The power spectral density of the output of wind turbines provides information on the character of fluctuations in turbine output. Here both 1-second and 1-hour samples are used to estimate the power spectrum of several wind farms. The measured output power is found to follow a Kolmogorov spectrum over more than four orders of magnitude, from 30s to 2.6 days. This result is in sharp contrast to the only previous study covering long time periods, published 50 years ago. The spectrum defines the character of fill-in power that must be provided to compensate for wind's fluctuations when wind is deployed at large scale. Installing enough linear ramp rate generation (such as a gas generator) to fill in fast fluctuations with amplitudes of 1% of the maximum fluctuation would oversize the fill-in generation capacity by a factor of two for slower fluctuations, greatly increasing capital costs. A wind system that incorporates batteries, fuel cells, supercapacitors, or other fast-ramp-rate energy storage systems would match fluctuations much better, and can provide an economic route for deployment of energy storage systems when renewable portfolio standards require large amounts of intermittent renewable generating sources.