Revisiting Grid-Forming and Grid-Following Inverters: A Duality Theory

Yitong Li, Yunjie Gu, Tim Green

Research output: Contribution to journalArticlepeer-review

95 Citations (SciVal)
149 Downloads (Pure)


Power electronic converters for integrating renewable energy resources into power systems can be divided into grid-forming and grid-following inverters. They possess certain similarities, but several important differences, which means that the relationship between them is quite subtle and sometimes obscure. In this article, a new perspective based on duality is proposed to create new insights. It successfully unifies the grid interfacing and synchronization characteristics of the two inverter types in a symmetric, elegant, and technology-neutral form. Analysis shows that the grid-forming and grid-following inverters are duals of each other in several ways including a) synchronization controllers: frequency droop control and phase-locked loop (PLL); b) grid-interfacing characteristics: current-following voltage-forming and voltage-following current-forming; c) swing characteristics: current-angle swing and voltage-angle swing; d) inner-loop controllers: output impedance shaping and output admittance shaping; and e) grid strength compatibility: strong-grid instability and weak-grid instability. The swing equations are also derived in dual form, which reveal the dynamic interaction between the grid strength, the synchronization controllers, and the inner-loop controllers. Insights are generated into cases of poor stability in both small-signal and transient/large-signal. The theoretical analysis and simulation results are used to illustrate cases for single-inverter systems, two-inverter systems, and multi-inverter networks.
Original languageEnglish
Pages (from-to)4541 - 4554
JournalIEEE Transactions on Power Systems
Issue number6
Early online date16 Feb 2022
Publication statusPublished - 30 Nov 2022


  • Duality
  • Frequency control
  • Inverters
  • Phase locked loops
  • Power system dynamics
  • Power system stability
  • Synchronization
  • Voltage control
  • frequency droop control
  • grid strength
  • grid-forming inverter (GFM)
  • gridfollowing inverter (GFL)
  • phase-locked loop (PLL)
  • synchronization

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


Dive into the research topics of 'Revisiting Grid-Forming and Grid-Following Inverters: A Duality Theory'. Together they form a unique fingerprint.

Cite this