--- title: "Conditions for parallel operation of transformers" subject: "Electrical Machines" chapter: 2 key: "semester_4/electrical_machines:parallel-operation-conditions" source: https://www.bctengineer.com/q/semester_4/electrical_machines/parallel-operation-conditions site: BCT Engineering --- # Conditions for parallel operation of transformers Electrical Machines · Chapter 2: Transformer - Asked in: 2074 Bhadra (old course) - Video: [Transformer Parallel Operation | Conditions for Transformer Parallel Operation | Hindi](https://www.youtube.com/watch?v=GY3nqk2Rpcs) — Electrical With Abhishek Joshi - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/parallel-operation-conditions - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-2 ## Question State the conditions for proper operation of two transformers in parallel giving reasons for imposition of each of these conditions. ## Short answer Transformers in parallel must have same voltage ratio to prevent circulating current, same polarity and phase sequence, equal per-unit impedance for proportional load sharing, and equal X/R ratio for equal power factors. Three-phase units also need identical vector group (phase displacement). ## Answer When the load is more than one transformer can carry, or for reliability and maintenance, two or more transformers are connected in parallel (primaries to the same supply, secondaries to the same bus). The following conditions must hold. #### Essential conditions 1. **Same voltage ratio (turns ratio).** *Reason:* if the ratios differ, the secondary no-load emfs differ. A circulating current $I_c = \Delta E/(Z_{A} + Z_{B})$ then flows between the secondaries even at no load, heating the windings and wasting power. Since the transformer impedances are small, even a 1% difference gives a large current. 2. **Same polarity (terminals connected correctly).** *Reason:* with wrong polarity the two secondary emfs add round the loop instead of opposing, which acts as a short circuit and causes a very large current that can burn the windings. 3. **Same phase sequence and zero relative phase displacement (three-phase units).** *Reason:* the secondary line voltages must coincide at every instant. Otherwise there is a voltage difference between the two bus-bar connections, giving large circulating currents. Transformers with the same vector group (for example Dyn11 with Dyn11) can be paralleled; a group with a 30° shift cannot be paralleled with one of 0°. 4. **Equal per-unit (percentage) impedance on their own kVA bases.** *Reason:* load is shared in inverse proportion to the per-unit impedance. If the per-unit impedances differ, the transformer with the lower value is overloaded while the other is lightly loaded, so the combined rating is not fully used. 5. **Same ratio of resistance to reactance ($R/X$).** *Reason:* if the $X/R$ ratios differ, the two load currents are out of phase with each other. Each transformer then works at a different power factor, and the total current is less than the arithmetic sum, so the combined capacity is reduced. #### Desirable but not essential - Same frequency (always satisfied if they are on the same supply). - kVA ratings that are not too different (ratio less than 3:1), since otherwise the impedance requirement is harder to meet. In short: equal ratio, correct polarity, the same phase relation, and equal per-unit impedance with the same $X/R$ ratio. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. If the voltage ratios of two parallel transformers differ: A. A circulating current flows between secondaries even at no load B. Load sharing is perfect C. Nothing happens D. Polarity reverses Answer: A. I = delta E/(ZA + ZB), large because impedance is small. (Key point: Equal ratio) 2. Wrong polarity in parallel causes: A. Small circulating current B. A very large current like a short circuit C. Lower voltage D. Better load sharing Answer: B. Secondary emfs add in the loop. (Key point: Polarity) 3. Load is shared in inverse proportion to: A. Resistance only B. kVA rating only C. Per-unit impedance on own kVA base D. Turns ratio Answer: C. The lower per-unit impedance gets overloaded if values differ. (Key point: Load sharing) 4. Different X/R ratios lead to: A. Higher efficiency B. Equal load sharing C. No effect D. Load currents out of phase, so total capacity is reduced Answer: D. Each unit works at a different pf; the total is less than the arithmetic sum. (Key point: Same X/R) ## Related in Electrical Machines - [Conditions for parallel operation of transformers](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Atransformer-parallel-conditions-reasons) — Electrical Machines I, chapter 2 - [Need and conditions for parallel operation of transformers](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Atransformer-parallel-operation-conditions) — Electrical Machines I, chapter 2 - [Load sharing of two transformers in parallel](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aparallel-transformers-load-sharing) — Electrical Machines, chapter 2 - [Load sharing of 50 kVA and 25 kVA transformers in parallel](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aparallel-50kva-25kva-60kva-load) — Electrical Machines I, chapter 2 - [Parallel transformers and per-unit impedance load sharing](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aparallel-operation-per-unit-impedance) — Electrical Machines I, chapter 2 ## Related in other subjects - [Parallel operation conditions and three lamp method](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aparallel-conditions-three-lamp) — Electric Machines II, chapter 1, asked 3× - [Parallel operation conditions and dark lamp synchronizing](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aparallel-conditions-dark-lamp) — Electric Machines II, chapter 1, asked 3×