A nonlinear adaptive control law for the stabilization of synchronous generators in a power network is designed, based on the new possibilities related with Smart Grids, in particular the insertion of remote measurements provided by Phasor Measurement Units (PMU). The proposed control system is designed in a robust way in order to cope with several uncertainties like the network parameters, and the intrinsic time delay on remote measurements. The proposed controller stability is rigorously proved, and computer simulations illustrate its good behavior, and suggest that the new measurement and data transmission devices can bring even better performance.