The increasing penetration of wind power leads to diverse stability issues, which present more extreme fluctuation and nonlinearity, especially under a weak grid. For the nonlinear transient process, it is particularly complex to estimate since no analytical solution can be found in math. To determine the transient stability of the grid-following (GFL) wind turbine, this article develops a third-order transient model of the GFL-doubly fed induction generator, which consists of a second-order phase-locked loop model and a first-order active power control model. Then, a motion discretization equal area criterion (MD-EAC) method is proposed to estimate the damping effect in the second-order system, which could enhance transient trajectory accuracy and improve stable region reliability. Based on MD-EAC, a power angle to time sequence mapping EAC (SM-EAC) method is proposed to perform the stability analysis in third-order systems with active power control. Finally, numerical simulation results are given to validate the effectiveness of the proposed MD-EAC and SM-EAC under various scenarios. And the mechanism of multi-swing stability is analyzed by numerical simulation and SM-EAC
