Study of Active Line Flow Constraints in DC Optimal Power Flow Problems

Efficiently and reliably operating electric power grids requires the frequent solution of optimization problems such as the DC Optimal Power Flow (DC OPF) problem. Solution of DC OPF problems can be challenging due to the large number of operational constraints imposed in these problems, especially limits on the line flows. Improving solver times can be facilitated by a better understanding of the active line flow constraints in DC OPF problems (i.e., the inequality constraints limiting line flows that are satisfied with equality at the solution). Considering a variety of test cases and a range of loading scenarios, this paper empirically characterizes the sets of active line flow constraints in DC OPF problems. Among other analyses, the paper compares the sets of redundant line flow constraints (i.e., constraints guaranteed to be inactive) that are identified by previously proposed constraint screening methods to the line flow constraints that are actually observed to be active over a range of scenarios. The results indicate that a large fraction of the line flow constraints which are not identified as being redundant by these screening methods are nevertheless inactive in the DC OPF solutions. This observation suggests the potential for improvements to the constraint screening methods. Laying the groundwork for achieving these improvements, this paper also identifies which line characteristics tend to be associated with active flow constraints and studies the relationships among sets of simultaneously active line flow constraints.