  The existence of multiple solutions to AC optimal power flow (ACOPF) problems
has been noted for decades. Existing solvers are generally successful in
finding local solutions, which are stationary points but may not be globally
optimal. In this paper, we propose a simple iterative approach to find globally
optimal solutions to ACOPF problems. First, we call an existing solver for the
ACOPF problem. From the solution and the associated dual variables, we form a
partial Lagrangian. Then we optimize this partial Lagrangian and use its
solution as a warm start to call the solver again for the ACOPF problem. By
repeating this process, we can iteratively improve the solution quality, moving
from local solutions to global ones. We show the effectiveness our algorithm on
standard IEEE networks. The simulation results show that our algorithm can
escape from local solutions to achieve global optimums within a few iterations.
