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

Abstract

The daily operation of real-world power systems and their underlying markets relies on the timely solution of the unit commitment problem. However, given its computational complexity, several optimization-based methods have been proposed to lighten its problem formulation by removing redundant line flow constraints. These approaches often ignore the spatial couplings of renewable generation and demand, which have an inherent impact of market outcomes. Moreover, the elimination procedures primarily focus on the feasible region and exclude how the problem's objective function plays a role here. To address these pitfalls, we move to rule out redundant and inactive constraints over a tight linear programming relaxation of the original unit commitment feasibility region by adding valid inequality constraints. We extend the optimization-based approach called umbrella constraint discovery through the enforcement of a consistency logic on the set of constraints by adding the proposed inequality constraints to the formulation. Hence, we reduce the conservativeness of the screening approach using the available historical data and thus lead to a tighter unit commitment formulation. Numerical tests are performed on standard test networks to substantiate the effectiveness of the proposed approach.