An extended-delta output is formed by adding voltages from selected winding segments. Their directions follow phase, polarity and connection. The target angle alone is insufficient: the sum must also have the required magnitude and phase sequence. IEC 61378-1 covers industrial converter-transformer specification, design and testing [1].
Write the segment vectors from the actual diagram before calculating turns. A reversed phase segment can change a 120-degree relationship into a 60-degree one, but that relationship must be demonstrated rather than assumed.
One explicit vector construction
For this assumed construction, let the available segment directions be 0° and 60°. Require their sum to have magnitude U and angle δ between those directions. Write U exp(jδ) = a + b exp(j60°), where a and b are segment voltage magnitudes.
Resolving components gives b = U sin δ/sin 60° and a = U sin(60° − δ)/sin 60°. With a common volts-per-turn e, required turns are Na = a/e and Nb = b/e.
| Illustrative target δ | a/U | b/U | Interpretation |
|---|---|---|---|
| 15° | About 0.81650 | About 0.29886 | Positive segments sum to unit magnitude at 15° |
| 0° | 1 | 0 | No second-vector contribution in this construction |
The fractions describe the defined vector triangle, not every extended-delta design. Changing segment directions or output reference changes the equations.
Recalculate after rounding turns
Assume this vector construction uses U/e = 100 turns and target δ = 15° with available segment directions 0° and 60°. Ideal turns are 81.6497 and 29.8858. Selecting 82 and 30 gives |82 + 30 exp(j60°)| = 100.4191 turns-equivalent and angle 14.9943°: magnitude is 0.4191% high and angle is 0.0057° low. Compare those two errors with the project’s separate ratio and phase limits; search other allowed integer pairs if either fails. Retain the resulting vectors, rather than the ideal target, in the production schedule.
Search permitted integer combinations or adjust a justified common turn scale within the complete design constraints. A combination that improves phase may change magnitude, core excitation or another segment’s duty.
Verify all output phases
Apply the same connection logic to every phase and check phase sequence, magnitude balance and angular separation. Then check loop-voltage closure where the winding connection forms a polygon or delta. A correct single output vector cannot establish that the complete circuit is consistent.
Include each tap if the tap changes the segment relationship. Source evidence from special-transformer testing shows why ratio and phase need to be assessed together, but it supplies no universal angle tolerance for this design.
Record segment directions, fractional-turn calculations and the selected integer turns beside their resulting voltage vectors. The reviewer can then check the phase and magnitude effect of rounding at the specific segment where it enters.
Check ratio and phase on the actual special connection and selected tap [2].
References
- IEC, IEC 61378-1:2011, Converter transformers – Part 1: Transformers for industrial applications.
- Gandhi Jeyaraj, S., Milne, R., and Mitchell, G., On-Site Testing of Special Transformers, Megger technical paper, Sections 2–6.