Determination and analysis of reservoir storage discretization in Jamishan dam using stochastic dynamic programming with different objective functions

Background and Objectives: Nowadays, water scarcity is the current issue in Iran. This issue made the more necessity of using the proper water resources management more than the past. Stochastic Dynamic programming (SDP) is one of the methods to obtain the reservoir operation rules. In this method, one of the most important factors to find the optimal solution is discretization of the storage capacity and reservoir inflow. In this research, some storage classes (3, 5, 7 and 10) are analyzed to achieve the optimum storage discretization by SDP method, considering tree types of objective function (α = 0, α = 0.5, α = 1) with the constant reservoir inflow classes.
Materials and Methods: In this study, the SDP model has been used to find the optimal storage of Jamishan reservoir by any objective functions. By using historical reservoir inflow time series, reservoir inflow and storage are discretized in 3 classes with equal length intervals method and also 3, 5, 7 and 10 classes by Moran method, respectively. This method is applied by driving objective function as a minimization of system damage for each composition of the reservoir inflow and storage classes (k, i). By achieving the steady policy at each period, the amount of reservoir Inflow, storage and release are deterministically defined.
Results: The results showed that the optimal storage capacity, only water supply of downstream demands considered as an objective function, is k=7 and there is minimum water deficit in case of α=0. In addition, this would be 10 classes in case of α=1, which the amount of difference between reservoir storage and its desirable would be changed from constant value and the first decreasing change would be appear. Obtaining reservoir storage classes is also affected by method of discretization since this value is obtained 10 for classic and Moran method and 7 in Savarenskiy method. That is selected k = 10 based on the objective function in case of α = 0.5 considered two objectives of reservoir release storage volume simultaneously.
Conclusion: In case of α=0, the objective function is only reservoir release and water allocation, and of the optimal class of reservoir storage would occur at the point where water deficit is constant by increasing the number of storage classifications which k=7 is the optimal class. In the second scenario the objective function which is α=1 is selected as the best discretized class of the reservoir storage which has the closest vicinity to the target storage (Ts). So, in this case, k=10 is the optimum reservoir storage. In the third scenario, α = 0.5, there is a difference between to find the optimal solution when consider the TS or Tr as the criteria. Both objective function are well regarded in this case and also the first decreasing changes is happened in k=10.