Phase-locked loop (PLL) with improper bandwidth could lead to potential instability issues for the grid-connected voltage source converters (VSCs) under weak grid conditions. The current loops of the VSCs can be designed faster as the development of the silicon carbide (SiC) and gallium nitride (GaN) semiconductor materials. It is questionable whether the PLL’s bandwidth could also be designed higher for faster current loop. Hence, the relationship between the bandwidth of the current loop and that of the PLL is studied first. It is revealed that the bandwidth of the PLL might not be increased linearly with the increasing of the bandwidth of the current loop, thus the traditional design principle, i.e. the bandwidth of the PLL is not higher than one-tenth of that of the current loop, might no longer be suitable. Thus, this paper proposes a design method of the PLL to make the grid-connected VSCs to have adequate stability margin and satisfactory dynamic performances under weak grid conditions. The current loop is deigned independently, while the PLL is designed considering the coupling between the current loop and the PLL under weak grid conditions. The simulations and experimental results verifies the theoretical analysis and the proposed design method.

Adaptive proportional resonant (PR) controllers, whose resonant frequencies are obtained by the phase-locked loop (PLL), are employed in grid connected voltage source converters (VSCs) to improve the control performance in the case of grid frequency variations. The resonant frequencies can be estimated by either synchronous reference frame PLL (SRF-PLL) or dual second order generalized integrator frequency locked loop (DSOGI-FLL), and there are three different implementations of the PR controllers based on two integrators. Hence, in this paper, system stabilities of the VSC with different implementations of PR controllers and different PLLs under weak grid conditions are analyzed and compared by applying the impedance-based method. First, the αβ-domain admittance matrixes of the VSC are derived using the harmonic linearization method. Then, the admittance matrixes are compared with each other, and the influences of their differences on system stability are revealed. It is demonstrated that if DSOGI-FLL is used, stabilities of the VSC with different implementations of the PR controllers are similar. Moreover, the VSC using a DSOGI-FLL is more stable than that using a SRF-PLL. The simulation and experimental results are conducted to verify the correctness of theoretical analysis.