Implied Constraint Satisfaction in Power System optimization: The Impacts of Load Variations

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 practical applications such as long-term planning, operation, and control of the system.This paper presents a constraint screening approach to identify constraints whose satisfaction is implied by other constraints in the problem, and can therefore be safely disregarded. The approach is targeted at problems which involve DC power flow constraints, and involves two steps. The first step uses simple analytical relationships to remove redundant limits on parallel lines. The second step uses optimization to consider interactions among all of the problem constraints. In essence, we solve a (relaxed) optimization problem for each constraint to identify whether it is redundant. Different from existing methods that focus on constraint screening for a given daily load profile, we consider ranges of load that are wide enough to represent yearly variations in loading. The constraint screening results are thus valid for long periods of time, 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 transmission constraints. This large reduction in constraints may enable computational gains across 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.