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Analysis of Russian Power Transmission Grid Structure: Small World Phenomena Detection

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Models, Algorithms, and Technologies for Network Analysis (NET 2016)

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Abstract

In this paper, the complex network theory is used to analyze the spatial and topological structure of the Unified National Electricity Grid (UNEG)—Russia’s power transmission grid, the major part of which is managed by Federal Grid Company of the Unified energy system. The research is focused on the applicability of the small-world model to the UNEG network. Small-world networks are vulnerable to cascade failure effects what underline importance of the model in power grids analysis. Although much research has been done on the applicability of the small-world model to national power transmission grids, there is no generally accepted opinion on the subject. In this paper we, for the first time, used the latticization algorithm and small-world criterion based on it for transmission grid analysis. Geo-latticization algorithm has been developed for a more accurate analysis of infrastructure networks with geographically referenced nodes. As the result of applying the new method, a reliable conclusion has been made that the small-world model is applicable to the UNEG. Key nodes and links which determine the small-world structure of the UNEG network have been revealed. The key power transmission lines are critical for the reliability of the UNEG network and must be the focal point in preventing large cascade failures.

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References

  1. Barrat, A., Barthelemy, M., Vespignani, A.: The effects of spatial constraints on the evolution of weighted complex networks. J. Stat. Mech. p. 503 (2005)

    Google Scholar 

  2. Barthelemy, M.: Spatial networks. Condens. Matter. Stat. Mech. Phys. Rep. 499, 1–101 (2011). arXiv:1010.0302

    MathSciNet  Google Scholar 

  3. Brain Connectivity Toolbox. http://www.brain-connectivity-toolbox.net (2016). Accessed 31 Aug 2016

  4. Caretta Cartozo, C., De Los Rios, P.: Extended navigability of small world networks: exact results and new insights. Phys. Rev. Lett. 102, 238703 (2009)

    Article  Google Scholar 

  5. Erdös, P., Rényi, A.: On random graphs I. Publ. Math. Debrecen 6, 290–297 (1959)

    MathSciNet  MATH  Google Scholar 

  6. Han, P., Ding, M.: Analysis of cascading failures in small-world power grid. Int. J. Energy Sci. IJES 1(2), 99104 (2011)

    Google Scholar 

  7. Humphries, M.D., Gurney, K.: Network small-world-ness: a quantitative method for determining canonical network equivalence. PLoS One 3, e0002051 (2008)

    Article  Google Scholar 

  8. Kim, C.J., Obah, O.B.: Vulnerability assessment of power grid using graph topological indices. Int. J. Emerg. Electr. Power Syst. 8(6) (2007) (Article 4)

    Google Scholar 

  9. Kleinberg, J.M.: Navigation in a small world. Nature 406, 845 (2000)

    Article  Google Scholar 

  10. NetworkX. https://networkx.github.io (2016). Accessed 31 Aug 2016

  11. OpenStreetMap. http://www.openstreetmap.org (2016). Accessed 31 Aug 2016

  12. Order of the Ministry of Energy of Russia: Shema i programma razvitiya ENES na 2013–2019 godi (Scheme and development program of the UNES on 2013–2019 years). Order of the Ministry of Energy of Russia from 19.06.2013 309 (2013)

    Google Scholar 

  13. Pagani, G.A., Aiello, M.: The power grid as a complex network: a survey. Phys. A Stat. Mecha. Appl. 392(11) (2011)

    Google Scholar 

  14. Pandit, S.A., Amritkar, R.E.: Random spread on the family of small-world networks. Phys. Rev. E 63 (2001)

    Google Scholar 

  15. Pepyne, J.: Topology and cascading line outages in power grids. J. Syst. Sci. Syst. Eng. 16(2) (2007). doi:10.1007/s11518-007-5044-8 (Systems Engineering Society of China & Springer)

  16. Petermann, T., De Los Rios, P.: Physical realizability of small-world networks. Phys. Rev. E 73, 026114 (2006)

    Article  Google Scholar 

  17. Python module to decode/encode Geohashes to/from latitude and longitude. Available at: https://github.com/vinsci/geohash/ (2016). Accessed 31 Aug 2016

  18. Rubinov, M., Sporns, O.: Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52, 1059–1069 (2010)

    Article  Google Scholar 

  19. Services for technological connection: power distribution centers. http://portaltp.fsk-ees.ru/sections/Map/map.jsp (2016). Accessed 31 Aug 2016

  20. Sporns, O., Zwi, J.: The small world of the cerebral cortex. Neuroinformatics 2, 145–162 (2004)

    Article  Google Scholar 

  21. Telesford, Q.K., Joyce, K.E., Hayasaka, S., Burdette, J.H., Laurienti, P.J.: The ubiquity of small-world networks. Brain Connect 1(5), 367–375 (2011)

    Article  Google Scholar 

  22. Watts, D.J.: Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press, Princeton, NJ, USA (2003)

    MATH  Google Scholar 

  23. Watts, D.J., Strogatz, S.: Collective dynamics of small-world networks. Nature 393, 440–442 (1998)

    Article  Google Scholar 

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Correspondence to Sergey Makrushin .

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Makrushin, S. (2017). Analysis of Russian Power Transmission Grid Structure: Small World Phenomena Detection. In: Kalyagin, V., Nikolaev, A., Pardalos, P., Prokopyev, O. (eds) Models, Algorithms, and Technologies for Network Analysis. NET 2016. Springer Proceedings in Mathematics & Statistics, vol 197. Springer, Cham. https://doi.org/10.1007/978-3-319-56829-4_9

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