Inflow stochastic models for the management of reservoir secondary yields

Abstract

Abstract Firm yield from a reservoir usually covers primary downstream water requirements. In many cases, as well as such requirements there are secondary needs, which are satisfied or not according to the decision-maker's subjective judgement in the various hydrologic situations. This paper describes a rather general approach for optimizing the release of these secondary yields, while keeping the primary deficits (deficits corresponding to releases less than firm yield) at their minimum possible value. This is first accomplished by an optimization model (mathematical program), minimizing the overall primary deficit. Such a program has multiple optimal solutions, among which one is chosen by another mathematical program, maximizing the overall secondary benefit. This final “solution” of the two mathematical programs is derived explicitly in the form of an optimal time-varying operating rule. Since the actual implementation of the rule would require knowledge of all future inflows at each time step, a heuristic modification is introduced. Precisely, at each time step, future is divided into two parts: next future, which is taken into account by introducing a forecast of its inflows into the procedure, and far, unpredictable future, which is taken into account by a severe “safety constraint” on its primary deficits. An application to an Italian reservoir is finally shown.