SYNCHRONIZING INDUCTION MOTORS 163
very close to synchronism, where the motor current is appreciably
increased by the exciting current. It is, then:
Wi = (ri + rs0)2.+ s2 (xi + £0)2, 1 , ,
m = (ri + srQ + 2 r)2 + s2 (xl + o;0)2; ' ( }
all the other equations remain the same.
From (15) and (16) follows
bl ~~ & __ % STXl O*1 "I" ST° "t~ j")
2 rami
hence, is always positive.
96. (61 — 6) is always positive, that is, the synchronizing
torque is positive in the first or lagging motor, and negative in
the second or leading motor; that is, the motor which lags in
position behind gives more power and thus accelerates, while the
motor which is ahead in position gives less power and thus
drops back. Hence, the two motor armatures pull each other
into step, if thrown together out of phase, just like two alternators.
The synchronizing torque (14) is zero if r = 0, as obvious,
as for r = 0 both motors are in step with each other. The syn-
chronizing torque also is zero if r = 90°, that is, the two motor
armatures are in opposition. The position of opposition is
unstable, however, and the motors can not operate in opposition,
that is, for r = 90°, or with the one motor secondary short-
circuiting the other; in this position, any decrease of r below
90° produces a synchronizing torque which pulls the motors
together, to r = 0, or in step. Just as with alternators, there
thus exist two positions of zero synchronizing power—with the
motors in step, that is, their secondaries in parallel and in phase,
and with the motors in opposition, that is, their secondaries in
opposition—and the former position is stable, the latter unstable,
and the motors thus drop into and retain the former position,
that is, operate in step with each other, within the limits of their
synchronizing power.
If the starting rheostat is short-circuited, or r = 0, it is, by
(15), 61 = b, and the synchronizing power vanishes, as is obvious,
since in this case the motor secondaries are short-circuited and
thus independent of each other in their frequency and speed.
With parallel connection of induction-motor armatures a syn-
chronizing power thus is exerted between the motors as long
as any appreciable resistance exists in the external circuit, and