Using Inflow Records to Approximate Solutions to Statistical Moment Equations of an Explicit Stochastic Reservoir Optimization Method

The Fletcher-Ponnambalam (FP) reservoir optimization method has been successfully applied to several case studies in the literature. As an explicit stochastic optimization problem, it requires the assumption of a probability distribution for the reservoir inflows in order to solve several integrals regarding the statistical moment equations for storage as well as probabilities of containment (storage within minimum and maximum levels), deficit (below minimum), and spill (above maximum). This technical note proposes an alternative way to approximate the solution of such integrals using the sample of historical inflow records. This does not involve the consideration of any distribution and leads to far shorter expressions as well as to less coding effort. The new formulation is applied to solve a water reservoir operation optimization problem for a major dam in Brazil. The results compare well with those from the current FP formulation and with those obtained by a Monte Carlo simulation of the monthly reservoir operation.