A tight MIP formulation of the unit commitment problem with start-up and shut-down constraints

EURO Journal on Computational Optimization - Tập 5 - Trang 177-201 - 2016
C. Gentile1, G. Morales-España2, A. Ramos3
1Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, Consiglio Nazionale delle Ricerche, Roma, Italy
2Department of Electrical Sustainable Energy, Delft University of Technology, Delft, The Netherlands
3Institute for Research in Technology (IIT) of the School of Engineering (ICAI), Universidad Pontificia Comillas, Madrid, Spain.

Tóm tắt

This paper provides the convex hull description of the single thermal Unit Commitment (UC) problem with the following basic operating constraints: (1) generation limits, (2) start-up and shut-down capabilities, and (3) minimum up and down times. The proposed constraints can be used as the core of any unit commitment formulation to strengthen the lower bound in enumerative approaches. We provide evidence that dramatic improvements in computational time are obtained by solving the self-UC problem and the network-constrained UC problem with the new inequalities for different case studies.

Tài liệu tham khảo

Carrion M, Arroyo J (2006) A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Trans Power Syst 21(3):1371–1378 Damci P, Kucukyavuz S, Rajan D, Atamtu A (2015) A polyhedral study of production ramping. Math Progr. doi:10.1007/s10107-015-0919-9 Frangioni A, Gentile C (2006) Solving nonlinear single-unit commitment problems with ramping constraints. Oper Res 54(4):767–775 Frangioni A, Gentile C (2015) An extended mip formulation for the single-unit commitment problem with ramping constraints. In: 17th British-French-German conference on Optimization, London, June 15–17 Frangioni A, Gentile C, Lacalandra F (2008) Solving unit commitment problems with general ramp constraints. Int J Electr Power Energy Syst 30(5):316–326 Frangioni A, Gentile C, Lacalandra F (2009) Tighter approximated MILP formulations for unit commitment problems. IEEE Trans Power Syst 24(1):105–113 Hedman K, Ferris M, O’Neill R, Fisher E, Oren S (2010) Co-Optimization of generation unit commitment and transmission switching with N-1 reliability. IEEE Trans Power Syst 25(2):1052–1063 Knueven B, Ostrowski J, Wang J (2015) Generating cuts from the ramping polytope for the unit commitment problem. http://www.optimization-online.org/DB_HTML/2015/09/5099.html. Accessed 7 Apr 2016 Lee J, Leung J, Margot F (2004) Min-up/min-down polytopes. Discr Optim 1(1):77–85 Malkin P (2003) Minimum runtime and stoptime polyhedra. Manuscript Morales-España G (2014) Unit commitment: computational performance, system representation and wind uncertainty management. Ph.D. thesis, Pontifical Comillas University, KTH Royal Institute of Technology, and Delft University of Technology, Spain Morales-España G, Correa-Posada CM, Ramos A (2015a) Tight and compact MIP formulation of configuration-based combined-cycle units. IEEE Trans Power Syst 31(2): 1–10 Morales-España G, Gentile C, Ramos A (2015b) Tight MIP formulations of the power-based unit commitment problem. OR Spectr 37(4):929–950 Morales-España G, Latorre J, Ramos A (2013a) Tight and compact MILP formulation for the thermal unit commitment problem. IEEE Trans Power Syst 28(4):4897–4908 Morales-España G, Latorre JM, Ramos A (2013b) Tight and compact MILP formulation of start-up and shut-down ramping in unit commitment. IEEE Trans Power Syst 28(2):1288–1296 Morales-España G, Ramos A, Garcia-Gonzalez J (2014) An MIP formulation for joint market-clearing of energy and reserves based on ramp scheduling. IEEE Trans Power Syst 29(1):476–488 Nemhauser GL, Wolsey LA (1999) Integer and combinatorial optimization. Wiley, New York Ostrowski J, Anjos MF, Vannelli A (2012) Tight mixed integer linear programming formulations for the unit commitment problem. IEEE Trans Power Syst 27(1):39–46 Rajan D, Takriti S (2005) Minimum up/down polytopes of the unit commitment problem with start-up costs. Research Report RC23628, IBM. http://domino.research.ibm.com/library/cyberdig.nsf/1e4115aea78b6e7c85256b360066f0d4/cdcb02a7c809d89e8525702300502ac0?OpenDocument. Accessed 7 Apr 2016 Silbernagl M, Huber M, Brandenberg R (2014) Improving accuracy and efficiency of start-up cost formulations in MIP unit commitment by modeling power plant temperatures. IEEE Trans Power Syst PP(99):1–9. doi:10.1109/TPWRS.2015.2450776 Tahanan M, Ackooij Wv, Frangioni A, Lacalandra F (2015) Large-scale Unit Commitment under uncertainty. 4OR 13(2):115–171 Williams HP (2013) Model building in mathematical programming, 5th edn. Wiley, New York Wolsey L (1998) Integer programming. Wiley, New York Wong P, Albrecht P, Allan R, Billinton R, Chen Q, Fong C, Haddad S, Li W, Mukerji R, Patton D, Schneider A, Shahidehpour M, Singh C (1999) The IEEE reliability test system-1996. A report prepared by the reliability test system task force of the application of probability methods subcommittee. IEEE Trans Power Syst 14(3):1010–1020