Showing posts with label Alternator. Show all posts
Showing posts with label Alternator. Show all posts

How to Draw Potier Triangle/ZPF Characteristics ?

Regulation by Zero Power Factor ( ZPF) method  of Alternator:

During the operation of the alternator, resistance voltage drop IaRand armature leakage reactance drop IaXL are actually emf quantities and the armature reaction reactance is a mmf quantity. To determine the regulation of the alternator by this method OCC, SCC and ZPF test details and characteristics are required.

-As explained earlier OC and SC tests are conducted and OCC and SCC are drawn.

-ZPF test is conducted by connecting the alternator to ZPF load and exciting the alternator in such way that the alternator supplies the rated current at rated voltage running at rated speed.
-To plot ZPF characteristics only two points are required. One point is corresponding to the zero voltage and rated current that can be obtained from scc and the other at rated voltage and rated current under zpf load.
-This zero power factor curve appears like OCC but shifted by a factor IXL vertically and horizontally by armature reaction mmf as shown below in figure. 



Following are the steps to draw ZPF characteristics:

-By suitable tests plot OCC and SCC. Draw air gap line. Conduct ZPF test at full load for rated voltage and fix the point B.

-Draw the line BH with length equal to field current required to produce full load
current on short circuit..
-Draw HD parallel to the air gap line so as to cut the OCC. Draw DE perpendicular to HB or parallel to voltage axis.
-Now, DE represents voltage drop IXL and BE represents the field current required to overcome the effect of armature reaction.
-Triangle BDE is called Potier triangle and XL is the Potier reactance. Find E from V, IRa, IXL and .
-Use the expression E =√ (V cos  ร˜+ IRa)² + (V sin ) + IXL)² to compute E. Find field current corresponding to E. Draw FG with magnitude equal to BE at angle (90+ ) from field current axis, where is the phase angle of current from voltage vector E (internal phase angle).
-The resultant field current is given by OG. Mark this length on field current axis. From OCC find the corresponding E0. Find the regulation.

Differences Between Electrical Degree And Mechanical Degree

Differences between electrical degree and mechanical degree

Many people get confused about what is electrical degree and mechanical degree. Well, to get a clear idea about this we have provided the following post.

We consider an alternator with two poles once and four poles once to clearly understand about electrical degree and mechanical degree.An alternator consists of conductors on stator and poles on rotor. But for understanding purpose we consider conductors are rotating and poles are stationary. Because of relative motion between conductors and poles emf is induced inside the conductor.

Two pole alternator:

Consider a two pole alternator with a conductor as shown in the following figure.
Position 1 :At this point velocity vector V is parallel to magnetic flux lines of poles(indicated by dotted line). So at this position conductors do not cut the flux lines, there will not be change in flux so emf induced inside the conductor is zero.

Position 2: Now conductor rotates to position 2.Velocity vector V is perpendicular to magnetic flux lines of poles. So at this position maximum amount of flux is cut by conductors, there will be maximum amount of change in flux so emf induced is maximum at this point.

Position 3: Now conductor rotates to position 3.At this point velocity vector V is parallel to magnetic flux lines of poles.So at this position conductors do not cut the flux lines, there will not be change in flux so emf induced inside the conductor is zero.

Position 4: Now conductor rotates to position 4.Velocity vector V is perpendicular to magnetic flux lines of poles. So at this position maximum amount of flux is cut by conductors, there will be maximum amount of change in flux so emf induced is maximum at this point.

So for one complete rotation of a conductor i.e, 360 degrees there will be two maximum positions of emf this is indicated in the following figure.

Induced emf inside the alternator is sinusoidal in nature.Two maximum peaks is 360 degrees.Conductor rotation angle is mechanical degree and emf wave cycle degree for one complete rotation of conductor gives electrical degree.

Here mechanical degree is equal to electrical degree which is 360 degrees. Since for one complete rotation of conductor one complete emf cycle is produced.

Four pole alternator:

Consider a four pole alternator with a conductor as shown in the following figure.



Position 1 :At this point velocity vector V is parallel to magnetic flux lines of poles(indicated by dotted line). So at this position conductors do not cut the flux lines, there will not be change in flux so emf induced inside the conductor is zero.

Position 2: Now conductor rotates to position 2.Velocity vector V is perpendicular to magnetic flux lines of poles. So at this position maximum amount of flux is cut by conductors, there will be maximum amount of change in flux so emf induced is maximum at this point.

Position 3: Now conductor rotates to position 3.At this point velocity vector V is parallel to magnetic flux lines of poles.So at this position conductors do not cut the flux lines, there will not be change in flux so emf induced inside the conductor is zero.

Position 4: Now conductor rotates to position 4.Velocity vector V is perpendicular to magnetic flux lines of poles. So at this position maximum amount of flux is cut by conductors, there will be maximum amount of change in flux so emf induced is maximum at this point.

Position 5: Now conductor rotates to position 5.At this point velocity vector V is parallel to magnetic flux lines of poles.So at this position conductors do not cut the flux lines, there will not be change in flux so emf induced inside the conductor is zero.

Position 6: Now conductor rotates to position 6.Velocity vector V is perpendicular to magnetic flux lines of poles. So at this position maximum amount of flux is cut by conductors, there will be maximum amount of change in flux so emf induced is maximum at this point.

Position 7: Now conductor rotates to position 7.At this point velocity vector V is parallel to magnetic flux lines of poles.So at this position conductors do not cut the flux lines, there will not be change in flux so emf induced inside the conductor is zero.

Position 8: Now conductor rotates to position 8.Velocity vector V is perpendicular to magnetic flux lines of poles. So at this position maximum amount of flux is cut by conductors, there will be maximum amount of change in flux so emf induced is maximum at this point.

So for one complete rotation of a conductor i.e, 360 degrees there will be four maximum positions of emf this is indicated in the following figure.
°


Induced emf inside the alternator is sinusoidal in nature.Four maximum peaks is 720 degrees.Conductor rotation angle is mechanical degree and emf wave cycle degree for one complete rotation of conductor gives electrical degree.

Here mechanical degree is 360 degrees and electrical degree is 720 degrees.  Since for one complete rotation of conductor two complete emf cycles are produced.

This says that electrical degree depends on number poles inside the alternator. Now we can obtain relation between mechanical degree and electrical degree as

360° mechanical = 360° ✕ P/2 electrical

P = number of poles

1° mechanical = (P/2)° electrical.

In this post we have discussed about difference between mechanical degree and electrical degree.

Synchronization of Alternator and Methods of Synchronization of alternator || Parallel Operation of Alternators/Generators

Synchronization of alternator and methods of synchronization of alternator

What is meant by synchronization of alternator?

Connecting a group of alternators parallel to a bus bar and the alternators should have same voltage and frequency as that of bus-bar. This is called synchronization of alternator. There are some conditions to be satisfied by the alternators which are to be connected in parallel to bus-bar to be in synchronization.

Conditions for synchronization of alternators: 

1. The terminal voltage of incoming alternator must be equal to the bus bar voltage.

2. The frequency of voltage generated by incoming alternator must be equal to busbar frequency.

3.The phase sequence of the three phases of the incoming alternator must be same as phase sequence of bus-bars.

4. The phase angle between the voltage generated by incoming alternator and voltage of bus-bar must be zero.

5. Always connect running alternator to bus-bar. If a stationary alternator is connected to bus-bar it will result in short circuit of stator winding.

The above conditions are to be satisfied by alternators to satisfy synchronization.

Why synchronization of alternators is necessary?

1.An alternator cannot deliver power to electric power system until its voltage,frequency,phase sequence and other parameters matches with the network to which the the alternator is connected.

2. The case of synchronization arises because we are connecting many alternators in parallel to supply the demanded load. So we need to match all the parameters of connected alternators with bus-bar to deliver power to load.

3. By synchronization we can match all the parameters of one alternator with the other alternator and also with the bus-bar and deliver the required power to load.

4. Synchronization of alternator is also called as paralleling of alternators.

Advantages of paralleling of alternators: 

We get a common doubt why we need to supply the load by paralleling small units of alternator rather than using a single larger unit? This is because we have many advantages by doing so. They are:

Continuity of service: 

In case of any damage to one of the alternators it can be removed.Supply to load is not interrupted because other alternators can supply the required load. But if u use a larger single unit even a small damage causes the interruption of supply.

Requirement of load:

As the load demanded is not same all the time, during light load periods we can run two or three alternators in parallel. When the demand is high we can add the required amount of alternators in parallel to meet the load demanded.

Reliability:

Several single units connected in parallel is more reliable than single larger unit because if a single unit gets damaged it can be removed and its work is compensated by other units which are running.

High efficiency:

An alternator runs efficiently when it is loaded at their rated value. By using required number of alternators for required demand i.e, light load or peak load we can load an alternator efficiently.

So because of above advantages we use paralleling of alternators.

Steps to connect alternators in parallel or synchronization of alternators:



1.Consider an alternator-1. It is supplying power to bus bar at rated voltage and frequency.

2. Now we need to connect another alternator let it be alternator-2 in parallel with the alternator-1. In order to match the frequency of alternator-2 with the frequency of bus-bar or alternator-1 (since alternator-1 and bus-bar are already in synchronism) we need to adjust the speed of alternator-2. Now the voltage of alternator-2 is to be matched with the voltage of bus-bar or voltage of alternator-1 (since alternator-1 and bus-bar are already in synchronism). For this purpose we need to vary the field rheostat until the voltage matches.

3. The three phase voltages generated by alternator must be same as the three phase voltages of bus-bar or alternator-1(since alternator-1 and bus-bar are already in synchronism).This can be achieved by matching the phase sequence and frequency of alternator-2 with bus bar or alternator-1(since alternator-1 and bus-bar are already in synchronism) phase sequence and frequency.

By following these steps synchronization of alternators is possible.


Methods for synchronization of alternators:

There are three methods for synchronization of alternators. These methods check whether the above mentioned conditions for synchronization of alternators is satisfied or not. The three methods are.

1. Three dark lamps method.

2. Two bright, One dark method.

3. Synchroscope method.

Three dark lamps method for synchronization of alternators:

Let us study synchronization of alternators using three dark lamps method in detail.

Circuit diagram for synchronization of alternators using three lamp method:




Procedure:

1. Consider alternator-1 is supplying power to load at rated voltage and rated frequency which means alternator-1 is already in synchronism with bus-bar.

2. Now we need to connect alternator-2 in parallel with alternator-1.

3. Across the 3 switches of alternator-2 three lamps are connected as shown in the figure.

4. To match the frequency of alternator-2 with the bus-bar frequency we need to run the prime mover of alternator-2 at nearly synchronous speed which is decided by the frequency of bus-bar and number poles present in alternator-2.

5. To match the terminal voltage of alternator-2 with bus-bar voltage we need to adjust the field current of alternator-2 until terminal voltage of alternator-2  matches with the bus-bar voltage. The required value of voltage can be seen in the voltmeter connected to bus-bar.

6.To know whether the phase sequence of alternator -2 matches with the bus-bar phase sequence we have a condition. If all the three bulbs ON and OFF concurrently then we say the phase sequence of alternator-2 matches with the phase sequence of  bus-bar. If the bulbs ON and OFF one after the other then the phase sequence is mismatching.

7. To change the connections of any two leads during the mismatch of phase sequence first off the alternator and change the connections.

8. ON and OFF rate of bulbs depends upon frequency difference of alternator-2 voltage and bus-bar voltage. Rate of flickering of bulbs is reduced when we match the frequency of alternator-2 with bus-bar voltage by adjusting the speed of prime mover of alternator-2

9. If all the conditions required for synchronization are satisfied then the lamps will become dark. 

10. Now close the switches of alternator -2 to synchronize with alternator-1.

11. Now the alternators are in synchronism.

Disadvantage of three dark lamps method for synchronization of alternators:

Flickering only says difference between frequency of voltages of alternator and bus bar but correct value of frequency of voltage of alternator cannot be found.

For example, if the bus bar frequency of voltage is 50 HZ and difference in frequency of voltage of bus-bar and alternator is 1 HZ the alternator frequency of voltage can be either 49 HZ or 51 HZ.

Two bright and one dark lamp method for synchronization of alternators:

Let us discuss synchronization of alternator using two bright and one dark lamp method.

Circuit diagram for synchronization of alternators using two bright and one lamp method:


Procedure:

1. Consider alternator-1 is supplying power to load at rated voltage and rated frequency which means alternator-1 is already in synchronism with bus-bar.

2. Now we need to connect alternator-2 in parallel with alternator-1.

3. Here lamp L-2 is connected similar to the three dark lamp method.

4. Lamps L-1 and and L-3 are connected in different manner. One end of lamp L-1 is connected to one of the phases other that the phase to which lamp L-2 is connected and the other end of lamp L-1 is connected to the phase to which lamp L-3 is connected.

5.Similarly one end of lamp L-3 is connected to a phase other than the phase to which lamp L-2 is connected and other end of lamp L-3 is connected to the phase to which lamp L-1 is connected as shown in the following circuit.

6. To match the terminal voltage of alternator-2 with bus-bar voltage we need to adjust the field current of alternator-2 until terminal voltage of alternator-2  matches with the bus-bar voltage. The required value of voltage can be seen in the voltmeter connected to bus-bar.

7. Depending upon the sequence of lamps L1,L2, L3 becoming dark and bright we can decide whether the alternator-2 frequency of voltage is higher or lower than bus-bar frequency.

8. If the sequence of bright and dark of lamps is L1-L2-L3 then the frequency of voltage of alternator-2 is higher than the bus-bar voltage. Now until the flickering reduces to a low value decreases the speed of prime mover of alternator-2.

9. If the sequence of bright and dark of lamps is L1-L3-L2 then the frequency of voltage of alternator-2 is less than the bus-bar voltage. Now until the flickering reduces to a low value increase the speed of prime mover of alternator-2.

10. When the  L1 and L3 are equally bright and lamp L2 is dark then close the switches.

11. Now the alternators are in synchronism.

Disadvantage of two bright and one dark lamp method for synchronization of alternators:

Phase sequence of the alternator cannot be checked by this method.

Synchroscope method for synchronization of alternators:

Let us discuss synchronization of alternator using synchroscope method.

Circuit diagram for synchronization of alternators using synchroscope method:


Procedure:

1. A synchroscope is used to achieve synchronization accurately.

2. It is similar to two bright and one dark lamp method and tells whether the frequency of incoming alternator is whether higher or lower than bus bar frequency.

3. This contains two terminals they are a) existing terminal b) incoming terminal.

4. Existing terminals are to be connected to bus-bar or existing alternator here in the diagram it is alternator-1 and incoming terminals are connected to incoming alternator which is alternator-2 according to the diagram which we have considered.

5. Synchroscope has a circular dial inside which a pointer is present and it can move both in clockwise and anti clockwise direction.

6. To match the terminal voltage of alternator-2 with bus-bar voltage we need to adjust the field current of alternator-2 until terminal voltage of alternator-2  matches with the bus-bar voltage. The required value of voltage can be seen in the voltmeter connected to bus-bar.

7. Depending upon the rate at which the pointer is rotating the difference of frequency of voltage between incoming alternator and bus-bar can be known.

8. And also if the pointer moves anti clockwise then the incoming alternator is running slower and has frequency less than the bus bar or existing alternator frequency and if the pointer moves clock-wise then the incoming alternator is running faster and has frequency greater than bus-bar or existing alternator frequency. So by adjusting the speed of prime mover of incoming alternator we can match the frequency with bus bar or existing alternator frequency. Frequency matches when the pointer is straight up-wards. At this point close the switch.

9. Now both the alternators are in synchronism.

So by these three methods synchronization of alternators is checked.

Today in this post we have learnt what is meant by synchronization of alternator and methods of synchronization of alternator.

To download this post on synchronization of alternator and methods of synchronization of alternator as PDF click here.

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 cos๐ž calculate value of ๐ž and draw current phasor Iph lagging or leading Vph by an angle ๐ž.

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 cos๐ž. So draw phase current Iaph  which lags Vph by an angle ๐ž.

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 sin๐ž

BC = Far cos๐ž


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 cos๐ž. So draw phase current Iaph  which leads Vph by an angle ๐ž.

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 sin๐ž

BC = Far cos๐ž

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 cos๐›Ÿ

Vph = rated voltage per phase.

Iaph = full load current per phase.

Ra = armature resistance per phase.

cos๐›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.

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