# Efficiency Optimization of the Main Operating Points of an EV Traction Motor
## 1 Introduction  
The increasing stringency of environmental regulations, depletion of energy resources, and growing environmental concerns have significantly increased the demand for electric and hybrid electric vehicles (EVs/HEVs) powered by motors [1, 2, 3, 4]. EVs and HEVs require electric motors with high power output and efficiency to accommodate the increased weight of batteries and ensure an adequate driving range. Consequently, permanent magnet synchronous motors (PMSMs) have gained attention because of their high power output and efficiency. Specifically, interior permanent magnet synchronous motors (IPMSMs), in which permanent magnets are embedded, are widely used because they can achieve a higher power output by integrating the reluctance torque generated by the difference in d-axis and q-axis inductances with the magnetic torque produced by the magnets [5, 6]. Additionally, a hairpin winding method using rectangular rather than conventional circular wires has also been adopted in motor manufacturing to achieve high power output and high efficiency. Employing rectangular wire increases the slot fill factor, enabling higher power output, and offers advantages such as simplifying the end-turn pattern and reducing the axial length and outer diameter, thereby enhancing performance [7, 8, 9];however, a rectangular wire has a larger cross-sectional area than a conventional circular wire, resulting in an increased impact of AC copper losses. This increase in AC copper loss is particularly pronounced in rectangular conductors and is closely related to the skin effect, proximity effect, and leakage flux. The skin effect occurs when alternating current concentrates on the surface of a conductor, reducing the effective cross-sectional area available for current flow. It is strongly influenced by factors such as frequency, permeability, and conductivity of the conductor. Rectangular conductors exhibit a more pronounced skin effect compared with circular conductors with the same cross-sectional area because their surface area-to-cross-sectional area ratio is higher. As a result, current tends to concentrate on the surface, leaving the central region with limited current flow, which increases resistance and contributes to higher AC copper loss. The proximity effect refers to the phenomenon where the alternating magnetic field generated by the current in adjacent windings induces eddy currents in other conductors, causing an uneven current distribution and additional losses. AC copper loss due to leakage flux occurs in several scenarios: When leakage flux arises from slot openings, when circulating currents are formed because of differences in leakage reactance within the slots, or when leakage flux flows into the slots due to core saturation. These factors are more pronounced in rectangular conductor structures and must be carefully considered during design. The AC copper loss varies depending on the shape of the motor and becomes more significant as the wire's cross-sectional area and rotation speed of the motor increase [10; 11; 12]; therefore, when optimizing the efficiency of IPMSMs using hairpin windings, the AC copper loss must be considered, and reducing the AC copper loss is necessary to achieve high efficiency [13; 14]. Many studies on optimal motor design for enhancing efficiency have performed optimization at a single point in the motor's operating range, typically by setting the rated speed as the optimization point; however, motor efficiency is significantly affected by copper loss in the low-speed region and by iron loss related to rotational speed in the high-speed region. Additionally, the AC copper loss is higher in the high-speed region than in the low-speed region; therefore, the optimal design approach varies depending on the selection of the optimization point. When the optimization point is determined by predicting the motor's operating points, a more efficient design can be achieved, and research in this area is ongoing.