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

A framework of systematic approach on unit commitment formulation is proposed in this paper. The framework is based on locally ideal conceptions to build strong valid inequalities for multi-period generation polytope subject to generation condition constraints. These inequalities define facets of the multi-period polytope for the unit commitment problem. This approach uses more binary variables to represent the state of the generator to obtain the tightest upper bounds of the generation limits and ramping constraints within multiple periods of a single generator. Through this approach, we proposed a multi-period formulation based on sliding windows which may have different sizes for each generator in the system to solve the unit commitment problems. Furthermore, a multi-period model is obtained to consider historical unit commitment status. The proposed model is compared with five other commonly used unit commitment models over a 24-hour scheduling window with 75 instances. The case study results validated the accuracy and effectiveness with superior computational cost reduction.