Transformer Load Loss (Pk) Optimization: CTC Conductors and Stray Loss Mitigation

Detailed formulation of I²R ohmic losses, winding eddy current losses (Pwe), stray losses in structural clamping parts (Pws), continuously transposed conductors

1. Load Loss Structure per IEC 60076-1

Total load loss (Pk) at rated current consists of DC ohmic resistance losses and stray losses:

Pk = Pdc + Pstray = I2 Rdc + Pwe + Pws

Loss Component Breakdown:

  • Pdc: Direct current I2 R resistance loss in copper or aluminium conductors.
  • Pwe: Eddy current losses inside the winding conductors caused by transverse leakage magnetic fields.
  • Pws: Stray losses in structural components (clamping beams, tie rods, core frames, and tank walls).

2. Mathematical Formulation of Winding Eddy Losses

For a conductor of thickness h perpendicular to the leakage flux density By:

Pwe ≈ (m · ω2 · By2 · h2) / (24 · ρ) [W]

Because Pwe is proportional to h2, replacing single solid conductors with Continuously Transposed Conductors (CTC) divided into individually insulated enamel strands reduces winding eddy losses by up to 80%.

3. Reference Temperature Correction per IEC 60076-1

Measured losses at test temperature Ttest are converted to reference temperature Tref (75°C for liquid-immersed, 120°C / 145°C for dry-type Class F/H):

Pk(Tref) = Pdc(Ttest) · (235 + Tref) / (235 + Ttest) + Pstray(Ttest) · (235 + Ttest) / (235 + Tref) [for Copper]

4. Practical Engineering Guidelines

  • For large power transformers (>10 MVA), magnetic copper or aluminium shielding plates along the internal tank perimeter suppress stray flux concentrations.

*Reference: IEC 60076-1:2011; IEEE Std C57.12.00-2021.*