Skip to main content
SpringerLink
Log in

Role of network topology in the synchronization of power systems

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I. Dobson, B.A. Carreras, V.E. Lynch, D.E. Newman, Chaos 17, 026103 (2007)

    Article  ADS  Google Scholar 

  2. R.V. Solé, M. Rosas-Casals, B. Corominas-Murtra, S. Valverde, Phys. Rev. E 77, 026102 (2008)

    Article  ADS  Google Scholar 

  3. L. Buzna, L. Issacharoff, D. Helbing, IJCIS 5, 72 (2009)

    Article  Google Scholar 

  4. V. Rosato, S. Bologna, F. Tiriticco, Electr. Power Syst. Res. 77, 99 (2007)

    Article  Google Scholar 

  5. A.E. Motter, Y.C. Lai, Phys. Rev. E 66, 065102 (2002)

    Article  ADS  Google Scholar 

  6. I. Simonsen, L. Buzna, K. Peters, S. Bornholdt, D. Helbing, Phys. Rev. Lett. 100, 218701 (2008)

    Article  ADS  Google Scholar 

  7. P. Crucitti, V. Latora, M. Marchiori, Phys. Rev. E 69, 045104 (2004)

    Article  ADS  Google Scholar 

  8. P. Hines, E. Cotilla-Sanchez, S. Blumsack, Chaos 20, 033122 (2010)

    Article  ADS  Google Scholar 

  9. Z. Qioung, J.W. Bialek, IEEE Trans. Power Syst. 20, 782 (2005)

    Article  Google Scholar 

  10. B. Carreras, D. Newman, I. Dobson, A. Poole, IEEE Trans. Circuits Syst. I 51, 1733 (2004)

    Article  Google Scholar 

  11. S.V. Buldyrev, R. Parshani, G. Paul, H.E. Stanley, S. Havlin, Nature 464, 1025 (2010)

    Article  ADS  Google Scholar 

  12. R. Bloomfield, L. Buzna, P. Popov, K. Salako, D. Wright, Lect. Notes Comput. Sci. 6027, 201 (2010)

    Article  ADS  Google Scholar 

  13. G. Filatrella, A. Nielsen, N. Pedersen, Eur. Phys. J. B 61, 485 (2008)

    Article  ADS  Google Scholar 

  14. L. Buzna, S. Lozano, A. Díaz-Guilera, Phys. Rev. E 80, 066120 (2009)

    Article  ADS  Google Scholar 

  15. Q. Zhou, J. Bialek, IEEE Trans. Power Syst. 20, 1663 (2005)

    Article  Google Scholar 

  16. M. Schläpfer, K. Trantopoulos, Phys. Rev. E 81, 056106 (2010)

    Article  ADS  Google Scholar 

  17. P. Kundur, J. Paserba, IEEE Trans. Power Syst. 19, 1387 (2003)

    Google Scholar 

  18. A. Bergen, D. Hill, IEEE Trans. Power Apparatus Syst. 100, 25 (1981)

    Article  Google Scholar 

  19. V. Latora, M. Marchiori, Phys. Rev. Lett. 87, 198701 (2001)

    Article  ADS  Google Scholar 

  20. R. Albert, I. Albert, G.L. Nakarado, Phys. Rev. E 69, 025103 (2004)

    Article  ADS  Google Scholar 

  21. D.J. Hill, G. Chen, Proceedings of the IEEE International Symposium on Circuits and Systems, ISCAS (2006), pp. 722–725

  22. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, New York, 1984)

  23. F. Dorfler, F. Bullo, SIAM J. Control Optim. (in press)

  24. J.A. Acebrón, L.L. Bonilla, R. Spigler, Phys. Rev. E 62, 3437 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  25. J.A. Acebrón, L.L. Bonilla, C.J. Pérez Vicente, F. Ritort, R. Spigler, Rev. Mod. Phys. 77, 137 (2005)

    Article  ADS  Google Scholar 

  26. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Phys. Rep. 469, 93 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  27. S.O. Hisa-Aki Tanaka, Allan J. Lichtenberg, Physica D 100, 279 (1997)

    Article  ADS  MATH  Google Scholar 

  28. H.A. Tanaka, A.J. Lichtenberg, S. Oishi, Phys. Rev. Lett. 78, 2104 (1997)

    Article  ADS  Google Scholar 

  29. Y.P. Choi, S.Y. Ha, S.B. Yun, Physica D 240, 32 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Seung-Yeal Ha, private communication

  31. L. Prignano, A. Díaz-Guilera, Phys. Rev. E 85, 036112 (2012)

    Article  ADS  Google Scholar 

  32. R. Albert, I. Albert, G.L. Nakarado, Phys. Rev. E 69, 025103 (2004)

    Article  ADS  Google Scholar 

  33. R. Kinney, P. Crucitti, R. Albert, V. Latora, Eur. Phys. J. B 46, 101 (2005)

    Article  ADS  Google Scholar 

  34. Network Analysis: Methodological Foundations, Lecture Notes in Computer Science, edited by U. Brandes, T. Erlenbach (Springer-Verlag, Berlin, Heidelberg, 2005)

  35. UCTE, System Disturbance on 4 November 2006, Final Report, UCTE, 2006

  36. A.W.G.L. Nemhauser, Integer and Combinatorial Optimization (John Wiley & Sohn, 1988)

Download references

Author information

Authors and Affiliations

  1. IPHES, Institut Català de Paleoecologia Humana i Evolució Social, 43003, Tarragona, Spain

    S. Lozano

  2. Àrea de Prehistoria, Universitat Rovira i Virgili (URV), 43002, Tarragona, Spain

    S. Lozano

  3. ETH Zurich, Clasiusstrasse 50, 8092, Zurich, Switzerland

    S. Lozano

  4. Department of Transportation Networks, University of Zilina, Univerzitna 8215/5, 01026, Zilina, Slovakia

    L. Buzna

  5. Departament de Física Fonamental, Universitat de Barcelona, 08028, Barcelona, Spain

    A. Díaz-Guilera

Authors
  1. S. Lozano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Buzna
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Díaz-Guilera
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Lozano.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lozano, S., Buzna, L. & Díaz-Guilera, A. Role of network topology in the synchronization of power systems. Eur. Phys. J. B 85, 231 (2012). https://doi.org/10.1140/epjb/e2012-30209-9

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2012-30209-9

Keywords

Search

Navigation