# Computationally Efficient PM Power Loss Mapping for
## 6 Verification  
The 3-D FEA model has many element grids, and the mutual matching between the grids is complicated and the calculation cycle long. Therefore, by combining the axial structural symmetry of the motor and the periodic symmetry of the motor radial direction, the 3-D FEA model is simplified, as shown in Figure 9. Figure 10 shows the eddy current density of PMs of a pole in 3-D FEA of the prototype under working conditions (speed is 600 rpm, pulse width modulation ratio is 0.99, and the carrier ratio is 27). The eddy current inside the PM forms a loop at the end of the PM, which can account for the influence of the end effect of the PM on the loss.  
Figure 9: 3-D FEA model of the prototype.  
The PM loss at several operating points of the characteristic curve of the rated operating condition is calculated using the fitting formula in Equation (15) and 3-D FEA. Figure 11 shows the comparison of the calculation results of the two methods. In the figure, the carrier ratio and amplitude modulation ratio are kept unchanged at 27 and 0.99, respectively. It can be seen that the predicted value of the fitting formula in Equation (15) is in good agreement with the 3-D FEA results. Smaller errors will inevitably occur, which come from the reaction of induced eddy currents and the end effect of PMs. To eliminate these errors, more finite element working points are needed to correct the fitting formula.  
Figure 11: Fitting formula in Equation (15) and 3-D FEA calculation of PM loss at several operating points under rated conditions.  
Figure 10: The eddy current density of PMs of a pole under 3-D FEA of the prototype (n = 600 rpm, M = 0.99, N = 27, T = 20 \({}^{\circ}\)C).  
In this study, the separation loss method is adopted, which means that the total loss that is about to be obtained is subtracted from other losses during the operation of the permanent magnet synchronous motor, and then the permanent magnet loss is obtained. The power analyzer is used to test the total input power when the motor is running, and then the torque sensor is connected to the rotor side of the motor to obtain the output power of the motor. The total loss of the motor is the difference between the input power and the output power. The total loss subtracts the copper loss, stator and rotor iron loss, and mechanical loss to obtain the permanent magnet loss. The experimental results and calculation results of the method proposed in this paper are shown in Figure 15.  
It can be seen from Figure 15 that the method proposed in this paper is consistent with the experimental data. The error is because the loss separation method inherits the errors of other loss measurements (stator and rotor iron loss, winding copper loss, mechanical loss, etc.), resulting in large PM losses.  
To eliminate the error of the separation loss method, in recent years, scholars have proposed the direct measurement method. The temperature sensor is used to accurately predict the temperature change of the permanent magnet, and then the eddy current loss of the permanent magnet is obtained according to the temperature field model of the motor. The arrangement of the temperature sensor in the rotor is restricted, and at the same time, it will have an impact on the structure of the rotor and the electromagnetic field of the motor. The implementation of this method is more difficult, and it is one of the directions of permanent magnet loss research in the future.  
In general, the proposed fitting formula can predict the PM loss relatively efficiently, while taking into account the influence of temperature factors and time harmonics. This method is effectively embedded in the design of the PMSM, improves the design efficiency, and shortens the design cycle.