  In this paper, we show that spatial correlation of renewable energy outputs
greatly influences the robustness of power grids. First, we propose a new index
for the spatial correlation among renewable energy outputs. We find that the
spatial correlation of renewable energy outputs in a short time-scale is as
weak as that caused by independent random variables and that in a long
time-scale is as strong as that under perfect synchronization. Then, by
employing the topology of the power grid in eastern Japan, we analyze the
robustness of the power grid with spatial correlation of renewable energy
outputs. The analysis is performed by using a realistic differential-algebraic
equations model and the result shows that the spatial correlation of the energy
resources strongly degrades the robustness of the power grid. Our result
suggests that the spatial correlation of the renewable energy outputs should be
taken into account when estimating the stability of power grids.
