Inherent SM Voltage Balance for Multilevel Circulant Modulation in Modular Multilevel DC–DC Converters

The modularity of a modular multilevel dc converter (MMDC) makes it attractive for medium-voltage distribution systems. Inherent balance of submodule (SM) capacitor voltages is considered as an ideal property, which avoids a complex sorting process based on many measurements thereby reducing costs and enhancing reliability. This article extends the inherent balance concept previously shown for square-wave modulation to a multilevel version for MMDCs. A switching duty matrix
d_U
is introduced: it is a circulant matrix of preset multilevel switching patterns with multiple stages and multiple durations. Inherent voltage balance is ensured with a full-rank
d_U
. Circulant matrix theory shows that this is equivalent to a simplified common factor criterion. A nonfull rank
d_U
causes clusters of SM voltage rather than a single common value, with the clusters indicated by the kernel of the matrix. A generalized coprime criterion is developed into several deductions that serve as practical guidance for design of multilevel circulant modulation. The theoretical development is verified through full-scale simulations and downscaled experiments. The effectiveness of the proposed circulant modulation in achieving SM voltage balance in an MMDC is demonstrated.