Three Phase Transformer

What You'll Learn

This chapter introduces the fundamental principles behind three phase transformers: what they are, how their core and windings are arranged, and how these choices affect performance in power systems. You will learn the physical construction details-core types (core-form vs shell-form), standard winding configurations (Y/Y, Y/Δ, Δ/Y, Δ/Δ), and how phase relationships and vector group notation describe their behavior. These basics matter because transformer topology sets line-to-line voltages, fault currents, harmonic behavior, and grounding practices that you will encounter in design or operation tasks.

We build on elementary electromagnetic induction and single-phase transformer concepts so you can move from familiar ideas (flux linkage, turns ratio) to how three separate phases are combined to produce balanced multi-phase operation. This chapter connects to later chapters on vector groups, parallel operation, and transformer protection by establishing the vocabulary and intuition you will use there.

Learning Objectives

• Identify core types and winding configurations used in three phase transformers.
• Explain how winding connections determine phase shifts and voltage relationships.
• Calculate basic line and phase voltages from turns ratios in a sample three phase arrangement.

How It Works

A three phase transformer is, at its simplest, three single-phase windings arranged on a common magnetic circuit or three separate cores so they share magnetizing flux and physical space. The goal is to step voltages up or down for three-phase systems while preserving phase relationships.

Key terms

• Core-form transformer - an arrangement where windings surround limbs of a rectangular laminated core; common in distribution units.
• Shell-form transformer - windings are enclosed within a central core; often used where leakage reactance control or robust short-circuit strength is needed.
• Delta (Δ) connection - each winding connects end-to-end to form a closed loop; line voltage equals winding (phase) voltage.
• Wye (Y, star) connection - one end of each winding connects to a common neutral; line voltage is √3 times the winding (phase) voltage.
• Vector group - notation (e.g., Dyn11) that specifies primary/secondary connections and phase shift (in 30° steps).

Concrete example: A 11 kV/400 V distribution transformer with a Dyn11 vector group is common. "D" indicates primary delta, "y" (lowercase) indicates low-voltage star with neutral brought out, "n" denotes neutral, and "11" means a 330° (or -30°) phase shift per IEC convention. This determines how the transformer's secondary aligns with the system for parallel operation and protective relay settings.

Step-by-step behavior

1. Magnetizing flux is produced by primary windings when energized. In a core-form, flux flows through all three limb cores; in a three-limb shell or three separate cores, flux paths differ and affect leakage reactance.

2. Each primary winding induces a secondary voltage according to turns ratio. In Y-connected windings the phase voltage ratio applies; in Δ-connected, the line-to-line relationship governs.

3. Phase relationships depend on connections: a Δ-Y transformer's secondary phases are shifted by ±30° relative to primary phases, affecting vector group designation and system compatibility.

Practical note: Leakage reactance is influenced by core geometry and the physical placement of windings. Shell-form transformers often give lower leakage reactance for a given winding arrangement-useful in station transformers where inrush and short-circuit behavior are critical.

Worked Example

Problem: Design-check a three-phase transformer with 11 kV delta primary and 400 V star secondary. The transformer nameplate specifies an ideal turns ratio such that phase-to-phase primary voltage (V1_LL) = 11,000 V and phase-to-neutral secondary voltage (V2_Ph) = 230 V. Verify the turns ratio per phase and compute line voltages on the secondary side, assuming balanced conditions.

Steps:

1. Identify given voltages: Primary line (V1_LL) = 11,000 V (delta primary means winding voltage = line voltage = 11,000 V). Secondary phase (V2_Ph) = 230 V (star secondary).

2. Determine primary phase/winding voltage: For delta, V1_Ph = V1_LL = 11,000 V.

3. Compute turns ratio (a) defined as N1/N2 = V1_Ph / V2_Ph = 11,000 / 230 ≈ 47.826.

4. Compute secondary line voltage (V2_LL) from star connection: V2_LL = √3 V2_Ph = 1.732 230 ≈ 397.4 V. Round to standard nominal 400 V for nameplate.

5. Interpret result: The applied turns ratio ensures that when 11 kV is present on the primary delta, the secondary delivers approximately 400 V line-to-line in star with neutral available.

Final answer: The per-phase turns ratio is approximately 47.83:1 and the secondary line voltage is ≈ 397.4 V (nominal 400 V).

Check Your Understanding

1. Sketch a core-form three-phase transformer and name one advantage and one drawback of this core type....