Environmental Engineering Reference
In-Depth Information
Then the optimal value of C P opt = C P ( l opt ) is kept and by choosing l opt = l R ,
AEP
Max in eqn (10). The second term of in the integral of the right side of eqn
(10) is determined by the wind speed probability function f ( V ).
5.2.4 In case of constant-speed WT
In case of fi xed-speed WT, l varies with V in proportion to 1/ V . Therefore, an
optimal value of design tip-speed ratio l opt may vary from l R . It will be soon
understood if eqn (10) is rewritten as:
r
V
V
1
R
out
3
3
AEP
=
A
fVVCV V VCV
(
)
(
) d
+
(
)
fV V
(
) d
(13 )
P
R
P
R
2
V
V
in
R
Since C P is a function of V , AEP is also a function of V , but depends on C P ( V )
and f ( V ). This means an optimal rated wind speed V R and an optimal design wind
speed V D will be obtained through making AEP
Max. taking into account the
characteristics of WT, i.e. C P ( V ), and wind, i.e. f ( V ), which are independent of
each another.
An empirical formula is known as
V
≈−
(1.2
1.5)
V
(14 )
R
mean
where V mean is the annual mean wind speed at the site and is statistically given as
follows when the wind characteristics follow Weibull distribution:
1
[]
( 15 )
V
=
E V
=
V
f V
()d
V
=
C
Γ
1
+
mean
k
0
where
Γ
denotes the Gamma function.
5.2.5 Multi-point optimal rotor design
A goal is to give AEP a maximum value of the integration in eqn (10). One of the
simplest methods is “Multi-points design method”, with which some desirable
power curve is delivered by combination of plural design points. Various original
designs are possible, but most important thing is to fi nd a solution that the operation
modes together with the power curve of a SWT will most fi t to the characteristics of
the wind at the site where to install the WT.
It is very often experienced that under low wind speed conditions just around
cut-in wind speed, a fi xed-pitch SWT will hard to start rotation or generation if it
stands still, however it will soon do if it is in idling state. Let assume that cut-in
and rated wind speed are 2.5 and 10 m/s, respectively. The ratio of the power out-
put is 1:64. Although the power output at cut-in wind speed is less than 2% of that
at rated wind speed, fast start-up performance will result in better availability in
time and higher energy production.
 
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