This work aims the description, modeling and simulation of the incorporation of a power system stabilizer (PSS) in variable speed wind turbines in order to dampen oscillation in power grids. The proposed PSS aims to alter the nature of the electric power injected by the wind farms to, in some sense, mimic the oscillatory behavior of synchronous generators and allows dampening these transient oscillations. The main advantage of this stabilizing action lies in the fact that the wind turbines, by decoupling the electrical frequency of the network respect its rotational speed by the inclusion of power electronic converters, allows the injection of oscillating power without risk of suffering stability issues. This allows to improve the oscillation damping between different synchronous generators.The proposed PSS has been analyzed in a grid of three areas: an area comprises the infinite bus; the second one a synchronous generator and the third one contains a synchronous generator and a wind farm. The PSS takes as reference the active power injected by the synchronous generator of the third area using synchrophasors. Finally, it is studied the performance of the PSS for a particular case of the Uruguayan power grid. In this scenario, the second area is composed by the hydro power plant Baygorria; the third area is comprised by the hydro power plant Terra and the wind farms Palmatir and Agua Leguas; finally, the first area is the rest of the power system.