In this paper, the regulation control problem of the active and reactive power at the common connection point between a doubly fed induction generator and the grid is approached. The proposed controller is developed exploiting the passivity properties of the considered model for the control system. It is considered the existence of a wind turbine that delivers a time-varying torque to the generation unit which exhibits a highly nonlinear structure due to the variations of the wind speed. From a theoretical perspective, the main feature of the contribution lies in the fact that it is formally proved that the equilibrium point of the closed-loop system that corresponds to the desired power exhibits practical global asymptotic stability properties. This characteristic is obtained applying well-known theory from the perturbed nonlinear dynamical systems theory. However, in the numerical evaluation of the proposed controller, it is illustrated how these properties are indeed stronger since asymptotic stability is achieved.