Optimizing the profit from a complex cascade of hydroelectric stations with recirculating water

Abstract

In modern reversible hydroelectric power stations it is possible to reverse the turbine and pump water up from a downstream reservoir to an upstream one. This allows the use of the same volume of water repeatedly and was specifically developed for hydro-electric stations operating with insufficient water supply. Pumping water upstream is usually done at times of low demand for electricity, to build up reserves in order to be able to produce energy during peak hours, thus balancing the load and making a profit on the price difference. In this paper, we consider a branched model for hydroelectric power stations interacting in a complex cascade arrangement. The goal of this study is to provide guidance in decision-making aimed at maximizing the profit. A detailed analysis is made of a simpler reservoir configuration, which indicates that even though the problem is nonlinear, a bang-bang type of control is optimal, where the power stations are operated at maximum rates of flow. Some simple relation- ships between price and timing of decisions are calculated directly. A numerical algorithm is also developed.