Equivalent Circuit of a Transformer

06/03/2025

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 $E 1$ is equivalent to the primary applied voltage $V 1$ minus the primary voltage drop. This voltage gives rise to the no - load current $I 0$ 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 $I 0$ 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 $R 0$ and a pure reactance $X 0$ , across which the voltage is $E 1$ (or equivalently, V1−primary voltage drop).

The terminal voltage

V 2

across the load is equal to the induced electromotive force

E 2

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

I 0

typically accounts for only 3 to 5% of the full-load rated current, the parallel branch comprising resistance

R 0

and reactance

X 0

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 R

0 -X 0

branch. The simplified circuit diagram of the transformer is as follows:

Topics

Machines Transformer Circuit Analysis

Wenzhou Rockwell Transformer Co., Ltd. It is a high - tech enterprise integrating R & D, production, sales, and service. It focuses on the manufacturing of power transformers and supporting equipment, and is committed to providing efficient, reliable, and energy - saving power transmission and distribution solutions for global customers. We can offer: •Distribution transformers and substations •Outdoor switchgears and breakers(recloser) •Switchgears and it’s components (GIS, RMU, VCB, SF6 CB) Market and Service: We always take customers as the orientation and provide customized services according to their requirements. Our products are exported to the Middle East, Africa, Northern Europe, South America, and many other countries and regions. Drive the future of electricity with technological innovation and become a leading global supplier of intelligent power equipment.