Impedance Circuit Model of Grid-Forming Inverter: Visualizing Control Algorithms as Circuit Elements

Y. Li, Y. Gu, Y. Zhu, A. Junyent Ferre, X. Xiang, T. C. Green

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The impedance model is widely used for analyzing power converters. However, the output impedance is an external representation of a converter system, i.e., it compresses the entire dynamics into a single transfer function with internal details of the interaction between states hidden. As a result, there are no programmatic routines to link each control parameter to the system dynamic modes and to show the interactions among them, which makes the designers rely on their experience and heuristic to interpret the impedance model and its implications. To overcome these obstacles, this article proposes a new modeling tool named as impedance circuit model, visualizing the closed-loop power converter as an impedance circuit with discrete circuit elements rather than an all-in-one impedance transfer function. It can reveal the virtual impedance essence of all control parameters at different impedance locations and/or within different frequency bandwidths, and show their interactions and coupling effects. A grid-forming voltage source inverter is investigated as an example, with considering its voltage controller, current controller, control delay, voltage/current dq-frame cross-decoupling terms, output-voltage/current feedforward control, droop controllers, and three typical virtual impedances. The proposed modeling tool is validated by frequency-domain spectrum measurement and time-domain step response in simulations and experiments.
Original languageEnglish
Article number9162492
Pages (from-to)3377-3395
Number of pages19
JournalIEEE Transactions on Power Electronics
Issue number3
Early online date7 Aug 2020
Publication statusPublished - 31 Mar 2021

Bibliographical note

Funding Information:
Manuscript received October 28, 2019; revised March 18, 2020 and June 4, 2020; accepted August 4, 2020. Date of publication August 7, 2020; date of current version October 30, 2020. This work was supported by the Engineering and Physical Sciences Research Council under Grants EP/R030235/1, EP/S000909/1, and EP/T021780/1. Recommended for publication by Associate Editor R. Burgos. (Corresponding author: Yunjie Gu.) Yitong Li, Yue Zhu, Adrià Junyent-Ferré, Xin Xiang, and Timothy C. Green are with the Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2BU, U.K. (e-mail: yitong.li15@; [email protected]; adria.junyent-ferre@imperial.; [email protected]; [email protected]).

Publisher Copyright:
© 1986-2012 IEEE.


  • Grid-forming inverter
  • impedance circuit model
  • output impedance shaping
  • power system stability
  • virtual impedance
  • voltage source inverter (VSI)

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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