We provide a comprehensive overview of mixed-integer programming formulations for the unit commitment (UC) problem. UC formulations have been an especially active area of research over the past 12 years due to their practical importance in power grid operations, and this paper serves as a capstone for this line of work. We additionally provide publicly available reference implementations of all formulations examined. We computationally test existing and novel UC formulations on a suite of instances drawn from both academic and real-world data sources. Driven by our computational experience from this and previous work, we contribute some additional formulations for both generator production upper bounds and piecewise linear production costs. By composing new UC formulations using existing components found in the literature and new components introduced in this paper, we demonstrate that performance can be significantly improved—and in the process, we identify a new state-of-the-art UC formulation.

We present a novel formulation for startup cost computation in the unit commitment problem (UC). Both our proposed formulation and existing formulations in the literature are placed in a formal, theoretical dominance hierarchy based on their respective linear programming relaxations. Our proposed formulation is tested empirically against existing formulations on large-scale UC instances drawn from real-world data. While requiring more variables than the current state-of-the-art formulation, our proposed formulation requires fewer constraints, and is empirically demonstrated to be as tight as a perfect formulation for startup costs. This tightening can reduce the computational burden in comparison to existing formulations, especially for UC instances with large reserve margins and high penetration levels of renewables.

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