Minimization of water losses for optimal hydroelectric power generation

This paper deals with the problem of reducing water losses during power generation in hydro-power valleys. Because the main resources is water, it is important to guarantee that the demanded power per hour is generated in such a way that water is used as much as possible along the valleys. That is achieved by minimizing the spilling flows. The natural interactions between power units and the fact that these units have to respect different real-time constraints (the demanded power generation, for instance) suggest the use of more advanced techniques for optimal coordination. In this work, an explicit Model Predicted Control is proposed for tackle the problem of system constraints together with the problem of water losses minimization. Firstly, a model of the system including a model of the exogenous disturbances is proposed. Here an extended observer is designed and used to solve the control problem. Then, the original control problem is established and rewritten in terms of a Quadratic Program problem. After that, a very simple explicit solution of the Quadratic Program problem is proposed by using a geometrical approach. This allows its implementation in realtime applications and it could be more intuitive for engineers piloting hydropower plants. The paper includes a realistic simulation that is intended for illustrating the behavior of the controlled system for reducing the spilling flows.