## 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

Open circuit test on synchronous machine:**short circuit test on the alternator.**
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:**

I
_{f} A |
V
_{oc(Line)} _{ } V_{} |
V
_{oc(phase)} = V_{oc(line)}/ |

**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:**

I
_{f} A |
I
_{asc }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 I

_{f}
1. I

_{f}is kept same as before in the short circuit test.
2. Now terminals of the synchronous machine is removed.

3. As I

_{f}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 I

_{f}
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 I

_{f}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 I

_{f}is constant and I_{f}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 I

_{f}.### 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.**