--- title: "Percentage differential protection of alternator" subject: "Switchgear and Protection" chapter: 7 key: "semester_6/switchgear_and_protection:alternator-percentage-differential" source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/alternator-percentage-differential site: BCT Engineering --- # Percentage differential protection of alternator Switchgear and Protection · Chapter 7: Protective Relays - Asked in: 2070 Bhadra, 8 marks; 2073 Bhadra, 8 marks (asked 2 times) - Video: [SGP412 Simple Differential Protection of Alternators](https://www.youtube.com/watch?v=Or79KmTrbx0) — Lectures in Electrical Engineering - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/alternator-percentage-differential - Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-7 ## Question Explain with a neat sketch the percentage differential protection of an alternator. ## Short answer Percentage differential protection compares currents at both ends of stator winding. A restraining coil carries through current, while an operating coil carries the difference. It trips when differential current exceeds a set percentage of through current, providing stability against CT errors during external faults and sensitivity for internal faults. ## Answer **Percentage (biased) differential protection** of an alternator compares the current entering and leaving each phase winding; it trips when the difference exceeds a fixed percentage of the through current. It protects the stator against phase-to-phase and phase-to-earth faults (Merz-Price scheme with bias). #### Why "percentage" (biased) is needed In a simple differential (circulating current) scheme, the two CTs of a phase never match perfectly. During heavy external faults, CT saturation and ratio errors make a spill current flow in the relay, which can cause a false trip. A **restraining (bias) coil** carrying the through current raises the operating current in proportion to the load, so the relay stays stable on external faults but is sensitive to internal faults. #### Arrangement ```text Neutral side Line side CT1 ┌──── stator winding ────┐ CT2 ──(○)──┤ ├──(○)──► to bus │ I₁ I₂ │ │ │ └──R/2──┬───────────┬──R/2────┘ │ restraining coil R │ └────► O ◄─────────────┘ operating coil (mid-point) (one such set per phase; star point of CTs connected to the relay neutral) ``` - Identical CTs are placed at the neutral end and the line end of each phase winding. - CT secondaries are connected so that their currents circulate in the pilot wires. - The **restraining coil** is connected in the pilot wires (carries (I₁ + I₂)/2). - The **operating coil** is connected between the mid-point of the restraining coil and the CT star point (carries I₁ − I₂). #### Operation - **Normal load or external fault:** I₁ = I₂, so the operating coil current is nearly zero. Any small spill current due to CT mismatch is overcome by the large restraining torque. - **Internal fault:** current in the faulty winding differs at the two ends (or one end gets reversed current when the generator is in parallel with others). A large differential current I₁ − I₂ flows in the operating coil, its torque exceeds the restraining torque and the relay trips the generator breaker and field breaker. **Operating condition:** ```text |I₁ − I₂| > K × (|I₁| + |I₂|)/2 + I₀ K = bias slope (typically 5–20%), I₀ = minimum pick-up ``` #### Characteristic ```text Operating │ / Trip zone current │ / |I₁−I₂| │ / slope K │ / │____/ No-trip (restrain) zone └────────────────────── through current (I₁+I₂)/2 ``` #### Features - Protects about 85–90% of the winding against earth faults (when neutral is earthed through resistance, faults near the neutral give little current); a separate restricted earth fault or 100% stator earth fault relay covers the rest. - Fast, selective; unaffected by load or external faults. - Needs CTs of identical characteristics; pilot wires are short since both CTs are near the machine. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is a restraining (bias) coil used in the differential protection of an alternator? A. To make the relay slower on internal faults B. To stop false tripping from CT mismatch/saturation spill current during heavy external faults C. To increase the CT ratio D. To supply the field breaker Answer: B. CT errors and saturation cause spill current on external faults; the restraining coil raises the operating threshold in proportion to through current so the relay stays stable. (Key point: Why bias is needed) 2. In the scheme described, which currents do the operating coil and restraining coil carry? A. Operating: (I1+I2)/2; restraining: I1-I2 B. Both carry I1 only C. Operating: I1-I2; restraining: (I1+I2)/2 D. Operating: I1+I2; restraining: I1-I2 Answer: C. The operating coil carries the difference I1-I2 and the restraining coil carries the through (average) current (I1+I2)/2. (Key point: Operating and restraining coils) 3. What happens in the relay for an external fault compared with an internal fault? A. External: large operating current, trips; internal: restrains B. External: I1 = I2 so operating current is near zero and restraint dominates; internal: large I1-I2 exceeds restraint and trips C. Both cases give identical operating current D. External fault trips only the field breaker Answer: B. For through faults the two CT currents are equal so there is almost no operating current; for internal faults the difference is large and the operating torque exceeds the restraining torque. (Key point: Behaviour on external vs internal fault) 4. The operating condition |I1-I2| > K(|I1|+|I2|)/2 + I0 means that: A. The relay trips when the difference exceeds a percentage (slope K) of the through current plus a minimum pick-up B. The relay trips only when I1 = I2 C. K is the CT ratio D. I0 is the restraining current Answer: A. K is the bias slope (about 5-20%) and I0 the minimum pick-up, so the threshold grows with through current. 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