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Fix-and-optimize procedures for solving the long-term unit commitment problem with pumped storages

Author

Listed:
  • Alexander Franz

    (Clausthal University of Technology)

  • Julia Rieck

    (University of Hildesheim)

  • Jürgen Zimmermann

    (Clausthal University of Technology)

Abstract

In this paper, we consider a long-term unit commitment problem with thermal and renewable energy sources, where system operating costs have to be minimized. The problem is enhanced by adding pumped storages, where water is stored in reservoirs, being turbinated or pumped up if it is beneficial in terms of reducing the operating costs. We present a tight mixed-integer linear programming model with a redefinition of decision variables and a reformulation of constraints, e.g., for the spinning reserve. The model serves as a basis for a new decomposition method, where fix-and-optimize schemes are used. In particular, a time-oriented, a unit-oriented, and a generic fix-and-optimize procedure are presented. A computational performance analysis shows that the mixed-integer linear model is efficient in supporting the solution process for small- and medium-scale instances. Furthermore, the fix-and-optimize procedures are able to tackle even large-scale instances. Particularly, problem instances with real-world energy demands, power plant-specific characteristics, and a one-year planning horizon with hourly time steps are solved to near-optimality in reasonable time.

Suggested Citation

  • Alexander Franz & Julia Rieck & Jürgen Zimmermann, 2019. "Fix-and-optimize procedures for solving the long-term unit commitment problem with pumped storages," Annals of Operations Research, Springer, vol. 274(1), pages 241-265, March.
    • Handle: RePEc:spr:annopr:v:274:y:2019:i:1:d:10.1007_s10479-018-2900-5
    DOI: 10.1007/s10479-018-2900-5
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    References listed on IDEAS

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    1. Christoph Weber, 2005. "Uncertainty in the Electric Power Industry," International Series in Operations Research and Management Science, Springer, number 978-0-387-23048-1, September.
    2. Rieck, Julia & Ehrenberg, Carsten & Zimmermann, Jürgen, 2014. "Many-to-many location-routing with inter-hub transport and multi-commodity pickup-and-delivery," European Journal of Operational Research, Elsevier, vol. 236(3), pages 863-878.
    3. Helber, Stefan & Sahling, Florian, 2010. "A fix-and-optimize approach for the multi-level capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 123(2), pages 247-256, February.
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    5. Niknam, Taher & Khodaei, Amin & Fallahi, Farhad, 2009. "A new decomposition approach for the thermal unit commitment problem," Applied Energy, Elsevier, vol. 86(9), pages 1667-1674, September.
    6. Ralf Gollmer & Matthias Nowak & Werner Römisch & Rüdiger Schultz, 2000. "Unit commitment in power generation – a basic model and some extensions," Annals of Operations Research, Springer, vol. 96(1), pages 167-189, November.
    7. Jebaraj, S. & Iniyan, S., 2006. "A review of energy models," Renewable and Sustainable Energy Reviews, Elsevier, vol. 10(4), pages 281-311, August.
    8. 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.
    9. Möst, Dominik & Keles, Dogan, 2010. "A survey of stochastic modelling approaches for liberalised electricity markets," European Journal of Operational Research, Elsevier, vol. 207(2), pages 543-556, December.
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    Cited by:

    1. Zhu, Yongqiu & Goverde, Rob M.P., 2020. "Integrated timetable rescheduling and passenger reassignment during railway disruptions," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 282-314.
    2. Alexander Franz & Julia Rieck & Jürgen Zimmermann, 2020. "A long-term unit commitment problem with hydrothermal coordination for economic and emission control in large-scale electricity systems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(1), pages 235-259, March.

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    More about this item

    Keywords

    Unit commitment problem; Pumped storages; Hydrothermal coordination; Volatile residual demand patterns; Mixed-integer linear programming model; Fix-and-optimize procedure;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • Q41 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Demand and Supply; Prices
    • Q42 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Alternative Energy Sources

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