regulatiom of alternators

8/10/2019 Regulatiom of Alternators

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When voltage is applied across any two terminals, then one phase winding appears in parallel with series combinatio

of other two.

Hence the equivalent resistance across the terminals is parallel combination of the resistance Raand 2Ra.

... RRY Ra | |Ra /ph

Thus in delta connected alternator, the armature resistance per phase is to be calculated from the equivalent resistanc

observed across any two line terminals.

Armature Leakage Reactance

When armature carries a current, it produces its own flux. Some part of this flux completes its path through the a

around the conductors itself. Such a flux is called leakage flux. This is shown in the Fig. 1.

Fig. 1 Armature leakage flux

Note : This leakage flux makes the armature winding inductive in nature. So winding possesses a leakage reacatnce, i

addition to the resistance.

So if 'L' is the leakage inductance of the armature winding per phase, then leakage reactance per phase is give

by XL = 2 f L /ph. The value of leakage reactance is much higher than the armature resistance. Similar to the d.c

machines, the value of armature resistance is very very small.

Armature Reaction

When the load is connected to the alternator, the armature winding of the alternator carries a current. Every curren

carrying conductor produces its own flux so armature of the alternator also produces its own flux, when carrying a curren

So there are two fluxes present in the air gap, one due to armature current while second is produced by the filed winding

called main flux. The flux produced by the armature is called armature flux.

Note : So effect of the armature flux on the main flux affecting its value and the distribution is called armature reaction.

The effect of the armature flux not only depends on the magnitude of the current flowing through the armature windin

but also depends on the nature of the power factor of the load connected to the alternator.

Now we will study the effect of nature of the load power factor on the armature reaction.

1.1 Unity Power Factor Load

Consider a purely resistive load connected to the alternator, having unity power factor. As induced e.m.f. E ph drives

current of Iaph and load power factor is unity, Eph and Iph are in phase with each other.
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Fig. 3 Armature reaction for zero leading p.f. load

It can be seen from the phasor diagram and waveforms shown in the Fig. 2, the armature flux and the main field flu

are in the same direction i.e. they are helping each other. This results into the addition in main flux.

Note : Such an effect of armature reaction due to which armature flux assists field flux is called magnetising effect of th

armature reaction.

As this effect adds the flux to the main flux, greater e.m.f. gets induced in the armature. Hence there is increase in th

terminal voltage for leading power factor loads.

For intermediate power factor loads i.e. between zero lagging and zero leading the armature reaction is partly cros

magnetising and partly demagnetising for lagging power factor loads or partly magnetising for leading power factor loads.1.4 Armature Reaction Reactance (Xar)

In all the conditions of the load power factors, there is change in the terminal voltage due to the armature reaction

Mainly the practical loads are inductive in nature, due to demagnetising effect of armature reaction, there is reduction in th

terminal voltage. Now this drop in the voltage due to the interaction of armature and main flux. This drop is not across any

physical element.

But to quantify the voltage drop due to the armature reaction, armature winding is assumed to have a fictitiou

reactance. This fictitious reactance of the armature is called armature reaction reactance denoted as Xar /ph. And the dro

due to armature reaction can be accounted as the voltage drop across this reactance as IarXar.

Note : The value of this reactance changes as the load power factor changes, as armature reaction depends on the loapower factor.

Concepts of Synchronous Reactance and Impedance

The sum of fictitious armature reaction reactance accounted for considering armature reaction effect and the leakag

reactance of the armature called synchronous reactance of the alternator demoted as X s.

So Xs = XL + Xar /ph

As both XL and Xar are ohmic values per phase, synchronous reactance is also specified as ohms per phase.

Now from this, it is possible to define an impedance of the armature winding. Such an impedance obtained b

combining per phase values of synchronous reactance and armature resistance is called synchronous impedance of th

alternator denoted as Zs.

So Zs = Ra + j Xs /ph

And | Zs | = (Ra2+ j (Xs)

2)

For getting a standard frequency, alternator is to be driven at synchronous speed. So word synchronous used i

specifying the reactance and impedance is referred to the working speed of the alternator. Generally impedance of th
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winding is constant but in case of alternator, synchronous reactance depends on the load and its power factor condition

hence synchronous impedance also varies with the load and its power factor conditions.

Equivalent Circuit of an Alternator

From the previous discussion it is clear that in all there are three important parameters of armature winding namel

armature resistance Ra, leakage reactance XL and armature reaction reactance Xar. If Eph is induced e.m.f. per phase on n

load condition then on load it changes to E ' due to armature reaction as shown in the equivalent circuit. As current flow

through the armature, there are two voltage drops across R a and XLas Ia Raand respectively. Hence finally terminal voltag

Vtis less than E'by the amount equal to the drops across Ra and XL.

Fig. 1 Equivalent circuit

In practice, the leakage reactance XLand the armature reaction reactance Xarare combined to get synchronou

reactance Xs.

Hence the equivalent circuit of an alternator gets modified as shown in the Fig. 1.

Fig. 2 Equivalent circuit of an alternator

Thus in the equivalent circuit shown,

Eph = induced e.m.f. per phase on no load

Vtph = terminal voltage per phase on load

Iaph = armature resistance per phase

Zs = synchronous impedance per phase

In a d.c. generators, we have seen that due to the armature resistance drop and brush drop it is not possible to have all th

induced e.m.f. available across the load. The voltage available to the load is called terminal voltage. The concept is same i

case of alternators. The entire induced e.m.f. can not be made available to the load due to the various internal voltag

drops. So the voltage available to the load is called terminal voltage denoted as. In case of three phase alternators as all th

phases are identical, the equations and the phasor diagrams are expressed on per phase basis.
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As cos= 1, so sin = 0 hence does not appear in the equation.

Note : The phasor diagrams can be drawn by considering voltage Vph as a reference phasor. But to derive the relationship

current phasor selected as a reference makes the derivation much more simplified. Hence current is selected as a referenc

phasor.

It is clear from the phasor diagram that V ph is less than Ephfor lagging and unity p.f. conditions due to demagnetisin

and cross magnetising effects of armature reaction. While V ph is more than Ephfor leading p.f. condition due to th

magnetising effect of armature reaction.

Thus in general for any power factor condition,

(Eph)2= ( Vph cos + Ia Ra)

2+ (Vph sin Ia Xs)

2

+ sign for lagging p.f. loads

- sign for leading p.f. loads

and Vph = per phase rated terminal voltage

Ia = per phase full load armature current

Voltage Regulation of an Alternator

Under the load condition, the terminal voltage of alternator is less than the induced e.m.f. Eph. So if load is disconnecte

, Vph will change from Vph to Eph, if flux and speed is maintained constant. This is because when load is disconnected, I a

zero hence there are no voltage drops and no armature flux to cause armature reaction. This change in the terminal voltag

is significant in defining the voltage regulation.

Note : The voltage regulation of an alternator is defined as the change in its terminal voltage when full load is removedkeeping field excitation and speed constant, divided by the rated terminal voltage.,

So if Vph = Rated terminal voltage

Eph = No load induced e.m.f.

the voltage regulation is defined as,

The value of the regulation not only depends on the load current but also on the power factor of the load. For lagging and

unity p.f. conditions there is always drop in the terminal voltage hence regulation values are always positive. While for

leading capacitive load conditions, the terminal voltage increases as load current increases. Hence regulation is negative in

such cases. The relationship between load current and the terminal voltage is called load characteristics of an alternator.

Such load characteristics for various load power factor conditions are shown in Fig. 1.
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Fig. 1 Load characteristics of an alternator

KVA Rating of an Alternator

The alternators are designed to supply a specific voltage to the various loads. This voltage is called its rated termina

voltage denoted as VL. The power drawn by the load depends on its power factor. Hence instead of specifying rating of aalternator in watts, it is specified in terms of the maximum apparent power which it can supply to the load. In three phas

circuits, the apparent power is 3VLIL, measured in VA (volt amperes). This is generally expressed in kilo volt amperes an

is called kVA rating of an alternator where I Lis the rated full load current which alternator can supply. So for a given rate

voltage and kVA rating of an alternator, its full load rated current can be decided.

Consider 60 kVA, 11 kV three phase alternator.

In this case kVA rating = 60

........ 10-3

to express the product in kilo volt amperes

... 60 = 3 x 11 x 103x IL x 10

-3

... IL = 3.15 A

This is the rated full load current of an alternator. But load current is same as the armature current. So from kVA rating

it is possible to determine full load armature current of an alternator which is important in predicating the full load regulatio

of an alternator for various power factor conditions. Similarly if load condition is different than the full load, the correspondin

armature current can be determined from its full load value.

Note : Ia at half load = 1/2 x Ia at full load. It reduces in the same proportion in which load condition reduces.

Hence regulation at any p.f. and at any load condition can be determined.

Regulation of Synchronous Generator : Introduction

The regulation of an alternator can be determined by various methods. In case of small capacity alternators it can b

determined by direct loading test while for large capacity alternators it can be determined by synchronous impedanc

method.
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The synchronous impedance method has some short comings. Another method which is popularly used is ampere

turns method. But this method also has certain disadvantages. The disadvantages of these two methods are overcome in

method called zero power factor method. Another important theory which gives accurate results is called Blondel's tw

reaction theory. Thus there are following methods available to determine the voltage regulation of an alternator,

1. Direct loading method

2. Synchronous impedance method or E.M.F. method

3. Ampere-turns method or M.M.F. method

4. Zero power factor method or potier triangle method5. ASA modified from of M.M.F. method

6. Two reaction theory

Voltage Regulation by Direct Load

The Fig. 1 shows the circuit diagram for conducting the direct loading test on the three phase alternator. The sta

connected armature is to be connected to a three phase load with the help of triple pole single throw (TPST) switch. Th

field winding is excited by separate d.c. supply. To control the flux i.e. the current through field winding, a rheostat i

inserted in series with the field winding. The prime mover is shown which is driving the alternator at its synchronous speed.Procedure : The alternator is first driven at its synchronous speed Ns by means of a prime mover.

Fig. 1 Circuit diagram for direct loading test on alternator

Now Eph ..... (From e.m.f. equation)

By giving d.c. supply to the field winding, the field current is adjusted to adjust the flux so that rated voltage is availabl

across the terminals. This can be observed on the voltmeter connected across the lines. The load is then connected bymeans of a TPST switch. The load is then increased so that ammeter reads rated value of current. This is full load conditio

of the alternator. Again adjust the voltage to its rated value by means of field excitation using a rheostat connected. Th

throw off the entire load by opening the TPST switch, without changing the speed and the field excitation. Observe th

voltmeter reading. As load is thrown off, there is no armature current and associated drops. So the voltmeter reading in thi

situation indicates the value of internally induced e.m.f. called no load terminal voltage. Convert both the reading to phas

values. The rated voltage on full load is Vph while reading when load is thrown off is Eph. So by using the formula,
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the full load regulation of the alternator can be determined. The value of the regulation obtained by this method is accurate

as a particular load at required p.f. is actually connected to the alternator to note down the readings.

Note : But for high capacity alternators, that much full load can not be simulated or directly connected to the alternato

Hence method is restricted only for small capacity alternators.

Example : While supplying a full load, running at synchronous speed, the terminal voltage of an alternator is observed to b

1100 V. When the load is thrown off, keeping field excitation and speed constant, the terminal voltage is observed to be

1266 V. Assuming star connected alternator, calculate its regulation on full load.

Solution : On full load, terminal voltage is 1100 V.

So VL = 1100 V

... Vph = VL/3 = 635.0853 V

When load is thrown off, VL = 1266 V. But on no load,

VL = Eline

... Eline = 1266 V

... Eph = 1266/3

= 730.925 V

Synchronous Impedance Method or E.M.F. Method

The method is also called E.M.F. method of determining the regulation. The method requires following data to calculat

the regulation.

1. The armature resistance per phase (Ra).

2. Open circuit characteristics which is the graph of open circuit voltage against the field current. This is possible b

conducting open circuit test on the alternator.

3. Short circuit characteristics which is the graph of short circuit current against field current. This is possible by conductin

short circuit test on the alternator.

Let us see, the circuit diagram to perform open circuit as well as short circuit test on the alternator. The alternator i

coupled to a prime mover capable of driving the alternator at its synchronous speed. The armature is connected to th

terminals of a switch. The other terminals of the switch are short circuited through an ammeter. The voltmeter is connecte

across the lines to measure the open circuit voltage of the alternator.

The field winding is connected to a suitable d.c. supply with rheostat connected in series. The field excitation i.e. fie

current can be varied with the help of this rheostat. The circuit diagram is shown in the Fig. 1.
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Fig. 1 Circuit diagram for open circuit and short circuit test on alternator

1.1 Open Circuit Test

Procedure to conduct this test is as follows :

i) Start the prime mover and adjust the speed to the synchronous speed of the alternator.

ii) Keeping rheostat in the field circuit maximum, switch on the d.c. supply.

iii) The T.P.S.T switch in the armature circuit is kept open.

iv) With the help of rheostat, field current is varied from its minimum value to the rated value. Due to this, flux increasing th

induced e.m.f. Hence voltmeter reading, which is measuring line value of open circuit voltage increases. For various value

of field current, voltmeter readings are observed.

The observation for open circuit test are tabulated as below :

Observation table for open circuit test :

From the above table, graph of (Voc)phagainst Ifis plotted.

Note : This is called open circuit characteristics of the alternator, called O.C.C. This is shown in the Fig. 2.
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Fig. 2 O.C.C. and S.C.C. of an alternator

1.2 Short Circuit TestAfter completing the open circuit test observation, the field rheostat is brought to maximum position, reducing fiel

current to a minimum value. The T.P.S.T switch is closed. As ammeter has negligible resistance, the armature gets sho

circuited. Then the field excitation is gradually increased till full load current is obtained through armature winding. This ca

be observed on the ammeter connected in the armature circuit. The graph of short circuit armature current against fiel

current is plotted from the observation table of short circuit test. This graph is called short circuit characteristics, S.C.C. Th

is also shown in the Fig. 2.

Observation table for short circuit test :

The S.C.C. is a straight line graph passing through the origin while O.C.C. resembles B-H curve of a magnetic materia

Note : As S.C.C. is straight line graph, only one reading corresponding to full load armature current along with the origin i

sufficient to draw the straight line.

1.3 Determination of From O.C.C. and S.C.C.

The synchronous impedance of the alternator changes as load condition changes. O.C.C. and S.C.C. can be used t

determine Zs for any load and load p.f. conditions.

In short circuit test, external load impedance is zero. The short circuit armature current is circulated against th

impedance of the armature winding which is Zs. The voltage responsible for driving this short circuit current is internal

induced e.m.f. This can be shown in the equivalent circuit drawn in the Fig. 3.
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Fig. 3 Equivalent circuit on short circuit

From the equivalent circuit we can write,

Zs = Eph/ Iasc

Now value of Iasc is known, which can observed on the alternator. But internally induced e.m.f. can not be observe

under short circuit condition. The voltmeter connected will read zero which is voltage across short circuit. To determine Z s

is necessary to determine value of E which is driving Iasc against Zs.

Now internally induced e.m.f. is proportional to the flux i.e. field current I f.

Eph If ...... from e.m.f. equation

So if the terminal of the alternator are opened without disturbing I fwhich was present at the time of short circuite

condition, internally induced e.m.f. will remain same as Eph. But now current will be zero. Under this condition equivalen

circuit will become as shown in the Fig. 4.

Fig. 4

It is clear now from the equivalent circuit that as Ia= 0 the voltmeter reading (Voc)phwill be equal to internally induce

e.m.f. (Eph).

This is what we are interested in obtaining to calculate value of Zs. So expression for Zs can be modified as,

So O.C.C. and S.C.C. can be effectively to calculate Zs.

The value of Zs is different for different values of I fas the graph of O.C.C. is non linear in nature.

So suppose Zs at full load is required then,

Iasc = full load current.

From S.C.C. determine Ifrequired to drive this full load short circuit Ia. This is equal to 'OA', as shown in the Fig.2.

Now for this value of If, (Voc)phcan be obtained from O.C.C. Extend kine from point A, till it meets O.C.C. at point C. Th

corresponding (Voc)phvalue is available at point D.

(Voc)ph = OD

While (Iasc)ph= OE
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at full load

General steps to determine Zs at any load condition are :

i) Determine the value of (Iasc)phfor corresponding load condition. This can be determined from known full load current of th

alternator. For half load, it is half of the full load value and so on.ii) S.C.C. gives relation between (Iasc)phand If. So for (Iasc)phrequired, determine the corresponding value of Iffrom S.C.C.

iii) Now for this same value of If, extend the line on O.C.C. to get the value of (Voc)ph. This is (Voc)ph for same If, required t

drive the selected (Iasc)ph.

iv) The ratio of (Voc)phand (Iasc)ph, for the same excitation gives the value of Zs at any load conditions.

The graph of synchronous impedance against excitation current is also shown in the Fig. 2.

1.4 Regulation Calculations

From O.C.C. and S.C.C., Zs can be determined for any load condition.

The armature resistance per phase (Ra) can be measured by different methods. One of the method is applying d.c

known voltage across the two terminals and measuring current. So value of Ra per phase is known.

So synchronous reactance per phase can be determined.

No load induced e.m.f. per phase, Eph can be determined by the mathematical expression derived earlier.

where Vph = Phase value of rated voltage

Ia = Phase value of current depending on the load condition

cos = p.f. of load

Positive sign for lagging power factor while negative sign for leading power factor, Ra and Xs values are known from th

various tests performed.

The regulation then can be determined by using formula,

1.5 Advantages and Limitations of Synchronous Impedance Method

The main advantages of this method is the value of synchronous impedance Zsfor any load condition can be calculated

Hence regulation of the alternator at any load condition and load power factor can be determined. Actual load need not be

connected to the alternator and hence method can be used for very high capacity alternators.

The main limitation of this method is that the method gives large values of synchronous reactance. This leads to hig

values of percentage regulation than the actual results. Hence this method is called pessimistic method.
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M.M.F. Method of Determining Regulation

This method of determining the regulation of an alternator is also called Ampere-turn method or Rothert's M.M.F

method. The method is based on the results of open circuit test and short circuit test on an alternator.

For any synchronous generator i.e. alternator, it requires m.m.f. which is product of field current and turns of field winding fo

two separate purposes.

1. It must have an m.m.f. necessary to induce the rated terminal voltage on open circuit.

2. It must have an m.m.f. equal and opposite to that of armature reaction m.m.f.

Note : In most of the cases as number of turns on the field winding is not known, the m.m.f. is calculate and expressed

terms of the field current itself.

The field m.m.f. required to induce the rated terminal voltage on open circuit can be obtained from open circuit tes

results and open circuit characteristics. This is denoted as FO.

We know that the synchronous impedance has two components, armature resistance and synchronous reactance. No

synchronous reactance also has two components, armature leakage reactance and armature reaction reactance. In sho

circuit test, field m.m.f. is necessary to overcome drop across armature resistance and leakage reactance and also t

overcome effect of armature reaction. But drop across armature resistance and also to overcome effect of armaturreaction. But drop across armature resistance and leakage reactance is very small and can be neglected. Thus in sho

circuit test, field m.m.f. circulates the full load current balancing the armature reaction effect. The value of ampere-turn

required to circulate full load current can be obtained from short circuit characteristics. This is denoted as FAR.

Under short circuit condition as resistance and leakage reactance of armature do not play any significant role, th

armature reaction reactance is dominating and hence the power factor of such purely reactive circuit is zero lagging. Henc

FARgives demagnitising ampere turns. Thus the field m.m.f. is entirely used to overcome the armature reaction which i

wholly demagntising in nature.

The two components of total field m.m.f. which are FOand FAR are indicated in O.C.C. (open circuit characteristics) an

S.C.C. (short circuit characteristics) as shown in the Fig. 1.

Fig. 1

If the alternator is supplying full load, then total field m.m.f. is the vector sum of its two components FOand FAR. Th

depends on the power factor of the load which alternator is supplying. The resultant field m.m.f. is denoted as FR. Let u

consider the various power factors and the resultant FR.
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Zero lagging p.f.: As long as power factor is zero lagging, the armature reaction is completely demagnetising. Hence th

resultant FR is the algebraic sum of the two components FO and FAR. Field m.m.f. is not only required to produce rate

terminal voltage but also required to overcome completely demagnetising armature reaction effect.

Fig. 2

This is shown in the Fig. 2.

OA = FO

AB = FAR demagnetising

OB = FR = FO+ FAR

Total field m.m.f. is greater than FO.

Zero leading p.f.: When the power factor is zero leading then the armature reaction is totally magnetising and helps mai

flux to induce rated terminal voltage. Hence net field m.m.f. required is less than that required to induce rated voltag

normally, as part of its function is done by magnetising armature reaction component. The net field m.m.f. is the algebrai

difference between the two components FOand FAR. This is shown in the Fig. 3.

Fig. 3

OA = FO

AB = FAR magnetising

OB = FO- FAR= FR

Total m.m.f. is less than FOUnity p.f.: Under unity power factor condition, the armature reaction is cross magnetising and its effect is to distort the ma

flux. Thus and F are at right angles to each other and hence resultant m.m.f. is the vector sum of F Oand FAR. This is show

in the Fig.4.

Fig. 4

OA = FO

AB = FARcross magnetising

General Case: Now consider that the load power factor is cos . In such case, the resultant m.m.f. is to be determined b

vector addition of FO and FAR.

cos, lagging p.f.: When the load p.f. is cos lagging, the phase current I aph lags Vph by angle . The component FO is a

right angles to Vph while FARis in phase with the current Iaph. This is because the armature current Iaph decides the armatur

reaction. The armature reaction FARdue to current Iaph is to be overcome by field m.m.f. Hence while Finding resultant fie
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m.m.f.,- FAR should be added to vectorially. This is because resultant field m.m.f. tries to counterbalance armature reactio

to produce rated terminal voltage. The phasor diagram is shown in the Fig. 5.

From the phasor diagram the various magnitude are,

OA = FO , AB = FAR , OB = FR

Consider triangle OCB which is right angle triangle. The FAR is split into two parts as,

AC = FAR sin and BC = FAR cos

Fig. 5

... ( FR)

2= (FO + FAR sin )

2+ (FAR cos)

2................ (1)

From this relation (1), FRcan be determined.

cos, leading p.f.: When the load p.f. is cos leading, the phase current I aph leads Vph by . The component FO is at rig

angles to Vph and FAR is in phase with Iaph. The resultant FR can be obtained by adding - FAR to FO. The phasor diagram

shown in the Fig.6.

Fig. 6

From the phasor diagram, various magnitudes are,

AC = FAR sin and BC = FAR cos

OA = FO, AB = FAR and OB = FR

Consider triangle OCB which is right angles triangle.

... (OB)

2= (OC)

2+ (BC)

2

... ( FR)

2= (FO - FAR sin )

2+ (FAR cos) .................... (2)

From the relation (2), FRcan be obtained.

Using relations (1) and (2), resultant field m.m.f. FRfor any p.f. load condition can be obtained.

Once FRis known, obtain corresponding voltage which is induced e.m.f. E ph, required to get rated terminal voltage Vp

This is possible from open circuit characteristics drawn.
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Fig. 7

Once Ephis known then the regulation can be obtained as,

Note : To obtain Eph corresponding to FR, O.C.C. must be drawn to the scale, from the open circuit test readings.Note : This ampere-turn method gives the regulation of an alternator which is lower than the actually observed. Hence th

method is called optimistic method.

Important note : When the armature resistance is neglected then FO is field m.m.f. required to produce rated Vph at th

output terminals. But if the effective armature resistance is given then F O is to be calculated from O.C.C. such tha

FOrepresents the excitation (field current) required a voltage of Vph + Iaph Raph cos where

Vph = rated voltage per phase

Iaph = full load current per phase

Ra = armature resistance per phase

cos = power factor of the load

It can also be noted that, FRcan be obtained using the cosine rule to the triangle formed by FO, FAR and FOas shown

the Fig. 8.

Fig. 8

Using cosine rule to triangle OAB,

Students can use equations 1, 2 or 3 to calculate FR.
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The angle between Eo and Vph is denoted as and is called power angle. Neglecting Ra we can write,

Ia Xs cos = Eo sin

Pd = Vph Ia cos = internal power of machine

Note : This equation shows that the internal power of the machine is proportional to sin .

Zero Power Factor ZPF) Method

This method is also called potier method. In the operation of any alternator, the armature resistance drop and armatur

leakage reactance drop IXL are actually e.m.f. quantities while the armature reaction is basically m.m.f. quantity. In th

synchronous impedance all the quantities are treated as e.m.f. quantities as against this in M.M.F. method all are treated a

m.m.f. quantities. Hence in both the methods, we are away from reality.

Note : This method is based on the separation of armature leakage reactance and armature reaction effects. The armaturleakage reactance XL is called Potier reactance in this method, hence method is also called potier reactance method.

To determine armature leakage reactance and armature reaction m.m.f. separately, two tests are performed on th

given alternator. The two tests are,

1. Open circuit test

2. Zero power factor test

1.1 Open Circuit Test

The experimental setup to perform this test is shown in the Fig. 1.

Fig. 1

The steps to perform open circuit test are,

1. The switch S is kept open.

2. The alternator is driven by its prime mover at its synchronous speed and same is maintained constant throughout th

test.

3. The excitation is varied with the help of potential divider, from zero upto rated value in definite number of steps. The ope

circuit e.m.f. is measured with the help of voltmeter. The readings are tabulated.
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4. A graph of If and (Voc) i.e. field current and open circuit voltage per phase is plotted to some scale. This is open circu

characteristics.

1.2 Zero Power Factor Test

To conduct zero power factor test, the switch S is kept closed. Due to this, a purely inductive load gets connected to a

alternator through an ammeter. A purely inductive load has power factor of cos i.e. zero lagging hence the test is called zer

power factor test.

The machine speed is maintained constant at its synchronous value. The load current delivered by an alternator t

purely inductive load is maintained constant at its rated full load value by varying excitation and by adjusting variablinductance of the inductive load. Note that, due to purely inductive load, an alternator will always operate at zero p.

lagging.

Note : In this test, there is no need to obtain number of points to obtain the curve. Only two points are enough to construct

curve called zero power factor saturation curve.

This is the graph of terminal voltage against excitation when delivering full load zero power factor current.

One point for this curve is zero terminal voltage (short circuit condition) and the field current required to deliver full loa

short circuit armature current. While other point is the field current required to obtain rated terminal voltage while deliverin

rated full load armature current. With the help of these two points the zero p.f. saturation curve can be obtained as,

1. Plot open circuit characteristics on graph as shown in the Fig. 2.

Fig. 2

2. Plot the excitation corresponding to zero terminal voltage i.e. short circuit full load zero p.f. armature current. This point

shown as A in the Fig. 1 which is on the x-axis. Another point is the rated voltage when alternator is delivering full loa

current at zero p.f. lagging. This point is P as shown in the Fig. 1.

3. Draw the tangent to O.C.C. through origin which is line OB as shown dotted in the Fig. 1. This is called air line.

4. Draw the horizontal line PQ parallel and equal to OA.

5. From point Q draw the line parallel to the air line which intersects O.C.C. at point R. Join RQ and join PR. The triangl

PQR is called potier triangle.

6. From point R, drop a perpendicular on PQ to meet at point S.

7. The zero p.f. full load saturation curve is now be constructed by moving a triangle PQR so that R remains always o

O.C.C. and line PQ always remains horizontal. The doted triangle is shown in the Fig. 1. It must be noted that the potie

triangle once obtained is constant for a given armature current and hence can be transferred as it is.
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8. Through point A, draw line parallel to PR meeting O.C.C. at point B. From B, draw perpendicular on OA to meet it at poin

C. Triangles OAB and PQR are similar triangles.

9. The perpendicular RS gives the voltage drop due to the armature leakage reactance i.e. IXL.

10. The length PS gives field current necessary to overcome demagnetising effect of armature reaction at full load.

11. The length SQ represents field current required to induce an e.m.f. for balancing leakage reactance drop RS.

These values can be obtained from any Potier triangle such as OAB, PQR and so on.

So armature leakage reactance can be obtained as,

This is nothing but the potier reactance.

1.3 Use of Potier Reactance to Determine Regulation

To determine regulation using Potier reactance, draw the phasor diagram using following procedure :

Draw the rated terminal voltage Vph as a reference phasor. Depending upon at which power factor (cos) the regulatio

is to be predicted, draw the Current phasor Iph lagging or leading Vph by angle .

Draw Iph Raph voltage drop to Vph which is in phase with Iph. While the voltage drop Iph XLph is to be drawn perpendicular t

Iph Raph vector but leading Iph Raph at the extremely of Vph.

The Raph is to be measured separately by passing a d.c. current and measuring voltage across armature winding. Whi

XLph is Potier reactance obtained by Potier method.

Phasor sum of Vph rated, Iph Raph and Iph XLph gives the e.m.f. which is say E1ph.

Obtain the excitation corresponding to 1ph from O.C.C. drawn. Let this excitation be F f1. This is excitation required t

induce e.m.f. which does not consider the effect of armature reaction.

The field current required to balance armature reaction can be obtained from Potier triangle, which is say FAR.

... FAR = l (PS) = l (AC) = .....

The total excitation required is the vector sum of the Ff1 and FAR. This can be obtained exactly similar to the procedur

used in M.M.F. method.

Draw vector Ff1to some scale, leading E1phby 90o. Add FAR to Ff1 by drawing vector FAR in phase opposition to Iph. Th

total excitation to be supplied by field is given by FR.

The complete phasor diagram is shown in the Fig. 3.
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Fig. 3

Once the total excitation is known which is FR, the corresponding induced e.m.f. Eph can be obtained from O.C.C. Th

Eph lags FRby 90o. The length CD represents voltage drop due to the armature reaction. Drawing perpendicular from A an

B on current phasor meeting at points G and H respectively, we get triangle OHC as right angle triangle. Hence E1ph can b

determined analytically also.

Once Eph is known, the regulation of an alternator can be predicted as,

This method takes into consideration the armature resistance an leakage reactance voltage drops as e.m.f. quantitie

and the effect of armature reaction as m.m.f. quantity. This is reality hence the results obtained by this method are nearer t

the reality than those obtained by synchronous impedance method and ampere-turns method.

The only drawback of this method is that the separate curve for every load condition is necessary to plot if potie

triangles for various load conditions are required.

ASA Modification of M.M.F. Method

We have seen that neither of the two methods, M.M.F. method and E.M.F. method is capable of giving the reliabl

values of the voltage regulation. The error in the results of these methods is mainly due to the two reasons,

1. In these methods, the magnetic circuit is assumed to be unsaturated. This assumption is unrealistic as in practice. It i

not possible to have completely unsaturated magnetic circuit.

2. In salient pole alternators, it is not correct to combine field ampere turns and armature ampere turns. This is because th

field winding is always concentrated on a pole core while the armature winding is always distributed. Similarly the field an

armature m.m.f.s act on magnetic circuits having different reluctances in case of salient pole machine hence phaso

combination of field and armature m.m.f. is not fully justified.

Inspite of these short comings, due to the simplicity of constructions the ASA modified from of M.M.F. method is ver

commonly used fore the calculation of voltage regulation.
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Fig. 1

Consider the phasor diagram according to the M.M.F. method as shown in the Fig. 1 for cos lagging p.f. load. Th

FRis resultant excitation of FO and FAR where FO is excitation required to produce rated terminal voltage on open circuit whi

is m.m.f. required for balancing armature reaction effect.

Thus OB = FR= resultant m.m.f.

The angle between FAR and perpendicular to FO is , where cos is power factor of the load.

But OB = F resultant is based on the assumption of unsaturated magnetic circuit which is not true in practice. Actuall

m.m.f. equal to BB' is additional required to take into account the effect of partially saturated magnetic field. Thus the tota

excitation required is OB' rather than OB.

Let us see method of determining the additional excitation needed to take into account effect of partially saturate

magnetic circuit.

Construct the no load saturation characteristics i.e. O.C.C. and zero power factor characteristics. Draw the potie

triangle as discussed earlier and determine the leakage reactance XL for the alternator. The excitation necessary to balanc

armature reaction can also be obtained from the potier triangle. The armature resistance is known.

Construct ASA diagram, and draw phasor diagram related to the above equation.The ASA diagram has x-axis as field current and y-axis as the open circuit voltage. Draw O.C.C. on the ASA diagram

Then assuming x-axis as current phasor, draw Vph at angle , above the horizontal. The Vph is the rated terminal voltage

Add Ia Ra in phase with Ia i.e. horizontal and Ia XL perpendicular to Ia Ra to Vph. This gives the voltage E1ph.

Now with O as a central and radius E1phdraw an arc which will intersect y-axis at E1. From E1, draw horizontal lin

intersecting both air gap line and O.C.C. These points of intersection are say B and B'. The distance between the points BB

corresponding to the field current scale gives the additional excitation required to take into account effect of partiall

saturated field. Adding this to FR we get the total excitation as FR'. From this FR', the open circuit voltage E1phcan b

determined from O.C.C. using which the regulation can be determined. The ASA diagram is shown in the Fig. 2.
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Fig. 2

The resultant obtained by ASA method are reliable for both salient as well as nonsalient pole machines.
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regulatiom of alternators

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