This paper presents a new multilevel converter solution with modular structure and hybrid energy-storage integration suitable to drive modern/future high-power medium-voltage wind turbines. The hybrid energy-storage integration means that part of the converter submodules are built with batteries and part of them with conventional capacitors. Since traditional wind turbines are non-dispatchable generators, the integration of an energy storage system could be beneficial in multiple ways as the wind power plant could provide stability support to the grid, improvement of the unit commitment and economic dispatch, and the power plant owner could increase his revenues in the electricity market. The capacitors of the proposed converter are responsible to transfer the power produced by the wind turbine to the grid, and the batteries are only charged/discharged with the mismatch between the power produced by the turbine and the power to be injected into the grid, considering a dispatchable operation where the power injected into the grid is different from the power generated by the turbine. The medium-voltage structure could be an interesting option to overcome problems related to high currents in modern/future high-power wind turbines resulting in more efficient, more compact and lighter solutions. Modular multilevel converters are suitable to handle medium-voltage levels and they allow for a straightforward integration of energy storage systems in a decentralized manner.