310

ELECTRICAL APPARATUS

Exciting current:

/no = 77 = EY.

(28)

These are the equations from which the transformer theory of
the polyphase induction motor starts.

175. Since the frequency of the secondary currents is the fre-
quency of slip, hence varies with the speed, S = 1 — s, the sec-
ondary self-inductive reactance also varies with the speed, and
so the impedance:

(29)

The power output of the motor, per circuit, is

')

P = ($', 7J

efy*s (1

[ZZQs

(30)

where the brackets [ ] denote the absolute value of the term in-
cluded by it, and the small letters, e0, z, etc., the absolute values
of the vectors, E0, Z, etc.

Since the imaginary term of power seems to have no physical
meaning, it is:
Mechanical power output:

P =

(1 - s)
~

ZZl

(31)

This is the power output at the armature conductors, hence in-
cludes friction and windage.
The torque of the motor is:

D =

1 - s

[ZZos

[ZZ«s + ZZi+

(32)

The imaginary component of torque seems to represent the
radial force or thrust acting between stator and rotor. Omitting
this we have:

D eo2*2ri$ rrV)

JJ = p^^-----r~^r~—7—zr-zr^ (oo)

[ZZQs

+