Find impedence given per unit value-transformer
In fact, the connection does not change the inductance of the transformers, but it does change the voltage that is applied to the coil terminals.
If you take three coils and connect in D (delta), you will have the line voltage applied directly over each coil. This means that the phase voltage will be equal to the line voltage.
If you take those same three coils and connect Y (star), the phase voltage will become √3 times lower than the line voltage.
Probably from this, the formula you presented was derived.