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Optimal management of pumped hydroelectric production with state constrained optimal control

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  • Athena Picarelli
  • Tiziano Vargiolu

Abstract

We present a novel technique to solve the problem of managing optimally a pumped hydroelectric storage system. This technique relies on representing the system as a stochastic optimal control problem with state constraints, these latter corresponding to the finite volume of the reservoirs. Following the recent level-set approach presented in O. Bokanowski, A. Picarelli, H. Zidani, "State-constrained stochastic optimal control problems via reachability approach", SIAM J. Control and Optim. 54 (5) (2016), we transform the original constrained problem in an auxiliary unconstrained one in augmented state and control spaces, obtained by introducing an exact penalization of the original state constraints. The latter problem is fully treatable by classical dynamic programming arguments.

Suggested Citation

  • Athena Picarelli & Tiziano Vargiolu, 2019. "Optimal management of pumped hydroelectric production with state constrained optimal control," Papers 1909.06854, arXiv.org.
    • Handle: RePEc:arx:papers:1909.06854
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    1. Zhao, Guangzhi & Davison, Matt, 2009. "Optimal control of hydroelectric facility incorporating pump storage," Renewable Energy, Elsevier, vol. 34(4), pages 1064-1077.
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    3. 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.
    4. Luca Capriotti & Yupeng Jiang & Gaukhar Shaimerdenova, 2019. "Approximation Methods For Inhomogeneous Geometric Brownian Motion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-16, March.
    5. Giorgia Callegaro & Luciano Campi & Valeria Giusto & Tiziano Vargiolu, 2017. "Utility indifference pricing and hedging for structured contracts in energy markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 265-303, April.
    6. Bastian Felix, 2014. "Valuation Of Multiple Hyro Reservoir Storage Systems In Competitive Electricity Markets," EWL Working Papers 1401, University of Duisburg-Essen, Chair for Management Science and Energy Economics, revised Apr 2014.
    7. McDonald, Robert L & Siegel, Daniel R, 1985. "Investment and the Valuation of Firms When There Is an Option to Shut Down," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 331-349, June.
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