WIND ENERGY SYSTEMS - Cd3wd

Chapter 4—Wind Turbine Power 4–17
rating, 0.9 for a 20-kW rating, 0.93 for a 200-kW rating, and 0.96 for a 2-MW rating. The
efficiency continues to climb with size, exceeding 0.98 for the very large generators in coal and
nuclear power plants. This variation in efficiency with rating is different from the efficiencies
of the turbine and transmission, which were assumed to not vary with size. The differences
between very small and large generators are significant, and should be included in any detailed
economic study.
The effects of rated power and actual power on generator efficiency can all be combined in
an empirical equation[10]. When expressed in terms of the input shaft power to the generator,
this expression is
η g = X − (0.5)Y (1 − Y )(X2 +1)
X
where the parameters X and Y are given by
(18)
X = P t
P tR
(19)
( )
10
6 0.215
Y =0.05
(20)
P eR
In these equations, P tR and P eR are the rated mechanical power input and the rated electrical
power output in watts of the generator. Equation eq:4.18 is plotted in Fig. 14 for three rated
generator sizes: 20 kW (20 ×10 3 W), 200 kW, and 2000 kW. The curves are seen to be very
similar in shape to the transmission efficiency curves of Fig. 13.
The power output of the electrical generator can now be determined, conceptually at least,
by finding C p , η m and η g for a given turbine and wind speed, multiplying them together to find
the overall efficiency, and then multiplying that by the power in the wind. This can be done
by reading values from graphs or by analytical techniques if the appropriate mathematical
models have been defined. Design values of turbine rated rotational speed and rated sizes of
the transmission and generator can be varied, and the process repeated. Optimum values can
be determined which will maximize the energy production per dollar of investment.
The selection of ratings is somewhat of an art, partly because commercial products are
made in discrete size increments. A company which manufactured a 25-kW and a 30-kW
generator would probably not manufacture a 27-kW generator. We are therefore forced to
choose a size which is not exactly equal to the theoretically desired value. Consider, for
example, the Sandia 17-m Darrieus turbine with shaft power production shown in Fig. 10.
The peak shaft power is 30 kW. We would want to select a transmission of at least this input
rating. If there is a 30-kW transmission built for this class of service, it would be selected.
Otherwise, a 35- or 40-kW transmission would probably be chosen. This would allow a safety
factor and perhaps increase the operational life of the transmission.
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001