Equivalent Circuit of a Transformer

The equivalent circuit diagram of any device can be extremely useful for predicting how the device will behave under different operating conditions. It is essentially a circuit - based depiction of the equations that describe the device's performance.

The simplified equivalent circuit of a transformer is constructed by representing all of the transformer's parameters on either the secondary side or the primary side. The equivalent circuit diagram of the transformer is presented below:

Let the equivalent circuit of a transformer be considered, with a transformation ratio K = E₂/E₁.The induced electromotive force E₁ is equivalent to the primary applied voltage V₁ minus the primary voltage drop. This voltage gives rise to the no - load current I₀ in the primary winding of the transformer. Since the value of the no - load current is extremely small, it is often neglected in many analyses.Consequently,  I1≈I1′. The no - load current I₀ can be further decomposed into two components: the magnetizing current I_m and the working current I_w.These two components of the no - load current are a result of the current drawn by a non - inductive resistance R₀ and a pure reactance X₀, across which the voltage is E₁ (or equivalently, V1−primary voltage drop).

The terminal voltage V₂ across the load is equal to the induced electromotive force E₂ in the secondary winding minus the voltage drop in the secondary winding.

Equivalent Circuit with All Quantities Referred to the Primary Side

In this scenario, to construct the equivalent circuit of the transformer, all parameters need to be referred to the primary side, as depicted in the figure below:

The following are the values of resistance and reactance given below

Secondary resistance referred to the primary side is given as:

The equivalent resistance referred to the primary side is given as:

Secondary reactance referred to the primary side is given as:

The equivalent reactance referred to the primary side is given as:

Equivalent Circuit with All Quantities Referred to the Secondary Side

The following is the equivalent circuit diagram of the transformer when all parameters are referred to the secondary side.

The following are the values of resistance and reactance given below

Primary resistance referred to the secondary side is given as

The equivalent resistance referred to the secondary side is given as

Primary reactance referred to the secondary side is given as

The equivalent reactance referred to the secondary side is given as

Simplified Equivalent Circuit of Transformer

Since the no-load current I₀ typically accounts for only 3 to 5% of the full-load rated current, the parallel branch comprising resistance R₀ and reactance X₀ can be omitted without introducing significant errors in analyzing the transformer's behavior under loaded conditions.

Further simplification of the transformer's equivalent circuit is achieved by neglecting this parallel R₀-X₀ branch. The simplified circuit diagram of the transformer is as follows: