3. Design of Synchronous Machine€¦ · 3.18 Design aspects direct axis and quadrature axis synchronous reactance of synchronous machine Direct axis quantity in synchronous machine

3. Design of Synchronous Machine

Shital Patel, EE Department Design of AC Machines (2170909) 1

3.1 Design difference between salient pole and non-salient pole

synchronous machine

Synchronous machines are classified as rotating armature type or rotating field type.

Rotating armature type synchronous machine

In rotating armature type synchronous machine armature winding is on the rotor and

field winding is on stator. Electrical output in case of alternator or electrical input in case

of synchronous motor is carried out via slip rings and brushes.

This type of arrangement is preferred to small rating because of insulation problems and

difficulty to transmit large current through brushes.

Rotating field type synchronous machine

In rotating field type synchronous machine armature winding is on the stator and field

winding is on rotor. Electrical output in case of alternator is directly supplied to load and

electrical input in case of synchronous motor is directly carried out from supply. Field

excitation is given from exciter through slip ring.

This type of arrangement is universally preferred because large power can be transferred

from armature i.e. no slip ring or brushes

According to the shape of the field winding arrangement, rotating field type synchronous

machines is classified as salient pole and non-salient pole synchronous machines.

(a) Salient pole synchronous machine

In this type of machine, rotor contain large number of projected poles mounted on a

magnetic wheel. The projected poles are made up of laminated of steel. The field winding

is kept on these poles and it is supported by pole shoes.

It has large diameter and smaller axial length.

Used for low speed machine i.e. such as 100 to 1500 RPM.

More number of poles are required to attain the required frequency with low speed i.e.

number of pole 4 to 60.

Due to non-sinusoidal flux distribution generated emf waveform is not as good i.e. more

harmonics.

Need damper windings to prevent rotor oscillations during operation.

Windage loss and noise are more.

Weak in construction.

Typically used in hydro power plants.

(b) Non-salient pole synchronous machine

In this type of machine, rotor is of cylindrical shape with parallel sided slots. The field

winding is kept in to the slots.

It has smaller diameter and large axial length.

Used for high speed machine i.e. 1500 to 3000 RPM.

Less number of poles are required to attain the required frequency with low speed i.e.



number of pole 2 to 4.

Due to sinusoidal flux distribution generated emf waveform is better i.e. less harmonics.

No need of damper windings to prevent rotor oscillations during operation.

Windage loss and noise are less.

Robust in construction.

Typically used in nuclear, gas and thermal power plants.

3.2 Output equation of synchronous machine

=Output (kVA)

=Number of phases

=Voltage per phase (V)

=Current per phase (A)

=Turns per phase

=Winding factor

=Number of pole

=Total number of conductor

=Total flux around the airgap (Wb)

=

ph

ph

ph

w

av

Q

m

E

I

T

K

p

Z

B

2

s

Specific magnetic loading (Wb/m )

=Specific electric loading (AT/m)

=Output co-efficient

D=Stator bore diameter (m)

L=Core length (m)

n =Synchronous speed (rps)

o

ac

C

Output of an AC machine

-3

-3

-3

-3

-3

Number of phases × Voltage per phase ×Current per phase ×10

10

4.44 10

4.44 102 2

1.11 10

1.11 Total magnetic loading Tot

ph ph

ph w ph

sw z

w z s

w

Q

m E I

m f T K I

pn Zm K I

m

K p I Z n

K

-3

-3

2 -3 2

2

al electric loading 10

1.11 10

1.11 10

s

w av s

av w s

o s

n

K DLB Dac n

B acK D Ln

C D Ln



Output equation in terms of peripheral speed

2 -3 2

2

2 -3

2-3

1.11 10

1.11 10

1.11 10

av w s

aav w s

s

aav w

s

Q B acK D Ln

VB acK Ln

n

V LB acK

n

3.3 Factors affecting selection of specific magnetic loading for synchronous

machine

The total flux around the armature or stator periphery at the air gap is called the total

magnetic loading.

The average flux density over the air gap of rotating machine is called specific magnetic

loading.

Total flux around the airgap

Area of flux path around the airgapav

pB

DL

In some of the cases, maximum gap density is selected in design instead of specific

magnetic loading.

Average gap density

Ratio of pole arc to pole pitchav

g

BB

(a) Voltage

Synchronous machine designed for low voltage, occupies less insulation space thus larger

space is left for teeth. This allows to choose larger value of gap flux density.

(b) Iron loss

A low value of flux density in the air gap retains low value of flux in the iron parts of the

machine therefore machine will have less iron loss and increased efficiency.

(c) Stability

The maximum power output of a machine under steady state condition is inversely

proportional to synchronous reactance.

max

s

EVP

X

If lower value of flux density is selected, flux per pole is less and hence larger number of

turns per phase required for armature winding. This results in increased value of leakage

reactance and hence reduced value of power and steady state stability.

(d) Transient short circuit current

A lower value of flux density results in increased value of leakage reactance and hence

increased leakage reactance reduces value of armature current under short circuit.

(e) Parallel operation

Parallel operation of synchronous generators depends on the synchronizing power.



Higher the synchronizing power, higher will be the ability of the machine to operate in

synchronism. The synchronizing power is inversely proportional to the synchronous

reactance and hence the machines designed with higher value air gap flux density will

have better ability to operate in parallel with other machines.

The usual value of average gap flux density for

Salient pole machine: 0.52 to 0.65 Wb/m2

Turbo alternator: 0.54 to 0.65 Wb/m2

3.4 Factors affecting selection of specific electric loading for synchronous

machine

The total number of ampere conductor around the armature or stator periphery is called

the total electric loading.

The number of armature or stator ampere conductor per meter of armature periphery at

the air gap is called specific electric loading.

Total armature ampere conductor

Armature periphery at airgapz

I Zac

D

Choice of specific electric loading generally affects the copper loss, temperature rise, over

load capacity and cost of machine.

(a) Copper loss Large value of specific electric loading leads to employ higher number of turns i.e. more

copper in the machine, which means more copper loss and higher temperature rise.

(b) Voltage

For high voltage machine, insulation space required is more i.e. slot space factor is less.

For such machine if specific electric loading selected is more, number of turns per phase

will be more and hence it will be difficult to accommodate the more number of turns in

slots.

Hence, it recommended to select high value of specific electric loading for low voltage

machine.

(c) Synchronous reactance

Large value of specific electric loading leads to higher value of leakage reactance and

armature reaction and consequently higher synchronous reactance.

So, machines designed with high value of specific electric loading will have poor voltage

regulation, lower value of current under short circuit condition, low value of steady state

stability limit and small value of synchronizing power.

The usual value of specific electric loading for

Salient pole machine: 20,000 to 40,000 A/m

Turbo alternator: 50,000 to 75,000 A/m



3.5 Factors affecting the separation of D and L for synchronous machine

Stator bore diameter D and gross length L can be separated from D2L product of the

output equation.

The ratio of pole arc to pole pitch is the deciding factor for the separation of D and L. Pole

arc can be taken as approximately equal to gross length of the stator core.

Pole arcRatio

Pole pitchs

b L

Value of diameter D depends upon type of pole used and permissible peripheral speed.

Salient pole machine can be constructed with round or rectangular pole structure.

Diameter of the machine is quite larger than the axial length.

The usual value of ratio of pole arc to pole pitch are;

Round pole: 0.6 to 0.7

Rectangular pole: 1 to 5

Diameter for round pole will be large compared to rectangular pole. Separated value of D

and L from above relation, must satisfy the limiting value of peripheral speed that the

rotor can withstand its centrifugal forces produced under runaway speed.

Limiting value of peripheral speeds for different pole structure are;

Bolted pole structure: 50 m/s

Dove tail pole structure: 80 m/s

Normal design: 30 m/s

Turbo alternators will have larger speed i.e. 3000 rpm, hence diameter of the machine is

kept smaller than the axial length.

As diameter of the rotor is limited due to the consideration of permissible peripheral

speed limit, stator bore diameter is generally calculated based on peripheral speed.

Peripheral speed of turbo alternators is limited to a value below 175 m/s as design

consideration.

3.6 What is Short circuit ratio (SCR)?

Short circuit ratio (SCR) of a synchronous machine is the ratio of field current required to

produce rated voltage on open circuit to field current required to circulate rated current

at short circuit.

Speed of machine under both the condition is the rated speed and saturation of a machine

is considered neglected.

SCR of a synchronous machine is an important parameter because it governs the

performance parameter such as voltage regulation, stability limit, parallel operation and

cost.



O.C.C

S.C.C

Per

un

it v

olt

age

Per

un

it c

urr

ent

Field current

A

C

B

D

Eq O

F igure 2. 1 O.C.C and S.C.C characteristics of synchronous machine

Field current required to produce rated voltage on open circuit

Field current required to circulat

tan

tan

1

1

Per unit voltage on open cir

e rated current at short ci i

u

t

i

rcu

c

SCR

OA

OE

AB

ED

AB

ED

AB

AC

ACAB

q

q

t

Corresponding per unit current on short circuit

1

dX

SCR is the reciprocal of synchronous reactance of machine. The value of Xd for given load

is affected by saturation condition. For each machine, value of SCR is fixed and it is defined

at rated voltage.

The usual value of SCR for

Salient pole machine: 1.0 to 1.5

Turbo alternator: 0.5 to 0.7



3.7 Effect of short circuit ratio (SCR) on the performance of synchronous

machine

(a) Stability

The maximum power output of a machine under steady state condition is inversely

proportional to synchronous reactance.

max

s

EVP

X

Hence, machine with low SCR will have high value of synchronous reactance Xs and

consequently lower stability and maximum power output. Hence machine designed with

high SCR is good from stability point of view.

(b) Voltage regulation

Machine with low SCR will have high value of synchronous reactance Xs that will lead to

greater change in voltage under fluctuating load condition i.e. poor voltage regulation of

machine.

(c) Short circuit current

Machine with low SCR will have high value of synchronous reactance Xs that indicates

smaller value of short circuit current.

But large value of short circuit current can be controlled, thus synchronous generators

are not designed for low SCR to limit short circuit current.

(d) Parallel operation

Parallel operation of synchronous generators depends on the synchronizing power.

Higher the synchronizing power, higher will be the ability of the machine to operate in

synchronism. The synchronizing power is inversely proportional to the synchronous

reactance.

Hence, machine with low SCR will have high value of synchronous reactance Xs, hence it

will difficult to keep machine in synchronism.

Reduction in synchronizing power makes machine more sensitive to torque and voltage

disturbances.

Also reduced synchronizing power will lead to disconnection of individual units and

operation of auto reclosing type circuit breaker.

(e) Self-excitation

Machine with low SCR will have high value of synchronous reactance Xs and that will lead

to large voltage on open circuit due to self-excitation owning to large capacitive current

drawn by transmission lines.

Machine designed with high SCR

o High stability limit

o Low inherent voltage regulation

o High short circuit current

o Large air gap



o Large field mmf

o Expensive

Today’s trend is to design synchronous machine with low SCR because of the

advancement in fast acting control and excitation system.

3.8 Factors affecting selection of length of air gap for synchronous machine

Synchronous machines are designed with large air gap compared to induction motor.

(a) Short circuit ratio (SCR)

Length of air gap in synchronous machine affects the value of SCR and hence it influences

a parameter such stability, voltage regulation, short circuit current, parallel operation,

self-excitation. Hence, choice of air gap length is very critical in case of synchronous

machines.

A large air gap length offers large reluctance to the path of flux produced by the armature

mmf which reduces the effect of armature reaction. This results in small value of

synchronous reactance and high value of SCR.

Machine with large air gap length i.e. low synchronous reactance and high value of SCR

will have,

o Small inherent voltage regulation

o High stability

o High synchronizing power

o Better cooling at gap surface

o Low tooth pulsation loss

o Low noise level

o Small unbalance magnetic pull

Machine with small air gap length i.e. high synchronous reactance and low value of SCR

will draw large field mmf that results in increase in the cost of machine.

(b) Shape of pole phase

lglgx

x

Figure 2. 2 Pole face profile



The ratio of pole arc to pole pitch, ψ varies from 0.67 to 0.75. Common practice is to select

value of ψ =0.70

If value of ψ > 0.75, interpolar flux leakage becomes excessive leading to high flux density

in pole body and improper flux distribution over armature.

If value of ψ < 0.67, leaves insufficient overhang of the pole shoe to support the field coil

in radial direction.

In salient pole machine, the length of air gap is not constant over pole arc but it increases

from centre outward.

g

cos

Where,

1.5 to 2.25 l

0.1 to 0.25

g

gx

gx

ll

x

l

x

Estimation of air gap length

Salient pole machine with open type of slot

Lentgh of air gapRatio 0.01 to 0.015

Pole pitch

gl

Turbo alternator with massive rotor

Lentgh of air gapRatio 0.02 to 0.025

Pole pitch

gl

OR

Mmf required across air gap is 80% of no load field mmf

80%

8,00,000 0.8

0.8

8,00,000

g fo

g g g fo

fo

g

g g

AT AT

B l k AT

ATl

B k

2

Air gap mmf (AT)

No load field mmf per pole (AT)

2.7

Armature mmf per pole (AT)

Maximum flux density in the air gap (Wb/m )

Air gap length (mm)

Gap contra

g

fo

a

ph ph w

a

g

g

g

AT

AT

AT SCR

I T kSCR

p

AT

B

l

k

ction factor



3.9 Factors affecting selection of number of armature slot for synchronous

machine

The number of slots needs to be selected properly because it affects the machine

performance, size and cost.

There are no thumb rules for selection of number of slots. But considering do’s and don’ts

associated with number of slots, suitable number of slots per pole per phase is selected.

However the following points are to be considered for the selection of number of slots.

(a) Leakage reactance

For less number of slots, insulation required for slot will be less which results in less slot

width. Therefor leakage flux has small path through air gap that increases leakage flux

and hence increased leakage reactance.

(b) Tooth pulsation

Tooth ripples in field from and tooth pulsation losses in pole face reduces when large

number of narrow slots are used.

(c) Flux density in iron

Large number of slots occupies more space for insulation that reduces the available teeth

cross section area. Teeth becomes narrow and mechanical weak when available area is

less. Also, narrow teeth results in excessive teeth flux density in teeth. Higher value of

teeth flux density gives rise to iron loss in teeth.

(d) Balanced winding

To ovoid overheating of rotor surface due to space harmonic, it is required to select

number of armature slot that gives balanced winding.

(e) Hot spot temperature

Large number of slots will have less conductor per slot that keeps conductors more

distant to each other in slot and hence allows more space for the circulation of air. This

will reduce occurrence of internal hot spot temperature.

(f) Cost

Larger number of slots leads more number of coils to wind, insulate and install

comprising higher cost.

Guideline for selection of number of armature slots

o Slot pitch should lie between 25 to 60 mm.

Slot pitch 25 mm for low voltage machine

Slot pitch 40 mm up to 6 kV machine

Slot pitch 60 mm up to 15 kV machine

o Slot per pole per phase can be 3 to 4 for salient pole machine and 7 to 9 for turbo

alternator. Slot per pole per phase can be fractional number to reduce magnitude of

higher order harmonic.

o Slot loading should not exceed 1500 A.

o Number of conductor per slot must be an even integer with double layer winding.



3.10 Design aspects to decide size of armature slots for synchronous

machine

Number of slots, conductor cross-section, conductor per slot and types of winding decides

the dimensions of slots.

Conductors will be arranged depth wise and width wise inside the slot such a way that it

has mechanically strong tooth width. Width of slot will be dependent on rated terminal

voltage, as it fixes the thickness of main insulation coil sides and slot.

But width of tooth should not be too large as it results in narrow and deep slots. The

deeper slots offers large leakage reactance.

Ratio of slot depth to slot width is assumed in the range of 4 to 5 that helps to keep tooth

flux density within permissible limit i.e. 1.1 to 1.8 Wb/m2.

In turbo alternator variation in flux density along the depth of the slot is large i.e. small

internal diameter, hence the width of the tooth is estimated corresponding to the flux

density at the top of the tooth. The flux density at this section should be within

permissible limit of 1.8 Wb/m2.

(min)Minimum width of tooth,

1.8t

s i t s i

p pW

S L B S L

In salient pole alternators variation in flux density along the depth of the slot is not large

i.e. large internal diameter, hence width of the tooth is estimated corresponding to the

flux density at the middle section of the tooth. The flux density at this section should be

within permissible limit of 1.8 Wb/m2.

Wedge

Conductor

Slot insulation

Lip

Coil separator

Coil insulation

Ws

ds

Figure 2. 3 Slot dimensions



Stator turn per phase,4.44

Total stator conductor, 3 2

Stator conductor per slot ,

Stator current per phase,3 cos

Stator conductor cross section area,

Copper area in ea

ph

ph

w

s ph

sss

s

s

ph

ss

s

ET

f K

Z T

ZZ

S

PI

V

Ia

sch slot, A

Copper area in each slotSlot space factor

Area of each slot,

Number of stator slots

s ss

s

a Z

Where

S

As per voltage rating of machine, slot insulation of 0.5 to 0.7 mm thick and additional

insulation of 0.5 to 1.5 mm as coil separator between two layers of coil is provided.

Wedge and lip of 3 to 50 mm is added at top of the slot to hold the conductors inside the

slot.

3.11 Design aspects of armature winding used for synchronous machine

Armature winding of synchronous machine is a stationary element so, many a times it is

also called stator winding.

It is designed for star connected with neutral grounded to get advantage of reduction in

insulation cost and eliminated triplen harmonics from line voltage.

Armature winding of synchronous machine is usually single layer or double layer type.

Open type of slot is used to accommodate double layer lap winding and semi-closed slot

is used to accommodate single layer concentric winding.

Machine with small flux per pole will have large number of turns, hence multi-turn coil

with either single layer concentric winding or double layer lap winding is used.

Modern trend is to use double layer lap integral slot winding with 60° phase spread or

fractional slot winding with the coil span that gives minimum generated space harmonics.

Generally capacity of winding machine to pull out coil is limited to 75×25 mm2 with

length of conductor in slot portion 3 m and pole pitch not more than 0.8 m. Hence, multi-

turn coil cannot be wound for machine having current per circuit more than 1500 A.

Bar winding with two bars in each slot is used for machine having current greater than

1500 A. Large number of conductor insulated from each other and connected in parallel

are put in two layers along the width of armature slot.



Wedge

Conductor

Slot insulation

Lip

Coil separator

Coil insulation

Figure 2. 4 Multi-turn coil winding

Wedge

Conductor

Slot insulation

Lip

Coil separator

Coil insulation

Figure 2. 5 Bar winding

(a) Multi-turn coil winding

Greater flexibility in the selection of number of slots i.e. conductor per slot

Former wound or machine wound coil is prepared so labor cost is less

Bending of top coils is required

Replacement is difficult

End connection of coils are easier

Full transposition of the strands of coils is not mandatory to eliminate the eddy current

loss

Each turn of the multi turn coil is required to insulate accurately, so increases the amount

of insulation and reduces the space available for the copper in the slot.

(b) Bar winding

Less flexibility in the selection of number of slots i.e. conductor per slot

Handmade coil is prepared so labor cost is high

Bending of top coils is not required

Replacement is easy

End connection of coils are difficult

Full transposition of the strands of coils is mandatory to eliminate the eddy current loss

Bars per slot insulation is twice as thick as main insulation to earth so, no additional

insulation is required to withstand impulse voltage.

3.12 Methods to eliminate harmonic torque in synchronous machine

Primary source of harmonic in synchronous machine is due to the non-sinusoidal field

form. Hence elimination of harmonic primarily focuses on making field form more

sinusoidal. Main source of reluctance to the path of flux is air gap, hence variation in air

gap round the machine need to be sinusoidal.

In cylindrical pole machine, length of air gap is uniform round the machine, so only way

to obtain sinusoidal field form is to generate mmf of field winding to vary as per sine law.



This is achieved by distributing winding in different slot.

In salient pole machine, length of air gap is non uniform round the machine i.e. length of

air gap is about 1.5 to 2.25 times that at pole centre. In this case approximation of

sinusoidal field form is achieved by skewing of the pole faces.

An ideal sinusoidal field form is very difficult to achieve, hence compensatory feature is

that harmonic generated in emf wave has to be eliminated through proper design of

winding.

(a) Chording

Harmonic emf can be reduced considerably by choosing proper value of chording angle α

because generated emf is proportional to cos(nα/2) where n is the harmonic order.

(b) Distributed winding

Armature winding of synchronous machine is distributed type because distribution

factor for harmonic is very small compared to fundamental i.e. comparative magnitude of

harmonic is small.

(c) Fractional slot winding

Slot harmonic emf almost gets reduced from output wave with the use of fractional slot

winding because distribution factor is very small for harmonic compared to fundamental.

3.13 Design aspects of pole for synchronous machine

2

p

2

p

p

p

p

fo

a

Flux per pole (Wb)

A =Area of pole (m )

B =Flux density in pole (Wb/m )

L =Length of pole (m)

h =Heigth of pole (m)

b =Width of pole (m)

AT =No load field mmf (AT)

AT =Armature mmf per pole (AT)

SCR=Shor

p

fl

f

f

mt

f

f

t circuit ratio

AT =Field mmf at full load (AT)

h =Heigth of field winding (m)

d =Depth of field winding (m)

L = Length of mean turn of field winding (m)

R =Resistance of field winding ( )

T =Number of tu

2

f

f

f

f

rns in each field coils

a =Cross section area of conductor of field winding (mm )

I =Field current (A)

Q =Copper loss in each field coil (Watt)

q =Permissible loss per unit surface for normal temperature 2

f

rise (Watt/m )

S =Space factor



Pole design involves the determination of pole height, pole cross section area and field

winding.

2

Leakage Co-efficient Useful flux per pole

0.9

for rectangular pole

for circular pole4

p

p

p

pi

p

p

pi

p pi p

p p

AB

BC

B

L L

L L

A L b

A b

Value of leakage co-efficient generally rages from 1.15 to 1.2 and permissible limit of flux

density in pole body is limited to 1.5 to 1.7 Wb/m2.

Approximate value of field mmf is estimated to find the dimensions of pole and field

winding.

2.7

fo a

ph ph w

AT AT SCR

I T kSCR

p

Select suitable mmf scale to draw vector diagram that will help to calculate field mmf at

full load.

o

I

a

c

b

d

(90-F )

F

Figure 2. 6 Phasor diagram

o Draw oa = ATfo

o Draw ab = ATa at angle (90 - F) to oa, where cosF = power factor (lag)

o Cut off ac such as ac = Kr × ab, where Kr is cross reaction co-efficient and it depends

on ratio of pole arc to pole pitch

o Join oc and extend it



o Drop a perpendicular from b on oc extended, cutting it at d

o Join od = ATfl

Copper area of field winding depends on current density i.e. 3 to 4 a/mm2.

Space factor for strip on edge winding is in the range of 0.8 to 0.9 and for large round

conductor it is 0.75.

Full load field mmf = =

Current density in field winding

Copper area Total field

Copper area of field winding

of field win winding area =

Space factor

Total field windinHeight of field

ding

winding =

fl

f

AT

g area

fd

Total height of pole combines height of field winding, height of pole shoe and

miscellaneous space taken by flanges or curvature.

Height of field winding+Heigth of pole shoe+Space wasted in curvature

0.1 to 0.2 0.02

p

p f s c

p f p

h

h h h h

h h h

3.14 Design aspects of damper winding for synchronous machine

Damper windings are used to damp the oscillations occurred due to sudden change in

load at synchronous machine. They are heavy copper bars placed in pole shoes. Damper

bars are riveted at each end to form short circuited grid.

In some cases the short circuited end rings are carried out around the rotor so that they

form two short circuit ring around the periphery.

In synchronous generator, damper windings are provide to suppress negative sequence

field and to damp the oscillations in the case of haunting.

Let, amplitude of fundamental mmf of one phase of poly phase winding is;

( , )0

1 1

1 1

4 sincos

4For 1, 0,

2

Where,

2 2

2 2

24

x t m dnn

m d

ph ph ph phsm s

ph ph

d

nxAT AT t K

n

n t x AT AT K

T I T IIAT qZ q

qp p

T IAT K

p

This pulsating mmf can be resolved in to two rotating mmf i.e. synchronous mmf and

inverse mmf each having half the magnitude.



Hence, damper winding must be capable to develop the mmf equal to inverse mmf.

1

1

1

Fundamental mmfMmf of damper winding =

2

2

24

2

4 2

2

4 20.955

2 6

0.143

ph ph

d

ph ph

d

AT

T IK

p

T IK

p

ac

ac

Total cross section area of damper bar can be derived by selection suitable value of

current density in bars.

Mmf of damper winding

Mmf of damper winding 0.143

0.143

0.143

d d d d d d d

d d

d

d

T I T a A

ac

A ac

acA

Total cross section area of damper bars are distributed into small cross section based on

number of bars selected.

2

Total area of damper bars per pole

Number of damper bars per pole

4

4

d

dd

d

dd

d

a

Ad

n

Ad

n

Damper winding slot pitch is usually take same as stator slot pitch. In some case slot pitch

of damper winding is taken 20% less by stator slot pitch in order to reduce current

induced by tooth ripple.

Length of damper bars are kept higher than length of core in order to rivet it at both end.

1.1 for small machine

0.1 for large machined

L L

L

When damper bars are completely buried in pole shoes i.e. in iron material, it offers



acceptable inductance that causes damper bar current to lag. By opening hole to the air

gap, inductance is reduced and power factor of damper winding is improved.

Damper bars are in continuous centrifugal force due to high peripheral speed of machine,

so special care must be made while laying it in pole shoes.

3.15 Estimation of mmf required for various parts of synchronous machine

Total field mmf at no load (AT)

Mmf of yoke (AT)

Mmf of armature core (AT)

Mmf of armature teeth (AT)

Mmf of airgap(AT)

Mmf of pole (AT)

Mmf of yoke (AT/m)

Mmf of armature co

fo

y

c

t

g

p

y

c

AT

AT

AT

AT

AT

AT

at

at

re (AT/m)

Mmf of armature teeth (AT/m)

Mmf of pole (AT/m)

Length of flux path in armature core (m)

Length of flux path in armature yoke (m)

Depth of armature slot (mm)

Depth of armature

t

p

c

y

s

c

at

at

l

l

d

d

(min)

(max)

core (mm)

Net iron length (m)

Gap contraction factor

Minimum flux in pole (Wb)

Maximum flux in pole (Wb)

Useful flux (Wb)

Leakage flux between pole shoes (Wb)

Leakage flux bet

i

g

p

p

sl

pl

L

K

p

s

p

s

ween pole bodies (Wb)

Axial length of pole shoe (m)

Axial length of pole body (m)

Height of pole shoe at pole tip (m)

h =Heigth of pole (m)

b =Width of pole shoe (m)

b =Width of pole (m)

C =Distance

s

p

s

L

L

h

p

between adjacent pole shoes (m)

C =Distance between bodies of adjacent pole (m)

In salient pole machine, flux produced by field circuit passes through various parts such

as yoke, armature core, armature teeth, air gap and pole that will draw mmf.

Total field mmf at no load

fo c t g p yAT AT AT AT AT AT



Mmf of armature core

Corresponding to flux density in armature core the value of mmf per meter and the length

of flux path in core is taken equal to one half of the mean core diameter.

2 22

2

c c c

cs

c

AT at l

dD d

atp

Mmf of armature teeth

For parallel sided slot used in synchronous machine will have tapered teeth, so the flux

density at 1/3rd height of teeth from narrow end is calculated.

Corresponding to this flux density value of mmf per meter is selected.

t t sAT at d

Mmf of air gap

1

8,00,000

8,00,0001.08

g g g g

mg g

AT B l K

Bl K

Mmf of pole

Flux in pole is equals to the useful flux that passes through air gap and enters in to the

armature considering leakage flux. But flux in pole is not uniform due to change in shape

and size of pole body and pole shoe.

Hence, it is assumed that 2/3rd length of pole body carries useful flux pulse leakage flux

between pole shoes while 1/3rd length carries useful flux plus leakage flux from both pole

shoes and pole bodies.

Thus flux at the top of pole is minimum and at pole bottom it is maximum.

(min)

(min)

104 1.47 log 1

2

p slp

p p

s s ssl o l s

s s

l c t g

r s

s s

BA A

L h bAT h

C C

AT AT AT AT

D hC b

p

(max)

(max)

102 1.47 log 1

2

p sl pl

p

p p

p p p

pl o l p

p p

l c t g

r s p

p s

BA A

L h bAT h

C C

AT AT AT AT

D h hC b

p

Corresponding to the minimum and maximum flux density, mmf per meter is used such

that total mmf for pole body is

(max) (min)

2

3 3

pl pl

p p p

h hAT at at



Mmf of yoke

Flux in yoke is the useful flux plus leakage flux from both pole shoes and pole bodies,

hence flux density corresponding to this flux

2sl pl

y

y

y y

BA L d

Corresponding to flux density and dimension of yoke, mmf per meter in yoke is

2 22

2

y y y

y

r pl

y

AT at l

dD h

atp

3.16 Design aspects to estimate full load field mmf of synchronous machine

d.c.

a.c.

l

a.c.

l

r =Armature d.c. resistance per phase

r =Armature effective a.c. resistance per phase

x =Armature leakage reactance per phase

R =Per unit armature resistance per phase

X =Per unit armature l

c

( )

( )

eakage reactance per phase

P Total armature copper loss (Watt)

Length of mean turn of armature m

Length of turn embedded in slot m

Length of turn in overhang m

Cross section area of a

mts

mts s

mts o

s

L

L

L

a

2

2

( )

rmature conductor m

Resistivity of copper Ω/m and mm

Average eddy current loss factor

=Number of conductor layers

' Height of conductor in each layer(mm)

Slot leakage reactance Ω

Overhang le

s av

s

o

K

N

h

x

x

akage reactance Ω

Armature slot leakage permeance H

Overhang leakage permeance H

Length of overhang m

Armature slot per pole per phase

s

o

oL

q

(a) Armature resistance

Armature resistance is affected by the copper material housed in slot section of the

conductor and overhang section.



. .

( ) ( )

( )

( )

Where,

2

2.5 0.06 0.2

mtsd c ph

s

mts mts s mts o

mts s

mts o

Lr T

a

L L L

L L

L kV

Eddy current copper loss in slot section of conductor is significantly large while eddy

current copper loss in over hang section is very small. Hence, it is neglected in overhang

section.

. .

( ) ( ) ( )

( )

( )

24

( )

Where,

2

2.5 0.06 0.2

1 '9

mtsa c ph

s

mts s av mts s mts o

mts s

mts o

s av

Lr T

a

L K L L

L L

L kV

NK h

Per unit armature resistance

. .

. .

ph a c

a c

ph

I rR

E

(b) Armature leakage reactance

Armature leakage reactance helps to predict the behavior of synchronous machine under

sudden short circuit.

It is also helpful to estimate voltage regulation of machine under various load condition.

Approximate estimation of leakage reactance is carried out by considering leakage from

slots section and overhang.

2

2

2 2

,

8

8 8

l s o

ss ph

o s

o o so ph ph

x x x

Where

x fT Lpq

K

L Yx fT fT

pq pq

Per unit armature leakage reactance



ph l

l

ph

I xX

E

Estimation of full load field mmf

o

I

a

b

d

c

f

e

g

Figure 2. 7 Estimation of full load field mmf

o Select suitable voltage scale and current scale

o Draw oa = Voltage per phase = V = Eph

o Draw oI = Armature current per phase at power factor angle F w.r.t Eph

o Draw ab = Resistance voltage drop per phase = (Iph)(rac) and parallel to oI

o Draw bc = Leakage reactance voltage drop per phase = (Iph)(Xl) and perpendicular to

oI

o Join oc = Generated voltage drop = Eg

o Corresponding to Eg, find ATgen = Field mmf from O.C.C.

o Plot od = ATgen on some scale

o Draw de = Field mmf equivalent to armature mmf per pole at full load perpendicular

to oI at d.

Field mmf equivalent to armature mmf per pole=2.7

ph ph w

d

I T KP

p

o Find value of Kr corresponding to ratio pole arc to pole pitch

o On line de cut off df = Kr x de

o Join of and extend it

o Draw perpendicular from e on of extended cutting it at gi

o Measure og = Full load field mmf = ATfl



3.17 Design aspects of field winding of synchronous machine

Synchronous machine with less number of pole uses wire wound field coils and

synchronous machine with large number of pole uses glass covered rectangular strip field

coils.

Machine with class B insulation has inter turn insulation with two layers of treated

asbestos paper and machine with class F insulation has inter turn insulation with three

layers of epoxy treated asbestos paper.

Field coils are combined under 4 to 12 MN/m2 pressure.

Exciter voltage of 125 V for small and medium machine and 250 V for large machine is

preferred. Filed winding is usually designed for 15 to 20 % less voltage then exciter

voltage in order to allow voltage drop between field and exciter.

Mean turn length of field winding, 2 0.9 0.01

Voltage across field winding, (0.8 to 0.85) Exciter voltage

(0.8 to 0.85)Voltage across each field coil,

Resistance of each field coi

mtf p f

f

ef

L L b d

V

VE

p

l,

Also,

Height of field winding, Space used by flanges and spool

Number of turns of field winding,

Current density in fi

f mtff

f

ff

f

f mtff

f f

f f mtf fl mtff

f f

f pl s

flf

f

T LR

a

ER

I

T LE

I a

I T L AT La

E E

h h h

ATT

I

2 2

eld winding,

Copper loss in each field coil,

Cooling surface of each field coil, 2 ( )

0.08 to 0.12Cooling co-efficient,

1 0.1

Temperature rise of field

ff

f

f mtff f f f

f

mt f f

f

a

I

a

T LQ I R I

a

S L h d

CV

coil, f ff

Q C

Sq



3.18 Design aspects direct axis and quadrature axis synchronous reactance

of synchronous machine

Direct axis quantity in synchronous machine is one whose magnetic effect is along the

field pole axis i.e. field pole axis are also known as direct axis.

Hence, direct axis synchronous reactance is the reactance offered to the armature flux

when peak of armature mmf is directed along the field pole axis.

In this condition, the air gap length offered is minimum, thus reluctance is minimum and

armature flux is maximum.

Quadrature axis quantity in synchronous machine is one whose magnetic effect is

perpendicular to field pole axis.

Hence, quadrature axis synchronous reactance is the reactance offered to the armature

flux when peak of armature mmf coincides with the quadrature axis.

In this condition, the air gap length offered is maximum, thus reluctance is maximum and

armature flux is minimum.

2 2

6

2

1

Magnetising reactance per phase

Per unit magnetising reactance

Per unit direct axis armature reaction reactance

Flux distribution co-efficient for d

7.54, 10

,

,

i

ph w

m

g g

ph m

m

ph

ad d m

fT K DLx

p l K

I xX

E

X A X

1 1

11

1

,

sin,

4sin2

,

rect axis

Reduction factor for direct axis armature mmf

Flux density ratio

Per unit quadrature axis armature reaction reactance

Flux distr

,

ibution co-efficie

d d

d

m

g

aq q m

A A

BA

B

X A X

1nt for quadrature axis

Per unit direct axis synchronous reactance,

Per unit quadrature axis synchronous reacta

4 1 si

nc

n,

e,

5q

d ad l

q aq l

A

X X X

X X X



Estimation of no-load voltage and load angle

I

Eg

V

F

Id

Iq

IdXd

IqXq

IXl

ψ

δ

Figure 2. 8 Phasor diagram of salient pole generator

Generated voltage per phase

No-load voltage per phase

Power factor

Power angle

Direct axis current = Isin

Quadrature axis current = Ic

c

os

os

g

o

d

q

E

E

I

I

Documents

3. Design of Synchronous Machine€¦ · 3.18 Design aspects direct axis and quadrature axis synchronous reactance of synchronous machine Direct axis quantity in synchronous machine