The Unit Commitment (UC) problem, which determines the day-ahead dispatch of generation units, is one of the key problems in power system operation. A long list of formulations that claim to solve this problem more efficiently have been proposed. However, comparing them is not easy due to the different interpretations of constraints (e.g., ramps, reserves, startup/shutdown) and the heuristic component of the solution process of most solvers. This paper proposes a general framework to establish a systematic procedure for comparing different formulations. In addition, we propose a statistical analysis to obtain robust conclusions about the performance of these formulations. The proposed framework provides insights to guide future formulation selection and im-provement. We apply the procedure to the three current state-of-the-art formulations: tight and compact (TC), state transition (ST), and projected two-binary-variable (2bin). Our results show that we can distinguish the impact of different constraints in each formulation as well as the influence of the solver’s heuristic pro-cess, in a statistically significant manner. For instance, there is statistical evidence that TC formulation is the fastest formulation in small case studies, while there is no statistical evidence to de-termine that one formulation is faster than the other in large-scale case studies.
Keywords: mixed-integer linear programming (MIP), unit commitment (UC), tightness, compactness, reformulations.
Registration date: 2018-09-19