WIND ENERGY SYSTEMS - Cd3wd

Chapter 2—Wind Characteristics 2–28
Many hand calculators have a built-in routine for computing mean and standard deviation.
The answers of the previous example can be checked on such a machine by anyone willing to
punch in 115 numbers. In other words, Eq. 19 provides a convenient shortcut to finding the
variance as compared with the method indicated by Eq. 16, or even by direct computation on
a hand calculator.
Both the mean and the standard deviation will vary from one period to another or from
one location to another. It may be of interest to some people to arrange these values in rank
order from smallest to largest. We can then immediately pick out the smallest, the median,
and the largest value. The terms smallest and largest are not used much in statistics because
of the possibility that one value may be widely separated from the rest. The fact that the
highest recorded surface wind speed is 105 m/s at Mt. Washington is not very helpful in
estimating peak speeds at other sites, because of the large gap between this speed and the
peak speed at the next site in the rank order. The usual practice is to talk about percentiles,
where the 90 percentile mean wind would refer to that mean wind speed which is exceeded by
only 10 % of the measured means. Likewise, if we had 100 recording stations, the 90 percentile
standard deviation would be the standard deviation of station number 90 when numbered in
ascending rank order from the station with the smallest standard deviation. Only 10 stations
would have a larger standard deviation (or more variable winds) than the 90 percentile value.
This practice of using percentiles allows us to consider cases away from the median without
being too concerned about an occasional extreme value.
We shall now define the probability p of the discrete wind speed u i being observed as
p(u i )= m i
n
(20)
By this definition, the probability of an 8 m/s wind speed being observed in the previous
example would be 42/115 = 0.365. With this definition, the sum of all probabilities will be
unity.
w∑
p(u i ) = 1 (21)
i=1
Note that we are using the same symbol p for both pressure and probability. Hopefully,
the context will be clear enough that this will not be too confusing.
We shall also define a cumulative distribution function F (u i ) as the probability that a
measured wind speed will be less than or equal to u i .
i∑
F (u i )= p(u j ) (22)
j=1
The cumulative distribution function has the properties
Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001