Mean-field approach for frequency synchronization in complex networks of two oscillator types

TL;DR

This paper introduces a mean-field model to analyze frequency synchronization in complex oscillator networks with bipolar frequency distributions, relevant for power grid stability, accounting for heterogeneity and large phase differences.

Contribution

The authors develop a mean-field framework that models synchronization onset, form, and stability in heterogeneous oscillator networks with bipolar frequencies, including regimes with large phase differences.

Findings

Model accurately predicts synchronization onset and regimes.

Framework captures large phase difference regimes.

Internal metrics assess mean-field assumption validity.

Abstract

Oscillator networks with an asymmetric bipolar distribution of natural frequencies are useful representations of power grids. We propose a mean-field model that captures the onset, form and linear stability of frequency synchronization in such oscillator networks. The model takes into account a broad class of heterogeneous connection structures and identifies a functional form as well as basic properties that synchronized regimes possess classwide. The framework also captures synchronized regimes with large phase differences that commonly appear just above the critical threshold. Additionally, the accuracy of mean-field assumptions can be gauged internally through two model quantities. With our framework, the impact of local grid structure on frequency synchronization can be systematically explored.