In delta zig-zag connection the primary is connected in delta.Each secondary winding is made in two halves such as a1-a2,b1-b2,c1-c2 and the six halves are then connected to form a zig zag connection.A1,a1,a2 are of same polarity and similarly for other phases.If the voltage of each half of the transformer secondary is V1/2,the pjase voltage of the secondary system is (sqrt(3)/2)*V2 and the line voltage is 3/2*V2. Thus in delta zig zag connection the line voltage transformation ration is 1.5 times the phase turn-ratio is 3/2 times line transformation ratio.

A zig-zag transformer is a special form of autotransformer used to provide grounding (earthing) on three-phase systems that otherwise have no connection to ground . It has primary windings but no secondary winding.They provides a path for current that is common to all three phases.Another application includes control of harmonic currents