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A tight MIP formulation of the unit commitment problem with start-up and shut-down constraints

Author

Listed:
  • C. Gentile

    (Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, Consiglio Nazionale delle Ricerche)

  • G. Morales-España

    (Delft University of Technology)

  • A. Ramos

    (Universidad Pontificia Comillas)

Abstract

This paper provides the convex hull description of the single thermal Unit Commitment (UC) problem with the following basic operating constraints: (1) generation limits, (2) start-up and shut-down capabilities, and (3) minimum up and down times. The proposed constraints can be used as the core of any unit commitment formulation to strengthen the lower bound in enumerative approaches. We provide evidence that dramatic improvements in computational time are obtained by solving the self-UC problem and the network-constrained UC problem with the new inequalities for different case studies.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurjco:v:5:y:2017:i:1:d:10.1007_s13675-016-0066-y
    DOI: 10.1007/s13675-016-0066-y
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    References listed on IDEAS

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    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.
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    Cited by:

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    2. Pavičević, Matija & Kavvadias, Konstantinos & Pukšec, Tomislav & Quoilin, Sylvain, 2019. "Comparison of different model formulations for modelling future power systems with high shares of renewables – The Dispa-SET Balkans model," Applied Energy, Elsevier, vol. 252(C), pages 1-1.
    3. Yang, Linfeng & Li, Wei & Xu, Yan & Zhang, Cuo & Chen, Shifei, 2021. "Two novel locally ideal three-period unit commitment formulations in power systems," Applied Energy, Elsevier, vol. 284(C).
    4. Eldridge, B. & O’Neill, R. & Hobbs, B., 2018. "Pricing in Day-Ahead Electricity Markets with Near-Optimal Unit Commitment," Cambridge Working Papers in Economics 1872, Faculty of Economics, University of Cambridge.
    5. 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.
    6. Andersen, Anders N. & Østergaard, Poul Alberg, 2019. "Analytic versus solver-based calculated daily operations of district energy plants," Energy, Elsevier, vol. 175(C), pages 333-344.
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    8. Halmschlager, Daniel & Beck, Anton & Knöttner, Sophie & Koller, Martin & Hofmann, René, 2022. "Combined optimization for retrofitting of heat recovery and thermal energy supply in industrial systems," Applied Energy, Elsevier, vol. 305(C).
    9. Philipsen, Rens & Morales-España, Germán & de Weerdt, Mathijs & de Vries, Laurens, 2019. "Trading power instead of energy in day-ahead electricity markets," Applied Energy, Elsevier, vol. 233, pages 802-815.

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