The key player problem in complex oscillator networks and electric power grids : resistance centralities identify local vulnerabilities

Tyloo, Melvyn Sandy (Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland ; School of Engineering, HES-SO Valais-Wallis, HEI, HES-SO // University of Applied Sciences Western Switzerland) ; Pagnier, Laurent (Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland ; School of Engineering, HES-SO Valais-Wallis, HEI, HES-SO // University of Applied Sciences Western Switzerland) ; Jacquod, Philippe (School of Engineering, HES-SO Valais-Wallis, HEI, HES-SO // University of Applied Sciences Western Switzerland ; Department of Quantum Matter Physics, University of Geneva, Geneva, Switzerland)

Identifying key players in coupled individual systems is a fundamental problem in network theory. We investigate synchronizable network-coupled dynamical systems such as high-voltage electric power grids and coupled oscillators on complex networks. We define key players as nodes that, once perturbed, generate the largest excursion away from synchrony. A spectral decomposition of the coupling matrix gives an elegant solution to this identification problem. We show that, when the coupling matrix is Laplacian, key players are peripheral in the sense of a centrality measure defined from effective resistance distances. For linearly coupled systems, the ranking is efficiently obtained through a single Laplacian matrix inversion, regardless of the operational synchronous state. The resulting ranking index is termed LRank. When nonlinearities are present, a weighted Laplacian matrix inversion gives another ranking index, WLRank. LRank provides a faithful ranking even for well-developed nonlinearities, corresponding to oscillator angle differences up to approximately Δθ ≲ 40°.


Article Type:
scientifique
Faculty:
Ingénierie et Architecture
School:
HEI-VS
Institute:
Institut Énergie et environnement
Date:
2019-11
Pagination:
10 p.
Published in:
Science Advances
Numeration (vol. no.):
2019, vol. 5, no. 11, article no. eaaw8359
DOI:
ISSN:
2375-2548
ISBN:
978-1-7281-3637-0
Appears in Collection:



 Record created 2020-01-24, last modified 2020-01-24

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