This paper proposes a model of the doubly fed induction generator (DFIG) suitable for transient stability studies. The main assumption adopted in the model is that the current control loops, which are much faster than the electromechanic transients under study, do not have a significant influence on the transient stability of the power system and may be considered instantaneous. The proposed DFIG model is a set of algebraic equations which are solved using an iterative procedure. A method is also proposed to calculate the DFIG initial conditions. A detailed variable-speed windmill model has been developed using the proposed DFIG model. This windmill model has been integrated in a transient stability simulation program in order to demonstrate its feasibility. Several simulations have been performed using a base case which includes a small grid, a wind farm represented by a single windmill, and different operation points. The evolution of several electric variables during the simulations is shown and discussed.