A multiphase multilevel power converter includes a phase module having submodules with an energy storage device. An energy storage device voltage is connectable and disconnectiable as a submodule voltage between two submodule poles. To attenuate higher-frequency components of the connection voltage, a passive frequency filter is provided for each phase module, having a resonant frequency above a sampling frequency of a digital regulating system connecting disconnected submodule voltages and disconnecting connected submodule voltages at successive sampling times. To avoid exciting the point of resonance of the frequency filter, the drive has a controller briefly connecting and again disconnecting at least one of the disconnected submodule voltages at least once within a sampling interval of the regulating system for a submodule voltage connected by the regulating system. A method for driving the multiphase multilevel power converter is also provided.