What adaptive neuronal networks teach us about power grids

TL;DR

This paper explores the fundamental connection between power grid and neuronal networks, showing that models of power grids can be viewed as adaptive networks, revealing new multicluster states and failure phenomena.

Contribution

It establishes a formal relation between power grid models and adaptive neuronal networks, introducing new multicluster states and insights into cascading failures.

Findings

Phase oscillator models with inertia relate to adaptive networks.

Discovery of a new multicluster state in phase oscillators.

Cascading line failures in power grids are analogous to adaptive neuronal network phenomena.

Abstract

Power grid networks, as well as neuronal networks with synaptic plasticity, describe real-world systems of tremendous importance for our daily life. The investigation of these seemingly unrelated types of dynamical networks has attracted increasing attention over the last decade. In this paper, we provide insight into the fundamental relation between these two types of networks. For this, we consider well-established models based on phase oscillators and show their intimate relation. In particular, we prove that phase oscillator models with inertia can be viewed as a particular class of adaptive networks. This relation holds even for more general classes of power grid models that include voltage dynamics. As an immediate consequence of this relation, we find a novel type of multicluster state for phase oscillators with inertia. Moreover, the phenomenon of cascading line failure in power grids is translated into an adaptive neuronal network.