GATE 2017 EE – Question 56
Two parallel connected, three-phase, 50 Hz, 11 kV, star-connected synchronous machines A and B, are operating as synchronous condensers. They together supply 50 MVAR to a 11 kV grid. Current supplied by both the machines are equal. Synchronous reactances of machine A and machine B are 1 $\Omega$ and 3 $\Omega$, respectively. Assuming the magnetic circuit to be linear, the ratio of excitation current of machine A to that of machine B is ________. (Give the answer up to two decimal places.)
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Correct answer: 0.7 to 0.79
Explanation
The total current is $\frac{50 \times 10^6}{\sqrt{3} \times 11000} = 2624$ A, so each machine supplies 1312 A. The phase voltage is $\frac{11000}{\sqrt{3}} = 6351$ V. Each condenser is overexcited, so $E = V + X_sI$. Then $E_A = 6351 + 1 \times 1312 = 7663$ V and $E_B = 6351 + 3 \times 1312 = 10287$ V. With a linear magnetic circuit the excitation current is proportional to $E$, so the ratio is $\frac{7663}{10287} = 0.745$.