Actually, a delta connection simply has your three secondary coils in a triangle (hopefully phased correctly
. There is _no_ ground connection required for a delta.
There are three common possibilities.
1) Corner grounded delta, where one of the phase conductors is at ground potential.
2) High leg delta, where one of the secondary coils is center tapped, and the center tap grounded.
3) Ungrounded delta. No ground connection at all. Phase to ground faults don't produce significant current flow, but failures can lead to extremely high voltages across insulation.
In the case of 1 or 3 the transformer is necessary to provide the grounded neutral for single phase loads. In the case of 2 I don't know why the transformer would be required.