  Replacing conventional power sources by renewable sources in current power
grids drastically alters their structure and functionality. The resulting grid
will be far more decentralized with an distinctly different topology. Here we
analyze the impact of grid topologies on spontaneous synchronization,
considering regular, random and small-world topologies and focusing on the
influence of decentralization. We employ the classic model of power grids
modeling consumers and sources as second order oscillators. We first analyze
the global dynamics of the simplest non-trivial (two-node) network that exhibit
a synchronous (normal operation) state, a limit cycle (power outage) and
coexistence of both. Second, we estimate stability thresholds for the
collective dynamics of small network motifs, in particular star-like networks
and regular grid motifs. For larger networks we numerically investigate
decentralization scenarios finding that decentralization itself may support
power grids in reaching stable synchrony for lower lines transmission
capacities. Decentralization may thus be beneficial for power grids, regardless
of their special resulting topology. Regular grids exhibit a specific
transition behavior not found for random or small-world grids.
