Optimisation of water resources systems with statistical inflows

Abstract

The optimisation of water resources systems has been the subject of several investigations throughout the world. Methods of optimisation such as linear, nonlinear and dynamic programming have been considered by many workers in the field. Dynamic programming has been one of the most widely used methods owing to its natural characteristics of being able to deal with discrete dynamic models and no limitations on the types of equations governing the system, constraints, or cost functional. Dynamic programming, although useful, has its shortcomings in the amount of storage and time consumed on a digital computer. In an attempt to use dynamic programming, several approximation schemes have been proposed. The `successive approximation?, `incremental dynamic programming?, and `corridoring? are three such proposals. The primary concern of the last approach used in this study is that in each iteration a corridor is formed around a previously defined trajectory and a new trajectory is obtained by applying the discrete differential dynamic programming within the present corridor, hence reducing the computer time and memory requirements. In this paper a four-reservoir water-resources system with four power plants, two input rivers, and an irrigation area is considered. Optimum trajectories are obtained for the reservoirs' water storages and releases assuming statistical data for the rivers' inflows and evaporations. Limitations of the approximate dynamic programming solution are discussed.