---
title: "Three phase transformer connections and applications"
subject: "Electrical Machines"
chapter: 2
key: "semester_4/electrical_machines:three-phase-transformer-connections"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/three-phase-transformer-connections
site: BCT Engineering
---

# Three phase transformer connections and applications

Electrical Machines · Chapter 2: Transformer

- Asked in: 2075 Baisakh (old course), 5+3 marks
- Video: [3-phase Transformer Connections | Star-to-Star, Delta-to-Delta, Star-to-Delta & Delta-to-Star](https://www.youtube.com/watch?v=CUpoOHMlMdY) — Electrical Deck
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/three-phase-transformer-connections
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-2

## Question

Explain the different three phase transformer connections with neat sketch. Write their application also.

## Short answer

The four basic connections are star–star (Yy) for small HV units, delta–delta (Dd) for industrial loads, star–delta (Yd) for step-down at substations, and delta–star (Dy) for step-up at generating stations and distribution. Yd and Dy introduce 30° phase shift; Dd and Yy provide 0° shift.

## Answer

A three-phase transformer bank can be formed from three single-phase transformers or from one three-phase unit. The primary and secondary windings can each be connected in star (Y) or delta (Δ), giving four basic connections.

Let $V_L$ be the primary line voltage, and $a = N_1/N_2$ the turns ratio per phase.

#### 1. Star–Star (Y–Y)

```text
   Primary (star)            Secondary (star)
  A o--(N1)--+              a o--(N2)--+
  B o--(N1)--+--o N         b o--(N2)--+--o n
  C o--(N1)--+              c o--(N2)--+
```
- Line voltage ratio $V_{L1}/V_{L2} = a$. No phase shift between primary and secondary (0°).
- Needs a neutral connection, otherwise unbalanced loads and third-harmonic voltages cause trouble.
- **Applications:** small high-voltage, low-current transformers, since each phase winding carries only $V_L/\sqrt3$ and needs less insulation; small distribution loads with a neutral (4-wire).

#### 2. Delta–Delta (Δ–Δ)

```text
   Primary (delta)           Secondary (delta)
         A                          a
         o                          o
    N1  / \  N1                N2  / \  N2
       /   \                      /   \
    B o-----o C                b o-----o c
        N1                         N2
```
- $V_{L1}/V_{L2} = a$. No phase shift (0°). Line current = $\sqrt3\times$ phase current.
- Third-harmonic currents circulate in the delta, so the voltages stay sinusoidal. If one transformer fails, the other two can supply 58% of the original load in **open delta (V–V)**.
- **Applications:** large low and medium-voltage industrial loads where continuity of supply is needed and the load is balanced.

#### 3. Star–Delta (Y–Δ)

```text
   Primary (star)            Secondary (delta)
  A o--(N1)--+                      a
  B o--(N1)--+--o N                 o
  C o--(N1)--+                 N2  / \  N2
                                  /   \
                               b o-----o c
                                   N2
```
- $V_{L1}/V_{L2} = \sqrt3\,a$, with a 30° phase shift between primary and secondary line voltages (for example Yd1, where the secondary lags by 30°).
- When stepping down, the star primary on the HV side has a phase voltage of only $V_L/\sqrt3$, so less insulation is needed, and the delta secondary lets third-harmonic currents circulate.
- **Applications:** step-down transformers at the receiving end of a transmission line (substations).

#### 4. Delta–Star (Δ–Y)

```text
   Primary (delta)           Secondary (star)
         A                  a o--(N2)--+
         o                  b o--(N2)--+--o n
    N1  / \  N1             c o--(N2)--+
       /   \
    B o-----o C
        N1
```
- $V_{L2}/V_{L1} = \sqrt3/a$ (step-up), with a 30° shift. The star secondary provides a neutral.
- **Applications:** step-up transformers at the generating station and distribution transformers (11 kV/415 V, Dyn11), giving a 4-wire supply. The delta suppresses third-harmonic currents.

#### Comparison

| Connection | Line ratio | Phase shift | Typical use |
|---|---|---|---|
| Y–Y | $a$ | 0° | Small HV units |
| Δ–Δ | $a$ | 0° | Industrial loads |
| Y–Δ | $\sqrt3a$ | 30° | Step-down |
| Δ–Y | $V_{L2}/V_{L1} = \sqrt3/a$ | 30° | Step-up, distribution |

Other connections: open delta (V–V) for 58% capacity, the Scott connection for 3-phase to 2-phase conversion, and zig-zag for earthing.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. A Y-Y connection has line voltage ratio and phase shift of:
   A. a and 0 degrees
   B. sqrt3 a and 30 degrees
   C. a and 30 degrees
   D. a/sqrt3 and 0 degrees
   Answer: A. Line ratio equals the turns ratio; no phase shift. (Key point: Y-Y)

2. A star-delta transformer gives:
   A. Line ratio a and 0 degrees
   B. Line ratio sqrt3 a and a 30 degree shift
   C. Line ratio a/sqrt3 and 0 degrees
   D. Line ratio 3a and 60 degrees
   Answer: B. Primary phase voltage is VL/sqrt3, secondary phase = line voltage. (Key point: Y-Delta)

3. If one transformer of a delta-delta bank fails, the remaining two (open delta) supply:
   A. 100%
   B. 67%
   C. 58% of the load
   D. 33%
   Answer: C. Open delta capacity is 1/sqrt3 = 57.7% of the original bank. (Key point: Delta-Delta open delta)

4. Delta-star is used for:
   A. Step-down at receiving end only
   B. HV transmission only
   C. Phase conversion
   D. Step-up at generating stations and distribution (4-wire) supply
   Answer: D. The star gives a neutral; the delta suppresses third harmonic currents. (Key point: Delta-Star use)

## Related in Electrical Machines

- [Three-phase transformer connections](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Athree-phase-transformer-connections) — Electrical Machines I, chapter 2
- [Scott connection for three-phase to two-phase](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ascott-connection) — Electrical Machines I, chapter 2

## Related in other subjects

- [Three-phase connections and series RC phasor](https://www.bctengineer.com/question.md?key=semester_1%2Ffundamental_of_electrical_and_electronics_engineering%3Athree-phase-connections-series-rc) — Fundamental of Electrical and Electronics Engineering, chapter 3
- [Output equation of three phase transformer](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Aoutput-equation-three-phase-transformer) — Electric Machine Design, chapter 3, asked 2×
- [Design: 125 kVA 6600/400 V three phase transformer](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adesign-125kva-three-phase-windings) — Electric Machine Design, chapter 3, asked 4×
- [Cavity magnetron with 45° phase shift and applications](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Acavity-magnetron-45-applications) — RF and Microwave Engineering, chapter 5