Question

Describe briefly how the primary equivalent T circuit is created in transformers and what physical quantities its elements represent.

Answer 1

Equivalent Circuit of Transformer Referred to Primary:

For drawing equivalent circuit of transformer referred to primary, first we have to establish general equivalent circuit of transformer then, we will modify it for referring from primary side. For doing this, the complete vector diagram of a transformer which is shown in the figure below.

Let us consider the transformation ratio be,

In the figure above, the applied voltage to the primary is V₁ and voltage across the primary winding is E₁. Total current supplied to primary is I₁. So the voltage V₁ applied to the primary is partly dropped by I₁Z₁ or I₁R₁ + j.I₁X₁ before it appears across primary winding. 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,

From the vector diagram above, it is found that the total primary current I₁ has two components, one is no – load component I_o and the other is load component I₂′. As this primary current has two components or branches, so there must be a parallel path with primary winding of transformer.

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 load component I₂′ flows through the primary winding of transformer and induced voltage across the winding is E₁ as shown in the figure right. This induced voltage E₁ transforms to secondary and it is E₂ and load component of primary current I₂′ is transformed to secondary as secondary current I₂. Current of secondary is I₂. So the voltage E₂ across secondary winding is partly dropped by I₂Z₂ or I₂R₂ + j.I₂X₂ before it appears across load. The load voltage is V₂. 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: