The Unit Commitment (UC) consists of optimal resource scheduling in electric power systems to minimize the total system operational costs, while operating the system and units within secure technical limits. Mixed-Integer Linear Programming (MIP) has become a very popular approach to solving UC problems due to significant improvements in off-the-shelf MILP solvers. Despite the significant improvements in MIP solving, the time required to solve UC problems continues to be a critical limitation that restricts their size and scope. Nevertheless, improving an MIP formulation can dramatically reduce its computational burden and so allow the implementation of more advanced and computationally demanding problems.

The computational performance of an MIP formulation is mainly influenced by its tightness and compactness. Creating tight or compact computationally efficient MIP formulations is a non trivial task because the obvious formulations are very weak or very large, and trying to improve the tightness (compactness) usually means harming the compactness (tightness). We present an MIP-based UCs that is simultaneously tight and compact. Consequently, significantly lowering the computational burden compared with other UC formulations commonly found in the literature. Furthermore, the computational advantage becomes more significant by using the tight and compact formulations as the core of further extended UC problems, such as stochastic UC and power-based UCs.