Small-signal converter admittance in the pn-frame: systematic derivation and analysis of the cross-coupling terms

Gabriele Amico, Agustí Egea Àlvarez, Paul Brogan, Shuo Zhang

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)
48 Downloads (Pure)


A methodology is presented to derive the small-signal admittance of a converter based control system in the pn-frame. Such a methodology makes use of a set of derived equations which link the qd-frame small-signal admittance data to the corresponding pn-frame small-signal admittance terms. Compared to existing results providing the pn-frame small-signal impedance of a grid connected converter, the presented technique allows a calculation of the pn-frame small-signal admittance (or impedance) when additional elements are present in the controller, as in many practical designs. The presented technique is therefore generic and provides a systematic way to calculate the pn-frame admittance regardless of the used converter control scheme. In the study, the method has been applied to assess how different parts of the controller affect the pn-frame admittance terms and, in particular, the cross-coupling which exists between its positive and negative sequence terms. Thereby, the results of the proposed methodology have been used to study the impact of the negative sequence current compensator on the stability performance of a grid-connected converter. Experimental tests using a real hardware set up are used to support the obtained results.
Original languageEnglish
Pages (from-to)1829-1838
Number of pages11
JournalIEEE Transactions on Energy Conversion
Issue number4
Early online date28 Jun 2019
Publication statusPublished - 31 Dec 2019


  • voltage source converter
  • mirror frequency effect
  • dual vector current control
  • impedance-based stability criterion


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