Bayesian stochastic optimization of reservoir operation using uncertain forecasts

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Abstract
Operation of reservoir systems using stochastic dynamic programming (SDP) and Bayesian decision theory (BDT) is investigated in this study. The proposed model, called Bayesian stochastic dynamic programming (BSDP), which includes inflow, storage, and forecast as state variables, describes streamflows with a discrete lag 1 Markov process, and uses BDT to incorporate new information by updating the prior probabilities to posterior probabilities, is used to generate optimal reservoir operating rules. This continuous updating can significantly reduce the effects of natural and forecast uncertainties in the model. In order to test the value of the BSDP model for generating optimal operating rules, real‐time reservoir operation simulation models are constructed using 95 years of monthly historical inflows of the Gunpowder River to Loch Raven reservoir in Maryland. The rules generated by the BSDP model are applied in an operation simulation model and their performance is compared with an alternative stochastic dynamic programming (ASDP) model and a classical stochastic dynamic programming (SDP) model. BSDP differs from the other two models in the selection of state variables and the way the transition probabilities are formed and updated.