  Renewable generators perturb the electric power grid with heavily
non-Gaussian and time correlated fluctuations. While changes in generated power
on timescales of minutes and hours are compensated by frequency control
measures, we report subsecond distribution grid frequency measurements with
local non-Gaussian fluctuations which depend on the magnitude of wind power
generation in the grid. Motivated by such experimental findings, we simulate
the sub-second grid frequency dynamics by perturbing the power grid, as modeled
by a network of phase coupled nonlinear oscillators, with synthetically
generated wind power feed-in time series. We derive a linear response theory
and obtain analytical results for the variance of frequency increment
distributions. We find that the variance of short-term fluctuations decays, for
large inertia, exponentially with distance to the feed-in node, in agreement
with numerical results both for a linear chain of nodes and the German
transmission grid topology. In sharp contrast, the kurtosis of frequency
increments is numerically found to decay only slowly, not exponentially, in
both systems, indicating that the non-Gaussian shape of frequency fluctuations
persists over long ranges.
