Daily Operation of Reservoir Subject to Yearly Probabilistic Constraints

This paper addresses the problem of determining the optimal daily operating policy of a small reservoir subject to yearly probabilistic constraints on floods and shortages. The problem is difficult to solve because the reservoir inflows on day k are stochastic and correlated with those on days k-1,k-2,... ,k-n. The problem is broken down into two subproblems that are solved with a set of inflow scenarios and not with the conditional probability distributions of the inflows. The first subproblem determines the conditions to be respected each day for the yearly probabilistic constraints to be satisfied. The second finds the reservoirʹs optimal feedback operating policy for each day of the year that respects those conditions. This method is applied to the Kenogami reservoir located in Quebec, Canada, and the results are presented. The method is robust, fast to execute, and easy to program. Furthermore, it does not require that the problem be linear or differentiable.