Question

Two single phase transformers having the same voltage ratio on no-load operate in parallel to supply a load of 1500 kVA at 0.8 p.f. lagging. One transformer is rated at 700 kVA and has a per unit equivalent impedance of (0.01+j0.06) and the other is rated at 800 kVA and has per unit impedance of (0.01+j0.05). The load shared by transformer 1 will be ______kVA. (Answer upto 2 decimal places)

• A. 634.85

Answer 1

The correct option is A 634.85
We consider that the per unit impedance of transformers are referred to a common base of 800 kVA

$\text{Equivalent impedance of transformer-1,}$

$Z_A=\frac{800}{700}(0.01+j0.06)$
$=(0.0114+j0.0686)p.u.$
$=\left(0.0695\angle {80.56}^{\circ }\right)p.u.$

$\text{Similarly for transformer-2,}$

$Z_B=(0.01+j0.05)p.u.=0.051\angle {78.69}^{\circ }p.u.$
$Z_A+Z_B=(0.0214+J0.1186)$
=$0.1205\angle {79.77}^{\circ }p.u.$

$\text{Load,}$ $S_L=1500\angle -{36.86}^{\circ }kVA$

$\text{Now, load shared by transformer-1;}$

$S_A=\frac{Z_B}{Z_A+Z_B}{S}_L$

$=\frac{0.051\angle {78.69}^{\circ }}{0.1205\angle {79.77}^{\circ }}\times 1500\angle -{36.86}^{\circ }$

$=634.854\angle -{37.94}^{\circ }kVA$

$\text{and}$ $S_B=\frac{Z_A}{Z_A+Z_B}{S}_L$

$=\frac{0.0695\angle {80.56}^{\circ }}{0.1205\angle {79.77}^{\circ }}\times 1500\angle -{36.86}^{\circ }$

$=865.145\angle -{36.07}^{\circ }kVA$