Equivalent Circuit of
an Induction Motor Rotor
• Consider just a single phase.
• The power and torque developed by the motor
will be three times that of one phase.
ECE 441
1
The rotor resistance depends upon the rotor conductors
as well as an external rheostat if the machine has a
“wound rotor”.
The reactance of the rotor is caused by “leakage” flux
and is called the “leakage reactance”.
ECE 441
2
X r  2 f r Lr
f r  sf BR
X r  2 ( sf BR ) Lr  s(2 f BR Lr )
X r  sX BR
ECE 441
3
The equivalent circuit in terms of slip is shown below.
Z r  Rr  jsX BR
sEBR
Ir 
Rr  jsX BR
Ir 
EBR
Rr
 jX BR
s
ECE 441
4
The blocked-rotor voltage and rotor inductance are
constant and the rotor resistance varies with the slip.
EBR 0 EBR
Ir 

  r
Zr
Zr
 r
s
s
ECE 441
5
Magnitude and Phase of the rotor current
EBR
EBR
Ir 

Zr
Rr 2
2
( )  X BR
s
s


1 X BR
 r  tan 
R
 r
 s





ECE 441
6
Locus of the Rotor Current
• Plot the magnitude and phase of the rotor
current as functions of the slip.
EBR
EBR
Ir 

Zr
Rr 2
2
( )  X BR
s
s


1 X BR
 r  tan 
 Rr
 s





ECE 441
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ECE 441
8
Amperes and Degrees
Amperes and Degrees
Ir and θr are maximum at blocked rotor and approach
zero as the rotor accelerates to synchronous speed.
ECE 441
9
Phasor Diagram of the rotor current
Synchronous Speed (s=0)
“Blocked Rotor” (s=1)
ECE 441
10
Zr
X BR

s sin  r
EBR
EBR
Ir 

Zr
X BR
s
sin  r
EBR
Ir 
sin  r
X BR
Equation of the semicircle tangent to the horizontal axis
at the origin with a diameter of EBR/XBR.
ECE 441
11