What are the causes of unbalance current during no load test of transformer?

OK

Since you see the current between two phases on the delta winding, this means the one winding is either at fault, or (more likely) the secondary has a fault - I would guess one high voltage winding has a fault somewhere along its winding to earth (the star point being earthed) or has an inter-turn winding fault.

This phase will be the one corresponding to the branch of the delta connecting both current taking phases (~8A).

Can you flash test the hv windings - ~27-35kV as it may be an insulation breakdown issue, so won't be shown via an insulation resistance test?

If its an inter-turn winding fault it is a little more difficult to detect with an assembled tx.

(The above assumes there is absolutely nothing connected on the hv side - obviously if there is a single phase load/fault in that part of the system it will reflect as a phase-phase load/fault on the primary )
The star point is not earthed, All the transformer test results are satisfactory, Test we conducted are following;
IR (Both Windings), TTR, Open Circuit Test, Winding resistance
 

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Created
za1820,
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Julie.,
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