I think a Ynyn0 +D1 is a wye-wye transformer with a delta tertiary winding.
Both the high voltage and low voltage wye windings have neutral terminals. I believe the neutrals are tied together as inidcated by the lower case n's. The D1 tertiary winding may not supply any load. It may be there to provide for circulating zero sequence and 3rd harmonic currents.
A Dyn1 transformer is the more common delta primary, wye secondary transformer with a neutral on the secondary.
At higher voltages, it is cheaper to make a wye winding since the insulation can be graded from the high voltage end to the neutral end. The neutral end is at or near ground potential so not as much insulation is needed. On a delta HV winding, the complete winding needs the full high voltage insulation.
The delta tertiary winding on a Ynyn0 +D1 can be small if its only purpose is to provide a path for zero sequence currents. But it could be used to supply small loads. For example, one substation had a 45 MVA, 245 kV-69 kV, Y-Y transformer with a 13.8 kV delta tertiary. The tertiary fed a 150 kVA, 13.8 kV- 120/208 V transformer for station service power.
The Ynyn0 design might also be required to match the existing phase angles of the two systems. A Dyn1 introduces a phase shift between the two windings.
