  The paper establishes tight lower bound for effective conductivity tensor
$K_*$ of two-dimensional three-phase conducting anisotropic composites and
defines optimal microstructures. It is assumed that three materials are mixed
with fixed volume fractions and that the conductivity of one of the materials
is infinite. The bound expands the Hashin-Shtrikman and Translation bounds to
multiphase structures, it is derived using the technique of {\em localized
polyconvexity} that is a combination of Translation method and additional
inequalities on the fields in the materials; similar technique was used by Nesi
(1995) and Cherkaev (2009) for isotropic multiphase composites. This paper
expands the bounds to the anisotropic composites. The lower bound of
conductivity (G-closure) is a piece-wise analytic function of eigenvalues of
$K_*$, that depends only on conductivities of components and their volume
fractions. Also, we find optimal microstructures that realize the bounds,
developing the technique suggested earlier by Albin Cherkaev and Nesi (2007)
and Cherkaev (2009). The optimal microstructures are laminates of some rank for
all regions. The found structures match the bounds in all but one region of
parameters; we discuss the reason for the gap and numerically estimate it.
