  Planar partial $3$-trees are subgraphs of those planar graphs obtained by
repeatedly inserting a vertex of degree $3$ into a face. In this paper, we show
that planar partial $3$-trees have $1$-string $B_1$-VPG representations, i.e.,
representations where every vertex is represented by an orthogonal curve with
at most one bend, every two curves intersect at most once, and intersections of
curves correspond to edges in the graph. We also that some subclasses of planar
partial 3-trees have L-representations, i.e., a $B_1$-VPG representation where
every curve has the shape of an L.
