Parameters of an Armature winding of an alternator

There are three important parameters of an armature winding of an alternator. These are,

1. Armature resistance R_a

2. Armature leakage reactance X_L

3. Reactance corresponding to armature reaction

 Every armature winding has its own resistance. The effective resistance of an armature winding per phase is denoted as R_{aph Ω}/ph or R_a Ω/ph.

       Generally the armature resistance is measured by applying the known d.c. voltage and measuring the d.c. current through it. The ratio of applied voltage and measured current is the armature resistance. But due to the skin effect, the effective resistance under a.c. conditions is more than the d.c. resistance. Generally the effective armature resistance under a.c. conditions is taken 1.25 to 1.75 times the d.c. resistance.

       While measuring the armature resistance, it is necessary to consider how the armature winding is connected whether in star or delta. Consider a star connected armature winding as shown in the Fig. 1.

Fig. 1 Star connected alternator

       When the voltage is applied across any two terminals of an armature winding, then the equivalent resistance is the series combination of the two resistance of two different phase windings,

.^..     R_RY = Resistance between R-Y terminals

              = R_a + R_a = 2R_a

       where R_a = armature resistance per phase

.^..     R_a = R_RY/2  Ω/ph

       Thus in star connected alternator, the armature resistance per phase is half of the resistance observed across any two line terminals.

       Consider the delta connected alternator as shown in the Fig. 2.

Fig. 2  Delta connected alternator

       When voltage is applied across any two terminals, then one phase winding appears in parallel with series combination of other two.

       Hence the equivalent resistance across the terminals is parallel combination of the resistance R_a and 2R_a.

.^..     R_RY  R_a  | | R_a  Ω/ph

       Thus in delta connected alternator, the armature resistance per phase is to be calculated from the equivalent resistance observed across any two line terminals.

Armature Leakage Reactance

When armature carries a current, it produces its own flux. Some part of this flux completes its path through the air around the conductors itself. Such a flux is called leakage flux. This is shown in the Fig. 1.

Fig. 1  Armature leakage flux

Note : This leakage flux makes the armature winding inductive in nature. So winding possesses a leakage reacatnce, in addition to the resistance.

       So if 'L' is the leakage inductance of the armature winding per phase, then leakage reactance per phase is given by X_L  = 2 π f L  Ω/ph. The value of leakage reactance is much higher than the armature resistance. Similar to the d.c. machines, the value of armature resistance is very very small.

Armature Reaction

When the load is connected to the alternator, the armature winding of the alternator carries a current. Every current carrying conductor produces its own flux so armature of the alternator also produces its own flux, when carrying a current. So there are two fluxes present in the air gap, one due to armature current while second is produced by the filed winding called main flux. The flux produced by the armature is called armature flux.

Note : So effect of the armature flux on the main flux affecting its value and the distribution is called armature reaction.

      The effect of the armature flux not only depends on the magnitude of the current flowing through the armature winding but also depends on the nature of the power factor of the load connected to the alternator.

       Now we will study the effect of nature of the load power factor on the armature reaction.

1.1  Unity Power Factor Load

       Consider a purely resistive load connected to the alternator, having unity power factor. As induced e.m.f. E_ph drives a current of I_aph  and load power factor is unity, E_ph and I_ph  are in phase with each other.

       If Φ_f  is the main flux produced by the field winding responsible for producing E_phthen E_ph lags Φ_f  by 90^o .

       Now current through armature I_a, produces the armature flux say Φ_a. So flux Φ_aand I_a are always in the same direction.

      This relation between Φ_f , Φ_a, E_ph and I_aph  can be shown in the phasor diagram. (See Fig. 1)

Fig. 1  Armature reaction for unity power factor

       It can be seen from the phasor diagram that there exists a phase difference of  90^o between the armature flux and the main flux. The waveforms for the two fluxes are also shown in the Fig. 1. From the waveforms it can be seen that the two fluxes oppose each other on the left half of each pole while assist each other on the right half of each pole. Hence average flux in the air gap remains constant but its distribution gets distrorted.

Note : Hence such distorting effect of armature reaction under unity p.f. condition of the load is called cross magnetising effect of armature reaction.

       Due to such distortion of the flux, there is small drop in the terminal voltage of the alternator.

1.2 Zero Lagging Power Factor Load

       Consider a purely inductive load connected to the alternator having zero lagging power factor. This indicates that I_aph  driven by E_ph lags E_ph by 90^o which is the power factor angle Φ.

       Induced e.m.f. E_ph lags main flux Φ_f by 90^o while Φ_a is in the same direction as that of  I_a. So the phasor diagram and the waveforms are shown in the Fig. 2.

       It can be seen from the phasor diagram that the armature flux and the main flux are exactly in opposite direction to each other.

Note : So armature flux tries to cancel the main flux. Such an effect of armature reaction is called demagnetising effect of the armature reaction.

       As this effect causes reduction in the main flux, the terminal voltage drops. This drop in the terminal voltage is more than the drop corresponding to the unity p.f. load.

Fig. 2  Armature reaction for zero lagging p.f. load

1.3 Zero Leading Power Factor Load

       Consider a purely capacitive load connected to the alternator having zero leading power factor. This means that armature current I_aph  driven by E_ph, leads E_phby 90^o, which is the power factor angle Φ.

       Induced e.m.f. E_ph lags Φ_f by 90^o while I_aph  and Φ_a are always in the same direction. The phasor diagram and the waveforms are shown in the Fig. 3.

Fig. 3 Armature reaction for zero leading p.f. load

       It can be seen from the phasor diagram and waveforms shown in the Fig. 2, the armature flux and the main field flux are in the same direction i.e. they are helping each other. This results into the addition in main flux. 

Note : Such an effect of armature reaction due to which armature flux assists field flux is called magnetising effect of the armature reaction.

       As this effect adds the flux to the main flux, greater e.m.f. gets induced in the armature. Hence there is increase in the terminal voltage for leading power factor loads.

       For intermediate power factor loads i.e. between zero lagging and zero leading the armature reaction is partly cross magnetising and partly demagnetising for lagging power factor loads or partly magnetising for leading power factor loads.

1.4 Armature Reaction Reactance (X_ar)

       In all the conditions of the load power factors, there is change in the terminal voltage due to the armature reaction. Mainly the practical loads are inductive in nature, due to demagnetising effect of armature reaction, there is reduction in the terminal voltage. Now this drop in the voltage due to the interaction of armature and main flux. This drop is not across any physical element.

       But to quantify the voltage drop due to the armature reaction, armature winding is assumed to have a fictitious reactance. This fictitious reactance of the armature is called armature reaction reactance denoted as  X_ar Ω/ph. And the drop due to armature reaction can be accounted as the voltage drop across this reactance as I_arX_ar.

Note : The value of this reactance changes as the load power factor changes, as armature reaction depends on the load power factor.