b Transformer currents and voltages Figure 741 Wye delta connected transformer

# B transformer currents and voltages figure 741 wye

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(b) Transformer currents and voltages Figure 7.41 Wye-delta connected transformer Wye-Delta Connection The physical turns ratio for the wye-delta transformer is then At the primary side, the amplitude of the line-to-line voltage is 3 times the line-to-neutral voltage and the phase shift between these voltages is 30° for a balanced system A ba ab AN I I V V s p N N T Y 30 120 3 j j e e AN AN AN BN AN AB V V V V V V Wye-Delta Connection The phase shift between the primary V AB and secondary line-to-line voltages V ab is also 30° The secondary line-to-line voltage V ab drives current through the load Further analysis reveals that the wye-delta transformer shifts both the line current and the line-to-line voltage by 30°. The secondary line currents lag the primary line currents by –30°; and the secondary line voltages lag the primary line voltages by –30°. 30 240 3 j j e e ba ba ba ac ba a I I I I I I Transformers Karady & Holbert 17 EEE 360 Three-Phase Transformers Example for Wye–Delta Connection Wye-Delta Connection Example Three 100 kVA , 7.2 kV/120 V, x tr = 10% transformers are connected wye-delta to form a three-phase bank The three-phase bank is loaded by 240 kW, pf = 0.8 lagging The transformer impedance is placed on the wye side The equivalent circuit is Wye-Delta Connection Example Calculate the transformer reactance ܺ ்௥ ൌ ݔ ௧௥ ܸ ்௥௣ ܵ ்௥ ൌ ሺ0.1ሻ ሺ7200 Vሻ 100 ൈ 10 VA ൌ 51.84 Ω Place the transformer reactance on the wye side The turns ratio of the transformer is the ratio of the primary and secondary rated voltages ܶ ்௥ ܸ ்௥௣ ܸ ்௥௦ 7200 V 120 V ൌ 60 Line-to-neutral voltage Line-to-line voltage Wye-Delta Connection Example The reference voltage is the supply network phase AN (line-to-neutral) voltage: V AN = 7.2 kV The supply network phase BN (line-to-neutral) voltage, has the same amplitude but shifted by –120° ܄ ۰ۼ ൌ ሺ7.2 kVሻ ݁ ି௝ ଵଶ଴° ൌ ሺെ3.6 െ ݆ 6.235ሻ kV The supply network line-to-line voltage is ܄ ۯ۰ ൌ ܄ ۯۼ െ ܄ ۰ۼ ൌ 7.2 െ െ3.6 െ ݆ 6.235 kV ܄ ۯ۰ 10.8 ൅ ݆ 6.235 kV ܄ ۯ۰ ൌ 12.47 kV Wye-Delta Connection Example The transformer primary voltage in the no-load condition is the same as the supply network voltage The transformer primary voltages in phases AN is the reference voltage: ܄ ۯۼ ൌ 7.200 kV ܸ ஻ே ൌ 7200 ∗ ݁ ି௝∗ଵଶ଴ ௗ௘௚ = ( -3600-6235j)V The line-to-line voltage in phase AB ܸ ஺஻ ൌ ܸ ஺ே െ ܸ ஻ே ൌ 7200ܸ െ െ3600 െ 6235݆ ܸ ܸ ஺஻ 10.8 ൅ 6.235݆ ܸ݇, ܸ ஺஻ ൌ 12.41 ܸ݇ Wye-Delta Connection Example The voltages V ab and V AN are in the same leg of the iron core, consequently the two voltages are in phase Accordingly, the secondary line-to-line voltage V ab is in phase with transformer primary line-to-neutral V AN voltage 