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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 demonstrate computational efficiency and solution quality benefits of formulation tightening. 

Unit Commitment is an important problem faced by independent system operators. It is usually formulated as a Mixed Binary Linear Programming (MBLP) problem, and is believed to be NP hard. To solve UC problems efficiently, an idea is through formulation tightening. If constraints can be transformed to directly delineate an MBLP problem’s convex hull during data preprocessing, then the problem can be solved by using linear programming methods. The resulting formulation can be reused for other data sets, tremendously reducing computational requirements. To achieve the above goal, both unit- and system-level constraints are tightened with synergistic combination in this paper. Unit-level constraints are tightened based on existing cuts and novel “constraint-and-vertex conversion” and vertex projection processes. To tighten system-level constraints, selected cuts are applied and some potentially powerful cuts are identified. Numerical results demonstrate the effectiveness of tightening unit- and system-level constraints.