# Equivalent Circuit of Transformer

The **equivalent circuit of transformer** is shown in the figure.

## No load Components

The no-load primary current *I*_{o} has two components, namely *I*_{m} and *I*_{w}.

Where *I*_{m} = magnetizing component = *I*_{o} sin φ_{o}

and *I*_{w} = core-loss component = *I*_{o} cos φ_{o}.

*I*_{w}supplies for the no-load losses and is assumed to flow through the no-load resistance which is also known as core-loss resistance (R_{o}).- The magnetizing component,
*I*_{m}is assumed to be flowing through a reactance which is known as magnetizing reactance, X_{o}. - The parallel combination of R
_{o}and X_{o}is also known as the**exciting circuit**.

From the **equivalent circuit of transformer**,

R_{o} = V_{1}/*I*_{w} and X_{o} = V_{1}/*I*_{m}.

- The core-loss resistance (R
_{o}) and the magnetizing reactance (X_{o}) of a transformer are determined by the open circuit test of transformer.

## Primary Components

- The resistance R
_{1}and reactance X_{1}correspond to the winding resistance (DC resistance) and leakage reactance of the primary winding. - The total current
*I*_{1}on the primary side is equal to the phasor sum of*I*_{o}and*I*_{2}’. *I*_{2}’ = K*I*^{2}is the additional primary current which flows due to the load connected on the secondary side of the transformer.

## Secondary Components

- The resistance R
_{2}and reactance X_{2}correspond to the winding resistance and leakage reactance of the secondary winding. - Load impedance Z
_{L}can be resistive, inductive or capacitive. - The
*equivalent circuit of single phase transformer*is further simplified by transferring all the quantities to either primary or secondary side. - This is done in order to make the calculations easy.

## Equivalent Circuit of Transformer Referred to Primary

All the components on the secondary side of the transformer are transferred to the primary side as shown in the figure.

- R
_{2}’, X_{2}’ and Z_{L}’ are the values of R_{2}, X_{2}and Z_{L}referred to primary respectively. - The values of these components are obtained as follows:

R_{2}’ = R_{2}/K^{2} , X_{2}’ = X_{2}/K^{2} and Z_{L}’ = Z_{L}/K^{2}

where K = N_{2}/N_{1} (transformation ratio).

- The current
*I*_{2}and voltage E_{2}are also transferred to the primary side as*I*_{2}’ and E_{2}’ respectively. The expressions for*I*_{2}’ and E_{2}’ are as follows:

E_{2}’ = E_{2}/K and *I*_{2}’ = K*I*_{2}

## Equivalent Circuit of Transformer Referred to Secondary

The *equivalent circuit of transformer* referred to the secondary side is shown in the figure.

- Components R
_{1}’, X_{1}’, R_{o}’ and X_{o}’ are the primary components referred to secondary. The expressions for these components are as follows:

R_{1}’ = K^{2}R_{1} , X_{1}’ = K^{2}X_{1}

R_{o}’ = K^{2}R_{o} , X_{o}’ = K^{2}X_{o}

- The primary voltages and currents also get transferred to the secondary side as
*I*_{1}’, V_{1}’,*I*_{o}’, E_{1}’ respectively and are given by:

*I*_{1}’ = *I*_{1}/K , E_{1}’ = KE_{1} , *I*_{o}’ = *I*_{o}/K

where K = N_{2}/N_{1} (transformation ratio).

# Approximate Equivalent Circuit of Transformer

An approximate equivalent circuit is one which is obtained by shifting the exciting circuit to the left of R_{1} and X_{1} as shown in the figure.

Although this shifting creates an error in the voltage drop across R_{1} and X_{1} yet it greatly simplifies the calculation work and gives much simplified equivalent circuit.

- Now it is possible to combine the resistances R
_{1}with R_{2}’ and X_{1}with X_{2}’. So R_{1}and R_{2}’ are combined to obtain the equivalent resistance of transformer referred to the primary R_{01}.

Therefore, R_{01} = R_{1} + R_{2}’ = R_{1} + R_{2}/K^{2}

- Similarly X
_{1}and X_{2}’ can be combined to obtain the equivalent reactance of transformer referred to primary X_{01}.

Therefore, X_{01} = R_{1} + R_{2}’ = R_{1} + R_{2}/K^{2}

Now the impedance of the transformer referred to the primary is given by,

Z_{01 }= R_{01} + jX_{01}

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- Open Circuit Test of Single Phase Transformer
- Short Circuit Test on Single Phase Transformer
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