Cost-Driven Screening of Network Constraints for the Unit Commitment Problem

Tight Data-Driven Linear Relaxations for Constraint Screening in Robust Unit Commitment

“…For expository purposes, we carry out our developments using a simplified single-period unit commitment [11], [13], [24] according to the following simplifying assumptions:…”

“…Alternatively, the notion of umbrella constraint was introduced when identifying redundant constraints which do not alter the feasibility region of the original UC problem when they are removed from the original problem [6]. Similarly, references [10]- [13] use a bound tightening technique [14] and solve two optimization problems for each transmission line in the power system over linear programming (LP) relaxations of the feasible region to remove as many redundant constraints as possible from the full UC formulation. Also, the authors of [15] used Clarkson's redundancy removal algorithm that is based on LP and requires solving multiple maximization problems [16] for each possible line flow contingency constraint in a SCOPF.…”

“…Third, to yield optimal solutions in constraint screening problems means screening out not only redundant constraints with respect to the feasibility region but also as guided by the UC problem's objective function. In other words, a UC's nonactive constraints can be part of its minimal feasible region, but they are never active constraints as they do not oppose the minimization the UC's objective function [13], [24].…”

“…Furthermore, we introduce a valid upper bound inequality constraint whose calculation is based on past UC solution runs as suggested by [13] to eliminate further non-binding constraints. This allows the elimination of unrealistic generation schedules-with, for example, prohibitively high costs-as we run UCD.…”

“…This allows the elimination of unrealistic generation schedules-with, for example, prohibitively high costs-as we run UCD. In contrast to the suggestion from [13], we include a conservativeness factor to mitigate model misspecification and infeasibility, a known weakness of "predict-then-optimize" approaches [29].…”