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Optimal management of pumped hydroelectric production with state constrained optimal control

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  • Picarelli, Athena
  • Vargiolu, Tiziano

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.

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  • Picarelli, Athena & Vargiolu, Tiziano, 2021. "Optimal management of pumped hydroelectric production with state constrained optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 126(C).
    • Handle: RePEc:eee:dyncon:v:126:y:2021:i:c:s0165188920301081
    DOI: 10.1016/j.jedc.2020.103940
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    4. Zhao, Guangzhi & Davison, Matt, 2009. "Optimal control of hydroelectric facility incorporating pump storage," Renewable Energy, Elsevier, vol. 34(4), pages 1064-1077.
    5. 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.
    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.
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