**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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