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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barrat, A., Barthelemy, M., Vespignani, A.: The effects of spatial constraints on the evolution of weighted complex networks. J. Stat. Mech. p. 503 (2005)
Barthelemy, M.: Spatial networks. Condens. Matter. Stat. Mech. Phys. Rep. 499, 1–101 (2011). arXiv:1010.0302
Brain Connectivity Toolbox. http://www.brain-connectivity-toolbox.net (2016). Accessed 31 Aug 2016
Caretta Cartozo, C., De Los Rios, P.: Extended navigability of small world networks: exact results and new insights. Phys. Rev. Lett. 102, 238703 (2009)
Erdös, P., Rényi, A.: On random graphs I. Publ. Math. Debrecen 6, 290–297 (1959)
Han, P., Ding, M.: Analysis of cascading failures in small-world power grid. Int. J. Energy Sci. IJES 1(2), 99104 (2011)
Humphries, M.D., Gurney, K.: Network small-world-ness: a quantitative method for determining canonical network equivalence. PLoS One 3, e0002051 (2008)
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)
Kleinberg, J.M.: Navigation in a small world. Nature 406, 845 (2000)
NetworkX. https://networkx.github.io (2016). Accessed 31 Aug 2016
OpenStreetMap. http://www.openstreetmap.org (2016). Accessed 31 Aug 2016
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)
Pagani, G.A., Aiello, M.: The power grid as a complex network: a survey. Phys. A Stat. Mecha. Appl. 392(11) (2011)
Pandit, S.A., Amritkar, R.E.: Random spread on the family of small-world networks. Phys. Rev. E 63 (2001)
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)
Petermann, T., De Los Rios, P.: Physical realizability of small-world networks. Phys. Rev. E 73, 026114 (2006)
Python module to decode/encode Geohashes to/from latitude and longitude. Available at: https://github.com/vinsci/geohash/ (2016). Accessed 31 Aug 2016
Rubinov, M., Sporns, O.: Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52, 1059–1069 (2010)
Services for technological connection: power distribution centers. http://portaltp.fsk-ees.ru/sections/Map/map.jsp (2016). Accessed 31 Aug 2016
Sporns, O., Zwi, J.: The small world of the cerebral cortex. Neuroinformatics 2, 145–162 (2004)
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)
Watts, D.J.: Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton University Press, Princeton, NJ, USA (2003)
Watts, D.J., Strogatz, S.: Collective dynamics of small-world networks. Nature 393, 440–442 (1998)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-56829-4_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-56828-7
Online ISBN: 978-3-319-56829-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)