On the Dynamics of Inherent Balancing of Modular Multilevel DC-AC-DC Converters

X. Xiang, Y. Gu, K. Chen, A. Astolfi, T. C. Green

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Modular multilevel dc-ac-dc converters (MMDACs) serve as an enabler for dc distribution systems. The modular multilevel structure enables flexible voltage transforms, but raises issues over balancing of the submodule (SM) capacitor voltages. This letter focuses on the dynamics of inherent balancing of MMDACs under circulant modulation. We provide an invariance-like result using a variant of Barbalat's Lemma and prove that the SM capacitor voltages converge to the kernel of the circulant switching matrix, which is the intersection of the invariant sets for each switching state. We further interpret the balancing dynamics as a permuted linear time-invariant system and prove that the envelop of the balancing trajectories is governed by the eigenvalues of the permuted state-transition matrix. This result extends previous full-rank criterion for inherent balancing in a steady state and provides new insight into the dynamic behavior of MMDACs.
Original languageEnglish
Article number9113340
Pages (from-to)34-40
Number of pages7
JournalIEEE Transactions on Power Electronics
Issue number1
Early online date10 Jun 2020
Publication statusPublished - 31 Jan 2021

Bibliographical note

Funding Information:
Manuscript received May 8, 2020; revised June 2, 2020; accepted June 6, 2020. Date of publication June 9, 2020; date of current version September 4, 2020. This work was supported by the Engineering and Physical Sciences Research Council of U.K. (EPSRC) under Awards EP/S000909/1 and EP/T001623/1. (Corresponding author: Yunjie Gu.) The authors are with the Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2BU, U.K. (e-mail: [email protected]; [email protected]; kaiwen.chen16@ imperial.ac.uk; [email protected]; [email protected]).

Publisher Copyright:
© 1986-2012 IEEE.


  • Barbalat's lemma
  • circulant modulation
  • inherent balancing
  • invariance principle
  • permuted linear time-invariant (LTI) systems

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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