Optimal weekly releases from a seasonal reservoir: 1. Deterministic future

A technique was developed to maximize the returns from the operation of a seasonal alpine reservoir for the production of electrical energy. The emphasis rests on a comprehensive approach to the problem, and the following fields were considered: hydrology, power economics, operations research, and decision theory. The solution technique to determine the optimal releases strategy is first developed for the deterministic case. It is based on the solution of the system of equations given by the Kuhn‐Tucker conditions. As the direct solution of this system of equations is complicated, an alternative approach was devised. The operation period is divided into two parts: the drawdown phase and the refill phase. For each of these phases, the optimality conditions are solved by a procedure akin to Masse's constrained calculus of variations, the physical constraints being first ignored, and then introduced in a stepwise manner. A preliminary study of the approximate nature of the optimal releases sequence provides a good starting point in the variational procedure and the number of iterations necessary to arrive at the optimum is reduced to a minimum. The application of the developed technique to a seasonal reservoir fed by an alpine watershed showed that the method is both feasible and attractive. It is also well suited for generalization to the case of an uncertain future; to be presented in a second paper.