  In this paper, we consider the problem of optimally coordinating the response
of a group of distributed energy resources (DERs) in distribution systems by
solving the so-called optimal power flow (OPF) problem. The OPF problem is
concerned with determining an optimal operating point, at which some cost
function, e.g., generation cost or power losses, is minimized, and operational
constraints are satisfied. To solve the OPF problem, we propose distributed
algorithms that are able to operate over time-varying communication networks
and have geometric convergence rate. We solve the second-order cone program
(SOCP) relaxation of the OPF problem for radial distribution systems, which is
formulated using the so-called DistFlow model. Theoretical results are further
supported by the numerical simulations.
