  Decarbonization in the energy sector has been accompanied by an increased
penetration of new renewable energy sources in electric power systems. Such
sources differ from traditional productions in that, first, they induce larger,
undispatchable fluctuations in power generation and second, they lack inertia.
Therefore, substituting new renewables for traditional generation induces
stronger and more frequent disturbances and modifies the way disturbances
propagate across AC electric power grids. Recent measurements have indeed
reported long, non-Gaussian tails in the distribution of local grid-frequency
data. Large frequency deviations may induce grid instabilities, leading in
worst-case scenarios to cascading failures and large-scale blackouts. In this
manuscript, we investigate how correlated noise disturbances, characterized by
the cumulants of their distribution, propagate through meshed, high-voltage
power grids. We show that for a single source of fluctuations,
non-Gaussianities in the form of finite skewness and positive kurtosis of the
noise distribution propagate over the entire network when the noise correlation
time is larger than the network's intrinsic time scales, but that they vanish
over short distances if the noise fluctuates rapidly. We furthermore show that
a Berry-Esseen theorem leads to the vanishing of non-Gaussianities as the
number of uncorrelated noise sources increases. Our results show that the
persistence of non-Gaussian fluctuations of feed-in power have a global impact
on power-grid dynamics when they fluctuate over time scales larger than the
intrinsic time scales of the system, which, we argue, is the relevant regime in
real power grids. Our predictions are corroborated by numerical simulations on
realistic models of power grids.
