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

Kai Pan (kpan***at***ufl.edu)
Yongpei Guan (guan***at***ise.ufl.edu)

Abstract: In this paper, we consider the polyhedral structure of the integrated minimum-up/-down time and ramping polytope for the unit commitment problem. Our studied generalized polytope includes minimum-up/-down time constraints, generation ramp-up/-down rate constraints, logical constraints, and generation upper/lower bound constraints. We derive strong valid inequalities by utilizing the structures of the unit commitment problem, and 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 problems corresponding to different minimum-up/-down time limits and parameter assumptions. In addition, more generalized strong valid inequalities (including one, two, and three continuous variable cases respectively) are introduced to strengthen the multi-period formulations, and we further prove 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 on solving both the network-constrained unit commitment problem and the self-scheduling unit commitment problem, for which our derived approach outperforms the default CPLEX significantly.

Keywords: strong valid inequalities; polyhedral study; unit commitment; convex hull

Category 1: Integer Programming (Cutting Plane Approaches )

Category 2: Applications -- Science and Engineering


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Entry Submitted: 06/02/2015
Entry Accepted: 06/03/2015
Entry Last Modified: 06/05/2015

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