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 :


(i)  The main flux '
φ' linking both primary and secondary windings.

(ii) Primary leakage flux φL1 linking with primary winding only, and

(iii) Secondary leakage flux φL2 linking with secondary winding only as shown in the figure.

Transformer with Leakage Reactance & Leakage Flux

     The primary leakage flux φL1, is proportional to primary ampere-turns alone, ( because the secondary turns do not link with φL1 ). The φL1 is in phase with I1 and produces self-induced e.m.f. eL1 in primary given by

 eL1  =  ( 2π f L1 ) × I1

Where

    L1  =  self-inductance of the primary winding produced by primary leakage flux φL1.

     So, Primary leakage reactance 

X1  =  2 π f L1  =  eL1 / I1   


    Similarly secondary leakage flux, φL2 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 φL2 is in phase with I2 and produces self-induced e.m.f. 

eL2  =  ( 2π f L2 ) × I2

Where

    L2  =  self-inductance of the secondary winding produced by secondary leakage flux φL2.

   Secondary leakage reactance 

X2  =  2 π f L2  =  eL2 / 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 primary.

   X1 = Leakage reactance of primary winding.

   X2' = Leakage reactance of secondary winding referred to primary.

   K = Transformation ratio of transformer. 

Transformer with Leakage Reactance & Leakage Flux

Total equivalent leakage reactance referred to secondary is given by,  



    When 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. 

Transformer with Leakage Reactance & Leakage Flux

Total equivalent leakage reactance referred to secondary is given by,  



     When 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


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