New developments on equivalent thermal in hydrothermal optimization: an algorithm of approximation

In this paper we revise the classical formulation of the problem of the optimization of hydrothermal systems. First we demonstrate that a number of thermal plants can be substituted by a single one that behaves equivalently to the entire set. We then calculate the equivalent plant in the case where the cost functions are general (nonquadratic). We prove that the equivalent thermal plant is a second-order polynomial with piece-wise constant coefficients. Moreover, it belongs to the class C1. Next we calculate the equivalent plant in the case of imposing constraints of minimum or maximum thermal power. Finally, we present an example and execute the proposed algorithm using Mathematica package.