Transient chaos enforces uncertainty in the British power grid

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.

Predicting Basin Stability of Power Grids using Graph Neural Networks

“…Hence, it may be assumed that every trajectory labeled as stable in that way will indeed converge to the synchronous state for t → ∞. On the other hand, trajectories who are classified as unstable may converge to many different kinds of attractors [37], [38]. However, we occasionally observed so-called long transient states at specific nodes, which do eventually converge to the synchronous state but fail to do so before t = 500.…”

Predicting basin stability of power grids using graph neural networks

“…Hence, it may be assumed that every trajectory labeled as stable in that way will indeed converge to the synchronous state for t → ∞. On the other hand, trajectories who are classified as unstable may converge to many different kinds of attractors [44,45]. However, we occasionally observed so-called long transient states at specific nodes, which do eventually converge to the synchronous state but fail to do so before t = 500.…”

Focusing on transient chaos

“…In this section, we provide an overview of contributions to the focus issue, which describe the emergence of transient chaos in various applications, including self-organization of active particles [8], dynamics of power grids [9], applications in medicine [10] and magnetohydrodynamics [11], as well as in machine learning [12].…”

“…Another application where transient chaos plays an important role is mentioned by Halekotte et al in [9]. This paper considers the conditions of stable operation of the power grid described using the Kuramoto model with inertia and the network topology representing the high-voltage transmission grid of the United Kingdom.…”