The time variation of wind speeds and windfarm power output in Kansas

Abstract

On the Kansas plains, 1-min average wind speeds have high autocorrelations, with a value of about 0.9 with a lag of 32 min. In the winter, spring, and fall, 10 min average wind speed autocorrelation functions drop to 0 in 20 to 30 hr. Some cyclic behavior is noticed in the winter and fall correlations, with a period of several days. It is believed that this cyclic behavior is due to the passage of fronts. Only the summer season data showed a marked diurnal cycle. For short lag times up to about 30 min, the autocorrelation function of 1 min averaged wind machine output dropped more rapidly than that of wind speed. For longer lag times the 10 min averaged output autocorrelation was very similar to that of the wind speed. Wind speeds averaged for 1 min has a cross-correlation across a wind site which was a function of distance. The correlation dropped to about 0.83 at a distance of 21.7 km (13.5 mi). Wind machine output was less well correlated with a drop to about 0.69 at a spacing of 21.7 km. The autocorrelation function of a windfarm consisting of a large number of wind machines dropped much less rapidly than that of a single wind machine, as would be expected. A windfarm consisting of 100 MOD-2 wind machines with a spacing of 1.61 km by 0.80 km had a correlation of about 0.98 for a 10 min lag time when 1 min averaged output was considered.