Three-Winding Transformer (Tertiary Winding): Principle, Construction, Equivalent Circuit & Applications
A three-winding transformer—often called a tertiary winding transformer—adds a third coil to the standard primary–secondary pair. This extra winding unlocks powerful capabilities: suppression of triple harmonics, voltage stabilization under unbalance, earth-fault current paths, and a convenient way to supply auxiliaries at a different voltage. Below is a complete, student-friendly guide you can use for study or as a polished reference article.
What Is a Three-Winding Transformer?
A three-winding (triple-wound) transformer contains three electrically separate windings: primary (input), secondary (main output), and tertiary (auxiliary/stabilizing). It can transfer energy to two distinct circuits at once, offering flexibility in voltage levels and system control.
Why Add a Tertiary Winding? (Key Purposes)
The tertiary winding serves one or more of the following purposes:
| Purpose | How It Helps |
|---|---|
| Supply station auxiliaries | Feeds lighting, motors, controls at a convenient voltage without a separate transformer. |
| Phase-compensating devices | Connects capacitor banks or synchronous condensers on EHV systems via a dedicated winding. |
| Load balancing | Balances split-winding generators and asymmetrical loads, reducing voltage unbalance. |
| Earth-fault current path | Provides sufficient zero-sequence current for protective relays to operate correctly. |
| Harmonic suppression | Closed-delta tertiary circulates triplen (3rd, 9th, …) harmonics, cleaning the waveform. |
| Stabilization | Limits voltage unbalance; when used mainly for stability it’s often called a stabilizing winding. |
Principle of Operation
As with any transformer, the primary establishes a core flux that links the other windings. The difference here is that both secondary and tertiary receive induced e.m.f. simultaneously and can deliver power to separate loads. During faults or unbalanced conditions, the tertiary—especially in a closed-delta—allows circulating currents to flow, compensating unbalance and limiting distortion.
Governing Equations
Current balance and magnetizing relationships (all per phase, referenced appropriately):
I₁N₁ = −(I₂N₂) + (I₃N₃) + I₀N₁ (1)
I₁ = I₂′ + I₃′ + I₀ (2)
where I₂′ = −I₂·(N₂/N₁) and I₃′ = −I₃·(N₃/N₁)Induced-e.m.f. equations using self and mutual leakage impedances (values reduced to a consistent base):
E₁ = −(I₂Z₁₂ + I₃Z₁₃) − I₁Z₁₁ (3)
E₂ = −(I₁Z₁₂ + I₃Z₂₃) − I₂Z₂₂ (4)
E₃ = −(I₁Z₁₃ + I₂Z₂₃) − I₃Z₃₃ (5)Construction & Winding Arrangements
Three-winding transformers can be built as a single 3-phase unit or as three 1-phase units in a bank. The windings operate at three distinct voltages—commonly labeled HV, MV, and LV. The HV winding is placed nearest to the core to optimize insulation and leakage reactance.
Common radial arrangements (from core outward):
- LV → MV → HV
- MV → LV → HV
Unlike a two-winding transformer, the overall kVA of a three-winding design is taken as the largest kVA rating among its windings. The tertiary’s cross-section is chosen for its duty— either continuous loading (auxiliary supply) or short-duration currents (fault control, balancing).
Equivalent Circuit & Short-Circuit Tests
Each winding is modeled by its resistance and leakage reactance; mutual terms capture coupling effects. You can determine the six equivalent leakage impedances via short-circuit (SC) tests, energizing two windings while the third is open:
SC between 1 & 2 (3 open): Z′₁₂ = Z₁₁ + Z₂₂ + 2Z₁₂ (6)
SC between 2 & 3 (1 open): Z′₂₃ = Z₂₂ + Z₃₃ + 2Z₂₃ (7)
SC between 3 & 1 (2 open): Z′₃₁ = Z₃₃ + Z₁₁ + 2Z₃₁ (8)From these, solve for the self-impedances:
Z₁₁ = ½ (Z′₁₂ + Z′₃₁ − Z′₂₃) (9)
Z₂₂ = ½ (Z′₁₂ + Z′₂₃ − Z′₃₁) (10)
Z₃₃ = ½ (Z′₂₃ + Z′₃₁ − Z′₁₂) (11)Role of Closed-Delta Tertiary (Balancing & Harmonics)
Without a tertiary, unbalanced loading can depress the middle-phase voltage and increase distortion. A closed-delta tertiary provides a circulating path for zero-sequence and triplen-harmonic components, cleaning the flux waveform and helping the primary current remain balanced and nearly sinusoidal.
- Supplies third-harmonic magnetizing current locally → improved e.m.f. waveform.
- Shares unbalanced load currents → mitigates voltage unbalance.
- Reduces excitation needed for a stable, sinusoidal flux.
Advantages & Limitations
Key Advantages
- Flexibility: Multiple voltage levels from one transformer.
- Stability: Balances currents under asymmetrical loading.
- Power quality: Suppresses triplen harmonics via closed delta.
- Protection: Enables adequate earth-fault current for relays.
- Economy: Reduces need for separate auxiliary transformers.
Limitations
- Higher initial cost and design complexity.
- Additional copper/iron losses; careful thermal design required.
- Tertiary may run lightly loaded except during unbalance/fault duty.
Practical Applications
- Power stations: Tie generators, feeders, and station service at different voltages.
- HV/EHV substations: Feed auxiliaries and harmonic filters via tertiary.
- Inter-system links: Interconnect networks operating at dissimilar voltages.
- Load centers: Improve voltage profile and balance across feeders.
- Reactive power devices: Interface synchronous condensers or capacitor banks.
Frequently Asked Questions
1) What’s the main job of a tertiary winding?
To stabilize operation—by balancing unbalanced currents, suppressing triplen harmonics, providing earth-fault current—and to supply auxiliaries at a different voltage.
2) Why is the tertiary often connected in a closed delta?
Closed delta offers a natural path for zero-sequence and triplen-harmonic currents, preventing them from appearing in line voltages and improving waveform quality.
3) Is the transformer kVA equal to the sum of all three windings?
No. The overall transformer kVA is taken as the largest kVA rating among its windings.
4) What decides the copper size of the tertiary?
Its duty: continuous (auxiliary load) or short-time (fault control/balancing). In practice, cross-section is often chosen from fault-current thermal limits.
5) Can a three-winding transformer be built as single-phase units?
Yes. Three single-phase transformers can be banked for a 3-phase system, though a single 3-phase unit is more common in large installations.
Conclusion
The three-winding transformer is indispensable in modern power systems. By adding a tertiary winding, it strengthens stability, improves power quality, enables effective protection, and conveniently supplies auxiliary loads. Although costlier than a standard two-winding design, its system-level benefits—especially at HV/EHV—more than justify the investment.