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 submodule (SM) capacitor voltages is considered as an ideal property which avoids complex sorting process based on many measurements thereby reducing costs and enhancing reliability. This paper extends the inherent concept previously shown square-wave modulation to version MMDCs. A switching duty matrix dU introduced: circulant preset multi-level patterns with multiple stages durations. ensured full-rank dU. Circulant theory shows that this equivalent simplified common factor criterion. non-full rank causes clusters SM rather than single value, indicated by kernel matrix. generalized co-prime criterion developed into several deductions serve practical guidance design modulation. theoretical development verified through full-scale simulations down-scaled experiments. effectiveness proposed in achieving MMDC demonstrated.