WIND ENERGY SYSTEMS - Cd3wd

Chapter 2—Wind Characteristics 2–53
r =
w∑
(ū ai − ū a )(ū bi − ū b )
i=1
(67)
w∑
∑ w √ (ū ai − ū a ) 2 (ū bi − ū b ) 2
i=1
i=1
In this expression, ū a is the long term mean speed at site a, ū b is the long term mean
speed at site b, ū bi is the observed monthly or yearly mean at site b, andw is the number of
months or years being examined. We assume that the wind speed at site b is linearly related
to the speed at site a. We can then plot each mean speed ū bi versus the corresponding ū ai .
We then find the best straight line through this cluster of points by a least squares or linear
regression process. The correlation coefficient then describes how closely our data fits this
straight line. Its value can range from r =+1tor = −1. At r = +1, the data falls exactly
onto a straight line with positive slope, while at r = −1, the data falls exactly onto a straight
line with negative slope. At r = 0, the data cannot be approximated at all by a straight line.
Example
The yearly mean wind speeds for Dodge City, Wichita, and Russell, Kansas are given in Table 2.6.
These three stations form a triangle in central Kansas with sides between 150 and 220 km in length.
Dodge City is west of Wichita, and Russell is northwest of Wichita and northeast of Dodge City. The
triangle includes some of the best land in the world for growing hard red winter wheat. There are few
trees outside of the towns and the land is flat to gently rolling in character. Elevation changes of 10 to
20 m/km are rather typical. We would expect a high correlation between the sites, based on climate
and topography.
There were several anemometer height changes over the 26 year period, so in an attempt to eliminate
this bias in the data, all yearly means were extrapolated to a 30 m height using the power law and an
average exponent of 0.143. As mentioned earlier in this chapter, this assumption should be acceptable
for these long term means.
A plot of Russell wind speeds versus Dodge City speeds is given in Fig. 23, and a similar plot
for Russell versus Wichita is given in Fig. 24. A least squares fit to the data was computed using a
hand held calculator with linear regression and correlation coefficient capability. The equation of the
straight line through the points in Fig. 23 is ū b = 0.729ū a + 3.59 with r = 0.596. The corresponding
equation for Fig. 24 is ū b = 0.181ū a + 11.74 with r = 0.115. Straight lines are drawn on these figures
for these equations.
It can be seen from both the figures and the correlation coefficients that Russell winds are poorly
predicted by Dodge City winds and are hardly predicted at all by Wichita winds. Years with mean
speeds around 14 knots at Wichita display mean speeds between 12.3 and 16 knots at Russell. This
gives further support to the conclusion made by Justus that one year’s data with a 90 % confidence
interval at a candidate site is just as good as extrapolating from adjacent sites.
In examining the data in Table 2.6, one notices some clusters of low wind speed years and
high wind speed years. That is, it appears that a low annual mean wind may persist through
the following year, and likewise for a high annual mean wind. If this is really the case, we may
select a site for a wind turbine in spite of a poor wind year, and then find the performance of
Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001