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

TL;DR

This paper introduces a cost-driven approach to enhance the elimination of redundant network constraints in the unit commitment problem, improving computational efficiency while maintaining solution feasibility.

Contribution

It proposes a novel tightening method for LP-relaxation using economic valid inequalities, increasing constraint reduction in optimization-based filtering.

Findings

Significantly reduces line-flow constraints in UC formulations.

Maintains feasibility of the unit commitment solutions.

Enhances computational speed of UC problem solving.

Abstract

In an attempt to speed up the solution of the unit commitment (UC) problem, both machine-learning and optimization-based methods have been proposed to lighten the full UC formulation by removing as many superfluous line-flow constraints as possible. While the elimination strategies based on machine learning are fast and typically delete more constraints, they may be over-optimistic and result in infeasible UC solutions. For their part, optimization-based methods seek to identify redundant constraints in the full UC formulation by exploring the feasibility region of an LP-relaxation. In doing so, these methods only get rid of line-flow constraints whose removal leaves the feasibility region of the original UC problem unchanged. In this paper, we propose a procedure to substantially increase the line-flow constraints that are filtered out by optimization-based methods without jeopardizing their appealing ability of preserving feasibility. Our approach is based on tightening the LP-relaxation that the optimization-based method uses with a valid inequality related to the objective function of the UC problem and hence, of an economic nature. The result is that the so strengthened optimization-based method identifies not only redundant line-flow constraints but also inactive ones, thus leading to more reduced UC formulations.