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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
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    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.
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    Cited by:

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    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 Dec 2022.

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