The optimal power flow (OPF) problem is nonconvex and generally 
hard to solve. We show that the dual of an equivalent form of
OPF is a semidefinite program (SDP) and hence convex.  We prove
a sufficient condition under which the duality gap is zero, in
which case an optimal solution of the OPF problem can be 
efficiently computed from a solution of the dual problem.  
Interestingly, the standard IEEE benchmark systems with 
14, 30, 57, 118 and 300 buses all satisfy this condition and
are therefore efficiently solvable.