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.
Morales-España, Germán, Claudio Gentile, and Andres Ramos. “Tight MIP Formulations of the Power-Based Unit Commitment Problem.” OR Spectrum, May 23, 2015, 1–22. doi:10.1007/s00291-015-0400-4. Open access paper available online: http://link.springer.com/article/10.1007/s00291-015-0400-4