  We propose a novel algorithm to solve optimal power flow (OPF) that aims at
dispatching controllable distributed energy resources (DERs) for voltage
regulation at minimum cost. The proposed algorithm features unprecedented
scalability to large distribution networks by utilizing an information
structure based on networked autonomous grids (AGs). Specifically, each AG is a
subtree of a large distribution network that has a tree topology. The topology
and line parameters of each AG are known only to a regional coordinator (RC)
that is responsible for communicating with and dispatching the DERs within this
AG. The reduced network, where each AG is treated as a node, is managed by a
central coordinator (CC), which knows the topology and line parameters of the
reduced network only and communicates with all the RCs. We jointly explore this
information structure and the structure of the linearized distribution power
flow (LinDistFlow) model to derive a hierarchical, distributed implementation
of the primal-dual gradient algorithm that solves the OPF. The proposed
implementation significantly reduces the computation burden compared to the
centrally coordinated implementation of the primal-dual algorithm. Numerical
results on a 4,521-node test feeder show that the proposed hierarchical
distributed algorithm can achieve an improvement of more than tenfold in the
speed of convergence compared to the centrally coordinated primal-dual
algorithm.
