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T-07a: Three-Phase Transformer Connections

Section: A | Priority: 🟡 MEDIUM | Exam Frequency: 2/7 years (connections) + 2/7 (Y-Y limitations) Sources: Theraja Ch-33, VK Mehta Ch-7 (Art. 7.31–7.33), Slides L-11 S03–S14

Why This Topic Matters

Specific 3-phase connection questions appear in 2/7 papers (2018, 2024) as numericals and 2/7 papers (2021, 2023) as theory (Y-Y limitations). The real payoff is understanding context for Open-Delta (T-07b, 6/7 papers), vector groups (T-09), and parallel operation.

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📝 Key Definitions

Three-phase transformer bank: "Three-phase power can be transformed by using three single-phase transformers connected in a bank, or by using a single three-phase transformer. In either case, four types of connections are possible: Y-Y, Δ-Δ, Y-Δ, and Δ-Y." — VK Mehta, Art. 7.31

Y (Star) connection: "In star connection, similar ends (or start ends) of the three windings are connected to a common point called the neutral. Line voltage = $\sqrt{3}$ × phase voltage. Line current = phase current." — Theraja, Ch-33

Δ (Delta) connection: "In delta connection, the three windings are connected end-to-end in series to form a closed loop. Line voltage = phase voltage. Line current = $\sqrt{3}$ × phase current." — Theraja, Ch-33

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Four Standard Connections

Connection	Primary	Secondary	Phase Shift	Line Voltage Ratio (turns ratio $a$)
Y-Y	Star	Star	0°	$a:1$
Δ-Δ	Delta	Delta	0°	$a:1$
Y-Δ	Star	Delta	30° lead	$\sqrt{3}a:1$ (step-down)
Δ-Y	Delta	Star	30° lag	$a:\sqrt{3}$ (step-up)

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🏆 Golden Questions (Past Exam Archive)

🎯 Q1: What are the limitations of Y-Y connected transformers? How to overcome them?

Appeared: 2021 Q3(a) — 3 marks, 2023 Q4(b) — 4 marks

Full Answer:

Limitations:

1. Third harmonic voltage distortion. The magnetizing current of a transformer is non-sinusoidal and contains third harmonics. In a Y-Y transformer without grounded neutral, third harmonic currents have no path to flow (they are zero-sequence currents that need a neutral return). As a result, third harmonic EMFs appear in the line-to-neutral voltages, causing waveform distortion and potentially dangerous overvoltages.

2. Floating neutral problem. Under unbalanced loads, the neutral point shifts. Different phases get different voltages. One phase may get dangerously high voltage while another gets low voltage.

3. No phase shift. Y-Y gives 0° phase displacement. This limits flexibility in interconnection with other transformer groups that have 30° shifts.

Solutions:

(1) Connect the neutral to ground (4-wire system). This allows zero-sequence (third harmonic) currents to flow through the ground path. Eliminates harmonic voltages in phase-to-neutral voltages.

(2) Add a delta-connected tertiary winding. The delta provides a closed circulating path for third harmonic currents. This suppresses harmonic voltages without requiring a grounded neutral.

(3) Use Δ winding on at least one side (Y-Δ or Δ-Y connection). The delta winding inherently provides a closed path for third harmonic currents, eliminating the problem.

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🎯 Q2: 10 MVA, 11kV supply, through three Y-Δ transformers to a 230V load. Find kVA per transformer, voltage per coil, current per coil.

Appeared: 2018 Q3(b) — 6 marks

Full Answer:

Given: Total $S=10$ MVA = 10000 kVA. Primary: Y-connected at 11 kV line. Secondary: Δ-connected at 230V line.

kVA per transformer: Each transformer handles one-third:

$$S_{\text{each}}=\frac{10000}{3}=\boxed{3333.3\text{ kVA}}$$

Primary (Y-connected, 11kV line):

In Y connection: $V_{\text{phase}}=V_{\text{line}}/\sqrt{3}$ and $I_{\text{phase}}=I_{\text{line}}$.

$$V_{1,\text{coil}}=\frac{11000}{\sqrt{3}}=\boxed{6351\text{ V}}$$

$$I_{1,\text{coil}}=I_{1,\text{line}}=\frac{S_{\text{each}}\times 1000}{V_{1,\text{coil}}}=\frac{3333300}{6351}=\boxed{524.8\text{ A}}$$

Secondary (Δ-connected, 230V line):

In Δ connection: $V_{\text{phase}}=V_{\text{line}}$ and $I_{\text{phase}}=I_{\text{line}}/\sqrt{3}$.

$$V_{2,\text{coil}}=V_{2,\text{line}}=\boxed{230\text{ V}}$$

$$I_{2,\text{coil}}=\frac{S_{\text{each}}\times 1000}{V_{2,\text{coil}}}=\frac{3333300}{230}=\boxed{14492\text{ A}}$$

Line current on secondary: $I_{2,\text{line}}=\sqrt{3}\times 14492=25095$ A.

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🎯 Q3: Advantages of a transformer bank. Line voltage ratios for 10:1 turns ratio in different connections.

Appeared: 2018 Q4(c) — 4 marks

Full Answer:

Advantages of transformer bank (3 single-phase transformers instead of one 3-phase transformer):

1. Flexibility in maintenance: Can disconnect/replace one transformer at a time without complete shutdown.
2. Emergency operation: If one transformer fails, the remaining two can operate in open-Δ (V-V) at 57.7% capacity. No complete outage.
3. Expandability: Can build up the bank in stages as load grows.
4. Transportation: Three smaller transformers are easier to transport than one large 3-phase unit.

Line voltage ratios (turns ratio per phase = $a=10:1$):

Connection	Phase ratio	Line Voltage Ratio
Y-Y	10:1	10:1
Δ-Δ	10:1	10:1
Δ-Y	10:1	$10:\sqrt{3}$ = 5.77:1 (step-up on secondary)
Y-Δ	10:1	$\sqrt{3}\times 10:1$ = 17.32:1
Open-Δ	10:1	10:1 (same as Δ-Δ but 57.7% capacity)

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⚡ Exam Tips & Common Mistakes

1. Y: $V_{\text{phase}}=V_{\text{line}}/\sqrt{3}$, $I_{\text{phase}}=I_{\text{line}}$. Δ: $V_{\text{phase}}=V_{\text{line}}$, $I_{\text{phase}}=I_{\text{line}}/\sqrt{3}$.
2. Y-Δ and Δ-Y introduce a 30° phase shift. Critical for parallel operation (must match vector groups).
3. Each transformer in a bank handles $S_{\text{total}}/3$.

🔗 Related Topics

• T-07b: Open Delta — What happens when one Δ-Δ transformer fails
• T-09: Vector Groups — Phase shifts from different connections
• T-08: Scott Connection — 3-phase to 2-phase conversion

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