Fluctuations represent a major challenge for the incorporation of electric power from large windfarms 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 windturbines 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.