  The deepening penetration of renewable energy is challenging how power system
operators cope with the associated variability and uncertainty in the unit
commitment problem. Given its computational complexity, several
optimization-based methods have been proposed to lighten the full unit
commitment formulation by removing redundant line flow constraints. These
approaches often ignore the spatial couplings of multi-side renewable
generation and demand. To address this pitfall, we rule out redundant
constraints over a tightened linear programming relaxation of the original unit
commitment feasibility region by adding a constraint that efficiently models
the correlation of residual demand variations. We set forth a novel, tractable
and robust polyhedral uncertainty envelope induced by a given set of scenarios
to characterize the tightening constraint. We propose a data-driven umbrella
constraint discovery problem formulation that substantially increase the
network constraints filtration in unit commitment. Numerical tests are
performed on standard IEEE test networks to substantiate the effectiveness of
the approach.
