Impedance-Based Stability Analysis of Voltage-Controlled MMCs Feeding Linear AC Systems

Heng Wu, Xiongfei Wang, Lukasz Kocewiak

Research output: Contribution to journalJournal articleResearchpeer-review


This paper addresses the small-signal stability of voltage-controlled modular multilevel converters (MMCs) feeding linear ac systems. By using the harmonic state-space (HSS) modeling method, the ac-side impedance matrices of the MMC with the open-loop and closed-loop voltage control are derived, and their relationship is also explicitly given. It is revealed that the ac voltage regulator has the same effect on the centered diagonal element of the impedance matrix (IM) of the MMC as that of two-level voltage-source converters (VSCs). Moreover, when the MMC is feeding linear ac loads, the return-ratio matrix of the cascaded system has an eigenvalue that is equal to the ratio between the centered diagonal element of the IM of the MMC and the load impedance, which, consequently, facilitates the stability evaluation by checking that single-input single-output impedance ratio as a necessary condition. These findings also provide physical insights into the sub-synchronous oscillation (SSO) of the voltage-controlled MMC with the proportional resonant (PR) regulator, and a proportional integral resonant (PIR) regulator is further introduced to mitigate the SSO. Finally, time-domain simulations verify the effectiveness of the theoretical analysis.
Original languageEnglish
JournalIEEE Journal of Emerging and Selected Topics in Power Electronics
Publication statusE-pub ahead of print - 2020


  • Modular multilevel converter (MMC)
  • Impedance model
  • Stability
  • Sub-synchronous oscillation

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