## 4 Thermal Performance Comparison  
In order to evaluate the thermal performance of the semi-stranded coil, the power losses should be estimated at different operating conditions and frequencies [28]. Then, the electromagnetic performance is coupled with a finite element thermal model to measure the temperature profile during one cycle of the Worldwide harmonized Light-duty vehicles Test Cycles (WLTC), shown in Figure 6. In the WLTC, the speed varies as a function of time. The WLTC cycle is divided into four parts with different top speed (Low, Medium, and High, Extra High). In each part, the speed has a certain fluctuating pattern with increasing and decreasing speeds. In the first part (Low), the top speed is about 55 km/h. In the second part (Medium), the top speed is about 75 km/h. In the third part (High), the top speed is nearly 100 km/h. In the final part (Extra high), the top speed is about 130 km/h. Based on the machine specifications and gear box ratio, the electrical frequency of the machine currents can be calculated. So, the higher the speed, the higher the frequency will become. The next step is to calculate the electromagnetic losses and export their values to a thermally coupled simulation. In the thermal simulation, the thermal conductivity of each  
Figure 5: Comparison between the solid single-strand copper coil and the semi-stranded coils. (**a**) Total losses in each turn at high frequency of 2 kHz; (**b**) total losses in the entire coil at different frequency levels.  
material must be inserted to have a high level of accuracy. Additionally, to emulate a real machine, the cooling jacket side must be added to the simulation.  
Using finite element thermal analysis, the maximum temperature value is calculated as a function of time as shown in Figure 7. As can be seen, at low and medium speeds, the maximum temperature in the semi-stranded coil rises relatively higher than that in the solid one. However, at high and extra-high speeds, the temperature in the semi-stranded coil starts to fall under the value in the solid coil. Under the same driving cycle (WLTC) and cooling conditions, the maximum temperature at the worst case scenario in the semi-stranded coil is 159.7 \({}^{\circ}\)C, which is significantly lower than its value in the solid coil (178.3 \({}^{\circ}\)C). This is also demonstrated in the thermal profile shown in Figure 8 at high frequency domain (i.e., extra-high speed). From this figure, it is noticed that the hot spot is located at upper two turns. This means that the cross slot leakage flux has high impact on the conventional solid conductor resulting in high AC losses. On the other hand, the hot spot of the semi-stranded coil is located nearly in the middle of the slot. This shows that the proposed approach has effectively limited the negative impact of the cross-slot leakage flux.  
Figure 6: Worldwide harmonized Light-duty vehicles Test Cycles (WLTC) for passenger vehicles with high power-to-weight ratio.  
Figure 7: Comparison between the maximum temperature under the same driving cycle (WLTC).  
With this being said, it is concluded that the semi-stranded coil is less prone to failure compared to the conventional solid one under the worst heating scenarios.