Identifying Redundant Flow Limits on Parallel Lines

Many power system optimization problems constrain line flows with limits specified in terms of the magnitudes of apparent power or current flows. The set of line-flow constraints may have redundancies (i.e., the feasible space may be unchanged upon removal of a subset of the line-flow constraints), which unnecessarily complicate optimization problems. This letter describes an algorithm for identifying redundant line-flow constraints corresponding to certain parallel lines. After formulating the constraints as ellipsoids in the voltage variables, redundancies are detected from the absence of intersections between pairs of ellipsoids corresponding to parallel lines. This algorithm is demonstrated using several large test cases.