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Stochastic dual dynamic programming applied to nonconvex hydrothermal models

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  • 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
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    References listed on IDEAS

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    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.
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    3. 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.
    4. 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.
    5. 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.
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    9. 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.
    10. 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.
    11. 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.
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    13. 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.
    14. 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).

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