560 ROTATING MACHINES
then be rotating in the direction opposite that of the rotating mmf, so the machine will act as a
brake and the speed will rapidly come to zero, at which time the electric supply can be removed
from the machine. Such a reversal of two supply lines of the three-phase system, a useful method
of stopping the motor rapidly, is generally referred to aspluggingorplug-braking.If the electric
supply is not removed at zero speed, however, the machine will reverse its direction of rotation
because of the change of phase sequence of the supply resulting from the interchange of the two
stator leads. The general form of the torque–speed curve (or torque–slip characteristic) for the
polyphase induction machine between rotor speed limits of−ωs≤ωm≤ 2 ωs, corresponding to
a range of slips− 1 ≤S≤2, is shown in Figure 13.1.6.
The torque that exists at any mechanical speed other than synchronous speed is known as an
asynchronous torque.The induction machine is also known as anasynchronous machine,since no
torque is produced at synchronous speed and the machine runs at a speed other than synchronous
speed. In fact, as a motor, the machine runs only at a speed that is less than synchronous speed
with positive slip. The factors influencing the general shape of the torque-speed characteristic
(shown in Figure 13.1.6) can be appreciated in terms of the torque equation, Equation (13.1.3).
Noting that the resultant air-gap fluxφis nearly constant when the stator-applied voltage and
frequency are constant, as seen by Equation (13.1.4), and that the rotor mmfFris proportional to
the rotor currentir, the torque may be expressed as
Te=K 1 irsinδr (13.1.8)
whereK 1 is a constant andδris the angle between the rotor mmf axis and the resultant flux or mmf
axis. The rotor currentiris determined by the rotor-induced voltage (proportional to slip) and the
rotor impedance. Since the slip is small under normal running conditions, as already mentioned,
the rotor frequencyfr=Sfsis very low (on the order of 3 Hz in 60-Hz motors with a per-unit slip
of 0.05). Hence, in this range the rotor impedance is largely resistive, and the rotor current is very
nearly proportional to and in phase with the rotor voltage; that is, the rotor current is very nearly
proportional to slip. An approximately linear torque–speed relationship can be observed in the
range of low values of slip in Figure 13.1.6. Further, with the rotor-leakage reactance being very
small compared with the rotor resistance, the rotor mmf wave lags approximately 90 electrical
degrees behind the resultant flux wave, and therefore sinδris approximately equal to unity.
As slip increases, the rotor impedance increases because of the increasing effect of rotor-
leakage inductance; the rotor current is then somewhat less than proportional to slip. The rotor
current lags further behind the induced voltage, and the rotor mmf wave lags further behind the
resultant flux wave, so that sinδrdecreases. The torque increases with increasing values of slip
up to a point and then decreases, as shown in Figure 13.1.6 for the motor region. The maximum
torque that the machine can produce is sometimes referred to as thebreakdown torque, because it
limits the short-time overload capability of the motor. Higher starting torque can be obtained by
inserting external resistances in the rotor circuit, as is usually done in the case of the wound-rotor
induction motor. These resistances can be cut out for the normal running conditions in order to
operate the machine with a higher efficiency. Recall that a synchronous motor has no starting
torque. It is usually provided with a damper or amortisseur winding located in the rotor pole
faces. Such a winding acts like a squirrel-cage winding to make the synchronous motor start as an
induction motor and come up almost to synchronous speed, with the dc field winding unexcited. If
the load and inertia are not too large, the motor will pull into synchronism and act as a synchronous
motor when the field winding is energized from a dc source.
So far the discussion of induction machines applies only to machines operating from a
polyphase supply. Of particular interest is the single-phase induction machine, which is widely
used as a fractional-horsepower ac motor supplying the motive power for all kinds of equipment