  The structure of the turbulence-driven power fluctuations in a wind farm is
fundamentally described from basic concepts. A derived tuning-free model,
supported with experiments, reveals the underlying spectral content of the
power fluctuations of a wind farm. It contains two power-law trends and
oscillations in the relatively low- and high-frequency ranges. The former is
mostly due to the turbulent interaction between the flow and the turbine
properties; whereas the latter is due to the advection between turbine pairs.
The spectral wind-farm scale power fluctuations $\Phi_P$ exhibits a power-law
decay proportional to $f^{-5/3-2}$ in the region corresponding to the
turbulence inertial subrange and at relatively large scales, $\Phi_P\sim
f^{-2}$. Due to the advection and turbulent diffusion of large-scale
structures, a spectral oscillation exists with the product of a sinusoidal
behavior and an exponential decay in the frequency domain.
