A Nonlinear Optimization Model of Water Allocation for Hydroelectric Energy Production and Irrigation

An optimal decision and control model was developed and used for dual purpose allocation of water from a reservoir. The model was constructed for the Hazbani-Dan Water System in the Upper Galilee (Israel). In this system about half of the Dan River water enters and is stored in a reservoir and is then released via a 70'' pipe either to a hydroelectric power station or to agricultural fields for irrigation. The electricity generated is sold to the national electricity utility according to a three-tiered pricing system which is a function of the time in the day and the season. The decision and control model maximizes the expected return on energy production subject to storage capacity and flow limitations. According to the policy of the system management, water demand for irrigation has to be satisfied and so it is taken as a constraint in the model. The following paper develops the model, exploring the feasibility conditions of the model and the uniqueness of the solution. An example containing a sensitivity analysis is given.