Odd triplen harmonics act like zero sequence currents. The delta provides a trap for zero sequence/triplen harmonics and turns the grounding point into a ground source.
At present time, in most cases delta winding on (high voltage) autotransformers, as well as YNyn transformers, is not only unnecessary, but also detrimental.
Magnetizing current for large unit is now less than 0.1%, and its zero sequence components are even lower. Furthermore the three-limbs core structure acts as a "phantom" delta tertiary: the high zero sequence reluctance acts as a low impedance path for zero sequence currents; proper design of flux shields allows to cope with umbalanced loads, with are by the way uncommon in high voltage transmission systems.
On the other hand, the delta winding is a weak point from the mechanical point of view, being interested by short circuit currents in case of single-phase to ground fault, which are the most common ones in the HV grid.
Of course, the tertiary winding also increase the cost, weight and losses of the ATR.
Since the '70s we eliminated tertiary delta windind in our YNyn transformers and autotransformers of any size (10 to 600 MVA).
The only (uncommon) case in which you could realy need a delta winding in an HV autotransformer is when you need to substantially reduce the earth fault factor of the transfmission network.
On LV application, you could need the delta winding only if the loads are significantly umbalanced.
Si duri puer ingeni videtur,
preconem facias vel architectum.
