Start-up/Shut-Down MINLP Formulations for the Unit Commitment with Ramp Constraints

In (Bacci et al. New MINLP formulations for the single-unit commitment problems with ramping constraints, 2019) the first MIP exact formulation was provided that describes the convex hull of the solutions satisfying all the standard operational constraints for the thermal units: minimum up- and down-time, minimum and maximum power output, ramp (including start-up and shut-down) limits, general history-dependent start-up costs, and nonlinear convex power production costs. That formulation contains a polynomial, but large, number of variables and constraints. We present two new formulations with fewer variables defined on the shut-down period and computationally test the trade-off between reduced size and possibly weaker bounds.