In a modular multi-level power converter, additional switching states are interleaved between main switching states that control output voltage or waveform. The additional switching states provide current from a DC-link to charge capacitors in respective modules or cells to an offset voltage from which the capacitor voltages are controlled toward a reference voltage during each switching cycle rather than being allowed to build up over a period of an output waveform of variable line frequency, possibly including zero frequency. Since the switching cycle is much shorter than the duration of a line frequency cycle and the capacitor voltages are balanced during each switching cycle, output voltage ripple can be limited as desired with a capacitor of much smaller value and size than would otherwise be required.