6 ELECTRICAL APPARATUS

Assuming tan a — 0.6, which is a fair value for a closed mag-
netic circuit of high hysteresis loss, it is:

5
Y' = - (0.6 - j),

the exciting admittance at slip, s.

Assume then, that such an admittance, Y', is connected in series
into the secondary circuit of the induction motor, for the pur-
pose of using the effective resistance of hysteresis, which in-
creases with the frequency, to control the motor torque curve.

The total secondary impedance then is:

-(»+

(8)

where: Y = g — jb is the admittance of the magnetic circuit at
full frequency, and
y = A/V + b2.
5. For illustration, assume that in the induction motor of the
constants:
eQ = 100;
70 = 0.02 - 0.2 j;
Z0 = 0.05 + 0.15.7";
Zi = 0.05 +0.15 j;
a closed magnetic circuit is connected into the secondary, of full
frequency admittance,
Y = g - jb}
and assume:
g = 0.66:
b=4;
thus, by (8):
Z'i = (0.05 + 0.11 s} + 0.335 js. (9)
The characteristic curves of this induction motor with hysteresis
starting device can now be calculated in the usual manner, dif-
fering from the standard motor only in that Zi is not constant,
and the proper value of ri} Xj and m has to be used for every
slip, s.
Fig. 2 gives the speed-torque curve, and Fig. 3 the load curves
of this motor.