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Stochastic Power Generation Unit Commitment in Electricity Markets: A Novel Formulation and a Comparison of Solution Methods

Author

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  • Santiago Cerisola

    (Instituto de Investigación Tecnológica (IIT), Escuela Técnica Superior de Ingeniería ICAI, Universidad Pontificia Comillas, 28015 Madrid, Spain)

  • Álvaro Baíllo

    (Banco Santander, Ciudad Grupo Santander, Boadilla del Monte, 28660 Madrid, Spain)

  • José M. Fernández-López

    (Banco Santander, Ciudad Grupo Santander, Boadilla del Monte, 28660 Madrid, Spain)

  • Andrés Ramos

    (Instituto de Investigación Tecnológica (IIT), Escuela Técnica Superior de Ingeniería, ICAI, Universidad Pontificia Comillas, 28015 Madrid, Spain)

  • Ralf Gollmer

    (Department of Mathematics, University Duisburg-Essen, D-47048 Duisburg, Germany)

Abstract

We propose a stochastic unit commitment model for a power generation company that takes part in an electricity spot market. The relevant feature of this model is its detailed representation of the spot market during a whole week, including seven day-ahead market sessions and the corresponding adjustment market sessions. The adjustment market sessions can be seen as an hour-ahead market mechanism. This representation takes into account the influence that the company's decisions exert on the market-clearing price by means of a residual demand curve for each market session. We introduce uncertainty in the form of several possible spot market outcomes for each day, which leads to a weekly scenario tree. The model also represents in detail the operation of the company's generation units. The model leads to large-scale mixed linear-integer problems that are hard to solve with commercial optimizers. This suggests the use of alternative solution methods. We test four solution approaches with a realistic numerical example in the context of the Spanish electricity spot market. The first is a direct solution with a commercial optimizer, which illustrates the mentioned limitations. The second is a standard Lagrangean relaxation algorithm. The third and fourth methods are two original variants of Benders decomposition for multistage stochastic integer programs. The first Benders decomposition algorithm builds approximations for the recourse function relaxing the integrality constraints of the subproblems. The second variant strengthens these cuts by performing one iteration of the Lagrangean of each subproblem. We analyze the advantages of these four methods and compare the results.

Suggested Citation

  • Santiago Cerisola & Álvaro Baíllo & José M. Fernández-López & Andrés Ramos & Ralf Gollmer, 2009. "Stochastic Power Generation Unit Commitment in Electricity Markets: A Novel Formulation and a Comparison of Solution Methods," Operations Research, INFORMS, vol. 57(1), pages 32-46, February.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:1:p:32-46
    DOI: 10.1287/opre.1080.0593
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    References listed on IDEAS

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    Cited by:

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    3. Choi, Dong Gu & Thomas, Valerie M., 2012. "An electricity generation planning model incorporating demand response," Energy Policy, Elsevier, vol. 42(C), pages 429-441.
    4. 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.
    5. 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.
    6. Ursavas, Evrim, 2017. "A benders decomposition approach for solving the offshore wind farm installation planning at the North Sea," European Journal of Operational Research, Elsevier, vol. 258(2), pages 703-714.
    7. Ragheb Rahmaniani & Shabbir Ahmed & Teodor Gabriel Crainic & Michel Gendreau & Walter Rei, 2020. "The Benders Dual Decomposition Method," Operations Research, INFORMS, vol. 68(3), pages 878-895, May.
    8. ARAVENA, Ignacio & PAPAVASILIOU, Anthony, 2016. "An Asynchronous Distributed Algorithm for solving Stochastic Unit Commitment," LIDAM Discussion Papers CORE 2016038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Zheng, Xiaojin & Yin, Meixia & Zhang, Yanxia, 2019. "Integrated optimization of location, inventory and routing in supply chain network design," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 1-20.
    10. Nils Löhndorf & David Wozabal & Stefan Minner, 2013. "Optimizing Trading Decisions for Hydro Storage Systems Using Approximate Dual Dynamic Programming," Operations Research, INFORMS, vol. 61(4), pages 810-823, August.
    11. Melamed, Michal & Ben-Tal, Aharon & Golany, Boaz, 2018. "A multi-period unit commitment problem under a new hybrid uncertainty set for a renewable energy source," Renewable Energy, Elsevier, vol. 118(C), pages 909-917.
    12. Trine K. Boomsma, 2019. "Comments on: A comparative study of time aggregation techniques in relation to power capacity-expansion modeling," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 406-409, October.
    13. Jiang, Ruiwei & Zhang, Muhong & Li, Guang & Guan, Yongpei, 2014. "Two-stage network constrained robust unit commitment problem," European Journal of Operational Research, Elsevier, vol. 234(3), pages 751-762.
    14. Fattahi, Salar & Ashraphijuo, Morteza & Lavaei, Javad & Atamtürk, Alper, 2017. "Conic relaxations of the unit commitment problem," Energy, Elsevier, vol. 134(C), pages 1079-1095.
    15. Lima, Ricardo M. & Novais, Augusto Q. & Conejo, Antonio J., 2015. "Weekly self-scheduling, forward contracting, and pool involvement for an electricity producer. An adaptive robust optimization approach," European Journal of Operational Research, Elsevier, vol. 240(2), pages 457-475.
    16. Jirutitijaroen, Panida & Kim, Sujin & Kittithreerapronchai, Oran & Prina, José, 2013. "An optimization model for natural gas supply portfolios of a power generation company," Applied Energy, Elsevier, vol. 107(C), pages 1-9.
    17. Steeger, Gregory & Rebennack, Steffen, 2017. "Dynamic convexification within nested Benders decomposition using Lagrangian relaxation: An application to the strategic bidding problem," European Journal of Operational Research, Elsevier, vol. 257(2), pages 669-686.
    18. Lara, Cristiana L. & Mallapragada, Dharik S. & Papageorgiou, Dimitri J. & Venkatesh, Aranya & Grossmann, Ignacio E., 2018. "Deterministic electric power infrastructure planning: Mixed-integer programming model and nested decomposition algorithm," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1037-1054.
    19. Kai Pan & Yongpei Guan, 2016. "Strong Formulations for Multistage Stochastic Self-Scheduling Unit Commitment," Operations Research, INFORMS, vol. 64(6), pages 1482-1498, December.

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