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## What is the Equivalent Circuit of a Transformer?

The equivalent circuit diagram of a transformer is a simplified circuit in which the impedance, resistance and leakage reactance of the transformer can be more easily calculated.

The equivalent impedance of transformer is an important parameter to be calculated. This calculation requires the equivalent circuit of transformer referred to the primary or equivalent circuit of transformer referred to secondary sides respectively. Percentage impedance is also a very essential parameter of the transformer.

Special attention is to be given to this parameter during installing a transformer in an existing electrical power system. Percentage impedance of different power transformers should be properly matched during parallel operation of power transformers.

The percentage impedance can be derived from the equivalent impedance of the transformer so, it can be said that the equivalent circuit of the transformer is also required during the calculation of the % impedance.

## 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, first we need to recall 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 V_{1} and voltage across the primary winding is E_{1}. Total current supplied to primary is I_{1}. So the voltage V_{1} applied to the primary is partly dropped by I_{1}Z_{1} or I_{1}R_{1} + j.I_{1}X_{1} before it appears across primary winding.

The voltage appeared across winding is countered by primary induced emf E_{1}. 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 I_{1} has two components, one is no – load component I_{o} and the other is load component I_{2}′. 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 I_{2}′ flows through the primary winding of transformer and induced voltage across the winding is E_{1} as shown in the figure right.

This induced voltage E_{1} transforms to secondary and it is E_{2} and load component of primary current I_{2}′ is transformed to secondary as secondary current I_{2}. Current of secondary is I_{2}.

So the voltage E_{2} across secondary winding is partly dropped by I_{2}Z_{2} or I_{2}R_{2} + j.I_{2}X_{2} before it appears across load. The load voltage is V_{2}.

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.Z_{2}.I_{2}.

Again I_{2}′.N_{1} = I_{2}.N_{2}

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:

If you’d like to study more electrical questions like this, check out our MCQs on transformers.

### Approximate Equivalent Circuit of Transformer

Since I_{o} is very small compared to I_{1}, it is less than 5% of full load primary current, I_{o} 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.

## Equivalent Circuit of Transformer Referred to Secondary

In a similar way, the approximate equivalent circuit of transformer referred to secondary can be drawn.

Where equivalent impedance of transformer referred to secondary, can be derived as