Role of specific energy in decomposition of time-invariant least-cost reservoir filling problem

A mathematical analysis highlighting the decomposition structure of the least-cost reservoir filling problem under time-invariant conditions is provided. It is shown, without loss of generality, that time invariance and unidimensionality of the state variable (for describing the evolution of the hydrodynamic system) are sufficient in order to achieve full (spatial and temporal) decomposition. Using this result, the role of specific energy in finding least-cost operational schedules for reservoir filling in a general “physically meaningful” hydrodynamic system is discussed.