--- title: "Percentage bias in differential relay" subject: "Switchgear and Protection" chapter: 7 key: "semester_6/switchgear_and_protection:percentage-bias-differential" source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/percentage-bias-differential site: BCT Engineering --- # Percentage bias in differential relay Switchgear and Protection · Chapter 7: Protective Relays - Asked in: 2072 Magh, 6 marks - Video: [Biased or Percentage Differential Relay - Introduction to Protective Relaying](https://www.youtube.com/watch?v=r7wTWYJo58w) — Ekeeda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/percentage-bias-differential - Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-7 ## Question What is meant by percentage bias? How is this achieved in practice in differential relay? Under what circumstances is a percentage differential relay preferred over the differential relay? ## Short answer Percentage bias makes operating current a set fraction (slope) of through current, preventing false trips from CT mismatch or saturation. It is achieved with restraining and operating coils in electromechanical relays or by software in numerical relays. Preferred when heavy through faults, tap changers, or unmatched CT ratios cause spill current. ## Answer **Percentage bias** means that the operating current needed to trip a differential relay is not a fixed value but a set **percentage of the through (restraining) current**. The relay operates only when ```text |I₁ − I₂| ≥ K × (I₁ + I₂)/2 + I_min ``` where K is the bias (slope), typically 10–40%. #### Need for bias In a simple differential relay, the CTs at the two ends are never perfectly matched. During heavy through faults the CTs may saturate unequally, and the transformer tap changer also causes mismatch. The resulting **spill current** may exceed a fixed setting and cause a false trip. With bias, the operating level rises as the through current rises, so the relay remains stable. #### How it is achieved in practice - The relay has a **restraining (bias) coil** and an **operating coil**. - The restraining coil is connected in the **pilot wire circuit**, with its mid-point tapped; it carries the average through current (I₁ + I₂)/2 and produces restraining torque. - The operating coil is connected between the **mid-point of the restraining coil** and the CT star point; it carries the differential current (I₁ − I₂) and produces operating torque. - In an induction or balanced-beam relay the two coils act on the same moving element in opposite directions. The ratio of the turns of the restraining and operating coils sets the percentage slope. - In static/numerical relays the same rule is applied in software, often with a dual slope (low slope at low current, steeper slope at high current). Transformer relays also add **harmonic restraint** (2nd harmonic for magnetising inrush, 5th for over-excitation), because inrush current flows on one side only and bias alone cannot stop it from tripping the relay. ```text CT1 ──────┬────R/2────●────R/2────┬────── CT2 │ restraining │ │ │ mid-point │ │ [Operating] │ │ │ │ └───────────┴───────────┘ ``` #### Characteristic ```text Operating │ / trip current │ / I₁ − I₂ │ / slope = K % │ / │__/ restrain (no trip) └────────────────────── through current (I₁+I₂)/2 ``` #### When a percentage differential relay is preferred - When the protected unit carries **heavy through-fault currents** that may saturate CTs (large generators, transformers). - When **CT ratios cannot be matched exactly** (e.g. transformer ratios that do not match standard CT ratios). - On transformers with **on-load tap changers**, where the ratio changes with tap position. - Where **long pilot leads** or unequal CT burdens cause unbalance. - In general, whenever high sensitivity to internal faults must be combined with high stability for external faults. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Percentage bias means the operating current needed to trip: A. Is fixed B. Is a fixed percentage of the through current C. Is zero D. Is a percentage of voltage Answer: B. The pickup rises with through current so it stays stable at heavy through faults. (Key point: Meaning of percentage bias) 2. In a biased relay, the operating coil is connected: A. In series with the restraining coil ends B. Between the mid-point of the restraining coil and CT star point, carrying I1 − I2 C. Across the supply D. In the primary Answer: B. The restraining coil carries (I1+I2)/2 and the operating coil carries the difference. (Key point: Coil arrangement) 3. Why is a simple differential relay unreliable on through faults? A. Pilots break B. CT mismatch and unequal saturation create spill current that may exceed the setting C. Voltage rises D. Relay is too slow Answer: B. Spill current grows with through current and can cause false trips. (Key point: Need for bias) 4. A percentage differential relay is preferred when: A. Fault currents are tiny B. CT ratios cannot match exactly or there are tap changers and heavy through faults C. Only a single CT exists D. Earth faults only Answer: B. These conditions create mismatch spill that a biased relay tolerates. (Key point: When preferred) ## Related in Switchgear and Protection - [Percentage differential relay: 125 MVA transformer](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Apercentage-differential-125mva) — Switchgear and Protection, chapter 7 - [Percentage differential relay: 150 MVA transformer](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Apercentage-differential-150mva) — Switchgear and Protection, chapter 7 - [Percentage differential protection of alternator](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aalternator-percentage-differential) — Switchgear and Protection, chapter 7, asked 2× - [Static differential relay](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Astatic-differential-relay) — Switchgear and Protection, chapter 8, asked 3× - [Static differential relay for two-winding transformer](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Astatic-differential-two-winding) — Switchgear and Protection, chapter 8 - [Differential protection: 11 kV, 100 MVA generator](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Agenerator-differential-11kv-6-ohm) — Switchgear and Protection, chapter 7 ## Related in other subjects - [Why NOS preferred over DOS](https://www.bctengineer.com/question.md?key=semester_7%2Fdistributed_system%3Anos-vs-dos-realization) — Distributed System, chapter 3, asked 2× - [Why serial transfer is preferred over parallel](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Aserial-vs-parallel-preferred) — Instrumentation II, chapter 3 - [T/F: ACSR preferred over AAAC](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-acsr-vs-aaac) — Transmission and Distribution System Design, chapter 4 - [NDT circumstances; ultrasonic pulse velocity test](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Andt-circumstances-upv) — Concrete Technology and Masonry Structure, chapter 5