As a typical power electronics interface device, the voltage source converter (VSC) usually uses phase-locked loop (PLL) to synchronize with the grid and its transient synchronous dynamics is complicated. Recently it is found that the PLL-VSC system can be described by a generalized swing equation which is similar to the swing equation for the synchronous generator. Differently it has a state-dependent damping term and the basin boundary of the stable operating point can show either a closed-loop or a fish-like pattern under different parameters. To deal with these difficulties, a trajectory reversing method is proposed to efficiently obtain the basin boundary of the post-fault stable operating point, and further the critical clearing angle and the associated critical clearing time. In addition, for the transient stability enhancement, an adaptive control strategy by varying equivalent PI controller parameters of PLL in terms of the system status is proposed. It is found that it can efficiently and quickly damp transient disturbances. Therefore, these two novel methods including the trajectory reversing method and the adaptive control method are expected to be valuable for transient stability analysis and enhancement of the PLL-VSC system.INDEX TERMS Voltage source converter, transient stability analysis, transient stability enhancement, statedependent damping, trajectory reversing method, adaptive control.