Equivalent Impedance

Equivalent Impedance

AU: May-03, Dec.-05, 19

• The transformer primary has resistance R₁ and reactance X₁. While the transformer secondary has resistance R₂ and reactance X₂. Thus we can say that the total impedance of primary winding is Z₁ which is,

Z₁ = R₁+jx₁ Ω ..............(6.11.1)

And the total impedance of the secondary winding is Z₂ which is,

Z₂ = R₂+jx₂ Ω ....................(6.11.2)

This is shown in the Fig. 6.11.1.

The individual magnitudes of Z₁ and Z₂ are,

Similar to resistance and reactance, the impedance also can be referred to any one side.

Let Z_1e = Total equivalent impedance referred to primary

Then Z_1e = R_le + jX_1e

Z_1e = Z₁ + Z '₂ = Z₁ = Z₂ /K² _.....(6.11.5)

Similarly Z_2e Total equivalent impedance referred to secondary

then

• The concept of equivalent impedance is shown in the Fig. 6.11.2. 

Ex. 6.11.1 A 33 kVA, 2200/220 V, 50 Hz, single phase transformer has the following parameters:

r₁ = 2.4 ohm, r₂= 0.03 ohm, x₁ = 6 ohm, x₂= 0.07 ohm. Calculate

a) Equivalent resistance, leakage reactance and impedance referred to HV side.

b) Equivalent resistance, leakage reactance and impedance referred to LV side.

c) Full load copper loss. AU: May-03, Dec.-19, Marks 8

Sol.:

Ex. 6.11.2 A single phase transformer with 10:1 turns ratio and rated at 50 kVA, 2400/240 V, 50 Hz is used to step down the voltage of a distribition system. The low tension voltage is kept constant at 240 V. Find the value of load impedance on the low tension side so that the transformer will be loaded fully. Find the value of maximum flux inside the core if the low tension side has 23 turns. AU: Dec.-05, Marks 6

Sol. :

Review Questions

1. Write a note on various winding parameters of a transformer.

2. A 15 kVA, 2200/110 V transformer has R₁= 1.75 Ω, R₂ = 0.0045 Ω. The leakage reactances are X₁ = 2.6 Ω and X₂ 0.0075 Ω. Calculate,

a) Equivalent résistance referred to primary

 b) Equivalent resistance referred to secondary

 c) Equivalent reactance referred to primary

d) Equivalent reactance referred to secondary

e) Equivalent impedance referred to primary

f) Equivalent impedance referred to secondary

g) Total copper loss.

[Ans. 3.55 Ω, 0.00887 Ω, 0.014 Ω, 6.6304 Ω, 0.01657 'Ω, 458.4194 W, 458.419 W]