This paper presents the estimation of minimum BESS capacity for regulating the output of wind farms considering power grid operating condition in Jeju Island. To analyze the characteristics of wind farm outputs with a BESS, the real data of wind farms, Sung-San, Sam-dal and Hang-Won wind farm, located in the eastern part of Jeju island is considered. The wind farms are connected to Sung-san substation to transfer the electric power to Jeju power grid. Consequently, at PCC (Point of Common Coupling), it can see a huge wind farm connected to the substation and thus it can be expected that the smoothing effect is affected by not only the different wind speeds for each area but also the different mechanical inertia of wind turbines. In this paper, two kinds of simulation have been carried out. One is to analyze the real data of wind farm outputs during a winter season, and the other is to connect a virtual BESS to eliminate the unintended generating power changes by the uncontrolled wind farm outputs as shown in the former data. In the conclusion, two kinds of simulation results show that BESS installed in the substation is more efficient than each wind farms with BESS, respectively.