0195136047.pdf

13.2 INDUCTION MACHINES 571

Tmax=

1

ωs

0. 5 m 1 V 12 a

R′′ 1 +

√

(R′′ 1 )^2 +(X′′ 1 +X′l 2 )^2

(13.2.15)

which can be verified by the reader. Equation (13.2.15) shows that the maximum torque is
independent of the rotor resistance. The slip corresponding to the maximum torque is directly
proportional to the rotor resistanceR 2 ′, however, as seen from Equation (13.2.14). Thus, when
the rotor resistance is increased by inserting external resistance in the rotor of a wound-rotor
induction motor, the maximum internal torque is unaffected, but the speed or slip at which
it occurs is increased, as shown in Figure 13.2.9. Also note that maximum torque and max-
imum power do not occur at the same speed. The student is encouraged to work out the
reason.
A conventional induction motor with a squirrel-cage rotor has about 5% drop in speed from
no load to full load, and is thus essentially a constant-speed motor. Employing a wound-rotor
motor and inserting external resistance in the rotor circuit achieves speed variation but results
in poor efficiency. Variations in the starting torque (atS=1) with rotor-circuit resistance can
also be seen from Figure 13.2.9. As stated in Section 13.1, we can obtain a higher starting torque
by inserting external resistances in the rotor circuit and then cutting them out eventually for
the normal running conditions in order to operate the machine at a higher efficiency. Creating
a sufficiently large rotor-circuit resistance might make it possible to achieve an almost linear
torque–slip relationship for the slip range of 0 to 1. For instance, two-phase servo motors
(used as output actuators in feedback control systems) are usually designed with very high rotor
resistance to ensure a negative slope for the torque–speed characteristic over the entire operating
range.
Since the stator resistance is quite low and has only a negligible influence, let us set
R 1 =R 1 ′′=0, in which case, from Equations (13.2.12) and (13.2.15), we can show that

T

Tmax

=

2

(S/SmaxT)+(SmaxT/S)

(13.2.16)

whereSandSmaxTare the slips corresponding toTandTmax, respectively.

1.0

3.0

2.5

2.0

1.5

1.0

0.5

0

0.8 0.6 0.4 0.2 0

0 0.2 0.4 0.6 0.8 1.0 Speed

Synchronous speed

Slip

Load

Tmax

T/Tfull load Stable operatingregion for motor

with resistance (R' 2 )A

(R' 2 )D

(R' 2 )C

(R' 2 )B

(R' 2 )A

(R' 2 )D > (R' 2 )C > (R' 2 )B > (R' 2 )A

NA

NB

NC

ND

Figure 13.2.9Effect of changing

rotor-circuit resistance on the torque–

slip characteristic of a polyphase in-

duction motor.