Solving Reservoir Management Problems With Serially Correlated Inflows
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This paper addresses the problem of determining the optimal daily operating policy of a small reservoir when the inflows are stochastic and multi-lag autocorrelated. This optimization problem is difficult to solve when the number of lags is large because each lag adds a state variable to the problem. The paper presents two methods which solve the problem in a very short time, whatever the number of lags. The first, which solves the optimization problem with stochastic dynamic programming, represents the multi-lag autocorrelation by a single hydrologic variable, whose value changes from day to day and is equal to the conditional mean of the daily inflow. The second uses a large set of inflow scenarios to determine the optimal warning curve for the reservoir. The optimal daily operating policy is shown to consist in maintaining the reservoir level on, or as close as possible to, that curve. Keywords: daily reservoir operation, stochastic dynamic programming, streamflow autoregressive model, spillage warning curve, hydrologic variable. 1 Introduction This paper tackles the problem of determining the optimal daily operating policy of a small reservoir over a period of one year. The problem is stochastic because the reservoir inflows are random and cannot be predicted long in advance. The difficulty in solving this problem comes from the persistence of the inflows, that is, the fact that the inflows in day t can be correlated to those in days 1, 2,..., t t tp −−−. Persistence exists when there are long periods of high and low inflows in the recorded data. Since floods and shortages usually occur in
daily reservoir operation, stochastic dynamic programming, streamflow autoregressive model, spillage warning curve, hydrologic variable.