We present a perfect formulation for a single generator in the unit commitment problem, inspired by the dynamic programming approach taken by Frangioni and Gentile. This generator can have characteristics such as ramping constraints, time-dependent start-up costs, and start-up/shut-down ramping. To develop this perfect formulation we extend the result of Balas on unions of polyhedra to present a framework allowing for flexible combinations of polyhedra using indicator variables. We use this perfect formulation to create a cut-generating linear program, similar in spirit to lift-and-project cuts, and demonstrate computational efficacy of these cuts in a utility-scale unit commitment problem.
University of Tennessee Knoxville, TN 37996 July 2017