The transient synchronization stability of converter-interfaced power systems under large disturbances presents significant challenges due to the lack of effective nonlinear dynamic system analysis methods. Therefore, taking the renewable energy transmission system via flexible HVDC system as the research scene, this paper establishes a transient interaction model of the system, constructs an analytical Lyapunov function, and estimates the stability region of the system by direct method. A critical energy-based transient synchronization stability criterion is then derived. Based on the theoretical derivation, the coupling relationship between the converters on renewable energy side and the flexible HVDC system side is revealed. From an energy perspective, the influence of control parameters on synchronization stability and the influence of control mode on stability assessment results are analyzed. Finally, a simulation model of a renewable energy transmission system based on modular multilevel converter based high voltage direct current transmission (MMC-HVDC) is developed in Matlab/Simulink to verify the effectiveness of the proposed method and the accuracy of the analysis results.