# Analysing and Computing the Impact of Geometric Asymmetric Coils on Transformer Stray Losses
## 4 Design Parameters and Loss Values
### Materials for Magnetic Shunts  
Three materials, namely Mill anneal electrical steel, Electrical Silicon Steel Grain Oriented (CRGO) and Amorphous Steel, were reviewed and analysed using finite element method (FEM) simulation. Mill Steel served as a reference point, with an approximate cost of $1200 per ton. It possesses a relative permeability of 2000 and a resistivity of 0.143 \(\mu\Omega\)m, for CRGO 0.48 \(\mu\Omega\)m and Amorphous Steel 1.3 \(\mu\Omega\)m, remembering that the relative permeability of these latter materials depends on their B-H curve. It is important to clarify that the manufacturer of these magnetic shunts uses scrap or residual material from the manufacturer of the core; the material was not purchased for this purpose. Also, the amorphous material is very fragile and difficult to work with, so it is rarely used as a shield for the tank, but it was considered to be analysed in this work since it is also in the scrap material from the cores.  
To standardise the sizing of the magnetic shunt plates and facilitate an objective comparison among the considered materials, the widely recognised magnetic field penetration formula [27] was employed. This approach ensures a systematic evaluation based on the thickness of the shunt plates, allowing for a comprehensive assessment of their performance characteristics.  
\[\delta=\sqrt{\frac{\rho}{\mu\pi f}}, \tag{10}\]  
where \(\rho\) is the material resistivity, \(\mu\) is the permeability of the material and \(f\) is the operating frequency of the transformer. Taking into account a magnetic shunt plate with a thickness of 1 mm, Figure 9a illustrates the magnetic field distribution across a 1 mm thick steel sheet for the various materials under analysis, accompanied by visible magnetic field lines. To enhance the clarity of the magnetic field distribution values within the magnetic shunts, a more detailed presentation has been provided in Figure 9b. Observing Figure 9b, it is evident that CRGO Electrical Steel exhibits a higher magnetic field absorption compared to other materials. However, its cost is higher than that of Mill anneal steel, which has garnered more popularity as a magnetic shunt material owing to its cost-effectiveness  
Figure 8: Magnetic Flux Density Distribution from HV winding to Rw wall.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **Lw** & **Rw** & **Fw** & **Bw** & **Gw** & **Tw** & **Tyb** & **Byb** \\ \hline Case 1 & 6565 & 3388 & 3025 & 2699 & 1534 & 603 & 524 & 682 \\ Case 2 & 6750 & 3419 & 3107 & 2761 & 1552 & 617 & 529 & 692 \\ Real & 6853 & 3457 & 3151 & 2814 & 1565 & 624 & 537 & 704 \\ Case 3 & 7394 & 3734 & 3416 & 3050 & 1690 & 680 & 581 & 760 \\ Case 4 & 7627 & 3837 & 3523 & 3129 & 1751 & 699 & 599 & 781 \\ \hline \end{tabular}
\end{table}
Table 5: Stray losses (W) with magnetics shunts.  
and satisfactory absorption capacity. On the other hand, the amorphous material sheet is recognised for its excellence in transformer core development due to its high permeability and resistivity, resulting in minimised electrical losses. Nevertheless, creating magnetic shunts using amorphous material is not technically or economically feasible due to its limited magnetic field penetration capacity as the format is incorrect.