Optimal hydrothermal scheduling with variable production coefficient

We consider the optimal operation of a hydroelectric plant supplemented by a set of thermal plants. The initial model gives rise to a discrete minimization problem with a convex cost function, submitted to both concave and convex restrictions. The geometry of the water reservoir is taken into account by a production coefficient, which is a function of the volume of available water. A slightly different formulation of the problem allows for a continuous limit, in which both the geometry of the restrictions and the optimal operation modes admit a simple description. Optimal operations correspond to juxtapositions of arcs in the boundary of the admissible set and pieces of geodesic-like trajectories in 1–1 space–time. For the general problem, we show existence of optimal operations, and, with stronger hypothesis, also uniqueness within a special class of thrifty operations. A numerical example, with data obtained from a concrete situation, is solved by making use of the characterization of optimal modes.