Environmental Engineering Reference
In-Depth Information
If the site pressure is not available (as is usually the case), the air density can be
estimated as a function of the site elevation and temperature, as follows:
P 0
RT
e (
gz
RT
) (
kg/m 3
ρ =
)
(10.11)
where
P 0 =
Standard sea-level atmospheric pressure in Pascal (101,325 Pa)
( C
=
=
) +
.
T
Air temperature (K), T (K)
T
273
15
807 m/s 2
=
(
.
)
g
the gravitational constant
9
z
=
the elevation of the temperature sensor above mean sea level (m).
After substituting the numerical values for P 0 , R , and g , the equation becomes
353
e 0 . 03417 T
.
05
kg/m 3
ρ =
(
)
(10.12)
T
While this equation is quite accurate (to within 0.2% at most sites), the error increases
with increasing elevation because the air pressure does not follow the exponential
function exactly.
10.1.7 Speed Frequency Distribution and Weibull Parameters
The speed frequency distribution is a critical piece of information as it is used directly
in estimating the power output of a wind turbine. The frequency distribution represents
the number of times in the period of record that the observed speed falls within
particular ranges, or bins. The speed bins are typically 0.5 or 1 m/s wide and span at
least the range of speeds defined for the turbine power curve, that is, from 0 to 25 m/s
and above. It is usually presented in reports as a bar chart, or histogram, covering all
directions. In addition, the wind speed frequency distribution by direction is stored in
a tabular format, which is used as an input to wind plant design software.
The Weibull distribution is a mathematical function that is often used to represent
the wind speed frequency distribution at a site. In the Weibull distribution, the prob-
ability density (the probability that the speed will fall in a bin of unit width centered
on speed v
)
is given by the equation:
v
A
k 1
k
A
k
e (
)
v
A
p
(
v
) =
(10.13)
There are two parameters in the Weibull function: A , the scale parameter, which is
of dimension speed and is related closely to the mean wind speed, and k , the non-
dimensional shape parameter, which controls the width of the distribution. Values of
k range from 1 to 3.5, the higher values indicating a narrower frequency distribution
(i.e., a steadier, less variable wind). A commonly observed k range is 1.6 to 2.4.
Within this range, the mean speed is about 0.89 times the scale factor. Figure 10-3
illustrates Weibull probability density curves for several values of k and constant A .
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