Tight and compact MILP formulation of start-up and shut-down ramping in unit commitment

Abstract

The Start-Up (SU) & Shut-Down (SD) ramps of thermal units must be considered in Unit Commitment (UC) formulations to accurately represent the unit’s power production. However, these ramps are usually ignored because they will considerably increase the computational burden of the UC problem. This paper presents a Mixed-Integer Linear Programming (MILP) formulation of SU & SD power trajectories of thermal units where the computational burden is considerably decreased in comparison to formulations commonly found in the literature. This is because the proposed formulation is i) tighter, i.e. the relaxed solution is nearer to the optimal integer solution; and ii) more compact, i.e. it needs fewer constraints, variables and nonzero elements in the constraint matrix. The proposed formulation is illustrated employing the self-UC problem faced by a thermal unit. Results show that not considering SU & SD ramps changes the commitment decisions causing a negative economic impact. We provide computational results comparing the proposed formulation with others found in the literature. The computation time was dramatically reduced as a natural consequence of the considerably tighter and more compact formulation.