Non-local impact of link failures in linear flow networks
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 fail...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2019-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ab13ba |
| _version_ | 1797750167150002176 |
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| author | Julius Strake Franz Kaiser Farnaz Basiri Henrik Ronellenfitsch Dirk Witthaut |
| author_facet | Julius Strake Franz Kaiser Farnaz Basiri Henrik Ronellenfitsch Dirk Witthaut |
| author_sort | Julius Strake |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:28:48Z |
| format | Article |
| id | doaj.art-c3868ed767e648fc95afda13ad878369 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:28:48Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-c3868ed767e648fc95afda13ad8783692023-08-08T15:35:59ZengIOP PublishingNew Journal of Physics1367-26302019-01-0121505300910.1088/1367-2630/ab13baNon-local impact of link failures in linear flow networksJulius Strake0Franz Kaiser1https://orcid.org/0000-0002-7089-2249Farnaz Basiri2Henrik Ronellenfitsch3Dirk Witthaut4https://orcid.org/0000-0002-3623-5341Forschungszentrum Jülich, Institute for Energy and Climate Research—Systems Analysis and Technology Evaluation (IEK-STE), D-52428 Jülich, Germany; University of Cologne , Institute for Theoretical Physics, D-50937 Köln, GermanyForschungszentrum Jülich, Institute for Energy and Climate Research—Systems Analysis and Technology Evaluation (IEK-STE), D-52428 Jülich, Germany; University of Cologne , Institute for Theoretical Physics, D-50937 Köln, GermanyForschungszentrum Jülich, Institute for Energy and Climate Research—Systems Analysis and Technology Evaluation (IEK-STE), D-52428 Jülich, GermanyDepartment of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of AmericaForschungszentrum Jülich, Institute for Energy and Climate Research—Systems Analysis and Technology Evaluation (IEK-STE), D-52428 Jülich, Germany; University of Cologne , Institute for Theoretical Physics, D-50937 Köln, GermanyThe 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.https://doi.org/10.1088/1367-2630/ab13bacomplex networksnetwork flowspower gridslink failure |
| spellingShingle | Julius Strake Franz Kaiser Farnaz Basiri Henrik Ronellenfitsch Dirk Witthaut Non-local impact of link failures in linear flow networks New Journal of Physics complex networks network flows power grids link failure |
| title | Non-local impact of link failures in linear flow networks |
| title_full | Non-local impact of link failures in linear flow networks |
| title_fullStr | Non-local impact of link failures in linear flow networks |
| title_full_unstemmed | Non-local impact of link failures in linear flow networks |
| title_short | Non-local impact of link failures in linear flow networks |
| title_sort | non local impact of link failures in linear flow networks |
| topic | complex networks network flows power grids link failure |
| url | https://doi.org/10.1088/1367-2630/ab13ba |
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