AC Machines Fundamentals
Introduction
• Synchronous machines: Motors and generators
whose magnetic field is supplied by a separate dc power
supply.
• Induction machines: Motors and generators
whose magnetic field is supplied by magnetic induction
transformer action.
Voltage Induced in a simple
Rotating Loop
c
b
Vab
cd
l
r
S
N
d
a
Vcd
ab
B
ein  (v  B).l  vBl sin 
+
-
eab  vBl sin ab

 ab
ebc  eda  0
ecd  vBl sin cd
ein  2vBLsin   max sin t
B
r
F
Induce Torque in current
Carrying Loop
c
b
  F d
l
d
F  i(l  B)  ilB
a
i
Bloop
 ab  (F )(r sinab )  rilB sin ab
 bc   da  0
 cd  ( F )(r sin cd )  rilB sin cd
 ind  2rilB sin 
cd

BS

ab
 ind  kBloop  Bs
Rotating Magnetic Field
• If three set of currents each of equal
magnitude and differing in phase by 120º flow
in 3 phase winding, then it will produce a
rotating magnetic field of constant magnitude.
a’
Apply three set of currents to the stator
will produce magnetic field intensity H
and magnetic flux B as follows:

c
b
Bbb’
Baa '  BM sin t0 T
Baa’
Bbb '  BM sin(t  120)120 T
Bcc'  BM sin(t  240)240 T
Bnet  1.5BM   90
Resulting net
magnetic field
b’
Bcc’
Bnet

a
t  0
c’
The relation between the Electrical
Frequency and Mechanical Speed
• The rotating magnetic flux in stator (Bnet or Bs) can be
represented by one North and one South pole (2 pole
machine). These magnetic poles complete one mechanical
rotation around the stator for each electrical rotation.
f e  f m , e  m
For 4-pole machine, the
mechanical pole move
halfway around the stator in
one electrical cycle:
e  2m , f e  2 f m , e  2m
In general:
P
P
P
 m , f e  f m , e   m
2
2
2
n P
120 f
f e  m  n/ m 
120
P
e 
MMF and flux distribution
on AC Machine
• The flux in a real machine doesn't behave in a simple manner
assumed above since there is ferromagnetic rotor in the center
of machine with small air gap between rotor and stator.
– The reluctance of air gap is much higher than the reluctance of either the
rotor and stator. So the flux density vector B takes the shortest possible
path across the air gap and jumps perpendicularly between the rotor and
stator.

How to produce sinusoidal voltage ? The flux
density must vary in sinusoidal manner.
nc  Nc cos
360
The most straight foreword way to achieve a
sinusoidal variations of m.m.f along the surface
of air gap is to distribute the turns of the windings
that produce the m.m.f in closely spaced slots
and to vary the number of conductors in each
slot in sinusoidal manner.

180
Fractional pitch winding is also
used to reduce harmonics and
get sinusoidal waves
Induced voltage in AC Machine
Airgap
c-d
• The magnitude of flux density at a
point around the rotor is given by :


BM
B  BM cos
• The magnitude of flux
density at a point around the
stator is given by :

a-b
c
B  BM cos(t   )
ein  (v  B).l
ein  eba  edc  2vBLcosmt   cost
For N number of coil in each slot
d
b
a
ein  Nc cost
Induced volt in 3 phase coils
eaa '(t )  Nc sin t
ebb' (t )  Nc sin(t 120)
ecc'(t )  Nc sin(t  240 )
RMS voltage in three phase stator:
EA  2Ncf  K
Induce torque in AC Machine
 ind  2rliBS sin   kBR  BS
 ind  kBR  Bnet
 ind  kBR Bnet sin 
AC Machine Power Flow
and Losses
Sync. Generator
Induction Motor