Tighter MIP formulations for the discretised unit commitment problem with min-stop ramping constraints
This paper elaborates compact MIP formulations for a discrete unit commitment problem with minimum stop and ramping constraints. The variables can be defined in two different ways. Both MIP formulations are tightened with clique cuts and local constraints. The projection of constraints from one variable structure to the other allows to compare and tighten the MIP formulations. This leads to several equivalent formulations in terms of polyhedral descriptions and thus in LP relaxations. We analyse how MIP resolutions differ in the efficiency of the cuts, branching and primal heuristics. The resulting MIP implementation allows to tackle real size instances for an industrial application.
KeywordsOR in energy Unit commitment problem Ramping constraints Mixed integer programming Polyhedron Constraint reformulation
Mathematics Subject Classification90C11 Mixed integer programming 90C90 Applications of mathematical programming 90B30 Production models
This paper was written in the Ph.D. thesis (Dupin 2015) financed by the French Defence Procurement Agency of the French Ministry of Defence (DGA). Some results of this paper were presented in the ROADEF 2011 congress organised by the French association for operations research and decision making support. This work was awarded with a prize for junior researchers in the ROADEF 2011 congress. The author addresses special thanks to Pierre-Edouard Adenot and Pierre Bazot for their support, and to Catherine Cook for her help in writing the English version of this paper.
- Beale EML, Tomlin JA (1970) Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. OR 69:447–454Google Scholar
- Cong G, Meyers C, Rajan D, Parriani T (2015) Parallel strategies for solving large unit commitment problems in the California ISO planning model. In: IEEE parallel and distributed processing symposium (IPDPS), pp 710–719Google Scholar
- Damcı-Kurt P, Küçükyavuz S, Rajan, D, Atamtürk A (2013) A polyhedral study of production ramping. Mathematical Programming, pp 1–31Google Scholar
- Dupin N (2015) Modélisation et résolution de grands problèmes stochastiques combinatoires: application à la gestion de production d’électricité. Ph.D. thesis Université Lille 1Google Scholar
- Morales-España G, Latorre JM, Ramos A (2013) Tight and compact MILP formulation for the thermal unit commitment problem. IEEE Trans Power Syst 28(4):4897–4908Google Scholar
- Morales-España G, Latorre JM, Ramos A (2013) Tight and compact MILP formulation formulation of start-up and shut-down ramping in unit commitment. IEEE Trans Power Syst 28(2):1288–1296Google Scholar
- Morales-España G, Gentile C, Ramos A (2015) Tight MIP formulations of the power-based unit commitment problem. OR Spectrum, pp 1–22Google Scholar
- Rajan D, Takriti S (2005) Min-up/down polytopes of the unit commitment problem with start-up costs. Tech. rep, IBM Research ReportGoogle Scholar