This paper establishes the whole dynamic model of wind turbine generator system which contains the wind speed model and DFIG wind turbines model .A simulation sample based on the mathematical models is built by using MATLAB in this paper. Research are did on the performance characteristics of doubly-fed wind generators (DFIG) which connected to power grid with three-phase ground fault and the disturbance by gust and mixed wind. The capacity of the wind farm is 9MW which consists of doubly-fed wind generators (DFIG). Simulation results demonstrate that the three-phase ground fault occurs on grid side runs less affected on the stability of doubly-fed wind generators. However, as a power source, fluctuations of the wind speed will run a large impact on stability of double-fed wind generators. The results also show that if the two disturbances occur in the meantime, the situation will be very serious