  When the shunt elements in the Pi circuit line model are assumed zero, it has
been proved that branch flow models are equivalent to bus injection models and
that the second-order cone relaxation of optimal power flow problems on a
radial network is exact under certain conditions. In this note we propose a
branch flow model that includes nonzero line shunts and prove that the
equivalence and the exactness of relaxation continue to hold under essentially
the same conditions as for zero shunt elements.
