Control of coupled oscillator networks with application to microgrid technologies

TL;DR

This paper presents a control method for coupled oscillator networks, enhancing synchronization stability in complex systems like microgrids by stabilizing key oscillators based on network dynamics.

Contribution

It introduces a novel control approach that stabilizes coupled oscillators by targeting problematic nodes, with effectiveness influenced mainly by coupling strength and network dynamics.

Findings

Control stabilizes synchronized states in oscillator networks.

Number of oscillators needing control depends on coupling and heterogeneity.

Control effectiveness is less affected by network structural heterogeneity.

Abstract

The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies we study here control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions--a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. Interestingly, the amount of control, i.e., number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.