Building blocks of the basin stability of power grids

TL;DR

This paper systematically analyzes how basin stability, a measure of synchronization robustness, depends on transmission strength in small power grid networks, revealing distinct stability patterns linked to network structure.

Contribution

It characterizes the functional forms of basin stability dependence on transmission strength in small networks, identifying key structural factors influencing stability.

Findings

Basin stability shapes fall into a few well-defined classes.

Network structure, especially edges and betweenness, influences stability patterns.

The study provides a systematic classification of stability behaviors in small networks.

Abstract

Given a power grid and a transmission (coupling) strength, basin stability is a measure of synchronization stability for individual nodes. Earlier studies have focused on the basin stability's dependence of the position of the nodes in the network for single values of transmission strength. Basin stability grows from zero to one as transmission strength increases, but often in a complex, nonmonotonous way. In this study, we investigate the entire functional form of the basin stability's dependence on transmission strength. To be able to perform a systematic analysis, we restrict ourselves to small networks. We scan all isomorphically distinct networks with an equal number of power producers and consumers of six nodes or less. We find that the shapes of the basin stability fall into a few, rather well-defined classes, that could be characterized by the number of edges and the betweenness of the nodes, whereas other network positional quantities matter less.