A reduced order model of double fed induction generator（DFIG） for small signal stability analysis is investigated. Firstly， an 8th order detailed model to describe the DFIG electromagnetic process is established. Based on the 8th order model， a simplified 2nd order model with the phase-locked loop（PLL） dynamic state is presented according to the attenuation speed of the relationship between various physical quantities of the DFIG， and the factors of affecting the simplified 2nd order model stability are analyzed. Finally， using the Lyapunov eigenvalue theory， the stability boundaries of the detailed model， and the 2nd order model and the 6th order model put forward by the conventional method are compared through numerical examples. The results show that， the simplified 2nd order model is more consistent with the description of the detailed 8th order model than the 6th model on the small signal stability of the system.