Modeling of the Phase Detector of a Synchronous-Reference-Frame Phase-Locked Loop Based on Second-Order Approximation

Grid inverters need a synchronization algorithm to connect with the grid which is often a phase-locked loop (PLL). Conventionally, small-signal models are used to tune such PLL and to assess stability in steady state; however, they can misjudge the dynamic behaviors, in particular, during large phase perturbation due to grid faults. To address this issue, a more accurate model of PLL-based synchronization of the grid inverter with second-order approximation terms valid not only for the steady state but also for phase transients has been developed in this paper. Stability criterion based on the developed model has been proposed to assess the harmonic stability during phase perturbations. The model accuracy and the effectiveness of the stability criterion have been comprehensively evaluated and validated by simulation and experiments.