Stability Analysis with PLL Effects for a Grid-Following Inverter Based on Complex Vector Control

This paper analyzes stability of a grid-following inverter (GFI) based on the complex vector control in the
$\alpha\beta$
domain and a phase-lock loop (PLL) control in the dq domain. It is known that the frequency transfer function of this PLL may affect mutual interactions between GFI and line impedances. This paper analyzes the stability of the mixed-domain control. Considering frequency coupling effects by the PLL control, it is found that the passivity of the inverter is violated. The investigated results are validated by analytical derivation, simulation, and experiment.