Transformer Vector Group Formulas
Transformer vector group formulas: the turns ratio of a delta-star unit, the line and phase currents on each side and the phase shift from the clock number.
The formulas
| To find | Formula |
|---|---|
| Line voltage ratio | a = VH / VL |
| Turns ratio, delta primary and star secondary | N1 / N2 = VH / (VL / √3) = √3 × a |
| Line current on a side | I = S × 1000 / (√3 × V) |
| Delta winding phase current | Iph = Iline / √3 |
| Phase shift from the clock number n | angle = n × 30° (low voltage lags high voltage) |
VH and VL are the line voltages of the high and low side in volts and S the rating in kVA. In a delta winding the phase voltage is the line voltage and the phase current is the line current divided by √3. In a star winding the phase voltage is the line voltage divided by √3 and the phase current is the line current. The letters give the connection (capital for the high-voltage side, small for the low side, D delta, Y star, n for a neutral), and the number is the clock position of the low-voltage phasor when the high-voltage phasor is at twelve. Transformers can only be paralleled when they have the same group.
Worked example: a 1,000 kVA, 11 kV delta / 415 V star unit
- Line ratio = 11,000 / 415 = 26.51
- LV phase voltage = 415 / √3 = 239.6 V, so the turns ratio is 11,000 / 239.6 = 45.91
- LV line current = 1000 × 1000 / (√3 × 415) = 1,391 A
- HV line current = 1000 × 1000 / (√3 × 11,000) = 52.49 A and the delta phase current is 52.49 / √3 = 30.3 A
Common vector groups
| Group | Phase shift of the low-voltage side |
|---|---|
| Dyn1 | 30° lagging |
| Dyn5 | 150° lagging |
| Dyn11 | 330° lagging (30° leading) |
| Yd1 | 30° lagging |
| Yy0 | 0° |
Frequently asked questions
Why is Dyn11 common in distribution?
The delta winding traps the third harmonic and zero-sequence current of an unbalanced load, and the star side gives a neutral for single-phase loads.
What does the number in the group mean?
It is the clock position of the low-voltage phasor against the high-voltage phasor at twelve, and each hour is 30°.
Can I parallel a Dyn11 with a Dyn1?
No. The 60° difference in phase would drive a large circulating current.
Is the turns ratio the same as the voltage ratio?
Not for a delta-star unit. The turns ratio is √3 times the line voltage ratio because the star winding has a phase voltage of VL / √3.
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