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Power-Grids as Complex Networks: Emerging Investigations into Robustness and Stability

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Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Power grids are ubiquitous engineering systems composed of tens or even hundreds of interconnected subsystems. Such systems resemble a complex network in the sense that both the link structure and the node dynamics are influential to its overall behavior. Several decades of intensive research on power grids were not enough to uncover the intricacies of stability issues triggered by the structure-dynamics interplay. In this context, several attempts have been made to approach these issues. In this chapter, we review a number of recent results in the topic of robustness and stability in power grids, developed within the framework of the Theory of Complex Networks, especially those concerned with the description of node dynamics by means of the second-order Kuramoto model.

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Notes

  1. 1.

    Following the definition in Ref. [38], a detour at a node u belonging to the shortest path between nodes r and s, \(P_{G}(r,s)=\left\{ r,...,u,v,...,s\right\} \), is defined as the shortest path between u and s that does not go through link (u, v), that is, \(P_{G-(u,v)}(u,s)\).

  2. 2.

    Node adjacent to a dead tree.

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Author information

Authors and Affiliations

  1. UFFS - Federal University of Fronteira Sul, Rodovia RS 135 km 72, Erechim, RS, Brazil

    J. M. V. Grzybowski

  2. INPE - National Institute for Space Research, Av. dos Astronautas, 1758, Jd. Granja, São José dos Campos, SP, Brazil

    Elbert E. N. Macau

  3. ITA - Aeronautics Institute of Technology, Pça. Mal. Eduardo Gomes, 50-Vila das Acácias, São José dos Campos, SP, Brazil

    T. Yoneyama

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  1. J. M. V. Grzybowski
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  2. Elbert E. N. Macau
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  3. T. Yoneyama
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Correspondence to J. M. V. Grzybowski .

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Editors and Affiliations

  1. Stern College for Women, Yeshiva University, New York, New York, USA

    Mark Edelman

  2. INPE/LAC, Instituto Nacional de Pesquisas Espaciai, São José dos Campos, São Paulo, Brazil

    Elbert E. N. Macau

  3. Departamento de Fisica, Universidad Rey Juan Carlos, Móstoles, Madrid, Spain

    Miguel A. F. Sanjuan

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Grzybowski, J.M.V., Macau, E.E.N., Yoneyama, T. (2018). Power-Grids as Complex Networks: Emerging Investigations into Robustness and Stability. In: Edelman, M., Macau, E., Sanjuan, M. (eds) Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-68109-2_14

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