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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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