Improvements to storage management models using explicit probabilistic contraints

Methods integrating reservoir storage bounds using indicator functions into the system's water balance equation were introduced in the last two decades by Fletcher and Ponnambalam (FP Method). This method provided expressions for means and variances of storage volumes better than known explicit methods so far while avoiding both simulation and discretization of state and decision variables. In this paper, in addition, we introduce new probabilistic constraints on both storage volumes and controlled releases. This enhanced formulation is applied to solve a water reservoir operation optimization problem for a major dam in Brazil. The results for statistical moments and probability levels compare well with those obtained by a Monte Carlo simulation of the monthly reservoir operations thus providing an efficient computational tool.