Groupe d’études et de recherche en analyse des décisions

G-2004-88

Solving a Stochastic Reservoir Management Problem with Multi-Lag Autocorrelated Inflows

There are many advantages to taking account of multi-lag autocorrelation of the inflows in a reservoir management problem: the flood and water shortage risks dimin- ish, there are fewer spillages, and the generation of hydro plants downstream from the reservoir increases. The disadvantage is that the number of state variables in the optimization problem increases with the number of lags. This paper shows that it is possible to adequately represent the multi-lag autocorrelation by a single hydrologic variable, whose value change from day to day and is equal to the conditional mean of the daily inflow. The paper also shows how to determine the probability distribution of the hydrologic variable for one day as a function of the hydrologic variable and the inflow of the preceding day. This is done for cases where the inflows are represented by a linear autoregressive (AR) model and linear autoregressive-moving-average (ARMA) model. The reservoir management problem is solved with Stochastic Dynamic Pro- gramming (SDP). Numerical results are presented.

, 17 pages