  Optimal power flow (OPF) is an important problem for power generation and it
is in general non-convex. With the employment of renewable energy, it will be
desirable if OPF can be solved very efficiently so its solution can be used in
real time. With some special network structure, e.g. trees, the problem has
been shown to have a zero duality gap and the convex dual problem yields the
optimal solution. In this paper, we propose a primal and a dual algorithm to
coordinate the smaller subproblems decomposed from the convexified OPF. We can
arrange the subproblems to be solved sequentially and cumulatively in a central
node or solved in parallel in distributed nodes. We test the algorithms on IEEE
radial distribution test feeders, some random tree-structured networks, and the
IEEE transmission system benchmarks. Simulation results show that the
computation time can be improved dramatically with our algorithms over the
centralized approach of solving the problem without decomposition, especially
in tree-structured problems. The computation time grows linearly with the
problem size with the cumulative approach while the distributed one can have
size-independent computation time.
