The synchronization stability of a direct drive permanent magnet synchronous generator (PMSG) is closely related to the dynamic characteristics of the phase-locked loop (PLL). The loss of synchronization stability may easily lead to massive disconnection of wind farm. To this end, a quantitative analysis method based on energy function method to analyze the transient synchronization stability of PMSG-based wind farms. Based on certain assumptions, this paper first reduces the order of the grid-side control system of the PMSG on the premise of retaining the influence of inertial control and outer-loop control on the dynamic characteristics of the PLL. Then, based on a reduced order control system, the generalized swing equation of the PMSG considering the influence of inertial control and outer-loop control is established. Based on the generalized swing equation, the first integration method is used to derive the unit level transient energy function. Based on the grid connected equivalent circuit of the PMSG-based wind farm, the transient energy function at the station level is derived, and the critical energy value of the system is determined by the potential energy boundary surface method. Finally, the correctness of the derived results and the effectiveness of the energy function are verified in the four-machine system of a PMSG-based wind farm. The influence of inertial control parameters on synchronization stability is also analyzed. This work is supported by the National Natural Science Foundation of China (No. 51637005).