WIND ENERGY SYSTEMS - Cd3wd

Chapter 6—Asynchronous Generators 6–7
generated emf E will be greater than zero whenever the armature is spinning, even though the
field current is negligible. These effects of the iron circuit yield a plot of E versus I f such as
showninFig.3.E starts at a positive value, increases rapidly for small I f , and finally levels
off for larger I f . Two angular velocities, ω m1 and ω m2 , are shown on the figure. Increasing
ω m merely expands the curve for E without changing its basic shape.
Figure 3: Magnetization curve of dc generator.
The generated emf E is given by Kirchhoff’s voltage law as
E = I a R a + I f R f V (4)
R a is much smaller than R f , so when the diode current is zero, which causes I a = I f ,theI a R a
term is very small compared with R f I f . Therefore, to a first approximation, we can write
E ≃ I f R f (5)
This equation is just a straight line passing through the origin of Fig. 3. We therefore
have a voltage E being constrained by both a nonlinear dc generator and a linear resistor.
The generator requires the voltage to vary along the nonlinear curve while the field resistor
requires it to vary along the straight line. Both requirements are met at the intersection of the
nonlinear curve and the straight line, and this intersection defines the equilibrium or operating
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001