Résumés
Résumé
L'article que nous proposons s'inscrit dans le cadre des problèmes d'optimisation bimensionnelle (irrigation & salubrité) des ressources en eau durant la période d'étiage. Sur le cas du système NESTE, la résolution est effectuée selon deux approches :
- un modèle de programmation dynamique avec état de dimension deux (niveau des réserves, niveau dans la rivière) où, dans la solution numérique, les variables sont discrétisées;
- un modèle « synthétique » où l'on calcule une probabilité de non dépassement caractérisant l'état hydrique des ressources du système. Une règle empirique permet d'associer à cette grandeur une décision de consigne à effectuer.
Les résultats numériques sont comparés sur une série de chroniques historiques. Les avantages et les inconvénients de chacune des deux approches sont mis en lumière sur le cas réel du système NESTE.
Mots-clés:
- Gestion de réservoir,
- programmation dynamique,
- gestion du risque,
- aide à la décision,
- modélisation,
- soutien d'étiage,
- irrigation
Abstract
This paper deals with bicreteria (irrigation & water quality) weekly operation of a water resource system during dry period. Two ways of handling the problem are assessed and compared on a real case study :
- a stochastic dynamic programming modal with a two dimensional state (reservoirs level, river level) that is numerically solved by discretization ;
- a more « synthetic » model where the state is expressed in term of a tail aera probability related to the consumption of all the present water resources in the future. A practical decision rule is based upon the associated critical value.
Numerical results are plotted on historical varies for both methods.
From the present application to the NESTE system, the conclusions are :
1) Both procedures allow the system manager to formulate operating strategies in a rational way :
- An operating rule can be derived to allocate water so as to meet a combination of the various objectives. It is expressed as a feedback law linking what we know from the state of the system to how we control its evolution.
- Both methods need a parameter to be set up by stochastic simulation.
- They give close results on the basis of the past data and can be conveniently proposed to system managers.
2) The system analysis approach is based on stochastic dynamic programming. If can be efficiently used to derive optimal feedback ruses of operation and can routinely deal with complex decisions such as limiting irrigation when a shortage is to occur or take the risk to keep going and decrease output targets for water quality management. At the same time, this procedure entails heavy computing time, uneasy interpretation of the weighting coefficient between irrigation and water quality objectives, and a rather artificial elicitation of the global compromise.
Such an approach is very well fit for simulation because it is composed of elementary blocks that are gathered in a transition relationship to describe the system's dynamic evolution. This approach also provides a means to get an optimal policy as long as the system manager accepts the necessity to formulate an objective function consistently with dynamic programming (i. e. stages are separable and additive). Of course this optimal allocation should be carefully examined because of modal uncertainties influencing both the system response and the hydrological behaviour.
3) The synthetic method may appear more attractive from the engineering point of view for the following reasons :
- the state is easily interpreted in terms of « dry year with a return period of 10, normal year, exceptionally wet year » and so on. The trade-off coefficient is the volume one wants to keep in the reservoirs at time T for a wet year. Consequently if the parameter is chosen with « good sense », no optimization scheme is needed.
- there is no computation except a mass balance equation and a normal probability law adjustment which is very easy because it deals with cumulative quantities.
4) Such models are designed to serve only as multicriterion decision making aids. In very dry days such as occurred in summer 1976 or 1989 in France they cannot create additional water resources... still, they can help the system manager by constant up dated multidimensional estimation of the risks that may be encountered when following different operation rotes. In the case of the NESTE system, a real-scale experiment began in 1989: in real time operation, both models worked on line as decision-making supports, and the system manager made a thorough study of the hydrological conditions when the two approaches did not agree on the same stragegy for the following week.
Keywords:
- Reservoir operation,
- dynamic programming,
- risk management,
- decision making,
- modeling,
- low flow augmentation,
- irrigation
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