Two novel locally ideal three-period unit commitment formulations in power systems

The thermal unit commitment problem has historically been formulated as a mixed integer quadratic programming problem, which is difficult to solve efficiently, especially for large-scale systems. The tighter characteristic reduces the search space; therefore, as a natural consequence, it significantly reduces the computational burden. In the literature, many tightened formulations for a single unit with parts of constraints were reported without a clear derivation process. In this paper, a systematic approach is developed to create tight formulations. The idea is to use new variables in high-dimensional space to capture all the states of a single unit within three periods and then use these state variables systematically to derive three-period locally ideal expressions for a subset of the constraints in unit commitment. Meanwhile, the linear dependence of those new state variables is leveraged to keep the compactness of the obtained formulations. Based on this approach, we propose two tight models. The proposed models and other four state-of-the-art models are tested on 56 instances over a scheduling period of 24 h for systems ranging from 10 to 1080 generating units. The simulation results show that our proposed unit commitment formulations are tighter and more efficient (Increased by 13.6%) than other state-of-the-art models. After transforming our models into mixed integer linear programming formulations, our models are still tighter and more efficient (Increased by 67.3%) than other models.