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Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints

Author

Listed:
  • Antonio Frangioni

    (Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy)

  • Claudio Gentile

    (Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti,” C.N.R., Viale Manzoni 30, 00185 Rome, Italy)

Abstract

We present a dynamic programming algorithm for solving the single-unit commitment (1UC) problem with ramping constraints and arbitrary convex cost functions. The algorithm is based on a new approach for efficiently solving the single-unit economic dispatch (ED) problem with ramping constraints and arbitrary convex cost functions, improving on previously known ones that were limited to piecewise-linear functions. For simple convex functions, such as the quadratic ones typically used in applications, the solution cost of all the involved (ED) problems, consisting of finding an optimal primal and dual solution, is O ( n 3 ). Coupled with a special visit of the state-space graph in the dynamic programming algorithm, this approach enables one to solve (1UC) with simple convex functions in O ( n 3 ) overall.

Suggested Citation

  • Antonio Frangioni & Claudio Gentile, 2006. "Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints," Operations Research, INFORMS, vol. 54(4), pages 767-775, August.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:4:p:767-775
    DOI: 10.1287/opre.1060.0309
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    References listed on IDEAS

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    1. A. Belloni & A.L. Lima & M.E. Maceira & C.A. Sagastizábal, 2003. "Bundle Relaxation and Primal Recovery in Unit Commitment Problems. The Brazilian Case," Annals of Operations Research, Springer, vol. 120(1), pages 21-44, April.
    2. C. H. Bannister & R. J. Kaye, 1991. "A Rapid Method for Optimization of Linear Systems with Storage," Operations Research, INFORMS, vol. 39(2), pages 220-232, April.
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    Cited by:

    1. Luis Montero & Antonio Bello & Javier Reneses, 2022. "A Review on the Unit Commitment Problem: Approaches, Techniques, and Resolution Methods," Energies, MDPI, vol. 15(4), pages 1-40, February.
    2. C. Gentile & G. Morales-España & A. Ramos, 2017. "A tight MIP formulation of the unit commitment problem with start-up and shut-down constraints," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 177-201, March.
    3. Haoxiang Yang & Harsha Nagarajan, 2022. "Optimal Power Flow in Distribution Networks Under N – 1 Disruptions: A Multistage Stochastic Programming Approach," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 690-709, March.
    4. Wim Ackooij & Jérôme Malick, 2016. "Decomposition algorithm for large-scale two-stage unit-commitment," Annals of Operations Research, Springer, vol. 238(1), pages 587-613, March.
    5. F. Babonneau & R. T. Foguen & A. Haurie & R. Malhamé, 2021. "Coupling a Power Dispatch Model with a Wardrop or Mean-Field-Game Equilibrium Model," Dynamic Games and Applications, Springer, vol. 11(2), pages 217-241, June.
    6. Fattahi, Salar & Ashraphijuo, Morteza & Lavaei, Javad & Atamtürk, Alper, 2017. "Conic relaxations of the unit commitment problem," Energy, Elsevier, vol. 134(C), pages 1079-1095.
    7. Wim Ackooij, 2014. "Decomposition approaches for block-structured chance-constrained programs with application to hydro-thermal unit commitment," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(3), pages 227-253, December.
    8. Ben Knueven & Jim Ostrowski & Jianhui Wang, 2018. "The Ramping Polytope and Cut Generation for the Unit Commitment Problem," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 739-749, November.
    9. Pascale Bendotti & Pierre Fouilhoux & Cécile Rottner, 2019. "On the complexity of the Unit Commitment Problem," Annals of Operations Research, Springer, vol. 274(1), pages 119-130, March.
    10. Kai Pan & Ming Zhao & Chung-Lun Li & Feng Qiu, 2022. "A Polyhedral Study on Fuel-Constrained Unit Commitment," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3309-3324, November.
    11. Guanglei Wang & Hassan Hijazi, 2018. "Mathematical programming methods for microgrid design and operations: a survey on deterministic and stochastic approaches," Computational Optimization and Applications, Springer, vol. 71(2), pages 553-608, November.
    12. L. A. C. Roque & D. B. M. M. Fontes & F. A. C. C. Fontes, 2014. "A hybrid biased random key genetic algorithm approach for the unit commitment problem," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 140-166, July.
    13. Wim Ackooij & Debora Daniela Escobar & Martin Glanzer & Georg Ch. Pflug, 2020. "Distributionally robust optimization with multiple time scales: valuation of a thermal power plant," Computational Management Science, Springer, vol. 17(3), pages 357-385, October.
    14. Wim Ackooij & Jérôme Malick, 2016. "Decomposition algorithm for large-scale two-stage unit-commitment," Annals of Operations Research, Springer, vol. 238(1), pages 587-613, March.
    15. Fatma Kılınç-Karzan, 2016. "On Minimal Valid Inequalities for Mixed Integer Conic Programs," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 477-510, May.
    16. Xu, Qingyang & Sun, Feihu & Cai, Qiran & Liu, Li-Jing & Zhang, Kun & Liang, Qiao-Mei, 2022. "Assessment of the influence of demand-side responses on high-proportion renewable energy system: An evidence of Qinghai, China," Renewable Energy, Elsevier, vol. 190(C), pages 945-958.

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