WIND ENERGY SYSTEMS - Cd3wd

Chapter 6—Asynchronous Generators 6–12
Figure 5: Permanent-magnet generator connected to a resistive load.
It is desirable to maintain the three line currents at about the same value to minimize
torque fluctuations. It is shown in electrical machinery texts that a three-phase generator
will have a constant shaft torque when operated under balanced conditions. A single-phase
generator or an unbalanced three-phase generator has a torque that oscillates at twice the
electrical frequency. This makes the generator noisy and tends to shorten the life of the shaft,
bearings, and couplers. This is one of the primary reasons single-phase motors and generators
are seldom seen in sizes above about 5 kW. The PM generator will have to be built strongly
enough to accept the turbine torque fluctuations, so some imbalance on the generator currents
should not be too harmful to the system, but the imbalance will need to be minimized to keep
the noise level down, if for no other reason.
The electrical output power P e (the power delivered to the load) of the PM generator per
phase is
The magnitude of the current is
P e = I 2 a R a W/phase (12)
|I a | =
|E a |
√
(Rs + R a ) 2 + X 2 s
A (13)
Therefore the output power can be expressed as
E 2
P e =
aR a
(R s + R a ) 2 + Xs
2
The generated voltage E a can be written as
W/phase (14)
E a = k e ω V (15)
This is basically the same equation as Eq. 1. Here the constant k e includes the flux per
pole since the PM generator is a constant flux machine and also includes any constant factor
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001