1

READING MATERIAL FOR B.E. STUDENTS

OF RGPV AFFILIATED ENGINEERING COLLEGES

BRANCH V SEM ELECTRICAL AND ELECTRONICS

SUBJECT ELECTRICAL MACHINES II

Professor MD Dutt

Addl General Manager (Retd)

BHARAT HEAVY ELECTRICALS LIMITED

Professor(Ex) in EX Department

Bansal Institute of Science and Technology

Kokta Anand Nagar BHOPAL

Presently Head of The Department ( EX)

Shri Ram College Of Technology

Thuakheda BHOPAL

Sub Code EX 503 Subject Electrical Machines II

UNIT III Synchronous Machine I

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EX 503

UNIT III Synchronous Machine I

RG PV Syllabus

Construction, types of prime movers, excitation system including brushless

excitation. Polyphase distributive winding, integral slot winding and

fractional windings, emf equation, generation of harmonics and their

elimination. Armature reaction, synchronous reactance and impedance.

Equivalent circuit of alternator, relation between generated voltage and

terminal voltage. Voltage regulation of alternators using synchronous

impedance,mmf,zpf and new ASA method.

INDEX

S No Topic Page

1 Construction , types of prime mover 3,4,5,6,7

2 Excitation system including brushless excitation 7,8,9

3 Polyphase distributive winding, integral slot winding and

fractional windings, emf equation

9,10,11,12

4 Generation of harmonics and their elimination 12,13,

5 Armature reaction, synchronous reactance & impedance 13,14,15

6 Equivalent circuit of alternator 15,16

7 Relation between generated voltage and terminal voltage 16,17,18

8 Voltage regulation of alternators using synchronous impedance 18,19,20,21

9 MMF,ZPF and new ASA method. 21,22,23,24

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CONSTRUCTION FEATURES AND TYPE OF PRIME MOVERS.

In the electrical machines-1 in 4th

semester we have gone through the following topics

(1) Transformer,

(2) And three phase induction motor.

The induction motor is a asynchronous machine. The synchronous machine is the

machine which operates at synchronous speed. To work out synchronous speed the

following formula is used.

N =

N = speed

F = frequency

P = poles

First of all we will revise what we had learnt in 4th

semester for induction motor, As the

induction motor is a rotating machine the synchronous generators are also rotating

machine having mainly following feather`s.

Construction features:-

As induction motor the synchronous generators have three main component.

(1) An Armature winding in the stator

(2) A magnetic circuit, called exciting or field winding for the production of flux.

(3) An arrangement to cut the magnetic flux by armature winding.

CONSTRUCTION OF SYNCHRONOUS MOTOR:- The synchronous motor

essentially consists of two parts mainly the armature ( stator) and field magnet system (

rotor).

STATOR : - The armature is an iron ring formed of laminations of special magnetic

material ( silicon sheet steel) . It is having slots on the inner periphery to accommodate

armature conductors and is known as stator. The whole structure is held in a cast iron or

fabricated frame. The field rotates in between the stator, flux of rotating field cuts the

stator core continuously and causes eddy current losses in the core. The laminations are

insulated from each other by thin layer of varnish.

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ROTOR:- Similar to DC field system the rotor field system of synchronous machine is

excited by DC 125- 250V DC supply from exciter which is mounted on the same shaft.

Rotors are of two type

1) Salient pole type rotor

2) Smooth cylindrical rotor

The rotor of this type is used entirely for low speed alternators. These type of machines

are called projected pole type machines. The poles are made from lamination punched

from silicon sheet steel and joined together by pole rivets. The each lamination is

insulated by thin layer varnish. The damper windings are provided at the pole shoes for

avoiding hunting. The pole faces are so shaped that airgap is minimum at centre and

increases from the pole centre for the sinusoidal flux so that the induced EMF is

sinusoidal. The end of the field windings are connected through sliprings to a DC

source. They have following special features:-

i) Salient pole field structure has large diameter and short shaft lengths

ii) The pole shoes cover about ⅔ of pole pitch

iii) These are employed in HYDRO turbine or diesel engines, where RPM is low (

100rpm to 325 rpm)

SMOOTH CYLINDRICAL ROTOR

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The rotor of this type is used in very high speed alternators. ( Steam Turbine) To reduce

the peripherals velocity the diameter of this type of rotor is small and the axial length is

increased. Such rotor normally have two or four poles. It consists of steel forgings with

radial slots in which field copper ,usually strips are placed. The coils are held by steel or

bronze wedges and coil ends are fastened by metal strips. This type of rotor have

uniform air gap. For getting sinusoidal EMF slots are shapes machined in the rotor

forging.

i) Less windage loss

ii) Very high operating speed ( 3000rpm)

iii) Robust construction and noiseless operation.

A synchronous generators is a doubly excited energy conversion device because its

field winding is always energized from separate D.C. source. The armature winding

either export A.C. power in the case of synchronous generator or import A.C. power in

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this case the machine is in motoring mode.

TYPES OF PRIME MOVERS FOR SYN GENERATORS

A synchronous generators is a machine for converting mechanical power

from a prime movers to A.C. electric power of specific voltage and

frequency . A synchronous machine rotates at constant speed which is

called synchronous speed . The prime movers are –

= Hydro turbine

= Steam turbine

= Diesel Engine

The size of synchronous generator depends on the speed of the prime movers.

Normally the hydro turbine are slow speed machine . So the rotor of hydro

turbine driven machine has to accommodate, more number of poles for obtaining

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synchronous speed. So salient pole generator are driven by hydro turbine . The

diameter D is large compare to core length.

Where the speed of prime movers is high the cylindrical rotor construction is

used and the size of generator depends on the mechanical strength of the material

of shaft. The centrifugal forces in case steam turbine driven generator is very

high. Due to this the diameter of cylindrical rotor machine are less compare to the

core length.

In addition to the criteria of speed, The synchronous machine are large in size

and lots of heat is generated due to the losses in the machine. The size of

generator depends upon the type of cooling used to take away the heat generated.

= Closed circuit water cooled CACW

= Closed circuit air cooled CACA

= Closed circuit hydrogen cooled

= Closed circuit with water flow through the conductor

So the two major points which are the main consideration for the size of

synchronous generator is speed and cooling

EXCITATION SYSTEM FOR SYNCHRONOUS MACHINES

In large synchronous machines, the field winding is always provided on rotor, the

D.C. excitation to field winding is provided by fallowing three methods.

1) D.C. Excitation

2) Static Excitation

3) Brushless Excitation

1) D.C. Excitation – In D.C. excitation system three machines are used, one is

called pilot exciter, another is called main exciter and main 3 phase alternators

are mechanically coupled and they are mounted and driven by the single shaft

. The pilot exciter is D.C. shunt generator feeding the DC supply to field

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winding of main exciter. The armature output of main field exciter is fitted

through brushes and slip rings to the main field of the alternators, as shown in

figure. This type of excitation requires maintenance of slip rings and

commutator of both the pilot exciter and main exciter armature to alternatively

static excitation or brushless excitation system are more popularly used now a

days for large rating machines.

2.STATIC Excitation – In this method of excitation of power through regulator

and current transformer and potential transformer are drown from main and fed

to thyristor bridge after stepping down the voltage by transformer TR, The D.C.

output of the thyristor bridge is fed through the brushes and slip ring to the field

winding of main alternators .Initially the D.C. excitation is provided to main field

winding from 125v battery bank to establish the field current in the exciter . After

building of the A.C. voltage sufficiently, the alternator is disconnected from

battery and switched on to the thyristor bridge output. The advantages of static

excitations are –

i)The excitation system is simple in design and provide fast response

characteristics as required in modern power system .

ii)Since there is no commutator of pilot and main exciter the friction, windage

and commutator losses are nil in this case , The maintenance cost is reduced .

iii) Since excitation is taken directly from the alternator terminal voltage ,

the system performance improves considerably .

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3)BRUSHLESS Excitation System – A signal is picked from alternator terminal

through CT and PT ,controls the firing angle of thyristor bridge , this enables the

control of field current of the main exciter which depend upon the output voltage

.This scheme of excitation does not require any sliding contacts and brushes . In

large turbo generator excitation system require large D.C. current which needs

cumbersome and complicated brush gear design , in this brushless excitation the

brushgear is totally eliminated.

POLYPHASE DISTRIBUTED WINDINGS

The different polyphase distributed A.C. windings are as follows :-

SINGLE LAYER WINDING:- In a single layer winding , the armature has

each slot occupied by only one coil side , and in this way the number of coil in

the armature winding is equal to half the number of slot .This type of winding

can be either full pitched or short pitched. These type of winding requires

considerable space for the end connection of coils and in rarely used .

DOUBLE LAYER WINDING:- In a double layer winding , each slot of the

armature is accommodated by two coil per slot . If a coil has its one side coil

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in the top layer of particular slot than its other coil side will lie in the bottom

layer of a slot which is located at a pole pitch apart from the top conductor .

Synchronous machines and induction machines are generally wound with the

double layer type of winding If the number of slot per pole pre phase is whole

number, the winging is called as integral slot winding and the number of slot

per pole per phase is a fraction , than this type of winding is known as

fractional slot winding.

INTEGRAL SLOT WINDINGS:- Let us assume that the full pitch or pole

pitch of a winding is 6 slot per pole. If the coil pitch is taken as equal to full

pitch, then upper coil side in slot 1 should be connected to the bottom coil

side in slot number 7 (+6). Since there are 6 slots per phase of 180 degree the

slot

angular pitch is Y =180/6 = 30 for a phase

Spread of 60 degree , slot 1 and 2 must contain coil sides pertaining to

phase A , upper side in slot 2 must be connected to bottom coil side in slot

number 8 (2+6) ,winding is further completed for phase A only. It can be

concluded that for full pitch integral slot winding, each slot contain coil

sides belonging to the same phase.

FRACTIONAL SLOT WINDING – In fractional slot winding the

number of slots per phase per pole is not a whole number, but from the

view point of symmetry, the number of slot must be divisible by the

number of phase.

Say a machine having 4 poles and 90 slots the per phase per pole figure

works out to be 30.

THE ADVANTAGES OF THESE TYPE OF WINDINGS ARE AS

FOLLOWS

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1. This type of windings reduces the high frequency harmonics in the EMF

and MMF wave forms.

2. This windings permit the use of already existing slotting number for the

armature lamination , because the armature slot need not to be a multiple

of number of poles. For the 4 pole 90 slot machine the per pole slot is 22.5

only.

EMF EQUATION

Let us assume that A synchronous machine is running at speed = N rpm

Number of turn pre pole = T

Now if the number of poles is P and the flux per pole is wb then the flux

cut by each conductors is equal to

= P × Per Revolution

= P ( N ∕ 60) per second

So Average EMF Generated

= P N volt/conductor

60

= ZP N volt per turn

60

= Z P N T volt per phase

60

= 4 . f . . T volt per phase

Where f is the frequency of generated EMF in Hz

So RMS value of EMF generated

= 1.11 4 f . T volt

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= 4.44 Kw f T volt

In the above EMF equation Kw is winding factor

Kw = Kp Kd

The fundamental EMF per pole is

Eph1 = 4.44 f Kw1 Nph 1

For 3rd

harmonic

Eph3 = 4.44 3f K3w Nph 3

In general , for nth harmonic ,EMF per phase is

Ephn = 4.44 nf Kwn Nph n

Ephn Eph1 = K Wn n KW1 1

GENERATION OF HARMONICS AND THEIR ELEMINATION,

The harmonics in a synchronous machine is generated due to the non

sinusoidal field flux , The field flux wave form along the air gap periphery

is not sinusoidal due to the harmonic EMF are always generated in the

synchronous generators.

Field flux wave form can be made as much sinusoidal as possible by

following method

1. Small air gap at the pole centre and large air gaps towards the pole ends

, in the salient pole machine tends to make the field flux sinusoidal by

designing pole shape suiting to this.

2. If possible the pole faces to have skew.

3. In turbo alternator , the air gap is uniform , so the field winding is

distributed in such a manner in the slots to make the field flux wave

form almost sine wave .

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In spite of all attempts mentioned above , the field wave form along the air

gap periphery is not sinusoidal .As a result harmonics EMF are always

generated. These are suppressed and eliminated as fallows.

1)DISTRIBUTION- The distribution of armature winding along the air

gap periphery tends to make the EMF wave form sinusoidal.

2)CHORDING :- With the coil span less than pole pitch, the harmonics

can be eliminated.

3)SKEWING – By skewing the armature slots , only tooth harmonics or

slot harmonics can be eliminated .

4)FRACTIONAL SLOT WINDING – In fractional slot winding the space

relation between teeth and slot under a given pole face is not the same

and under the next pole and the succeeding pole faces .

5)ALTERNATOR CONNECTION – Star or delta connection of

alternators suppresses the triple harmonics .

ARMATURE REACTION. LEAKAGE REACTANCE, SYNCHRONOUS

REACTANCE AND IMPEDANCE , EQUIVALENT CIRCUIT OF

ALTERNATOR.

Armature reaction : armature reaction is the effect of armature M.M.F. or flux on

the main field M.M.F. or flux , it has three effect 1. Magnetizing.2.Demagnetizing.

3.Cross magnetizing or distortional.

Φf ϕar

ϕr

Vt=Er

Ia Zero P.F Lagging

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Ia Φf ϕar

ϕr

Vt=Er Zero P.F Leading

ϕr ϕar

Φf

Ia Vt=Er Unity P.F

a)Zero P.F. lagging : In the case of lagging zero P.F. the armature flux

and the main field flux are in direct opposition to each other effect in this

case is demagnetizing. The E.M.F. generated is reduced here and therefore

the field excitation will hare to increase to compensate the decrement of the

E.M.F.

b)Zero P.F. leading : In this case the armature flux is in the phase of the

main field flux and the main field flux which result an increased resultant

flux and hence the armature reaction in this case is magnetizing the E.M.F.

generated is increased and therefore the field excitation will have to be

decreased to compensate the increment of the E.M.F.

c)Unity P.F.: - in the case of unity power factor distortional and the average

field strength remains constant.

Motoring mode:- The armature reaction M.M.F. and flux are in phase and

are in phase opposition to armature current for generating and motoring

machine. So the nature of armature reaction for motoring machines are

apposite of that for generating machines.

The effect are still cross magnetizing distort in case of unity power factor.

The effect is magnetizing in the case of zero power factor lagging and

demagnetizing effect in the case of zero P.F. leading for synchronous

machines operating on motoring mode.

For all the intermediate lagging P.F. say 0.8 log the effect due to armature

reaction is portly distortional and portly demagnetizing in the case of

motoring machines.

For all the intermediate leading P.F. say 0.7 leading the effect portly

distortional and portly magnetizing in case of a generating machine and

portly distortional and portly demagnetizing in case of motoring machine .

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Hence the nature of armature reaction flux each dependent upon the

operating power factor of the machine.

Synchronous impedance :- The actual voltage generated by a machine are

the summation of two component voltage .

Other component of generated voltage is called the armature reaction voltage

Ear. This is the voltage that must be added to the excitation voltage to take

care of the effect of armature reaction with the generated voltage.

Ea = Eexc + Ear

Since armature reaction result, in a voltage effect in a circuit caused by

change in flux by the current in the same circuit , its effect is of the nature

of inductive reaction can be expressed is

Ear = - J Xar Ia

The inductive reactance Xar is a field our reactance which will result in a

voltage in the armature circuit . The terminal voltage is –

V = Ea – JXar Ia –JXaIa +RaIa

In the above equation –

RaIa = armature resistance drop.

XaIa = armature leakage reactance drop.

XarIa = armature reaction voltage drop .

Xs = Xa + Xar = synchronous reactance

V = Ea – Jxs Ia -Ra Ia

V = Ea - Ia (Ra +JXs)

V = Ea – ZsIa

So,

Zs = Ra +J Xs

This is synchronous impendence.

Equivalent circuit of synchronous alternator :-

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The equivalent circuit diagram representing Zs , for a synchronous machine is

given here with-

RELATION BETWEEN GENERATED VOLTAGE AND TERMINAL

VOLTAGE , DETERMINATION OF EQUIVALENT CIRCUIT PARAMETERS,

Relation between generated voltage and terminal voltage shown in the circuit is

for a cylindrical rotor synchronous generator.

V = TERMINAL VOLTAGE PER PHASE

Ef = excitation voltage per phase

Ia = armature current

= phase angle between Ef and V

The Ef leads V by angle , V = V 0 , Ef = Ef

The synchronous impedance is given by,

Zs = Ra + Xs = Zs Q , Ef = V + Zs Ia

Ia =

Determination of equivalent circuit parameters.

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The following test are performed on an alternating to find out its performed

parameters.

(a) D.C. resistance test.

(b) Open circuit test.

(c) S.C. test.

D.C. resistance test Assume that the alternator is connected in star

with D.C. field winding open. Measure the resistance by ammeter–voltmeter

method or by using Wheatstone bridge . The average of three sets of

resistance Rt is taken. The value of Rt is divided by 2 to obtain D.C.

resistance per phase. The alternator should be at rest since the effect of

A.C. resistance is large than D.C. resistance due to the skin effect.

Open circuit test The alternator is run at rated synchronous speed and

the load connection are kept open ,the all load are disconnected. The fields

current is set to zero, Now the field current is gradually increased in steps, and

the terminal voltage Et is measured at each step. The excitation current may be

increased to get about 25% more than the rated voltage of the alternator. A graph

is plotted between the open phase voltage = Ep = Et/ √ 3 and field current If.

The characteristics curve, so plotted is called open circuit curve obtained by

open circuit test.

Short circuit test The armature terminal are shorted through. Three ammeters

are connected in series. The field current should be kept at zero and machine is

rotated at synchronous speed. The field current is increased in steps and the

armature current is measured at each step.

The field current may be increased a get armature current upto 150%

of the rated value. The value of field current If and the average corresponding

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armature reading are recorded. The curve so plotted between field current and

short circuit current Ise is called S.C.C. or short circuited characteristics.

S

SHORTSYNCHRONOUS GENERATOR UNDER LOAD , EFFECT OF EXCITATION

VARIATION

When a alternator is loaded, the load current Ia starts flowing which results in various

drops as

a) Armature reactance drop Ia X ar

b) Leakage reactance drop Ia X al

c) Armature resistance drop IaRa

These drops reduces the no load voltage Eo to a new value Eo Ia (Ra+Xar+Xal). This is

called the on load terminal voltage and is different from the no load terminal voltage,

hence by loading the alternator the armature terminal voltages changes.

When an alternator is loaded with lagging power factor load, its no load

terminal voltage, Eo decreases to a new value v+ but for the leading power factor the

full load terminal voltage V+ increases and hence the full load terminal voltage is

greater then the no load terminal voltage.

The computation of voltage regulation of an alternator is necessary for the

following reasons

a) The winding insulation of alternator should be able to with stand the voltage rise.

b) The voltage regulation effects the parallel operation of alternator.

c) The type of AVR equipment which are used gets terminated from the voltage

regulator.

d) Steady state short circuit conditions and the stability condition of the alternator is

greatly affected by voltage regulation.

EFFECT OF EXCITATION VARIATION

The effect of field current on the synchronous machine power factor can also be

explained with phasor diagram. For simplicity armature resistance ra is neglected and

synchronous reactance Xs and terminal voltage V+ are assumed it remain constant.

P = Ef Vt∕ Xs sinδ = V+ Ia cosФ

for constant power output, therefore Ef sinδ and Ia cosφ must remain constant because

V+ and Xs are constant. This means that the field current is varied. Excitation voltage

Ef varies but the component of Ef normal of Vt, Ef sin δ must remain constant. As Ef

varies Ia Xs and therefore armature current also varies but in a such a manner as to keep

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Ia cosφ, when the excitation voltage Ef, the machine is under excited and the armature

current Ia, must lag VT by P.F angle Ф, so that the relation Ef + Jia Xs = Vt, when the

excitation voltage is increased to Ef2 by increasing. In order to satisfy the relation Ef +

JIa Xs = Vt. The phasor of armature current must change to Ia2 when the excitation is

increased Ef3, the load angle must decrease from δ2 to δ3 so that Ef3 sin δ3 = Ef2 sin

δ2 = Ef1 sin δ, in order to satisfy the voltage relation

Ef + j Ia Xs = Vt again,

The phase of armature current Ia3 is pushed ahead of Vt therefore, the machine operates

at a leading power factor, the active component of armature current are equal Ia1cos φ1

= Ia2 cosφ2 = Ia3 cosφ3.

REGULATION CURVE, REGULATION BY SYNCHRONOUS IMPEDANCE

METHOD, MMF METHOD, Z.P.F AND ASA METHOD, EFFECT OF AVR

POWER AND TORQUE RELATION.

VOLTAGE REGULATION :- the voltage regulation of a synchronous generator is the

rise in voltage at the determined when the load is reduced from full load to zero, the

speed and field current remaining constant.

It can be expressed as

Per unit voltage regulation = | Ea | - | V| ∕ | V|

Percent voltage regulation = | Ea | - | V| X 100 ∕ | V |

Where | E| = magnitude of generated voltage per phase

|V| = magnitude of rated terminal voltage per phase

The voltage regulation depends upon the power factor of the load. For unity and lagging

p.f there is always a voltage drop with to increase of load, but for a certain leading

power f, the full load voltage regulation is zero.

DETERMINATION OF VOLTAGE REGULATION :- the following methods are used

to determine the voltage regulation of smooth cylindrical both type alternator

a) Direct load test

b) Indirect method

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DIRECT LOAD TEST :- The alternator is run at synchronous speed and its terminal

voltage is adjusted to its rated voltage value V. The load is varied until the ammeter

and wattmeter’s indicate the rated value at the given power factor.

INDIRECT METHOD :- For large alternators, the four indirect method which are

used to predetermine the voltage regulation of smooth cylindrical rotor machine are

a) Synchronous impedance method or emf method

b) Ampere turn method or mmf method

c) Zero p.f method or potier method

d) ASA method

SYNCHRONOUS METHOD OR EMF METHOD :- The synchronous impedance

method is based on the concept of replacing the effect of armature reaction by fictitious

reactance.

For a synchronous generator

V = Ea – Zs Ia

Zs = Ra + j Xs

In order to determine the synchronous impedance Zs is measured and then the value of

Ea is calculated from the value of Ea and V the voltage regulation calculated.

CALCULATION OF Zs :- The open circuit characteristics and short circuit

characteristics S.C.C. are drawn on the same graph sheet taking the value of field

current on X axis and voltage on Y axis . determine the field current that gives the

alternator voltage per phase. The synchronous impedance Zs will then be equal the

O.C.C. voltage divided by short circuit current at that field current at that field current

which gives the rated emf per phase.

Zs = Open circuit voltage per phase

Short circuit current in armature

The synchronous reactance is found as follows

Consider the field current If = OA, that produces rated alternator voltage per phase,

corresponding to this field current the open circuit voltage AB. The corresponding

current in armature is AC

Zs = AB in volts

AC in amperes

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REGULATION BY M.M.F , Z.P.F. and ASA METHOD effect of AVR

power and torque relation.

M.M.F. Magneto Motive Force method:-this method is also known as ampere

turn method. The synchronous impedance method is based on the concept of

replacing the effect of armature reaction by a fictitious reactance. The M.M.F.

method replaces the effect of armature leakage reactance by an equivalent

additional armature reaction M.M.F. so this M.M.F.may be combined with the

armature reaction MMF

The following information is required to predict the regulation by M.M.F.

method.

(a) The resistance of winding per phase.

(b) Open circuit characters at synchronous speed.

(c) Short circuit characteristic.

This method makes use of the phasor diagram of M.M.F.

The following procedure is used for drawing the phasor diagram at lagging P.F. cos

(1) The armature terminal voltage per phase (V) is taken along OA as the

reference phasor.

(2) Armature current Ia is drown lagging the phasor of V for lagging P.F.

angle for which the regulation is to be calculated.

(3) The armature resistance drop phasor IaRa is drawn is phase with Ia along

the line A.C., join O and C, OC represent the E.M.F.

(4) From the open circuit characteristic, the field current If1’ corresponding to E

is noted, draw the field current If1’’, leading the voltage E by 90 .

(5) From the S.C.C. determine the field current IF2 required to circulate the

rated current on short circuit condition, this is the field current IF2 required

to overcome the synchronous reactance drop IaXs. Draw the field current

IF2 in phase opposition to current Ia, than IF2 = IF2 )

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(6) Determine the phasor sum of field current If1’ and If2. This given resultant

field current IF which would generate a voltage Eo under no load condition

of the alternate. The open circuit E.M.F. Eo corresponding to field current

If is found from O.C.C.

(7) The % regulation is found from the relation regulation =

100.

Zero power factor method or potier method :- consider a point on

Z.P.F. curve corresponding to rated terminal voltage V and a field current

of OM = If for this condition of operation, the armature reaction mmf has

a value expressed in equivalent field current LM ( = Iar = Far/If)

Than the equivalent field current of resultant M.M.F. would be OL(=Ir =

).This field current OL would result in a generated voltage Eg=(=LC)

from the no load saturation curve, since for lagging zero power factor

operation.

Eg = V + Ia Xa2

The vertical distance A.C. must be equal to the leakage reactance voltage

drop IaXa2, which Ia is the armature current.

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Xa2 =

The triangle formed by the Vertices a,b,c is called the potier triangle.

Voltage regulation =

100.

New ASA method:- This method is just a modification of mmf method.

For both the type of cylindrical as well as salient pole synchronous machine, the

new A.S.A. method required O.C.C. an Z.P.F.C. though the latter may not be

known completely, only two point A and F` are sufficient to be known on the

Z.P.F.C. The point A is obtained by loading the over excited alternator by an

under excited synchronous motor till full load armature current at rated voltage is

flowing. The point F` is obtained by noting the field excitation (Fa + Fal),

required to circuit full load armature current when the alternator is short

circuited. The armature reactance Xai is determined by potier reactance drop

B.C. The armature drop IaRa is neglected than Q = angle .

The m.m.f. phasor diagram is drawn in which Fr` =O`G is taken from air gap

line at rated voltage OO`. The m.m.f. (Fa + Fal) is equal to OF` and this s drawn

as GH making an angle 90 + with Fr`. The resultant of Fr` and (Fa + Fal) is

O`H.

Now determine Er = Vt + Ia (ra+j ac) and use the magnitude of Er in obtaining

the saturation effect. A horizontal line is drawn through K, so that OK = Er. This

line inters set air gap line at H and the OCC at M. The distance HM, on the field

excitation O`M = Ff. Now corresponding to O`M = Ff = OF. Excitation voltage

Power flow equation :- in practical poly phase synchronous machines Ra Xs

and Ra the armature resistance can be neglected in the power flow equations.

When armature resistance Ra is neglected

Zs =Xs ,

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Pog =

sin

Qog =

cos – /Xs

Pig =

cos = pog

Qig =

-

cos

Pog (max) =

= pig (max).

Effect of excitation and torque relation, in general, the alternators operation in

steady state condition when operating in parallel and synchronized with the lees.

The load speed characterizes of the prime mover should be draping, that means

the speed of the prime mover should decrease slightly with the increasing load.

The speed droop are also called governor droop. The speed regulation can be

expressed as-

speed drop =

Nnl = No load speed,

Nf1 = full load speed.

The voltage dips/ increase are corrected by the AVR by adjusting the field or

excitation current. Ior speed dips or increase is adjusting by the opening of

governor for LP stage module or IP stage module or HP stage module of steam

turbine so that at shaft more or less torque is available. Usually the speed torque

relation are linear and the droop varies from 2 to 4 percent from no load to full

load.

The amount of power generated by the alternator is determined by its prime

mover. The speed of prime mover is fixed, but its torque can be varied. This is

done by the controlling governors placed on the turbine or prime movers.