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.*