Analysis and Criterion for Inherent Balance Capability in Modular Multilevel DC–AC–DC Converters

Modular multilevel dc-ac-dc converters (MMDAC) have emerged recently for high step-ratio connections in medium-voltage distribution systems. Extended phase-shift modulation has been proposed and was found to create the opportunity for inherent balance of submodule capacitor voltages. This letter presents fundamental analysis leading to clear criterion for the inherent balance capability in MMDAC. A sufficient and necessary condition, with associated assumptions, to guarantee this capability is established. Using the mathematics of circulant matrices, this condition is simplified to a coprime criterion which gives rise to practical guidance for the design of an MMDAC. Experiments on downscaled prototypes and simulations on full-scale examples both provide verification of the analysis and criterion for the inherent balance capability of MMDAC.