Harmonic transfer-function model of three-phase synchronous reference frame PLL under unbalanced grid conditions

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Abstract

The synchronous reference frame (SRF) phase-locked loop (PLL) is widely used in three-phase grid-connected converter systems. For the balanced grid condition, the PLL can be linearized in the dq frame, and the derived small-signal model is linear time-invariant (LTI), which can be readily analyzed with classical control theories. However, in the unbalanced grid, the presence of the negative-sequence voltage leads to frequency-coupling dynamics in the SRF-PLL, which cannot be characterized by the dq-frame LTI model. This paper thus proposes a harmonic transfer-function model of the SRF-PLL under three-phase unbalanced grid conditions based on the linear time-periodic theory. It is found that the negative-sequence voltage can result in considerable phase error, which yields three time-periodic coefficients in the dynamic model of SRF-PLL. Simulations and experimental results corroborate the effectiveness of the model. The frequency-coupling effects are verified in the time domain and the frequency domain.
Original languageEnglish
Title of host publicationProceedings of the 34th Annual IEEE Applied Power Electronics Conference and Exposition, APEC 2019
Number of pages8
PublisherIEEE Press
Publication dateMar 2019
Pages58-65
Article number8721842
ISBN (Print)978-1-5386-8331-6
ISBN (Electronic)978-1-5386-8330-9
DOIs
Publication statusPublished - Mar 2019
Event34th Annual IEEE Applied Power Electronics Conference and Exposition, APEC 2019 - Anaheim, United States
Duration: 17 Mar 201921 Mar 2019

Conference

Conference34th Annual IEEE Applied Power Electronics Conference and Exposition, APEC 2019
CountryUnited States
CityAnaheim
Period17/03/201921/03/2019
SponsorIEEE Industry Applications Society (IAS), IEEE Power Electronics Society (PELS), Power Sources Manufacturers Association (PSMA)
SeriesIEEE Applied Power Electronics Conference and Exposition (APEC)
ISSN2470-6647

Keywords

  • Harmonic transfer function
  • Linear time-periodic
  • PLL
  • Small-signal model
  • Synchronous reference frame
  • Unbalanced grid

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  • Cite this

    Liao, Y., Wang, X., Yue, X., & Gong, H. (2019). Harmonic transfer-function model of three-phase synchronous reference frame PLL under unbalanced grid conditions. In Proceedings of the 34th Annual IEEE Applied Power Electronics Conference and Exposition, APEC 2019 (pp. 58-65). [8721842] IEEE Press. IEEE Applied Power Electronics Conference and Exposition (APEC) https://doi.org/10.1109/APEC.2019.8721842