Torque Equation
Transformer and IM Analogy
• An Induction motor is directly related to a transformer – Rotating Transformer
• Primary – Stator Secondary – Rotor
• Power transfer by induction principle
• Stator – Stationary Rotor – Rotating
• No conceptual change between Stator & primary of a Transformer
• Airgap in IM increases the reluctance of flux path and reduces coupling
between stator and rotor
• Rotor elements are related to slip fr = s f
• Emf induced in rotor ckt will be sE2 if E2 is the emf induced under standstill
condition
Equivalent circuit of an Induction motor
Stator component
Rotor component
Load Component
Depend on slip s
No Load component
Rotor circuit at stand still
At stand still s=1:
Induced Emf/phase = E2
Rotor Resistance and Reactance/phase = R2 & X2
X 2  2fL2
RotorimpedanceZ  R22  X 22
Rotorcurrent / phase 
E2
R22  X 22
Rotor circuit At Slip s
At slip s:
Induced Emf/phase = sE2
Rotor Resistance and Reactance/phase = R2 & X2
fr  sf
X 2  2sfL2  sX 2
RotorimpedanceZ  R22  ( sX 2 ) 2
Rotorcurrent / phase 
sE2
R22  s 2 X 22
Torque Equation
Torque in an induction motor depends on
1. Induced Voltage in Rotor E2 due to Stator Flux
2. Current in the Rotor I2
3. Cosine of angle between them Cos ɸ2
TorqueTE2 I 2Cos2
T  kE2 I 2Cos2
Constant of Proportionality K not same as the transformation ratio
T  kE2 I 2Cos2
Rotorcurrent / phaseI 2 
Cos2 
T  kE2
R s X
2
2
R2
R s X
2
2
2
2
2
sE2
R22  s 2 X 22
2
General Equation for Torque
in an Induction Motor
sE2
ksR2 E2
T 2 2 2
R2  s X 2
R2
R22  s 2 X 22
2
2
2
Torque – Speed Characteristics of IM
• Low slip region – slip increases linearly with increased load and mechanical speed
decreases linearly with load – rotor reactance negligible – rotor PF approx. unity – rotor
current increases linearly with slip – entire normal steady-state operation in this region –
linear speed drop T ά slip (linear line)
• Moderate slip region – rotor freq. higher – rotor reactance is on same order of resistance –
rotor current no longer increases rapidly – PF starts to drop – peak torque occurs – for
incremental increase in load , increase in rotor current exactly balanced by decrease in
rotor PF
• High slip region – induced torque
decreases with increase in load – since
increase in rotor current completely
Moderate s
High s
Low s
over-shadowed by decrease in rotor PF
T ά 1/slip (rectangular hyperbola)
S=1
S MT 
R2
X2
S=0
2
General Equation for Torque in Induction Motor
ksR E
T  2 2 22 2
R2  s X 2
Torque – Speed Characteristics of IM
• Max torque or pullout or breakdown torque – 2 to 3 times rated torque
• Starting torque- slightly higher than rated torque, motor will start carrying any load that it
can supply at full power
Pull-out torque – 200 to 250% of rated torque
Starting torque – 150% of rated torque
Normal
Operating Region
Torque – Speed Characteristics of IM
• If rotor driven faster than sync speed – direction of induced torque reverses – machine
becomes generator
• reversing direction of mag.field – switching any two stator phases – used to very rapidly
stop IM - Plugging
Effect of Rotor resistance on Torque of IM
• Slip ring or Wound rotor – Addition of Resistance in rotor
• rotor resistance increased – pull out speed of motor decreases but the max.torque remains
constant
• Advantage – to start heavy loads – max.torque can be adjusted to occur at starting
condition
• Extra resistance can be removed and max.torque will move
upto near sync.speed for regular operation