Multistability and Variations in Basin of Attraction in Power-grid Systems

TL;DR

This paper investigates the complex stability behavior of power-grid systems, revealing non-intuitive effects of coupling strength on synchronization stability due to multistability transitions, which are crucial for preventing catastrophic failures.

Contribution

It uncovers the counterintuitive nonmonotonic relationship between coupling strength and stability, linking it to multistability transitions in simple graph structures relevant to power grids.

Findings

Synchronization stability can decrease with increasing coupling strength.

Transitions in multistability cause sudden drops in stability.

Understanding multistability is key to preventing power grid failures.

Abstract

Power grids sustain modern society by supplying electricity and thus their stability is a crucial factor for our civilization. The dynamic stability of a power grid is usually quantified by the probability of its nodes' recovery to phase synchronization of the alternating current it carries, in response to external perturbation. Intuitively, the stability of nodes in power grids is supposed to become more robust as the coupling strength between the nodes increases. However, we find a counterintuitive range of coupling strength values where the synchronization stability suddenly droops as the coupling strength increases, on a number of simple graph structures. Since power grids are designed to fulfill both local and long-range power demands, such simple graph structures or graphlets for local power transmission are indeed relevant in reality. We show that the observed nonmonotonic behavior is a consequence of transitions in multistability, which are related to changes in stability of the \emph{unsynchronized} states. Therefore, our findings suggest that a comprehensive understanding of changes in multistability are necessary to prevent the unexpected catastrophic instability in the building blocks of power grids.