IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v218y2012i3p687-697.html
   My bibliography  Save this article

Stochastic dual dynamic programming applied to nonconvex hydrothermal models

Author

Listed:
  • Cerisola, Santiago
  • Latorre, Jesus M.
  • Ramos, Andres

Abstract

In this paper we apply stochastic dual dynamic programming decomposition to a nonconvex multistage stochastic hydrothermal model where the nonlinear water head effects on production and the nonlinear dependence between the reservoir head and the reservoir volume are modeled. The nonconvex constraints that represent the production function of a hydro plant are approximated by McCormick envelopes. These constraints are split into smaller regions and the McCormick envelopes are used for each region. We use binary variables for this disjunctive programming approach and solve the problem with a decomposition method. We resort to a variant of the L-shaped method for solving the MIP subproblem with binary variables at any stage inside the stochastic dual dynamic programming algorithm. A realistic large-scale case study is presented.

Suggested Citation

  • Cerisola, Santiago & Latorre, Jesus M. & Ramos, Andres, 2012. "Stochastic dual dynamic programming applied to nonconvex hydrothermal models," European Journal of Operational Research, Elsevier, vol. 218(3), pages 687-697.
    • Handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:687-697
    DOI: 10.1016/j.ejor.2011.11.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711010496
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2011.11.040?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Latorre, Jesus M & Cerisola, Santiago & Ramos, Andres, 2007. "Clustering algorithms for scenario tree generation: Application to natural hydro inflows," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1339-1353, September.
    2. David P. Morton, 1998. "Stopping Rules for a Class of Sampling-Based Stochastic Programming Algorithms," Operations Research, INFORMS, vol. 46(5), pages 710-718, October.
    3. Matthias Nowak & Werner Römisch, 2000. "Stochastic Lagrangian Relaxation Applied to Power Scheduling in a Hydro-Thermal System under Uncertainty," Annals of Operations Research, Springer, vol. 100(1), pages 251-272, December.
    4. Jeff Linderoth & Alexander Shapiro & Stephen Wright, 2006. "The empirical behavior of sampling methods for stochastic programming," Annals of Operations Research, Springer, vol. 142(1), pages 215-241, February.
    5. C. Beltran-Royo, 2009. "The radar method: an effective line search for piecewise linear concave functions," Annals of Operations Research, Springer, vol. 166(1), pages 299-312, 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. Gómez-Pérez, Jesús D. & Latorre-Canteli, Jesus M. & Ramos, Andres & Perea, Alejandro & Sanz, Pablo & Hernández, Francisco, 2024. "Improving operating policies in stochastic optimization: An application to the medium-term hydrothermal scheduling problem," Applied Energy, Elsevier, vol. 359(C).
    2. Martin N. Hjelmeland & Arild Helseth & Magnus Korpås, 2019. "Medium-Term Hydropower Scheduling with Variable Head under Inflow, Energy and Reserve Capacity Price Uncertainty," Energies, MDPI, vol. 12(1), pages 1-15, January.
    3. Egging, Ruud, 2013. "Benders Decomposition for multi-stage stochastic mixed complementarity problems – Applied to a global natural gas market model," European Journal of Operational Research, Elsevier, vol. 226(2), pages 341-353.
    4. Fredo, Guilherme Luiz Minetto & Finardi, Erlon Cristian & de Matos, Vitor Luiz, 2019. "Assessing solution quality and computational performance in the long-term generation scheduling problem considering different hydro production function approaches," Renewable Energy, Elsevier, vol. 131(C), pages 45-54.
    5. Schäffer, Linn Emelie & Helseth, Arild & Korpås, Magnus, 2022. "A stochastic dynamic programming model for hydropower scheduling with state-dependent maximum discharge constraints," Renewable Energy, Elsevier, vol. 194(C), pages 571-581.
    6. Duenas, Pablo & Ramos, Andres & Tapia-Ahumada, Karen & Olmos, Luis & Rivier, Michel & Pérez-Arriaga, Jose-Ignacio, 2018. "Security of supply in a carbon-free electric power system: The case of Iceland," Applied Energy, Elsevier, vol. 212(C), pages 443-454.
    7. Zhang, Chaoyi & Jiao, Zaibin & Liu, Junshan & Ning, Keer, 2023. "Robust planning and economic analysis of park-level integrated energy system considering photovoltaic/thermal equipment," Applied Energy, Elsevier, vol. 348(C).
    8. 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.
    9. Silva, Rodolfo Rodrigues Barrionuevo & Martins, André Christóvão Pio & Soler, Edilaine Martins & Baptista, Edméa Cássia & Balbo, Antonio Roberto & Nepomuceno, Leonardo, 2022. "Two-stage stochastic energy procurement model for a large consumer in hydrothermal systems," Energy Economics, Elsevier, vol. 107(C).
    10. Lohmann, Timo & Hering, Amanda S. & Rebennack, Steffen, 2016. "Spatio-temporal hydro forecasting of multireservoir inflows for hydro-thermal scheduling," European Journal of Operational Research, Elsevier, vol. 255(1), pages 243-258.
    11. Zhong, Zhiming & Fan, Neng & Wu, Lei, 2024. "Multistage Stochastic optimization for mid-term integrated generation and maintenance scheduling of cascaded hydroelectric system with renewable energy uncertainty," European Journal of Operational Research, Elsevier, vol. 318(1), pages 179-199.
    12. Hohmann, Marc & Warrington, Joseph & Lygeros, John, 2020. "A moment and sum-of-squares extension of dual dynamic programming with application to nonlinear energy storage problems," European Journal of Operational Research, Elsevier, vol. 283(1), pages 16-32.
    13. Escudero, Laureano F. & Monge, Juan F. & Rodríguez-Chía, Antonio M., 2020. "On pricing-based equilibrium for network expansion planning. A multi-period bilevel approach under uncertainty," European Journal of Operational Research, Elsevier, vol. 287(1), pages 262-279.
    14. Moreira, Alexandre & Pozo, David & Street, Alexandre & Sauma, Enzo & Strbac, Goran, 2021. "Climate‐aware generation and transmission expansion planning: A three‐stage robust optimization approach," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1099-1118.
    15. Rodríguez, Jesús A. & Anjos, Miguel F. & Côté, Pascal & Desaulniers, Guy, 2021. "Accelerating Benders decomposition for short-term hydropower maintenance scheduling," European Journal of Operational Research, Elsevier, vol. 289(1), pages 240-253.
    16. Tejada-Arango, Diego A. & Wogrin, Sonja & Siddiqui, Afzal S. & Centeno, Efraim, 2019. "Opportunity cost including short-term energy storage in hydrothermal dispatch models using a linked representative periods approach," Energy, Elsevier, vol. 188(C).

    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. Güzin Bayraksan & David P. Morton, 2011. "A Sequential Sampling Procedure for Stochastic Programming," Operations Research, INFORMS, vol. 59(4), pages 898-913, August.
    2. Yankai Cao & Carl D. Laird & Victor M. Zavala, 2016. "Clustering-based preconditioning for stochastic programs," Computational Optimization and Applications, Springer, vol. 64(2), pages 379-406, June.
    3. Anthony Papavasiliou & Shmuel S. Oren, 2013. "Multiarea Stochastic Unit Commitment for High Wind Penetration in a Transmission Constrained Network," Operations Research, INFORMS, vol. 61(3), pages 578-592, June.
    4. Panos Parpas & Berk Ustun & Mort Webster & Quang Kha Tran, 2015. "Importance Sampling in Stochastic Programming: A Markov Chain Monte Carlo Approach," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 358-377, May.
    5. Maria Vespucci & Francesca Maggioni & Maria Bertocchi & Mario Innorta, 2012. "A stochastic model for the daily coordination of pumped storage hydro plants and wind power plants," Annals of Operations Research, Springer, vol. 193(1), pages 91-105, March.
    6. Jangho Park & Rebecca Stockbridge & Güzin Bayraksan, 2021. "Variance reduction for sequential sampling in stochastic programming," Annals of Operations Research, Springer, vol. 300(1), pages 171-204, May.
    7. Schulze, Tim & McKinnon, Ken, 2016. "The value of stochastic programming in day-ahead and intra-day generation unit commitment," Energy, Elsevier, vol. 101(C), pages 592-605.
    8. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    9. Xiaotie Chen & David L. Woodruff, 2024. "Distributions and bootstrap for data-based stochastic programming," Computational Management Science, Springer, vol. 21(1), pages 1-21, June.
    10. Shi, Qingxin & Li, Fangxing & Dong, Jin & Olama, Mohammed & Wang, Xiaofei & Winstead, Chris & Kuruganti, Teja, 2022. "Co-optimization of repairs and dynamic network reconfiguration for improved distribution system resilience," Applied Energy, Elsevier, vol. 318(C).
    11. Jörn Dunkel & Stefan Weber, 2010. "Stochastic Root Finding and Efficient Estimation of Convex Risk Measures," Operations Research, INFORMS, vol. 58(5), pages 1505-1521, October.
    12. Klein Haneveld, W.K. & Vlerk, M.H. van der, 2000. "Optimizing electricity distribution using two-stage integer recourse models," Research Report 00A26, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    13. Ke, Xinda & Wu, Di & Rice, Jennie & Kintner-Meyer, Michael & Lu, Ning, 2016. "Quantifying impacts of heat waves on power grid operation," Applied Energy, Elsevier, vol. 183(C), pages 504-512.
    14. Soham Ghosh & Sujay Mukhoti, 2023. "Non-parametric generalised newsvendor model," Annals of Operations Research, Springer, vol. 321(1), pages 241-266, February.
    15. Masato Wada & Felipe Delgado & Bernardo K. Pagnoncelli, 2017. "A risk averse approach to the capacity allocation problem in the airline cargo industry," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(6), pages 643-651, June.
    16. Zhu, Y. & Li, Y.P. & Huang, G.H., 2012. "Planning municipal-scale energy systems under functional interval uncertainties," Renewable Energy, Elsevier, vol. 39(1), pages 71-84.
    17. Tejada-Arango, Diego A. & Wogrin, Sonja & Siddiqui, Afzal S. & Centeno, Efraim, 2019. "Opportunity cost including short-term energy storage in hydrothermal dispatch models using a linked representative periods approach," Energy, Elsevier, vol. 188(C).
    18. Aydin, Nezir & Murat, Alper, 2013. "A swarm intelligence based sample average approximation algorithm for the capacitated reliable facility location problem," International Journal of Production Economics, Elsevier, vol. 145(1), pages 173-183.
    19. Salazar, Juan M. & Diwekar, Urmila & Constantinescu, Emil & Zavala, Victor M., 2013. "Stochastic optimization approach to water management in cooling-constrained power plants," Applied Energy, Elsevier, vol. 112(C), pages 12-22.
    20. Arjmand, Reza & Rahimiyan, Morteza, 2016. "Statistical analysis of a competitive day-ahead market coupled with correlated wind production and electric load," Applied Energy, Elsevier, vol. 161(C), pages 153-167.

    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:eee:ejores:v:218:y:2012:i:3:p:687-697. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.