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      Multistability and anomalies in oscillator models of lossy power grids

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          Abstract

          The analysis of dissipatively coupled oscillators is challenging and highly relevant in power grids. Standard mathematical methods are not applicable, due to the lack of network symmetry induced by dissipative couplings. Here we demonstrate a close correspondence between stable synchronous states in dissipatively coupled oscillators, and the winding partition of their state space, a geometric notion induced by the network topology. Leveraging this winding partition, we accompany this article with an algorithms to compute all synchronous solutions of complex networks of dissipatively coupled oscillators. These geometric and computational tools allow us to identify anomalous behaviors of lossy networked systems. Counterintuitively, we show that loop flows and dissipation can increase the system’s transfer capacity, and that dissipation can promote multistability. We apply our geometric framework to compute power flows on the IEEE RTS-96 test system, where we identify two high voltage solutions with distinct loop flows.

          Abstract

          Dissipatively coupled oscillators, describing lossy flows in power grids, are challenging to analyze due to asymmetry of couplings. Here, Delabays et al. reveal counterintuitive behaviours of increased capacity and increased stability in a network of lossy oscillators.

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          Most cited references52

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          From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators

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            Synchronization in complex networks

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              The IEEE Reliability Test System-1996. A report prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee

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                Author and article information

                Contributors
                robindelabays@ucsb.edu
                Journal
                Nat Commun
                Nat Commun
                Nature Communications
                Nature Publishing Group UK (London )
                2041-1723
                6 September 2022
                6 September 2022
                2022
                : 13
                Affiliations
                [1 ]GRID grid.133342.4, ISNI 0000 0004 1936 9676, Center for Control, Dynamical Systems, and Computation, UC Santa Barbara, ; Santa Barbara, CA 93106-5070 USA
                [2 ]GRID grid.213917.f, ISNI 0000 0001 2097 4943, School of Electrical and Computer Engineering, Georgia Institute of Technology, ; Atlanta, GA 30332-0250 USA
                Article
                32931
                10.1038/s41467-022-32931-8
                9448753
                36068214
                76d5e22b-adce-4008-8685-07e66afd8b13
                © The Author(s) 2022

                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/.

                Funding
                Funded by: FundRef https://doi.org/10.13039/501100001711, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (Swiss National Science Foundation);
                Award ID: P400P2_194359
                Award Recipient :
                Funded by: FundRef https://doi.org/10.13039/100000181, United States Department of Defense | United States Air Force | AFMC | Air Force Office of Scientific Research (AF Office of Scientific Research);
                Award ID: FA9550-22-1-0059
                Award Recipient :
                Categories
                Article
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                © The Author(s) 2022

                Uncategorized
                electrical and electronic engineering,complex networks
                Uncategorized
                electrical and electronic engineering, complex networks

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