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**Torque Slip Characteristics of Induction Motor**

The torque slip characteristics of
**three phase induction motor
**is the important characteristics that gives information about the torque
generation at the different slip regions in an induction motor.
Additionally, this characteristics help us to study certain aspects of three
phase induction motors like Importance of
**slip in induction motor**,
**speed Control of the Induction Motor**, Braking of the induction motor, Operation of Induction Generator
etc.

To ease the study of torque slip characteristics, the operation of the
three-phase induction motor is majorly divided into two regions i.e.
**Low Slip Region** and **High Slip Region, **ranging the value of
slip between 0 to 1 (as discussed in slip in induction motor). Zero slip
means the induction motor runs at synchronous speed and the slip = 1 is at
the starting of three phase induction motor.

Additionally, the operation of induction machine is further divided into
two more region i.e. **Negative Slip Region **and
**the region in which slip is greater than one** this further division
help us in the study of operation of induction generator and braking of
induction motor respectively.

The
**torque equation of three phase induction motor**
is given by.

where,

T = Torque developed in induction motor

K = proportionality constant

Er = induced emf in rotor

Rr = rotor resistance

Xr = rotor reactance

S = slip

**Low Slip Region**

For low value of slip (sXr)^{2 }in the denominator of torque
equation is very low as compared to rotor resistance and it can be
neglected. So, for low slip region the toque equation becomes.

From above equation it is clearly seen that, for low slip region torque
is directly proportional to slip and inversely proportional to rotor
resistance.

**Note :-
**From above statement** **we can understand the importance of slip i.e.
if there is no slip then no torque is developed in three phase induction
motor.

**High Slip Region**

For high slip region the term (sXr)^{2 }is much greater than Rr
in numerator of the torque equation so, it cannot be neglected. In that
case Rr in numerator can be neglected.

So, for high slip region the torque equation of three phase induction
motor becomes

From above equation, it is clearly shown that for high slip region torque
is inversely proportional to slip (assuming that the voltage, rotor
reactance, and rotor resistance is constant).

** **

**Negative Slip Region**

Negative slip in induction motor means that the speed of the induction
motor is greater than the synchronous speed. This is the case in which an
induction machine works as an induction generator.

**Region in which slip > 1**

When slip is greater than one it means that the direction of the rotation
of the motor is reversed. It is the case of plugging (Electrical Braking
of Three Phase Induction Motor) in which the direction of rotation of the
motor is reversed by reversing any two phase of the three phase induction
motor.

In this case the maximum value of the slip goes up-to 2.

** **

** **

###
**Torque Slip Characteristics of Induction Machine**

**
**

So, after analyzing all the four cases we understand that an induction
motor or induction machine can be operated in three modes i.e. Motoring
Zone (0<s<1), Generating Zone (s<0), Braking Zone
(1>s<2).

The overall torque slip characteristics of three phase induction motor or
an induction machine represents as shown in figure.

The region lies in which slip lies between 0 to 1 is the motoring zone.
In this zone we see that torque slip characteristics is straight between s
= 0 to s = s_{m} (s_{m} is the value of slip at which the
maximum torque occurs). This is the stable operating region of induction
motor. In that region torque is directly proportional to slip.

The region between s = s_{m} to s = 1 is unstable region and it
is not recommended that the motor to be operated in this region. In this
region torque is inversely proportional to slip.

However, an induction motor can be operated in this region by adding the
external resistance in rotor circuit.

**Effect of adding rotor resistance induction motor**

If we increase the rotor resistance than according to the torque equation
in low slip region, the slip should increase to supply the constant
torque. And, also the slip at which maximum torque occurs is also
increased. It is clearly shown in the given figure.

In above figure we can see that s_{m1}, s_{m2} and s_{m3}
are the different values of slip at which maximum torque occurs after
adding R_{1}, R_{2}, and R_{3}. From discussion it
is concluded that R1>R2>R3 and the region in which torque and slip
have linear relationship is increases with the resistance.

So, we can say that torque generation is possible at higher slip region
or lower speed i.e. during starting of induction motor.

So, adding external resistance in the rotor circuit is very helpful
practice in the starting of induction motor and it can only be done in
case of slip ring induction motor.

**Conclusion**

From this discussion it is concluded that operating region of the
induction motor lies between 0 and s_{m} (slip at which maximum
torque occurs) values of slip. However, it can be operated in high slip
region with the help of additional resistance that is added to the rotor
circuit.

Addition of external resistance to the rotor circuit has done to start
the slip ring induction motor.

Addition of external resistance to the rotor circuit results increase in
rotor losses hence motor efficiency decreases that’s why this practice has
been done only in starting.

__related posts__

**#_****starting methods of induction motor**

**#_torque in three phase induction motor**

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