Coprime Polynomial Based Dual-circulant Modulation for Inherent Submodule Voltage Balancing in MMDC

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

Research output: Contribution to journalArticlepeer-review


The modular multilevel dc-dc converters (MMDCs) have attracted much interest in medium voltage dc applications, but have to face the main issue of balancing submodule (SM) capacitor voltages. This paper proposes a dual-circulant modulation and proves it possessing the inherent balancing capability for arbitrary operation cases. High-speed communication for real-time sensor data transfer could be avoided, which reduces implementation costs and also enhances the system reliability. Two sets of circular switching patterns are preset and combined to complete the full constrains on SM voltages. The associated polynomial of circulant matrix is introduced and the coprime of polynomials demonstrates the full-rank feature of the extended switching matrix that promises the inherent balancing for any operation cases. Then the switching patterns are reallocated and optimized to keep the SM uniformity and reduce the capacitor voltage ripple at the same time. Full-scale simulations on MMDC models and down-scaled experiments on prototypes are both presented, which validates the inherent voltage balancing capability and the optimization of SM capacitor voltage ripple with the proposed dual-circulant modulation.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalIEEE Transactions on Industrial Electronics
Early online date1 Dec 2022
Publication statusE-pub ahead of print - 1 Dec 2022


  • circulant matrix
  • coprime associated polynomial
  • dual-circulant modulation
  • inherent submodule voltage balancing
  • Modular multilevel dc converter

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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