Hi,
The ∆-Y and Y- ∆ connections are not possible using the autotransformer.
The Y-Y connection must share a common neutral between the high-voltage and low-voltage windings, so the neutrals of the circuits connected to these windings cannot be isolated.
A ∆ – ∆ autotransformer connection is theoretically possible; however, this will create a peculiar phase shift. The phase shift is a function of the ratio of the primary to secondary voltages and it can be calculated from the vector diagram. This phase shift cannot be changed or eliminated and for this reason, autotransformers are very seldom connected as ∆ – ∆ transformers.