## 2 Optimized Geometric and Operational Design of an Induction Motor
### Finite Element Method (FEM) Simulation
Rotor copper losses \(\mathrm{P}_{\mathrm{rcu}}\) were calculated using Equation (14):  
\[\mathrm{P}_{\mathrm{rcu}}=3\;I_{r}^{2}\times\left(\mathrm{R}_{r}+\mathrm{R} _{\mathrm{ext}}\right) \tag{14}\]  
This means that if a high \(\mathrm{R}_{\mathrm{ext}}\) was maintained for an extended period, thermal losses increased, reducing the efficiency of the WRIM. Unlike SCIMs, where rotor heat dissipation is passive, WRIMs require active cooling mechanisms for the rotor windings and external resistors. Liquid cooling may be necessary for high-power marine applications to maintain thermal stability and prevent excessive heating. An FEM analysis for SCIM revealed that reducing the rotor bar height by 5% and adjusting the stator slot width decreased core losses by approximately 8%, leading to a final efficiency of 95.2%. The WRIM FEM incorporated an external resistance which affected torque and efficiency at different slip values. This external resistance was varied between 0.15 \(\Omega\) to 0.45 \(\Omega\) to analyze its impact on torque-speed characteristics. WRIM simulations included rotor winding loss analysis due to higher resistive losses in the copper windings compared to SCIM bars. FEA-based thermal modeling was performed to ensure adequate cooling performance, especially under high-load conditions. Sensitivity analysis further indicated that fine-tuning the rotor slot shape and air gap length enhanced the machine's overall performance, leading to improved torque characteristics and reduced thermal stress. Increasing the rotor slot depth by 4% and optimizing the winding distribution resulted in a 10-12% reduction in rotor copper losses, improving efficiency by up to 94.5%, i.e., slightly lower than SCIM, due to additional slip ring losses. Additionally, optimizing the external rotor resistance within the identified optimal range ensured maximum starting torque while minimizing steady-state losses, achieving an optimal balance between efficiency and controllability in marine propulsion applications. WRIMs facilitate improved speed control through external rotor resistance adjustment, eliminating the need for complex frequency inverters. However, for high-power propulsion, integrating a sophisticated inverter system with Field-Oriented Control (FOC) or Direct Torque Control (DTC) enhances performance. WRIMs generate a more controlled and stable magnetic field, improving torque smoothness and reducing oscillations. The ability to regulate the magnetic field dynamically can enhance performance under varying ship load conditions. WRIM rotors typically use copper windings instead of aluminum or copper bars in SCIMs, increasing material costs but offering performance advantages. Additional costs arise from the slip ring and brush maintenance, but the overall cost-effectiveness depends on long-term operational requirements. One major drawback of WRIMs compared to SCIMs is the higher maintenance requirement due to wear on slip rings and brushes. Regular inspection and replacement of brushes are necessary to ensure reliability in continuous ship operation environments. Due to its solid rotor construction, SCIMs generally have a 6-8% lower mass compared to WRIMs for the same power rating. However, they require larger stator dimensions to accommodate higher currents, increasing volume by 3-5%. For WRIMs, the inclusion of rotor windings and slip rings increases the mass by 10-12% but allows for a more compact stator design, optimizing the overall machine volume to fit within ship engine rooms. Table 3 provides a detailed comparison of the features between the two motor options for high-power (10 MW) electric ship propulsion. In the selection of an induction motor for ship propulsion, SCIMs are generally preferred when efficiency and low maintenance are the primary concerns, particularly in applications requiring constant speed operation without frequent torque variations. Their long lifecycle and minimal intervention needs make them a cost-effective solution for continuous-duty marine propulsion systems.