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.