## 2 Optimized Geometric and Operational Design of an Induction Motor
### Finite Element Method (FEM) Simulation
The optimization focused on minimizing losses and improving thermal and electromagnetic performance. FEM simulations iteratively adjusted rotor bar height, stator slot width, and air gap length. Constraints included limiting the stator winding current density to 6 A/mm\({}^{2}\), ensuring thermal stability, and adhering to material and manufacturing specifications using NEMA Class A copper bars. The implementation of this algorithm resulted from an investigation into the initial geometry of the motor. Specifically, a first algorithm was implemented to change the current density of the stator windings from 5 A/mm\({}^{2}\) to 6 A/mm\({}^{2}\) with a step of 0.1 A/mm\({}^{2}\). In this way, the operating slip and the new nominal operating points were found. Regarding the range of the current density of the stator windings, an increase up to 6 A/mm\({}^{2}\) was applied, although this was the upper limit before forced cooling would have been required; this was nonetheless acceptable due to the fact that the motor was immersed in seawater, so there was sufficient cooling of the stator windings. A sensitivity analysis revealed critical relationships between key parameters and performance metrics. The optimization of the motor began with the selection of the two parameters that were to be optimized. Initially, a sensitivity analysis was carried out for the height and width of the stator teeth. Then, the two variables that were optimized through sensitivity analysis concerned the stator tooth shoe and its height. The last pair in the analysis consisted of the height and width of the rotor teeth. The initial and final values of the parameters, as well as the change step, were selected based on construction constraints and the existing design. Increasing the air gap length reduced torque ripple by 15% but required larger stator slots, while increasing the rotor bar height by 5% reduced core losses by 8% due to improved magnetic flux paths. The final optimized design achieved 95.2% efficiency, reduced copper losses, and minimized torque ripple. Table 1 shows the basic final optimized characteristics (electrical and mechanical) of the machine, taking into account the sum of the individual losses of the motor. Similarly, the geometric characteristics of the induction motor are highlighted in Table 2, including both the initial and final optimized values. Our design comprised a multi-pole motor with 14 poles (7 pair), 48 slots in the stator, and 60 rods in the rotor. The choice of the number of slots for both the stator and the rods was based on the criterion of reducing vibrations, noise, and the occurrence of extended alignment torque and other parasitic phenomena that can occur during motor operation. The number of stator windings was chosen to achieve a distributed winding double layer. In addition, it was considered appropriate to increase the length of the air gap in order to significantly increase the current required to create a magnetic field which induced currents in the rotor. The stator's outer and inner diameters were slightly adjusted for better magnetic flux management. The dimensions of the stator and rotor slots increased slightly to improve efficiency and reduce torque ripple. The airgap length was slightly increased for improved cooling and magnetic performance. The yoke and tooth dimensions were optimized to balance mechanical strength and core losses. These adjustments ensured the motor achieved higher efficiency, better cooling, and reduced losses, aligning with the constraints and objectives of the optimization process. The double layer winding compared to single layer brought about lower core losses due to the lower harmonic content of the magnetic force caused by the drum reaction. At the same time, the torque ripple was also reduced by using such a winding [43]. The maximum acceptable value for the current density of stator winding \(J_{\mathrm{s}}\) was set to 6 A/mm\({}^{2}\). The rotor bars were made of copper and their design was based on NEMA specifications