All theories claim that there is a phase displacement of 180 deg between the voltage in primary and secondary. How this phase shift is over come when designing a transformer? For example a Dyn11 Transformer is having only 30 Deg phase shift and not 180 plus or minus 30 Deg. Please explain.
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All theories claim that there is a phase displacement of 180 deg between the voltage in primary and secondary.
What you say is 100% incorrect.
If you wind two coils together on a core and you applied AC to one of them and then used an oscilloscope to look at the voltage waveforms on the driven coil and the undriven coil you will find that the two AC voltages are in phase. They are only 180 degrees out of phase if you reversed the scope connections to one of the windings.
This can be easily proven by considering the same two windings being put in parallel and driven by an AC signal - if one were naturally prone to produce a 180 degrees phase shift then when connecting them in parallel across an AC source, infinite current would flow.
For the DYN 11 configuration you have to understand 3phase theory. Here's the phasor diagram that explain the 30 degree phase shift: -
See also this stack exchange answer for more details on the 30 degree phase shift.
