Hi Reza,

I would say that the answer depends on which vector group is getting swapped with which one ? The concept has been used in different transformer combos.

For example, in early 1990's there used to be a primitive FACTS device (now dated, as far as I know !) called the inter-phase power controller, that worked on exactly such a principle.

-Sanjay

Yes, power flow is affected by selection of power transformer's vector groups.

http://www.electrical4u.com/vector-group-test-of-power-transformer/

http://waset.org/publications/16272/the-effect-of-transformer-s-vector-group-on-retained-voltage-magnitude-and-sag-frequency-at-industrial-sites-due-to-faults

http://electrical-engineering-portal.com/principles-of-transformers-in-parallel-connection-1

http://electrical-engineering-portal.com/understanding-vector-group-transformer-1

The vector group of a transformer does not change the power flow of a system. Basically, the power flow is the steady state condition of the system and therefore must assume that all transformers are properly connected. If you had a transformer improperly connected, given its vector group, you would have a system fault and thus could not have a steady state.