Scott connection — three-phase to two-phase conversion

Reference notes

The Scott connection, devised by Charles F. Scott of Westinghouse around 1890, converts between three-phase and two-phase systems using just two single-phase transformers. Use Next → to walk through the wiring, the geometric derivation of the 86.6 % teaser ratio, the phasor proof that the two outputs are 90 ° apart, and modern applications.

Why 3-φ ↔ 2-φ conversion still matters

• Legacy two-phase systems — early AC infrastructure (Niagara Falls, 1895) used 2-φ. Some industrial 2-φ loads still exist in older US municipal plants.
• Single-phase AC electric railway — traction feeders draw large single-phase loads. Connecting them L-L to a 3-φ grid creates severe unbalance. A Scott substation transformer splits the load between two adjacent track sections fed in quadrature, so the 3-φ grid sees a roughly balanced load.
• Two-phase motor drives and instrumentation — some legacy 2-φ control systems, certain instrument-transformer protective schemes.

The two-transformer set

• Main transformer M — full primary connected line-to-line across phases B and C (so the primary sees V_BC). Center tap O brought out at exactly the midpoint.
• Teaser transformer T — primary rated for 86.6 % of V_L, connected between phase A and the center tap O of M.
• Both secondaries are wound for the same voltage; together they form the 2-φ output.

Geometric derivation — the 0.866 ratio

Draw the 3-φ supply as an equilateral triangle of line-to-line voltages with vertices A, B, C, each side of length V_L:

• The mid-tap O of M sits at the midpoint of side BC.
• The teaser primary V_AO is the altitude from vertex A to the opposite side.
• Altitude of an equilateral triangle = (√3 / 2) · side length:

So the teaser primary must be wound for 86.6 % of V_L at the same volts-per-turn as M to produce a matching secondary voltage.

Phasor proof of 90° output

• M's secondary voltage is in phase with V_BC.
• T's primary V_AO is perpendicular to V_BC — because in any equilateral triangle the altitude from a vertex is perpendicular to the opposite side.
• Therefore T's secondary V₂ is perpendicular to M's secondary V₁ — exactly 90 ° apart. With equal magnitudes, the result is a balanced two-phase output:

Load balance — bidirectional

• Balanced 2-φ load (equal kVA, equal PF on both secondaries) → balanced 3-φ primary currents, equal magnitudes, 120 ° apart. Phase A carries the teaser current; phases B and C each carry the main current plus half the teaser return through the mid-tap.
• Unbalanced 2-φ load → unbalanced 3-φ primary. The unbalance is far smaller than connecting the same single-phase load directly line-to-line on the 3-φ grid, but it's not zero.

The Le Blanc alternative

The Le Blanc connection uses three single-phase transformers with specific tap arrangements and achieves perfect balance for any 2-φ load condition. Costs more iron and copper than Scott. Preferred where strict balance matters; Scott is the practical choice when only two transformers are available and modest unbalance is acceptable.

Modern applications

• Single-phase AC traction substations — convert 3-φ HV grid (138 kV / 230 kV) into two 25-kV or 50-kV feeders for adjacent track sections, run in 90 ° quadrature so the upstream grid sees balanced load.
• Legacy 2-φ industrial motors — elevators, certain water-plant drives. Many are gradually being replaced with VFD-driven 3-φ motors.
• Instrument transformer applications — Scott-derived quadrature voltages for certain relaying schemes.

Keyboard shortcuts

• The phasor panel shows the equilateral triangle of line voltages with V_AO as the altitude — a direct geometric derivation of why the Scott bank produces 90 ° outputs.