A Study of Three-Period Ramp-Up Polytope

The unit commitment (UC) problem is a very important problem in the power industry [1]. It seeks to minimize system-wide operational costs of power generators by providing an optimal schedule of power production while meet the demand and other technical constraints. By the combinatorial nature of the operational constraints, UC problem is difficult to solve to optimality for practical large-scale instances [2]. In this project, we consider a relaxation of UC problem with ramping constraints and production limits. Ramping constraints are used to control the change in production level for a generator from one period to the next. DamciKurt et al (2013) [2] present the the complete description of two-period ramping relaxation convex hull, and also describe a few classes of multi-period inequalities. We give the complete description of three-period ramp-up polytope, show that this description includes one new inequality which cannot be obtained as a special case of previously known multi-period ineqaulities. This new inequality can be used to further strengthen the ramping formulation of multi-period case. Independently, Pan and Guan (2015) [3] study the integrated ramping and minimum up/down time polytope, and also describe the convex hull of the three-period version of their polytope.