--- title: "Static differential relay for two-winding transformer" subject: "Switchgear and Protection" chapter: 8 key: "semester_6/switchgear_and_protection:static-differential-two-winding" source: https://www.bctengineer.com/q/semester_6/switchgear_and_protection/static-differential-two-winding site: BCT Engineering --- # Static differential relay for two-winding transformer Switchgear and Protection · Chapter 8: Static and Digital Relays - Asked in: 2070 Bhadra, 8 marks - 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-two-winding - Whole chapter: https://www.bctengineer.com/md/semester_6/switchgear_and_protection/chapter-8 ## Question Describe the circuit of static differential relay for protection of two winding transformer. ## Short answer A static differential relay for a two-winding transformer compares HV and LV CT currents after interposing CTs correct ratio and 30° phase shift. The bias circuit produces a restraint voltage proportional to through current; the spill circuit produces an operating voltage from the differential current. A 2nd-harmonic filter provides restraint during magnetizing inrush. An amplitude comparator checks if operating voltage exceeds K×restraint plus harmonic voltage; a high-set unit trips instantly for heavy internal faults. Output trips both HV and LV breakers. ## Answer For a **two-winding power transformer**, a static differential relay compares the currents of the HV and LV CTs (after ratio and phase correction) and trips when the spill current exceeds a set percentage of the through current, with **harmonic restraint** to stay stable during magnetising inrush. #### Circuit / block diagram (one phase) ```text HV══CT1════[TRANSFORMER]════CT2══LV │ (Δ/Y) │ [Interposing CT, [Interposing CT, ratio & 30° corr.] ratio & 30° corr.] │ i1 i2 │ ├──[Bias rect.]──┬─[Bias rect.]──┤ │ │ V_r │ └──────[Spill CT / summing]──────┘ │ i1 − i2 ┌───────────┼─────────────┐ [Fundamental] [2nd harmonic] [Unrestrained filter → filter → high-set rectifier] rectifier] level det.] │ V_o │ V_h │ ┌─────▼─────────────▼──┐ │ │ Comparator: │ │ │ V_o > K·V_r + V_h ? │ │ └─────────┬────────────┘ │ └──────────[OR]──────────┘ │ [Amplifier → thyristor] │ Trip HV & LV CBs ``` #### Description of the circuit 1. **Main CTs and interposing CTs:** main CTs on both sides; interposing (auxiliary) CTs match the current magnitudes (inverse of voltage ratio) and correct the 30° phase shift of Δ/Y connection. They also remove zero-sequence currents so that external earth faults do not cause tripping. 2. **Bias (restraint) circuit:** i1 and i2 are rectified separately and summed across resistors to give V_r ∝ (|i1| + |i2|)/2 – the through current. 3. **Operating (spill) circuit:** the difference current (i1 − i2) is passed through a filter tuned to 50 Hz and rectified to give V_o. 4. **Second-harmonic restraint:** a 100 Hz filter extracts the 2nd harmonic in the spill current. During inrush (2nd harmonic > about 15–20% of fundamental) V_h becomes large and blocks tripping. A 5th-harmonic filter may be used for over-excitation restraint. 5. **Comparator:** an amplitude comparator (op-amp) checks V_o > K·V_r + V_h. K is the bias slope (15–40%) which covers CT mismatch, tap-changer range and CT errors. 6. **Unrestrained (high-set) unit:** for very heavy internal faults (spill > 8–10 × rating) it trips immediately without waiting for harmonic analysis, because CT saturation may produce harmonics. 7. **Output:** OR gate, amplifier and thyristor/auxiliary relay trip both HV and LV circuit breakers. **Result:** stable for load, external faults and inrush; fast (about 1–2 cycles) and sensitive for internal winding faults. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What are the functions of the interposing CTs? A. Match current magnitudes, correct the 30 degree Delta/Star phase shift, and remove zero-sequence current B. Increase the burden C. Generate DC D. Provide the trip signal Answer: A. They compensate ratio and phase mismatch so that load and external faults give near-zero spill. (Key point: Interposing CTs) 2. The comparator trips when: A. V_o > K*V_r + V_h B. V_o < K*V_r C. V_h = 0 D. V_r > V_o Answer: A. Operating voltage must exceed bias plus harmonic restraint; K (15-40%) covers CT mismatch and tap range. (Key point: Trip condition) 3. Why is a 100 Hz (2nd harmonic) filter included? A. Inrush current is rich in 2nd harmonic, so it blocks tripping during inrush B. To detect internal faults faster C. To remove the bias D. To measure load Answer: A. A large 2nd harmonic (above about 15-20%) makes V_h large and blocks the trip. (Key point: Second harmonic restraint) 4. Why is an unrestrained high-set unit included? A. To trip immediately for very heavy internal faults when CT saturation may produce harmonics B. To block tripping C. To detect inrush D. To supply DC Answer: A. For spill above 8-10 times rating it trips at once, bypassing harmonic restraint. (Key point: High-set unit) ## Related in Switchgear and Protection - [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× - [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 - [Differential protection of power transformer](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Atransformer-differential-protection) — Switchgear and Protection, chapter 7 - [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 - [Percentage bias in differential relay](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Apercentage-bias-differential) — Switchgear and Protection, chapter 7 ## Related in other subjects - [Reluctances and air gap flux of two-winding core](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Atwo-winding-core-reluctance-airgap-flux) — Electrical Machines I, chapter 1 - [Protection for alternator and step-up transformer](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Amega-project-protection) — Power Plant Design, chapter 4 - [Transformer protection, selection and vector group](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Atransformer-protection-vector-group) — Power Plant Design, chapter 4 - [Design: 100 kVA 11/132 kV transformer with winding data](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adesign-100kva-11-132kv) — Electric Machine Design, chapter 3, asked 3×