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ISSN 2542-1905 (Online)

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Khramenkov V. A. On the conditions for safe connection to hub-cluster power grids. Izvestiya VUZ. Applied Nonlinear Dynamics, 2022, vol. 30, iss. 4, pp. 424-435. DOI: 10.18500/0869-6632-2022-30-4-424-435, EDN: CGKJXX

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On the conditions for safe connection to hub-cluster power grids

Khramenkov Vladislav Anatolevich, Institute of Applied Physics of the Russian Academy of Sciences

Purpose of this work is studying of the dynamics of a power grid model that results from the expansion of a highly centralized grid, i.e. a hub-cluster, by adding a small subgrid. The main attention is paid to the study of possible power grid operation regimes and their characteristics. Methods. Numerical simulation of power grid operation, the dynamics of which is described by the Kuramoto equations with inertia, is used. Results. Various power grid operation regimes and the boundaries of their existence in the parameter space are given. The main characteristics of these regimes, such as the probability of realization and the magnitude of oscillations of regime variables, are considered. The conditions for safe connection to hub-cluster power grids are obtained. Conclusion. The dynamics of power grid consisting of two subgrids and its operation regimes are considered. Based on the characteristics of these regimes, their safety for subgrids is determined. The results obtained made it possible to formulate conditions for a safe connection to hub-cluster power grids.

This work was supported by the Scientific and Education Mathematical Center «Mathematics for Future Technologies» (Project No. 075-02-2022-883). The author acknowledges to professor Nekorkin Vladimir Isaakovich and Dmitrichev Aleksey Sergeevich for useful suggestions and discussions of the results
  1. Zhdanov PS. Stability Issues for Electrical Systems. Moscow: Energiya; 1979. 456 p. (in Russian).
  2. Hruschev YV, Zapodovnikov KI, Yushkov AY. Electromechanical Transients in Electric Networks: Training Manual. Tomsk: Tomsk Polytechnic University Publishing; 2012. 160 p. (in Russian).
  3. Sauer PW, Pai MA. Power System Dynamics and Stability. Englewood Cliffs: Prentice-Hall; 1998. 361 p.
  4. Witthaut D, Timme M. Braess’s paradox in oscillator networks, desynchronization and power outage. New J. Phys. 2012;14(8):083036. DOI: 10.1088/1367-2630/14/8/083036.
  5. Manik D, Timme M, Witthaut D. Cycle flows and multistability in oscillatory networks. Chaos. 2017;27(8):083123. DOI: 10.1063/1.4994177.
  6. Coletta T, Jacquod P. Linear stability and the Braess paradox in coupled-oscillator networks and electric power grids. Phys. Rev. E. 2016;93(3):032222. DOI: 10.1103/PhysRevE.93.032222.
  7. Tchuisseu EBT, Gomila D, Colet P, Witthaut D, Timme M, Schafer B. Curing Braess’ paradox by secondary control in power grids. New J. Phys. 2018;20(8):083005. DOI: 10.1088/1367- 2630/aad490.
  8. Witthaut D, Timme M. Nonlocal failures in complex supply networks by single link additions. Eur. Phys. J. B. 2013;86(9):377. DOI: 10.1140/epjb/e2013-40469-4.
  9. Grzybowski JMV, Macau EEN, Yoneyama T. Power-grids as complex networks: Emerging investigations into robustness and stability. In: Edelman M, Macau E, Sanjuan M, editors. Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives. Understanding Complex Systems. Cham: Springer; 2018. P. 287–315. DOI: 10.1007/978-3-319-68109-2_14.
  10. Filatrella G, Nielsen AH, Pedersen NF. Analysis of a power grid using a Kuramoto-like model. Eur. Phys. J. B. 2008;61(4):485–491. DOI: 10.1140/epjb/e2008-00098-8.
  11. Rohden M, Sorge A, Timme M, Witthaut D. Self-organized synchronization in decentralized power grids. Phys. Rev. Lett. 2012;109(6):064101. DOI: 10.1103/PhysRevLett.109.064101.
  12. Motter AE, Myers SA, Anghel M, Nishikawa T. Spontaneous synchrony in power-grid networks. Nat. Phys. 2013;9:191–197. DOI: 10.1038/nphys2535.
  13. Fortuna L, Frasca M, Fiore AS. Analysis of the Italian power grid based on Kuramoto-like model. In: 5th International Conference on Physics and Control (PhysCon 2011). Leon, Spain, 5-8 September 2011. Singapore: World Scientific; 2012. P. 1–5.
  14. Menck PJ, Heitzig J, Kurths J, Schellnhuber HJ. How dead ends undermine power grid stability. Nat. Commun. 2014;5(1):3969. DOI: 10.1038/ncomms4969.
  15. Lozano S, Buzna L, D´iaz-Guilera A. Role of network topology in the synchronization of power systems. Eur. Phys. J. B. 2012;85(7):231. DOI: 10.1140/epjb/e2012-30209-9.
  16. Nishikawa T, Motter AE. Comparative analysis of existing models for power-grid synchronization. New J. Phys. 2015;17(1):015012. DOI: 10.1088/1367-2630/17/1/015012.
  17. Schmietendorf K, Peinke J, Friedrich R, Kamps O. Self-organized synchronization and voltage stability in networks of synchronous machines. Eur. Phys. J. Spec. Top. 2014;223(12):2577–2592. DOI: 10.1140/epjst/e2014-02209-8.
  18. Dmitrichev AS, Zakharov DG, Nekorkin VI. Global stability of a synchronous regime in hub clusters of the power networks. Radiophys. Quantum Electron. 2017;60(6):506–512. DOI: 10.1007/s11141-017-9820-0.
  19. Anvari M, Hellmann F, Zhang X. Introduction to Focus Issue: Dynamics of modern power grids. Chaos. 2020;30(6):063140. DOI: 10.1063/5.0016372.
  20. Gajduk A, Todorovski M, Kocarev L. Stability of power grids: An overview. Eur. Phys. J. Spec. Top. 2014;223(12):2387–2409. DOI: 10.1140/epjst/e2014-02212-1.
  21. Khramenkov VA, Dmitrichev AS, Nekorkin VI. Dynamics and stability of two power grids with hub cluster topologies. Cybernetics and Physics. 2019;8(1):29–33. DOI: 10.35470/2226-4116- 2019-8-1-29-33.
  22. Khramenkov VA, Dmitrichev AS, Nekorkin VI. Threshold stability of the synchronous mode in a power grid with hub cluster topology. Izvestiya VUZ. Applied Nonlinear Dynamics. 2020;28(2):120–139 (in Russian). DOI: 10.18500/0869-6632-2020-28-2-120-139.
  23. Khramenkov V, Dmitrichev A, Nekorkin V. Partial stability criterion for a heterogeneous power grid with hub structures. Chaos, Solitons & Fractals. 2021;152:111373. DOI: 10.1016/j.chaos.2021.111373.
  24. Khramenkov VA, Dmitrichev AS, Nekorkin VI. New scenario of Braess’s paradox in power grids. Chaos. 2022 (submitted).