Conditions for parallel operation of transformers

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.