Three-Phase Transformer A three-phase system in used to generate and transmit electric power. Three-phase voltages are raised or lowered by means of three-phase transformers. A three-phase transformer can be built in two ways By suitably connecting a bank of three single-phase transformers By constructing a three-phase transformer on a common magnetic structure (Y−Y , ∆ − ∆ , Y− ∆ or ∆ −Y)

Three-Phase Transformer Connections The primary or secondary windings may be connected in either star (Y) or delta (∆)arrangement. The four most common connections are Y-Y ∆-∆ Y-∆ ∆-Y.

Y-Y Connection

∆-∆ Connection

Y-∆ Connection

∆-Y Connection

Three-Phase Transformation with Two Single-Phase Transformers connection of two identical single-phase transformers in open delta(or V-V connection) T-T connection (or Scott connection) of two non identical single-phase transformers

Open-Delta or V-V Connection

The transformer windings ab and bc will deliver power given by Pab = Vab Ia cos (30° + φ) Pbc = Vcb Ic cos (30° − φ) Let Vab = Vcb = V, the voltage rating of transformer secondary winding Ia = Ic = I, current rating of the transformer secondary winding

p.f. = 1 i.e. φ= 0° ... For resistive load Power delivered to the resistive load by V-V connection is Pv = Pab + Pbc = Vab Ia cos (30° + φ) + Vcb Ic cos (30° − φ) = Vab Ia cos (30°) + Vcb Ic cos (30°) = V I cos (30°) + V I cos (30°) = 2 V I cos (30°)

With all the three transformers connected in delta, the power delivered to the resistive load is P = 3 V I Pv / P = 2 V I cos (30°) / 3 V I = 0.577 Hence the power-handling capacity of a V-V circuit (without overheating the transformers) is 57.7% of the capacity of a complete ∆-∆ circuit of the same transformers

In a V-V circuit, only 86.6% of the rated capacity of the two transformers is available.

Power Factor of Transformers in V-V Circuit When V-V circuit is delivering 3-phase power, the power factor of the two transformers is not the same If the load power factor angle is φ, then p.f. of transformer 1 = cos (30°− φ) p.f. of transformer 2 = cos (30° + φ)

i) When load p.f. = 1 i.e. φ = 0° In this case, each transformer will have a power factor of 0.866. ii) When load p.f. = 0.866 i.e. φ= 30° In this case, one transformer will have a p.f. of cos (30°−30°) = 1 and the other of cos (30° + 30°) = 0.5 When load p.f = 0.5 i.e. φ= 60° p.f. of cos (30°−60°) = 0.866 and the other of cos (30° + 60°) = 0.

Applications of Open Delta or V-V Connection The circuit can be employed in an emergency situation when one transformer in a complete ∆-∆circuit must be removed for repair and continuity of service is required. Upon failure of the primary or secondary of one transformer of a complete ∆-∆ circuit, the system can be operated as V-V circuit and can deliver 3-phase power (with reduced capacity) to a 3-phase load.

Scott Connection or T-T Connection