Analysis of frequency characteristics of phase-locked loops and effects on stability of three-phase grid-connected inverter

For grid-connected inverters, phase-locked loop (PLL) is an indispensable part for grid currents to track grid voltages. Hence, PLL will have a nonnegligible effect on the stability of the interconnected system involving a grid-connected inverter and a power grid. Therefore, it is necessary to model the frequency characteristic of PLL and analyze its effect on the system stability. In this paper, three kinds of the commonly used PLL circuits are firstly employed to model and compare their frequency characteristics. Second, the impedances of the inverter are modeled with the equivalent impedance model of PLL displayed, and the influences of different PLLs on the impedance characteristics of the inverter are compared. Then, the effects of PLLs on the stability of the interconnected system are studied to discuss the stability boundary conditions of the system. Based on the equivalent impedance model of the PLL, the optimized design method of the PLL is proposed from the perspective of optimizing the inverter impedance characteristics to improve the system stability. Finally, the simulation and experimental results are presented to verify the correctness of the PLL frequency characteristics and the inverter impedance models, and confirm the effectiveness of the optimized design method.