what is the purpose of tertiary delta winding in auto transformer ?

A tertiary delta winding transformer would be used for the following:

1) To limit the fault level on the LV
system by subdividing the infeed that is, double secondary transformers.

2) The interconnection of several
power systems operating at different supply voltages.

3) The regulation of system voltage
and of reactive power by means of a synchronous capacitor connected to the
terminals of one winding.

It is desirable that a
three-phase transformer should have one set of three-phase windings connected
in delta thus providing a low-impedance path for third-harmonic currents. The
presence of a delta connected winding also allows current to circulate around
the delta in the event of unbalance in the loading between phases, so that this
unbalance is reduced and not so greatly fed back through the system.