Equivalent Circuit of Single Phase Transformer

Equivalent Circuit of Transformer

AU : May-03,04,09,10, Dec.-04,08,09,11,12

• The term equivalent circuit of a machine means the combination of fixed and variable resistances and reactances, which exactly simulates performance and working of the machine.

• For a transformer, no load primary current lo has two components,

I_m = I₀  sin ϕ₀ = Magnetising component

I_c = I₀ cos ϕ₀ = Active component

• I_m produces the flux and is assumed to flow through reactance X₀ called no load reactance while I_c is active component representing core losses hence is assumed to flow through the resistance R₀. Hence equivalent circuit on no load can be shown as in the Fig. 6.13.1. This circuit consisting of R₀ and X₀ in parallel is called exciting circuit. From the equivalent circuit we can write,

R₀ = V₁ / I_c and X₀ = V₁ / I_m

• When the load is connected to the transformer then secondary current I₂ flows. This causes voltage drop across R₂ and X₂. Due to I₂, primary draws an additional current

•I'₂ = I₂ / K. Now I₁ is the phasor addition of I₀ and I'₂. This I₁ causes the voltage drop across primary resistance R₁ and reactance X₁.

• Hence the equivalent circuit can be shown as in the Fig. 6.13.2.

• But in the equivalent circuit, windings are not shown and it is further simplified by transferring all the values to the primary or secondary. This makes the transformer calculations much easy.

So transferring secondary parameters to primary we get,

While transferring the values remember the rule that

Low voltage winding → High current → Low impedance

High voltage winding → Low current → High impedance

• Thus the exact equivalent circuit referred to primary can be shown as in the Fig. 6.13.3.

• Similarly all the primary value can be referred to secondary and we can obtain the equivalent circuit referred to secondary.

Similarly the exciting circuit parameters also gets transferred to secondary as R'₀ and X'₀. The circuit is gris shown in the Fig. 6.13.4.

• Now as long as no load branch i.e. exciting branch is in between Z₁ and Z'₂, the impedances cannot be combined. So further simplification of the circuit can be done. Such circuit is called approximate equivalent circuit.

1. Approximate Equivalent Circuit

• To get approximate equivalent circuit, shift the no load branch containing R₀ and X₀ to the left of R₁ and X₁. By doing this we are creating an error that the drop across R₁ and X₁ due to Io is neglected. Hence such is equivalent circuit is called approximate equivalent circuit.

• So approximate equivalent circuit referred primary can be as shown in the Fig. 6.13.5.

In this circuit now R₁ and R'₂ can be combined to get equivalent resistance referred to primary R_1e discussed earlier. Similarly X₁ and X₂ can combined to get X_1e. And equivalent circuit can be simplified as shown in the Fig. 6.13.6.

• In the similar fashion, the approximate equivalent circuit referred to secondary also can be obtained.

Review Questions

1. Explain in detail step by step the procedure to draw the equivalent circuit of transformer. AU: May-03, Dec.-12, Marks 8

2. Derive the equivalent circuit of a single phase two winding transformer. AU May-04, 09, 10, Dec.-04, 08, 09, 11, Marks 8