UNIT-V-Synchronous Machines

Output equations – choice of loadings – Design of salient pole machines – Short circuit ratio – shape of pole face – Armature design – Armature parameters – Estimation of air gap length –Design of rotor –Design of damper winding– Determination of full load field mmf – Design of field winding – Design of turbo alternators – Rotor design.

TYPES OF SYNCHRONOUS MACHINES

It is classified as

• Salient pole machines and • cylindrical rotor machines depending upon the construction.

SALIENT POLE MACHINES:

driven by water wheels or diesel engines. operate at low speeds.

requires large no.of poles to produce the required frequency.

has projected poles and the field coils are mounted on the poles.

CYLINDRICAL ROTOR MACHINES:

 Driven by steam turbines and gas turbines.  Run at very high speeds.

 Have slots on the outer periphery of smooth cylindrical rotor.

 Field conductors are placed on this slots.

• Synchronous machines operating on general power supply networks may be divided into the following categories:

I. HYDRO-GENERATORS:

 Prime mover - water wheel.  speed - 100 to 1000rpm.  capacity - 750 MW

II. TURBO-ALTERNATORS:

 Prime mover- steam turbine or gas turbine  Speed - 3000rpm

 Capacity - 1000MW

III. ENGINE DRIVEN:

 Prime mover- I.C engine (diesel or petrol)  Speed - 1500rpm

 Capacity - 20MW

IV. MOTORS:

 Motors are manufactured with wide ranging capacity.

 They are provided with damper windings.

V. COMPENSATORS:

 Speed - 3000rpm  Rating - 100MVAR

CONSTRUCTION

• Stationary armature, rotating field type of construction is preferred.

• High speed alternators have non-salient pole rotor (Turbo alternators) and they have either 2-pole or 4-pole.

• Slow speed alternators have salient pole rotor (water wheel alternators) and they have more than 4 poles.

• In a synchronous generator, a DC current is applied to the rotor winding producing a rotor magnetic field. The rotor is then turned by external means producing a rotating magnetic field, which induces a 3-phase voltage within the stator

winding.

• In a synchronous motor, a 3-phase set of stator currents

produces a rotating magnetic field causing the rotor magnetic field to align with it. The rotor magnetic field is produced by a DC current applied to the rotor winding.

• Field windings are the windings producing the main magnetic field (rotor windings for synchronous machines); armature windings are the windings where the main voltage is induced (stator windings for synchronous machines).

Construction of synchronous

machines

The rotor of a synchronous machine is a large electromagnet. The magnetic poles can be either salient (sticking out of rotor surface) or non-salient construction.

Non-salient-pole rotor: usually two- and four-pole rotors. Salient-pole rotor: four and more poles.

OUTPUT EQUATION OF SYNCHRONOUS MACHINES

The output equation of A.C machine is given by, Q = C_o D2L n_s x 10-3 and

The output coefficient, C_o = 11 B_av ac K_w x 10-3 Where,

Q = kVA output for alternator and kVA input for synchronous motor.

D = diameter of the stator bore, m L = length of the stator core, m n_s = synchronous speed, rps

B_av= specific magnetic loading, Wb/m2

Ac = specific electric loading, amp.cond/m K_w = stator winding factor.

CHOICE OF LOADING

• Choice of specific magnetic loading depends on: Iron loss

Voltage rating Stability

Parallel operation

Transient short circuit current

• Choice of specific electric loading depends on: Copper loss

Temperature rise Voltage rating

Synchronous reactance Stray load losses

CHOICE OF SPECIFIC MAGNETIC LOADING (B_av )

i) high B_av→ high flux density in the teeth and core

→high iron loss → higher temperature rise.

ii) high B _av → low Tph → low leakage reactance (Xl ) → high short circuit current

iii) In high voltage machines slot width required is more to

accommodate thicker insulation→smaller tooth width → small allowable B_av

iv) Stability : P_max =VE/Xs .

Since high B_av gives low Tph and hence low Xl P_max increases and improves stability.

v) Parallel operation : Ps = (VE sinδ)/Xs ; where δ is the torque angle. So low Xs gives higher value for the synchronizing power leading stable parallel operation of synchronous

generators.

GUIDE LINES :

Non-salient pole alternator : 0.54 – 0.65 Wb/m2

CHOICE OF SPECIFIC ELECTRIC LOADING (ac)

• COPPER LOSS AND TEMPERATURE RISE:

High value of ac → higher copper loss leading high temperature rise. So choice of depends on the cooling method used.

• OPERATING VOLTAGE :

High voltage machines require large insulation and so the slot space available for conductors is reduced. So a lower value for ac has to be chosen.

• SYNCHRONOUS REACTANCE (Xs) :

High value of ac results in high value of Xs , and this leads to, a) poor voltage regulation

b) low steady state stability limit.

• STRAY LOAD LOSSES:

Increase with increase in ac. Guide lines :

Non-salient pole alternators : 50, 000 – 75,000 A/m Salient pole alternators : 20,000 – 40,000 A/m

DESIGN OF SALIENT POLE MACHINES

 Diameter of stator bore

 Outer diameter Dr = D length of air gap  The selection of diameter D depends upon

(i) the type of poles used (ii) permissible peripheral speed  Two types of poles

(i) Round poles (ii) Rectangular poles

Round poles – ratio of b_s is between 0.6 to 0.7

Length of poles = Width of pole shoe (or) L= b_s

Rectangular poles – Ratio of pole arc to pole pole pitch varies between 1 to 5 . Not should exceed for normal machines

 Otherwise the design of field system becomes not economical  Ratio L / τ = 1 to 5

 The deciding factor is the peripheral speed with circular poles larger than with rectangular poles

 The value of allowable peripheral speed  Bolted on pole construction = 50m/s

 Dovetailed and T head constructions - 80 m/s

SHORT CIRCUIT RATIO (SCR)

• SCR = Field current required to produce rated voltage

on open circuit / Field current required to

produce rated current on short circuit

= 1/ direct axis synchronous reactance

= 1/Xd

• Thus SCR is the reciprocal of Xd , if Xd is defined in p.u.

value for rated voltage and rated current. But Xd for a

given load is affected by saturation conditions that then

exists, while SCR is specific and univalued for a given

machine.

• For Salient pole Hydroelectric generators , SCR varies

from 1.0 - 1.5

O.C.C and S.C.C Characteristics

op

SCR

os

EFFECT OF SCR ON MACHINE PERFORMANCE:

i) Voltage regulation :

A low SCR → high Xd → large voltage drop → poor voltage regulation..

ii) Parallel operation :

A low SCR → high Xd → low synchronizing power → parallel operation becomes difficult.

iii) Short circuit current :

A low SCR → high Xd →low short circuit

current. But short circuit current can be limited by other means not necessarily by keeping a low

iv) Self Excitation :

Alternators feeding long transmission lines should not be designed with small SCR as this would lead to large terminal voltage on open circuit due to large capacitance currents.

Summarizing ,high value of SCR leads to, i) high stability limit

ii) low voltage regulation iii) high short circuit current iv) large air gap

The present trend is to design machines with low value of SCR, this is due to the recent development in fast acting control and excitation systems.

SHAPE OF POLE FACE

• The ratio of pole arc to pole pitch varies Ψ between 0.67 and 0.75.

• If value of Ψ is too large Ψ >0.75  Interpolar flux leakage becomes excessive leading to high value of flux density in pole body and improper flux distribution over the armature

• If the value Ψ <0.67  Insufficient overhang of the pole shoe to support the field coil in radial direction

• Common practice is to use a value of Ψ = 0.7

• In salient pole machine the length of air gap is not constant over the pole arc but increase from centre outwards in order to produce the required flux distribution

•

.

• Fig : Shape of pole face for sinusoidal flux distribution

/ cos

x

l

l











_

_





ARMATURE DESIGN

• The winding in synchronous machines may be single layered or double layered type.

• Machines having larger values of flux per pole have small

number of turns per phase

• High voltage machines with small value of flux per pole have a larger number of turns per phase

 Number of Armature slots  Coil span

 Turns per phase  Conductor section

Double layered windings have following advantages over the single layered windings

 Ease manufacture of coils  Low cost of windings

 Less no. of coils required

 Fractional slot pitch coil can be used

The single layer windings have the following advantages

 Higher efficiency

NUMBER OF ARMATURE SLOTS

The following factors should be considered for selection of armature slots

Balanced windings – Unbalanced windings leads to over heating of rotor surface

Cost – fewer coils to wind , insulate

Hot spot temperatures – conductors are close to each other leaving small space for air circulation it gives rise to internal temperature

Leakage reactance – Number of slots is small , Lr increased Tooth ripples – Pulsation loss in pole face decreased if large number of slot is used

Flux density in Iron -larger number of slots a greater space is taken up by insulation , results in narrower teeth giving flux

• The value of slot pitch y_s serves as a guide for choosing the number of armature slots

• Y_s < 25mm for low voltage machines • Y_s < 40mm for 6 kV machines

• Y_s < 25mm for machines up to 15KW.

• Fractional slot windings reduces the distribution factor for higher harmonics that reducing their corresponding generated emfs and making the voltage waveforms nearly sinusoidal

• Coil Span – Highest amplitude in flux distribution curve of salient pole generators are 5th _{and 7}th _{harmonics .}

• The maximum reduction of harmonics is given by a coil span of 8.33% of pole pitch

Turns per phase

• Flux per pole

• Turns per phase

(All turns of a phase connected in series) • But if there a ‘a’ parallel paths

av

B

l







4.44

E

T

fK





4.44

E

a

T

fK







Conductor section

Current in each conductor

But if there a ‘a’ parallel paths , the conductor current is

Area of cross section of conductor

δ_s = current density in armature conductors in A/mm2

3

10 / (3

)

I



I



kVA



E

/

I



I

a

I

a





Armature resistance

Lmts= length of mean of stator m, a= area of stator conductor, mm2

The stator d.c. resistance per phase

Armature copper loss

Effective a.c.resistance per phase

Per unit armature resistance

ARMATURE PARAMETERS . mts d c ph s

L

r

T

a





(

')

2

9

T

_N

I

L

ah

L

a













_





_





(

')

2

9

T

_N

r

L

ah

L

a











_





_





(

) /

R



I



r

E

Armature Leakage reactance

Stator leakage reactance per phase

Overhang leakage reactance per phase

The value of overhang permeance

K= 0.23 X 10-6 for Concentric windings K= 0.29 X 10-6 for Barrel windings

2

8

x

fT

L

pq







8

x

fT

L

pq







2 2

KL

L

y





ESTIMATION OF AIRGAP LENGTH

• No load field mmf per pole is equal to the product of armature mmf per pole and the short circuit ratio

• The value of armature mmf per pole

• Mmf Required for air gap = 0.8 AT_fo =800,000B_gK_gl_g • Where B_g=maximum flux density in the air gap

• Length of air gap at the centre of the pole l_g

0 f a

AT



AT



SCR

2.7

I T K

AT

SCR

p





0.8

800000

AT

l

B K



1000, 000

K AT

B K



DESIGN OF ROTOR

• Flux in the pole body

• Φ

= leakage coefficient x useful flux per pole = C

Φ

• The value of leakage coefficient C

lies between 1.15

to 1.2

• Area of cross section of pole body

• The flux density in pole body Bp has a permissible

value of 1.5 to 1.7 wb / m

• For rectangular poles

• For circular poles

p p p

A

B





0.98

A



L b

4

A

_{  }







b





HEIGHT OF POLE

• An approximate estimation of full load mmf can be

made by the method given below

• No load mmf

• Armature mmf per pole

0

f

a

AT



SCR AT



2.7

/

AT



I T K

p

DESIGN OF DAMPER WINDINGS

• It depends of damper winding depends upon the purpose for which it is provided.

• In synchronous generator , it is provided to suppress the

negative sequence field and to damp the oscillation when the machines starts hunting

• Function – provide starting torque and to develop damping power when the machine starts hunting

• The amplitude of fundamental mmf AT_l of one phase of a polyphase winding is obtained

*

4

2

2

AT

AT K

I T

I

AT

qZ

p









Current in each conductor I

= I

Conductors per slot

MMF of damper winding

Ampere conductors per pole

1

4 2

I T K

AT

p





6

.

I T

ac

p





2 2

.

6

0.143

.

ac

k

ac













• Let total area of damper bars per pole

• Area per pole of damper pass provided

• Pole arc=number of bars per pole x y_s x0.8

• Length of each damper bar Ld= 1.1L for small machines Ld= L+0.1m for large machines Cross section of damper bars

Circular Bars

Area of each ring

0.143

A





ac



0.2

/

A



ac



 

A

a

N



4

(0.8 1)

a

d

A

to A







  







METHODS OF ELIMINATING HARMONICS

By using,

i) distributed windings ii) fractional coil pitch

iii) fractional slot windings iv) skewing

v) large air gap.

Further calculations needed after determining D and L : i) Flux per pole = Φ = B_av (π DL/p )

ii) T_ph is calculated from the EMF equation taking E_ph = V_ph

iii) I _ph = (Qx 103 _{) / √ 3 V} L

iv) Armature MMF/pole = At_a = 2.7 I _ph T _phK_w /p

v) Effective area per pole = 0.6 – 0.65 times actual area.

DETERMINATION OF FULL LOAD FIELD MMF

The value of mmf calculated by

1.

Select the suitable voltage

2.

Draw oa= voltage per phase (Eph=V)

3.

Draw oI = armature current per phase at angle Φ w.r.to

Eph(where cosΦ=p.f lagging )

4.

Draw ab=resistance drop per phase =Iph rac and

parallel to oI

5.

Draw bc= leakage reactance drop per phase = Iph xl

and perpendicular to oIJoin oc . Then oc is the

generated voltage

6.

Join oc . Then oc is the generated voltage

7.

Plot od =ATgen to some scale

8.

Draw de =field mmf equivalent to armature mmf per

pole at full load perpendicular to oI at d.

• Determination of full load field mmf AT

9. Find the value of Kr 10. Join of and extend it

11. Draw a perpendicular from e on of extended cutting it at gi Field mmf equivalent to armature mmf per pole

2.7

I T K

fieldmmf

p





sin

4 sin

/ 2

value













DESIGN OF FIELD WINDINGS

• Wire wound coils are generally used for machines with a small number of poles

• The field coil of alternators having large number of poles are wound with glass covered rectangular strips

• The field coils of large slow speed alternators use strip on edge windings wherein the bare with strip on edge conductors

• For machine with class B insulation , interturn consists of 2layers of treated asbestos paper , with thickness of 0.18m • Due to pressing and consolidation thickness of interturn

insulation is reduced from 0.36mm to 0.26mm

• The pole body insulation is of epoxy glass laminates is 4mm thick

• Coil is consolidated under a pressure which varies 4 to 12MN/m2

Procedure

The voltage across the field coil

We know h_pl be height of the pole

Voltage across the field coil

Area of the conductors

Current density in field conductors is 3 to 4 A/mm2

(0.8 0.85)

to

Ve

E

p



h



h



h

I T L

a



AT

L

a

E





• Calculation of length of mean turn

bp

Lm

L 5mm

• Field winding depth

• The resistance of the winding is calculated at 75 degree c

• Cooling coefficient to rotating field coils

• The minimum clearance between adjacent field coils is 15mm

Pole pitch mm Winding depth mm

0.1 25 0.2 35 0.4 45 f mtf f f

T

L

R

a





0.08 0.12

1 0.1

to

c

V





DESIGN OF TURBO ALTERNATORS

• In turbo-alternators the diameter is limited by the

maximum peripheral speed, V

.

• Peripheral speed, V

= πDn

.

• Diameter, D= V

/ πn

.

• The output kVA, Q = C

D

L n

x 10

and

The output coefficient, C

= 11 B

ac K

x 10

So, Q=11 B

ac K

x 10

( V

/ πn

) ² L n

• The value of specific loadings for conventionally

cooled alternators are:

B

=0.54 to 0.65 Wb/m

ac

= 50000 to 75000 amp.cond/m

• The value of specific loadings for large water cooled

alternators are:

B

=0.54 to 0.65 Wb/m

Length of air gap

Taking sinusoidal distribution of flux density in the air gap

For all practical purposes Bg is taken as 1.5Bav and Kg as 1.1

NOTE:

The armature slot, winding, turns per phase and conductor designs of turbo-alternator are same as that of salient pole alternator. 6

0.5

10

ac

l

k B







( / 2)

B





B

STATOR DESIGN

• The number of slots per pole per phase is 8 to 9 used.

• The slot pitch is normally about 25 to 60mm but in case of turbo alternator is 75mm to 90mm

• The stator conductors must be subdivided and transposed to reduce eddy current losses

• Two layer windings chorded by about 1/6 pole pitch and more commonly eliminates 5th and 7th as well as 17th & 19th

harmonics

• The current density in the stator windings of water cooled generator is about 8 to 9.5 A/mm2 _{and conventionally cooled}

machine is 4 A/mm2

• The deep slot is used to increase leakage reactance. This is done to reduce the forces under short circuit conditions

ROTOR DESIGN-TURBO ALTERNATORS

• The width of the rotor slots is limited by stresses at

the root of the teeth and by hoop stress in the end

rotating rings

• The insulation thickness varies from 0.25 to 0.33 mm

per 100V across the windings

• Rotor density may be about 2.5 A/mm

for

conventionally cooled machines. Modern direct

cooled generators about 9.5-14 A/mm

PROCEDURE FOR ROTOR WINDING DESIGN

• Full load field mmf can be taken as twice the armature mmf • Full load field mmf

• Voltage across the field coil

τ-coil span

• The length of mean turn of field winding is approximated

2

2.7

/

AT

AT

AT

I T K

p





2

2.3

0.24

L



L







(0.8 0.85)

to

V

E

p



• Area of the field coil

• Assume a suitable current density of field windings

Total area of field conductors

Conductors per slot

Sr= number of wound slots in the rotor

fl mtf f f

AT

L

a

E





2

pAT

a





2

pAT

a S



