The zigzag connection is a three-phase connection and is constructed as shown in Figure below. There are three pairs of windings, each having a 1:1 turns ratio. The left-hand set of windings shown in the figure is a conventional Y connection, a′-b′-c′, with the neutral N brought out.
The open ends of the Y are electrically connected to the right-hand set of windings as follows: a′connects to the right-hand winding paired with to the b′-N winding, b′connects to the right-hand winding paired to c′-N winding, and c′connects to the right-hand winding paired to the a′-N winding. The opposite ends of the right-hand windings are brought out as the phase terminals
a, b, and c.
If three currents, equal in magnitude and phase, are applied to the three terminals, the ampere-turns of the a′-N winding cancel the ampere-turns of the c′- c winding, the ampere-turns of the b′-N winding cancel the ampere turns of the a′-a winding, and the ampere-turns of the c′-N winding cancel the ampere turns of the b′-b winding. Therefore, the transformer allows the three in-phase currents to easily flow to neutral. If three currents, equal in magnitude but 120°out of phase with each other, are applied to the three terminals, the ampere-turns in the windings cannot cancel and the transformer restricts the current flow to the negligible level of magnetizing current. Therefore, the zigzag winding provides an easy path for in-phase currents but does not allow the flow of currents that are 120° out of phase with each other and we can assume Z1=Z2 = very big.
Also for obtaining of R0 and X0 you can use the following equation: