Predicting Stability Boundary of a Single-phase Grid-tied Inverter using Small-signal DQ-Frame Model

Stability analysis of a grid-tied inverter is vital due to the non-linear nature of the synchronous reference frame phase-locked-loop (SRF-PLL) and its interaction with the other system dynamics present. The precise stability boundary prediction of a single-phase system is challenging due to the absence of orthogonal quantities. A single-phase system can be modeled in the DQ-frame by introducing fictitious orthogonal quantities. This paper aims to identify the stability boundary of a single-phase grid-tied inverter using the DQ-frame small-signal model and compares these stability predictions with the results obtained with a harmonic state-space model. The stability boundary of the system is predicted using Floquet theory applied to the small-signal model. The model has been validated using detailed switched simulations of a single-phase grid-tied inverter.