Predicting the Oscillatory Regimes of Global Synchrony Induced by Secondary Clusters

TL;DR

This paper develops a theoretical framework to predict when secondary synchronized clusters cause oscillations in power grid models, providing criteria to control these oscillatory regimes.

Contribution

It introduces an analytical method to identify conditions for secondary cluster emergence and oscillations in inertial synchronization systems.

Findings

Identifies an onset crossover mass $ ilde{m}^* \,\simeq\ 3.865$ for secondary clusters.

Provides quantitative criteria for the emergence and disappearance of secondary clusters.

Determines the coupling strength regimes where global synchrony exhibits oscillations.

Abstract

Synchronization systems with effective inertia, such as power grid networks and coupled electromechanical oscillators, are commonly modeled by the second-order Kuramoto model. In the forward process, numerical simulations exhibit a staircase-like growth of global synchrony, reflecting temporal oscillations induced by secondary synchronized clusters of whirling oscillators. While this behavior has been observed previously, its governing conditions have not been quantitatively determined in terms of analytical criteria. Here, we develop a self-consistent theoretical framework that explicitly characterizes the secondary synchronized clusters. This analysis identifies an onset crossover mass $\tilde{m}^* \simeq 3.865$ for the emergence of secondary clusters and yields quantitative criteria for predicting both the crossover mass and the termination coupling strength at which they vanish. As a result, we determine the oscillatory regimes of coupling strengths over which global synchrony shows temporal oscillations, providing practical guidance for controlling and avoiding undesirable oscillatory behavior in inertial synchronization systems, such as power grids.