Alternator Basics.pdf

Synchronous Generators
Dr. Francis M. Fernandez
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 1
Jan 2020

 Synchronous generator is the common type
used in generating stations
 It runs at constant speed and generates
constant frequency output
 The filed poles are on the rotor side and the
armature is on stator side
 The armature winding is placed in the slots
on stator core
 Field poles are excited with a dc supply
 DC supply to the filed poles are given
through a pair of slip rings
EXCITER
GENERATOR
TURBINE

Types of Construction
Salient Pole type Cylindrical Rotor type
N
S
S
N
Field
winding
Field pole
Armature
conductors
N
S
Stator
Cylindrical
rotor

Why Armature on Stator?
 Power in the field system is much less
compared to the generated power,
which is easily handled by the slip
rings.
 When the armature is on the stator
side, generated power is directly taken
out without the help of slip rings.
N
S
Excitation
Voltage
Slip
Rings
Stator
Windings

Relation between Speed and Frequency
N
S
A
A’
N
S
S
N
A
A’
1 revolution per second (RPS)
makes 1 Hertz
1 revolution per second (RPS)
makes 2 Hertz
2 Pole 4 Pole General case
2 f
RPS
P

where is the freuency
and is the number of poles
f
P
120
,
f
RPM N
P


Synchronous Speed
 Synchronous speed is the speed at which the generator should run to
produce a constant frequency
- freuency
- number of poles
- speed in RPM
f
P
N
Number of cycles per revolution
2
Revolution per second
60
Cycles per second
2 60 2 60
120
,
P
N
P N P N
f
f
RPM N
P


 
  
 

N
S
S
N
A
A’

Three Phase Generator
N
S
R'
Y
B
R
Y' B'
120o
 There will be three sets of similar
windings
 Windings are placed 120 degrees apart
 Practically each phase winding will be
distributed across several slots

Practical Winding

Single Layer Winding

Winding example (Full pitch)
No of poles: 2, No of slots: 12, Double layer → Slots/pole/phase = 12/(2x3) = 2
N
S

Winding example (Full pitch)
3 phase
2 pole
12 slot
Double layer winding

Winding example (Short Chorded)
No of poles: 2, No of slots: 12, Double layer → Slots/pole/phase = 12/(2x3) = 2
N
S

Winding example (Short Chorded)
3 phase
2 pole
12 slot
Double layer winding

Features of Short Chording
 Saves copper in end connections
 Improve wave shape (reduce harmonics)
 Reduce losses – both copper loss and core loss
 Reduced voltage compared to full pitch
N
S

Slot Angle
180
Slot angle =
Slots/pole N
S
180
Slot angle = 30
6
 
In this case (2 pole, 12 slot):
For a 4 pole 36 slot machine:
180
Slot angle = 20
9
 

Pitch Factor
If the coil is full pitched,
Total induced voltage in a coil = 2E
Let the voltage induced in a conductor is E
If the coil is short pitched by an angle
Total induced voltage = 2 E cos
2



Pitch Factor
If the coil is full pitched,
Total induced voltage in a coil = 2E
Let the voltage induced in a conductor is E
If the coil is short pitched by an angle
Total induced voltage = 2 cos
2
E


c
Resultant emf of chorded coil
Pitch factor,
Resultant emf of full piched coil
2 cos
2
= cos
2 2
K
E
E




Also known as coil span factor

Distribution factor
d
emf with distributed winding
Distribution facor,
emf with concentrated winding
K 
180
Slot angle, =
Slots/pole

= Slots/pole/phase
m
= phase spread angle
m
N
S

Distribution factor
d
emf with distributed winding
Distribution facor,
emf with concentrated winding
K 
AB = 2 sin
2
r


Arithematic sum = 2 sin
2
m r

Vector sum = 2 sin
2
m
r

d
2 sin sin
2 2
=
2 sin sin
2 2
m m
r
K
m r m
 
 


Example
For a 3 phase 36 slot 4 pole winding find the distribution factor
180 180
Slot angle, = 20
Slots per pole 9
   
36
Slots/pole/phase, 3
4 3
m  

d
3 20
sin sin
2 2
Distribution factor, = 0.956
20
sin 3 sin
2 2
m
K
m



 

EMF Equation
Number of coil sides in series per phase
Number of poles
Frequency
Speed in RPM
Flux per pole
Z
P
f
N




 
In one revolution each conductor is cut by webers
P

d P
  
60
dt
N
 Average emf induced volts
60 60
d P NP
dt
N
  
  
Substituting for N
120
Average emf induced 2 volts
60
P f
f
P

   
N
S
S
N
A
A’

EMF Equation
For the total winding, average emf 2
4
f Z
f T
 
 
RMS value 4.44 f T
 
Considering pitch factor and distribution factor,
c d
RMS value of per phase voltage, 4.44 volts
E K K f T
 
d
sin
2
=
sin
2
m
K
m


c cos
2
K



Example
A 4 pole 3 phase star connected alternator having 60 slots with 4 conductor per slot runs at
1500 rpm. Coils are short pitched by 3 slots. If the phase spread is 60 degrees, find the line
voltage induced fir for a flux per pole of 0.75 Wb distributed sinusoidally in space. All turns per
phase are in series.
60
Slots/pole/phase, 5
4 3
m  

180 180
Slot angle, = 12
Slots/pole 15
   
 
Coil pitch 15 3 12 144
      
Short chording angle, 180 144 36
    

60 4
Number of turns, 40
2 3
T

 

d
5 12
sin sin
2 2
= 0.957
12
sin 5 sin
2 2
m
K
m



 

c
36
cos cos 0.951
2 2
K

  
c d
Per phase voltage 4.44
4.44 0.951 0.957 0.75 50 40 6061.3 volts
K K f T
 
      
ph
Line voltage 3
3 6061.3 10498.5 volts
V
 
  

Harmonics
 Defined as sinusoidal voltages and currents at
frequencies other than the fundamental frequency.
 Harmonic frequencies are integer multiples of the
fundamental frequency






0
0 )]
sin(
)
cos(
[
)
(
n
n
n nx
b
nx
a
a
x
f

Kc and Kd for Harmonic Frequencies
dn
sin
2
=
sin
2
mn
K
n
m


cn cos
2
n
K


where is the harmonic order
n
if = 5 and = 36
n   c5
5 36
cos 0
2
K

 
Short chording can help to eliminate harmonics

Line voltage with harmonics in generated emf
VRY = VR - VY
Phase voltage
Line voltage
Third Harmonic
voltages

Line voltage with harmonics in generated emf
Phase voltage
Line voltage
Third Harmonic
voltages
Third harmonics cancel in line voltage
VRY = VR - VY

Slot Harmonics
4 February 2020 DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 29
 Distortion of flux occur due to variation of
reluctance between the slot area and tooth area
 Distortion of flux produce distortion in voltage
waveform which is known as slot harmonics
 Slot harmonics is reduced either by skewing of
field poles or by incorporating fractional slot
winding

Methods for Elimination of Harmonics
 120 Degrees phase spread
 Eliminates 3rd order harmonics
 Short Chording
 Eliminates 5th and 7th order harmonics
 Fractional slot winding
 Eliminates slot harmonics
 Skewing of field poles
 Eliminates slot harmonics
 Star connection
 Eliminates triplen (order 3, 9, 15 etc) harmonics

120 Degree Phase Spread Winding
60°

Fractional Slot Winding

Example
Calculate the rms value of induced voltage per phase of a 3 phase, 10 pole, 50 Hz, alternator
with 2 slots per pole per phase and 4 conductor per slot in 2 layers. The coil span is 150 degrees.
Flux per pole has a fundamental component of 0.12 Wb and a 20 % third harmonic component.
Also find the line voltage.
Slots/pole/phase, 2
m 
180 180
Slot angle, = 30
Slots/pole 6
   
 
Short chording angle, 180 150 30
    
Slots/pole 2 3 6
  
10 2 4
Number of turns, 40
2
T
 
 

d
2 30
sin sin
2 2
= 0.966
30
sin 2 sin
2 2
m
K
m



 

c
30
cos cos 0.966
2 2
K

  
c d
Per phase fundamental voltage 4.44
4.44 0.966 0.966 0.12 50 40 995 volts
K K f T
 
      
d3
2 3 30
sin sin
2 2
= 0.707
3 30
sin 2 sin
2 2
mn
K
n
m


 
 


c3
3 3 30
cos cos 0.707
2 2
K
 
  

3
0.2 0.12
0.008 Wb
3

   3 150 Hz
f 
c3 d3 3 3
Per phase third harmonic voltage 4.44
4.44 0.707 0.707 0.008 150 40 106 volts
K K f T
 
      
2 2
1 3
2 2
Per phase voltage
995 106 1000 volts
E E
 
  
Line voltage 3 995 1723.4 volts
  

Thank You

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