Instability phenomenon of type-4 wind turbine during grid faults is increasingly concerned by researchers and may result in failure of low-voltage ride through (LVRT), especially when connected to a high-impedance ac grid. In order to carry out the stability analysis for type-4 wind turbines during deep voltage sag, dynamic model, which reflects the interaction between phase locked loop (PLL) and alternating current control (ACC), is first developed. Eigenvalues and modal analysis show that there is a risk that a pair of poorly damped poles may become unstable, which is mainly dominated by PLL as well as the interaction between PLL and ACC. The mechanism of small-signal instability during LVRT is identified as the insufficiency of damping. Complex torque coefficient approach is further proposed to study the characteristic of the damping component, which is composed of the inherent one determined by PLL and the additional influenced by ACC. Finally, simulated results are presented to verify the analytical results.