**Equivalent Circuit of 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 the transformer is an important parameter to be calculated. This calculation requires the equivalent circuit of the transformer referred to as the primary or equivalent circuit of the 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. The percentage impedance of different power transformers should be properly matched during the 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.

**Table of contents**

**Table of contents**

**1. Approximate Equivalent Circuit of Transformer**

**2. Equivalent Circuit of Transformer Referred to Secondary**

**3****. Equivalent Circuit of Transformer Referred to Primary**

**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 a good approximation to ignore the excitation circuit in the approximate equivalent circuit of the transformer.

The winding resistance and reactance being in series can now be combined into equivalent resistance and reactance of the transformer, referred to any particular side. In this case, it is side 1 or the primary side.

**Equivalent Circuit of Transformer Referred to Secondary**

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

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

**Equivalent Circuit of Transformer Referred to Primary**

For drawing the equivalent circuit of the transformer referred to as primary, first, we have to establish a general equivalent circuit of the transformer then, we will modify it for referring from the primary side. To do this, first, we need to recall the complete vector diagram of a transformer 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 the voltage across the primary winding is E_{1}. The total current supplied to the 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 the primary winding.

The voltage that appeared across the 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 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 the primary winding of the transformer.

This parallel path of current is known as the excitation branch of an equivalent circuit of the 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 the transformer and the 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 the load component of primary current I_{2}′ is transformed to secondary as secondary current I_{2}. The current of the 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 the load. The load voltage is V_{2}.

The complete equivalent circuit of the transformer is shown below.

Now if we see the voltage drop in the secondary from the 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 the above equation, the secondary impedance of the transformer referred to as primary is,

So, the complete equivalent circuit of the transformer referred to as primary is shown in the figure below:

**Source: Electrical4u**