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

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

3. 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

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

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

6. 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

7. 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

8. SIMULATION MODEL

9. RESULTS