In this work we model the dynamics of power grids in terms of a two-layer network, and use the Italian high voltage power grid as a proof-of-principle example. The first layer in our model represents the power grid consisting of generators and consumers, while the second layer represents a dynamic communication network that serves as a controller of the first layer. The dynamics of the power grid is modelled by the Kuramoto model with inertia, while the communication layer provides a control signal Pc

i for each generator to improve frequency synchronization within the power grid. We propose different realizations of the communication layer topology and of the control signal, and test the control performances in presence of generators with stochastic power output. When using a control topology that allows all generators to exchange information, we find that a control scheme aimed to minimize the frequency difference between adjacent nodes operates very efficiently even against the worst scenarios with the strongest perturbations. On the other hand, for a control topology where the generators possess the same communication links as in the power grid layer, a control scheme aimed at restoring the synchronization frequency in the neighborhood of the controlled node turns out to be more efficient.