synchronous generator characteristics--saravanan t y

Electrical Machines-III Synchronous Generator Characteristics

T. Y. Saravanan M. Tech., NECGUDUR 45

UNIT II

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2.1. Harmonics:

The distortion in an output or input Voltage or Current wave form is called known as

harmonics.

The ripples due to slotting of armature are always opposite to slots and a tooths which are

causing them. Thus the harmonics which is generated in the emf is due tom slotting called slot

harmonics.

The air-gap offers maximum reluctance to the flux path, if made to vary sinusoidal around the

machine the field form and would be sinusoidal

Thus in general it can be seen that ideal sinusoidal field form is very difficult to obtain whether

the machine is salient pole type or cylindrical type rotor construction.

2.2. Harmonics in generated emf wave form:

The major sources of harmonics in an alternator in the output voltage wave form are as

follows:

i. The non-sinusoidal wave form of the field flux.

ii. Variation in reluctance of the air-gap due to the

slotting of the stator core.

These are explained by the methodology of wave

shaping as follows.

The flux distribution curve in the air-gap of

an alternator shown in figure is not usually as

rectangular as in a dc machine, but it is not a

perfectly sinusoidal unless the machine has a salient

pole rotor with specially shaped pole shoes, or a

cylindrical rotor with sinusoidal distributed field winding.



The induced emf wave per conductor is similar to flux wave since induced emf per conductor is

directly proportional to flux density at constant speed.

i.e., e = B l v volts

Where, l = length of conductor is constant and

v = velocity or speed is constant

If the winding is full-pitched one, the emfs, induced in two coil sides of each coil will be in

phase and of the same magnitude because at any instant both the sides of the coil lie under

corresponding positions of opposite poles. Hence for full-pitched winding, the induced emf wave

in early coil will have same shape as the emf induced in each coil side.

If concentrated winding is employed, the resulting emf wave will be of the same shape as the

flux density curve (B) as above which is flat-topped.

Let us consider, a phase belt consisting of 3-coils of a 3- alternator having 3 slots per pole per

phase is shown in figure.

The shape of emf wave for each of the

3-full-pitch coils giving one phase of the

winding will be of the shape, as shown in

figure by curves I, II and III respectively

below.

The slot displacement angle between

the adjacent slots is 20 electrical apart.

i.e., = 1800

n =

1800

9= 200

The resultant emf per phase would be the

phasor sum of the induced emfs in the three

coils which may be obtained by adding the

ordinates of three emfs waves.

The resultant emf per phase (Ep) wave is not flat

topped but is almost sine wave.

Hence the distributed winding is employed to give

emf wave nearly sinusoidal. By using distributed

winding, breadth factor for harmonics is very much less

than for fundamental. So that harmonics are reduced in

the resultant emf wave.



For a fractional pitch winding, the emf in each coil may be obtained first by adding the emfs of

each coil side graphically and then resultant emf per phase may be obtained by adding the coil

emfs.

The resultant emf per phase for a fractional or short-pitch winding will be more nearly sinusoidal

than for full-pitch winding.

2.3. Suppression of harmonics in generated emf:

In general for synchronous generators, non-sinusoidal field flux wave form is the major cause

of harmonics in the emf waveform. If field flux waveform is a sinusoidal then there should be no

harmonics in the synchronous generator emf waveform.

In case of salient pole machines, if the air-gap is made to vary sinusoidal around the machine, the

field produced is sinusoidal. An approximate of sinusoidal field form is obtained by skewing the

pole faces.

In cylindrical rotor machines, the length of air-gap is uniform throughout, therefore the

sinusoidal field wave form is obtained, and the mmf of the field winding is made to vary as

nearly sinusoidal as possible.

Now if we consider that an amount of saturation in iron parts, the sinusoidal field form cannot be

obtained in salient pole machines even if the air-gap length is varied sinusoidal.

In cylindrical rotor machines even if the mmf distribution in air-gap is made sinusoidal because

air-gap around the outer periphery should be uniform. An ideal sinusoidal wave form is very

difficult to achieve, and therefore harmonics developed in induced emf.

The harmonics can be easily eliminated from the alternator generated induced emf wave form by

properly designing the windings. The various methods for elimination of harmonics from the

output voltage are,

Pole (Normal) Skewed Face Pole

Skew Pole Face



1) Distributing the armature winding properly.

2) Short-chording or fractionally pitched the armature winding by making the coil-span or

coil-pitch less than a full pole-pitch. (i.e., short-pitch winding)

3) Skewing the pole faces usually through one slot-pitch.

4) In case of salient pole, if we maintain small air-gap at the pole centre and large air-gap

towards the pole ends tends to make the field flux sinusoidal as shown in above figure.

5) Skewing the armature slots, only tooth or slot harmonics can be eliminated.

6) Fractional slot winding: Higher order harmonics can be drastically reduced by using

fractional slot winding. The flux pulsations can be reduced by having number of slots per

pole arc as an integer plus 1/2.

7) Larger air-gap length causes the increases in reluctance which will reduce the harmonics.

8) By making the alternator connections i.e., star or delta connections of alternators suppress

triplen harmonics (multiples of three) from appearing across lines.

2.4. Rating of Alternators:

All power equipments or apparatus whether it is steam engine or gas engine or electric

machine have power ratings defined as the power which can be safely and efficiently delivered by a

machine under some specific conditions or the rating of AC machinery such as alternators,

transformers and cables are determined by their heating and hence by losses them.

Electrical apparatus or machine is usually rated at the load, which it can carry without over-

heating and damage to insulation i.e., rating of electric machine is governed by the temperature

rise caused by the internal losses of the machine. The copper loss in the armature (I2R) depends

upon the strength of the armature current and core loss on voltage and these losses are

independent of power factor.

The output in KW is proportional to power factor for the alternator of a given KVA. For

example output of 1000 KVA alternator will be of full load is 200, 500, 800 and 1000 KW at

power factor of 0.2, 0.5,0.8 and unity respectively, but copper losses in armature will remain

same regardless of power factor.

The prime mover which drives the alternator, have a rating independent of power factor and it

depends on kW output.

Finally we can say that the alternators are rated in kVA or kW at specified power factor.

Other name plate details include:

1. Voltage 2. Current

3. Frequency 4. Speed

5. Number of Poles 6. Field current & Voltage

7. Maximum Temperature rise 8. Number of Phases



2.5. Leakage Reactance or armature leakage reactance (XL):

Leakage reactance is an inductive reactance formed due to air-gap in between armature

conductors and field poles

In an a.c. machine, any flux set up by the

load current which does not contribute to

the useful flux or main flux of the machine

is a leakage flux.

This leakage fluxes may be classified as

1. Slot leakage

2. Tooth head leakage

3. Coil-end or overhang leakage

When a current flow through the armature

conductors or stator conductors, the flux is set up a

portion of this flux does not cross the air-gap, but

completes its path in stator as shown in figure.

Such a flux is known as leakage flux.

This effect gives the armature a reactance which is numerically equal to 2 f L. L, in henries, is

the leakage inductance of winding

This leakage flux is proportional to stator or armature current, since the magnetic path it covers is

not normally saturated. It also depends on the phase angle between the stator current and voltage

applied across the stator.

The leakage flux sets up an emf of self inductance leading the load current I by 2 and

proportional to load current I in magnitude. Hence armature winding is assumed to possess

leakage reactance (XL) such that the voltage drop due to it, I XL is equal to an emf set by leakage

flux. A part of the generated emf is used up to overcome this leakage reactance drop in addition to

armature drop.

i.e., Generated emf = phasor sum of terminal voltage, armature resistance drop.

2.6. Armature Reaction:

The action of armature flux on main flux is called known as Armature Reaction.

In dc machine, the armature mmf (ampere-turns) acts on the magnetic circuit of the machine in

such a way as to distort the air-gap flux and to charge its magnitude. For a given armature

current, the direction and magnitude of armature reaction depends on the position of brushes.

In an alternator, somewhat similar conditions exist. For a given armature current, the magnitude

and direction of the armature reaction cannot depends on the brush position as in case of dc



machine, but depends on phase displacement of stator current I with respect to emf E induced

in the stator winding by the field winding flux.

i.e., for,

DC Machine Armature Reaction depends on position of brushes.

Alternator Armature Reaction depends on phase angle displacement of load current I and

induced emf E.

In an alternator the phase displacement or phase angle - between current I and emf E can

be within the limits of,

2

2

We will consider three cases,

i.e.,

i. When = 0 i.e., when the power factor of load is unity.

ii. When = +2 i.e., when the power factor is zero and lagging.

iii. When = -2 i.e., when the power factor of load is zero and leading.

2.6.1. At unity power factor:



The distribution of the stator currents and fluxes of an alternator with zero phase displacement

between current I and emf E (i.e., when pf is unity) Assuming the rotation of the poles to be

clockwise is shown in above figure.

The crosses (+) and dots (.) appeasing in the conductor cross sections indicate the

instantaneous direction of the emfs induced and currents flowing.

Cross indicating the inward direction and dot indicating the outward direction. The maximum of

the fundamental wave of the field will be opposite to the pole centers and at the same points the

conductors have their maximum induced emf.

With =0 the conductors carrying the maximum current will also be at the same points, as shown

in the figure. The armature reaction mmf is perpendicular to the main field mmf, as in case of a

dc machine with brushes on the neutral axis.

This causes the distortion of the flux due to main field and asymmetrical distribution of the flux

density under the pole shoe. The flux density under the trailing pole tips increases somewhat,

while under the leading pole lips it decreases.

The axis of the resultant field is displaced under the action of armature reaction mmf in a

direction opposite to that of rotation of the rotor.

Hence armature reaction at unity power factor has got distorting effect.

2.6.2. At lagging zero power factor:



The distribution of currents and fluxes with phase angle = +2 radians i.e., for a purely

inductive load is shown above. The current maximum will be shifted in space by an angle 900 from

the emf maximum, which coincides with the centre of the poles. This shift will be opposite to

direction of rotation, because the fundamental armature reaction wave rotates in step with the field

poles.

While when = +2, current wave lags behind the emf wave by an angle 900. The field created by the

armature reaction mmf will be in opposite to main field flux and will,

Therefore, have a wholly de-magnetizing effect.

2.6.3. At leading zero power factor:

The distribution of currents and fluxes with phase angle -2 i.e., for a purely capacitive load is

shown below.

The maximum current will be shifted to the right from the maximum emf, which remains as before

under the pole centres and the armature reaction will,

Therefore have a wholly magnetizing effect on the main field.



For any power factor cos of load, the armature reaction has cross-magnetizing component

proportional I cos and demagnetizing component proportional to I sin, and is taken +ve for

lagging power and ve for leading power factor.

The phasor sum of the fundamental armature winding and field winding mmf waves constitutes,

in a synchronous machine, the mmf creating the resultant magnetic flux.

2.7. Nature of Armature Reaction:

The nature of the armature reaction is dependent on the power factor at which the machine is

operating and upon the operating mode of synchronous machine. For simplicity of explanation, it will

be assumed that the armature resistance (Ra) and leakage reactance (XL) are negligible so that,

Vt = Eg The below phasor diagrams, with component fluxes indicated therein for an alternator for

zero power factor lagging, zero power factor leading, unity power factor. The following observations

are immediately made from the phasor diagrams.

Where, ar = armature flux component

f = field flux component

r = resultant flux component

Armature reaction is demagnetizing (ar opposes f) when a alternator supplies zero power factor

lagging current.

Armature reaction is magnetizing (ar aids f) when a alternator supplies zero power factor

leading current.

Armature reaction is mostly cross-magnetizing (i.e., at 900 to f) though it has a small

demagnetizing component shown when an alternator supplies a unity power factor current.

From the above discussion, we conclude that for an alternator,



It supplies a lagging power factor current; the armature reaction has both demagnetizing and

cross-magnetizing components.

It supplies leading power factor current, the armature reaction has both magnetizing and cross-

magnetizing components.

2.8. SYNCHRONOUS IMPEDANCE:

2.8.1. Synchronous Reactance: (XS) [XS = XL + Xa]

The armature reactance is the reactance which is due to armature reaction.

The emf set up due to armature reaction mmf is always quadrature with load current IL and is

proportional to it. Thus it is equivalent to an emf induced in an inductive coil and the effect of

armature reaction can, therefore, be considered equivalent to reactance drop IXa. Where Xa which takes care of the armature reaction effect.

The armature winding possess a certain leakage reactance (XL) already discussed. The sum of

XL and Xa is called the synchronous reactance.

XS = XL + Xa

2.8.2. Effective Resistance: (Re)

The effective resistance of the armature winding is somewhat greater than the conductor

resistance called the dc resistance. This is due to additional loss, over the purely I2R loss, inside and

sometimes outside the conductor due to alternating current (AC). The main sources of this additional

loss are,

i. Eddy current in the outer periphery.

ii. Magnetic hysteresis in the surrounding material.

iii. Eddy currents or unequal current distribution in the conductor itself.

In many cases it is sufficiently accurate to measure armature resistance by dc called the effective

resistance (Re) which is large enough to take care of these additional losses. Re can vary widely

from 1.25 to 1.75 or more times to dc resistance depending upon design.

2.8.3. Synchronous impedance: (ZS)

When the synchronous reactance (XS) is combined with the armature resistance (Re), then the

quantity obtained is called the Synchronous impedance (ZS).

i.e., ZS = Re + jXS

Armature winding effective resistance (Re) in alternators usually very small in comparison to

synchronous reactances (XS) and therefore ZS may be assumed to XS.



2.9. Alternator ON-LOAD:

If the excitation of an alternator adjusted to give normal voltage at no-load and then a load is

applied, the terminal voltage of an alternator changes, even though the speed is kept constant. The

voltage usually falls, but in certain circumstances it may rise even.

The change in terminal voltage of an alternator with the change in load supplied by it is due to

the following reasons.

i. Voltage drop account of armature effective resistance (Re).

ii. Voltage drop on account of leakage reactance (XL).

iii. Voltage drop on account of armature reaction.

From the Phasor diagram of lagging

power factor,

Ia is taken as reference vector

OD2 = OB2 + BD2

E02 = OD2 = (OA + AB)2 + (BC + CD)2

E0 =(V cos + IaRe)2+(V sin + IaXs)2

From the Phasor diagram of leading

power factor,

V is taken as reference vector

OC2 = OD2 + DC2

E02 = OC2 = (OE + ED)2 + (BD - BC)2

E0 = (V cos + IaRe)2+V sin - IaXs2

O A B

C

D

V

Ia

Ia Re

I a X

l I a

Xa

I a X

S

E0

V cos Ia Re

V si

n

Lagging Power Factor

O A

B

C

D

E

V

Ia

E0

Leading Power Factor



From the Phasor diagram of unity

power factor,

OD2 = OC2 + CD2

E02 = OD2 = (OB + BC)2 + (CD)2

E0 = ( V +IaRe)2+(IaXs)2

2.10. Equivalent Circuit:

When the alternator is operating at no-load (i.e., rotor is rotating and energized and stator is

open-circuited) its circuit diagram is shown below.

Each phase generates an emf E0 per phase as shown. The equivalent circuit of an alternator for

one phase is shown.

At no-load, the terminal voltage V per phase is equal to excitation (or) generated emf E0 per phase

i.e., V = E0

O A B C

D

V Ia Ia Re

I a X

l I a

Xa

I a X

S

E0

Unity Power Factor



2.11. Load characteristics:

Already we know that if the exciting current and speed remain constant, the terminal voltage

of an alternator changes with the change in the load (or) armature current.

The relation-ship between the terminal voltage (V) and load current (I) of an alternator is known as

its Load characteristics.

The curves showing the variation of terminal voltage V with load current I for constant

excitation for different power factor loads are given.

The curves are plotted in terms of percentage values general operating conditions can be

marked better in

this way.

Normally the terminal voltage falls with increase in load current, but when the power factor is

leading one, the load characteristic may rise at first. Each curve is nearly straight line at the

beginning but trends to droop because, with the increase in load current, the angle of lag between

current and emf, owing to the original field increases.

The highest current is obtained when the alternator terminals are short-circuited, the value being

given as

Isc=E0Zs

(A)

where, E0 is non-load terminal voltage and Zs is the synchronous impedance.

(Percent Load Current)

(Per

cent

Ter

min

al V

olta

ge)

100

220

Vt (

Vol

ts)

Isc (Amps)

0.8 Leading PF

0.8 Lagging PF

Unity PF

0



2.12. Experimental determination of Zs:

2.12.1. Open circuit test:

The connection for open circuit test is shown in the above circuit diagram. The armature

winding i.e., load terminals are opened and machine should be run at rated or synchronous

speed. The field winding is connected to dc source in series with a field rheostat and an

ammeter.

By adjusting the field rheostat to maximum to minimum the field current If is taken from

ammeter in steps minimum to maximum respectively. Then Eg0 is also minimum to maximum

taken from voltmeter in steps up to rated value.

Draw the open circuit characteristic curve (OCC curve) from the above readings. i.e., If on x-

axis and Eg on y-axis. The Ego which we obtained from voltmeter is line value that should be

represent in a graph as phase value. i.e., [For a star Ego/ph = Ego/line

3 ].

2.12.2. Short circuit test:

The connection for the short circuit test is shown in the below circuit diagram. In this test also

the machine should be maintained at constant speed by the prime mover.

All the 3- load terminals of 3- alternator as shorted. Rheostat of sufficiently high ohmic value

is inserted in the dc field circuit to keep the current in the circuit very low.

Now the field current If is adjusted to Isc or Irated of 3- alternator by varying the field rheostat.

From the If and Isc the SCC curve (Short Circuit Characteristic) is obtained.



2.12.3. OC & SC Characteristic curves:

The synchronous impedance Zs can be obtained by above graphical representation of occ

and scc curve.

i.e., ZS = Open circuit induced emf

Short circuit current

Zs = EocIsc



2.13. Determination of effective armature resistance: (Re)

The effective armature resistance (Re) per phase can be measured directly by Ammeter-

Voltmeter (A-V method) or by using Wheatstone bridge

The above circuit is used to measure the effective armature resistance per phase. The DC supply

is connected to the any one phase of armature winding through rheostat, ammeter in series and

voltmeters to parallel.

Then the rheostat can be varied from maximum to minimum in steps the Va and Ia values are

noted by voltmeter and ammeter respectively and taken average with gives Re. i.e. Ra = VaIa

.

The Re value which we obtained is dc by converting it to AC value is multiplied 1.5 due to skin

effect.

i.e., RAC = 1.5RDC

Finally, we obtained the synchronous impedance Zs from OC and SC test, Re obtained by A-V

method then Xs as,

Synchronous Reactance =XS = ZS2 - Re2



2.14. Winding factor: (Harmonics Consideration)

The product of distribution factor (Kd) and the pitch factor (Kp) is referred as the winding

factor (Kw).

Kw = Kd*Kp

3- alternators are invariably star-connected to eliminate 3rd and 9th harmonics (i.e. multiples of 3,

called triplen) from line emfs through 5th and 7th harmonic emfs of reduced magnitude are present

in the lines.

Already we know the emf equation of 3- alternator,

i.e. Eph

= 4.44 KpKd f T volts.

From the above equation, the fundamental emf per phase is,

Ep1 = 4.44 * Kw1 * 1 * (1f) * T .. (1)

For 3rd harmonic, emf per phase is

Ep3 = 4.44 * Kw3 * 3 * (3f) * T .. (2)

In general, for hth harmonic, emf per phase is

Eph = 4.44 * Kwh * h * (hf) * T .. (3)

Here subscripts 1, 3 and h denotes fundamental, third and hth harmonics respectively.

From Eph and Ep1 expressions, the hth harmonic and fundamental rms phase emfs are related

(3)(1)

= EphEp1

= KwhKw1

* h h1

..(3a)

Also,

1= total value of fundamental flux per pole

= (Avg. Flux density) . (Area under pole)

= 2

B1* DL

P

= 2DL

P.B1 ..(4)

Where,

B1 = peak value of fundamental component of flux density.

D = Air-gap diameter of armature.

L = Core Length of armature.

Similarly, 3 from equ, (4) as

3=2DL3P

B3



In general,

h=2DLhP

Bh

From the above,

h1

= 1h

. BhB1

BhB1

= hh1

From equation 3a

Eph Ep1

= KwhKw1

.hh1

EphEp1

= KwhKw1

.h.1h

.BhB1

Eph Ep1

= KwhKw1

.BhB1

The rms phase emf is,

Eph=[Ep12+Ep32 + ---+Eph2]1/2

2.15. Fictitious Poles:

In case of a magnets dipole it is not possible to identify any two particular points as poles of

the magnet. So, every magnetic dipole is supposed to be made up of two imaginary poles called

fictitious poles of equal strength but opposite polarity.

The fictitious poles can be obtained by extending the magnetic lines of forces inside the magnet.

Thus, the actual distance between the fictitious poles is less than the distance between the ends of the

magnet. The distance between the fictitious poles of a magnet is called the magnetic length of the

magnet. It is represented by 21, where / is the distance of each pole of the magnet from its centre. So,

the actual magnetic length of a magnet is slightly less than its geometrical length. The relation

between these lengths is as follows. Magnetic length = 5/6 geometrical length.



Problems

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synchronous generator characteristics--saravanan t y

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