A method for charging and/or discharging energy storage devices is performed in a multilevel converter including at least one phase module branch having a series circuit of submodules each with at least one power semiconductor circuit for connection or disconnection of an energy storage device in a circuit parallel to the power semiconductor circuit and a submodule sensor for detection of an energy storage actual value. An energy change state is obtained and a determination is made as to whether connected energy storage devices in a phase module branch can be charged or discharged. The next energy storage device to be switched in each phase module branch is selected by predetermined logic dependent on an energy change state, through which energy stored in energy storage devices is kept approximately at the same level. A high clock rate is simultaneously avoided for connection and disconnection of the selected energy storage device.