Help
Cart
Skip main navigation

Available Issues

April 12, 2013 - April 13, 2026

Available Issues

April 12, 2013 - April 13, 2026

On Mixed-Integer Programming Formulations for the Unit Commitment Problem

Published Online:25 Jun 2020https://doi.org/10.1287/ijoc.2019.0944

References

  • Anjos MF, Conejo AJ (2017) Unit commitment in electric energy systems. Foundations Trends Electric Energy Systems 1(4):220–310.Google Scholar
  • Arroyo JM, Conejo AJ (2000) Optimal response of a thermal unit to an electricity spot market. IEEE Trans. Power Systems 15(3):1098–1104.Crossref, Google Scholar
  • Atakan S, Lulli G, Sen S (2018) A state transition MIP formulation for the unit commitment problem. IEEE Trans. Power Systems 33(1):736–748.Crossref, Google Scholar
  • Barrows C, Bloom A, Ehlen A, Ikaheimo J, Jorgenson J, Krishnamurthy D, Lau J (2020) The IEEE reliability test system: A proposed 2019 update. IEEE Trans. Power Systems 35(1):119–127.Crossref, Google Scholar
  • Brandenberg R, Huber M, Silbernagl M (2017) The summed start-up costs in a unit commitment problem. EURO J. Comput. Optim. 5(1–2):203–238.Crossref, Google Scholar
  • Carrión M, Arroyo JM (2006) A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Trans. Power Systems 21(3):1371–1378.Google Scholar
  • Castillo A, Laird C, Silva-Monroy CA, Watson JP, O’Neill RP (2016) The unit commitment problem with AC optimal power flow constraints. IEEE Trans. Power Systems 31(6):4853–4866.Crossref, Google Scholar
  • Chen Y, Wang F (2017) MIP formulation improvement for large scale security constrained unit commitment with configuration based combined cycle modeling. Electr. Power Systems Res. 148(July):147–154.Crossref, Google Scholar
  • Chen Y, Casto A, Wang F, Wang Q, Wang X, Wan J (2016) Improving large scale day-ahead security constrained unit commitment performance. IEEE Trans. Power Systems 31(6):4732–4743.Crossref, Google Scholar
  • Damcı-Kurt P, Küçükyavuz S, Rajan D, Atamtürk A (2016) A polyhedral study of production ramping. Math. Programming 158(1–2):175–205.Crossref, Google Scholar
  • Dillon TS, Edwin KW, Kochs HD, Taud R (1978) Integer programming approach to the problem of optimal unit commitment with probabilistic reserve determination. IEEE Trans. Power Apparatus Systems 97(6):2154–2166.Crossref, Google Scholar
  • Frangioni A, Gentile C (2006) Perspective cuts for a class of convex 0–1 mixed integer programs. Math. Programming 106(2):225–236.Crossref, Google Scholar
  • Frangioni A, Gentile C (2015a) An extended MIP formulation for the single-unit commitment problem with ramping constraints. 17th British-French-German Conf. Optim., London, June.Google Scholar
  • Frangioni A, Gentile C (2015b) New MIP formulations for the single-unit commitment problems with ramping constraints. IASI Research Report 15-06, IASI (Istituto di Analisi dei Sistemi ed Informatica), Rome.Google Scholar
  • Frangioni A, Gentile C, Lacalandra F (2009) Tighter approximated MILP formulations for unit commitment problems. IEEE Trans. Power Systems 24(1):105–113.Crossref, Google Scholar
  • Garver LL (1962) Power generation scheduling by integer programming-development of theory. Trans. Amer. Inst. Electr. Engineers Part III: Power Apparatus Systems 81(3):730–734.Google Scholar
  • Gentile C, Morales-Espana G, Ramos A (2017) A tight MIP formulation of the unit commitment problem with start-up and shut-down constraints. EURO J. Comput. Optim. 5(1–2):177–201.Crossref, Google Scholar
  • Guan Y, Pan K, Zhou K (2018) Polynomial time algorithms and extended formulations for unit commitment problems. IISE Trans. 50(8):735–751.Crossref, Google Scholar
  • Gurobi Optimization, Inc (2018) Gurobi optimizer reference manual. Accessed June 17, 2018, https://www.gurobi.com/documentation/.Google Scholar
  • Hart WE, Watson JP, Woodruff DL (2011) Pyomo: Modeling and solving mathematical programs in Python. Math. Programming Comput. 3(3):219–260.Crossref, Google Scholar
  • Hart WE, Laird CD, Watson JP, Woodruff DL, Hackebeil GA, Nicholson BL, Siirola JD (2017) Pyomo—Optimization Modeling in Python, vol. 67, 2nd ed. (Springer Science & Business Media, Cham, Switzerland).Crossref, Google Scholar
  • Hedman KW, O’Neill RP, Oren SS (2009) Analyzing valid inequalities of the generation unit commitment problem. Power Systems Conf. Exposition (IEEE, Piscataway, NJ), 1–6.Google Scholar
  • Hua B, Baldick R (2017) A convex primal formulation for convex hull pricing. IEEE Trans. Power Systems 32(5):3814–3823.Crossref, Google Scholar
  • International Business Machines Corporation (2018) IBM CPLEX optimizer. Accessed June 17, 2018, https://www.ibm.com/analytics/cplex-optimizer.Google Scholar
  • Knueven B, Ostrowski J, Wang J (2018a) The ramping polytope and cut generation for the unit commitment problem. INFORMS J. Comput. 30(4):739–749.Link, Google Scholar
  • Knueven B, Ostrowski J, Watson JP (2018b) Exploiting identical generators in unit commitment. IEEE Trans. Power Systems 33(4):4496–4507.Crossref, Google Scholar
  • Knueven B, Ostrowski J, Watson JP (2020) A novel matching formulation for startup costs in unit commitment. Math. Programming Comput. 12:225–248.Google Scholar
  • Krall E, Higgins M, O’Neill RP (2012) RTO unit commitment test system. Federal Energy Regulatory Commission. Accessed June 17, 2018, https://ferc.gov/legal/staff-reports/rto-COMMITMENT-TEST.pdf.Google Scholar
  • Lee J, Leung J, Margot F (2004) Min-up/min-down polytopes. Discrete Optim. 1(1):77–85.Google Scholar
  • Malkin P (2003) Minimum runtime and stoptime polyhedra. Working paper, CORE, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.Google Scholar
  • Morales-España G, Latorre JM, Ramos A (2013a) Tight and compact MILP formulation for the thermal unit commitment problem. IEEE Trans. Power Systems 28(4):4897–4908.Crossref, Google Scholar
  • 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 Systems 28(2):1288–1296.Crossref, Google Scholar
  • Muckstadt JA, Wilson RC (1968) An application of mixed-integer programming duality to scheduling thermal generating systems. IEEE Trans. Power Apparatus Systems PAS-87(12):1968–1978.Crossref, Google Scholar
  • Nowak MP, Römisch W (2000) Stochastic lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty. Ann. Oper. Res. 100(1–4):251–272.Crossref, Google Scholar
  • O’Neill RP (2017) Computational issues in ISO market models. Presentation, Workshop on Energy Systems and Optimization, November 9--10, Georgia Tech, Atlanta.Google Scholar
  • Ostrowski J, Anjos MF, Vannelli A (2012) Tight mixed integer linear programming formulations for the unit commitment problem. IEEE Trans. Power Systems 27(1):39–46.Crossref, Google Scholar
  • Ostrowski J, Anjos MF, Vannelli A (2015) Modified orbital branching for structured symmetry with an application to unit commitment. Math. Programming 150(1):99–129.Crossref, Google Scholar
  • Pan K, Guan Y (2016) A polyhedral study of the integrated minimum-up/-down time and ramping polytope. Working paper, University of Florida, Gainsville.Google Scholar
  • Pan K, Guan Y (2017) Convex hulls for the unit commitment polytope. Working paper, University of Florida, Gainsville.Google Scholar
  • Queyranne M, Wolsey LA (2017) Tight MIP formulations for bounded up/down times and interval-dependent start-ups. Math. Programming 164(1–2):129–155.Crossref, Google Scholar
  • Rajan D, Takriti S (2005) Minimum up/down polytopes of the unit commitment problem with start-up costs. IBM Research Report RC23628, W0506–W050, IBM, Yorktown Heights, NY.Google Scholar
  • Rothberg E (2018) Personal correspondence, chief executive officer and cofounder, Gurobi Optimization, March 30.Google Scholar
  • Silbernagl M (2016) A polyhedral analysis of start-up process models in unit commitment problems. PhD thesis, Technische Universität München, Munich, Germany.Google Scholar
  • Silbernagl M, Huber M, Brandenberg R (2016) Improving accuracy and efficiency of start-up cost formulations in MIP unit commitment by modeling power plant temperatures. IEEE Trans. Power Systems 31(4):2578–2586.Crossref, Google Scholar
  • Simoglou CK, Biskas PN, Bakirtzis AG (2010) Optimal self-scheduling of a thermal producer in short-term electricity markets by MILP. IEEE Trans. Power Systems 25(4):1965–1977.Crossref, Google Scholar
  • Sridhar S, Linderoth J, Luedtke J (2013) Locally ideal formulations for piecewise linear functions with indicator variables. Oper. Res. Lett. 41(6):627–632.Crossref, Google Scholar
  • Takriti S, Krasenbrink B, Wu LSY (2000) Incorporating fuel constraints and electricity spot prices into the stochastic unit commitment problem. Oper. Res. 48(2):268–280.Link, Google Scholar
  • Van den Bergh K, Delarue E, D’haeseleer W (2014) DC power flow in unit commitment models. TME working paper–energy and environment EN2014-12. Accessed June 17, 2018, https://www.mech.kuleuven.be/en/tme/research/energy_environment/Pdf/wpen2014-12.pdf.Google Scholar
  • Wu L (2016) Accelerating NCUC via binary variable-based locally ideal formulation and dynamic global cuts. IEEE Trans. Power Systems 31(5):4097–4107.Crossref, Google Scholar
  • Yang L, Zhang C, Jian J, Meng K, Xu Y, Dong Z (2017) A novel projected two-binary-variable formulation for unit commitment in power systems. Appl. Energy 187(February):732–745.Crossref, Google Scholar
Previous
Back to Top
Next
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.
Agree