Synchronization in complex oscillator networks and smart grids

The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A widely adopted model of a coupled oscillator network is characterized by a population of heterogeneous phase oscillators, a graph describing the interaction among them, an...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2013-02, Vol.110 (6), p.2005-2010
Main Authors: Dörfler, Florian, Chertkov, Michael, Bullo, Francesco
Format: Article
Language:English
Subjects:
Accuracy
Buses
Complex networks
Connectivity
Electric power
Mechanical oscillators
Natural frequencies
Network topology
Oscillators
Physical Sciences
Power supply
Smart grids
Topology
Transmission lines
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Summary:The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A widely adopted model of a coupled oscillator network is characterized by a population of heterogeneous phase oscillators, a graph describing the interaction among them, and diffusive and sinusoidal coupling. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here, we present a unique, concise, and closed-form condition for synchronization of the fully nonlinear, nonequilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters; they are statistically correct for almost all networks; and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks, such as electrical power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex network scenarios and in smart grid applications.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1212134110