Question

The resistance and leakage reactance of a 10 kVA, 50 Hz, 2300/230 V distribution transformer are:

$r_1=3.96\Omega$, $r_2=0.0396\Omega$
$x_1=15.8\Omega$, $x_2=0.158\Omega$

The transformer delivers rated kVA at 0.8 p.f lagging to a load on LV side to maintain 230 V across load terminals. The HV side voltage is _________V.

• A. 2411.69

Answer 1

The correct option is A 2411.69
$\text{Turns ratio}=\frac{2300}{230}=10$

$r_2^{\prime }=r_2\times a^2=100\times 0.0396$

$=3.96\Omega$

$x_2^{\prime }=x_2\times a^2=100\times 0.158$

$=15.8\Omega$

$\text{Rated current on HV side at 0.8 p.f. lagging}$

$2300\times I_1=10kVA$

$I_1=4.35\angle -{36.87}^{\circ }$

$\text{Taking}{V}_2^{\prime }\text{as reference}$

$V_1=V_2^{\prime }+I_1(r_1+r_2^{\prime })+j{I}_1(x_1+x_2^{\prime })$

$=2300\angle 0^{\circ }+(4.35\angle -{36.87}^{\circ }\times (7.92+j31.6\left)\right)$

$=2411.69\angle {2.12}^{\circ }V$