Introducing third winding in Transformer
With two identical windings both driven in phase, the winding with the highest supply voltage will produce the magnetization current for the core. In addition to that magnetization current, it will also supply a potentially excessive current to the winding that is driven with a lower voltage. 

This scenario will cause a significant volt drop across the leakage reactances and inevitably reduce the voltage that excites the core magnetization inductance. Because of the leakage component volt-drops, the magnetization current would reduce.