  Fluctuations represent a major challenge for the incorporation of electric
power from large wind-farms into power grids. Wind farm power output fluctuates
strongly in time, over various time scales. Understanding these fluctuations,
especially their spatio-temporal characteristics, is particularly important for
the design of backup power systems that must be readily available in
conjunction with wind-farms. In this work we analyze the power fluctuations
associated with the wind-input variability at scales between minutes to several
hours, using large eddy simulations (LES) of extended wind-parks, interacting
with the atmospheric boundary layer. LES studies enable careful control of
parameters and availability of wind-velocities simultaneously across the entire
wind-farm. The present study focuses on neutral atmospheric conditions and flat
terrain, using actuator-disk representations of the individual wind-turbines.
We consider power from various aggregates of wind-turbines such as the total
average power signal, or signals from sub-averages within the wind-farm.
Non-trivial correlations are observed due to the complex interactions between
turbines placed downstream of each other, and they lead to noticeable spectral
peaks at frequencies associated with the inter-turbine spacings when the
wind-direction is completely fixed. In that case we observe that the frequency
spectra of the total wind-farm output show a decay that follows approximately a
$-5/3$ power-law scaling regime, qualitatively consistent with some
observations made in field-scale operational wind-parks (Apt, 2007). We find
that these features are still observed when the wind-speed varies in magnitude.
However, significant changes in the wind-direction over time tend to smooth out
the observed spectral peak and reduce the extent of the observed $-5/3$
power-law.
