  The present paper discusses the application of the recently proposed
Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method to
non-convex AC Optimal Power Flow Problems (OPF) in a distributed fashion. In
contrast to the often used Alternating Direction of Multipliers Method (ADMM),
ALADIN guarantees locally quadratic convergence for AC OPF. Numerical results
for 5 to 300 bus test cases indicate that ALADIN is able to outperform ADMM and
to reduce the number of iterations by about one order of magnitude. We compare
ALADIN to numerical results for ADMM documented in the literature. The improved
convergence speed comes at the cost of increasing the communication effort per
iteration. Therefore, we propose a variant of ALADIN that uses inexact Hessians
to reduce communication. Additionally, we provide a detailed comparison of
these ALADIN variants to ADMM from an algorithmic and communication
perspective. Moreover, we prove that ALADIN converges locally at quadratic rate
even for the relevant case of suboptimally solved local NLPs.
