The dynamic coupling effect, which is introduced by the dual-sequence phase-locked loops (PLLs) used in doubly- fed induction generator (DFIG) based wind energy generation systems (WEGSs) during asymmetric low voltage ride-through (LVRT) in weak grid, needs attention. In order to study this new dynamic coupling effect, an equivalent two-degree-of-freedom (2-DOF) spring damper particle model is used in this paper to develop a small-signal model for the dual-sequence PLLs. The dynamic interaction between the positive-sequence (PS) and negative-sequence (NS) PLLs is unveiled. Moreover, the impact of the dynamic coupling between the dual-sequence PLLs on the dynamic stability during the steady-state stage of an asymmetric fault is analyzed. The analysis results show that the dynamic coupling between the dual-sequence PLLs will cause drift in the frequency and damping for the PS and NS PLL modes. This will change the instability modal of the system and introduce the risk of dynamic instability. Hence, the effectiveness of existing control strategies for enhancing the dynamic stability will be decreased. Finally, a novel PLL structure is designed to improve the dynamic stability of the system during the steady-state stage of an asymmetric fault. The effectiveness of the proposed strategy is verified by simulations and experiments.