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 = V₁/I_w and X_o = V₁/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 R₁ and reactance X₁ correspond to the winding resistance (DC resistance) and leakage reactance of the primary winding.

The total current I₁ on the primary side is equal to the phasor sum of I_o and I₂’.
I₂’ = KI² is the additional primary current which flows due to the load connected on the secondary side of the transformer.

Secondary Components

The resistance R₂ and reactance X₂ 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.

- R₂’, X₂’ and Z_L’ are the values of R₂, X₂ and Z_L referred to primary respectively.
- The values of these components are obtained as follows:

R₂’ = R₂/K² , X₂’ = X₂/K² and Z_L’ = Z_L/K²

where K = N₂/N₁ (transformation ratio).

- The current I₂ and voltage E₂ are also transferred to the primary side as I₂’ and E₂’ respectively. The expressions for I₂’ and E₂’ are as follows:

E₂’ = E₂/K and I₂’ = KI₂

Equivalent Circuit of Transformer Referred to Secondary

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

- Components R₁’, X₁’, R_o’ and X_o’ are the primary components referred to secondary. The expressions for these components are as follows:

R₁’ = K²R₁ , X₁’ = K²X₁
R_o’ = K²R_o , X_o’ = K²X_o

- The primary voltages and currents also get transferred to the secondary side as I₁’, V₁’, I_o’, E₁’ respectively and are given by:

I₁’ = I₁/K , E₁’ = KE₁ , I_o’ = I_o/K
where K = N₂/N₁ (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 R₁ and X₁ as shown in the figure.

Although this shifting creates an error in the voltage drop across R₁ and X₁ yet it greatly simplifies the calculation work and gives much simplified equivalent circuit.

- Now it is possible to combine the resistances R₁ with R₂’ and X₁ with X₂’. So R₁ and R₂’ are combined to obtain the equivalent resistance of transformer referred to the primary R₀₁.

Therefore, R₀₁ = R₁ + R₂’ = R₁ + R₂/K²

- Similarly X₁ and X₂’ can be combined to obtain the equivalent reactance of transformer referred to primary X₀₁.

Therefore, X₀₁ = R₁ + R₂’ = R₁ + R₂/K²

Now the impedance of the transformer referred to the primary is given by,
Z₀₁= R₀₁ + jX₀₁

Equivalent Circuit of Transformer