WIND ENERGY SYSTEMS - Cd3wd

Chapter 4—Wind Turbine Power 4–15
These results illustrate the fact that the rated overall efficiency may be significantly lower than the
maximum coefficient of performance of the turbine itself. This is not a major problem if the various
efficiencies are high below the rated wind speed. For wind speeds at or above rated, the power in the
wind is large enough that somewhat lower efficiencies do not prevent rated power from being reached.
The rated overall efficiency just defined is only valid at rated wind speed. We need to
know the overall efficiency at lower wind speeds to determine the energy production of the
turbine, so we need to determine the individual efficiencies. We have already examined the
variation of C p , so we shall now consider η m and η g .
Transmission losses are primarily due to viscous friction of the gears and bearings turning
in oil. At fixed rotational speed, the losses do not vary strongly with transmitted torque. It
is therefore reasonable to assume that the transmission loss is a fixed percentage of the low
speed shaft rated power. The actual percentage will vary with the quality of the transmission,
but a reasonable value seems to be 2 percent of rated power per stage of gears. The maximum
practical gear ratio per stage is approximately 6:1, so two or three stages of gears are typically
required. Two stages would have a maximum allowable gear ratio of (6) 2 :1 = 36:1 so any
design requiring a larger gear ratio than this would use three stages.
Suppose that q is the number of gear stages. The transmission efficiency is then
η m = P t
= P m − (0.02)qP mR
(17)
P m P m
where P mR is the rated turbine shaft power.
This equation is plotted in Fig. 13 for one, two, and three stages. It can be seen that
the transmission efficiency is not very good for low power inputs. It is therefore desirable to
choose ratings such that the transmission is operating above the knee of the curve in Fig. 13
as much as possible.
Example
How many gear stages are required in the transmission for the Sandia 17-m Darrieus to drive a
1800 r/min generator for each of the proposed speeds of 42 and 52.5 r/min? Assume the maximum
gear ratio for a single stage is 6:1.
The overall gear ratio at 42 r/min is 1800/42 = 42.86:1, while at 52.5 r/min it is 1800/52.5 =
34.29:1. Operating at 42 r/min requires a 3 stage transmission while a 2 stage transmission would be
adequate at 52.5 r/min. The transmission for the 52.5 r/min system will therefore be more efficient
and probably less expensive than the corresponding transmission for the 42 r/min system. This would
encourage us to use the higher speed system, if possible.
It should be mentioned that synchronous generators are also made to operate at 1200 r/min for
only a small increase in cost over the 1800 r/min version. Therefore, the possibility of using a 1200
r/min generator should be examined if the 42 r/min mode is selected. This would present an overall
gear ratio of 1200/42 = 28.57:1, which could be accomplished with a two stage transmission.
The generator losses may be considered in three categories: hysteresis and eddy current
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001