Introduction to Wind Turbine Technology - Small Wind Turbines: Analysis, Design, and Application - page 16

The definition ( 1.17 ) immediately gives rise to an operational difficulty: what is
the appropriate T s to use in determining I u ? T s should be sufficiently large that any
increase would not alter the value of I u . In practice, this usually cannot be
achieved, and as a compromise, the most common T s used in wind turbine
applications is 10 min. This time is a compromise in that it captures the high
frequency fluctuations seen in Fig. 1.7 but misses most of the low frequency
changes associated with weather patterns. T s = 10 min is mandated by the
International Electrotechnical Commission (IEC) standard for the determination of
the power curve—see Measnet [ 11 ] for a freely-available summary.
I u depends on z 0 , increasing from around 0.1 (10%) for smooth terrain up to 0.2
(20%) or more for rough terrain at high z 0 . Turbulence also depends on height,
usually decreasing with increasing h. It can also affect the determination of turbine
power—see Exercise 1.23 at the end of this chapter—and influence the turbine
loads—see Chap. 9 . To determine the average power output from any turbine and
to undertake load analysis, it is necessary to know the probability of the wind
speed. This probability can be viewed as either the probability density function,
p(U), or the cumulative probability, C(U). The former measures the occurrence of
a particular wind speed, whereas the latter gives the probability that the wind speed
is less than U. Mathematically, the two are related by dC/dU = p.
The most common assumption, used, for example, in IEC 61400-2, is the so-
called Rayleigh distribution

Þ 2

C ð U Þ¼ 1 e p U = 2 U

ð

ð 1 : 18 Þ

and

p ðÞ¼ pU

2 U 2 e p U = 2 U

Þ 2

ð

ð 1 : 19 Þ

Note the use of the overbar in ( 1.18 ) and ( 1.19 ) to denote the average value of U as
it is necessary to distinguish between the U, typically found by averaging over
10 min, and its average U.
The Raleigh distribution is a special case of the Weibull distribution which is
commonly used for approximating the wind speed probability distribution.
Knowing p(U) allows calculation of the average power output for a particular site,
according to

P ¼ Z

1

P ðÞ p ðÞ dU ð 1 : 20 Þ

0

This determination is shown in Fig. 1.8 for the power curve in Fig. 1.4 and a
mean wind speed of 5 m/s. The ratio of the average power to the rated power is
called the capacity factor, a crucial parameter in determining the economics of
wind energy systems. For the data in Fig. 1.8 the capacity factor is 0.15. In
practice the capacity factor varies widely, reaching nearly 50% at a few very