Learning Power Grid Outages With Higher-Order Topological Neural Networks

With the increase in cyber-physical threats and extreme weather events, resilience of the power system has become a problem of utmost societal importance. In this article, we propose a novel approach for resilience improvement of power distribution networks, based on the notions of persistent homology and simplicial neural networks (SNNs) which are new directions in graph learning. In particular, tools of persistent homology allow us to capture the most essential topological descriptors of the distribution network. In turn, extending the convolutional operation to simplicial complexes on the distribution network, using the Hodge-Laplacian analytics, enables us to describe complex interactions among multi-node higher order graph substructures. Such higher order graph substructures are of particular importance in distribution networks, since a change in power demand at a load bus (or the power supplied from a substation) will produce a corresponding perturbation in nodal variables (such as the bus voltages) and edge variables (such as branch currents). We validate our new Higher-Order Topological Neural Networks (HOT-Nets) model for contingency classification of three test distribution networks, the IEEE 37-bus feeder, IEEE 123-bus feeder, and the 342-bus low voltage network. Our experiment results on two case studies (i.e., (i) with sensors placed at all the buses alone in the networks and (ii) with partial observability in the networks) indicate that HOT-Nets substantially outperforms 9 state-of-the-art methods, yielding relative gains of up to 14.04% in terms of system resilience classification.