New Mixed-Integer Nonlinear Programming Formulations for the Unit Commitment Problems with Ramping Constraints

References

• Arroyo J, Conejo A (2000) Optimal response of response of a thermal unit to an electricity spot market. IEEE Trans. Power Systems 15(3):1098–1104.Crossref, Google Scholar
• Arroyo J, Conejo A (2004) Modeling of start-up and shut-down power trajectories of thermal units. IEEE Trans. Power Systems 19(3):1562–1568.Crossref, Google Scholar
• Bacci T, Frangioni A, Gentile C (2019) A counterexample to an exact extended formulation for the single-unit commitment problem. Technical Report 19-03, IASI–CNR, Rome.Google Scholar
• Bard J (1988) Short-term scheduling of thermal-electric generators using Lagrangian relaxation. Oper. Res. 36(5):765–766.Link, Google Scholar
• Bartholomew E, O’Neill R, Ferris M (2008) Optimal transmission switching. IEEE Trans. Power Systems 23(3):1346–1355.Crossref, Google Scholar
• Bienstock D (2013) Progress on solving power flow problems. Optima 93:1–8.Google Scholar
• Bienstock D, Escobar M, Gentile C, Liberti L (2022) Mathematical programming formulations for the alternating current optimal power flow problem. AOR 314(1):217–315.Google Scholar
• Borghetti A, Frangioni A, Lacalandra F, Nucci C (2003a) Lagrangian heuristics based on disaggregated bundle methods for hydrothermal unit commitment. IEEE Trans. Power Systems 18:313–323.Crossref, Google Scholar
• Borghetti A, Frangioni A, Lacalandra F, Nucci C, Pelacchi P (2003b) Using of a cost-based unit commitment algorithm to assist bidding strategy decisions. Borghetti A, Nucci C, Paolone M, eds. Proc. IEEE 2003 Powerteck Bologna Conf. (IEEE, New York).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
• Bruno S, Di Lullo M, Felici G, Lacalandra F, La Scala M (2014) Tight unit commitment models with optimal transmission switching: Connecting the dots with perturbed objective function. Complexity in Engineering (COMPENG) (IEEE, New York), 1–8.Crossref, Google Scholar
• Carrión M, Arroyo J (2006) A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Trans. Power Systems 21(3):1371–1378.Crossref, Google Scholar
• Castro J, Frangioni A, Gentile C (2014) Perspective reformulations of the CTA problem with L2 distances. Oper. Res. 62(4):891–909.Link, Google Scholar
• D’Ambrosio C, Frangioni A, Gentile C (2019) Strengthening the sequential convex MINLP technique by perspective reformulations. Optim. Lett. 13(4):673–684.Crossref, Google Scholar
• Damci P, Küçükyavuz S, Rajan D, Atamturk A (2016) A polyhedral study of production ramping. Math. Programming 158(1):175–205.Crossref, Google Scholar
• Edmonds J (1971) Matroids and the greedy algorithm. Math. Programming 1(1):127–136.Crossref, Google Scholar
• Fattahi S, Ashraphijuo M, Lavaei J, Atamtürk A (2017) Conic relaxations of the unit commitment problem. Energy 134:1079–1095.Crossref, Google Scholar
• Frangioni A, Gendron B (2013) A stabilized structured Dantzig-Wolfe decomposition method. Math. Programming 140(1):45–76.Crossref, Google Scholar
• Frangioni A, Gentile C (2006a) 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 (2006b) Solving nonlinear single-unit commitment problems with ramping constraints. Oper. Res. 54(4):767–775.Link, Google Scholar
• Frangioni A, Gentile C (2009) A computational comparison of reformulations of the perspective relaxation: SOCP vs. cutting planes. Oper. Res. Lett. 37(3):206–210.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 Conference on Optimization, London.Google Scholar
• Frangioni A, Gentile C (2015b) New MIP formulations for the single-unit commitment problems with ramping constraints. Technical Report 15-06, IASI–CNR, Rome.Google Scholar
• Frangioni A, Furini F, Gentile C (2016) Approximated perspective relaxations: A project & lift approach. Comput. Optim. Appl. 63(3):705–735.Crossref, Google Scholar
• Frangioni A, Furini F, Gentile C (2017) Improving the approximated projected perspective reformulation by dual information. Oper. Res. Lett. 45(5):519–524.Crossref, Google Scholar
• Frangioni A, Gentile C, Hungerford J (2020) Decompositions of semidefinite matrices and the perspective reformulation of nonseparable quadratic programs. Math. Oper. Res. 45(1):15–33.Link, 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
• Frangioni A, Gentile C, Lacalandra F (2011b) Sequential Lagrangian-MILP approaches for unit commitment problems. Internat. J. Electr. Power Energy Systems 33(3):585–593.Crossref, Google Scholar
• Frangioni A, Gentile C, Grande E, Pacifici A (2011a) Projected perspective reformulations with applications in design problems. Oper. Res. 59(5):1225–1232.Link, Google Scholar
• Garver L (1962) Power generation scheduling by integer programming–Development and theory. Trans. Amer. Inst. Electr. Engrg. Part III: Power Apparatus Systems 81(3):730–734.Crossref, Google Scholar
• Gentile C, Morales-España 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):117–201.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
• Guan Y, Pan K, Zhou K (2020) Correction to “polynomial time algorithms and extended formulations for unit commitment problems”. IISE Trans. 52(4):486–487.Google Scholar
• Günlük O, Linderoth J (2008) Perspective relaxation of MINLPs with indicator variables. Lodi A, Panconesi A, Rinaldi G, eds. Proc. 13th IPCO, Lecture Notes in Computer Science, vol. 5035 (Springer-Verlag, New York), 1–16.Google Scholar
• Hijazi H, Bonami P, Cornuéjols G, Ouorou A (2012) Mixed-integer nonlinear programs featuring “on/off” constraints. Comput. Optim. Appl. 52(2):537–558.Crossref, Google Scholar
• Hiriart-Urruty JB, Lemaréchal C (1993) Convex Analysis and Minimization Algorithms I—Fundamentals. Grundlehren der Mathematischen Wissenschaften, vol. 306 (Springer-Verlag, New York).Google Scholar
• Hobbs B, Rothkopf M, O’Neill R, Chao H (2001) The Next Generation of Unit Commitment Models (Kluwer, New York).Crossref, Google Scholar
• Jeon H, Linderoth J, Miller A (2017) Quadratic cone cutting surfaces for quadratic programs with on-off constraints. Discrete Optim. 24:32–50.Crossref, Google Scholar
• Knueven B, Ostrowski J, Wang J (2018) 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 J (2020) On mixed-integer programming formulations for the unit commitment problem. INFORMS J. Comput. 32(4):857–876.Abstract, Google Scholar
• Lasserre J (2010) On representations of the feasible set in convex optimization. Optim. Lett. 4(1):1–5.Crossref, Google Scholar
• Lee J, Leung J, Margot F (2004) Min-up/min-down polytopes. Discrete Optim. 1(1):77–85.Crossref, Google Scholar
• Malkin P, Wolsey L (2004) Minimum runtime and stoptime polyhedra. Manuscript.Google Scholar
• Morales-España G, Gentile C, Ramos A (2015) Tight mip formulations of the power-based unit commitment problem. OR Spectrum 37(4):929–950.Crossref, Google Scholar
• Morales-España G, Latorre J, Ramos A (2013) 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
• Ostrowski J, Anjos M, 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
• Pan K, Guan Y (2016) A polyhedral study of the integrated minimum-up/-down time and ramping polytope. Preprint, submitted April 7, https://arxiv.org/abs/1604.02184.Google Scholar
• Rajan D, Takriti S (2005) Minimum up/down polytopes of the unit commitment problem with start-up costs. Report RC23628, IBM, Armonk, NY.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
• Sioshansi R, O’Neill R, Oren S (2008) Economic consequences of alternative solution methods for centralized unit commitment in day-ahead electricity markets. IEEE Trans. Power Systems 23(2):344–352.Crossref, Google Scholar
• Spliethoff H (2010) Power Generation from Solid Fuels, Power Systems (Springer, Berlin Heidelberg).Crossref, Google Scholar
• Takriti S, Birge J (2000) Using integer programming to refine Lagrangian-based unit commitment solutions. IEEE Trans. Power Systems 15(1):151–156.Crossref, Google Scholar
• Takriti S, Birge JR, Long E (1996) A stochastic model for the unit commitment problem. IEEE Trans. Power Systems 11(3):1497–1508.Crossref, Google Scholar
• Taktak R, D’Ambrosio C (2017) An overview on mathematical programming approaches for the deterministic unit commitment problem in hydro valleys. Energy Systems 8(1):57–79.Crossref, Google Scholar
• van Ackooij W, Danti Lopez I, Frangioni A, Lacalandra F, Tahanan M (2018) Large-scale unit commitment under uncertainty: An updated literature survey. Ann. Oper. Res. 271(1):11–85.Crossref, Google Scholar
• Wei L, Gómez A, Küçükyavuz S (2022) Ideal formulations for constrained convex optimization problems with indicator variables. Math. Programming 192(1–2):57–88.Crossref, Google Scholar
• Wolsey L (1998) Integer Programming (Wiley-Interscience, New York).Google Scholar
• Wood A, Wollenberg B (1996) Power Generation, Operation and Control, 2nd ed. (Wiley, New York).Google Scholar
• Wuijts RH, van den Akker M, van den Broek M (2021) An improved algorithm for single-unit commitment with ramping limits. Electric Power Systems Res. 190:106720.Crossref, Google Scholar
• Xie W, Deng X (2020) Scalable algorithms for the sparse ridge regression. SIAM J. Optim. 30(4):3359–3386.Crossref, Google Scholar
• Zhai Q, Guan X, Gao F (2010) Optimization based production planning with hybrid dynamics and constraints. IEEE Trans. Automat. Control 55(12):2778–2792.Crossref, Google Scholar
• Zhuang F, Galiana F (1988) Toward a more rigorous and practical unit commitment by Lagrangian relaxation. IEEE Trans. Power Systems 3(2):763–773.Crossref, Google Scholar