Delay master stability of inertial oscillator networks

TL;DR

This paper develops an analytical method to assess the stability of synchronized states in networks of inertial oscillators with delays, crucial for future power grid stability amid renewable energy integration.

Contribution

It extends the master stability formalism to include constant delays, providing necessary and sufficient conditions for stability in inertial oscillator networks.

Findings

Delay impacts bifurcation points depending on network topology.

The method distinguishes between phase and frequency delays.

Application to power grid models highlights stability challenges.

Abstract

Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled inertial oscillators with constant delay. Building on the master stability formalism, our technique provides necessary and sufficient delay master stability conditions. We apply it to two classes of potential future power grids, where processing delays in control dynamics will likely pose a challenge as renewable energies proliferate. Distinguishing between phase and frequency delay, our method offers an insight into how bifurcation points depend on the network topology of these system designs.