A polyhedral study of production ramping

A State Transition MIP Formulation for the Unit Commitment Problem

“…We give the two-period ramping polytope below. With respect to the two-period ramping polytope defined in [14], the above definition has some differences. For instance, we consider both the ramp up and ramp down constraints together, which were treated separately in [14].…”

“…A similar argument also applies to (9b) when the generator is turned on at time t. In fact, these (along with many others) were the motivation behind studying tighter ramping constraints and valid inequalities in [13], [14], [27], [28]. In particular, [14] provided the following strengthened ramping constraints:…”

“…When the reserve requirements are neglected, the ramping inequalities (20a) and (20b) of the new formulation are equivalent to the facet-defining two-period ramping inequalities of the base formulation, proposed by [14], i.e., constraints (10a) and (10b). In contrast, the ramping constraints in MLR are such that the state variables do not explicitly guide the ramping rates of generators.…”

“…. l g − 1}, constraints (14) are omitted because their right-hand side will be no larger than zero and will be trivially satisfied due to the nonnegativity of the variables.…”

“…The popularity of MIP led to significant advances in the mathematical description of specific features of the UC problem. For instance, [11] have identified the convex hull for a minimum up/downtime polytope, [12] provided the convex hull of generation limits and this minimum up/downtime polytope, [13] provided strengthened inequalities of a ramping polytope, and [14] provided the convex hull of a two-period ramping polytope.…”