Block Diagonal Dominance-based Model Reduction Method Applied to MMC Asymmetric Stability Analysis

Haoxiang Zong, Chen Zhang*, Jing Lyu, Xu Cai, Marta Molinas

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Frequency-domain model reduction is a crucial concern in applying the prevailing impedance method for the stability analysis of complex systems, e.g., the modular multilevel converter (MMC). Recently, it has been shown that under symmetric conditions, a 2×2 matrix-based impedance model characterizing the two coupled frequencies of MMC are sufficient for its stability analysis. However, when the asymmetry occurs, principally, a much higher number of frequency couplings will appear in the MMC and thereby leads to a significant rise in the model dimension. Enlighted by this issue, there is an urgent need of finding a suitable frequency-domain method that can serve as a general criterion for model reduction. To this end, this paper proposes a block diagonal dominance (BDD)-based model reduction method and applied it to the asymmetric MMC. Basically, the BDD can decompose an N-dimensional task to N one-dimensional tasks, via which a significant reduction in model dimension can be realized. It is shown that by properly shifting the impedance model from one domain to another (e.g., α-β domain to $d-q$ domain), the BDD property can be achieved for most asymmetric scenarios. Finally, various case studies considering different asymmetry degrees are conducted to validate the effectiveness of the proposed method.
Original languageEnglish
JournalIEEE Transactions on Energy Conversion
Issue number3
Pages (from-to)2438 - 2451
Publication statusPublished - 2021


  • MMC
  • Asymmetric
  • Reduced-order model
  • Block diagonal dominance (BDD)
  • Impedance
  • Stability


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