--- title: "Static differential relay" subject: "Switchgear and Protection" chapter: 8 key: "semester_6/switchgear_and_protection:static-differential-relay" source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/static-differential-relay site: BCT Engineering --- # Static differential relay Switchgear and Protection · Chapter 8: Static and Digital Relays - Asked in: 2070 Magh, 8 marks; 2073 Bhadra, 8 marks; 2077 Chaitra, 8 marks (asked 3 times) - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/static-differential-relay - Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-8 ## Question Explain the working principle of static differential relay with the proper block diagram and circuit diagram. ## Short answer It compares line and terminal currents. Spill current |i1−i2| is rectified to V_o; bias voltage V_r ∝ (|i1|+|i2|)/2 from separate rectifiers. Amplitude comparator trips when V_o > K·V_r (percentage bias). Harmonic restraint (e.g. 2nd) blocks trip during transformer inrush. ## Answer A **static differential relay** compares the currents at the two ends of a protected zone (transformer, generator, bus) using electronic circuits. It trips when the difference (spill) current exceeds a set percentage of the through (bias) current. #### Block diagram ```text CT1 ─┐ ┌─ CT2 ▼ ▼ [Aux CT] [Aux CT] │ i1 i2 │ ├────────┬───────────────┤ │ │ │ [Bias rect] [Diff (spill) [Bias rect] │ rectifier] │ └──► Σ bias │ operate ◄─┘ │ │ ┌────▼─────▼─────┐ │ Amplitude │ │ comparator │ └───────┬─────────┘ [Level detector] [Harmonic restraint] [Amplifier]→[Output]→Trip ``` #### Circuit (simplified) ```text CT1 sec (i1) CT2 sec (i2) │ │ ├─[bridge B1]─┐ ┌─[bridge B2]─┤ │ ▼ ▼ │ │ R_b ─┴──┴─ R_b │ │ bias voltage V_r │ │ ∝ (|i1| + |i2|)/2 │ └────────[bridge B3]───────────┘ spill |i1 − i2| │ R_o → V_o (operate) │ [comparator: V_o − K·V_r > 0 ?] → trip ``` #### Working principle 1. Auxiliary CTs step down currents i1 and i2 and correct ratio/phase mismatch. 2. **Bias (restraining) circuit:** rectifies i1 and i2 and forms V_r ∝ (|i1| + |i2|)/2, the through current. 3. **Operating (spill) circuit:** rectifies the difference |i1 − i2| to give V_o. 4. **Comparator:** an amplitude comparator (rectifier bridge or op-amp) compares V_o with K·V_r. Trip when |i1 − i2| > K·(|i1|+|i2|)/2 (percentage bias, K ≈ 10–40%). 5. **Harmonic restraint (for transformers):** a filter extracts the 2nd harmonic of the spill current; if it is large (inrush), the trip is blocked. 5th-harmonic restraint blocks tripping during over-excitation. 6. **Level detector and output:** when the comparator output exceeds threshold, a transistor/thyristor switches the trip relay. #### Advantages over electromechanical type Very fast (about 1 cycle), low CT burden, precise bias slope, easy harmonic restraint, and unaffected by vibration. Used for transformer, generator and busbar protection. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. When does a static differential relay trip? A. When the spill current exceeds a set percentage of the through (bias) current B. When the through current exceeds the spill current C. When both CT currents are equal D. When voltage is zero Answer: A. Trip when |i1-i2| > K(|i1|+|i2|)/2, a percentage bias characteristic. (Key point: Trip condition) 2. What does the bias (restraining) voltage V_r represent? A. The difference |i1 - i2| B. The through current, proportional to (|i1|+|i2|)/2 C. The line voltage D. The harmonic content Answer: B. The rectified currents are summed to give the through-current restraint. (Key point: Bias circuit) 3. What does the operating voltage V_o represent? A. The sum of the two CT currents B. The rectified difference (spill) current |i1 - i2| C. The CT ratio error D. The DC supply Answer: B. The operating circuit rectifies the difference current and compares it with K x V_r. (Key point: Operating circuit) 4. What is 2nd-harmonic restraint used for in transformer differential protection? A. To block tripping during magnetising inrush B. To speed up tripping for faults C. To remove the bias D. To measure frequency Answer: A. Inrush current is rich in 2nd harmonic, so a large 2nd harmonic blocks the trip; 5th harmonic restrains for over-excitation. 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