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

Shiyuan Fan, Xin Xiang, Jing Sheng, Yunjie Gu, Huan Yang, Wuhua Li, Xiangning He, Timothy C Green

Research output: Contribution to journalArticlepeer-review

16 Citations (SciVal)
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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 dU 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 dU. Circulant matrix theory shows that this is equivalent to a simplified common factor criterion. A nonfull 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 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.

Original languageEnglish
Pages (from-to)1352-1368
Number of pages17
JournalIEEE Transactions on Power Electronics
Issue number2
Early online date15 Oct 2021
Publication statusPublished - 1 Feb 2022


  • Inherent balance
  • modular multilevel dc converter (MMDC)
  • multilevel circulant modulation
  • submodule (SM) capacitor voltage

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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