Wind Characteristics - Wind Energy: Renewable Energy and the Environment - page 42

If the observations of wind speeds are compiled into a histogram, then the number of observa-
tions, n j , in each wind speed bin could be changed to a frequency or probability by dividing the
number of observations in a bin by the total number of observations:

c

n
N

c

£ 1 £

1

,

j , and

(3.11)

f j 1

N n j f

j

j j

where c is the number of classes or bins. If the wind speed units are changed or if the wind speed is
changed due to height, then the resulting histogram or frequency distribution should be normalized
to contain the same number of observations.
Of course, for a large number of observations, a computer program or a spreadsheet would alle-
viate a lot of drudgery. Notice that the average wind speed (same as mean wind speed) is just the
summation of the probability times the wind speed for each class in a frequency distribution:

c

£ 1

(3.12)

v f v

a j j

j

The average power/area can be calculated from a selected wind speed histogram or wind speed
frequency distribution by

P
AN nv

0.5 R

c c

£ £

(3.13)

avg avg 3 3

0.5 R fv

jj avg jj

j 1 j 1

Note the wind power potential is calculated from the sum. In one sense the individual power/area
values are in energy/time for each class (bin). So if the energy in each bin is calculated and summed,
then the average wind power potential can also be calculated from this total energy divided by the
number of hours.

3.7 TURBULENCE
The wind will vary by location and time and be influenced by terrain, vegetation, and obstacles.
Besides the mean wind speed, the variability of a set of data is represented by the standard devia-
tion. For more detail, see Rohatgi and Nelson [9, Chapters 9 and 10]. The standard deviation for a
set of wind speed data is

05 .

§ ¶

N

1
1

£

¨
¨

2

·
·

(3.14)

S ( vv

j

)

N

© ¸

j 1

where v is the mean wind speed. Because N - 1 is close to N for a large sample, for data loggers and
spreadsheets the standard deviation is calculated from

N N

£ v
N

£ j

2

v j

j

S 2

j 1 1

, v v

N

In general, there are two different calculations, the standard deviation of the average values and
the standard deviation of a set of data. If the average 1 h wind speeds are placed in 1 m/s bins for a
month or a year, then a standard deviation can be calculated for each bin. This is different than the
standard deviation of the 1 Hz data, which are averaged over 10 min or 1 h.