Synchronous Generatorsee.cet.ac.in/downloads/Notes/Machines/Alternator Basics.pdf · 2020-02-04 ·...

$: Synchronous Generatorsee.cet.ac.in/downloads/Notes/Machines/Alternator Basics.pdf · 2020-02-04 · Coil pitch 15 3 12 144 ... field poles or by incorporating fractional slot winding.$
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


EXCITER

GENERATOR

TURBINE

Types of Construction


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.


N

S

ExcitationVoltage

SlipRings

StatorWindings

Relation between Speed and Frequency


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


- 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


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


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 phase2 pole12 slotDouble 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 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


N

S

Slot Angle


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


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


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


d

emf with distributed windingDistribution facor,

emf with concentrated windingK

180Slot angle, =

Slots/pole

= Slots/pole/phasem

= phase spread anglem

N

S

Distribution factor


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


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


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


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


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


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


0

0 )]sin()cos([)(n

nn nxbnxaaxf

Kc and Kd for Harmonic Frequencies


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


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


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.


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


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


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


Thank You

Synchronous Generatorsee.cet.ac.in/downloads/Notes/Machines/Alternator Basics.pdf · 2020-02-04 ·...

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Transcript of Synchronous Generatorsee.cet.ac.in/downloads/Notes/Machines/Alternator Basics.pdf · 2020-02-04 ·...