synchronous generatorsee.cet.ac.in/downloads/notes/machines/alternator basics.pdf · 2020-02-04 ·...
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Synchronous GeneratorsSynchronous Generators
Dr. Francis M. Fernandez
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 1
Jan 2020
Synchronous Generators
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
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 2
EXCITER
GENERATOR
TURBINE
Types of Construction
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 3
Salient Pole type Cylindrical Rotor type
N
SS
N
Fieldwinding
Field pole
Armatureconductors
N
S
Stator
Cylindricalrotor
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.
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 4
N
S
ExcitationVoltage
SlipRings
StatorWindings
Relation between Speed and Frequency
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 5
N
S
A
A’
N
SS
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 fRPS
P
where is the freuency
and is the number of poles
f
P
120,
fRPM N
P
Synchronous Speed
Synchronous speed is the speed at which the generator should run to produce a constant frequency
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 6
- freuency
- number of poles
- speed in RPM
f
P
N
Number of cycles per revolution2
Revolution per second60
Cycles per second2 60 2 60
120,
P
N
P N P Nf
fRPM N
P
N
SS
N
A
A’
Three Phase Generator
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 7
N
S
R'
YB
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
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 8
Single Layer Winding
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 9
Winding example (Full pitch)
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 10
No of poles: 2, No of slots: 12, Double layer → Slots/pole/phase = 12/(2x3) = 2
N
S
Winding example (Full pitch)
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 11
3 phase2 pole12 slotDouble layer winding
Winding example (Short Chorded)
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 12
No of poles: 2, No of slots: 12, Double layer → Slots/pole/phase = 12/(2x3) = 2
N
S
Winding example (Short Chorded)
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 13
3 phase2 pole12 slotDouble 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
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 14
N
S
Slot Angle
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 15
180Slot angle =
Slots/pole N
S
180Slot angle = 30
6
In this case (2 pole, 12 slot):
For a 4 pole 36 slot machine:
180Slot angle = 20
9
Pitch Factor
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 16
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 cos2
Pitch Factor
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 17
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 cos2
E
c
Resultant emf of chorded coilPitch factor,
Resultant emf of full piched coil
2 cos2= cos
2 2
K
E
E
Also known as coil span factor
Distribution factor
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 18
d
emf with distributed windingDistribution facor,
emf with concentrated windingK
180Slot angle, =
Slots/pole
= Slots/pole/phasem
= phase spread anglem
N
S
Distribution factor
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 19
d
emf with distributed windingDistribution facor,
emf with concentrated windingK
AB = 2 sin2
r
Arithematic sum = 2 sin2
m r
Vector sum = 2 sin2
mr
d
2 sin sin2 2 =
2 sin sin2 2
m mr
K
m r m
Example
For a 3 phase 36 slot 4 pole winding find the distribution factor
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 20
180 180Slot angle, = 20
Slots per pole 9
36Slots/pole/phase, 3
4 3m
d
3 20sin sin
2 2Distribution factor, = 0.95620
sin 3 sin2 2
m
K
m
EMF Equation
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 21
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 webersP
d P 60
dtN
Average emf induced volts60 60
d P NP
dtN
Substituting for N120
Average emf induced 2 volts60
P ff
P
N
SS
N
A
A’
EMF Equation
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 22
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 dRMS value of per phase voltage, 4.44 voltsE K K f T d
sin2 =
sin2
m
K
m
c cos2
K
Example
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 23
A 4 pole 3 phase star connected alternator having 60 slots with 4 conductor per slot runs at1500 rpm. Coils are short pitched by 3 slots. If the phase spread is 60 degrees, find the linevoltage induced fir for a flux per pole of 0.75 Wb distributed sinusoidally in space. All turns perphase are in series.
60Slots/pole/phase, 5
4 3m
180 180Slot angle, = 12
Slots/pole 15
Coil pitch 15 3 12 144 Short chording angle, 180 144 36
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 24
60 4Number of turns, 40
2 3T
d
5 12sin sin
2 2 = 0.95712
sin 5 sin2 2
m
K
m
c
36cos cos 0.951
2 2K
c dPer phase voltage 4.44
4.44 0.951 0.957 0.75 50 40 6061.3 volts
K K f T
phLine 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
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 25
0
0 )]sin()cos([)(n
nn nxbnxaaxf
Kc and Kd for Harmonic Frequencies
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 26
dn
sin2 =
sin2
mn
Kn
m
cn cos2
nK
where is the harmonic ordern
if = 5 and = 36n c5
5 36cos 0
2K
Short chording can help to eliminate harmonics
Line voltage with harmonics in generated emf
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 27
VRY = VR - VY
Phase voltage
Line voltage
Third Harmonic voltages
Line voltage with harmonics in generated emf
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 28
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
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 30
120 Degree Phase Spread Winding
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 31
60°
Fractional Slot Winding
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 32
ExampleCalculate 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.
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 33
Slots/pole/phase, 2m
180 180Slot angle, = 30
Slots/pole 6
Short chording angle, 180 150 30
Slots/pole 2 3 6
10 2 4Number of turns, 40
2T
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 34
d
2 30sin sin
2 2 = 0.96630
sin 2 sin2 2
m
K
m
c
30cos cos 0.966
2 2K
c dPer phase fundamental voltage 4.44
4.44 0.966 0.966 0.12 50 40 995 volts
K K f T
d3
2 3 30sin sin
2 2 = 0.7073 30
sin 2 sin2 2
mn
Kn
m
c3
3 3 30cos cos 0.707
2 2K
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 35
3
0.2 0.120.008 Wb
3
3 150 Hzf
c3 d3 3 3Per phase third harmonic voltage 4.44
4.44 0.707 0.707 0.008 150 40 106 volts
K K f T
2 21 3
2 2
Per phase voltage
995 106 1000 volts
E E
Line voltage 3 995 1723.4 volts
DEPT. OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING TRIVANDRUM 36
Thank You