Zero Power Factor ( ZPF) Method/Potier Triangle Method of Voltage Regulation of Alternator

Voltage regulation of synchronous machine by zero power factor method or potier method

This post is about voltage regulation of synchronous machine by zero power factor method or potier method.

Already in the previous posts we have learnt what is meant by voltage regulation of a synchronous machine. To see this post click on the below provided  link.

Advantage of calculating voltage regulation of synchronous machine by zero power factor method or potier method:

 1. In the before methods that is voltage regulation of synchronous machine by e.m.f method or synchronous impedance method and voltage regulation of synchronous machine by m.m.f method or ampere turn method  drop due to armature reaction is considered as leakage reactance drop and drop due to leakage reactance is considered as armature reaction drop respectively.So these two methods are away from reality and doesn't give correct value of voltage regulation. 

To study voltage regulation of synchronous machine by e.m.f method or synchronous impedance method and voltage regulation of synchronous machine by m.m.f method or ampere turn method refer below link:


2.But while calculating voltage regulation of synchronous machine by zero power factor method or potier method we separate armature leakage reactance and armature reaction effects and calculate voltage regulation so we get almost correct value of voltage regulation by zero power factor method or potier method. 


Tests required to be performed to calculate voltage regulation of synchronous machine by zero power factor method or potier triangle method:

As discussed above to separate armature reaction m.m.f and armature leakage reactance we perform following tests.They are:

1. Open circuit test.

2. Zero power factor test.

Open circuit test on synchronous machine:

Now let us discuss how to conduct open circuit test on synchronous machine.

Circuit diagram for conducting open circuit test on synchronous machine:

Below diagram shows circuit diagram for conducting open circuit test on synchronous machine.

Circuit connections for conducting open circuit test on synchronous machine:

1. Armature is star connected.

2. A potential divider is connected in series with the dc supply this whole setup is connected in series with the field which helps to adjust the excitation of the field.

3. A group of three parallel connected pure reactors are connected to a TPST switch S.

4. Switch S is kept open.

In this way circuit connections are to be made to conduct open circuit test on synchronous machine.

Procedure to conduct open circuit test on synchronous machine:

1. Make connections as per the circuit diagram.

2. Now with the help of prime mover make the synchronous machine to run at synchronous speed. This speed is to be maintained throughout the experiment.

3.Now switch on dc supply.With the help of potential divider vary the excitation from zero to rated value step wise and  get the open circuit e.m.f from the voltmeter . Note down all the values which helps you to draw open circuit characteristics of synchronous machine. 

4. open circuit characteristics of synchronous machine is a graph between If and (Voc)ph.

Here,

 If = Field current.

(Voc)ph = open circuit voltage per phase.

Observations table for open circuit test on synchronous machine:

               If A
    Voc(Line)   V
 Voc(phase) = Voc(line)/






Zero power factor test on synchronous machine:

Now let us discuss how to conduct zero power factor test on synchronous machine.

Circuit diagram for conducting zero power factor test on synchronous machine:

Below diagram shows circuit diagram for conducting zero power factor test on synchronous machine.


Circuit connections for conducting zero power factor test on synchronous machine:

1. Armature is star connected.

2. A potential divider is connected in series with the dc supply this whole setup is connected in series with the field which helps to adjust the excitation of the field.

3. A group of three parallel connected pure reactors are connected to a TPST switch S.

4. Switch S is kept closed.

In this way circuit connections are to be made to conduct zero power factor test on synchronous machine.

Procedure to conduct zero power factor test on synchronous machine:

1. Make connections as per the circuit diagram.

2. Now with the help of prime mover make the synchronous machine to run at synchronous speed. This speed is to be maintained throughout the experiment.
tive.
3. As the switch S is closed  power is delivered to the purely reactive load by synchronous machine. The power delivered to the load is to be maintained at its rated full load value by adjusting the variable reactance of the reactor(inductor) and also by varying the excitation of field.

4. As the load is purely reactive load alternator will operate at zero power factor lagging.

5. Here the values to be noted are not many only two values are required to plot the graph for zero power factor test.

What are the requirements for plotting the graph to calculate the values of leakage reactance drop and armature reaction drop ?

1. Firstly we need to draw the open circuit characteristics of synchronous machine curve . This can be obtained by plotting the graph between open circuit voltage against field current whose values are obtained by conducting open circuit test on synchronous machine.

2. To obtain zero power curve we require two points they are:

a)  At short circuit condition field current required to give full load short circuit armature current.

b) Field current required to give rated terminal voltage while delivering rated full load armature current.

Graph for calculating the values of leakage reactance drop and armature reaction drop:

Steps for drawing the graph to calculate the value of leakage reactance drop and armature reaction drop:

1. Draw the open circuit characteristics curve. For different values of field current plot its corresponding values of open circuit voltage whose values are already tabulated by conducting the open circuit test on alternator

2. Now plot the full load zero power factor curve by using two values.

a) Field current at short circuit full load zero power factor armature current which is denoted by A.

b) Field current required to give rated terminal voltage while delivering rated full load armature current which is denoted by P.

3. To the open circuit characteristics curve draw a tangent through the origin. This is called air gap line it is shown in the graph by dotted line OB.

4.Now draw a line PQ which is parallel and equal to OA as seen in the graph.

5.Now draw a line parallel to air gap line from Q such that it intersects the open circuit characteristics curve at R.

6. Now join RQ and RP. 

7. The triangle obtained is called potier triangle.


8. Now from point R draw a perpendicular on to QP. It touches QP at point S.

9. The potier triangle obtained is constant for a given armature current.

10. Now draw a line parallel to PR through point A such that it meets the open circuit characteristics curve at B.

11. Now draw a perpendicular to OA from B which intersects OA at point C. 

12. Now triangles OAB and PQR are similar triangles.

13. The length of the perpendicular RS gives the voltage drop due to armature leakage reactance i.e. XLph.

14. The length of PS gives field current required to overcome demagnetizing effect of armature reaction at full load.

15. Length SQ represents field current required to induce an e.m.f for balancing leakage reactance drop RS.

So armature leakage reactance can be obtained as follows

length (RS) = length( BC) = (Iaph)f.l × Xlph.

Xlph = length (RS) or  length( BC) / (Iaph)f.l

Xlph is called potier reactance.

Determination of voltage regulation by zero power factor method or potier method using potier reactance:

In order to determine voltage regulation by zero power power factor method or potier method using potier reactance we need to draw a phasor to get required values i.e Eph and Vph.

Steps to draw phasor for calculating voltage regulation by zero power factor method or potier method using potier reactance:

1. Take the rated terminal voltage Vph as reference vector.

2. Depending upon the power factor cos𝞍 calculate value of 𝞍 and draw current phasor Iph lagging or leading Vph by an angle 𝞍.

3. Draw IphRaph voltage drop to Vph and it should be in phase with Iph.

4. Volatge drop IphXlph is to be drawn perpendicular to IphRaph vector and leading this IphRaph at the extreme point of Vph.

5.Raph is measure by applying known dc voltage to the Raph and calculating the current value Raph can be obtained by Raph = V/I.

6. Here Xlph is potier reactane.

Now we get E1ph from the above calculated values and it is given by,


7.Now from open circuit characteristics graph obtain value of excitation Ff1 corresponding to E1ph vector.

8.This Ff1 gives excitation required to induce e.m.f without considering the effect of armature reaction.

9. Field current  Far required to balance armature reaction can be obtained from potier triangle. 

10. Far = length ( PS ) = length ( AC).

11. Now the total excitation required is the vwctor sum of Ff1 and Far.

12. The procedure to obtain this is same as the procedure used in calculation of voltage regulation of synchronous machine by m.m.f method or ampere turn method.

You can see this post on voltage regulation by m.m.f method or ampere turn method from the below provided link.

13. Draw a vector Ff1 leading E1ph by 90°.

14. Iph anf Far are in same phase. Now Add -Far and Ff1.

15. Far can be obtained by drawing a vector opposite to Iph.

16. The total excitation to be supplied by field is nothing but Fr which is the resultant m.m.f or field m.m.f.

Phasor diagram for calculating voltage regulation by zero power factor method or potier method using potier reactance:


Steps for calculating voltage regulation of synchronous by zero power factor method or potier method using potier reactance:

1.Total excitation Fr is calculated by adding -Far and Ff1.

2. Now for this Fr corresponding value of e.m.f is calculated from open circuit characteristics graph. To understand refer  calculation of voltage regulation of synchronous machine by m.m.f method or ampere turn method this link is already provided above.

3. length CD represents drop due to armature reaction.

4. Now draw perpendiculars from A and B onto current phasor. It intersects current phasor at points G and H respectively.

5. Now we obtain a right angled triangle OHC.

6. Now E1ph can be determined analytically by using pythogerous theorem.

(E1ph)2 =  (Iph)2 + (Iph Rph + Iph Xph)2

7. In the similar manner we obtain Eph by using pythogerous theorem.

(Eph)2 =  (Iph)2 + (Iph Rph + Iph Xph)2+ Armature reaction drop.

Now voltage regulation of synchronous machine by zero power factor method or potier triangle method is calculated by using,

Voltage Regulation%  = (Eph - Vph / Vph) × 100

Here we get almost accurate value of voltage regulation as we have considered drops due to leakge reactance and armature reaction separately. Because of few assumptions made we get small deviation of voltage regulation from actual value of voltage regulation.

Assumptions made in calculating voltage regulation of synchronous machine by using zero power factor method or potier method:

1.Armature resistance is neglected in over all calculation of voltage regulation of synchronous machine by zero power factor method or potier triangle method. As this value is there will be no significant error due to this assumption.

2. Perfect reactor(inductor) is not present so practically we don't get zero power factor load.

look at graph that we have considered for calculating potier reactance.


3. In this we have assumed distances RS , R'S' and BC as equal. Which means that leakage reactance drop in power factor test and short circuit test are equal. But this cant be same as the excitation under short circuit condition i.e at point A is OA while for zero power factor test i.e, point P is OA'.Excitation OA' is higher than OC. P corresponds to saturation condition and has larger leakage flux. As this value is assumed to be unchanged we get error due to this.

In this way we calculate voltage regulation of synchronous machine by zero power factor method or potier method.

Voltage regulation of synchronous machine by M.M.F method or ampere turn method

Calculation of voltage regulation of synchronous machine by M.M.F method or ampere turn method 

In this post let us see how to calculate voltage regulation of synchronous machine by M.M.F method or ampere turn method.

Requirements for Calculating voltage regulation of synchronous machine by M.M.F method or ampere turn method:

1.  Any synchronous machine requires m.m.f to induce rated terminal voltage on open circuit. This m.m.f is denoted by Fo. To calculate this we conduct open circuit test on synchronous machine.

2. In the same way a synchronous machine also requires  m.m.f  to act opposite to armature reaction such that it helps full load current to flow in the armature.This m.m.f is denoted by Far.To calculate this we conduct short circuit test on synchronous machine.

3. From open circuit test on synchronous machine we obtain open circuit characteristics of synchronous machine and from short circuit test on synchronous machine we obtain short circuit characteristics of synchronous machine.

For details about open circuit test on synchronous machine , open circuit characteristics of  synchronous machine and short circuit test on synchronous machine , short circuit characteristics of synchronous machine refer below link.

Graph for calculating voltage regulation of synchronous machine by M.M.F method or ampere turn method:

The graph shown below is the combined graph of open circuit characteristics of synchronous machine and short circuit characteristics of synchronous machine.


Note: As in many cases we don't know the number of turns though m.m.f is product of current and turns here we express m.m.f in terms of field current.

What is meant by Fo and Far ?

Now let us see in detail about Fo and Far

1.Fo is the field m.m.f required to induce rated terminal voltage when the armature is open circuited. This value can be obtained from open circuit characteristics of synchronous machine by conducting open circuit test on synchronous machine.

2. Synchronous impedance has two components namely synchronous reactance and armature resistance .

3. Synchronous resistance further contains two components namely armature leakage reactance and armature reaction reactance.

4. In short circuit test on synchronous machine field m.m.f is required to overcome drop across armature resistance, leakage reactance and armature reaction and allow full load current to pass through short circuited armature. But the drop due to armature resistance, leakage reactance is very small and can be neglected. So the m.m.f required to allow full load current to pass through short circuited armature by balancing armature reaction is Far which can be obtained from short circuit characteristics of synchronous machine by conducting short circuit test on synchronous machine.

Calculation of resultant m.m.f Fr for calculating voltage regulation of synchronous machine by M.M.F method or ampere turn method:

When the alternator supplies full load the total field m.m.f Fr is the vector sum of Fo and Far. And this depends on the  power factor of load which the synchronous machine is supplying.

Now lets see how Fr is calculated for different load conditions:

Zero lagging power factor load:

1. If the load has zero power factor lagging then the armature reaction is demagnetizing in nature.

2. So resultant m.m.f Fr is algebraic sum of two vectors Fo and Far.

3. So here field m.m.f should be able to provide not only rated terminal voltage but also it should overcome demagnetizing armature reaction.

This can be represented as follows:


OA = Fo

AB = Far

OB = Fr = Fo + Far

This shows total field m.m.f is greater than Fo.

Steps to draw vector diagram for calculating resultant m.m.f Fr for  lagging power factor load:

1.  load power factor is lagging and it is represented by cos𝞍. So draw phase current Iaph  which lags Vph by an angle 𝞍.

2. Fo is at right angle to Vph.

3. Far will be in phase with the Iaph because armature current Iaph decides armature reaction.

4. This Far has to be overcome by resultant m.m.f  Fr which is also called field m.m.f so - Far should be added to Fo vertically so that Fr counter balances armature reaction and produce rated voltage.

Phasor diagram for calculating resultant m.m.f Fr for lagging power factor load:

Expression for resultant m.m.f or field m.m.f Fr for lagging power factor load:

From diagram,

OA =  Fo 

AB = Far

OB = Fr

From right angled triangle OCB

Far can be split into two parts 

AC = Far sin𝞍

BC = Far cos𝞍


Hence, Fr can be calculated in this way.


 Calculating voltage regulation of synchronous machine by M.M.F method or ampere turn method for lagging power factor load:

To calculate voltage regulation of synchronous machine by m.m.f method or ampere turn method draw the graph of open circuit characteristics of synchronous machine and short circuit characteristics of synchronous machine and indicate values of Fo , Far , Fr as shown below.

Graph for calculating voltage regulation of synchronous machine by M.M.F method or ampere turn method for lagging power factor load:



Steps for calculating voltage regulation of synchronous machine by M.M.F method or ampere turn method for lagging power factor load from graph:

1. Calculate Fo value from open circuit test on synchronous machine and mark it on x - axis. Now extend this point on to open circuit characteristics of synchronous machine curve and extend this point on y - axis which gives the value of Vph of synchronous machine.

2. Calculate Far value from short circuit test on synchronous machine and mark it on x - axis. Now extend this point on to short circuit characteristics of synchronous machine line and extend this point on y - axis which gives the value of rated Isc of synchronous machine.

3. Now calculate Fr value from the equation

 and and mark it on x - axis. Now extend this point on to open circuit characteristics of synchronous machine curve and extend this point on y - axis which gives the value of Eph of synchronous machine.

So finally we get voltage regulation of synchronous machine by m.m.f method or ampere turn method  for lagging power factor load by using below formula

Voltage regulation% = (Eph - Vph / Vph) × 100.

Hence in this way we have calculated voltage regulation of synchronous machine by m.m.f method or ampere turn method  for lagging power factor load.

Zero leading power factor:

1. If the load has zero power factor leading then the armature reaction is magnetizing in nature.

2. This will help main flux to induce rated terminal voltage.

3. So net m.m.f is less than that required to produce rated voltage.

4. So net m.m.f is algebraic difference between the two components Fo and Far.

This can be represented as follows:

OA = Fo

AB = Fr

OB = Fr = Fo - FAar

This shows total m.m.f is less than Fo.

Steps to draw vector diagram for calculating resultant m.m.f  for  lagging power factor load:

1.  load power factor is leading and it is represented by cos𝞍. So draw phase current Iaph  which leads Vph by an angle 𝞍.

2. Fo is at right angle to Vph.

3. Far will be in phase with the Iaph because armature current Iaph decides armature reaction.

4. Fr is obtained by adding - Far to Fo.

Phasor diagram for calculating resultant m.m.f Fr for leading power factor load:


Expression for resultant m.m.f or field m.m.f  Fr for leading power factor load:

From diagram,

AC = Far sin𝞍

BC = Far cos𝞍

OA = Fo

AB = Far

OB = Fr

From right angled triangle OCB


Hence, Fr can be calculated in this way.

Calculating voltage regulation of synchronous machine by M.M.F method or ampere turn method for leading power factor load:

To calculate voltage regulation of synchronous machine by m.m.f method or ampere turn method draw the graph of open circuit characteristics of synchronous machine and short circuit characteristics of synchronous machine and indicate values of Fo , Far , Fr as shown below.

Graph for calculating voltage regulation of synchronous machine by M.M.F method or ampere turn method for leading power factor load:


Steps for calculating voltage regulation of synchronous machine by M.M.F method or ampere turn method for leading power factor load from graph:

1. Calculate Fo value from open circuit test on synchronous machine and mark it on x - axis. Now extend this point on to open circuit characteristics of synchronous machine curve and extend this point on y - axis which gives the value of Vph of synchronous machine.

2. Calculate Far value from short circuit test on synchronous machine and mark it on x - axis. Now extend this point on to short circuit characteristics of synchronous machine line and extend this point on y - axis which gives the value of rated Isc of synchronous machine.

3. Now calculate Fr value from the equation
and and mark it on x - axis. Now extend this point on to open circuit characteristics of synchronous machine curve and extend this point on y - axis which gives the value of Eph of synchronous machine.

So finally we get voltage regulation of synchronous machine by m.m.f method or ampere turn method  for leading power factor load by using below formula.

Voltage regulation% = (Eph - Vph / Vph) × 100.

Hence in this way we have calculated voltage regulation of synchronous machine by m.m.f method or ampere turn method  for leading power factor load.

Important point to be noted while calculating voltage regulation of synchronous machine by m.m.f method or ampere turn method :

Fo is the field m.m.f required to give rated Vph when armature resistance is neglected. But if armature resistance Raph is given then Fo calculated from open circuit characteristics of synchronous machine represents excitation required to produce voltage of Vph + Iph Ra cosπ›Ÿ

Vph = rated voltage per phase.

Iaph = full load current per phase.

Ra = armature resistance per phase.

cosπ›Ÿ = power factor of load.

Calculation of resultant m.m.f Fr by cosine rule:


Resultant m.m.f  Fr can be calculated from cosine rule for both lagging and leading power factor loads.

Phasor diagrams:


by using cosine rule from triangle OAB,


In this way we can calculate Fr from cosine rule.

And hence calculate voltage regulation of synchronous machine by m.m.f method or ampere turn method  by using

Voltage regulation% = (Eph - Vph / Vph) × 100.

Where Eph and Vph can be calculated from open circuit characteristics of synchronous machine and short circuit characteristics of synchronous machine as seen above.

In this method drop due to leakage reactance is also considered as drop due to armature reaction so we get voltage regulation less than actual regulation. Hence it is called optimistic method. 

Today we have learnt how to calculate voltage regulation of synchronous machine by m.m.f method or ampere turn method . 

In the next post we are going to learn  voltage regulation of synchronous machine by zero power factor method or potier method.

You can download this post on  voltage regulation of synchronous machine by m.m.f method or ampere turn method  as PDF here.






 































   










Voltage Regulation of Synchronous Machine (Alternator) by E.M.F Method or Synchronous Impedance Method.

Voltage regulation of synchronous machine by EMF method or synchronous impedance method

In this post we are going to learn how to calculate voltage regulation of synchronous machine by EMF method or synchronous impedance method.

Requirements for calculating voltage regulation by EMF method or synchronous impedance method:
1. Per phase resistance of armature Ra.

2.Graph of open circuit characteristics which is drawn between open circuit voltage and field current. This can be obtained by conducting open circuit test on the alternator.

3.Graph of short circuit characteristics which is drawn between short circuit voltage and field current. This can be obtained by conducting short circuit test on the alternator.
Open circuit test on synchronous machine:
Let's see how open circuit test on synchronous machine is done.
Circuit diagram for conducting open circuit test on synchronous machine:

Circuit connections for conducting open circuit test on synchronous machine:
1.Firstly connections are to be made as given in the circuit diagram:

2. Armature is connected to TPST switch terminals on one side the terminals of TPST switch on other side are short circuited with the help of ammeter.

3. An alternator is coupled to the prime mover which can drive the alternator at synchronous speed.

4. A voltmeter is connected across the lines to measure the open circuit voltage of alternator.

5. A rheostat is connected in series with the field winding. 

6. Field winding is excited by using D.C supply and flux is adjusted by adjusting the rheostat. Flux adjustment is nothing but adjust the current flow through field winding.
Procedure for conducting open circuit test on synchronous machine:
1. By adjusting the prime mover make the synchronous machine to run at synchronous speed.

2.Now rheostat in the field circuit is kept at maximum position and switch on dc supply.

3. Now keep TPST switch in the open position.

4. Now by adjusting the rheostat field current is changed from minimum to maximum and the corresponding values of open circuit voltage is noted down.
Observations table for open circuit test on synchronous machine:
               If A
    Voc(Line)   V
 Voc(phase) = Voc(line)/







By using above table draw the graph between E0 against If
Graph of open circuit characteristics of synchronous machine:
This is called open circuit characteristics of synchronous machine which is obtained by conducting open circuit test on synchronous machine.

Short circuit test on synchronous machine:
Let's see how short circuit test on synchronous machine is done.
Circuit diagram for conducting short circuit test on synchronous machine:
Circuit connections for conducting short circuit test on synchronous machine:
1.Firstly connections are to be made as given in the circuit diagram:

2. Armature is connected to TPST switch terminals on one side the terminals of TPST switch on other side are short circuited with the help of ammeter.

3. An alternator is coupled to the prime mover which can drive the alternator at synchronous speed.

4. A voltmeter is connected across the lines to measure the open circuit voltage of alternator.

5. A rheostat is connected in series with the field winding. 

6. Field winding is excited by using D.C supply and flux is adjusted by adjusting the rheostat. Flux adjustment is nothing but adjust the current flow through field winding.
Procedure for conducting short circuit test on synchronous machine:
1. By adjusting the prime mover make the synchronous machine to run at synchronous speed.

2.Now rheostat in the field circuit is kept at maximum position and switch on dc supply so field current will have minimum value.

3.Now close the TPST switch as the ammeter has negligible resistance armature will be short circuited.

4.Adjust the field excitation until full load current is obtained through the ammeter connected to armature circuit. 

5. Note down short circuited armature current value for different values of field current.
Observations table for short circuit test on synchronous machine:
               If A
    Iasc A





By using above table draw the graph between Iasc against If.

Graph of short circuit characteristics of synchronous machine:

The above graph is called short circuit characteristics of synchronous machine and is obtained by conducting short circuit test on synchronous machine. This curve resembles a B-H curve of a magnetic material.
Calculating synchronous impedance Zs from open circuit characteristics and closed circuit characteristics:
Now let's calculate synchronous impedance of synchronous machine. 
Requirements for calculating synchronous impedance:
1.To calculate synchronous impedance we require values of open circuit emf and short circuit current

2.From short circuit test on synchronous machine short circuit current can be calculated and from open circuit test on synchronous machine open circuit voltage can be calculated
Short circuit test on synchronous machine equivalent circuit:

Procedure for calculating Short circuit current:
1.External load impedance of short circuit test is zero
2.So short circuit armature current flows through the impedance Zs. 
3. voltage responsible for this short circuit current to flow is emf which is induced internally.

Now from the circuit,

                                     Zs = Eph / Iasc.

The value of Iasc can be noted down from the ammeter reading but the voltmeter reading will be zero as it shows voltage across the short circuited terminals. So we need to calculate  calculate the voltage which helps Iasc to flow through  Zs which can be calculated by conducting open circuit test on synchronous machine
Open circuit test on synchronous machine equivalent circuit:

Procedure for calculating open circuit voltage:
From E.M.F equation we know that 

Internally induced emf Eph is directly proportional to flux which means field current

Eph 𝝰 𝞍 𝛂 If

1.  If is kept same as before in the short circuit test.

2. Now terminals of the synchronous machine is removed.

3. As If is same internally induced E.M.F will be same but current will be zero.

4. Now ammeter gives zero reading but voltmeter gives the open circuit e.m.f which is equal to internally induced e.m.f.

Now Eph = (Voc)ph since open circuit.

Now we can calculate synchronous impedance as

Zs = phase voltage on open circuit / phase current on short circuit ,at same excitation 

Zs = (Voc)ph / (Iasc)ph at same  If

In this way we can calculate Zs from open circuit characteristics of synchronous machine and short circuit characteristics of synchronous machine.

As Zs is different for different values of If we can calculate it from graph of open circuit characteristics of synchronous machine and short circuit characteristics of synchronous machine.

To calculate synchronous impedance Zs we need to draw open circuit characteristics and short circuit characteristics on a same graph as shown below:

Graph for open circuit characteristics and closed circuit characteristics:

Procedure for calculating  synchronous impedance from open circuit characteristics of synchronous machine and short circuit characteristics of synchronous machine:

1. From short circuit characteristics of synchronous machine determine If required to drive full load short circuit current.

2. From the same  If value draw a line such that it touches both open circuit characteristics of synchronous machine and short circuit characteristics of synchronous machine.

3. Now extend this line on to Y-axis which gives open circuit voltage and short circuit current.

4. Now calculate Zs from the below formula

Zs = (Voc)phase /  (Iasc)phase where If is constant and If is at Isc = Irated.

It can also be calculated for different load conditions the process is same but Isc may not be equal to rated for the corresponding  If.

Calculation of voltage regulation by E.M.F method or synchronous impedance method:

Now let's calculate voltage regulation of synchronous machine by E.M.F method or synchronous impedance method.

Few requirements are there to calculate voltage regulation of synchronous machine by E.M.F method or synchronous impedance method.

Requirements for calculating voltage regulation of synchronous machine by E.M.F method or synchronous impedance method:

1. Armature resistance per phase. This can be calculated by many methods one of the ways is applying known dc voltage across the two terminals and calculating the value of current. Now 
Ra will be

Ra = v / i

2. synchronous impedance Zs which we have calculated in the before steps.

Expression for for calculating voltage regulation of synchronous machine by E.M.F method or synchronous impedance method:
Now let's see derivation for calculating voltage regulation of synchronous machine by E.M.F method or synchronous impedance method

Now, 

From this synchronous reactance per phase is determined

Now no load E.M.F per phase Eph can be calculated by the following expression:


For lagging power factor we use positive sign and for leading power factor we use negative sign.

Now voltage regulation of synchronous machine by E.M.F method or synchronous impedance method is given by

Voltage regulation% = (Eph - Vph / Vph) × 100.

Value of Eph is calculated from above expression.

So we have determined voltage regulation of synchronous machine by E.M.F method or synchronous impedance method.

Advantage of  Calculating voltage regulation by E.M.F method or synchronous impedance method:
1. Zs at any load value can be determined so voltage regulation of alternator  at any load condition and load power factor can be calculated

2. Total actual load need not to be connected for determining voltage regulation of synchronous machine by E.M.F method or synchronous impedance method.

Limitations of  Calculating voltage regulation by E.M.F method or synchronous impedance method:
Here we have considered drop due to armature reaction as additional leakage reactance this method gives large values of synchronous reactance. This gives large values of percentage voltage regulation than actual value. This method is also called Pessimistic method.