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Analysis of a power grid using a Kuramoto-like model

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  • G. Filatrella
  • A. H. Nielsen
  • N. F. Pedersen

Abstract

We show that there is a link between the Kuramoto paradigm and another system of synchronized oscillators, namely an electrical power distribution grid of generators and consumers. The purpose of this work is to show both the formal analogy and some practical consequences. The mapping can be made quantitative, and under some necessary approximations a class of Kuramoto-like models, those with bimodal distribution of the frequencies, is most appropriate for the power-grid. In fact in the power-grid there are two kinds of oscillators: the “sources" delivering power to the “consumers". Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Suggested Citation

  • G. Filatrella & A. H. Nielsen & N. F. Pedersen, 2008. "Analysis of a power grid using a Kuramoto-like model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(4), pages 485-491, February.
    • Handle: RePEc:spr:eurphb:v:61:y:2008:i:4:p:485-491
    DOI: 10.1140/epjb/e2008-00098-8
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    Cited by:

    1. Maïzi, Nadia & Mazauric, Vincent & Assoumou, Edi & Bouckaert, Stéphanie & Krakowski, Vincent & Li, Xiang & Wang, Pengbo, 2018. "Maximizing intermittency in 100% renewable and reliable power systems: A holistic approach applied to Reunion Island in 2030," Applied Energy, Elsevier, vol. 227(C), pages 332-341.
    2. Ashkan Nami & José Luis Rodríguez Amenedo & Santiago Arnaltes Gómez & Miguel Ángel Cardiel Álvarez, 2018. "Active Power Filtering Embedded in the Frequency Control of an Offshore Wind Farm Connected to a Diode-Rectifier-Based HVDC Link," Energies, MDPI, vol. 11(10), pages 1-20, October.
    3. Zou, Yanli & Wang, Ruirui & Gao, Zheng, 2020. "Improve synchronizability of a power grid through power allocation and topology adjustment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    4. Ren, Hai-Peng & Song, Jihong & Yang, Rong & Baptista, Murilo S. & Grebogi, Celso, 2016. "Cascade failure analysis of power grid using new load distribution law and node removal rule," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 239-251.
    5. Wang, Xuan & Zheng, Zhigang & Xu, Can, 2023. "Explosive synchronization in phase oscillator populations with attractive and repulsive adaptive interactions," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    6. Ren, Hai-Peng & Gao, Yuan & Huo, Long & Song, Ji-hong & Grebogi, Celso, 2020. "Frequency stability in modern power network from complex network viewpoint," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    7. Lucas Cuadra & Sancho Salcedo-Sanz & Javier Del Ser & Silvia Jiménez-Fernández & Zong Woo Geem, 2015. "A Critical Review of Robustness in Power Grids Using Complex Networks Concepts," Energies, MDPI, vol. 8(9), pages 1-55, August.
    8. Li, Fan & Liu, Shuai & Li, Xiaola, 2023. "Effect of phase shift on the dynamics of a single-machine infinite-bus power system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    9. Arinushkin, P.A. & Vadivasova, T.E., 2021. "Nonlinear damping effects in a simplified power grid model based on coupled Kuramoto-like oscillators with inertia," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Bayani, Atiyeh & Jafari, Sajad & Azarnoush, Hamed & Nazarimehr, Fahimeh & Boccaletti, Stefano & Perc, Matjaž, 2023. "Explosive synchronization dependence on initial conditions: The minimal Kuramoto model," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    11. HyungSeon Oh, 2019. "Analytical solution to swing equations in power grids," PLOS ONE, Public Library of Science, vol. 14(11), pages 1-30, November.
    12. Carlo Bianca, 2022. "On the Modeling of Energy-Multisource Networks by the Thermostatted Kinetic Theory Approach: A Review with Research Perspectives," Energies, MDPI, vol. 15(21), pages 1-22, October.
    13. Frasca, Mattia & Gambuzza, Lucia Valentina, 2021. "Control of cascading failures in dynamical models of power grids," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    14. Zhang, Guidong & Li, Zhong & Zhang, Bo & Halang, Wolfgang A., 2013. "Understanding the cascading failures in Indian power grids with complex networks theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3273-3280.
    15. Lacerda, Juliana C. & Freitas, Celso & Macau, Elbert E.N., 2022. "Elementary changes in topology and power transmission capacity can induce failures in power grids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    16. Yang, Li-xin & Jiang, Jun & Liu, Xiao-jun, 2019. "Impacts of node arrangements on synchronization of a ring oscillatory power network," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 60-65.
    17. Khramenkov, Vladislav & Dmitrichev, Aleksei & Nekorkin, Vladimir, 2021. "Partial stability criterion for a heterogeneous power grid with hub structures," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    18. Antonio Scala & Sakshi Pahwa & Caterina M. Scoglio, 2015. "Cascade failures and distributed generation in power grids," International Journal of Critical Infrastructures, Inderscience Enterprises Ltd, vol. 11(1), pages 27-35.

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