Asymmetric Complex-Vector Models With Application to VSC–Grid Interaction

Lennart Harnefors, Xiongfei Wang, Shih-Feng Chou, Massimo Bongiorno, Marko Hinkkanen, Mikko Routimo

Research output: Contribution to journalJournal articleResearchpeer-review


The properties of complex space-vector models for asymmetric three-phase systems are investigated in this article. Most importantly, three alternative methods for the stability analysis of the asymmetric closed-loop systems are presented. The end results avoid the usage of matrix manipulations. It is shown how the theory can be applied to modeling and stability analysis of a grid-connected voltage-source converter (VSC). The methods are compared using numerical examples.

Original languageEnglish
Article number8985279
JournalI E E E Journal of Emerging and Selected Topics in Power Electronics
Issue number2
Pages (from-to)1911-1921
Number of pages11
Publication statusPublished - 2020



  • Complex space vectors
  • complex transfer functions
  • converter control
  • passivity
  • stability

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