## 4 Experimental Results for 3 kW Six-Phase PMa-SynRM
### Torque Characteristic on Load  
In order to confirm the torque characteristics in the steady state, a load test was performed for six-phase operation at 480 r/min. The average torque for each current was measured by setting the D- and Q-axis currents between 2 to 10 A, and the same load angle was applied as that in the FEM analysis results in Table 6. Average torque, error rate, torque constant, and torque RF for each current are shown in Table 9.  
Figure 11: Experimental setup for testing.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Instrument** & **Model** \\ \hline Servo motor & HD-805 \\ Torque sensor & M425-S1 C \\ Oscilloscope & 6510e \\ DC power supply & 500 V 30 A (15 kW) \\
3 ph Inverter \(\times 2\) & Semikron AN-8005 \\ DSP & F28379D \\ JTAG emulator & XDS100 ver3.0 \\ \hline \hline \end{tabular}
\end{table}
Table 8: The experimental instruments.  
The error rate of the average torque obtained through FEM analysis and experimental results was the largest at 6.9% at 2 Arms, but the magnitude of the difference in torque was 0.2 Nm, which was negligible. At the rated 10 A, the torque error rate was 6.7% and the magnitude was 1.1 Nm, which could also be considered to be within the error range. The torque constant, which denotes the average torque per current, increased from 1.45 to 1.64 Nm/Arms as the current increased, and the average torque constant was calculated to be 1.55 Nm/Arms.  
As a result, the measured average torque satisfied the design requirements presented in Table 1, so the validity of the optimal design using LPM was verified through the experiment. Figure 13 shows the curves for the current and torque of a six-phase operation measured at a rated current of 10 A and a load angle of 23 deg, displaying U1 voltage, U1 current, torque, and speed at the upper-left corner.  
Next, an experiment was performed with a three-phase winding assuming a fault state, as shown in Figure 1. The experiment was conducted under the same operating conditions as those of the six-phase one, and results are shown in Table 10 and Figure 14. The actual measured RF value was significantly reduced compared to the FEM analysis results in Table 6 for three-phase operation, as in the RF results measured during six-phase operation. The average torque during three-phase operation was between 47% and 48% of that of six-phase operation, and the torque ratio showed a decreasing trend as the current increased. This phenomenon occurred because the magnetic flux that should have been concentrated in the stator core of UVW1, which was operating normally, leaked into the core of the UVW2 phase that had a fault [34]. Figure 15 shows the magnetic flux density distribution of six- and three-phase FEM simulations, respectively; magnetic flux, which was low in Figure 15a, increased in the box region of Figure 15b, which was a fault condition. In addition, as the magnitude of the current increased, magnetic resistance increased due to the saturation of the stator iron core, resulting in an increase in the amount of leaked  
Figure 12: BEMF curve at 480 r/min.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Currents** & **Load Angle** & **Torque** & **Torque** & **Torque Error** & **Torque** \\
**[Arms]** & **[deg]** & **FEA [Nm]** & **Exp. [Nm]** & **[\%]** & **Constant** \\ \hline
2 & 6 & 3.1 & 2.9 & 6.9 & 1.45 \\
4 & 12 & 6.4 & 6.1 & 4.9 & 1.53 \\
5 & 15 & 8.1 & 7.7 & 5.2 & 1.54 \\
6 & 17 & 9.9 & 9.3 & 6.5 & 1.55 \\
8 & 21 & 13.6 & 12.9 & 5.4 & 1.61 \\
10 & 23 & 17.5 & 16.4 & 6.7 & 1.64 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparison of torque characteristics in relation to current for six-phase operation.