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

In this article, 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 (nonglobal) 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.