Environmental Engineering Reference
In-Depth Information
interest rates for borrowed money, and estimates for future electricity prices.
Readers interested in these issues can find much useful information in the first-rate
user manuals for the Retscreen software mentioned above.
Only the following simple question is considered: what height maximises the
average energy output per unit P
total
? This deceptively simple question can
be answered easily only for the very specific conditions considered in
Sect. 1.6
.
If the terrain is flat for a sufficient distance all around the turbine, and the
roughness length is constant, then the mean wind speed is given by Eq.
1.14
or
1.15
. The former is more useful for our purposes. If the turbine output depends on
the average wind speed as shown by the linear fit to the data in Fig.
12.1
, with the
''offset'' wind speed, U
0
= 2.75 m/s in this case, then the ratio to be maximised is
proportional to
Þ
m
U
0
a
þ
bh
U
10
h
=
10
ð
ð
12
:
2
Þ
where U
10
is the 10 m wind speed, h is in m, and m is the exponent from Eq.
1.14
whose typical values are listed in Table
1.3
. Note that the U
0
will be less than the
cut-in wind speed, 3.5 m/s for the Skystream, because of the spread of the wind
speed distribution. Differentiating (
12.2
) with respect to h, and equating the result
to zero, gives the optimum height, h
opt
, as the solution to (Fig.
12.4
)
m
¼
0
ma
bh
opt
þ
m
1
þ
U
0
U
10
10
h
opt
ð
12
:
3
Þ
Increasing m and U
0
and decreasing U
10
all increase the optimum height. In
general, Eq.
12.3
is implicit in h
opt
and can only be solved analytically for specific
values of m, such as m = which is of no practical use. This equation was
evaluated using Matlab's function
fzero
in the code shown below
Fig. 12.4 Optimum tower
height for Skystream 2.4 kW
turbine for varying 10 m
wind speeds and power law
exponent
35
U
10
= 3.5 m/s
U
10
= 4.0 m/s
U
10
= 4.5 m/s
U
10
= 5.0 m/s
30
25
20
15
10
5
0.1
0.15
0.2
0.25
0.3
Power law exponent, m
Search WWH ::
Custom Search