###### Abstract  
With increasing worries about the environment, there is a rising focus on saving energy in various industries. In the e-mobility industry of electric motors, permanent magnet synchronous motors (PMSMs) are widely utilized for saving energy due to their high-efficiency motor technologies. However, challenges like environmental degradation from rare earth development and difficulties in controlling magnetic field fluctuations persist. To address these issues, active research focuses on the wound field synchronous motor (WFSM), known for its ability to regulate field current efficiently across various speeds and operating conditions. Nevertheless, compared with other synchronous motors, the WFSM tends to exhibit relatively lower efficiency and torque density. Because the WFSM involves winding both the rotor and the stator, it results in increased copper and iron losses. In this article, a model that enhances torque density by inserting permanent magnets (PMs) into the rotor of the basic WFSM is proposed. This proposed model bolsters the d axis magnetic flux, thereby enhancing the motor's overall performance while addressing environmental concerns related to rare-earth materials and potentially reducing manufacturing costs when compared with those of the PMSM. The research methodology involves a comprehensive sensitivity analysis to identify key design variables, followed by sampling using optimal Latin hypercube design (OLHD). A surrogate model is then constructed using the kriging interpolation technique, and the optimization process employs a micro-genetic algorithm (MGA) to derive the optimal model configuration. The algorithm was performed to minimize the use of PMs when the same torque as that of the basic WFSM is present, and to reduce torque ripple. Error assessment is conducted through comparisons with finite element method (FEM) simulations. The optimized permanent-magnet-assisted WFSM (PMa-WFSM) model improved efficiency by 1.08% when it was the same size as the basic WFSM, and the torque ripple decreased by 5.43%. The proposed PMa-WFSM derived from this article is expected to be suitable for use in the e-mobility industry as a replacement for PMSM. w 0 2024 202 are often preferred due to their relatively high power density and suitability for high-speed operations, especially in the case of PMSM [8]. Consequently, rare-earth PM motors have emerged as the dominant choice in contemporary industrial settings [9]. However, challenges such as high costs, the unstable supply chain of rare-earth materials, and complexities in controlling weak field regions have heightened interest in alternative solutions like the WFSM [10]. The WFSM offers an advantage by enabling the direct manipulation of the field current through the winding of field coils with the DC current, facilitating a broad operating range and high efficiency in high-speed area [11; 12]. Especially for traction application, it is crucial to meet the torque and speed requirements. Up to the rated speed, a consistent rated torque must be maintained, and as the speed increases, the torque should decrease to maintain a constant output [13]. To achieve the same output as a PMSM, the WFSM must be designed accordingly, necessitating a focus on achieving high power density. In the case of WFSM, a significant challenge arises with high current densities, leading to rotor core saturation. This phenomenon introduces nonlinear variations in output performance and torque, exacerbating concerns about temperature rise. Therefore, meticulous attention to the number of coil turns and the selection of rotor current is crucial for high power density [14; 15]. Furthermore, considering the inherent presence of reluctance torque in the WFSM, it is essential to account for both the d axis inductance and the q axis inductance. The process involves winding coils around the rotor to generate magnetic flux, resulting in the d axis inductance (\(L_{d}\)) having higher magnetic resistance compared with the q axis inductance (\(L_{q}\)) [10].