Three Phase Transformers And Three Winding Transformers

Three Phase transformers

Three phase transformers usually have all three phases on one iron structure and can be connected in Y(Star) – Δ(Delta),  Δ(Delta) – Y(Star). Other possible connections are Y – Y and,   Δ – Δ where the first symbol refers to the connection of the primary windings and the second symbol refers to the connection of the secondary winding.

Three Winding transformers.

Some transformers have three windings: primary, secondary and tertiary windings. It is possible to measure three impedances by the standard short circuit tests as follows

Z_ps = Leakage impedance measured in primary with secondary short circuited and tertiary open.

Z_pt = Leakage impedance measured in primary with tertiary short circuited and secondary open

Z_st = Leakage impedance measured in secondary with tertiary short circuited and primary open

We note that

Zps = Zp + Zs

Zpt = Zp + Zt                                                                             {*}

Zst = Zs + Zt

Where Zp, Zs and Zt are  the impedances of the primary, secondary and tertiary windings referred to the primary circuit and Zps, Zpt, Zst are the measured impedances referred to the primary circuit.

Solving the equation {*} simultaneously will yield

Z_p  = ½ (Z_ps + Z_pt - Z_st)

Z_s  = ½ (Z_ps + Z_st - Z_pt)

Z_t  = ½ (Z_pt + Z_st - Z_ps)

 

The impedance of the three windings are connected in star to represent the equivalent circuit of a three winding transformer with magnetizing current neglected.