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

arXiv: https://arxiv.org/abs/2105.13094 · HTML: https://mlsanity.com/paper/2105.13094/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2021.

## Built on by (most cited first, 1 of 1)

- [A Unified Mamba--MoE Surrogate for Closed-Loop Simulation and Measurement-Window Forecasting of Inverter Transients](https://mlsanity.com/paper/2608.15051/) (2026)

## Abstract (arXiv)

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 simple single-inverter-infinite-bus systems and a multi-inverter power network.