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What are the impacts if I connect transformers in parallel having different short-circuit impedance?

For successful parallel operation, the transformers require:
  • the same phase-angle relation – clock-hour number (additional possible combinations are mentioned below);
  • the same ratio with some tolerance and similar tapping range;
  • the same relative short-circuit impedance – percentage impedance – with some tolerance, this also means that the variation of relative impedance across the tapping range should be similar for the two transformers.
It is not advisable to combine transformers of widely different power rating (e.g. more than 1:2). The natural relative impedance for optimal designs varies with the size of the transformer.
Transformers built according to different design concepts are likely to present different impedance levels and different variation trends across the tapping range.

When parallel connections made between transformers with different short-circuit impedances, a reduction of total power occurs, the below example illustrates this: 

Let us assume that three transformers operate in parallel.
The first transformer has 800 kVA rated power and 4.4% short-circuit impedance. The rated power and the short-circuit impedance of the other two transformers is 500 kVA and 4.8%, and 315 kVA and 4.0%, respectively.
Calculate the maximum total load of the three transformers.
Among the three transformers, the third transformer has the minimum short-circuit impedance
• The load of transformer 1
Pn,1 = P1 × (Uk,min)/(Uk,1) = 800 × 4/4.4 = 728 kVA
• The load of transformer 2
Pn,1 = P2 × (Uk,min)/(Uk,2) = 500 × 4/4.8 = 417 kVA
• The load of transformer 3
Pn,1 = P3 × Uk,min)/(Uk,2) = 315 × 4/4 = 315 kVA
• The maximum load of the three transformers is:
Ptot = Pn,1 + Pn,2 + Pn,3 = 728 + 417 + 315 = 1460 kVA
• The three transformers have total installed power:
P = P1 + P2 + P3 = 800 + 500 + 315 = 1615 kVA
From the above, it is concluded that the maximum total load (1460 kVA) represents the 90.4% of the total installed power (1615 kVA).
It should be noted that, in order the maximum total load to be equal to the total installed power, the transformers must have the same short-circuit impedance.
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