Quantitative Stability Conditions for Grid-Forming Converters With Complex Droop Control

TL;DR

This paper provides a comprehensive analysis of the transient stability of grid-forming converters with complex droop control, establishing conditions for stability and characterizing instability phenomena.

Contribution

It offers the first quantitative stability conditions for complex droop control, extending analysis from second-order to full-order system dynamics.

Findings

Complex droop control always has steady-state equilibria.

Quantitative conditions ensure global asymptotic stability under disturbances.

Unstable trajectories are bounded, leading to limit cycle oscillations.

Abstract

In this paper, we analytically study the transient stability of grid-connected converters with grid-forming complex droop control, also known as dispatchable virtual oscillator control. We prove theoretically that complex droop control, as a state-of-the-art grid-forming control, always possesses steady-state equilibria whereas classical droop control does not. We provide quantitative conditions for complex droop control maintaining transient stability (global asymptotic stability) under grid disturbances, which is beyond the well-established local (non-global) stability for classical droop control. For the transient instability of complex droop control, we reveal that the unstable trajectories are bounded, manifesting as limit cycle oscillations. Moreover, we extend our stability results from second-order grid-forming control dynamics to full-order system dynamics that additionally encompass both circuit electromagnetic transients and inner-loop dynamics. Our theoretical results contribute an insightful understanding of the transient stability and instability of complex droop control and offer practical guidelines for parameter tuning and stability guarantees.