  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 satisfy first and second order optimality
conditions, but may not be globally optimal. In this paper, we propose a simple
iterative approach to improve the quality of 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 of 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.
