Analysis of Dynamical Robustness to Noise in Power Grids

Resilience of power grids is a problem of tremendous practical and theoretical relevance. In this work, we model a power grid as a complex network of coupled oscillators. We investigate the robustness of synchronization, associated with the normal operating regime of the network, to partial malfunctioning of the nodes. Differently from previous efforts on power grid resilience, node malfunctioning is not modeled by removing a node from the network. Instead, we insert a continuous perturbation into the node dynamical equation, which reduces the degree of synchronization of the network. This framework enables an analytical treatment of the problem, ultimately leading to a detailed quantification of the criticality of each network node. The approach is applied to the UCTE European transmission network 1st synchronous area and to the IEEE 118-bus test case. The identification of nodes which are more critical to synchronization yields non-trivial hints at a complex interplay between topology and dynamics in shaping dynamical robustness of power grids.