## 4 Verification of Design Method Using a Small-Scaled MG-PMSM Prototype
### Derivation of the Design Model for 4.5 kW-Class Small-Scaled MG-PMSM
As shown in Table 8, the measured value is 68.6 V\({}_{\text{fund-peak}}\) at the rated speed based on the fundamental wave peak value of phase Back-EMF, the calculated value is 72.3 V\({}_{\text{fund-peak}}\), and the difference ratio is about 5.1%. The difference between the calculated value of the Back-EMF and the measured value is due to the additionally included harmonic components in the measured waveform. Here, it is found that harmonic components are additionally included in the Back-EMF waveform due to the non-uniformity of the air gap due to the manufacturing tolerance of the MG-PMSM prototype. Next, the load performance test is conducted by applying servo motors for load devices to the pole piece rotor and the PM rotor, respectively. The load performance test was performed by measuring the torque generated while changing the input current of the 4.5 kW-class MG-PMSM prototype for each speed through the speed command of the servo motors. Figure 17 shows the measurement result by load performance test of the 4.5 kW-class MG-PMSM prototype. Figure 17a,b shows the 3-phase input current waveform and the generated torque waveform in the pole piece rotor under the following driving conditions, respectively (pole piece/PM rotor@30/-21 rpm, I\({}_{\text{phase}}\) = 3 A/6.5 Hz). In addition, the unbalance of the 3-phase input current occurs more significantly in the load test than in the no-load test. Some torque ripple occurs during the load test due to manufacturing and mechanical errors of the MG-PMSM prototype, but it is confirmed that the pole piece rotor torque converges to about 41.3 Nm. Figure 18 shows the comparison of the experimental and calculated values of the torque generated in the pole piece rotor by the load performance test of the 4.5 kW-class MG-PMSM prototype. Figure 18a shows the comparison results when the rotational speeds of the pole piece rotor are 30 and 45 rpm, and Figure 18b shows the torque error rate distribution between experimental and  
Figure 16: Measurement and calculation wave comparison of no-load phase Back-EMF of 4.5 kW-class MG-PMSM prototype (pole piece/PM rotor@214/155 rpm): (**a**) Experimental wave; (**b**) Calculated wave. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Contents** & **Calculation** & **Measurement** & **Difference Rate** \\ \hline Back-EMF\({}_{\text{Phase-rms}}\) & 50.0 V & 50.2 V & 0.4\% \\ \hline Back-EMF\({}_{\text{Phase-fund-peak}}\) & 72.3 V & 68.6 V & 5.1\% \\ \hline Frequency & 23.18 Hz & 22.75 Hz & 1.9\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison results between calculated value and measured value of no-load Back-EMF at rated speed (pole piece/PM rotor@214/155 rpm). calculated values in the low speed-torque region. As shown in Figure 18, when comparing the experimental results and calculated results related to the torque generated in the pole pieces rotor, it can be confirmed that the difference rate is up to 11%. The large difference between the experimental results and the calculated results is caused by the accumulation of measurement errors due to increased torque ripple due to the eccentricity of the rotor due to poor manufacturing of the pole pieces rotor during the manufacturing of the MG-PMSM prototype. In particular, it showed a tendency to generate a large torque error as the vibration of the MG-PMSM prototype increased in the region where the input current and rotation speed were large. As shown in Figure 18b, it was confirmed that the error rate within 5% was kept constant in the stable operation area where vibration did not occur significantly according to the comparison result between the analysis value and the test value of the torque generated by the input current according to the pole piece rotation speed of MG-PMSM prototype. Figure 17: Measurement result by load performance test of 4.5 kW-class MG-PMSM prototype (pole piece/PM rotor@30/21 rpm): (**a**) Phase of 3-phase current (6.5 Hz, 3 A); (**b**) Torque on the pole piece rotor.