La Houille Blanche
Number 5, Août 1965
|Page(s)||434 - 444|
|Published online||24 March 2010|
L'application du calcul des probabilités aux problèmes d'exploitation des réservoirs
Stochastic reservoir theory
Ingénieur au Centre de Recherche et d'Essais de Chatou (E.D.F.).
The purpose of stochastic-or conjectural-reservoir theory is to determine and study the probability law for the filling states of a reservoir-or a system of reservoirs-the inflows into which are the result of a given stochastic process, and the outflows from which are governed by a set operating policy which may be associated with water levels in the reservoir. Changes in reservoir state can be formally expressed by a system of equations (2) for a fairly general composite management rule. Moran's well-known data are reviewed, which are based on the independence probability of the successive inflows, and on a very much simplified operating policy. Water level probability is then given by the integral equation of the form (15). The simulation method available for more complex hypotheses is briefly described. The main subject of the article is a description of a method for the calculation of reservoir water levels, based on the assumption of probable dependence of successive inflows, which are themselves assumed to be linked by a simple Markoff chain. In the case of the simplified operating rule, the probability law governing the reservoir water level and inflow for the same period can be calculated by the general formula (20). By allowing for a particular Markoff scheme described by formula (21), the water level relationship which is the solution of integral equation (25) can be calculated. A similar method is applied to the case of a multi-purpose operating policy, which leads to formula (28). Paragraph VIII of the article deals with the practical solution of the integral equations obtainecl. It is shown that these can be solved by replacing them by a linear system of fairly complex form (29), (30), (31) easily dealt with by a computer. Paragraph IX describes a mode whereby the basic a ssumptions for the theory described in this article are verified, and which can give a fairly realistic representation of the stochastic processes associated with reservoir inflows.
© Société Hydrotechnique de France, 1965