Synchronization assessment in power networks and coupled oscillators

Synchronization problems in complex networks have recently attracted tremendous scientific interested. Moreover, assessing the existence, stability, and robustness of synchronous states is a pervasive topic in the operation of power networks. Scientists in both communities have long aimed to identify sharp synchronization conditions as functions of the network topology and parameters. This paper proposes an insightful approach to this problem based on algebraic graph theory. We present a novel synchronization condition applicable to a general coupled oscillator model. We rigorously establish that our condition is exact for various interesting network topologies and parameters. Via statistical studies we show that our condition predicts accurately the existence of stable synchronous solutions for generic networks as well as various power network test cases. From these statistical studies, we conclude that our proposed condition is correct for almost all network topologies and parameters. Indeed, we also show that there exist possibly-thin sets of network topologies and parameters, where our condition is not sufficiently tight.