Estimating the Optimal Capacity for Reservoir Dam based on Reliability Level for Meeting Demands

One of the practical and classic problems in the water resource studies is estimation of the optimal reservoir capacity to satisfy demands. However, full supplying demands for total periods need a very high dam to supply demands during severe drought conditions. That means a major part of reservoir capacity and costs is only usable for a short period of the reservoir lifetime, which would be unjustified in economic analysis. Thus, in the proposed method and model, the full meeting demand is only possible for a percent time of the statistical period that is according to reliability constraint. In the general methods, although this concept apparently seems simple, there is a necessity to add binary variables for meeting or not meeting demands in the linear programming model structures. Thus, with many binary variables, solving the problem will be time consuming and difficult. Another way to solve the problem is the application of the yield model. This model includes some simpler assumptions and that is so difficult to consider details of the water resource system. The applicationof evolutionary algorithms, for the problems have many constraints, is also very complicated. Therefore, this study pursues another solution.
In this study, for development and improvement the usual methods, instead of mix integer linear programming (MILP) and the above methods, a simulation model including flow network linear programming is used coupled with an interface manual code in Matlab to account the reliability based on output file of the simulation model. The acre reservoir simulation program (ARSP) has been utilized as a simulation model. A major advantage of the ARSP is its inherent flexibility in defining the operating policies through a penalty structure specified by the user. The ARSP utilizes network flow optimization techniques to handle a subset of general linear programming (LP) problems for individual time intervals. The objective of the LP application is to minimize a cost function, which reflects relative benefits derived from a particular operating policy. In this model, the priority for supplying different demands is defined based on a penalty structure. In this approach, the original system elements are delineated by nodes and arcs. Accordingly, nodes are junction points and arcs are the basic elements used to represent channels, and reservoir storages for each time interval. There are arcs connecting reservoir and demand nodes to the source and sink node. The source node supplies water to nodes within the network to simulate local inflow and the sink node receives flow from nodes within the network to represent consumptive use. Application of the simulation model causes that the configuration of the water resource system with more details is investigated. In this research, tree alternative for reliability including 80, 85 and 90 percent were considered, which are usual reliability for satisfying demands in water resource management in Iran. Then, for the each reliability, optimal reservoir volume was calculated along with optimal flow in each arc. The inflow to the model is established based on a long-term period of historical data (48 years) with monthly time interval.
Results Evaluation of the alternative, defined for reliability, demonstrated if the reliability increases from 85 to 90 %, the incremental volume of the reservoir will be considerable. In fact, for a higher reliability the model must supply water for a more severe drought. However, for the reliability from 80 to 85% the required incremental volume is negligible. Thus, selecting the reliability of 85% is more justified, by which the optimal reservoir volume will be 4.6 million cubic meters. Additionally, increasing of the reliability resulted in decreasing in average deficit and modified shortage index (MSI). However, these two deficit indexes have no same descending trend. The MSI has a less variations versus the reliability that is due to use square deficit in its formulation.
The model used in this research, in comparison to the MILP that is a common method for solving the above problem, make a reform in the traditional mass balance and flow routing in the network. The results show the reservoir capacity sensitivity versus the reliability, in which the sensitivity amount is affected by the intensity and duration drought periods. In fact, with considering higher reliability for supplying demands, a variation of the required reservoir volume has an ascending trend. Thus, application of predefined reliability, that is a common method in designing reservoir volume in Iran, is not appropriate for all drought conditions. In this regard, a sensitivity analysis of reservoir volume versus the reliability accompanying an economical analysis is recommended.