In recent years, wind generation has been fast growing and become one of the major generation resources in power systems. Since the wind generation does not inherently equip with frequency support functions, the power system frequency response degrades as the wind penetration increases. Therefore, frequency support control of wind generation has gained increasing focus. However, the dynamic models of wind generation systems, which are required by the control design and analysis, are commonly very complicated and difficult to obtain, especially for the doubly-fed induction generator based wind turbine (DFIG-WT). In this paper, the authors propose a simplified dynamic model for the DFIG-WT. The proposed analytical model is derived from the detailed model by selectively neglecting very fast dynamics while keeping the critical ones. It is suitable for frequency control studies. The model accuracy is first validated against the detailed DFIG-WT model in Simulink. Then, the wind frequency control function is studied based on the proposed model.