Effect of Leakage Reactances

Effect of Leakage Reactances

• 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. 6.10.1.

• The fluxϕ_L1 is the primary leakage flux which is produced due to primary current I₁. It is in phase with I, and links with primary only.

• The flux ϕ_L2 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 leakage flux ϕ_L1 there is self induced e.m.f. e_L1 in primary. While due to leakage flux ϕ_L2 there is self induced e.m.f. e_L2 in secondary. The primary voltage V₁ has to overcome this voltage e to produce E1 while induced e.m.f. E₂ has to overcome e_L2 to produce terminal voltage V₂. Thus the self induced e.m.f.s are treated as the voltage drops across the fictitious reactances placed in series with the windings. These reactances are called leakage reactances of the winding.

So X₁ = Leakage reactance of primary winding.

and X₂ = Leakage reactance of secondary winding.

• The value of X ₁ is such that the drop I₁X₁ is nothing but the self induced e.m.f. e_L1 due to flux ϕ_L1 The value of X₂ is such that the drop I₂X₂ is equal to the self induced e.m.f. e₁₂ due to flux ϕ_L2

• Leakage fluxes link with the respective windings only and not to both the windings. To reduce the leakage, as mentioned, in the construction both the winding's are placed on same limb rather than on separate limbs.

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 reactances 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 reactance referred to primary is X_1e given by,

X_1e = X₁ + X '₂ where X '₂ = X₂ /K²

While the total leakage reactance referred to secondary is X_2e given by,

X_2e = X₂ + X '1 where X '₁ =K² X₁

And  K = N₂ / N₁ = Transformation ratio