Derivation of Hydropower Rules for Multireservoir Systems and Its Application for Optimal Reservoir Storage Allocation

Abstract

Hydropower operating rules can guide reservoir release and storage for maximizing hydropower generation. The optimal hydropower operating rules are usually derived by numerical hydropower simulation methods. This study focuses on the analytical solution to optimal hydropower rules for storage allocation of a multireservoir system. An energy function, the E-function, is proposed to describe the objective of hydropower generation. The E-function for a multireservoir system can be represented as a function of two variables: the proportional coefficient (alpha, which represents the proportional relationship between any two reservoirs in a multireservoir system) and the total increment in storage. The alpha discriminant deduced from the E-function is used to infer the optimal reservoir storage allocation for maximum hydropower generation. With the Ankang-Danjiangkou reservoirs as a case study, the E-function and the alpha discriminant were compared with the numerical hydropower simulation. The results indicated that (1) the E-function can be used to estimate the hydropower generation for multireservoir systems with acceptable hydropower generation estimation errors between the analytical E-function and the numerical hydropower simulation; and (2) the optimal reservoir storage allocation can be explicitly obtained using the alpha discriminant. These findings are helpful for understanding the allocation of reservoir storages in multireservoir systems.