Influenceoftheelevation-storagecurveintheoptimizationofhydro- plants

One of the most important physical characteristics of a reservoir is the elevation-storage curve. In most cases, linear simplification is applied to this curve, which is approximated as a linear relationship. However, this simplification can produce serious errors in the optimal solution. In this paper we consider a non-linear elevation-storage curve to be applied to the reservoir and therefore consider a non-linear problem. To obtain the optimal solution, the problem is formulated within the framework of optimal control theory using Pontryagin's Maximum Principle. The advantage of this technique with respect to previous methods lies in the possibility of obtaining theoretical results whose implementation (and computational complexity) is feasible regardless of the non-linear characteristics of the problem. Results of the application of the method to a numerical example are presented and we show the differences between the two approaches. This paper deals with the influence of the design of the reservoir in the optimization of hydro-plants, one of the important optimization problems in a hydrothermal power system. We represent the hydro-plant at a high level of detail and include inter-temporal constraints such as hydro reserves. We consider a non-linear elevation- storage curve to be applied to the reservoir and therefore consider a non-linear problem. In a hydro-plant, power is derived by converting the potential energy of water to electrical energy using a hy- draulic turbine which is connected to a generator. The output power P (MW) is given by