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

Heng Wu, Xiongfei Wang, Lukasz Kocewiak

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39 Citations (Scopus)


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 (IMs) 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 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 subsynchronous 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
Article number8692427
JournalIEEE Journal of Emerging and Selected Topics in Power Electronics
Issue number4
Pages (from-to)4060-4074
Number of pages15
Publication statusPublished - Dec 2020


  • Impedance model
  • modular multilevel converter (MMC)
  • stability
  • subsynchronous oscillation (SSO)


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