  Optimal power flow (OPF) problems are non-convex and large-scale optimization
problems with important applications in power networks. This paper proposes the
scheduled-asynchronous algorithm to solve a distributed semidefinite
programming (SDP) formulation of the OPF problem. In this formulation, every
agent seeks to solve a local optimization with its own cost function, physical
constraints on its nodal power injection, voltage, and power flow of the lines
it is connected to, and decision constraints on variables shared with neighbors
to ensure consistency of the obtained solution. In the scheduled-asynchronous
algorithm, every pair of connected nodes in the electrical network update their
local variables in an alternating fashion. This strategy is asynchronous, in
the sense that no clock synchronization is required, and relies on an
orientation of the electrical network that prescribes the precise ordering of
node updates. We establish the asymptotic convergence properties to the
primal-dual optimizer when the orientation is acyclic. Given the dependence of
the convergence rate on the network orientation, we also develop a distributed
graph coloring algorithm that finds an orientation with diameter at most five
for electrical networks with geometric degree distribution. Simulations
illustrate our results on various IEEE bus test cases.
