A Polyhedral Study of the Integrated Minimum-Up/-Down Time and Ramping Polytope

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In this paper, we study the polyhedral structure of an integrated minimum-up/-down time and ramping polytope, which has broad applications in variant industries.

• The polytope we studied includes minimum-up/-down time, generation ramp-up/-down rate, logical, and generation upper/lower bound constraints.
• By exploring its specialized structures, we derive strong valid inequalities and explore a new proof technique to prove these inequalities are sufficient to provide convex hull descriptions for variant two-period and three-period polytopes, under different parameter settings.
• For multi-period cases, we derive generalized strong valid inequalities (including one, two, and three continuous variables, respectively) and further prove that these inequalities are facet-defining under mild conditions.