Principles and dynamics of natural arm capacitor voltage balancing of a direct modulated modular multilevel converter

Natural capacitor voltage balancing of six arms of a direct modulated Modular Multilevel Converter (MMC) has been observed by several articles both by experiments and simulations. However, its principles have not been revealed clearly and its dynamics have not been analyzed analytically. In this paper it's shown that a DC component and a line frequency circulating current would be induced inside the converter inherently in case of arm capacitor voltage unbalance and the induced circulating current would transfer energy among six arms to balance arm capacitor voltage naturally without any closed-loop control. And the dynamics of natural arm capacitor voltage balancing have been analyzed mathematically and verified by both computer simulations and experiments.