Transformer with Leakage Reactance & Leakage Flux

What is Leakage Flux in a Transformer ?

We know that all the flux linked with primary winding is also linked with the secondary winding. But, in the actual transformer the total flux created does not link with the primary and secondary winding but is divided into three parts as follows :

1. The main flux 'Φ' linking both primary and secondary windings.
2. Primary leakage flux Φ_L1 linking with primary winding only. and
3. Secondary leakage flux Φ_L2 linking with secondary winding only as shown in the figure.

The primary leakage flux Φ_L1, is proportional to primary ampere-turns alone, (because the secondary turns do not link with Φ_L1). The Φ_L1 is in phase with I₁ and produces self-induced EMF e_L1 in primary given by,

e_L1 = (2π f L₁) × I₁

Where, L₁ is self-inductance of the primary winding produced by primary leakage flux Φ_L1. So, Primary leakage reactance.

X₁ = 2π f L₁ = e_L1/I₁ Ω

Similarly secondary leakage flux, Φ_L2 is produced by secondary ampere-turns. On no-load, there is no current in secondary and therefore no leakage flux exists across it. On load leakage flux Φ_L2 is in phase with I₂ and produces self-induced EMF

e_L2 = (2π f L₂) × I₂

Where L₂ is self-inductance of the secondary winding produced by secondary leakage flux Φ_L2. Secondary leakage reactance.

X₂ = 2π f L₂ = e_L2/I₂ Ω

Leakage Reactance of a Transformer :

By knowing the leakage reactance of the primary and secondary winding of the transformer. We can calculate the total leakage reactance of a transformer.

i. Leakage reactance of a transformer referred to primary :

Let,

• X₀₁ = Total leakage reactance referred to the primary.
• X₁ = Leakage reactance of primary winding.
• X₂' = Leakage reactance of secondary winding referred to the primary.
• K = Transformation ratio of transformer.

Total equivalent leakage reactance referred to secondary is given by,

While shifting the secondary reactance to the primary side we have to divide it with the square of the transformation ratio K of the transformer. i.e., X₂/K².

ii. Leakage reactance of a transformer referred to secondary :

Let,

• X₀₂ = Total leakage reactance referred to secondary.
• X₁' = Leakage reactance of primary winding referred to secondary.
• X₂ = Leakage reactance of secondary winding.
• K = Transformation ratio of transformer.

Total equivalent leakage reactance referred to secondary is given by,

While shifting the primary reactance to the secondary side we have to multiply it with the square of the transformation ratio K of the transformer. i.e., X₁*K².