WIND ENERGY SYSTEMS - Cd3wd

Chapter 4—Wind Turbine Power 4–24
the average power will be as large as possible for a given turbine area. The capital investment
in the turbine will be proportional to the turbine area so maximizing the average power will
minimize the cost per unit of energy produced. If the rated speed is chosen too low, we will
lose too much of the energy in the higher speed winds. If the rated speed is too high, the
turbine will seldom operate at capacity and will lose too much of the energy in the lower speed
winds. This means that the average power output will reach a maximum at a specific value
of rated wind speed. We can determine this value by evaluating Eq. 30 for various values of
u R and P eR .
We can gain some insight into this design step by normalizing Eq. 30. We first observe
that the quantity inside the brackets of Eq. 30 is called the capacity factor CF. Also called
the plant factor, it is an important design item in addition to the average power.
When we combine Eqs. 15, 16, and 30 we get
ρ
P e,ave = P eR (CF) = η o
2 Au3 R
(CF) W (31)
The choice of rated wind speed will not depend on the rated overall efficiency, the air
density, or the turbine area, so these quantities can be normalized out. Also, since the
capacity factor is expressed entirely in normalized wind speeds, it is convenient to do likewise
in normalizing Eq. 31 by dividing the expression by c 3 to get the term (u R /c) 3 . We therefore
define a normalized average power P N as
P N =
( )
P 3 e,ave
η o (ρ/2)Ac 3 =(CF) uR
(32)
c
Plots of P N are given in Fig. 17 for various values of the Weibull shape parameter k and for
two ratios of cut-in to rated speed. As argued earlier, most turbines will have cut-in speeds
between 0.4 and 0.5 of the rated wind speed, so these plots should bracket the designs of
practical interest.
We see that maximum power is reached at different values of u R /c for different values of
k. For u c =0.5u R , the maximum power point varies from u R /c =1.5to2.5ask decreases
from 2.6 to 1.4. As the cut-in speed is lowered to 0.4u R , the maximum power point varies
from u R /c = 1.6 to 3.0. If k = 2 at a particular site, the optimum value of u R /c is between
1.8 and 2.0. We saw in Chapter 2 that c is usually about 12 percent larger than the mean
wind speed, so the optimum design for energy production is a rated speed of about twice the
mean speed. If the mean wind speed at a site is 6 m/s, then the rated speed of the turbine
should be about 12 m/s.
This design choice only holds for wind regimes where k is about 2. In a trade wind regime,
k will be significantly larger than 2, so a rated speed perhaps 1.3 times the mean speed may
be a better choice in such locations.
We see that the curves for P N
are gently rounded near their maximum values so small
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001