WIND ENERGY SYSTEMS - Cd3wd

Chapter 6—Asynchronous Generators 6–9
The electrical power delivered to the battery is
P B = V B I B W (9)
The electrical power can be computed as a function of angular velocity if all the quantities
in Eq. 8 are known. In practice, none of these are known very precisely. E tends to be reduced
below the value predicted by Eq. 1 by a phenomenon called armature reaction. The resistance
of the copper wire in the circuit increases with temperature. R a and R b include the voltage
drops across the brushes of the generator and the diode, which are quite nonlinear. And
finally, V B varies with the state of charge of the battery. Each system needs to be carefully
measured if a detailed curve of power versus rotational speed is desired. General results or
curves applicable to a wide range of systems are very difficult to obtain, if not impossible.
Example
The Wincharger Model 1222 is a 12-V, 15-A self-excited dc shunt generator used for charging 12-V
batteries. By various crude measurements and intelligent estimates, you decide that R f =15Ω,R a =
0.2 Ω, R b =0.25Ω,V B =12V,andE = 0.015n + 8 V. This expression for E includes the armature
reaction over the normal operating range, hence is much flatter than the ideal expression of Eq. 1.
Assume the diode is ideal (no forward voltage drop when conducting) and plot E, I B ,andP e for n
between 0 and 600 r/min.
We first observe that I B = 0 whenever E ≤ V B . The rotational speed at which the battery starts
to charge is found by setting E = V B and solving for n.
0.015n +8=12
n = 4 = 270 r/min
0.015
The battery current will vary linearly with E and therefore with the rotational speed, according
to Eq. 7. We can plot the current I B by just finding one more point and drawing a straight line. At n
= 600 r/min, the battery current is given by
I B ≃
0.015(600) + 8 − 12
0.2+0.25
=11 A
The electrical power generated is nonlinear and has to be determined at several rotational speeds
to be properly plotted. When this is done, the desired quantities can be plotted as shown in Fig. 4.
The actual generated E starts at zero and increases as approximately the square of the rotational speed
until diode current starts to flow. Both flux and angular velocity are increasing, so Eq. 1 would predict
such a curve. When the diode current starts to flow, armature reaction reduces the rate of increase of
E. The flux also levels off because of saturation. E can then be approximated for speeds above 270
r/min by the straight line shown, which could then be extrapolated backward to intersect the vertical
axis, at 8 V in this case.
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001