Non-local impact of link failures in linear flow networks - Kölner UniversitätsPublikationsServer

Strake, Julius, Kaiser, Franz ORCID: 0000-0002-7089-2249, Basiri, Farnaz, Ronellenfitsch, Henrik and Witthaut, Dirk ORCID: 0000-0002-3623-5341 (2019). Non-local impact of link failures in linear flow networks. New J. Phys., 21. BRISTOL: IOP PUBLISHING LTD. ISSN 1367-2630

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DOI:10.1088/1367-2630/ab13ba

Abstract

The failure of a single link can degrade the operation of a supply network up to the point of complete collapse. Yet, the interplay between network topology and locality of the response to such damage is poorly understood. Here, we study how topology affects the redistribution of flow after the failure of a single link in linear flow networks with a special focus on power grids. In particular, we analyze the decay of flow changes with distance after a link failure and map it to the field of an electrical dipole for lattice-like networks. The corresponding inverse-square law is shown to hold for all regular tilings. For sparse networks, a long-range response is found instead. In the case of more realistic topologies, we introduce a rerouting distance, which captures the decay of flow changes better than the traditional geodesic distance. Finally, we are able to derive rigorous bounds on the strength of the decay for arbitrary topologies that we verify through extensive numerical simulations. Our results show that it is possible to forecast flow rerouting after link failures to a large extent based on purely topological measures and that these effects generally decay with distance from the failing link. They might be used to predict links prone to failure in supply networks such as power grids and thus help to construct grids providing a more robust and reliable power supply.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Strake, Julius	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Kaiser, Franz	UNSPECIFIED	orcid.org/0000-0002-7089-2249	UNSPECIFIED
Basiri, Farnaz	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Ronellenfitsch, Henrik	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Witthaut, Dirk	UNSPECIFIED	orcid.org/0000-0002-3623-5341	UNSPECIFIED