# FEA-Based Design Procedure for IPMSM and IM for a Hybrid Electric Vehicle
## 3 Design Procedure
### IPMSM Design Procedure
The following equation can be used to find the machine current (\(I_{s}\)) for generation of maximum torque:  
\[I_{s}=\frac{P_{out}}{\sqrt{3}V_{ll}\eta\cos(\varphi)} \tag{2}\]  
In Equation (2), \(P_{out}\) and \(V_{ll}\) are the output power and rms line voltage at the maximum speed at the end of the constant torque region. Standard Class F insulation is used, which allows operating temperatures of 145 \({}^{\circ}\)C with a hotspot temperature of 155 \({}^{\circ}\)C. The value of rated current is found as the current which produces this hotspot temperature limit in the windings [57]. From the value of rated current, the required PM volume can be found by means of a sensitivity analysis in FEA. Considering the advantages of the V-shape PM topology discussed in the Introduction section, this configuration is selected for the design. To optimize its value, the V angle is changed from 180\({}^{\circ}\) to 60\({}^{\circ}\) and the airgap flux density is monitored while the PM volume is kept roughly constant. The FEA results indicate that the 60\({}^{\circ}\) design provides an airgap flux density that is about 25% higher than the other two designs. This increased flux density presents an opportunity to reduce the number of turns in the machine, thereby achieving lower copper losses. Figure 4 shows the results for the three V angles. The back-emf waveform of the 60\({}^{\circ}\) design is more sinusoidal than the other two designs which gives a higher power factor. The total harmonic distortion (THD) of the back-emf for the 60\({}^{\circ}\) design is 1.4% while for the 180\({}^{\circ}\) and 150\({}^{\circ}\) designs it is 7.5% and 5%, respectively. Although the cogging torque of the machine with the 60\({}^{\circ}\) angle is larger than with the 180\({}^{\circ}\) angle (i.e., 15 Nm peak vs. 3 Nm peak), its percentage torque ripple at the rated point is 10% which is 7.3% smaller than the 180\({}^{\circ}\) design and 3.7% smaller than the 150\({}^{\circ}\) design. The higher average torque, lower ripple torque, and lower THD of the 60\({}^{\circ}\) design make it superior in terms of its electromagnetic performance. However, because of the larger width of the PMs in the 60\({}^{\circ}\) design, it has a smaller inner diameter and higher rotor weight. The short circuit current of the 60\({}^{\circ}\) design is also higher than the two other designs, which could increase the risk of demagnetization. As shown in Figure 4, the rated currents were found by considering the voltage and winding thermal constraints. These are affected by the number of turns and the airgap flux density. The 60\({}^{\circ}\) design has the highest rated current, followed by the 180\({}^{\circ}\) design. It should be highlighted that structural, vibration, and noise analysis are other factors which can be studied with consideration of the different PM angles to determine the optimum design. These analyses are out of the scope of this paper. Bar graphs of the stacked losses as a fraction of the input power for the three designs are presented in Figure 5. This shows that the majority of losses are due to the stator copper losses, followed by stator iron losses, and there are only a small amount of rotor iron and magnet losses. It should be highlighted that the number of turns per phase of the V-60 is about 25% less than the other designs. This reduction enables the use of a conductor with a larger cross-sectional area, which in turn helps achieve lower resistance. Consequently, the stator resistance of the V-60 design is 0.036 \(\Omega\), compared to 0.065 \(\Omega\) in the other designs. Although the winding resistance of V-60 is lower, its copper losses are approximately equal to the other designs because of its higher rated current. Figure 4: Two-dimensional FEA results of the studied PMSM V-shape rotors for different rotor magnet angles. The maximum continuous power (MCP) is reported @2800 rpm with Class F temperature rise. \(I_{sc}\) is the short circuit current.