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Frequency control is one of the most important tasks in electric power systems. At the same time, in modern power systems with inertia-free converter-interfaced generation, this task has become more complex. Such an issue is especially relevant for microgrids, which are characterized by a significant increase in the rate of change of frequency and its nadir or zenith. An effective way is through the use of energy storage systems (ESSs) with a grid-forming control in microgrids. For this purpose, this paper proposes a novel structure of the control algorithm based on a current-control virtual synchronous generator (CC-VSG), in which the damping is performed using a feedforward controller. In addition, a simple proportional–integral controller is added to the CC-VSG structure to control the state of charge of the ESS. The performed frequency analysis proves the independence of the different control loop operations within the developed CC-VSG. At the same time, a methodology based on the bandwidth separation of different control loops is proposed for the CC-VSG tuning, which allows for the achievement of the desired quality of frequency regulation in the microgrid, taking into account both the energy recovery and the permissible frequency variation. Finally, the time-domain simulation using PSCAD/EMTDC is performed to confirm the obtained results. [ABSTRACT FROM AUTHOR]