--- title: "Conditions for parallel operation of transformers" subject: "Electrical Machines I" chapter: 2 key: "semester_4/electrical_machines_i:transformer-parallel-conditions-reasons" source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/transformer-parallel-conditions-reasons site: BCT Engineering --- # Conditions for parallel operation of transformers Electrical Machines I · Chapter 2: Transformer - Asked in: 2074 Bhadra, 8 marks - Video: [parallel operation of transformer | transformer parallel operation | in hindi | numerical | single](https://www.youtube.com/watch?v=1k5PHBo5Yn8) — Mind of Engineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/transformer-parallel-conditions-reasons - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/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 Essential conditions: same voltage ratio and correct polarity to avoid circulating currents or short circuit; equal per-unit impedance so load shares proportionally to rating; similar X/R ratio to prevent phase difference between currents. For three-phase, same phase sequence and vector group are required. ## Answer Two transformers are in **parallel** when their primaries are connected to the same supply bus and their secondaries to the same load bus. Parallel operation is used to meet load beyond one unit's rating, for reliability (one can be taken out for maintenance) and to add capacity as load grows. ```text Supply bus ===+=============+==== | | [ T1 ] [ T2 ] | | Load bus ====+=============+==== -> load ``` #### Conditions and reasons **1. Same voltage ratio (same rated primary and secondary voltages)** - Reason: if the secondary EMFs differ, their difference drives a **circulating current** $I_c = \frac{E_A - E_B}{Z_A + Z_B}$ through the closed loop of the two secondaries even at no load. Because $Z_A + Z_B$ is small, even a small voltage difference gives a large current, causing extra copper loss, heating and reduced capacity. **2. Correct polarity** - Reason: if connected with opposite polarity, the two EMFs add round the loop instead of opposing. The loop then has $2E$ acting on a very small impedance, which is a **dead short circuit** and will damage the transformers. **3. Equal per-unit (percentage) impedance** - Reason: load divides in inverse ratio of ohmic impedance. Only when per-unit impedances on their own ratings are equal does each transformer carry load **in proportion to its kVA rating**. Otherwise the one with lower pu impedance gets overloaded before the bank reaches its full rating. **4. Same ratio of reactance to resistance (X/R)** - Reason: if X/R differ, the currents of the two transformers are not in phase with each other. Each then operates at a different power factor from the load, and the arithmetic sum of their currents exceeds the load current, causing extra loss and reduced useful capacity. **5. Same phase sequence (three-phase)** - Reason: if the sequence differs, in each cycle pairs of phases are short-circuited, giving very large currents. **6. Same phase displacement / vector group (three-phase)** - Reason: e.g. a Y-y (0°) and a Y-d (30°) cannot be paralleled; the 30° difference in secondary voltages gives a large circulating current. Transformers must be from the same group (e.g. Dyn11 with Dyn11). #### Summary | Condition | Essential? | Effect if not met | |---|---|---| | Same voltage ratio | Yes | Circulating current at no load | | Same polarity | Yes | Short circuit | | Same pu impedance | Desirable | Unequal load sharing, overloading | | Same X/R ratio | Desirable | Different pf, extra loss | | Same phase sequence | Yes (3-phase) | Short circuit between phases | | Same phase shift | Yes (3-phase) | Large circulating current | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why must parallel transformers have the same voltage ratio? A. To avoid saturation of the core B. Unequal secondary EMFs cause a circulating current even at no load C. To make polarity correct D. To equalise the X/R ratios Answer: B. The EMF difference drives Ic = (EA - EB)/(ZA + ZB) through the small loop impedance, giving large current and losses. (Key point: Voltage ratio) 2. What happens if two transformers are connected in parallel with the wrong polarity? A. The load is shared unequally B. The no-load current doubles only C. The EMFs add around the loop, causing a dead short circuit D. Only the power factor changes Answer: C. The two EMFs add (2E) around a very low-impedance loop, which is a short circuit. (Key point: Polarity) 3. Equal per-unit impedance is needed so that: A. Circulating current is zero B. Phase shift is zero C. Polarity is correct D. Each transformer shares load in proportion to its kVA rating Answer: D. Only then does each unit carry load in proportion to its rating; otherwise the lower-pu unit overloads first. (Key point: Per-unit impedance) 4. Why can a Y-y (0 degree) and a Y-d (30 degree) transformer not be paralleled? A. The 30 degree secondary voltage difference gives a large circulating current B. They have different kVA ratings C. Y-d has no neutral D. The frequency differs Answer: A. A phase displacement mismatch makes the secondary voltages unequal at every instant, causing large circulating current. 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