Optimal control for a cascade of hydroelectric power stations: Case study

Abstract

In this work we consider a simple model for a hydro-electric system with two power stations with reversible turbines. The problem is considered in the framework of optimal control theory. The objective is to find water flows to be turbined/pumped on each station and the corresponding volumes in the reservoirs that maximize the profit of selling energy. Restrictions on the water level in the reservoirs must be satisfied. The presence of state constraints and the nonconvexity of the cost function contribute to an increase of complexity of the optimal control problem. Using available software we obtain numerical results. Taking into account the profile of the solution we apply the maximum principle of Pontryagin and some new sufficient conditions of optimality to validate such solution. © 2015 Springer International Publishing.