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      Dynamically induced cascading failures in power grids

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          Abstract

          Reliable functioning of infrastructure networks is essential for our modern society. Cascading failures are the cause of most large-scale network outages. Although cascading failures often exhibit dynamical transients, the modeling of cascades has so far mainly focused on the analysis of sequences of steady states. In this article, we focus on electrical transmission networks and introduce a framework that takes into account both the event-based nature of cascades and the essentials of the network dynamics. We find that transients of the order of seconds in the flows of a power grid play a crucial role in the emergence of collective behaviors. We finally propose a forecasting method to identify critical lines and components in advance or during operation. Overall, our work highlights the relevance of dynamically induced failures on the synchronization dynamics of national power grids of different European countries and provides methods to predict and model cascading failures.

          Abstract

          Communication networks and power grids may be subject to cascading failures which can lead to outages. Here the authors propose to investigate cascades using dynamical transients of electrical power grids, thereby identifying possible vulnerabilities that might remain undetected with any static approach.

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          Error and attack tolerance of complex networks

          Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. In this paper we demonstrate that error tolerance is not shared by all redundant systems, but it is displayed only by a class of inhomogeneously wired networks, called scale-free networks. We find that scale-free networks, describing a number of systems, such as the World Wide Web, Internet, social networks or a cell, display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected by even unrealistically high failure rates. However, error tolerance comes at a high price: these networks are extremely vulnerable to attacks, i.e. to the selection and removal of a few nodes that play the most important role in assuring the network's connectivity.
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            From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators

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              Catastrophic cascade of failures in interdependent networks

              Many systems, ranging from engineering to medical to societal, can only be properly characterized by multiple interdependent networks whose normal functioning depends on one another. Failure of a fraction of nodes in one network may lead to a failure in another network. This in turn may cause further malfunction of additional nodes in the first network and so on. Such a cascade of failures, triggered by a failure of a small faction of nodes in only one network, may lead to the complete fragmentation of all networks. We introduce a model and an analytical framework for studying interdependent networks. We obtain interesting and surprising results that should significantly effect the design of robust real-world networks. For two interdependent Erdos-Renyi (ER) networks, we find that the critical average degree below which both networks collapse is =2.445, compared to =1 for a single ER network. Furthermore, while for a single network a broader degree distribution of the network nodes results in higher robustness to random failure, for interdependent networks, the broader the distribution is, the more vulnerable the networks become to random failure.
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                Author and article information

                Contributors
                benjamin.schaefer@tu-dresden.de
                marc.timme@tu-dresden.de
                v.latora@qmul.ac.uk
                Journal
                Nat Commun
                Nat Commun
                Nature Communications
                Nature Publishing Group UK (London )
                2041-1723
                17 May 2018
                17 May 2018
                2018
                : 9
                : 1975
                Affiliations
                [1 ]ISNI 0000 0001 2111 7257, GRID grid.4488.0, Chair for Network Dynamics, Center for Advancing Electronics Dresden (cfaed) and Institute for Theoretical Physics, , Technical University of Dresden, ; 01062 Dresden, Germany
                [2 ]ISNI 0000 0004 0491 5187, GRID grid.419514.c, Network Dynamics, , Max Planck Institute for Dynamics and Self-Organization (MPIDS), ; 37077 Göttingen, Germany
                [3 ]Forschungszentrum Jülich, Institute for Energy and Climate Research - Systems Analysis and Technology Evaluation (IEK-STE), 52428 Jülich, Germany
                [4 ]ISNI 0000 0000 8580 3777, GRID grid.6190.e, Institute for Theoretical Physics, , University of Cologne, ; 50937 Köln, Germany
                [5 ]ISNI 0000 0001 2171 1133, GRID grid.4868.2, School of Mathematical Sciences, , Queen Mary University of London, ; London, E1 4NS UK
                [6 ]ISNI 0000 0004 1757 1969, GRID grid.8158.4, Dipartimento di Fisica ed Astronomia, , Università di Catania and INFN, ; 95123 Catania, Italy
                Author information
                http://orcid.org/0000-0003-1607-9748
                http://orcid.org/0000-0002-3623-5341
                http://orcid.org/0000-0002-0984-8038
                Article
                4287
                10.1038/s41467-018-04287-5
                5958123
                29773793
                480e4c78-5628-48d7-bc97-bf026d74eccc
                © The Author(s) 2018

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

                History
                : 15 August 2017
                : 11 April 2018
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