“Black box” transformer: Y-Y, Y-Δ, or Δ-Δ connected?

As a preface, this is purely hypothetical. I know better than to use a transformer without knowing anything about it. I'm just trying to get an idea of whether this is possible, not whether it's a good idea.

Let's say I have a three-phase transformer that I know nothing about. I have three primary leads and three secondary leads, and that's it. No markings or anything, no datasheet, just a box with wires sticking out of it.

Is there any way to determine with external measurements how the windings are wired? I know that I can look at phase shift between primary and secondary to determine whether it's Y-Δ, but if there is no phase shift, is it possible to distinguish Y-Y from Δ-Δ? If there is phase shift, is it possible to determine which winding is Y and which is Δ?

Ideally I'd like answers that only involve measurements and physical properties. I'm aware there are conventions like using Δ on the high side of a Y-Δ transformer, but assume this transformer was wired by someone completely ignorant of any and all conventions and common sense. That means that either side could be Y or Δ without regard to relative voltages, and the neutral wire on a Y connection may not be present. You can assume the transformer is balanced, however, with three identical primary windings and three identical secondary windings.

• Where's the motivation given that even if you knew the star delta stuff you wouldn't be able to use it without knowledge of supply voltage and VA rating? – Andy aka Mar 16 '20 at 13:36
• The side that has the neutral terminal on it is the 'Y' side. – Neil_UK Mar 16 '20 at 13:52
• If you only have three primary and three secondary wires I would guess $\Delta - \Delta$ connection as I would expect to see neutral out if either was a 'Y' connection. But without details you can't use it. – Warren Hill Mar 16 '20 at 14:02
• @Andyaka This is a hypothetical scenario, I'm wondering if it's possible, not if it's useful. – Hearth Mar 16 '20 at 16:20
• @Neil_UK A Y connection without a neutral is possible too, though. Sure, you don't normally see that, but it's possible. – Hearth Mar 16 '20 at 16:21