This paper presents the study of the effect of increasing the penetration of Doubly Fed Induction Generators (DFIG) in the transient stability performance of a power system using a detailed model of the DFIG including the back to back converter that uses Direct Torque Control (DTC) and Direct Power Control (DPC) on the machine-and grid-side inverters respectively. The wind turbine model includes the relation between the power coefficient, the tip speed ratio, and the pitch angle, and a Maximum Power Point Tracking (MPPT) strategy to define the torque reference. The stability analysis evaluated the critical clearance time (CCT) of three-phase faults in the 9-bus IEEE power system considering different levels of wind power penetration. Additionally, a wind turbine with a squirrel cage induction generator (SQIG), and synchronous generator cases were simulated as comparison patterns. Furthermore, to evaluate the power system transient performance with high penetration of DFIG generation, the Transient Stability Index (TSI) and the Transient Rotor Angle Severity Index (TRASI) were calculated and compared.