82

ELECTRICAL APPARATUS

2. The self-inductive impedance of the commutating machine
comprising resistance and reactance of armature and of field,
and compensating winding, where such exists.

3. The effective impedance representing the commutating
machine.

It must be considered, however, that in (1) and (2) the re-
sistance is constant, the reactance proportional to the slip, s,
while (3) is proportional to the speed (1 — 5).
54. Let:

YQ = g— jb == primary exciting admittance
of the induction motor.

ZQ = TQ + jxQ = primary self-inductive im-
pedance of the induction
motor.

Zi — TI + jxi = secondary self-inductive im-
pedance of the induction
motor, reduced to full
frequency.

Z* = TZ + jx% = self-inductive impedance of
the commutating machine,
reduced to full frequency.

ZQ = pi + jp2 = effective impedance repre-
senting the voltage in-
duced in the commutating
machine, reduced to full
frequency.

The total secondary impedance, at slip, s, then is:

Z* = (
= [ri +

+ (r2 + jsxz) + (!—«) Oi +
+ (1 - a) pi] + j[s (a?i + a?a) + (1 - s) pa] (8)

and, if the mutual inductive voltage of the induction motor -is
chosen as base line, e, in the customary manner,
the secondary current is:

where:

+ rz + (1 — g) pi]

m

— s |s (#i + #2) + (i — s):

m

(9)

(10)