The paper presents different solutions applicable in power converter systems for connecting power grids with energy storage systems such as superconducting magnetic energy storage (SMES), supercapacitor energy storage (SES) or chemical batteries. Those systems are characterized by bidirectional current flow between energy storage and power grid. Two-level converters (AC-DC and DC-AC converters) dedicated for low power energy storage compatible with 3×400 V-type power grids are proposed. High power systems are connected with 3×6 kV-type power grids via transformers that adjust voltage to the particular energy storage or directly, based on multilevel power converters (AC-DC and DC-AC) or dual active bridge (DAB) systems. Solutions ensuring power grid compatibility with several energy storage systems of the same electrical parameters as well as of different voltage-current characteristics are also proposed. Selected simulation results illustrating operation of two system topologies of 200 kW power for two-level converter and neutral point clamped (NPC) three-level converter are presented.