Three-winding transformers

Reference notes

A three-winding transformer puts primary, secondary, and tertiary windings on a single iron core, sharing the same flux. Use Next → to walk through the three short-circuit-test impedances, the Y-equivalent circuit, simultaneous power flow patterns, and the regulation and protection considerations specific to 3-winding designs.

Construction & typical application

• Three windings — primary, secondary, tertiary — magnetically coupled by the same core flux.
• Common configuration: generator step-up (GSU). Primary at generator voltage (13.8 kV typical), secondary at grid voltage (138–345 kV), tertiary at station auxiliary voltage (6.6 or 13.8 kV). The tertiary saves the cost of a separate auxiliary distribution transformer.
• Each winding has its own kVA rating (e.g., 100/60/40 MVA = primary/secondary/tertiary).
• Auto-transformers nearly always include a delta tertiary (covered in the auto-transformer lesson).

Three measured impedances

Unlike a 2-winding transformer with a single short-circuit impedance, the 3-winding has three independent leakage impedances measured by pairwise short-circuit tests with the third winding open:

• Z_ps — short secondary, open tertiary, drive from primary.
• Z_pt — short tertiary, open secondary, drive from primary.
• Z_st — short tertiary, open primary, drive from secondary.

All three on a common kVA base.

Y-equivalent circuit

Model the three windings as three branches Z_p, Z_s, Z_t meeting at a common (fictitious) node N. From Z_ps = Z_p + Z_s, Z_pt = Z_p + Z_t, Z_st = Z_s + Z_t:

One leg can come out negative. This is valid math, not an error — it signals magnetic coupling effects that don't decompose into three separate physical inductors. Use the value as written for analysis.

Power flow patterns

• P → S: bulk flow from generator to grid (most kVA on the primary-secondary path).
• P → T: primary feeds tertiary station-service loads.
• P → S + T: simultaneous — the common case in service.
• S → T or T → S: when the primary is disconnected, power can still flow between secondary and tertiary via the magnetic coupling.

Power balance: V_p·I_p + V_s·I_s + V_t·I_t = losses (signs by current convention).

Regulation interdependence

Secondary terminal voltage in the Y-equivalent:

Increased tertiary current I_t increases the current through the shared primary leg Z_p, which drops the common-node voltage and therefore drops both secondary AND tertiary terminal voltages. Voltage regulators must account for this cross-coupling.

Applications beyond GSU + station service

• Auto-transformer with delta tertiary — triplen-harmonic suppression and neutral stabilization.
• Tie between three grids — interconnecting two transmission voltages plus a subtransmission feed.
• 12-pulse rectifier feed — two secondaries shifted 30° drive parallel 6-pulse bridges, cancelling 5th and 7th harmonics.
• Dual-rating industrial supplies — split-phase or harmonic-compensation loads.

Protection

ANSI 87T differential for a 3-winding transformer requires 3 sets of CTs (one per winding), summed on a common kVA base. Internal faults disturb the balance and trip the relay. Modern numerical relays auto-compensate for the three winding ratios and vector groups.

Other practical considerations

• Fault current contribution — when a fault occurs on the secondary, BOTH primary and tertiary feed it. Breaker interrupting ratings must include both contributions.
• kVA rating per winding — typically described as P/S/T MVA, e.g., 100/60/40. Flow patterns must respect ALL three simultaneously.
• OLTC placement — usually on one winding (most often the primary) since multiple OLTCs are mechanically and economically awkward. Tap changes on the primary affect both secondary and tertiary voltages proportionally.