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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.

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