  The energy bounds condition for intertwining operators of unitary rational
vertex operator algebras (VOAs) was studied, first by A.Wassermann for type $A$
affine VOAs, and later by T.Loke for $c<1$ Virasoro VOAs, and by
V.Toledano-Laredo for type $D$ affine VOAs. In this paper, we extend their
results to affine VOAs of type $B$, $C$, and $G_2$. As a consequence, the
modular tensor categories of these unitary vertex operator algebras are
unitary.
