Quantitative Stability Conditions for Grid-Forming Converters With Complex Droop Control
Xiuqiang He, Linbin Huang, Irina Subotić, Verena Häberle, Florian Dörfler
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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">transient stability</i> (global asymptotic stability) under grid disturbances, which is beyond the well-established local (non-global) stability for classical droop control. For the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">transient instability</i> of complex droop control, we reveal that the unstable trajectories are bounded, manifesting as limit cycle oscillations. Moreover, we extend our stability results from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">second-order</i> grid-forming control dynamics to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">full-order</i> 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.