Equivalent Circuit diagram of a single-phase Transformer

 

Equivalent Circuit diagram of the single-phase Transformer

The equivalent circuit diagram of a transformer is basically a diagram which can be resolved into an equivalent circuit in which the resistance and leakage reactance of the transformer are imagined to be external to the winding.

The equivalent circuit diagram of the transformer is given below:-

Where,
R₁ = Primary Winding Resistance.
R₂= Secondary winding Resistance.
I₀= No-load current.
I_µ = Magnetizing Component,
I_w = Working Component,
This I_µ & I_w are connected in parallel across the primary circuit. The value of E₁ ( Primary e.m.f ) is obtained by subtracting vectorially I₁ Z₁ from V₁ . The value of X₀ = E₁ / I₀ and R₀ = E₁ /I_w. We know that the relation of E₁ and E₂ is E₂ /E₁ = N₂ /N₁ = K, ( transformation Ratio )

From the equivalent circuit, we can easily calculate the total impedance of to transfer voltage, current, and impedance either to the primary or the secondary.

The secondary circuit is shown in fig-1. and its equivalent primary value is shown in fig- 2,

 

 

fig-1

fig-2

The total equivalent circuit of the transformer is obtained by adding in the primary impedance as shown in – Fig-3.

fig-3

And It can be simplified the terminals shown in fig – 4 & further simplify the equivalent circuit is shown in fig.- 5,

fig-4

At last, the circuit is simplified by omitting I₀ altogether as shown in fig- 5.

fig-5

From the equivalent circuit which is shown in fig.-3, the total impedance between the input terminal is,

This is so because there are two parallel circuits, one having an impedance of Z_m and the other having Z’₂ and Z’_L in series with each other.