ALTERNATING-CURRENT MOTORS

323

is reduced, and the speed variation, therefore, occurs without
loss of efficiency, and is similar in its character to the speed con-
trol of a direct-current shunt motor by varying the ratio between
the e.m.f. impressed upon the armature and that impressed upon
the field.

Substituting in the equations:

it is:

S + C = Si

+

+ ZoZ"/

/! = #
P

pjQ _ ------—•——------—

sZz/o + ^^i +
>S6o222Si (fi — <TO)

[sZZo + ZZi + Zo

(86)

(87)
(88)
(89)

These equations of J0 and Ji are the same as the polyphase
induction-motor equations, except that the slip from synchron-
ism, s, of the induction motor, is, in the numerator, replaced by
the slip from the no-load speed, $1.

Insertion of voltages into the armature of an induction motor
in phase with the primary impressed voltages, and by a com-
mutator, so gives a speed control of the induction motor without
sacrifice of efficiency, with a sacrifice, however, of the power-
factor, as can be shown from equation (87).

184. 2. The no-load speed of the polyphase shunt motor is in
synchronism, that is, the no-load slip, s0 = o, or the motor out-
put becomes zero at synchronism, just as the ordinary induction
motor, if, in equation (83):

hence:

or. substituting:

cos 0 + ^i sin 0 — cr0 = o;
— ?J- cos 0 + ^i sin 0t

1

— = tan

7*1

(90)

(91)

where ai is the phase angle of the rotor impedance, it is:

— 0),

= ~ cos

J 1