Synchronization in complex oscillator networks and smart grids

By Florian Dörfler, M. Chertkov, Francesco Bullo. Proceedings of the National Academy of Sciences of the United States of America, 2012

944 citations recorded by the source corpus.

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.

Subfields: Biomedical Engineering, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/511786a037059d6d296d114435523fbc8cbcf15f

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In Biomedical Engineering

In Computer Networks and Communications

Citations in the corpus

Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks (2008, background): “Therefore, if we are interested in coherent Kuramoto communities (e.g., motivated by power grid applications [54]), the partitions found with the ‘usual’ modularity could be misleading.”
Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators (2014, neutral): “[62–65]).”
Synchronization and power sharing for droop-controlled inverters in islanded microgrids (2012, neutral): “See [14, The-orems 1, 2(G1)] for additional information.”
The Kuramoto model in complex networks (2015, methodology): “In [352] a condition for synchronization on any arbitrary network was derived rigorously in terms of network topology and grid parameters .”
Chance-Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty (2012, background): “However, as shown recently in [22], one can formulate an accurate linear and static necessary condition for the loss of synchronicity.”
Breaking the Hierarchy: Distributed Control and Economic Optimality in Microgrids (2014, background): “(7)-(10)], and (by continuity) networks with sufficiently uniform R/X ratio lines.”
On the Existence and Linear Approximation of the Power Flow Solution in Power Distribution Networks (2014, background): “Interestingly, the role of similar spectral connectivity measures of the grid has been recently investigated also for grid synchronization and resilience problems (see the discussion in [34] and [35], respectively).”
Synchronization in complex networks and its application - A survey of recent advances and challenges (2014, background): “, 2007; Sepulchre, 2012) and synchronization theory, the conditions are presented, which can be interpreted as ‘‘the network connectivity has to dominate the network’s nonuniformity and the network’s losses’’ (Döfler & Bullo, 2013; Döfler et al., 2013).”
How dead ends undermine power grid stability (2014, methodology): “equations (7 and 8) used above, we divide equation (15) by Mios and define ai1⁄4Di/(Mios), Pi:1⁄4 Li/(Mios) and Kij:1⁄4YijViVj/(Mios).”
Synchronization in complex networks of phase oscillators: A survey (2014, methodology): “Under these assumptions, it can be shown (Dörfler et al., 2013) that the system of spring-interconnected particles obeys the dynamics M i ¨ θ i +D i ˙ θ i = τ i − n j=1 k ij sin(θ i −θ j ) , i ∈ {1, . . . , n}.”