In this paper, we consider the polyhedral structure of the integrated minimum-up/-down time and ramping polytope, which has broad applications in power generation scheduling problems. The generalized polytope we studied includes minimum-up/-down time, generation ramp-up/-down rate, logical, and generation upper/lower bound constraints. We derive strong valid inequalities for this polytope by utilizing its specialized structures. These inequalities, plus trivial inequalities described in the original formulation, are sufficient to provide the convex hull descriptions for variant two-period and three-period polytopes corresponding to different minimum-up/-down time limits. In addition, we derive more generalized strong valid inequalities (including one, two, and three continuous variable cases respectively) in polynomial size to strengthen the multi-period polytopes, and further prove that these inequalities are facet-defining under certain mild conditions. Finally, extensive computational experiments are conducted to verify the effectiveness of our proposed strong valid inequalities by testing the applications of these inequalities to solve both the network-constrained and self-scheduling unit commitment problems, for which our derived approach outperforms the default CPLEX significantly.
View A Polyhedral Study of the Integrated Minimum-Up/-Down Time and Ramping Polytope