A three-phase 11 kV, 100 MVA alternator is provided with differential protection. The percentage of winding to be protected against phase to ground fault is 85%. The relay is set to operate when there is 20% out of balance current. What is the value of primary earth fault current at which the relay operates?
DSSSB AE - 2023,
Answer: C
With differential protection, only 85 per cent of the winding is protected against a phase to ground fault, and the relay operates when the out of balance current is 20 per cent of the full load current.
\[ \begin{aligned} I_{FL} \\ &= \frac{100 \times 10^6}{\sqrt{3} \times 11 \times 10^3} \\ &= 5249\ \text{A} \end{aligned} \]
\[ \begin{aligned} I_{relay} = 0.2 \times 5249 \\ &= 1049.8\ \text{A} \approx 1.049\ \text{kA} \end{aligned} \]
The primary earth fault current at which the relay operates is therefore about 1.049 kA. The values of 10.49 kA, 0.1049 kA and 104.9 kA are slips of a power of ten. The answer is option C.
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