Analysis of DC voltage ripples in modular multilevel converters

In modular multilevel converters (MMC), a circulating current in each phase unit is caused by the DC voltage ripples of the phase unit. This paper analyzed the power transfer of MMC, the energy and voltage fluctuations of the storage capacitors in the sub-modules. An accurate model to determine the voltage ripples of a phase unit is derived, in consideration of the asynchronous fluctuations of the capacitor voltages in the upper and lower converter legs. Moreover, a simplified formula to express the amplitude and frequency of the dominant fluctuating component is obtained based on the assumption that the magnitude of the voltage ripples of a phase unit is much smaller than the DC voltage. According to the simplified formula, it can be derived that the voltage fluctuating components of phase unit are in negative sequence. The accurate model and the simplified formula are verified by time-domain simulations performed in PSCAD/EMTDC, and can be applied to calculate the DC voltage ripples of phase units in modular multilevel converters.