  Finding a global solution to the optimal power flow (OPF) problem is
difficult due to its nonconvexity. A convex relaxation in the form of
semidefinite programming (SDP) has attracted much attention lately as it yields
a global solution in several practical cases. However, it does not in all
cases, and such cases have been documented in recent publications. This paper
presents another SDP method known as the moment-sos (sum of squares) approach,
which generates a sequence that converges towards a global solution to the OPF
problem at the cost of higher runtime. Our finding is that in the small
examples where the previously studied SDP method fails, this approach finds the
global solution. The higher cost in runtime is due to an increase in the matrix
size of the SDP problem, which can vary from one instance to another. Numerical
experiment shows that the size is very often a quadratic function of the number
of buses in the network, whereas it is a linear function of the number of buses
in the case of the previously studied SDP method.
