Network centrality measures for classifying important components in electrical power systems based on linegraph transformation
Main Article Content
Abstract
Network theory techniques have recently contributed to the analysis of electrical power systems, enabling faster computational solutions. Taking advantage of the topological information of a network, it becomes possible to characterize its elements both locally (individual network components) and globally (interactions and behavior of the components). Identifying the crucial elements within an electrical system involves classifying each component based on its interaction with the entire network, considering, possibly, various operating conditions. Current network centrality measures predominantly focus on nodes, which represent connection buses in the system, to quantify the significance of individual elements. In this study, we employ the linegraph technique to transform links into nodes. Subsequently, we calculate and categorize the links (representing lines and transformers) of different electrical networks found in the literature using three centrality measures. Moreover, our methodology allows for the aggregation or combination of the indices from each measure, leading to a unified classification based on the importance of links in the considered electrical power systems. Analyzing diverse networks reveals a consistent empirical distribution of centrality indices, resulting in similar classifications of significant elements regardless of network size.
Keywords
Centrality measures, electrical networks, linegraph, link classification clasificación de enlaces, linegraph, medidas de centralidad, redes eléctricas
References
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[2] J. Arroyo and F. Galiana, “On the solution of the bilevel programming formulation of the terrorist threat problem,” IEEE Transactions on Power Systems, vol. 20, no. 2, pp. 789–797, 2005. [Online]. Available: https://doi.org/10.1109/TPWRS.2005.846198
[3] C. Rocco, J. Ramírez-Márquez, D. Salazar, and C. Yajure, “Análisis preliminar de la vulnerabilidad de un sistema de potencia mediante interdicción determinista multiobjetivo,” Revista de la Facultad de Ingeniería Universidad Central de Venezuela, vol. 25, pp. 61–69, 03 2010. [Online]. Available: https://bit.ly/46JapWe
[4] A. M. Amani and M. Jalili, “Power grids as complex networks: Resilience and reliability analysis,” IEEE Access, vol. 9, pp. 119 010–119 031, 2021. [Online]. Available: https://doi.org/10.1109/ACCESS.2021.3107492
[5] X. Chen, K. Sun, Y. Cao, and S. Wang, “Identification of vulnerable lines in power grid based on complex network theory,” in 2007 IEEE Power Engineering Society General Meeting, 2007. [Online]. Available: https://doi.org/10.1109/PES.2007.385733
[6] A. B. M. Nasiruzzaman and H. R. Pota, “Transient stability assessment of smart power system using complex networks framework,” in 2011 IEEE Power and Energy Society General Meeting, 2011. [Online]. Available: https://doi.org/10.1109/PES.2011.6038970
[7] U. Nakarmi, M. Rahnamay Naeini, M. J. Hossain, and M. A. Hasnat, “Interaction graphs for cascading failure analysis in power grids: A survey,” Energies, vol. 13, no. 9, 2020. [Online]. Available: https://doi.org/10.3390/en13092219
[8] C. M and R. S, “Análisis del sistema eléctrico venezolano desde la perspectiva de la teoría de redes complejas,” Revista de la Facultad de Ingeniería Universidad Central de Venezuela, vol. 23, pp. 103–109, 03 2008. [Online]. Available: https://bit.ly/3t2BIgk
[9] M. Newman, Networks: An Introduction (1st edn). Oxford Academic, 2010. [Online]. Available: https://doi.org/10.1093/acprof:oso/9780199206650.001.0001
[10] T. Bröhl and K. Lehnertz, “Centrality-based identification of important edges in complex networks,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 29, no. 3, Mar. 2019. [Online]. Available: http://dx.doi.org/10.1063/1.5081098
[11] R. Ortiz-Gaona, M. Postigo-Boix, and J. L. Melus-Moreno, “Centrality metrics and line-graph to measure the importance of links in online social networks,” International Journal of New Technology and Research, vol. 2, no. 12, 12 2016. [Online]. Available: https://bit.ly/3Ru4rnR
[12] O. de la Cruz Cabrera, M. Matar, and L. Reichel, “Edge importance in a network via line graphs and the matrix exponential,” Numerical Algorithms, vol. 83, no. 2, pp. 807–832, Feb 2020. [Online]. Available: https://doi.org/10.1007/s11075-019-00704-y
[13] F. Harary, Graph Theory. Addison-Wesley Publishing Company. University of Minnesota, 1969. [Online]. Available: https://bit.ly/4a9HYDV
[14] V. Pihur, S. Datta, and S. Datta, “Rankaggreg, an R package for weighted rank aggregation,” BMC Bioinformatics, vol. 10, no. 1, p. 62, Feb 2009. [Online]. Available: https://doi.org/10.1186/1471-2105-10-62
[15] P. Crucitti, V. Latora, and M. Marchiori, “A topological analysis of the italian electric power grid,” Physica A: Statistical Mechanics and its Applications, vol. 338, no. 1, pp. 92–97, 2004, proceedings of the conference A Nonlinear World: the Real World, 2nd International Conference on Frontier Science. [Online]. Available: https://doi.org/10.1016/j.physa.2004.02.029
[16] P. Hines and S. Blumsack, “A centrality measure for electrical networks,” in Proceedings of the 41st Annual Hawaii International Conference on System Sciences (HICSS 2008), 2008, pp. 185–185. [Online]. Available: https://doi.org/10.1109/HICSS.2008.5
[17] K. Stephenson and M. Zelen, “Rethinking centrality: Methods and examples,” Social Networks, vol. 11, no. 1, pp. 1–37, 1989. [Online]. Available: https://doi.org/10.1016/0378-8733(89)90016-6
[18] S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications, ser. Structural Analysis in the Social Sciences. Cambridge University Press, 1994. [Online]. Available: https://doi.org/10.1017/CBO9780511815478
[19] A. B. M. Nasiruzzaman, H. R. Pota, and M. A. Mahmud, “Application of centrality measures of complex network framework in power grid,” in IECON 2011 - 37th Annual Conference of the IEEE Industrial Electronics Society, 2011, pp. 4660–4665. [Online]. Available: https://doi.org/10.1109/IECON.2011.6120079
[20] S. Arianos, E. Bompard, A. Carbone, and F. Xue, “Power grid vulnerability: A complex network approach,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 19, no. 1, p. 013119, Feb 2009. [Online]. Available: https://doi.org/10.1063/1.3077229
[21] K. Wang, B. Zhang, Z. Zhang, X. Yin, and B. Wang, “An electrical betweenness approach for vulnerability assessment of power grids considering the capacity of generators and load,” Physica A: Statistical Mechanics and its Applications, vol. 390, no. 23, pp. 4692–4701, 2011. [Online]. Available: https://doi.org/10.1016/j.physa.2011.07.031
[22] E. Bompard, R. Napoli, and F. Xue, “Analysis of structural vulnerabilities in power transmission grids,” International Journal of Critical Infrastructure Protection, vol. 2, no. 1, pp. 5–12, 2009. [Online]. Available: https://doi.org/10.1016/j.ijcip.2009.02.002
[23] R. Herrero and M. Herrero, “La terminología del análisis de redes. Problemas de definición y de traducción,” Política y sociedad, 2000, vol. 33, 01 2000. [Online]. Available: https://bit.ly/46P6IOK
[24] M. E. J. Newman, “Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality,” Phys. Rev. E, vol. 64, p. 016132, Jun 2001. [Online]. Available: https://doi.org/10.1103/PhysRevE.64.016132
[25] M. Aruldoss, M. Lakshmi, and V. P. Venkatesan, “A survey on multi criteria decision making methods and its applications,” Science and Education Publishing, vol. 11, pp. 31–43, 2013. [Online]. Available: https://bit.ly/3GO3wbP
[26] R. Core Team, R: A language and environment for statistical computing. Foundation for Statistical Computing, Vienna, Austria, 2022. [Online]. Available: https://bit.ly/484HuNg
[27] V. Pihur, S. Datta, and S. Datta, “Weighted rank aggregation of cluster validation measures: a Monte Carlo cross-entropy approach,” Bioinformatics, vol. 23, no. 13, pp. 1607–1615, 2007. [Online]. Available: https://doi.org/10.1093/bioinformatics/btm158
[28] G. Csardi and T. Nepusz, “The igraph software package for complex network research,” Inter-Journal, vol. Complex Systems, p. 1695, 11 2005. [Online]. Available: https://bit.ly/3TdyNfs
[29] C. M. Rocco, K. Barker, and J. Moronta, “Determining the best algorithm to detect community structures in networks: application to power systems,” Environment Systems and Decisions, vol. 42, pp. 251–264, 2022. [Online]. Available: https://doi.org/10.1007/s10669-021-09833-z
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Jan 23, 2024
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Electrical Engineering
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