  In many power system optimization problems, we observe that only a small
fraction of the line flow constraints ever become active at the optimal
solution, despite variations in the load profile and generation costs. This
observation has far-reaching implications not only for power system
optimization, but also for the practical long-term planning, operation, and
control of the system. We formalize this empirical observation for problems
involving the DC power flow equations. We use a two-step constraint screening
approach to identify constraints whose satisfaction is implied by other
constraints in the problem, and can therefore be removed from the problem. For
the first screening step, we derive analytical bounds that quickly identify
redundancies in the flow limits on parallel lines. The second screening step
uses optimization-based constraint screening, where we solve a (relaxed)
optimization problem for each constraint to identify redundancies. Different
from existing methods, we specifically focus our approach on large ranges of
load variation such that the results are valid for long periods of time, thus
justifying the computational overhead required for the screening method.
Numerical results for a wide variety of standard test cases show that even with
load variations up to +/- 100% of nominal loading, we are able to eliminate a
significant fraction of the flow constraints. This large reduction in
constraints may enable a range of possible applications. As one illustrative
example, we demonstrate the computational improvements for the unit commitment
problem obtained as a result of the reduced number of constraints.
