Effect of Leakage Reactance

1. Effect of Leakage Reactance
       Uptill now it is assumed that the entire flux produced by the primary links with the secondary winding. But in practice it is not possible. Part of the primary flux as well as the secondary flux completes the path through air and links with the respecting winding only. Such a flux is called leakage flux. Thus there are two leakage fluxes present as shown in the Fig. 1.
Fig .1 Individual impedance

       The flux ΦL1 is the primary leakage flux which is produced due to primary current I1. It is in phase with I1 and links with primary only.
       The flux ΦL2 is the secondary leakage flux which is produced due to current I2. It is in phase with I2 and links with  the secondary winding only.
       Due to the leakage flux ΦL1 there is self induced e.m.f. eL1 in primary. While due to leakage flux ΦL2 there is self induced e.m.f. eL2 in secondary. The primary voltage V1 has to overcome this voltage eL1 to produce E1 while induced e.m.f. E2 has to overcome eL2 to produce terminal voltage V2. Thus the self induced e.m.f.s are treated as the voltage drops across the fictitious reactance placed in series with the windings. These reactances are called leakage reactance of the winding.
  So                       X1 = Leakage reacatnce of primary winding.
  and                      X2 = Leakage reactance of secondary winding.
       The value of X1 is such that the drop I1 X1 is nothing but the self induced e.m.f. eL1 due to fluxΦL1. The value of X2 is such that the drop  I2 X2 is equal to the self induced e.m.f. eL2 due to flux ΦL1.
       Leakage fluxes with the respective windings only and not to both the windings. To reduce the leakage, as mentioned, int eh construction both the winding's are placed on same limb rather than on separate limbs.
1.1 Equivalent Leakage Reactance
       Similar to the resistances, the leakage reactances also can be transferred from primary to secondary or viceversa. The relation through K2 remains same for the transfer of recatnaces as it is studied earlier for the resistances.
       Let X1 is leakage reactance of primary and X2 is leakage reactance of secondary.
       Then the total leakage reacatance referred to primary is X1e given by,
                           X1e = X1 + X2' where    X2' = X2/K2
       While the total leakage reacatnce referred to secondary is given by ,
                            X2e = X2 + X1' where X1' = K2 X1
And                      K = N2/N1 =transformation ratio

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