Stochastic Optimization of Multiple‐Reservoir‐System Operation

Abstract

A stochastic dynamic programming model for the optimization of hydropower prroduction of a multiple storage‐reservoir system with correlated inflows has been developed. Application was made to a subsystem of the Brazilian hydroelectric system. The model consists of two parts. An off‐line, one‐time‐only, deterministic dynamic program computes the value of the stored water in all of the reservoirs as a function of the several reservoir storages and the month of the year. The calculated values represent potential energy generation and are based on historical flow data. The on‐line program is formulated in terms of a stochastic dynamic program and conducted in real time for operational use. Each month a multidimensional search is made for the optimal set of reservoir releases that maximize system benefits. The search uses the probability transition matrices and the tables of stored‐water benefits for the particular month determined by the off‐line program. The optimization requires knowledge of the previous month's inflows and the starting storages for the current month; but these, of course, are observables and are readily determined. The following month, the on‐line search procedure is repeated to find the optimal releases for that month. The off‐line program also can be used to obtain trade‐offs between expected energy‐generation benefits and water‐management benefits consequent to some other objective, such as flood control. Model performance was checked against actual operational data for a Brazilian subsystem, and there are indications of superior performance by the model.