Electric Machines
Chapter 4
AC Machines
Dr Jalal Al Roumy
Israa University
2019/2020
Introduction:
 An electrical machine is a device that converts either
mechanical energy to electrical energy (called a
generator) or electrical energy to mechanical energy
(called a motor).
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Major Classes of Ac Machines:
AC Machines
Synchronous Machines
Magnetic field current is
supplied by a separate
dc power source
Induction Machines
Field current is supplied by
magnetic induction (transformer
action) into their field windings
The field circuits are located
on their rotors
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Simple Loop In Uniform Magnetic Field:
A loop of wire in uniform magnetic field produces sinusoidal
AC voltage
4
Stator & Rotor:
 The rotating part of the machine is called the rotor, and
the stationary part of the machine is called the stator.
Stator
Rotor
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Voltage Induced in a Simple Rotating Loop:
To determine the total voltage etot
on the loop, we will examine each
segment of the loop separately
and sum all the resulting voltages.
The voltage on each segment is
given by:
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Voltage Induced in a Simple Rotating Loop:
1. Segment ab:
2. Segment bc:
3. Segment cd:
4. Segment da:
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Voltage Induced in a Simple Rotating Loop:
The total induced voltage:
e ind  eba  ecb  edc  ead
e ind   Bl sin ab   Bl sin cd
e ind  2 Bl sin 
It can also be expressed as:
  t ,   r 
e ind  2r  Bl sin t
e ind  A B  sin t
max  A B
e ind  max sin t
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Voltage Induced in a Simple Rotating Loop:
In any real machine, the induced voltage depends on:
1. The flux in the machine
2. The speed of rotation
3. A constant representing the construction of the machine
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Torque Induced in Current-Carrying Loop:
10
Torque Induced in Current-Carrying Loop:
If a current flows in the loop, then a torque will be induced on
the wire loop.
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Torque Induced in Current-Carrying Loop:
The force on each segment of the
loop will be given by:
The torque on that segment will
then be given by:
  (force applied)(perpendicular distance)
  F  r sin 
  rF sin 
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Torque Induced in Current-Carrying Loop:
Fab  i (l  B )  ilB
down
 ab  (F )(r sin ab )
 ab  rilB sin ab clockwise
Fbc  i (l  B )  ilB into thepage
 bc  (F )(r sin bc )
 bc  0 since bc  0
Fcd  i (l  B )  ilB
up
 cd  (F )(r sin cd )
 cd  rilB sin cd clockwise
Fda  i (l  B )  ilB
out of the page
 da  (F )(r sin da )
 da  0 since da  0
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Torque Induced in Current-Carrying Loop:
The total induced torque:
 ind   ab   bc   cd   da
 ind  rilB sin ab  rilB sin cd
ab  cd
 ind  2rilB sin 
In any real machine, the torque depends on:
1.
2.
3.
4.
The strength of the rotor magnetic field
The strength of the external magnetic field
The angle between them
A constant representing the construction of the machine
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The Rotating Magnetic Field:
 If one magnetic field is produced by the stator and the
other one is produced by the rotor, then a torque will be
induced in the rotor causing the rotor to turn and align
itself with the stator magnetic field.
 If the stator magnetic field rotates, the induced torque in
the rotor would cause it to chase the stator magnetic
field around in a circle (principle of AC motor operation).
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The Rotating Magnetic Field:
 If a three-phase set of currents, of equal magnitude and
120° apart, flows in a three-phase winding, then it will
produce a rotating magnetic field of constant magnitude
(the fundamental principle of AC machine operation).
iaa' (t )  I M sin t A
ibb' (t )  I M sin(t 120) A
icc' (t )  I M sin(t  240) A
 The current in coil aa' flows into the a end of the coil and
out the a' end of the coil producing:
H aa' (t )  H M sin t0 A  turns / m
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The Rotating Magnetic Field:
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The Rotating Magnetic Field:
 The three-phase winding consists of 3 separate windings
spaced 120 apart around the machine surface.
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The Rotating Magnetic Field:
 The magnitude of H varies sinusoidally in time, but its
direction is always constant:
H aa' (t )  H M sin t0 A  turns / m
Hbb' (t )  H M sin(t 120)120 A  turns / m
H cc' (t )  H M sin(t  240)240 A  turns / m
 Hence, the resulting flux densities are:
Baa' (t )  BM sin t0 T
Bbb' (t )  BM sin(t  120)120 T
Bcc' (t )  BM sin(t  240)240 T
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The Rotating Magnetic Field:
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Proof of the Rotating Field Concept:
B net (t )  B M sin t 0  B M sin(t  120) 120  B M sin(t  240) 240
B net (t )  1.5B M sin t  xˆ  1.5B M cos t  yˆ
t  0  B net  1.5B M -90
t  90  B net  1.5B M 0
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Electric Frequency and Field Speed:
The magnetic poles complete one
mechanical rotation around the
stator surface for each electrical
cycle of the applied current:
The windings on the two-pole
stator occur in the order (taken
counter-clockwise):
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Electric Frequency and Field Speed:
a  c '  b  a'  c  b '  a  c '  b  a'  c  b '
e  2 m , f e  2f m , e  2m
P
P
P
e   m , f e  f m , e  m
2
2
2
nm
nm P
fm  , fe 
60
120
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Reversing the Direction of Field Rotation:
 If the current in any two of the three coils is swapped, the
direction of the magnetic field's rotation will be reversed.
 Hence, it is possible to reverse the direction of rotation
just by switching the connections on any two coils.
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Induced Voltage in AC Machines:
 A rotating magnetic field produces voltages in the stator.
Here is a rotating rotor with a sinusoidally distributed
magnetic field in the centre of a stationary coil.
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Induced Voltage in AC Machines:
B  B M cos 
from rotor side
B  B M cos(t   ) stator side
eba    B  .l
  180
eba    B  .l   Bl
out of page
eba   B M l cos  t  180 
ecb  0
(  B )  l
e dc    B  .l
e dc   Bl
  0
out of page
e ind  eba  edc
e ind   B M l cos(mt  180)   B M l cos mt
e ind  2 B M l cos mt
e ind  2(r m )B M l cos mt
e ind  2rlB M m cos mt
  2rlB M
e ind   cos mt 2-pole stator
e ind  N C  cos mt
e dc   B M l cos t
e ad  0
(  B )  l
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Induced Voltage in a 3-Phase Set of Coils:
e aa '  N C  sin t
ebb '  N C  sin(t  120o )
ecc '  N C  sin(t  240o )
E max  N C 
  2 f
E max  2 N C  f
EA
EA
2

N C f
2
 4.44N C  f
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Example:
In the figure shown: the peak flux density of the rotor magnetic field is 0.2
T, the mechanical rate of rotation of the shaft is 3600 rpm. The stator
diameter of the machine is 0,5 m, its coil length is 0.3 m, and there are 15
turns per coil. The machine is Y-connected.
(a) What are the 3-phase voltages of the generator as a function of time?
(b) What is the rms phase voltage of this generator?
(C) What is the rms terminal voltage of this generator?
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Solution:
  2rlB  dlB  0.5  0.3  0.2
  0.03 Wb
2  N
2  3600


60
  377 rad/s
60
E max  N C   15  0.03  377
E max  169.7 V
e aa '  169.7 sin 377t
V
ebb '  169.7 sin(377t  120o ) V
B  0.2 T , N  3600 rpm
diameter (d )  0.5 m
l  0.3 m , N C  15 turn
ecc '  169.7 sin(377t  240o ) V
EA 
VT 
E max 169.7

 120
2
2
3E A 
V
3  120  208 V
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Power Flows and Losses:
The efficiency of an AC
machine is defined by:
Pout

100%
Pin

Pin  Plosses
100%
Pin
Pout

100%
Pout  Plosses
Losses in AC Machines:
2
Electrical or Copper Losses ( I R )
Core Losses (Eddy and Hysteresis)
Mechanical Losses (Friction and Windage)
Stray Losses (Miscellaneous Losses)
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The Power-Flow Diagram:
For generator
For motor
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Voltage & Speed Regulation:
V nl V fl
VR 
V fl
for generators
n nl  n fl
SR 
n fl
for motors
nl  fl
SR 
fl
for motors
A small VR is better in the sense that the voltage at the
terminals of the generator is more constant with variations
in load.
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HW #3:
 4.1, 4.3, 4.4 & 4.6.
 Assignment is due to 11/10/2019.
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