  A semidefinite programming (SDP) relaxation globally solves many optimal
power flow (OPF) problems. For other OPF problems where the SDP relaxation only
provides a lower bound on the objective value rather than the globally optimal
decision variables, recent literature has proposed a penalization approach to
find feasible points that are often nearly globally optimal. A disadvantage of
this penalization approach is the need to specify penalty parameters. This
paper presents an alternative approach that algorithmically determines a
penalization appropriate for many OPF problems. The proposed approach
constrains the generation cost to be close to the lower bound from the SDP
relaxation. The objective function is specified using iteratively determined
weights for a Laplacian matrix. This approach yields feasible points to the OPF
problem that are guaranteed to have objective values near the global optimum
due to the constraint on generation cost. The proposed approach is demonstrated
on both small OPF problems and a variety of large test cases representing
portions of European power systems.
