  Solving optimal power flow (OPF) problems for large distribution networks
incurs high computational complexity. We consider a large multi-phase
distribution network of tree topology with a deep penetration of active
devices. We divide the network into collaborating areas featuring subtree
topology and subareas featuring subsubtree topology. We design a multi-level
implementation of the primal-dual gradient algorithm to solve the voltage
regulation OPF problems while preserving nodal voltage information and
topological information within areas and subareas. Numerical results on a
4,521-node system verify that the proposed algorithm can significantly improve
the computational speed without compromising any optimality.
