WIND ENERGY SYSTEMS - Cd3wd

Chapter 6—Asynchronous Generators 6–8
point. When the generator is turning at the angular velocity ω m1 , voltage and current will
build up only to point a. This is well below the capability of the generator and is not a
desirable operating point. If the angular velocity is increased to ω m2 the voltage will build up
to the value at point b. This is just past the knee of the magnetization curve and is a good
operating point in that small changes in speed or field resistance will not cause large changes
in E.
Another way of changing the operating point is to change the field resistance R f . The
slope of the straight line decreases as R f decreases so the operating point can be set any
place along the magnetization curve by the proper choice of R f . There are some practical
limitations to decreasing R f ,ofcourse.R f usually consists of an external variable resistance
plus the internal resistance of a coil of many turns of fine wire. Therefore R f can not be
reduced below the internal coil resistance.
The mode of operation of this generator is referred to as a self-excited mode. The residual
magnetism of the generator produces a small flux, which causes a small voltage to appear
across the field winding when the generator rotor is rotated. This small voltage produces
a small field current which helps to boost E to a larger value. This larger E produces a
still larger field current, which produces a still larger E, until equilibrium is reached. The
equilibrium point will be at small values of E for low speeds or high field resistance, and will
increase rapidly to a point past the knee of the magnetization curve as speed or field resistance
reaches some critical value. Once the voltage has built up to a value close to the rated voltage,
the generator can supply current to a load.
We now want to examine the operation of the self-excited shunt generator as a battery
charger, with the circuit of Fig. 2. We assume that switch S 1 is open, that the diode is an
open circuit when E is less than the battery voltage V B and a short circuit when E is greater
than V B ,andthatR B includes the resistance of the diode and connecting wires as well as the
internal resistance of the battery. When the diode is conducting, the relationship between E
and V B is
E = V B + I f R a + I B (R a + R b ) V (6)
The term I f R a is a very small voltage and can be neglected without a serious loss of
accuracy. If we do so, the battery current is given by
I B ≃ E − V B
R a + R b
A (7)
The electrical power produced by the shunt generator when the diode is conducting is
given by
P e = EI a ≃ EI f + E(E − V B
R a + R b
W (8)
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001