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The daily operation of real-world power systems and their underlying marketsrelies on the timely solution of the unit commitment problem. However, givenits computational complexity, several optimization-based methods have beenproposed to lighten its problem formulation by removing redundant line flowconstraints. These approaches often ignore the spatial couplings of renewablegeneration and demand, which have an inherent impact of market outcomes.Moreover, the elimination procedures primarily focus on the feasible region andexclude how the problem's objective function plays a role here. To addressthese pitfalls, we move to rule out redundant and inactive constraints over atight linear programming relaxation of the original unit commitment feasibilityregion by adding valid inequality constraints. We extend the optimization-basedapproach called umbrella constraint discovery through the enforcement of aconsistency logic on the set of constraints by adding the proposed inequalityconstraints to the formulation. Hence, we reduce the conservativeness of thescreening approach using the available historical data and thus lead to atighter unit commitment formulation. Numerical tests are performed on standardIEEE test networks to substantiate the effectiveness of the proposed approach.

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