New MIP Formulations for the Single-Unit Commitment Problems with Ramping Constraints

The Unit Commitment (UC) problem in electrical power production requires to optimally operate a set of power generation units over a short time horizon (one day to a week). Operational constraints depend on the type of the generation units (e.g., thermal, hydro, nuclear, ...). The Single-Unit Commitment (1UC) problem is the restriction of UC that considers only one unit; it is useful in deregulated systems (for the so-called self-scheduling), and when decomposition methods are applied to (multi-units) UC. Typical constraints in (1UC) concern minimum and maximum power output, minimum-up and -down time, start-up and shut-down limits, ramp-up and ramp-down limits. In this work we present the first MIP formulation that describes the convex hull of the feasible solutions of (1UC) further improved to include also ramp-up and ramp- down constraints. Our formulation has a polynomial number of both variables and constraints and it is based on the efficient Dynamic Programming algorithm proposed in [15].