## 2 Optimized Geometric and Operational Design of an Induction Motor
### Finite Element Method (FEM) Simulation
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Quantity** & **Symbol** & **Value** \\ \hline Output Power & P\({}_{\mathrm{out}}\) & 10,000.00 kW \\ Input Power & P\({}_{\mathrm{in}}\) & 10,504.38 kW \\ Electromagnetic Torque & T\({}_{\mathrm{out}}\) & 189.51 kNm \\ Poles (Pair of Poles) & 2\(p\) (\(p\)) & 14 (7) \\ Frequency & \(f\) & 60 Hz \\ Nominal Speed & n\({}_{\mathrm{m}}\) & 504 rpm \\ Slip & \(s\) & 2\% \\ Nominal Phase Current & I\({}_{\mathrm{ph}}\) & 1150 A \\ Nominal Voltage & V\({}_{\mathrm{n}}\) & 6.6 kV \\ Power Factor & PF & 0.80 \\ Copper Losses stator & P\({}_{\mathrm{scu}}\) & 132.30 kW \\ Copper Losses Rotor & P\({}_{\mathrm{rcu}}\) & 204.08 kW \\ Core Losses & P\({}_{\mathrm{core}}\) & 50.00 kW \\ Mechanical and Stray Losses & P\({}_{\mathrm{ms}}\) & 118.00 kW \\ Total Losses & P\({}_{\mathrm{tot}}\) & 504.38 kW \\ Efficiency Rate & \(\eta\)\% & 95.20\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main Optimized Characteristics of the Induction Motor. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Quantity** & **Symbol** & **Initial Value** & **Optimized Value** \\ \hline Outer diameter stator & D\({}_{\mathrm{o}}\) & 3100 mm & 3050 mm \\ Inner diameter stator & D & 2300 mm & 2250 mm \\ Outer diameter rotor & D\({}_{\mathrm{r}}\) & 2285 mm & 2235 mm \\ Shaft diameter & D\({}_{\mathrm{shaft}}\) & 1020 mm & 1020 mm \\ Motor axial length & L & 720 mm & 710 mm \\ Stator slots & Q\({}_{\mathrm{s}}\) & 42 & 48 \\ Rotor slots & Q\({}_{\mathrm{r}}\) & 54 & 60 \\ Airgap length & L\({}_{\mathrm{g}}\) & 6 mm & 6.2 mm \\ Stator opening width & H\({}_{\mathrm{s}0}\) & 8.2 mm & 8.0 mm \\ Stator base width & H\({}_{\mathrm{s}1}\) & 8.2 mm & 7.8 mm \\ Stator top width & H\({}_{\mathrm{s}2}\) & 145.0 mm & 140.0 mm \\ Stator slot opening height & B\({}_{\mathrm{s}0}\) & 37.5 mm & 38.0 mm \\ Stator tip height & B\({}_{\mathrm{s}1}\) & 56.0 mm & 55.0 mm \\ Stator body height & B\({}_{\mathrm{s}2}\) & 290.0 mm & 290.0 mm \\ Tooth width & w\({}_{\mathrm{st}}\) & 118.5 mm & 120.0 mm \\ Stator yoke length & T\({}_{\mathrm{bi}}\) & 240 mm & 245 mm \\ Rotor bar body height & H\({}_{\mathrm{r}}\) & 290 mm & 295 mm \\ Rotor bar opening width & Br\({}_{0}\) & 57.8 mm & 60.0 mm \\ Rotor bar base width & Br\({}_{\mathrm{r}1}\) & 29.0 mm & 30.0 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Initial and Optimized Geometrical Variables of the Induction Motor. for the construction class A bars. Finally, silicon-doped steel was used for the stator core and rotor. Due to the varying frequency of the magnetic materials, a specific process of pre-processing, analysis, and post-processing of the data had to be completed [44]. A view of the motor (1/2 part) under study is shown in Figure 3. A detailed illustration of its basic dimensions and the geometric characteristics of the stator and rotor are given in Figure 4, including the stator inner diameter, slot pitch, and air gap length. These parameters correspond directly to the variables listed in Table 2, offering a clear visual reference. Figure 5 shows the distribution of the magnetic field. We observed a high magnetic flux density with a strong concentration of the field around the slots, which is normal, as this is where the excitation currents that create the main magnetic field are located. In the rotor, the bars show areas of lower field density, as the field is induced in the bars by the changing stator field. In addition, in the air gap, the field appeared relatively uniform, indicating that the machine was well designed to reduce asymmetries and maintain a constant flow between  
Figure 4: Main geometric characteristics of the stator and rotor. Figure 5: Magnetic Flux Density Distribution of the Induction Motor. Figure 3: Cross-section view (1/2 part) of the induction motor. -stator and rotor. The rotor bars appeared to have different field densities. This was due to the varying magnetic flux induced as the rotor rotated, while the areas of high field density (near the bars) showed active current induction.