  We propose a model to create synthetic networks that may also serve as a
narrative of a certain kind of infrastructure network evolution. It consists of
an initialization phase with the network extending tree-like for minimum cost
and a growth phase with an attachment rule giving a trade-off between
cost-optimization and redundancy. Furthermore, we implement the feature of some
lines being split during the grid's evolution. We show that the resulting
degree distribution has an exponential tail and may show a maximum at degree
two, suitable to observations of real-world power grid networks. In particular,
the mean degree and the slope of the exponential decay can be controlled in
partial independence. To verify to which extent the degree distribution is
described by our analytic form, we conduct statistical tests, showing that the
hypothesis of an exponential tail is well-accepted for our model data.
