Linear Stability and the Braess Paradox in Coupled Oscillators Networks and Electric Power Grids

TL;DR

This paper explores how adding new connections in coupled oscillator networks and power grids can unexpectedly destabilize the system, demonstrating the occurrence of the Braess paradox in complex systems.

Contribution

It reveals that new couplings can either stabilize or destabilize systems, extending the understanding of the Braess paradox to power grids and coupled oscillators.

Findings

Adding couplings can enhance or reduce stability depending on location.

The Braess paradox can occur in power grids and oscillator networks.

New lines may lead to increased or decreased power flows.

Abstract

We investigate the influence that adding a new coupling has on the linear stability of the synchronous state in coupled oscillators networks. Using a simple model we show that, depending on its location, the new coupling can lead to enhanced or reduced stability. We extend these results to electric power grids where a new line can lead to four different scenarios corresponding to enhanced or reduced grid stability as well as increased or decreased power flows. Our analysis shows that the Braess paradox may occur in any complex coupled system, where the synchronous state may be weakened and sometimes even destroyed by additional couplings.