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?
Answer & step-by-step solution
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.
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.
Quick Trick
Always refer relay current to primary before using system voltage.
Common Mistake
Using 1.5 A directly as generator-side fault current.
तीन-फेज़ 20 MVA, 11 kV अल्टरनेटर का न्यूट्रल 5 ओम प्रतिरोध से अर्थ किया गया है। रिले 1.5 A असंतुलित धारा पर संचालित होने के लिए सेट है। CT का अनुपात 100/5 है। वाइंडिंग के 90% की सुरक्षा के लिए अर्थिंग प्रतिरोध का न्यूनतम मान क्या होना चाहिए?
उत्तर और चरणबद्ध हल
B — 2.12 Ω (आधिकारिक कुंजी)। CT अनुपात 100/5 = 20, इसलिए 1.5 A रिले पिकअप = 30 A प्राइमरी अवशिष्ट धारा। असुरक्षित 10% वाइंडिंग पर उपलब्ध वोल्टेज = 0.1 × 11000/√3 ≈ 635 V; अर्थिंग प्रतिरोध इस वोल्टेज और 30 A से संबंधित होता है।
विस्तृत हल (मूल भाषा में)
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.
Quick Trick
Always refer relay current to primary before using system voltage.
Common Mistake
Using 1.5 A directly as generator-side fault current.
ત્રણ-ફેઝ 20 MVA, 11 kV ઓલ્ટરનેટરનો ન્યુટ્રલ 5 ઓહ્મ અવરોધથી અર્થ કરેલો છે. રિલે 1.5 A અસંતુલિત પ્રવાહે કાર્ય કરવા સેટ છે. CTનો ગુણોત્તર 100/5 છે. વાઇન્ડિંગના 90%ના રક્ષણ માટે અર્થિંગ અવરોધનું લઘુતમ મૂલ્ય શું હોવું જોઈએ?
જવાબ અને પગલાવાર ઉકેલ
B — 2.12 Ω (સત્તાવાર કી). CT ગુણોત્તર 100/5 = 20, તેથી 1.5 A રિલે પિકઅપ = 30 A પ્રાઇમરી અવશેષ પ્રવાહ. અરક્ષિત 10% વાઇન્ડિંગ પર ઉપલબ્ધ વોલ્ટેજ = 0.1 × 11000/√3 ≈ 635 V; અર્થિંગ અવરોધ આ વોલ્ટેજ અને 30 A સાથે સંબંધિત છે.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
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.
Quick Trick
Always refer relay current to primary before using system voltage.
Common Mistake
Using 1.5 A directly as generator-side fault current.
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