It is always desirable to have one delta connection winding in the three phase transformer as delta connected three phase winding will offer low impedance path for the three phase currents. Also the presence of delta connected three phase winding allows to circulate the current around the delta winding in the event of unbalance loading condition.
Although power system designers aims to avoid use of star/star transformer in power system but cases will arise when the phase shift between the star/delta and delta/star is not applicable such as in the power station supplying power to auxiliary system. Therefore it is common practice to have a star/star with delta tertiary three winding transformer supplying power to the plant auxiliary system.
B/H Curve of the magnetic material (core of the transformer) is not linear. Is a sinusoidal voltage (flux) is applied across the primary winding, the magnetizing current obtained will not be sinusoidal in nature and consists of fundamental component and several harmonics. Third harmonic components predominate with several other higher harmonic components. If there is no delta connected winding, or if the star connections of the transformers are not grounded, the line to earth capacitance currents supply system lines supply the harmonic components. If the harmonic components cannot flow in any one of these paths then, secondary voltage will be distorted.