# 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 (CTC), and 75°C/120°C temperature corrections.

- **Category:** Winding Design & Losses
- **Author:** Voltformer Coil Design & Thermal Engineering
- **Publication Date:** 2026-03-29
- **Reading Time:** 8 min read
- **Key Tags:** #Load Loss, #Pk Loss, #CTC Cable, #Stray Loss, #IEC 60076-1
- **Canonical URL:** https://voltformer.com/articles/transformer-load-loss-pk-stray-loss-eddy-current-mitigation
- **Markdown Source:** https://voltformer.com/articles/transformer-load-loss-pk-stray-loss-eddy-current-mitigation.md

### 1. Load Loss Structure per IEC 60076-1

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

$$ P_k = P_{dc} + P_{stray} = I^2 R_{dc} + P_{we} + P_{ws} $$

#### Loss Component Breakdown:
- **$P_{dc}$:** Direct current $I^2 R$ resistance loss in copper or aluminium conductors.
- **$P_{we}$:** Eddy current losses inside the winding conductors caused by transverse leakage magnetic fields.
- **$P_{ws}$:** 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 $B_y$:

$$ P_{we} \approx \frac{m \cdot \omega^2 \cdot B_y^2 \cdot h^2}{24 \cdot \rho} \quad [\text{W}] $$

Because $P_{we}$ is proportional to $h^2$, 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 $T_{test}$ are converted to reference temperature $T_{ref}$ (75°C for liquid-immersed, 120°C / 145°C for dry-type Class F/H):

$$ P_k(T_{ref}) = P_{dc}(T_{test}) \cdot \frac{235 + T_{ref}}{235 + T_{test}} + P_{stray}(T_{test}) \cdot \frac{235 + T_{test}}{235 + T_{ref}} \quad [\text{for Copper}] $$

### 4. Practical Engineering Guidelines

- For large power transformers ($>10\text{ MVA}$), 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.*

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