This paper presents the determination method of the hybrid energy storage capacity for compensating the output of wind power when disconnecting from the grid. In the wind power output compensation, a lot of charging and discharging time with lithium-ion battery will be deteriorated the life time. And also, this fluctuation will cause some problems of the power quality and power system stability. To solve these kind of problems, many researchers in the world have been studied with BESS(Battery Energy Storage System) in the wind farm. But, BESS has the limitation of its output during very short term period, this means that it is difficult to compensate the very short term output of wind farm. Using the EDLC (Electric Double Layer Capacitor), it is possible to solve the problem. Installing the battery system in the wind farm, it will be possible to decrease the total capacity of BESS consisting of HESS (Hybrid Energy Storage System). This paper shows simulation results when not only BESS is connected to wind farm but also to HESS. To verify the proposed system, results of computer simulation using PSCAD/EMTDC program with actual output data of wind farms of Jeju Island will be presented.