AC MACHINES-1 (66761) Theory
4. Understand equivalent circuit of transformer, magnetic leakage and leakage reactance of transformer.
4.3. Derive the equivalent resistance of a transformer referred to primary.
Let us consider the transformation ratio be,
The voltage appeared across winding is countered by primary induced emf E1. So voltage equation of this portion of the transformer can be written as,
The equivalent circuit for that equation can be drawn as below,
This parallel path of current is known as excitation branch of equivalent circuit of transformer. The resistive and reactive branches of the excitation circuit can be represented as
The complete equivalent circuit of transformer is shown below.
Now if we see the voltage drop in secondary from primary side, then it would be ′K′ times greater and would be written as K.Z2.I2.
Again I2′.N1 = I2.N2
Therefore,
From above equation, secondary impedance of transformer referred to primary is,
So, the complete equivalent circuit of transformer referred to primary is shown in the figure below:
Approximate Equivalent Circuit of Transformer
Since Io is very small compared to I1, it is less than 5% of full load primary current, Io changes the voltage drop insignificantly. Hence, it is good approximation to ignore the excitation circuit in approximate equivalent circuit of transformer. The winding resistance and reactance being in series can now be combined into equivalent resistance and reactance of transformer, referred to any particular side. In this case it is side 1 or primary side.
