Polynomial time algorithms and extended formulations for unit commitment problems

References

• Balas, E. (1979) Disjunctive programming. Annals of Discrete Mathematics, 5, 3–51.
   Google Scholar
• Balas, E. (1998) Disjunctive programming: Properties of the convex hull of feasible points. Discrete Applied Mathematics, 89(1), 3–44.
   Web of Science ®Google Scholar
• Bixby, R.E. (2010) Mixed-integer programming: It works better than you may think, in Proceedings of the FERC Conference. Available from: https://www.ferc.gov/CalendarFiles/20100609110044-Bixby,https://%20Gurobi%20Optimization.pdf and https://www.ferc.gov/EventCalendar/EventDetails.aspx?ID=5182&CalType=%20&CalendarID=116&Date=06/02/2010&View=Listview.
   Google Scholar
• Carlson, B., Chen, Y., Hong, M., Jones, R., Larson, K., Ma, X. … Zak, E. (2012) MISO unlocks billions in savings through the application of operations research for energy and ancillary services markets. Interfaces, 42(1), 58–73.
   Web of Science ®Google Scholar
• Carrión, M. and Arroyo, J.M. (2006) A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Transactions on Power Systems, 21(3), 1371–1378.
   Web of Science ®Google Scholar
• Cheng, C.P., Liu, C.W. and Liu, C.C. (2000) Unit commitment by Lagrangian relaxation and genetic algorithms. IEEE Transactions on Power Systems, 15(2), 707–714.
   Web of Science ®Google Scholar
• Damcı-Kurt, P., Küçükyavuz, S., Rajan, D. and Atamtürk, A. (2016) A polyhedral study of production ramping. Mathematical Programming, 158(1–2), 175–205.
   Web of Science ®Google Scholar
• De la Torre, S., Arroyo, J.M., Conejo, A.J. and Contreras, J. (2002) Price maker self-scheduling in a pool-based electricity market: A mixed-integer LP approach. IEEE Transactions on Power Systems, 17(4), 1037–1042.
   Web of Science ®Google Scholar
• Frangioni, A. and Gentile, C. (2006) Solving nonlinear single-unit commitment problems with ramping constraints. Operations Research, 54(4), 767–775.
   Web of Science ®Google Scholar
• Frangioni, A., Gentile, C. and Lacalandra, F. (2009) Tighter approximated MILP formulations for unit commitment problems. IEEE Transactions on Power Systems, 24(1), 105–113.
   Web of Science ®Google Scholar
• Fu, Y. and Shahidehpour, M. (2007) Fast SCUC for large-scale power systems. IEEE Transactions on Power Systems, 22(4), 2144–2151.
   Web of Science ®Google Scholar
• Garver, L.L. (1962) Power generation scheduling by integer programming-development of theory. IEEE Transactions on Power Apparatus and Systems, 81(3), 730–734.
   Google Scholar
• Jabr, R.A. (2012) Tight polyhedral approximation for mixed-integer linear programming unit commitment formulations. IET Generation, Transmission & Distribution, 6(11), 1104–1111.
   Web of Science ®Google Scholar
• Jiang, R., Guan, Y. and Watson, J.-P. (2016) Cutting planes for the multistage stochastic unit commitment problem. Mathematical Programming, 157(1), 121–151.
   Web of Science ®Google Scholar
• Kazarlis, S.A., Bakirtzis, A.G. and Petridis, V. (1996) A genetic algorithm solution to the unit commitment problem. IEEE Transactions on Power Systems, 11(1), 83–92.
   Web of Science ®Google Scholar
• Knueven, B., Ostrowski, J. and Wang, J. (2016) Generating cuts from the ramping polytope for the unit commitment problem. Technical Report, University of Tennessee. Available from: http://www.optimization-online.org/DB_HTML/2015/09/5099.html. [29 July 2016].
   Google Scholar
• Lee, J., Leung, J. and Margot, F. (2004) Min-up/min-down polytopes. Discrete Optimization, 1(1), 77–85.
   Google Scholar
• Lowery, P.G. (1966) Generating unit commitment by dynamic programming. IEEE Transactions on Power Apparatus and Systems, PAS-85 (5), 422–426.
   Google Scholar
• Mantawy, A.H., Abdel-Magid, Y.L. and Selim, S.Z. (1998) A simulated annealing algorithm for unit commitment. IEEE Transactions on Power Systems, 13(1), 197–204.
   Web of Science ®Google Scholar
• Nemhauser, G.L. (2013) Integer programming: Global impact. Available at: https://smartech.gatech.edu/bitstream/handle/1853/49829/presentation.pdf?sequence=1. [29 July 2016].
   Google Scholar
• Ostrowski, J., Anjos, M.F. and Vannelli, A. (2012) Tight mixed integer linear programming formulations for the unit commitment problem. IEEE Transactions on Power Systems, 27(1), 39–46.
   Web of Science ®Google Scholar
• Padhy, N.P. (2004) Unit commitment—A bibliographical survey. IEEE Transactions on Power Systems, 19(2), 1196–1205.
   Web of Science ®Google Scholar
• Pan, K. and Guan, Y. (2015) A polyhedral study of the integrated minimum-up/-down time and ramping polytope. Technical Report, University of Florida.
   Google Scholar
• Papavasiliou, A. and Oren, S.S. (2013) Multiarea stochastic unit commitment for high wind penetration in a transmission constrained network. Operations Research, 61(3), 578–592.
   Web of Science ®Google Scholar
• Queyranne, M. and Wolsey, L.A. (2017) Tight MIP formulations for bounded up/down times and interval-dependent start-ups. Mathematical Programming, 164(1–2), 129–155.
   Web of Science ®Google Scholar
• Rahman, D.F., Viana, A. and Pedroso, J.P. (2014) Metaheuristic search based methods for unit commitment. International Journal of Electrical Power & Energy Systems, 59, 14–22.
   Web of Science ®Google Scholar
• Rajan, D. and Takriti, S. (2005) Minimum up/down polytopes of the unit commitment problem with start-up costs. IBM, Research Report RC23628. Available from: http://domino.research.ibm.com/library/cyberdig.nsf/1e4115aea78b6e7c85256b360066f0d4/cdcb02a7c809d89e8525702300502ac0?OpenDocument.
   Google Scholar
• Roque, L.A.C., Fontes, D.B.M.M. and Fontes, F.A.C.C. (2014) A hybrid biased random key genetic algorithm approach for the unit commitment problem. Journal of Combinatorial Optimization, 28(1), 140–166.
   Web of Science ®Google Scholar
• Roy, P.K. (2013) Solution of unit commitment problem using gravitational search algorithm. International Journal of Electrical Power & Energy Systems, 53, 85–94.
   Web of Science ®Google Scholar
• Saravanan, B., Das, S., Sikri, S. and Kothari, D.P. (2013) A solution to the unit commitment problem—A review. Frontiers in Energy, 7(2), 223–236.
   Google Scholar
• Shapiro, A., Dentcheva, D. and Ruszczyński, A. (2009) Lectures on Stochastic Programming: Modeling and Theory, Society for Industrial and Applied Mathematics, Philadelphia, PA.
   Google Scholar
• Snyder, W.L., Powell, H.D. and Rayburn, J.C. (1987) Dynamic programming approach to unit commitment. IEEE Transactions on Power Systems, 2(2), 339–348.
   Web of Science ®Google Scholar
• Swarup, K.S. and Yamashiro, S. (2002) Unit commitment solution methodology using genetic algorithm. IEEE Transactions on Power Systems, 17(1), 87–91.
   Web of Science ®Google Scholar
• Viana, A. and Pedroso, J.P. (2013) A new MILP-based approach for unit commitment in power production planning. International Journal of Electrical Power & Energy Systems, 44(1), 997–1005.
   Web of Science ®Google Scholar
• Wu, L. (2011) A tighter piecewise linear approximation of quadratic cost curves for unit commitment problems. IEEE Transactions on Power Systems, 26(4), 2581–2583.
   Web of Science ®Google Scholar
• Zheng, Q.P., Wang, J., Pardalos, P.M. and Guan, Y. (2013) A decomposition approach to the two-stage stochastic unit commitment problem. Annals of Operations Research, 210(1), 387–410.
   Web of Science ®Google Scholar
• Zhuang, F. and Galiana, F.D. (1988) Towards a more rigorous and practical unit commitment by Lagrangian relaxation. IEEE Transactions on Power Systems, 3(2), 763–773.
   Web of Science ®Google Scholar
• Zhuang, F. and Galiana, F.D. (1990) Unit commitment by simulated annealing. IEEE Transactions on Power Systems, 5(1), 311–318.
   Web of Science ®Google Scholar