WIND ENERGY SYSTEMS - Cd3wd

Chapter 6—Asynchronous Generators 6–13
between the mechanical angular velocity ω m and the electrical angular velocity ω. Afourpole
generator spinning at 1800 r/min will have ω m = 188.5 rad/s and ω = 377 rad/s, for example.
The ratio of electrical to mechanical angular velocity will be 1 for a two pole generator, 2 for
a four pole, 3 for a six pole, and so on.
This variation in generated voltage with angular velocity means that a PM generator which
has an open-circuit rms voltage of 250 V line to line at 60 Hz when the generator rotor is
turning at 1800 r/min will have an open circuit voltage of 125 V at 30 Hz when the generator
rotor is turning at 900 r/min. Wide fluctuations of voltage and frequency will be obtained
from the PM generator if the wind turbine does not have a rather sophisticated speed control
system. The PM generator must therefore be connected to loads which can accept such voltage
and frequency variations.
Lighting circuits would normally not be appropriate loads. Incandescent bulbs are not
bright enough at voltages 20 percent less than rated, and burn out quickly when the voltages
are 10 percent above rated. There will also be an objectionable flicker when the frequency
drops significantly below 60 Hz. Fluorescent bulbs may operate over a slightly wider voltage
and frequency range depending on the type of bulb and ballast. If lighting circuits must be
supplied by the PM generator, consideration should be given to using a rectifier and battery
system just for the lights.
It should be noticed that the rating of the PM generator is directly proportional to the
rotational speed. The rated current is related to the winding conductor size, which is fixed
for a given generator, so the output power V a I a will vary as E a or as the rotational speed.
The resistance R a has to be varied as E a varies to maintain a constant current, of course.
This means that a generator rated at 5 kW at 1800 r/min would be rated at 10 kW at 3600
r/min because the voltage has doubled for the same current, thus doubling the power. The
limitations to this increase in rating are the mechanical limitations of rotor and bearings, and
the electrical limitations of the insulation.
In Chapter 4 we saw that the shaft power input to the generator needs to vary as n 3 for
the turbine to operate at its peak efficiency over a range of wind speeds and turbine speeds.
Since n and ω are directly proportional, and the efficiency is high, we can argue that the
output power of the PM generator should vary as ω 3 for the generator to be an optimum load
for the turbine. The actual variation can be determined by explicitly showing the frequency
dependency of the terms in Eq. 14. In addition to E a , there is the reactance X s ,whichis
given by
X s = ωL s Ω (16)
The term L s is the inductance of the generator windings. It is not a true constant because of
saturation effects in the iron of the generator, but we shall ignore that fact in this elementary
treatment.
The frequency variation of the electrical output power is then given by
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001