Parallel Transformer Load Sharing Formulas

Parallel transformer formulas: how a load divides by rating and impedance, the loading of each unit and the largest load before one transformer is full.

The formulas

Sn is the rating in kVA and z the impedance in percent on its own rating. The unit with the lower impedance takes more than its share and is the first to reach 100%. The formula assumes that the transformers have the same voltage ratio, the same vector group and a similar X/R ratio, and it is a simple estimate of the division. In the largest load formula z,min is the lowest impedance, and the other units are then below their rating. Transformers with very different ratings (more than about 3 to 1) are not usually paralleled.

Worked example: 1,000 kVA at 5% with 630 kVA at 4.5%

A total load of 1,400 kVA.

1. Σ(Sn / z) = 1000 / 5 + 630 / 4.5 = 340
2. S1 = 1400 × (1000 / 5) / 340 = 823.5 kVA, which is 82.35% of its rating
3. S2 = 1400 × (630 / 4.5) / 340 = 576.5 kVA, which is 91.5% of its rating
4. Smax = 1000 × 4.5 / 5 + 630 = 1,530 kVA, against 1,630 kVA installed

Frequently asked questions

Why does the smaller transformer carry more of its rating?

It has the lower impedance, so it takes a larger share of the current. The share goes with the rating divided by the impedance.

What must match for paralleling?

The voltage ratio, the vector group (the phase shift) and the phase sequence. The impedances should be close, and the ratings not too far apart.

What if the impedances are equal?

Then the load divides in proportion to the ratings and every unit has the same loading.

Does the formula include the cables?

No. The impedance of the cables to each unit changes the share, so add it to the transformer impedance when it is not small.

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