3-winding transformer: tertiary (3rd) winding - zero-sequence current?

Hi guys,

I have a question about zero-phase current in a 3-winding transformer's tertiary winding. This is taken from Shorebrook PE Exam problem 22.

I understand that:

• Zero-sequence current does not flow in the primary winding because the primary winding is ungrounded, hence no ground fault path for zero-sequence current to flow.
  
• Zero-sequence current does flow in the secondary winding because the secondary winding is grounded, hence there is a ground fault path for zero-sequence to flow.
  

What I don't really understand is why zero-sequence current also flows in the tertiary winding even though the tertiary winding is ungrounded. Is it because the tertiary winding is typically on the same side of the core as the secondary winding in a 3-winding transformer?

Thanks for any help or input on this!

Technically there are zero sequence currents flow in the delta winding as circulating currents.