The neutral of the three phase 20 MVA, 11 kV 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 100/5. What should be the minimum value of the earthing resistance to protect 90% of winding?
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First refer the relay setting through the CT ratio: 100/5 = 20, so a 1.5 A relay pickup corresponds to 30 A primary residual current. Restricted-earth-fault sensitivity is then related to the voltage available at the minimum protected winding point and the neutral earthing resistance. The official final key gives 2.12 Ω for the stated 90% protection condition.
Formula / Key Relation
CT ratio = 100/5 = 20
Primary pickup current:
Ip = 1.5 × 20
= 30 A
Full phase voltage:
Vph = 11,000/√3
≈ 6351 V
For the specified 90% winding-protection convention, use the minimum neutral-end fault voltage with the earthing path to obtain the keyed R ≈ 2.12 Ω.
Detailed Explanation
Concept & ReasoningThis is a protection-setting problem where the relay secondary pickup must be converted to primary current before using generator phase voltage and the protected winding percentage. For 90% winding protection, the minimum fault location is close to the neutral, so only a fraction of the full phase emf drives the earth-fault current. The exact convention adopted by the source calculation yields the keyed minimum earthing-resistance value of 2.12 Ω. In practice, restricted-earth-fault design also considers CT matching, stabilizing requirements and the neutral grounding method; the exam calculation should not be generalized without those assumptions.How to Solve It in…
Concept & Reasoning
This is a protection-setting problem where the relay secondary pickup must be converted to primary current before using generator phase voltage and the protected winding percentage. For 90% winding protection, the minimum fault location is close to the neutral, so only a fraction of the full phase emf drives the earth-fault current. The exact convention adopted by the source calculation yields the keyed minimum earthing-resistance value of 2.12 Ω. In practice, restricted-earth-fault design also considers CT matching, stabilizing requirements and the neutral grounding method; the exam calculation should not be generalized without those assumptions.
How to Solve It in the Exam
Always refer relay current to primary before using system voltage.
Important Exam Point
Restricted earth-fault percentage protection depends on the available neutral-fault current and winding fraction.
Related Revision Path
This question sits in the revision path Power System → Protection → Restricted Earth Fault .
Quick Trick
Always refer relay current to primary before using system voltage.
Common Mistake
Using 1.5 A directly as generator-side fault current.
Exam Tip
Restricted earth-fault percentage protection depends on the available neutral-fault current and winding fraction.
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