s . so c - ph ] 1 3 A pr 2 01 7 Spatial uniformity in power - grid system

Robust synchronization is indispensable for stable operation of a power grid. Recently, it has been reported that a large number of decentralized generators, rather than a small number of large power plants, provide enhanced synchronization together with greater robustness against structural failures. In this paper, we systematically control the spatial uniformity of the geographical distribution of generators, and conclude that the more uniformly generators are distributed, the more enhanced synchronization occurs. In the presence of temporal failures of power sources, we observe that spatial uniformity helps the power grid to recover stationarity in a shorter time. We also discuss practical implications of our results in designing the structure of a power-grid network.