Three-phase transformer connections + vector groups

Reference notes

Use Next → on the narrator above to step through the four basic three-phase transformer connections — Yy, Dd, Yd, Dy — and learn the clock-notation language used to describe their phase displacement and the paralleling rules that follow.

From three single-phase transformers to a 3-phase bank

A three-phase transformer is just three identical single-phase transformers, one per phase, with their primaries connected together on the outside and their secondaries connected together on the outside. The choice of how to connect each side — star (Y) or delta (D) — is the vector group. We label the high-voltage terminals A, B, C in capitals and the low-voltage terminals a, b, c in lowercase. By convention, the high-voltage line voltage V_AB is drawn along the positive x axis as the reference phasor.

Vector-group notation

The vector group has three parts:

• Capital letter — high-voltage winding connection: Y for star, D for delta.
• Small letter — low-voltage winding connection: y for star, d for delta. An n after the letter (e.g. yn) means the neutral is brought out and grounded.
• Digit 0–11 — the clock position of the low-voltage line voltage relative to the high-voltage line voltage. The HV reference sits at 12 o'clock; each clock step is 30° clockwise (LV lagging). 0 means no shift; 1 means LV lags HV by 30°; 11 means LV leads HV by 30° (equivalent to lagging by 330°).

Yy0 — star-star, 0° displacement

Both windings are connected in star — three phase ends joined at a common neutral point, available for grounding on both sides. Phase voltages connect each line to neutral; line voltages connect line to line. On both sides:

Because the two stars have matching winding orientations, the HV and LV line voltages are in phase — clock position 0, hence Yy0.

Pure Yy without a tertiary delta is rarely used in power transformers. The reason is triplen harmonics — the 3rd, 9th, 15th, 21st… harmonics that arise from the non-linear magnetising current. Triplens are in phase across all three legs, so with both neutrals isolated they have no closed path to circulate; instead they distort the phase voltages. Adding a delta-connected tertiary winding gives the triplens a low-impedance loop and removes the distortion.

Dd0 — delta-delta, 0° displacement, optional open-delta

Both windings are connected in delta — each winding sees the full line voltage. On both sides:

The clock number is again 0 because both windings have matching orientations. Delta-delta has no neutral on either side, so it cannot directly feed single-phase line-to-neutral loads.

Its key operational advantage is the open-delta (V-V) standby: if one of the three single-phase units fails, you disconnect it and the remaining two still supply a balanced three-phase load. The catch is reduced capacity:

It buys time while a replacement transformer is procured — a meaningful resilience feature for industrial sites.

Yd1 — star-delta, LV lags by 30°

HV is star (so V_LL,HV = √3 · V_phase,HV and a neutral is available on the HV side). LV is delta (so V_LL,LV = V_phase,LV, no LV neutral). The clock number 1 means the LV line voltage points to 1 o'clock — exactly 30° clockwise of the HV reference, so LV lags HV by 30°.

Common applications: generator step-down transformers (the HV neutral lets you ground the generator's star point through a resistor or reactor); any setting where the HV side needs a neutral but the LV side does not.

Worked example — Yd1 voltage stepping

A Yd1 transformer steps down a 132 kV line-to-line HV voltage with a turn ratio (HV winding : LV winding) of 11 : 1. What is the LV phase voltage?

1. HV phase voltage = V_LL,HV / √3 = 132 / √3 ≈ 76.21 kV
2. LV phase voltage = HV phase voltage / turn ratio = 76.21 / 11 ≈ 6.93 kV
3. LV line voltage = LV phase voltage (because LV is delta) = 6.93 kV

The turn ratio always acts on phase voltages, not on line voltages. That is why getting the phase-vs-line conversion right on both sides is the heart of every three-phase transformer calculation.

Dyn11 — delta-star-neutral, LV leads by 30° (the distribution workhorse)

HV is delta. LV is star with grounded neutral (the n). The clock number 11 means the LV phasor sits at the 11 o'clock position — 30° counter-clockwise of the HV reference, so LV leads HV by 30° (equivalently, LV lags by 11 × 30° = 330° clockwise).

Dyn11 is by far the most common distribution transformer in the world. Two reasons:

• HV delta blocks zero-sequence currents from propagating to the transmission network and provides a closed loop for triplen harmonics in the magnetising current — so they don't distort the line voltages.
• LV grounded star gives the distribution feeder a neutral, so it can supply both three-phase line-to-line loads and single-phase line-to-neutral loads from the same transformer.

Yd1 and Dyn11 together cover the overwhelming majority of three-phase power transformers in service worldwide.

Paralleling rules — all four must match

To operate two three-phase transformers in parallel, four parameters must match:

1. Vector group — same phase displacement. Mismatched vector group creates a circulating current driven by the phase difference between the secondaries.
2. Voltage ratio — same V_HV : V_LV. Mismatched ratio creates a circulating current driven by the secondary voltage difference.
3. Percent impedance — same per-unit Z. Mismatched %Z causes the lower-impedance transformer to take a disproportionate share of the load.
4. Phase sequence — same ABC ordering. Mismatched phase sequence is a line-to-line short circuit at the moment of paralleling — the worst failure mode.

Two transformers from the same vector-group family (e.g. both Dyn11 or both Yd1) can be paralleled directly if the ratio and impedance match. Two transformers from different families with the same numeric shift but different letter orientation cannot be paralleled by simple lead reordering — the internal winding pattern doesn't match.

Why we suppress triplen harmonics

The transformer iron is non-linear; the magnetising current is rich in 3rd, 9th, 15th… harmonics. Those harmonics are in phase across all three legs (unlike the fundamental and the non-triplen harmonics, which are 120° apart). In a delta loop they circulate freely and dissipate as harmless circulating losses. In an isolated-neutral star with no delta loop they can't circulate, so they push the phase voltages into distorted, peaky shapes. A grounded neutral plus a low-impedance ground path can also drain them — but a delta winding (primary, secondary, or tertiary) is the cleanest solution and is why most three-phase transformers contain a delta somewhere in the design.

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