Convex Hulls for the Unit Commitment Polytope

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.