Complex-Valued Multi-Frequency Admittance Model of Three-Phase VSCs in Unbalanced Grids

Yicheng Liao, Xiongfei Wang, Xiaolong Yue, Lennart Harnefors

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This article proposes a multifrequency admittance model for voltage-source converters with three-phase unbalanced grid voltages. The model is derived with multiple complex vectors and harmonic transfer functions, which is merely dependent on its own input voltage trajectory, and can accurately capture the frequency-coupling dynamics. The dynamic effects of both the basic synchronous-reference-frame phase-locked loop (PLL) and its alternative with a notch filter of the negative-sequence voltage component are compared. It is revealed that the notch-filtered PLL significantly weakens the frequency-coupling effects, which leads to a reduced order of the admittance model. The developed model is validated by a frequency scan, and the frequency-coupling effects impacted by different PLLs and voltage unbalance factors are verified by the experimental tests. Finally, a case study on stability analysis in unbalanced grids proves the significance of the model.
Original languageEnglish
Article number8946704
JournalIEEE Journal of Emerging and Selected Topics in Power Electronics
Issue number2
Pages (from-to)1934-1946
Number of pages13
Publication statusPublished - Jun 2020


  • Complex vector
  • frequency coupling
  • harmonic transfer function (HTF)
  • modeling
  • phase-locked loop (PLL)
  • unbalanced grid
  • voltage-source converter (VSC)

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