## Empirical Investigation of Non-Convexities in Optimal Power Flow Problems. (arXiv:1804.04248v1 [math.OC])

Optimal power flow (OPF) is a central problem in the operation of electric
power systems. An OPF problem optimizes a specified objective function subject
to constraints imposed by both the non-linear power flow equations and
engineering limits. These constraints can yield non-convex feasible spaces that
result in significant computational challenges. Despite these non-convexities,
local solution algorithms actually find the global optima of some practical OPF
problems. This suggests that OPF problems have a range of difficulty: some
problems appear to have convex or "nearly convex" feasible spaces in terms of
the voltage magnitudes and power injections, while other problems can exhibit
significant non-convexities. Understanding this range of problem difficulty is
helpful for creating new test cases for algorithmic benchmarking purposes.
Leveraging recently developed computational tools for exploring OPF feasible
spaces, this paper first describes an empirical study that aims to charact查看全文