Nonlinear Stability of Complex Droop Control in Converter-Based Power Systems

Abstract

In this paper, we study analytically the transient stability of grid-connected distributed generation systems with gridforming (GFM) complex droop control, also known as dispatchable virtual oscillator control (dVOC). We prove theoretically that complex droop control, as a state-of-the-art GFM control, always possesses steady-state equilibria whereas classical p/f and q/v 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 GFM 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.

Grid-Forming Control: Advancements towards 100% Inverter-Based Grids—A Review

“…Nonlinear droop behaviour in frequency and voltage regulation was reported in [121] for the AHO-VOC inverter with decentralised and autonomous control for a system of interconnected inverters. The stability conditions for this nonlinear behaviour are addressed in [122], showing that nonlinear droop, also termed complex droop, presents better properties than conventional droop in the stable operation of the grid. Despite VOC's fast primary control, facilitated by instantaneous time-domain operation, it is difficult to incorporate into a hierarchical grid control, which is often required for both grid and island operation.…”