Abstract
An electric power supplier needs to build a transmission line between two jurisdictions. Ideally, the design of the new electric power line would be such that it maximizes some user-defined utility function, for example, minimizes the construction cost or the environmental impact. Due to reliability considerations, the power line developer has to install not just one, but two transmission lines, separated by a certain distance from one-another, so that even if one of the lines fails, the end user will still receive electricity along the second line. In other words, the optimal placement of the transmission lines corresponds to the topological design of a specialized unorthodox “supply chain”, where the multiple power lines serve towards the system’s resilience against catastrophic failures. We discuss how such a problem can be modeled, and in particular, demonstrate a setting that allows to solve the problem efficiently.
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References
Eppstein, D.: Finding the k shortest paths. In: 35th IEEE Symposium on Foundations of Computer Science, Santa Fe, pp. 154–165 (1994)
El-Amin, I., Al-Ghamdi, F.: An expert system for transmission line route selection. In: International Power Engineering Conference, vol. 2, pp. 697–702. Nanyang Technological University, Singapore (1993)
Garver, L.: Transmission network estimation using linear programming. IEEE Trans. Power Apparatus Syst. PAS-89, 1688–1697 (1970)
Cagigas, C., Madrigal, M.: Centralized vs. competitive transmission expansion planning: the need for new tools. In: Power Engineering Society General Meeting, vol. 2, pp. 13–17. IEEE (2003)
Xie, M., Zhong, J., Wu, F.: Multiyear transmission expansion planning using ordinal optimization. IEEE Trans. Power Syst. 22, 1420–1428 (2007)
Monteiro, C., Miranda, V., Ramirez-Rosado, I., Zorzano-Santamaria, P., Garcia-Garrido, E., Fernandez-Jimenez, L.: Compromise seeking for power line path selection based on economic and environmental corridors. IEEE Trans. Power Syst. 20, 1422–1430 (2005)
Shin, J., Kim, B., Park, J., Lee, K.: A new optimal routing algorithm for loss minimization and voltage stability improvement in radial power systems. IEEE Trans. Power Syst. 22, 636–657 (2007)
Altalink: Transmission Route Selection Process. http://www.altalink.ca/valueoftransmission/route-selection-process.cfm. Accessed 15 June 2015
Great River Energy: 5.0 Transmission Line Route Selection Methodology. http://www.greatriverenergy.com/deliveringelectricity/currentprojects/aml_routeselectionmethodology.pdf. Accessed 15 June 2015
Manitoba-Minnesota Transmission Project – Route Selection Process. https://www.hydro.mb.ca/projects/mb_mn_transmission/2014_r2_mmtp_siting_handout_web2.pdf. Accessed 15 June 2015
Donovan, J.: Georgia Transmission Corporation: a national model for sitting transmission lines. Electric Energy Online.com, Electric Energy T&D Magazine, July/August 2006
Laporte, G., Marín, A., Mesa, J., Perea, F.: Designing robust rapid transit networks with alternative routes. J. Adv. Transp. 45, 54–65 (2011)
Fortz, B., Labbe, M.: Two-connected networks with rings of bounded cardinality. Comput. Optim. Appl. 27, 123–148 (2004)
Fortz, B., Mahjoub, A., McCormick, S., Pesneau, P.: Two-edge connected subgraphs with bounded rings: polyhedral results and branch-and-cut. Math. Program. 105, 85–111 (2006)
Grotschel, M., Monma, C., Stoer, M.: Polyhedral and computational investigations for designing communication networks with high survivability requirements. Oper. Res. 43, 1012–1024 (1995)
Billinton, R., Allan, R.: Reliability Evaluation of Power Systems. Springer, New York (1996). https://doi.org/10.1007/978-1-4899-1860-4
Lisnianski, A., Levitin, G.: Multi-state System Reliability: Assessment, Optimization and Applications. World Scientific, Singapore (2003)
Hassin, R., Megiddo, N.: On orientations and shortest paths. Linear Algebra Appl. 114/115, 589–602 (1989)
Eilam-Tzoreff, T.: The disjoint shortest paths problem. Discrete Appl. Math. 85, 113–138 (1998)
Tutuncu, R., Toh, K., Todd, M.: Solving semidefinite-quadratic-linear programs using SDPT3. Math. Program. 95, 189–217 (2003)
CVX: Matlab software for disciplined convex programming, version 2.1. http://cvxr.com/cvx. Accessed 10 July 2017
Grant, M.C., Boyd, S.P.: Graph implementations for nonsmooth convex programs. In: Blondel, V.D., Boyd, S.P., Kimura, H. (eds.) Recent Advances in Learning and Control. Lecture Notes in Control and Information Sciences, vol. 371, pp. 95–110. Springer, London (2008). https://doi.org/10.1007/978-1-84800-155-8_7
Acknowledgements
We would like to thank Sara Ghandehari Shandiz, PhD student, Department of Chemical and Petroleum Engineering, and Joule Bergerson, Assistant Professor, Chemical and Petroleum Engineering, for introducing a specific instance of a power line routing problem and providing a sample data set. Last, but not least, we would like to sincerely thank the anonymous referees for the invaluable input that hopefully led to an improved version of the manuscript.
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Zinchenko, Y., Song, H., Rosehart, W. (2018). Optimal Transmission Network Topology for Resilient Power Supply. In: Temponi, C., Vandaele, N. (eds) Information Systems, Logistics, and Supply Chain. ILS 2016. Lecture Notes in Business Information Processing, vol 262. Springer, Cham. https://doi.org/10.1007/978-3-319-73758-4_10
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DOI: https://doi.org/10.1007/978-3-319-73758-4_10
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