Multi-Period Locally-Facet-Based MIP Formulations for Unit Commitment Problems

The thermal unit commitment (UC) problem has historically been formulated as a mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale systems. tighter characteristic reduces the search space, therefore, natural consequence, significantly computational burden. In literatures, many tightened formulations single with parts of constraints were reported without presenting explicitly how they derived. this paper, systematic approach developed formulate tight formulations. idea use more binary variables represent state so obtain tightest upper bound power generation limits and ramping unit. way, we propose multi-period formulation based on sliding windows may have different sizes each in system. Furthermore, model taking historical status into consideration obtained. Besides, sufficient necessary conditions facets single-unit polytope are provided redundant inequalities eliminated. proposed models three other state-of-the-art tested 73 instances scheduling time 24 hours. number generators test systems ranges from 10 1080. simulation results show that our than when window size greater 2.