https://hal-ensta-paris.archives-ouvertes.fr/hal-01232170Carpentier, PierrePierreCarpentierOC - Optimisation et commande - UMA - Unité de Mathématiques Appliquées - ENSTA Paris - École Nationale Supérieure de Techniques AvancéesAlais, Jean-ChristopheJean-ChristopheAlaisde Lara, MichelMichelde LaraCERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTechMulti-usage hydropower single dam management: chance-constrained optimization and stochastic viabilityHAL CCSD2017Chance constraintsStochastic viabilityStochastic optimal controlDynamic programmingHydroelectric dam managementEnergy management[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Carpentier, Pierre2019-07-04 15:32:432022-05-17 12:36:012019-07-04 16:57:39enJournal articleshttps://hal-ensta-paris.archives-ouvertes.fr/hal-01232170/document10.1007/s12667-015-0174-4application/pdf1We consider the management of a single hydroelectric dam, subject to uncertain inflows and electricity prices and to a so-called “tourism constraint”: the water storage level must be high enough during the tourist season with high enough probability. We cast the problem in the stochastic optimal control framework: we search at each time t the optimal control as a function of the available information at t. We lay out two approaches. First, we formulate a chance-constrained stochastic optimal control problem: we maximize the expected gain while guaranteeing a minimum storage level with a minimal prescribed probability level. Dualizing the chance constraint by a multiplier, we propose an iterative algorithm alternating additive dynamic programming and update of the multiplier value “à la Uzawa”. Our numerical results reveal that the random gain is very dispersed around its expected value; in particular, low gain values have a relatively high probability to materialize. This is why, to put emphasis on these low values, we outline a second approach. We propose a so-called stochastic viability approach that focuses on jointly guaranteeing a minimum gain and a minimum storage level during the tourist season. We solve the corresponding problem by multiplicative dynamic programming. To conclude, we discuss and compare the two approaches.Keywords