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The neutral of the three phase 20 MVA, 11kV alternator is earthed through a resistance of 5 ohms, the relay is set to operate when there is an out of balance current of 1.5 A. The CTs have a ratio of 1000/5. What percentage of the winding is protected against L-G faults?

  • a)
    76.4

  • b)
    23.6

  • c)
    73

  • d)
    None of the mentioned

Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The neutral of the three phase 20 MVA, 11kV alternator is earthed thro...
Given:
- Three phase alternator: 20 MVA, 11kV
- Neutral is earthed through a resistance of 5 ohms
- Relay is set to operate when there is an out of balance current of 1.5 A
- CT ratio: 100/5

To Find:
Percentage of the winding protected against L-G faults

Solution:
Step 1: Calculate the out of balance current:
The out of balance current is the current flowing through the neutral due to an earth fault.

Given resistance of neutral grounding: 5 ohms
Voltage of the alternator: 11kV

Using Ohm's Law, we can calculate the out of balance current (Iob):
Iob = V/R = 11000/5 = 2200 A

Step 2: Calculate the secondary current of the CTs:
The secondary current of the CTs can be calculated using the CT ratio.

Given CT ratio: 100/5

Primary current (Ip) = Iob
Secondary current (Is) = Ip × CT ratio = 2200 × (100/5) = 44000 A

Step 3: Calculate the percentage of winding protected:
The percentage of winding protected can be calculated using the formula:

Percentage of winding protected = (Is/Irated) × 100

Where Irated is the rated current of the winding.

Given MVA rating of the alternator: 20 MVA
Rated current (Irated) = MVA rating × 10^6 / (√3 × kV rating)
= 20 × 10^6 / (√3 × 11)
≈ 1039 A

Percentage of winding protected = (44000/1039) × 100
≈ 42.36%

Answer:
The percentage of the winding protected against L-G faults is approximately 42.36%.
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Community Answer
The neutral of the three phase 20 MVA, 11kV alternator is earthed thro...
The primary CT current for the relay operation = 1.5*1000/5 = 300 A
% winding unprotected = (Is*RV*100%)
= (300*5√3)/11000*100
= 23.6 %.
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The neutral of the three phase 20 MVA, 11kV alternator is earthed through a resistance of 5 ohms, the relay is set to operate when there is an out of balance current of 1.5 A. The CTs have a ratio of 1000/5. What percentage of the winding is protected against L-G faults?a)76.4b)23.6c)73d)None of the mentionedCorrect answer is option 'B'. Can you explain this answer?
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