Reservoir Management Using a Network Flow Optimization Model Considering Quadratic Convex Cost Functions on Arcs

The allocation of water resources between different users is a hard task for water managers because they must deal with conflicting objectives. The main objective is to obtain the most accurate distribution of the resource and the associated circulating flows through the system. This induces the need for a river basin optimization model that provides optimized results. This article presents a network flow optimization model to solve the water allocation problem in water resource systems. Managing a water system consists in providing water in the right proportion, at the right place and at the right time. Time expanded network allows to take into consideration the temporal dimension in the decision making. Since linear cost functions on arcs present many limitations and are not realistic, quadratic convex cost functions on arcs are considered here. The optimization algorithm developed herein extend the cycle canceling algorithm developed for linear cost functions. The methodology is applied to manage the three reservoirs of La Haute-Vilaine’s watershed located in the north west of France to protect a three vulnerable areas from flooding. The results obtained with the algorithm are compared to a reference scenario which consists in considering reservoirs transparent. The results show that the algorithm succeeds in managing the reservoir releases efficiently and keeps the flow rates below the vigilance flow in the vulnerable areas.