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Deutsche Physikalische Gessellschaft IOP Institute of Physics

Braess's paradox in oscillator networks, desynchronization and power outage

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Dirk Witthaut1,3 and Marc Timme1,2

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Paper

Robust synchronization is essential to ensure the stable operation of many complex networked systems such as electric power grids. Increasing energy demands and more strongly distributing power sources raise the question of where to add new connection lines to the already existing grid. Here we study how the addition of individual links impacts the emergence of synchrony in oscillator networks that model power grids on coarse scales. We reveal that adding new links may not only promote but also destroy synchrony and link this counter-intuitive phenomenon to Braess's paradox known for traffic networks. We analytically uncover its underlying mechanism in an elementary grid example, trace its origin to geometric frustration in phase oscillators, and show that it generically occurs across a wide range of systems. As an important consequence, upgrading the grid requires particular care when adding new connections because some may destabilize the synchronization of the grid—and thus induce power outages.

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Content from this work may be used under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

PACS

05.45.Xt Synchronization; coupled oscillators

89.75.Hc Networks and genealogical trees

84.70.+p High-current and high-voltage technology: power systems; power transmission lines and cables

Subjects

Electronics and devices

Statistical physics and nonlinear systems

Dates

Issue 8 (August 2012)

Received 3 June 2012

Published 29 August 2012

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