  Valve-point loading affects the input-output characteristics of generating
units, bringing the fuel costs nonlinear and nonsmooth. This has been
considered in the solution of load dispatch problems, but not in the planning
phase of unit commitment. This paper presents a mathematical optimization model
for the thermal unit commitment problem considering valve-point loading. The
formulation is based on a careful linearization of the fuel cost function,
which is modeled with great detail on power regions being used in the current
solution, and roughly on other regions. A set of benchmark instances for this
problem is used for analyzing the method, with recourse to a general-purpose
mixed-integer optimization solver.
