  In this work, we propose a control scheme for power grids subject to large
perturbations that cause the failure of a node of the grid. Under such
circumstances, the system may lose synchrony and, in addition, a cascade of
line failures can be triggered as an effect of the flow redistribution that
activates the protection mechanisms equipped on each line of the grid. To
devise a control action for addressing this problem, we adopt a multi-layer
network-based description of the power grid that incorporates an overflow
condition to model the possibility of cascading failures. The two other layers
of the structure are devoted to the control, one implements the distributed
proportional control law, and the other the integral control law. To exemplify
the application of our model, we study the Italian high-voltage power grid for
different parameters and topologies of the control layers.
