Loss of synchronization is one of the main issues for a grid-feeding converter in a weak grid after being subjected to a large disturbance. The synchronous transient is highly nonlinear due to phase movement and frequency limiters. However

none of the previous research has considered the anti-windup PI in the phase-locked loop

which is commonly implemented in reality and introduced as an additional nonlinear transient. This work provides a taxonomy to evaluate and compare the effect of different anti-windup PI limiters on synchronization stability

including clamping

back-calculation and combined method. Different anti-windup PI limiters allocate zeros and poles differently and have different impacts on damping and stability enhancement. A case study implemented in Matlab/Simulink serves to compare the trajectory of the converter phase and frequency using different anti-windup PI in the scenario of both with and without equilibrium points during the fault. Simulation results show that anti-windup PI limiters increase damping during the fault and thus improve the synchronization stability margin.