  The optimal power flow (OPF) problem is fundamental in power system
operations and planning. Large-scale renewable penetration in distribution
networks calls for real-time feedback control, and hence the need for fast and
distributed solutions for OPF. This is difficult because OPF is nonconvex and
Kirchhoff's laws are global. In this paper we propose a solution for balanced
radial distribution networks. It exploits recent results that suggest solving
for a globally optimal solution of OPF over a radial network through the
second-order cone program (SOCP) relaxation. Our distributed algorithm is based
on alternating direction method of multiplier (ADMM), but unlike standard ADMM
algorithms that often require iteratively solving optimization subproblems in
each ADMM iteration, our decomposition allows us to derive closed form
solutions for these subproblems, greatly speeding up each ADMM iteration. We
present simulations on a real-world 2,065-bus distribution network to
illustrate the scalability and optimality of the proposed algorithm.
