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Optimal power flow (OPF) is a central problem in the operation of electricpower systems. An OPF problem optimizes a specified objective function subjectto constraints imposed by both the non-linear power flow equations andengineering limits. These constraints can yield non-convex feasible spaces thatresult in significant computational challenges. Despite these non-convexities,local solution algorithms actually find the global optima of some practical OPFproblems. This suggests that OPF problems have a range of difficulty: someproblems appear to have convex or "nearly convex" feasible spaces in terms ofthe voltage magnitudes and power injections, while other problems can exhibitsignificant non-convexities. Understanding this range of problem difficulty ishelpful for creating new test cases for algorithmic benchmarking purposes.Leveraging recently developed computational tools for exploring OPF feasiblespaces, this paper first describes an empirical study that aims to characterizenon-convexities for small OPF problems. This paper then proposes and analyzesseveral medium-size test cases that challenge a variety of solution algorithms.

Empirical Investigation of Non-Convexities in Optimal Power Flow Problems