Role of network topology in the synchronization of power systems

Regular Article


We study synchronization dynamics in networks of coupled oscillators with bimodal distribution of natural frequencies. This setup can be interpreted as a simple model of frequency synchronization dynamics among generators and loads working in a power network. We derive the minimum coupling strength required to ensure global frequency synchronization. This threshold value can be efficiently found by solving a binary optimization problem, even for large networks. In order to validate our procedure, we compare its results with numerical simulations on a realistic network describing the European interconnected high-voltage electricity system, finding a very good agreement. Our synchronization threshold can be used to test the stability of frequency synchronization to link removals. As the threshold value changes only in very few cases when applied to the approximate model of European network, we conclude that network is resilient in this regard. Since the threshold calculation depends on the local connectivity, it can also be used to identify critical network partitions acting as synchronization bottlenecks. In our stability experiments we observe that when a link removal triggers a change in the critical partition, its limits tend to converge to national borders. This phenomenon, which can have important consequences to synchronization dynamics in case of cascading failure, signals the influence of the uncomplete topological integration of national power grids at the European scale.


Statistical and Nonlinear Physics 


  1. 1.
    I. Dobson, B.A. Carreras, V.E. Lynch, D.E. Newman, Chaos 17, 026103 (2007) ADSCrossRefGoogle Scholar
  2. 2.
    R.V. Solé, M. Rosas-Casals, B. Corominas-Murtra, S. Valverde, Phys. Rev. E 77, 026102 (2008) ADSCrossRefGoogle Scholar
  3. 3.
    L. Buzna, L. Issacharoff, D. Helbing, IJCIS 5, 72 (2009)CrossRefGoogle Scholar
  4. 4.
    V. Rosato, S. Bologna, F. Tiriticco, Electr. Power Syst. Res. 77, 99 (2007)CrossRefGoogle Scholar
  5. 5.
    A.E. Motter, Y.C. Lai, Phys. Rev. E 66, 065102 (2002) ADSCrossRefGoogle Scholar
  6. 6.
    I. Simonsen, L. Buzna, K. Peters, S. Bornholdt, D. Helbing, Phys. Rev. Lett. 100, 218701 (2008) ADSCrossRefGoogle Scholar
  7. 7.
    P. Crucitti, V. Latora, M. Marchiori, Phys. Rev. E 69, 045104 (2004) ADSCrossRefGoogle Scholar
  8. 8.
    P. Hines, E. Cotilla-Sanchez, S. Blumsack, Chaos 20, 033122 (2010) ADSCrossRefGoogle Scholar
  9. 9.
    Z. Qioung, J.W. Bialek, IEEE Trans. Power Syst. 20, 782 (2005)CrossRefGoogle Scholar
  10. 10.
    B. Carreras, D. Newman, I. Dobson, A. Poole, IEEE Trans. Circuits Syst. I 51, 1733 (2004) CrossRefGoogle Scholar
  11. 11.
    S.V. Buldyrev, R. Parshani, G. Paul, H.E. Stanley, S. Havlin, Nature 464, 1025 (2010) ADSCrossRefGoogle Scholar
  12. 12.
    R. Bloomfield, L. Buzna, P. Popov, K. Salako, D. Wright, Lect. Notes Comput. Sci. 6027, 201 (2010) ADSCrossRefGoogle Scholar
  13. 13.
    G. Filatrella, A. Nielsen, N. Pedersen, Eur. Phys. J. B 61, 485 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    L. Buzna, S. Lozano, A. Díaz-Guilera, Phys. Rev. E 80, 066120 (2009) ADSCrossRefGoogle Scholar
  15. 15.
    Q. Zhou, J. Bialek, IEEE Trans. Power Syst. 20, 1663 (2005) CrossRefGoogle Scholar
  16. 16.
    M. Schläpfer, K. Trantopoulos, Phys. Rev. E 81, 056106 (2010) ADSCrossRefGoogle Scholar
  17. 17.
    P. Kundur, J. Paserba, IEEE Trans. Power Syst. 19, 1387 (2003) Google Scholar
  18. 18.
    A. Bergen, D. Hill, IEEE Trans. Power Apparatus Syst. 100, 25 (1981)CrossRefGoogle Scholar
  19. 19.
    V. Latora, M. Marchiori, Phys. Rev. Lett. 87, 198701 (2001) ADSCrossRefGoogle Scholar
  20. 20.
    R. Albert, I. Albert, G.L. Nakarado, Phys. Rev. E 69, 025103 (2004) ADSCrossRefGoogle Scholar
  21. 21.
    D.J. Hill, G. Chen, Proceedings of the IEEE International Symposium on Circuits and Systems, ISCAS (2006), pp. 722–725Google Scholar
  22. 22.
    Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, New York, 1984)Google Scholar
  23. 23.
    F. Dorfler, F. Bullo, SIAM J. Control Optim. (in press)Google Scholar
  24. 24.
    J.A. Acebrón, L.L. Bonilla, R. Spigler, Phys. Rev. E 62, 3437 (2000) MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    J.A. Acebrón, L.L. Bonilla, C.J. Pérez Vicente, F. Ritort, R. Spigler, Rev. Mod. Phys. 77, 137 (2005)ADSCrossRefGoogle Scholar
  26. 26.
    A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Phys. Rep. 469, 93 (2008)MathSciNetADSCrossRefGoogle Scholar
  27. 27.
    S.O. Hisa-Aki Tanaka, Allan J. Lichtenberg, Physica D 100, 279 (1997) ADSMATHCrossRefGoogle Scholar
  28. 28.
    H.A. Tanaka, A.J. Lichtenberg, S. Oishi, Phys. Rev. Lett. 78, 2104 (1997) ADSCrossRefGoogle Scholar
  29. 29.
    Y.P. Choi, S.Y. Ha, S.B. Yun, Physica D 240, 32 (2011)MathSciNetADSMATHCrossRefGoogle Scholar
  30. 30.
    Seung-Yeal Ha, private communication Google Scholar
  31. 31.
    L. Prignano, A. Díaz-Guilera, Phys. Rev. E 85, 036112 (2012) ADSCrossRefGoogle Scholar
  32. 32.
    R. Albert, I. Albert, G.L. Nakarado, Phys. Rev. E 69, 025103 (2004) ADSCrossRefGoogle Scholar
  33. 33.
    R. Kinney, P. Crucitti, R. Albert, V. Latora, Eur. Phys. J. B 46, 101 (2005)ADSCrossRefGoogle Scholar
  34. 34.
    Network Analysis: Methodological Foundations, Lecture Notes in Computer Science, edited by U. Brandes, T. Erlenbach (Springer-Verlag, Berlin, Heidelberg, 2005)Google Scholar
  35. 35.
    UCTE, System Disturbance on 4 November 2006, Final Report, UCTE, 2006Google Scholar
  36. 36.
    A.W.G.L. Nemhauser, Integer and Combinatorial Optimization (John Wiley & Sohn, 1988)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.IPHES, Institut Català de Paleoecologia Humana i Evolució SocialTarragonaSpain
  2. 2.Àrea de Prehistoria, Universitat Rovira i Virgili (URV)TarragonaSpain
  3. 3.ETH Zurich, Clasiusstrasse 50ZurichSwitzerland
  4. 4.Department of Transportation NetworksUniversity of ZilinaZilinaSlovakia
  5. 5.Departament de Física FonamentalUniversitat de BarcelonaBarcelonaSpain

Personalised recommendations