Abstract: The issue of transient synchronization stability of phase-locked loop (PLL) synchronized converters connected to weak power grids is one of the main challenges in power systems with a high proportion of renewable energy. This paper, based on the dynamic process analysis of PLL-controlled converters under large disturbances, proposes an assessment method for the transient synchronization stability margin of such converters. This method is based on the transformation of virtual kinetic and potential energy during the acceleration and deceleration processes of the PLL. By extending the virtual power angle trajectory to approximate the boundary of the PLL dynamic system's stable domain and using the critical potential energy at the boundary exit point as an approximation of the local stability boundary, the stability margin is defined by calculating the distance between the PLL energy after fault recovery and the critical potential energy interface. The proposed method can be adopted to effectively assess the transient synchronization stability margin of phase-locked control converters. Compared to the results of existing methods, the evaluation results are closer to the true stability boundary, meeting the quantitative analysis needs for converter-driven stability in power systems. The correctness of the conclusions is verified by building and calculating a simulation model in MATLAB/Simulink.