Multilayer control of synchronization and cascading failures in power grids

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.