  We present a scalable solution method based on an alternating direction
method of multipliers and graphics processing units (GPUs) for rapidly
computing and tracking a solution of alternating current optimal power flow
(ACOPF) problem. Such a fast computation is particularly useful for mitigating
the negative impact of frequent load and generation fluctuations on the optimal
operation of a large electrical grid. To this end, we decompose a given ACOPF
problem by grid components, resulting in a large number of small independent
nonlinear nonconvex optimization subproblems. The computation time of these
subproblems is significantly accelerated by employing the massive parallel
computing capability of GPUs. In addition, the warm-start ability of our method
leads to faster convergence, making the method particularly suitable for fast
tracking of optimal solutions. We demonstrate the performance of our method on
grids having up to 70,000 buses by solving associated optimal power flow
problems with both cold start and warm start.
