Tight MIP formulations of the power-based unit commitment problem

This paper provides the convex hull description for the basic operation of slow- and quick-start units in power-based unit commitment (UC) problems. The basic operating constraints that are modeled for both types of units are (1) generation limits and (2) minimum up and down times. Apart from this, the startup and shutdown processes are also modeled, using (3) startup and shutdown power trajectories for slow-start units, and (4) startup and shutdown capabilities for quick-start units. In the conventional UC problem, power schedules are used to represent the staircase energy schedule; however, this simplification leads to infeasible energy delivery, as stated in the literature. To overcome this drawback, this paper provides a power-based UC formulation drawing a clear distinction between power and energy. The proposed constraints can be used as the core of any power-based UC formulation, thus tightening the final mixed-integer programming UC problem. We provide evidence that dramatic improvements in computational time are obtained by solving different case studies, for self-UC and network-constrained UC problems.