A unified impedance model of voltage-source converters with phase-locked loop effect

This paper proposes a unified impedance model for analyzing the effect of Phase-Locked Loop (PLL) on the stability of grid-connected voltage-source converters. In the approach, the dq-frame impedance model is transformed into the stationary αβ-frame by means of complex transfer functions and complex space vectors, which not only predicts the stability impact of the PLL, but reveals also its frequency coupling effect in the phase domain. Thus, the impedance models previously developed in the different domains can be unified. Moreover, the impedance shaping effects of PLL are structurally characterized for the current control in the rotating dq-frame and the stationary αβ-frame. Case studies based on the unified impedance model are presented, which are then verified in the time-domain simulations and experiments. The results closely correlate with the impedance-based analysis.