## 4 Results
### Full-Load Analysis  
The power transformer without magnetic shunts on the tank wall, with a vertical magnetic shunt manufactured and optimized by the transformer manufacturer and a horizontal magnetic shunt with the most suitable size and position obtained via parametric analysis, were analyzed for 100 ms at full load. Figure 11 shows the 3D transformer models representing the magnetic shunts on the transformer tank. The models illustrate three scenarios: the absence of a magnetic shunt within the transformer tank, the presence of vertical magnetic shunts within the transformer tank, and the presence of horizontal magnetic shunts within the transformer tank. Figure 12 displays the tank loss plots of the analysis results. The tank loss graphs presented here illustrate the performance of transformer models with varying magnetic shunt configurations. The models in question lack a magnetic shunt in the tank, possess a vertical magnetic shunt, and feature a horizontal magnetic shunt. Figure 13 provides an illustration of the current density distribution within the tank. The current densities depicted in Figure 13 correspond to transformer models that lack a magnetic shunt within the tank, possess a vertical magnetic shunt within the tank, and feature a horizontal magnetic shunt within the tank. Figure 14 illustrates the flux density distribution within the magnetic shunts. The aforementioned magnetic flux densities pertain to the vertical and horizontal magnetic shunt models.  
The simulation time was 13 h 31 min 49 s for the transformer model with a horizontal magnetic shunt in the tank; 13 h 5 min 10 s for the transformer model with a vertical magnetic shunt in the tank; and 12 h 21 min 37 s for the transformer model without a magnetic shunt in the tank. Table 7 compares the analysis and experimental results produced via the simulation for various scenarios. The modeling results for the vertical magnetic shunt closely match the experimental results obtained in the factory for the identical transformer. The simulation findings show a decrease of 2.27% in tank loss, 7.14% in shunt loss, and 2.39% in overall loss compared with the experimental results. These findings indicate that the experimental and simulation results agreed. The acquired results confirm the precision of the established model. Thus, the established model yields highly accurate findings in the context of horizontal magnetic shunts.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Magnetic Shunt Thickness (mm)**} \\ \cline{2-8}  & **5** & **10** & **15** & **20** & **25** & **30** & **35** \\ \hline Tank Loss (kW) & 0.335 & 0.076 & 0.050 & 0.047 & 0.045 & 0.042 & 0.042 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Variation of power loss (kW) in the tank due to parametric variation of the magnetic shunt thickness.  
Figure 10: Tank loss graph of parametric change in the magnetic shunt thickness.  
Figure 11: Three-dimensional view of the analyzed power transformer and magnetic shunt models: (**a**) without magnetic shunt; (**b**) with vertical magnetic shunt; and (**c**) with horizontal magnetic shunt.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Parameter** & **Without Magnetic** & **Vertical Magnetic** & **Horizontal Magnetic** & **Experimental Result** \\  & **Shunt** & **Shunts** & **Shunts** & **Experimental Result** \\ \hline Tank loss (kw) & 22.76 & 10.75 & 11.22 & 11.00 \\ Shunt loss (kw) & — & 0.26 & 0.38 & 0.28 \\ Shunt volume (cm\({}^{3}\)) & — & 154,518 & 114,600 & 154,518 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Comparison of analyses and experimental results for different types of magnetic shunts.  
Figure 12: Tank loss changes at full load: (**a**) tank loss graph at full load without magnetic shunt in transformer tank; (**b**) tank loss graph at full load with vertical magnetic shunt in transformer tank; and (**c**) tank loss graph at full load with horizontal magnetic shunt in transformer tank.