Multi-reservoir design using Pontryagin principle

Several successful applications of optimal control theory (OCT) based on the Pontryagin’s minimum principle have been recorded in literature. These applications were focused on optimizing the operating policy of multi-reservoir systems. In this study, the performance of OCT algorithm in designing multi-reservoir system is investigated. Three deterministic optimization models based on the OCT were developed to design the best storage strategies in a multi-reservoir system to supply water. Multi-objective programming methods were implemented in the three models in order to consider the two non-commensurate objectives of minimizing cost and water deficit. The applications of these models to a multi-reservoir system were compared to an existing dynamic programming model. The result of this study showed that in all cases, the developed OCT models presented sub-optimal solution in designing multi-reservoir systems.