Page 183 - Fluid Power Engineering

156 Chapter Eight

th
where δv n = 1 − v n /v 0 is the wind speed deficit at the n turbine that
has n − 1 upstream turbines, and δv kn is the wind speed deficit because
of turbine k on turbine n.

Turbulence Modeling
In addition to wind speed deficit, there is an increase in turbulence
because of wake. Modeling of turbulence is primarily done through
empirical models as theoretical models are less developed. Turbulence
intensity in wind resource assessments is defined in terms of 10-min
wind speed data as:

I 0 = σ(h)/v 10 (h) (8-16)

where I 0 is the ambient turbulence intensity at height h, σ(h)isthe
standard deviation, and v 10 (h) is the average of 10-min wind speed at
height h. If average and standard deviation are not measured at hub
height, then the following may be used to extrapolate turbulence to
hub height: 1

−γ

h 2
I 0 (h 2 ) = v 10 (h 1 )I 0 (h 1 ) (8-17)
h 1
where I 0 (h 2 ) is the ambient turbulence intensity at hub height; h 1 , h 2
are measurement and hub heights and γ is the shear.
The total turbulence intensity is computed using:

2
2
I = I + I + 2 (8-18)
0
T
where I T and I + are total turbulence intensities and additional turbu-
lence intensity because of wake.
There are several empirical turbulence models to compute I + . The
model suggested by IEC 61400-1, edition 3 is: 4,5
√
2
I = 0.9/(1.5 + 0.3 d v hub ) 2 (8-19)
+
where d is the distance between two turbines normalized by rotor
diameter. Additional details are available in IEC 61400-1. 5

Optimal Layout of Turbines in Wind Farm
The objective is to obtain a layout that produces the highest annual
energy while taking into account wake losses, and a variety of layout
related constraints. The prerequisites for an optimal layout of turbines
in a wind farm are: