Question

A single phase, 50 Hz, three winding transformer is rated at 2200 V on the HV side with a total of 250 turns of the two secondary windings, each can handle 220 kVA. One winding is rated at 550 V and the other is at 220 V. The magnitude of primary current (rms) will be____ A, when the rated current in the 220 V winding at upf and the rated current in 550 V winding is 0.6 p.f. lagging. Neglect all leakage impedance drops and magnetizing current.

• A. 101.84 A
• B. 151.25. A
• C. 178.88 A
• D. 191.35 A

Answer 1

The correct option is C 178.88 A

$\text{Consider the below circuit:}$

$\text{Rated current in winding - 1}$
$I_1=\frac{220\times 1000}{550}=400\angle -{53.13}^{\circ }A$

$\text{Rated current in winding - 2}$
$I_2=\frac{220\times 1000}{220}=1000\angle 0^{\circ }A$

Current in HV side due to rated current in winding - 1
$I_1^{\prime }=\frac{(400\angle -53.13)\times 0.55}{2.2}=100\angle -{53.13}^{\circ }A$

Current in HV side due to rated current in winding - 2

$I_2^{\prime }=\frac{\left(1000\angle 0^{\circ }\right)\times 0.22}{2.2}=100\angle 0^{\circ }A$

$\text{HV side current}=100\angle -{53.13}^{\circ }+100\angle 0^{\circ }$
$I=178.885\angle -26.565A$
$|I|=178.885A$