Stochastic Characterization of Optimal Response of a Hydroelectric System Via Dynamic Programming

Abstract

Optimal operation for Tietê River (Brazil) hydroelectric system composed of six hydroelectric plants is studied to characterize its stochastic aspects via dynamic programming. The optimization problem is expressed as the minimization of expected value of energy required to meet local demand for different periods of operation discretized in trimesters. The stochastic process of occurence of natural river discharge is represented by 4th order multivariate autoregressive model. Problem solution is obtained by Stochastic Dual Dynamic Programming (SSDP) via Benders1 decomposition as proposed by Pereira and Pinto (1985, 1988) which incorporates hydrologic variability admitting multiple equally likely future flow scenarios at each stage. Repeated optimizations are made with independent flow sequences to evaluate the importance of the number of flow scenarios in a tree-like structure of synthetic hydrologic inputs and the period of operation as regards the variability of the expected value of the energy import costs for optimal operation.