  Alternating-Current Optimal Power Flow (AC-OPF) is framed as a NP-hard
non-convex optimization problem that solves for the most economical dispatch of
grid generation given the AC-network and device constraints. Although there are
no standard methodologies for obtaining the global optimum for the problem,
there is considerable interest from planning and operational engineers in
finding a local optimum. Nonetheless, solving for the local optima of a large
AC-OPF problem is challenging and time-intensive, as none of the leading
non-linear optimization toolboxes can provide any timely guarantees of
convergence. To provide robust local convergence for large complex systems, we
introduce a homotopy-based approach that solves a sequence of primal-dual
interior point problems. We utilize the physics of the grid to develop the
proposed homotopy method and demonstrate the efficacy of this approach on U.S.
Eastern Interconnection sized test networks.
