IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v30y2018i4p739-749.html
   My bibliography  Save this article

The Ramping Polytope and Cut Generation for the Unit Commitment Problem

Author

Listed:
  • Ben Knueven

    (Department of Industrial and Systems Engineering, University of Tennessee, Knoxville, Tennessee 37996)

  • Jim Ostrowski

    (Department of Electrical Engineering at Southern Methodist University, Dallas, Texas 75205)

  • Jianhui Wang

    (Energy Systems Division, Argonne National Laboratory, Lemont, Illinois 60439)

Abstract

We present a perfect formulation for a single generator in the unit commitment problem, inspired by the dynamic programming approach taken by Frangioni and Gentile. This generator can have characteristics such as ramp-up/ramp-down constraints, time-dependent start-up costs, and start-up/shut-down limits. To develop this perfect formulation, we extend the result of Balas on unions of polyhedra to present a framework allowing for flexible combinations of polyhedra using indicator variables. We use this perfect formulation to create a cut-generating linear program, similar in spirit to lift-and-project cuts, and demonstrate computational efficacy of these cuts in a utility-scale unit commitment problem. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0802 .

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:30:y:2018:i:4:p:739-749
    DOI: 10.1287/ijoc.2017.0802
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ijoc.2017.0802
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2017.0802?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Antonio Frangioni & Claudio Gentile, 2006. "Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints," Operations Research, INFORMS, vol. 54(4), pages 767-775, August.
    2. Brian Carlson & Yonghong Chen & Mingguo Hong & Roy Jones & Kevin Larson & Xingwang Ma & Peter Nieuwesteeg & Haili Song & Kimberly Sperry & Matthew Tackett & Doug Taylor & Jie Wan & Eugene Zak, 2012. "MISO Unlocks Billions in Savings Through the Application of Operations Research for Energy and Ancillary Services Markets," Interfaces, INFORMS, vol. 42(1), pages 58-73, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jianqiu Huang & Kai Pan & Yongpei Guan, 2021. "Multistage Stochastic Power Generation Scheduling Co-Optimizing Energy and Ancillary Services," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 352-369, January.
    2. Skolfield, J. Kyle & Escobedo, Adolfo R., 2022. "Operations research in optimal power flow: A guide to recent and emerging methodologies and applications," European Journal of Operational Research, Elsevier, vol. 300(2), pages 387-404.
    3. Panagiotis Andrianesis & Dimitris Bertsimas & Michael C. Caramanis & William W. Hogan, 2020. "Computation of Convex Hull Prices in Electricity Markets with Non-Convexities using Dantzig-Wolfe Decomposition," Papers 2012.13331, arXiv.org, revised Oct 2021.
    4. Conleigh Byers & Brent Eldridge, 2022. "Auction designs to increase incentive compatibility and reduce self-scheduling in electricity markets," Papers 2212.10234, arXiv.org, revised Oct 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Lukas Hümbs & Alexander Martin & Lars Schewe, 2022. "Exploiting complete linear descriptions for decentralized power market problems with integralities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 451-474, June.
    5. Frederic Murphy & Axel Pierru & Yves Smeers, 2016. "A Tutorial on Building Policy Models as Mixed-Complementarity Problems," Interfaces, INFORMS, vol. 46(6), pages 465-481, December.
    6. 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.
    7. 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.
    8. 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.
    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. 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.
    11. 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.
    12. Abiodun, Kehinde & Hood, Karoline & Cox, John L. & Newman, Alexandra M. & Zolan, Alex J., 2023. "The value of concentrating solar power in ancillary services markets," Applied Energy, Elsevier, vol. 334(C).
    13. 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.
    14. John R. Birge, 2022. "George Bernard Dantzig," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 1909-1911, May.
    15. 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.
    16. 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.
    17. Fattahi, Salar & Ashraphijuo, Morteza & Lavaei, Javad & Atamtürk, Alper, 2017. "Conic relaxations of the unit commitment problem," Energy, Elsevier, vol. 134(C), pages 1079-1095.
    18. 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.
    19. Jianqiu Huang & Kai Pan & Yongpei Guan, 2021. "Multistage Stochastic Power Generation Scheduling Co-Optimizing Energy and Ancillary Services," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 352-369, January.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:orijoc:v:30:y:2018:i:4:p:739-749. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.