On the optimization of hydroelectric power generation with random water inflows

This paper investigates a method devised recently by Narcís Nabona for the optimization of the management of hydroelectric resources in a system of reservoirs under uncertainty conditions. The method is based in the transformation of the stochastic problem into a related deterministic one which can then be treated by multicommodity nonlinear network flows techniques. The paper is concerned with examining in full detail the mechanism of this transformation and in justifying it from the probabilistic point of view, leaving aside the question of modelling, already extensively surveyed by Nabona. It begins with a complete description of the problem, including the construction of a fairly general objective function depending on the cost of hydropower generation and the policy chosen to move the water across the network. Later, the use of the available statistical data is described successively for the case of one time interval and one fluvial basin, several intervals and only one basin and finally for the case of several basins.