Question

A 50 kVA, 440 V, 3 - phase, 50 Hz induction motor is provided with a 3 - phase step - down auto - transformer starter which steps down the voltage to 50% of the input. The starting current of the motor on rated voltage is 6 time the rated full - load current. Estimate the current drawn by the auto - transformer from the mains at starting. What is the starting kVA drawn by the auto - transformer ?

• A. 170.455 A, 95.73 kVA
• B. 125.613 A, 107 kVA
• C. 140.401 A, 129.903 kVA
• D. 98415 A, 75 kVA

Answer 1

The correct option is D 98415 A, 75 kVA


Given $x=50\%=0.5;$

$I_{fL}=\frac{50\times {10}^3}{\sqrt{3}\times 440}=65.61A$

Given $I_{st\left(m\right)}=6I_{fl}=6\times 65.61$

$=393.65A$

$I_{st\left(AT\right)}=x^2{I}_{st\left(m\right)}=(0.5{)}^2\times 393.65=98.412A$

$(kVA{)}_{st}=\sqrt{3}{I}_{st\left(AT\right)}\times 440$

$=\sqrt{3}\times 98.412\times 440=7500VA$

$=75\text{kVA}$