An efficient equivalent thermal cost function model for nonlinear mid-term hydrothermal generation planning

This paper presents an efficient model to represent nonlinear thermal generation costs in the mid-term hydrothermal generation planning problem. The proposed approach comprises two procedures: the first one consists in obtaining an exact piecewise quadratic equivalent thermal cost function for total thermal generation cost based on quadratic cost functions for each individual unit. The second procedure consists in using a dynamic piecewise linear model to represent such function in the optimization problem to be solved. The combination of both procedures yield a linearized model for the equivalent thermal generation cost curve for each system area and time step, which are represented in the problem as a set of constraints. Numerical results for some instances of the multi-period, stochastic nonlinear hydrothermal planning problem show a remarkable CPU time reduction and an improved accuracy in the final solution of the problem, as compared to an individual static piecewise linear model, which is the usual approach adopted in the literature.