1. INDUCTION MOTOR steady-state model (squirrel cage)
MEP 1523
ELECTRIC DRIVES
INDUCTION MOTOR steady-state model (squirrel cage)

2. Stator – 3-phase winding Rotor – squirrel cage / wound
Construction
120o a c’ b’ c b a’
Stator – 3-phase winding
Rotor – squirrel cage / wound

3. Construction Single N turn coil carrying current i
Spans 180o elec
Permeability of iron >> o
→ all MMF drop appear in airgap a  a’  
/2
-/2 -
Ni / 2
-Ni / 2

4. Construction Distributed winding
– coils are distributed in several slots
Nc for each slot 
(3Nci)/2
(Nci)/2 -
-/2
/2  

5. Distributed winding (full-pitch)
Construction
Distributed winding (full-pitch)
The resultant MMF is the total contribution of MMF from each coil
Considering only the space-fundamental component,
Concentrated
Distributed
Distributed space fundamental
Concentrated space fundamental

6. Phase a – sinusoidal distributed winding
Air–gap mmf
F()   2

7. Sinusoidal winding for each phase produces space sinusoidal MMF and flux
Sinusoidal current excitation (with frequency s) in a phase produces space sinusoidal standing wave MMF
Combination of 3 standing waves resulted in MMF wave rotating at:
p – number of poles
f – supply frequency

9. Rotating flux induced:
emf in stator winding (known as back emf)
Emf in rotor winding
Rotor flux rotating at synchronous frequency
Rotor current interact with flux producing torque
Rotor ALWAYS rotate at frequency less than synchronous, i.e. at slip speed: sl = s – r
Ratio between slip speed and synchronous speed known as slip

10. Stator voltage equation:
Vs = Rs Is + j(2f)LlsIs + Eag
Eag – airgap voltage or back emf
Eag = k f ag
Rotor voltage equation:
Er = Rr Ir + js(2f)Llr
Er – induced emf in rotor circuit
Er /s = (Rr / s) Ir + j(2f)Llr

11. Per–phase equivalent circuit
Llr
Lls Ir Rs + Vs – +
Eag – +
Er/s – Is Lm
Rr/s Im
Rs – stator winding resistance
Rr – rotor winding resistance
Lls – stator leakage inductance
Llr – rotor leakage inductance
Lm – mutual inductance
s – slip

12. We know Eg and Er related by
Where a is the winding turn ratio
The rotor parameters referred to stator are:
rotor voltage equation becomes
Eg = (Rr’ / s) Ir’ + j(2f)Llr’ Ir’

13. Per–phase equivalent circuit
Rr’/s + Vs – Rs
Lls
Llr’
Eag Is
Ir’ Im Lm
Rs – stator winding resistance
Rr’ – rotor winding resistance referred to stator
Lls – stator leakage inductance
Llr’ – rotor leakage inductance referred to stator
Lm – mutual inductance
Ir’ – rotor current referred to stator

14. Power and Torque
Power is transferred from stator to rotor via air–gap, known as airgap power
Lost in rotor winding
Converted to mechanical power = (1–s)Pag
 Pm = (1-s)Pag

15. Mechanical power, Pm = Tem r
Power and Torque
Mechanical power, Pm = Tem r
But, ss = s - r  r = (1-s)s
 Pag = Tem s
Therefore torque is given by (based on approximate equivalent circuit):

16. Power and Torque sm Tem Pull out Torque (Tmax) Trated r 0 rated s s

17. Steady state performance
The steady state performance can be calculated from equivalent circuit, e.g. using Matlab
Rr’/s + Vs – Rs
Lls
Llr’
Eag Is
Ir’ Im Lm

18. Steady state performance
Rr’/s + Vs – Rs
Lls
Llr’
Eag Is
Ir’ Im Lm
e.g. 3–phase squirrel cage IM
V = 460 V Rs= 0.25  Rr=0.2 
Lr = Ls = 0.5/(2*pi*50) Lm=30/(2*pi*50)
f = 50Hz p = 4

19. Steady state performance

20. Steady state performance