor and battery respectively absorbs the high frequency part and low frequency part of the wind fluctuations. Feedback elements are added to achieve a better performance of this management algorithm. While for a HESS applied to the stand-alone WTG system, the supercapacitor supports the frequency of the isolated system after the islanded operation and PI controllers are used. The control models are developed by the User Definition (UD) module on Power System Analysis Software Package (PSASP). Simulations are carried out to verify the control strategies effective and feasible.