Piecewise affine approximations for the control of a one-reservoir hydroelectric system |
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| Institution: | 1. Forintek Canada Corporation, Eastern Division, Faculti de foresterie et de giomatique, Université Laval, Quebec, Que., Canada GIK 7P4;2. Faculte des sciences de V administration, Universiti Laval, Quebec, Que., Canada GIK 7P4;1. NTNU - Department of Electric Power Engineering, O.S Bragstads plass 2E, 7034 Trondheim, Norway;2. SINTEF Energi AS, Sem Sælands vei 11, 7034 Trondheim, Norway;1. Institute of Hydropower & Hydroinformatics and Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116024, China;2. Department of Civil and Environmental Engineering, University of California, Davis 95616, USA;3. Institute of Hydropower & Hydroinformatics, Dalian University of Technology, Dalian 116024, China;1. Plan4 Engenharia, Rua Maria Luiza Agostinho, n 92, Itacorubi, Florianopolis, Brazil;2. Electric Power Optimization Centre, University of Auckland, New Zealand;3. Laboratório de Planejamento de Sistemas de Energia Elétrica, Universidade Federal de Santa Catarina, Brazil |
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| Abstract: | We analyze the computation of optimal and approximately optimal policies for a discrete-time model of a single reservoir whose discharges generate hydroelectric power. Inflows in successive periods are random variables. Revenue from hydroelectric production is represented by a piecewise linear function. We use the special structure of optimal policies, together with piecewise affine approximations of the optimal return functions at each stage of dynamic programming, to decrease the computational effort by an order of magnitude compared with ordinary value iteration. The method is then used to obtain easily computable lower and upper bounds on the value function of an optimal policy, and a policy whose value function is between the bounds. |
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