Self-healing networks: A theoretical approach to smart grids' resilience

To ensure a high quality of service to the users in the next generation of smart grids, self-healing capabilities are a crucial feature to be introduced. We show how distributed communication protocols can enrich complex networks with self-healing capabilities; an obvious field of applications are infrastructural networks distributing a commodity via a flow, like gas, water or electric power. We consider the case where the presence of redundant links allows to recover the connectivity of the system. We then introduce a theoretical framework to calculate the fraction of nodes still served for increasing levels of network damages. Such framework allows to analyse the interplay between redundancies and topology, a key point in improving the resilience of networked infrastructures to multiple failures.