Transient chaos enforces uncertainty in the British power grid

TL;DR

This paper investigates how multistability and chaotic dynamics in the British power grid lead to spatially variable uncertainty in response to perturbations, highlighting the role of network topology.

Contribution

It reveals the connection between network topology and chaotic responses, demonstrating how specific structures induce uncertainty in power grid stability.

Findings

Uncertainty varies strongly across different nodes.

Certain network motifs are linked to chaotic responses.

Chaotic saddle dynamics are associated with specific topological features.

Abstract

Multistability is a common phenomenon which naturally occurs in complex networks. If coexisting attractors are numerous and their basins of attraction are complexly interwoven, the long-term response to a perturbation can be highly uncertain. We examine the uncertainty in the outcome of perturbations to the synchronous state in a Kuramoto-like representation of the British power grid. Based on local basin landscapes which correspond to single-node perturbations, we demonstrate that the uncertainty shows strong spatial variability. While perturbations at many nodes only allow for a few outcomes, other local landscapes show extreme complexity with more than a hundred basins. Particularly complex domains in the latter can be related to unstable invariant chaotic sets of saddle type. Most importantly, we show that the characteristic dynamics on these chaotic saddles can be associated with certain topological structures of the network. We find that one particular tree-like substructure allows for the chaotic response to perturbations at nodes in the north of Great Britain. The interplay with other peripheral motifs increases the uncertainty in the system response even further.