Contributed Session Fri.1.MA 550

Friday, 10:30 - 12:00 h, Room: MA 550

Cluster 18: Optimization in energy systems [...]

Optimal control


Chair: Jean-Christophe Alais



Friday, 10:30 - 10:55 h, Room: MA 550, Talk 1

Jean-Christophe Alais
On managing the hydroelectric production of a dam by means of the viability theory


To manage a dam hydroelectric production, we have to cope with economic and tourist stakes which are mutually conflicting since they compete for the use of a common resource: the reservoir water. We first consider the expected gain stemming from the production as the criterion to maximize and the tourist stake is modelled as to ensure a storage level s during the tourist season, at a given probability level. This leads to a chance-constrained optimal control problem we solve by the Uzawa algorithm. Albeit the optimal strategy meets the a priori-specified requirements, the deviation of the reached gain from its expected value is significative. Therefore, handling the dam management this way may not be satisfactory when the dispersion of the reached gains is of interest. In another way, a viability approach to the problem may be to do our best to respect the storage level s during the tourist season while guarantying ourselves a reached gain g. Thus, we symmetrize the stakes by maximizing P(gain ≥ g, and, storage ≥ s). We design and then solve the problem, which is the occasion to study the maximization of a multiplicative gain by dynamic programming.


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