Systemic risk and recovery strategies in power networks and akin

In the first part of the talk I will concentrate on a possible mechanism for abrupt cascade failures in transmission power grids. I will consider both the cases of increasing loads and fluctuating sources (renewable energy). I will introduce a mean-field model and argue that abrupt failures are related to the long-range nature of Kirchoff's laws; hence, they are natural for any network distributing a commodity as a flow (like gas, water, oil). I will then generalise the model to the case of inter-dependent networks, showing the effects that the introduction of energy hubs could induce in a multi energy system. In the second part of the talk, I will consider a possible self-healing mechanism for distribution networks. I will analyse the case of radial (tree-like) networks with redundant links and investigate the effects of topology. I will then introduce an analytical model to predict the resilience of a self-healing network and confront the results with numerical simulations. Finally, I will introduce a simplified percolation models that highlights the importance of the underlying network topology and of the optimal placement of redundant links.