# Alternator on load

Whenever the load on the alternator is varied, the terminal voltage will also vary. This variation in terminal voltage is mainly due to three reasons: Voltage drop due to armature resistance IR_{a}, the voltage drop due to armature leakage reactance IX_{L}, and Voltage drop due to armature reaction.

Let us take a look at all those reasons in detail.

## Effect of Load on Alternator

### Voltage drop due to armature resistance

The armature winding resistance per phase will cause a IR_{a} voltage drop per phase.

The voltage drop due to armature resistance is in phase with the armature current I. Practically, this voltage drop is negligible.

### Voltage drop due to armature leakage reactance

When current flows through armature conductors, the flux will start to flow through the armature core. Some flux will take different paths and do not cross the air gap which is called leakage flux.

Here, the leakage flux depends on the current flowing through the conductor and its phase relationship with the terminal voltage. This leakage flux will set up an emf because of self-inductance. This emf is known as reactance emf, which leads the armature current I by 90^{0}.

Thus, the armature winding is said to possess a leakage reactance X_{L}. The voltage drop due to this reactance is IX_{L}. The generated emf has to overcome the voltage drop due to leakage reactance to give its output.

*E = V + I ( R _{a} + jX_{L} )*

This is illustrated in the below phasor diagram.

The above phasor diagram is constructed as below,

- The voltage phasor is taken as the reference phasor.
- The armature current lags behind the voltage by an angle Φ. Hence the current phasor is drawn at an angle Φ from the voltage phasor.
- The phasor for armature resistance drop is drawn parallel to the current phasor from the extremity of Voltage phasor V.
- Leakage reactance drop is drawn perpendicular to the current phasor from the extremity of IR
_{a}phasor. - Join 0 and the extremity of IX
_{L}phasor to get E_{b}.

### Voltage drop due to armature reaction

Armature reaction is the effect of armature flux on the main field flux. The effect of the armature reaction can be seen in the DC generator as well.

But compared to the DC generator, the power factor of the load in an alternator has a considerable effect on the armature reaction. While we talk about the power factor on loading conditions, we consider three cases.

- Unity power factor load.
- Zero power factor lagging load
- Zero power factor leading load.

The armature reaction in alternator produces different effects such as cross magnetizing effect, demagnetizing effect, and magnetizing effect. These effects cause distortion in the main field flux, thereby affecting the generated emf.

The voltage drop due to armature reaction may be assumed as there is a presence of fictitious reactance X_{a} called armature reactance reaction. The voltage drop due to the armature reactance reaction is represented as IX_{a}.

**The leakage reactance X _{L} and armature reaction reactance Xa together called synchronous reactance X_{S}.**

**X _{S}** =

**X**+

_{L}**X**

_{a}Thus the voltage drop in an alternator under loaded conditions is the total sum of voltage drop due to armature resistance, armature leakage reactance, and armature reaction reactance.

*V = I R _{a} + j I X_{L} + j I X_{a} = I ( R_{a} + j X_{L} + j X_{a} ) = I ( R_{a} + j ( X_{L} + X_{a }) ) *

V *= I ( R _{a} + j X_{S} ) = I Z_{S}*

Where *Z _{S}* is known as the

**synchronous impedance**of an alternator.

From the discussions above, it is clear that the variation in load causes the terminal voltage of the alternator to change. It is due to the synchronous impedance of the alternator.

Now let us look at the phasor diagrams of alternator for different load conditions.

## Phasor diagrams of Alternator on Load

To draw the phasor diagrams, let us know the terms used in the below diagrams.

*E _{0 }*is the no-load voltage. It is the maximum voltage induced in the armature without giving any load.

*E* is the load voltage. It is the induced voltage after overcoming the armature reaction. *E* is vectorially less than the no-load voltage.

*I* is the armature current per phase

*V* is the terminal voltage. It is vectorially less than *E* by *IZ* and also vectorially less than *E _{0}* by

*IZ*.

_{S}*Φ* is the cosine angle between terminal voltage and current.

The impedances are given by

where *X _{L}* is the leakage reactance,

*X*is the armature reaction reactance and

_{a}*X*is the synchronous reactance and

_{S}*Z*is the synchronous impedance.

_{S}### Unity power factor load

The phasor diagram of an alternator for unity power factor load is shown below.

**How the phasor diagram is drawn? Follow the below given procedure.**

- Voltage phasor V is taken as the reference phasor.
- For unity power factor load, V and I phasor are in phase. So the Current phasor I is drawn on the voltage phasor V.
- The phasor of Armature resistance drop IRa is drawn parallel to the current phasor from the extremity of V phasor.
- The armature leakage resistance drop IXL is drawn perpendicular to the current phasor, from the extremity of IRa phasor.
- Join V phasor and IXL phasor to get IZ phasor(shown as a dotted line).
- Join O and the extremity of IZ to get E(shown as a pink color line)
- Draw the armature reaction reactance drop phasor IXS perpendicular to the current phasor from the extremity of IXL phasor.
- Join V phasor and IXS phasor to get IZS phasor(shown as a dotted line).
- Join O and the extremity of IZS to get E0(shown as a pink color line)

### Lagging power factor load

The phasor diagram of an alternator for lagging power factor load is shown below.

The above phasor diagram is drawn by following the same procedure as explained for unity power factor.

The only change is that here current lags behind the voltage by an angle *Φ*. So draw the current phasor at an angle *Φ* with respect to voltage phasor V.

### Leading power factor load

The phasor diagram of an alternator for leading power factor load is shown below.

For the leading power factor load, the phasor diagram is also drawn similar to that of the unity power factor. But the only difference is that here current leads the voltage by an angle Φ. So the current phasor is drawn at an angle *Φ* with respect to voltage phasor V.

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