A Systematic Formulation Tightening Approach for Unit Commitment Problems

Unit Commitment is usually formulated as a Mixed Binary Linear Programming (MBLP) problem. When considering a large number of units, state-of-the-art methods such as branch-and-cut may experience difficulties. To address this, an important but much overlooked direction is formulation transformation since if the problem constraints can be transformed to directly delineate the convex hull in the data pre-processing stage, then a solution can be obtained by using linear programming methods without combinatorial difficulties. In the literature, a few tightened formulations for single units with constant ramp rates were reported without presenting how they were derived. In this paper, a systematic approach is developed to tighten formulations in the data pre-processing stage. The idea is to derive vertices of the convex hull without binary requirements. From them, vertices of the original convex hull can be innovatively obtained. These vertices are converted to tightened constraints, which are then parameterized based on unit parameters for general use, tremendously reducing online computational requirements. By analyzing short-time horizons, e.g., two or three hours, tightened formulations for single units with constant and generation-dependent ramp rates are obtained, beyond what is in the literature. Results based on the IEEE 118-bus and Polish 2383-bus systems demonstrate computational efficiency and solution quality benefits of formulation tightening. The approach is general and has great potential for tightening complicated MBLP problems in power systems and beyond.