Note on Alternator with load and Armature Reaction

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Alternator with load:

When the synchronous generator is connected to load as shown in the figure below , current flows from armature winding to the load.The voltage across the load i.e.terminal voltage V is less than induced voltage or emf E because of the following reasons:

» Voltage drop due to armature resistance(Ra)

» Voltage drop due to armature leakage reactance(XL)

» Voltage drop due to armature reaction.

fig:Synchronous generator with load
fig:Synchronous generator with load
fig:Per phase equivalent circuit
fig:Per phase equivalent circuit

Let, E = emf induced per phase in the stator winding

V = terminal voltage across the load per phase.

At no - load operation, the terminal voltage (V) equals to the emf induced (E).

Ra = Armature winding resistance per phase.

XL= Leakage reactance of armature winding per phase.

Then, the terminal voltage is given by:

Ṽ̃ =Ẽ̄̄ – (Ra +j XL)

fig:Phasor digram for unity power factor,lagging and leading case
fig:Phasor diagram for unity power factor,lagging and leading case

Armature Reaction in Synchronous Generator:

Armature reaction in a machine defined as the effect of armature magnetic flux on main magnetic flux.When the synchronous generator is loaded with an external load, current will flow through the armature windings. This armature current will set up its own magnetic field which is also rotating in nature. The effect of this armature field on the field produced by the rotor is known as armature reaction. The nature of armature reaction depends on the type of load i.e. power factor of the load.

Case I: Resistive load

If the load is purely resistive (V and I in the same phase), there will be no phase difference between the terminal voltage (V) & the armature current. Since the nature of flux will be in phase with armature current, the magnetic flux produced by three phase windings will have a similar waveform as that of the terminal voltage.

We have,

The equation of armature fluxes;

ØR = øm Sin ωt

ØY = øm Sin (ωt - 120°)

ØB = øm Sin (ωt - 240°)

When the magnet rotates 90° from its zero position, voltage & current in the R-coil will be positive maximum & voltage & current in the Y-coil & B- coil will be negative.

At ωt = 90°

ØR = øm Sin 90 ° = øm

Øy = øm Sin (ωt – 120°) = øm Sin (90° - 120°) = -1/2 øm

ØB = øm Sin (ωt - 240°) = øm Sin (90° - 240°) = -1/2 øm

The resultant flux will be,

ØyB =0.5 øm

Then resultant flux will be 0.5 øm + øm =1.5 øm

The resultant flux øA = 1.5 øm, which lags by an angle 90° with the direction of main flux (øm) .Both of these flux rotates with the same speed in the same direction. Therefore, at every instant the armature reaction flux (øA) try to distort the main flux (øm).

Hence, For unity power factor (Resistive load) , the armature reaction is cross-magnetizing in nature.

Case II: Inductive load

If the load is inductive i.e. load current (I) lags the terminal voltage (V) by an angle of α , then the waveforms of armature flux will also lag by an angle of α with respect to that in the case of a resistive load. So,after 90-degree rotation armature flux acts in the direction indicated below:

In this case, the armature reaction flux (øA) has two components:

ØA Sin α has the opposite direction to øm.

This component is known as a demagnetizing component.

ØA Cosα is the component along the direction perpendicular to øm. This component is known as cross- magnetizing component.

fig:Armature reaction for inductive load
fig:Armature reaction for inductive load

Hence, the Overall effect for the pure inductive load (lagging), the armature reaction is demagnetizing in nature.

Case III: Capacitive load

If the load is capacitive i.e. the load current (I) leads the voltage (V) by an angle of α , then the waveforms of armature flux will also lead the V by an angle of α with respect to that in the case of a resistive load.

In this case, again the armature reaction flux (øA ) has two components:

ØA Sinα: Component along the direction of øm.

This component is known as a magnetizing component.

ØA cosα: Component along the direction perpendicular to øm.

This component is known as cross- magnetizing component.

fig:Armature reaction for capacitive load
fig:Armature reaction for capacitive load

Hence,for the pure capacitive load (leading), the overall effect of armature reaction is magnetizing in nature.

For Resistive load,inductive load & for capacitive load, the armature reaction is cross-magnetizing,demagnetizing & magnetizing in nature respectively.

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