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 Page 1


 
 
 
 
 
Stator & Rotor Magnetic Fields 
o When a 3-phase supply is connected to the stator, than a magnetic field is set up 
whose speed of rotation is 
  
S
120f
N = 
P
 
  f = frequency of supply 
o If negative sequence currents are applied the rotating magnetic field rotates in 
opposite direction as compared to magnetic field produced by positive sequence 
currents. 
o The rotor rotates in same direction as the stator magnetic field with a speed, . 
  
?
sr
s
NN
slip s = 
N
 
              ? ?
rs
 N = N 1 s ?? 
o Speed of rotor magnetic field with respect to rotor 
s
= sN  
o speed of rotor magnetic field with respect to stator 
s
= N .   
Hence, stator & rotor magnetic fields are at rest with respect to each other. 
o Frequency of emf & current in rotor  = sf 
 
 
 
 
 
 
     With  
   respect  
       to 
Relative Speed of 
 Stator Stator 
Magnetic 
Field 
Rotor Rotor 
Magnetic 
Field 
Stator 0 N s N s(1-s) N s 
Stator 
Magnetic 
Field 
-Ns 0 -sNs 0 
Rotor -N s(1-s) sN s 0 sN s 
Rotor 
Magnetic 
Field 
-N s 0 -sN s 0 
 
  
 
Page 2


 
 
 
 
 
Stator & Rotor Magnetic Fields 
o When a 3-phase supply is connected to the stator, than a magnetic field is set up 
whose speed of rotation is 
  
S
120f
N = 
P
 
  f = frequency of supply 
o If negative sequence currents are applied the rotating magnetic field rotates in 
opposite direction as compared to magnetic field produced by positive sequence 
currents. 
o The rotor rotates in same direction as the stator magnetic field with a speed, . 
  
?
sr
s
NN
slip s = 
N
 
              ? ?
rs
 N = N 1 s ?? 
o Speed of rotor magnetic field with respect to rotor 
s
= sN  
o speed of rotor magnetic field with respect to stator 
s
= N .   
Hence, stator & rotor magnetic fields are at rest with respect to each other. 
o Frequency of emf & current in rotor  = sf 
 
 
 
 
 
 
     With  
   respect  
       to 
Relative Speed of 
 Stator Stator 
Magnetic 
Field 
Rotor Rotor 
Magnetic 
Field 
Stator 0 N s N s(1-s) N s 
Stator 
Magnetic 
Field 
-Ns 0 -sNs 0 
Rotor -N s(1-s) sN s 0 sN s 
Rotor 
Magnetic 
Field 
-N s 0 -sN s 0 
 
  
 
 
 
 
 
 
Inverted Induction Motor 
o When a 3 ?? supply is connected to the rotor & stator terminals are shorted or are 
connected to the resistive load. 
o Then a rotor magnetic field is set up which rotates at speed 
s
N with respect to rotor ; 
 where f is frequency of supply. 
o If rotor rotates at speed , than slip 
  
?
sr
s
NN
s = 
N
 
Here, the rotor rotates in a direction opposite to the direction of rotation of stator 
magnetic field. 
o Speed of rotor magnetic field with respect to stator 
  ? ?
s s s
= N N 1 s = sN ?? 
Speed of stator magnetic field 
s
= sN 
o Frequency of emf & current induced in stator = sf 
  f = supply frequency on rotor. 
 
 
 
 
 
 
     With  
   respect  
       to 
Relative Speed of 
 Stator Stator 
Magnetic 
Field 
Rotor Rotor 
Magnetic 
Field 
Stator 0 sN s N s(1-s) sN s 
Stator 
Magnetic 
Field 
-sN s 0 -N s 0 
Rotor -Ns(1-s) Ns 0 Ns 
Rotor 
Magnetic 
Field 
-sNs 0 -Ns 0 
 
Equivalent circuit of Induction Motor 
 
 
 
Page 3


 
 
 
 
 
Stator & Rotor Magnetic Fields 
o When a 3-phase supply is connected to the stator, than a magnetic field is set up 
whose speed of rotation is 
  
S
120f
N = 
P
 
  f = frequency of supply 
o If negative sequence currents are applied the rotating magnetic field rotates in 
opposite direction as compared to magnetic field produced by positive sequence 
currents. 
o The rotor rotates in same direction as the stator magnetic field with a speed, . 
  
?
sr
s
NN
slip s = 
N
 
              ? ?
rs
 N = N 1 s ?? 
o Speed of rotor magnetic field with respect to rotor 
s
= sN  
o speed of rotor magnetic field with respect to stator 
s
= N .   
Hence, stator & rotor magnetic fields are at rest with respect to each other. 
o Frequency of emf & current in rotor  = sf 
 
 
 
 
 
 
     With  
   respect  
       to 
Relative Speed of 
 Stator Stator 
Magnetic 
Field 
Rotor Rotor 
Magnetic 
Field 
Stator 0 N s N s(1-s) N s 
Stator 
Magnetic 
Field 
-Ns 0 -sNs 0 
Rotor -N s(1-s) sN s 0 sN s 
Rotor 
Magnetic 
Field 
-N s 0 -sN s 0 
 
  
 
 
 
 
 
 
Inverted Induction Motor 
o When a 3 ?? supply is connected to the rotor & stator terminals are shorted or are 
connected to the resistive load. 
o Then a rotor magnetic field is set up which rotates at speed 
s
N with respect to rotor ; 
 where f is frequency of supply. 
o If rotor rotates at speed , than slip 
  
?
sr
s
NN
s = 
N
 
Here, the rotor rotates in a direction opposite to the direction of rotation of stator 
magnetic field. 
o Speed of rotor magnetic field with respect to stator 
  ? ?
s s s
= N N 1 s = sN ?? 
Speed of stator magnetic field 
s
= sN 
o Frequency of emf & current induced in stator = sf 
  f = supply frequency on rotor. 
 
 
 
 
 
 
     With  
   respect  
       to 
Relative Speed of 
 Stator Stator 
Magnetic 
Field 
Rotor Rotor 
Magnetic 
Field 
Stator 0 sN s N s(1-s) sN s 
Stator 
Magnetic 
Field 
-sN s 0 -N s 0 
Rotor -Ns(1-s) Ns 0 Ns 
Rotor 
Magnetic 
Field 
-sNs 0 -Ns 0 
 
Equivalent circuit of Induction Motor 
 
 
 
 
 
 
 
   
If we refer all parameters on stator side 
 
 
 
 
 
22
11
2 2 2 2
22
NN
r = r ;  x = x
NN
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
??
??
??
 
1 1 1
N = N k
?
? 
Where  
1
N = no. of turns per phase on stator 
       
1
k ? = winding factor of stator winding 
 
2 2 2
N = N k
?
? 
   
2
N = number of turns per phase on rotor 
   
2
k ? = winding factor of rotor winding 
Tests Conducted on Induction Motor 
(i) No-Load Test 
o Conducted on Stator with no-load on rotor side. 
o It gives No-Load Losses ( Rotational Loss + Core Loss). 
  (ii) Blocked Rotor Test 
o Conducted on stator side keeping rotor blocked 
o It gives full load Copper Losses and equivalent resistance and equivalent reactance 
referred to Stator Side. 
 
Page 4


 
 
 
 
 
Stator & Rotor Magnetic Fields 
o When a 3-phase supply is connected to the stator, than a magnetic field is set up 
whose speed of rotation is 
  
S
120f
N = 
P
 
  f = frequency of supply 
o If negative sequence currents are applied the rotating magnetic field rotates in 
opposite direction as compared to magnetic field produced by positive sequence 
currents. 
o The rotor rotates in same direction as the stator magnetic field with a speed, . 
  
?
sr
s
NN
slip s = 
N
 
              ? ?
rs
 N = N 1 s ?? 
o Speed of rotor magnetic field with respect to rotor 
s
= sN  
o speed of rotor magnetic field with respect to stator 
s
= N .   
Hence, stator & rotor magnetic fields are at rest with respect to each other. 
o Frequency of emf & current in rotor  = sf 
 
 
 
 
 
 
     With  
   respect  
       to 
Relative Speed of 
 Stator Stator 
Magnetic 
Field 
Rotor Rotor 
Magnetic 
Field 
Stator 0 N s N s(1-s) N s 
Stator 
Magnetic 
Field 
-Ns 0 -sNs 0 
Rotor -N s(1-s) sN s 0 sN s 
Rotor 
Magnetic 
Field 
-N s 0 -sN s 0 
 
  
 
 
 
 
 
 
Inverted Induction Motor 
o When a 3 ?? supply is connected to the rotor & stator terminals are shorted or are 
connected to the resistive load. 
o Then a rotor magnetic field is set up which rotates at speed 
s
N with respect to rotor ; 
 where f is frequency of supply. 
o If rotor rotates at speed , than slip 
  
?
sr
s
NN
s = 
N
 
Here, the rotor rotates in a direction opposite to the direction of rotation of stator 
magnetic field. 
o Speed of rotor magnetic field with respect to stator 
  ? ?
s s s
= N N 1 s = sN ?? 
Speed of stator magnetic field 
s
= sN 
o Frequency of emf & current induced in stator = sf 
  f = supply frequency on rotor. 
 
 
 
 
 
 
     With  
   respect  
       to 
Relative Speed of 
 Stator Stator 
Magnetic 
Field 
Rotor Rotor 
Magnetic 
Field 
Stator 0 sN s N s(1-s) sN s 
Stator 
Magnetic 
Field 
-sN s 0 -N s 0 
Rotor -Ns(1-s) Ns 0 Ns 
Rotor 
Magnetic 
Field 
-sNs 0 -Ns 0 
 
Equivalent circuit of Induction Motor 
 
 
 
 
 
 
 
   
If we refer all parameters on stator side 
 
 
 
 
 
22
11
2 2 2 2
22
NN
r = r ;  x = x
NN
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
??
??
??
 
1 1 1
N = N k
?
? 
Where  
1
N = no. of turns per phase on stator 
       
1
k ? = winding factor of stator winding 
 
2 2 2
N = N k
?
? 
   
2
N = number of turns per phase on rotor 
   
2
k ? = winding factor of rotor winding 
Tests Conducted on Induction Motor 
(i) No-Load Test 
o Conducted on Stator with no-load on rotor side. 
o It gives No-Load Losses ( Rotational Loss + Core Loss). 
  (ii) Blocked Rotor Test 
o Conducted on stator side keeping rotor blocked 
o It gives full load Copper Losses and equivalent resistance and equivalent reactance 
referred to Stator Side. 
 
 
 
 
 
 
o 
01
R & 
01
X are equivalent winding resistance & equivalent leakage reactor referred to 
Stator side. 
o Wattmeter reading = 
2
sc 01
P = I R from this equation, we can calculate 
01
R 
o 
sc
01
sc
V
Z = 
I
   & 
22
01 01 01
X = Z R ? 
o We obtain
01
R , 
01
X & full load copper losses from this test. 
o 
01
R = R 1+ R 2’ ;  
01
X = X 1+ X 2’ 
Power Flow Diagram 
                                               
          
                          Rotor i/p = 
g
P (Airgap power) Mechanical Power Developed  
                                                                                                                                           
in
P                                                                                                                                                           
 
  Stator    Stator      Rotor   Rotor       Friction  &                                                                                                             
            
2
IR loss          core loss                                             
2
IR loss            core loss    windage loss 
                 
    
2
22
g
3I r
P = 
s
 
    
2
I = rotor current 
     s = slip 
    
2
r = rotor resistance per phase 
    Rotor 
u
C Loss 
2
2 2 g
= 3I r = sP 
    Mechanical power developed 
? ?
g g g
= P sP = 1-s P ? 
    Developed Torque,  
? ?
? ?
g g
m
e
rs
s
1-s P P
P
T =  =   
ww
1-s w
? 
 
Page 5


 
 
 
 
 
Stator & Rotor Magnetic Fields 
o When a 3-phase supply is connected to the stator, than a magnetic field is set up 
whose speed of rotation is 
  
S
120f
N = 
P
 
  f = frequency of supply 
o If negative sequence currents are applied the rotating magnetic field rotates in 
opposite direction as compared to magnetic field produced by positive sequence 
currents. 
o The rotor rotates in same direction as the stator magnetic field with a speed, . 
  
?
sr
s
NN
slip s = 
N
 
              ? ?
rs
 N = N 1 s ?? 
o Speed of rotor magnetic field with respect to rotor 
s
= sN  
o speed of rotor magnetic field with respect to stator 
s
= N .   
Hence, stator & rotor magnetic fields are at rest with respect to each other. 
o Frequency of emf & current in rotor  = sf 
 
 
 
 
 
 
     With  
   respect  
       to 
Relative Speed of 
 Stator Stator 
Magnetic 
Field 
Rotor Rotor 
Magnetic 
Field 
Stator 0 N s N s(1-s) N s 
Stator 
Magnetic 
Field 
-Ns 0 -sNs 0 
Rotor -N s(1-s) sN s 0 sN s 
Rotor 
Magnetic 
Field 
-N s 0 -sN s 0 
 
  
 
 
 
 
 
 
Inverted Induction Motor 
o When a 3 ?? supply is connected to the rotor & stator terminals are shorted or are 
connected to the resistive load. 
o Then a rotor magnetic field is set up which rotates at speed 
s
N with respect to rotor ; 
 where f is frequency of supply. 
o If rotor rotates at speed , than slip 
  
?
sr
s
NN
s = 
N
 
Here, the rotor rotates in a direction opposite to the direction of rotation of stator 
magnetic field. 
o Speed of rotor magnetic field with respect to stator 
  ? ?
s s s
= N N 1 s = sN ?? 
Speed of stator magnetic field 
s
= sN 
o Frequency of emf & current induced in stator = sf 
  f = supply frequency on rotor. 
 
 
 
 
 
 
     With  
   respect  
       to 
Relative Speed of 
 Stator Stator 
Magnetic 
Field 
Rotor Rotor 
Magnetic 
Field 
Stator 0 sN s N s(1-s) sN s 
Stator 
Magnetic 
Field 
-sN s 0 -N s 0 
Rotor -Ns(1-s) Ns 0 Ns 
Rotor 
Magnetic 
Field 
-sNs 0 -Ns 0 
 
Equivalent circuit of Induction Motor 
 
 
 
 
 
 
 
   
If we refer all parameters on stator side 
 
 
 
 
 
22
11
2 2 2 2
22
NN
r = r ;  x = x
NN
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
??
??
??
 
1 1 1
N = N k
?
? 
Where  
1
N = no. of turns per phase on stator 
       
1
k ? = winding factor of stator winding 
 
2 2 2
N = N k
?
? 
   
2
N = number of turns per phase on rotor 
   
2
k ? = winding factor of rotor winding 
Tests Conducted on Induction Motor 
(i) No-Load Test 
o Conducted on Stator with no-load on rotor side. 
o It gives No-Load Losses ( Rotational Loss + Core Loss). 
  (ii) Blocked Rotor Test 
o Conducted on stator side keeping rotor blocked 
o It gives full load Copper Losses and equivalent resistance and equivalent reactance 
referred to Stator Side. 
 
 
 
 
 
 
o 
01
R & 
01
X are equivalent winding resistance & equivalent leakage reactor referred to 
Stator side. 
o Wattmeter reading = 
2
sc 01
P = I R from this equation, we can calculate 
01
R 
o 
sc
01
sc
V
Z = 
I
   & 
22
01 01 01
X = Z R ? 
o We obtain
01
R , 
01
X & full load copper losses from this test. 
o 
01
R = R 1+ R 2’ ;  
01
X = X 1+ X 2’ 
Power Flow Diagram 
                                               
          
                          Rotor i/p = 
g
P (Airgap power) Mechanical Power Developed  
                                                                                                                                           
in
P                                                                                                                                                           
 
  Stator    Stator      Rotor   Rotor       Friction  &                                                                                                             
            
2
IR loss          core loss                                             
2
IR loss            core loss    windage loss 
                 
    
2
22
g
3I r
P = 
s
 
    
2
I = rotor current 
     s = slip 
    
2
r = rotor resistance per phase 
    Rotor 
u
C Loss 
2
2 2 g
= 3I r = sP 
    Mechanical power developed 
? ?
g g g
= P sP = 1-s P ? 
    Developed Torque,  
? ?
? ?
g g
m
e
rs
s
1-s P P
P
T =  =   
ww
1-s w
? 
 
 
 
 
 
 
Torque – Slip Characteristics 
If core loss is neglected then equivalent circuit looks like as shown 
  
? ?
? ?
m 1
e
m 11
V jX
V = 
r j X X ??
 
  
? ?
mm 11
ee
m 1
m 1
r X X X
R =  ; X = 
XX
XX
?
?
 
  
Torque developed, 
2
e 2
c
2
2
2
s e e 2
r mV
T = 
s
r
w R X X
s
??
??
??
??
??
??
??
????
?? ??
??
?
?
?
?
? ? ?
 
 
 
 
 
 
 
 
 
For Approximate analysis, 
Stator impedance is neglected; 
2
12
c
2
s
2
2
2
Vr
3
T = 
ws
R
X
s
??
??
??
??
??
??
??
??
??
?
?
?
?
?
 
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