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 paper extends the inherent balance concept previously shown for square-wave modulation to a multilevel version for MMDCs. A switching duty matrix dU is introduced: it is a circulant matrix of preset multi-level switching patterns with multiple stages and multiple durations. Inherent voltage balance is ensured with a full-rank dU. Circulant matrix theory shows that this is equivalent to a simplified common factor criterion. A non-full rank dU causes clusters of SM voltage rather than a single common value, with the clusters indicated by the kernel of the matrix. A generalized co-prime 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 down-scaled experiments. The effectiveness of the proposed circulant modulation in achieving SM voltage balance in an MMDC is demonstrated.