A general equivalent thermal cost function for economic dispatch problems

The objective function of the traditional convex thermal economic dispatch (TED) problem is the sum of quadratic generation cost functions for all units in the system. In this paper, we propose the construction of an equivalent thermal cost function for this type of problem, which can be obtained a priori by convolution of the individual functions for each unit. Such model takes into account lower and upper bounds for the generation of each unit and the optimality criteria of equal incremental cost for all marginal units. Once obtained this system-wide cost curve, one can solve the TED by simple algebraic calculus, instead of applying mathematical programming or stochastic-search like algorithms that have been proposed in the literature to handle this problem. The proposed approach is illustrated in test systems taken from the literature, ranging from 10 to 100 thermal units.