1. SPEED TORQUE CHARACTERSTICS OF 3 PHASE INDUCTION MOTORBY
GYAN VARDHAN TYAGI
DHEERAJ SHARMA

2. Three Phase Induction Motor

3. Based on the construction of the rotor, a 3-phase induction motor can be categorized into two types:
i. Squirrel Cage Induction Motor
ii. Wound Rotor or Slip Ring Induction Motor
In squirrel cage IM, the rotor consists of longitudinal conductor bars which are shorted at ends by circular conducting rings. Whereas, the wound rotor IM has a three phase balanced distributed winding even on the rotor side with as many number of poles as in the stator winding
The stator of both types of motors consists of a three phase balanced distributed winding with each phase mechanically separated in space by 120 degrees from the other two phase windings. This gives rise to a rotating magnetic field when current flows through the stator

4. The per phase equivalent circuit of an induction motor is shown below:

5. IM -Induction Motor
Rs -Stator Resistance
Rr -Rotor Resistance
Rr’ -Rotor Resistance Referred to Stator side
Xs -Stator Reactance
Xr -Rotor Reactance
Xr’ -Rotor Reactance Referred to Stator side
Xm -Leakage Inductance
I1 -Stator Current
I2 -Rotor Current
I2’ -Rotor Current Referred to Stator side
Im -Magnetizing Current
V0 -Stator Voltage
s -Slip
ωs- Synchronous Speed
ωm- Rotor Speed (Machine Speed)
Ωs -Average Synchronous Speed (in RPM)
f -Supply Frequency
p -No. of Poles
Pg- Air-gap Power
Pcu- Copper loss in the machine
Pm -Mechanical Power output of the machine
T -Torque Developed by the motor
sm- Slip at maximum torque

6. Tmax- Maximum Torque
ωsl- Slip Speed
ωf -Rotor Speed at Frequency f

7. CALCULATION OF TORQUE
s = (ω s – ωm)/ ω s ω s = 120f/p rpm

8. Power transferred to rotor (or air-gap power) Pg=3I2R/s
Rotor current
I2=V0/{(Rs+Rr/s)+j(Xs+Xr)}
Power transferred to rotor (or air-gap power)
Pg=3I2R/s
Rotor copper loss is
Pcu=3I2Rr

9. Electrical power converted into mechanical power
Pm=Pg-Pcu=3I22Rr{(1-s)/s}
Torque developed by motor
T=Pm/ ωm
Thus,
T= 3I22Rr/s ω s

10. SIMULATION MODEL

11. RESULTS ROTOR CURRENT

12. SPEED OF ROTOR

13. STATOR CURRENT

14. ELECTROMAGNETIC TORQUE

15. SPEED TORQUE CHARACTERSTICS