Operation of three hydroelectric dams using guide curves and stochastic dynamic programming

Abstract

Dynamic Programming (DP) is an optimization procedure developed in the 1950s by Richard Bellman (Bellman, 1957). It is a mathematical tool that has been applied in several fields, including engineering, artificial intelligence and economics, among others (Dormido et al., 2002). The area of water resources planning is no exception and applications with good results have been reported in several countries. A limitation is high computing costs, the need for many resources both in terms of time as well as memory, with the demand of these resources growing exponentially as the number of state variables increases. This work presents a way in which to organize a computing program to handle this problem as well as to determine policies for the optimal operations of a system of three serial hydropower dams by varying the penalties for deficits, spills and exceeding guide curves (the storage levels not to be surpassed during operation for the safety of the system, which are established by the National Water Commission). The policies obtained were simulated using historical records and synthetic records to test their benefit to the operations of the system.