138 ELECTRICAL APPARATUS

The torque curve of the induction motor at constant terminal
voltage consists of two branches, a stable branch, from the
maximum torque point to synchronism, and an unstable branch,
that is, a branch at which the motor can not operate on a load
requiring constant torque, from standstill to maximum torque.
With increasing slip, s, the current, i, in the motor increases. If

then D = torque of the motor, -p is positive on the stable,

negative on the unstable branch of the motor curve, and this
rate of change of the torque, with change of current, expressed
as fraction of the current, is:

1 dD

it may be called the stability coefficient of the motor.
If ks is positive, an increase of i} caused by an increase of
slip, Sj that is, by a decrease of speed, increases the torque, Z), and
thereby checks the decrease of speed, and inversely, that is, the
motor is stable.
'If, however, k3 is negative, an increase of i causes a decrease
of Dj thereby a decrease of speed, and thus further increase of i
and decrease of D; that is, the motor slows down with increas-
ing rapidity, or inversely, with a decrease of i, accelerates with
increasing rapidity, that is, is unstable.
For the motor used as illustration in the preceding, of the
constants e = 110 volts; Y = 0.01 - 0.1 j; ZQ = 0.1 + 0.3 3,
Z\ = 0.1 + 0.3 j9 the stability curve is shown, together with
speed, current, and torque, in Fig. 54, as function of the output.
As seen, the stability coefficient, k8, is very high for light-load,
decreases first rapidly and then slowly, until an output of 7000
watts is approached, and then rapidly drops below zero ; that is,
the motor becomes unstable and drops out of step, and speed,
torque, and current change abruptly, as indicated by the arrows
in Fig. 54.
The stability coefficient, ksj characterizes the behavior of the
motor regarding its load-carrying capacity. Obviously, if the
terminal voltage of the motor is not constant, but drops with
the load, as discussed in 1, a different stability coefficient results;
which intersects the zero line at a different and lower torque.
86. If the induction motor is supplied with constant terminal
voltage from a generator of close inherent voltage regulation