Convex Hulls for the Unit Commitment Polytope

TL;DR

This paper characterizes the convex hulls of various formulations of the unit commitment problem, providing polyhedral insights that can improve optimization efficiency in power system scheduling.

Contribution

It offers new convex hull descriptions for the integrated minimum-up/-down time and ramping polytopes under general time period settings, advancing the theoretical understanding of the problem.

Findings

Derived convex hulls for integrated minimum-up/-down time and ramping polytopes.

Unified polyhedral descriptions under general T-period settings.

Enhanced formulations for more efficient unit commitment optimization.

Abstract

In this paper, we consider the polyhedral structure of the unit commitment polytope. In particular, we provide the convex hull results for the problem under the following different settings: 1) the convex hulls for the integrated minimum-up/-down time and ramping polytope under the general $T$ time period setting in which the ramping rate equals to the gap between the generation upper and lower bounds and equals to half of the gap between the generation upper and lower bounds, respectively, 2) the convex hull for the integrated minimum-up/-down time and ramping-up polytope for the problem under the general $T$ time period setting, and 3) the convex hull for the integrated minimum-up/-down time and ramping-down polytope for the problem under the general $T$ time period setting.