This work discusses the use of a battery energy storage system applied to the smoothing of power generated at the output of wind turbines based on a fuzzy logic power control. The fuzzy control logic proposed can perform the aforementioned activity while the state of charge of the energy storage system is maintained within operational limits. In order to assess the fuzzy logic power control’s effectiveness at maintaining the state of charge levels within the allowed range, two operating situations are explored: one in which the state of charge is above the upper limit allowed, and another in which the state of charge is in the minimum value allowed. The numerical results show that, when using the battery energy storage system in conjunction with the control logic proposed, the active power provided as the point of common coupling by the wind turbines can be smoothed, thus contributing to the Electric Power System reliability and stability. The main results of this paper are based on measurements of wind and active power associated with a wind generation plant installed in the northeast region of Brazil and equipped with 2.1 MW wind turbines.