Developing monthly operating rules for a cascade system of reservoirs: Application of Bayesian Networks

Abstract

In this paper, a Bayesian Network (BN) is utilized for developing monthly operating rules for a cascade system of reservoirs which is mainly aimed to control floods and supply irrigation needs. BN is trained and verified using the results of a reservoir operation optimization model, which optimizes monthly releases from cascade reservoirs. The inputs of the BN are monthly inflows, reservoir storages at the beginning of the month, and downstream water demands. The trained BN provides the probability distribution functions of reservoirs' releases for each set of input data. The long-term optimization model in monthly scale is formulated to minimize the expected flood and agricultural water deficit damages. The optimization model is developed using an extended version of the Varying chromosome Length Genetic Algorithm (VLGA-II). To incorporate reservoir preparedness for controlling the probable floods in each month, damages associated with floods with different return periods have been considered in the optimization model. For this purpose, a short-term optimization model which provides the optimal hourly releases during floods is utilized and linked to a flood damage estimation model. Damages due to deficit in supplying agricultural water demands are also calculated based on the functions of crop yield responses to deficit irrigation. The developed models are applied to the cascade system of the Dez and Bakhtiari Reservoirs in Southwest of Iran. The result of the trained BN is compared with the rules developed using classical and fuzzy linear regressions and it is shown that the total damage obtained by the BN-based operating rules is about 60 percent less than the total damage obtained using the fuzzy and classical regression analyses. The average relative error in estimating optimal releases is also reduced about 30 percent by using the BN-based rules.