Asymmetric Impedance Model for Grid-Forming Converters With Droop Control

This article introduces an impedance model for a grid-forming (GFM) converter with droop control (Droop-GFM converter) connected to a weak power grid. The proposed model offers a more accurate and simpler alternative to the conventional minor-loop criterion and the generalized Nyquist stability criterion for studying the stability of a Droop-GFM converter, as it accounts for loading effects and uses only two transfer functions. Formulated in the $\alpha \beta$ frame, the model consists of only two balanced impedances, offering a clearer physical interpretation of the impedance asymmetry introduced by droop control, in contrast to dq-frame impedance matrix models. The model describes frequency coupling effects (the mirror frequency problem) across the entire frequency range, providing both a geometric and physical understanding of this phenomenon. It allows determination of the bandwidth of the frequency coupling region, and how this region changes based on the droop coefficients and the loading condition of the Droop-GFM converter. The theoretical findings are validated experimentally using a Droop-GFM converter in three distinct scenarios, including: weak power grid operation, a change in the droop coefficients, and a change in the power grid impedance.