Three Phase Voltage and Current

THREE PHASE VOLTAGE AND CURRENT

Where again, V_L is the line-to-line voltage, and V_P is the phase-to-neutral voltage on either the primary or the secondary side.

Other possible connections for three phase transformers are star-delta Yd, where the primary winding is star-connected and the secondary is delta-connected or delta- star Dy with a delta-connected primary and a star-connected secondary.

Delta-star connected transformers are widely used in low power distribution with the primary windings providing a three-wire balanced load to the utility company while the secondary windings provide the required 4th-wire neutral or earth connection.

When the primary and secondary have different types of winding connections, star or delta, the overall turns ratio of the transformer becomes more complicated. If a three- phase transformer is connected as delta-delta (Dd) or star-star (Yy) then the transformer could potentially have a 1:1 turns ratio. That is the input and output voltages for the windings are the same.

However, if the 3-phase transformer is connected in star - delta, (Yd) each star- connected primary winding will receive the phase voltage, Vp of the supply, which is equal to 1/√3 × V_L.

Then each corresponding secondary winding will then have this same voltage induced in it, and since these windings are delta-connected, the voltage 1/√3 × V_L will become the secondary line voltage. Then with a 1:1 turns ratio, a star-delta connected transformer will provide a √3:1 step-down line-voltage ratio.

Then for a star-delta (Yd) connected transformer the turns ratio becomes:

Star-Delta Turns Ratio

TR = N_P/N_S = V_P/√3V_S

Likewise, for a delta-star (Dy) connected transformer, with a 1:1 turns ratio, the transformer will provide a 1:√3 step-up line-voltage ratio. Then for a delta-star connected transformer the turns ratio becomes:

Delta-Star Turns Ratio

TR = N_P/N_S = V_P/√3V_S

Then for the four basic configurations of a three-phase transformer, we can list the transformers secondary voltages and currents with respect to the primary line voltage, V_L and its primary line current I_L as shown in the following table.

Three-phase Transformer Line Voltage and Current

Where: n equals the transformers "turns ratio" (T.R.) of the number of secondary windings N_S, divided by the number of primary windings N_P.(N_S/N_P) and V_L is the line-to-line voltage with V_P being the phase-to-neutral voltage.