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

TL;DR

This paper analyzes the polyhedral structure of an integrated unit commitment polytope, deriving strong inequalities and algorithms that improve solution efficiency for complex power system scheduling problems.

Contribution

It introduces new valid inequalities and proof techniques for the polytope, providing convex hull descriptions and facet conditions for multi-period cases.

Findings

Derived strong valid inequalities for two- and three-period polytopes.

Proposed polynomial-time separation algorithms for inequalities.

Outperformed default CPLEX in solving unit commitment problems.

Abstract

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. Moreover, we discover efficient polynomial time separation algorithms for these inequalities to improve the computational efficiency. 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 self-scheduling and network-constrained unit commitment problems, for which our derived approach outperforms the default CPLEX significantly.