This paper deals with the power smoothing of the wind power plants connected to a microgrid using a hybrid energy storage system (HESS). In a HESS, the power should be distributed between the battery and capacitor such that the capacitor supplies the peaks of power and its high‐frequency fluctuations, and the battery compensates for the rest. Besides, due to the relatively low lifetime of the batteries compared to the capacitors, it is preferred to transfer power fluctuations to the capacitor as much as possible. In this paper, methods for calculating the output, battery, and capacitor powers are presented. The output power is determined based on the grid restrictions and the battery SOC. The battery and capacitor powers are decided via an adaptive low‐pass filter. The cut‐off frequency of the low‐pass filter is specified by a fuzzy controller such that not only the power spikes and high‐frequency fluctuations are transferred to the capacitor but also the battery SOC variations are reduced. The simulation results show that for the presented wind speed profile, the output power determination reduces 13.7% of the HESS exchanged energy compared to the ramp limiting method. Besides, the proposed power distribution method reduces 92.6% of the unbeneficial charges and discharges of HESS and 8% of the battery exchanged energy compared to the condition that the constant cut‐off frequency filter is utilised. The experimental results confirm the effectiveness of the proposed output power determination and HESS power distribution methods. Analysing the methods’ cost proves that although the utilisation of the capacitor bank increases the system initial investment cost, it will return after a while relying on the units’ capacity, power fluctuations, control method etc.