# Analysing and Computing the Impact of Geometric Asymmetric Coils on Transformer Stray Losses
## 4 Design Parameters and Loss Values
### Estimation of the Impact of Winding Asymmetry  
The study used Finite Element Method (FEM) simulation and the proposed simple model (2) to assess the impact of asymmetry in transformer windings as well as to estimate losses associated with different heights and widths. Figure 6 illustrates magnetic field values obtained through FEM without magnetic shunts around the tank walls, showcasing variations in winding heights and widths. Case 4 characterised by larger dimensions of the outer winding (high-voltage winding) compared to the low-voltage winding yielded the highest values for stray magnetic fields. Conversely, Case 1, representing the ideal scenario with identical heights and widths for all windings, demonstrated the lowest values for stray magnetic fields. In Figure 7, a comparison for Case 1 reveals field values with and without magnetic shunts. Notably, the presence of magnetic shunt protection along certain walls led to a decrease in stray magnetic fields. However, in areas without protection, such as the left wall (Lw), the stray magnetic field increased. This observation underscores the effectiveness of magnetic shunts in reducing losses and highlights their practical utility in transformer design. Table 4 presents a compilation of results derived from varying the heights and thicknesses of the windings for the purpose of visualising their impact. Parameters Tyb and Byb were added, denoting Top yoke beams and Bottom yoke beams, respectively. The findings indicate that when the design aims for equal dimensions in both height and width, there is a noticeable reduction in the stray magnetic field. Consequently, this reduction contributes to a decrease in additional losses, amounting to approximately 4.2%. On the contrary, during the design phase, when the high voltage winding is configured with greater height and width than the low voltage winding, it results in an increase in the stray magnetic field. As a consequence, additional losses also increase, reaching approximately 16.1% in comparison to the ideal case (Case 1) and around 11.2% in the real case. The results, detailed in Table 5, demonstrate a consistent trend of magnetic shunts effectively contributing to a reduction in losses, achieving a significant decrease of around 44.2%. Figure 8 depicts the values of \(\mid\)B\({}_{\text{d}}\mid\) obtained through the proposed model (6)-(9) for both the real case and case 2. Notably, the values of He and \(\mid\)H\({}_{\text{d}}\mid\) were determined as \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Losses** & **By FEM** & \(\mid\)**1 B\(\mid\)d \(\mid\) by FEM** & **By (9 \& 2)** \\ \hline Lw, left side wall & 6853 W & 0.520 T & 6455 W \\ Rw right side wall & 3457 W & 0.428 T & 2720 W \\ Fw, front wall & 3151 W & 0.322 T & 3199 W \\ Bw, rear wall & 2814 W & 0.320 T & 3151 W \\ Bottom wall & 1565 W & 0.324 T & 1651 W \\ Top wall & 624 W & 0.211 T & 697 W \\ Top yoke beams & 530 W & 0.266 T & 499 W \\ Bottom yoke beams & 704 W & 0.299 T & 632 W \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Stray losses and \(\mid\)B\({}_{\text{d}}\mid\) estimation with magnetic shunts. \(7.69\times 10^{4}\) A/m and \(1.63\times 10^{4}\) A/m, respectively. This implies that this magnetic field strength would be present at a distance \(d\)--specifically at the edge of the right wall Rw of the tank (\(d\) = 381 mm). It is essential to clarify that the proposed model does not account for the ideal case due to the low probability of achieving symmetry in winding dimensions during manufacturing. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Lw** & **Rw** & **Fw** & **Bw** & **Gw** & **Tw** & **Tyb** & **Byb** \\ \hline Case 1 & 6171 & 6579 & 7972 & 7348 & 2416 & 868 & 1202 & 1569 \\ Case 2 & 6352 & 6757 & 8181 & 7532 & 2472 & 891 & 1226 & 1603 \\ Real & 6455 & 6853 & 8322 & 7694 & 2517 & 906 & 1252 & 1634 \\ Case 3 & 6958 & 7388 & 8996 & 8325 & 2711 & 978 & 1350 & 1763 \\ Case 4 & 7165 & 7600 & 9287 & 8540 & 2814 & 1013 & 1396 & 1812 \\ \hline \hline \end{tabular}
\end{table}