A Mathematical Analysis of Y-matrix Modulation: The Natural Self-Voltage Balancing Capability of Modular Multilevel Converter Under Arbitrary Level Number

The modular multilevel converter (MMC) is a promising topology for high- and medium-voltage applications for its unique advantages over traditional VSC topologies. The sub-module voltage balancing issue is one of the most important topics of MMC. As the count of output voltage levels increases, the balancing control for each submodule gets complex, which aggravates control burden of the system. To overcome this problem, a novel Y-matrix modulation (YMM) method has been proposed. It achieves submodule voltage balancing without any extra control mechanism by making full use of the natural self-voltage balancing characteristic of MMC with minimum arm inductor. However, an unsolved issue of the emerging YMM is that, the rank of the compound matrix of any two adjacent output voltage levels has not been derived theoretically, which means a complex rank-check algorithm is inevitable when the sub-module number is large. To fill this theoretical gap, a solid mathematical proof is provided in this paper, which shows that any compound matrix of two adjacent levels must have full rank. This analytical proof implies the automatic voltage balancing characteristic of MMC with arbitrary output voltage level. In other words, YMM can be applied in MMC topology without checking every compound matrix between adjacent levels. Simulation results of a YMM-based 5-level MMC under unbalanced initial capacitor voltages condition are provided to verify the inherent voltage balancing characteristic of MMC and the effectiveness of YMM on voltage balancing.