205
Here the, tip speed ratio equation is rewritten as
λ λ =
R
V
ω
(11.5)
In the above equation,
ω = angular speed in rad/s
V = wind speed average (m/s)
R = turbine radius (m)
To calculate the wind-generated energy the equation below is utilized:
Q
P
w
Time kWh
= ×(
)[
]
(11.6)
The direct measurements from a given motion cannot be used in obtaining velocity; thus, a lower motion should be first established using the equation below:
v Z
Z
Z
v Z
Z
Z
( )





 = ( )






ln
ln
r
r
0
0
(11.7)
with
Z = reference height (m)
Z 0  = surface roughness measurement (in crop lands = 0.1–0.25)
v(Z) = speed of wind at Z height (m/s)
v(Z r ) = speed of wind at Z (m/s)
The equation below represents the estimation of power output based on the
wind speed:
P v
v v
v v
P v v v
P
v
v v
v v
v v
k
k
k
k
w
C
R
C
R
C
R
R
R
F
C
F
and
( ) =
−
−
⋅
≤ ≤
≤ ≤
≤
≥








0
 
(11.8)
In the above equation,
P R  = represents the rated power
v C  = wind speed cut-in
v R  = total wind rated
v F  = cutout speed rated
k = shape factor of Weibull
Materials, Methods, and Simulation