## 4 Experimental Data and Simulation Results  
### Experimental Data  
A series of DC bias test of the RSM was carried out, which is presented in Table 4. The DC bias effects on the RSM with and without load are presented, respectively. Figure 9a shows five cycles of the no-load excitation current without the DC bias current, Figure 9b-d show five cycles of the no-load excitation current with 1 A, 3 A and 5 A DC bias current, respectively. As can be seen from the figure, the distortion of excitation current rose sharply as the DC bias current increased. The distortion occurred mainly in the first half of the cycle, peaking in the quarter cycle. For instance, the peak value of excitation current without DC bias current was 2.5 A, and the peak value increased to 8.5 A, 25.8 A, and 42.6 A with 1 A, 3 A and 5 A DC bias current, respectively. The distortion under 5 A DC bias current was 17 times higher than the rated excitation current. By contrast, the excitation current in last half of the cycle decreased with the DC bias current due to the opposite direction. DFT was then applied to the waveform of excitation and winding currents, respectively. Figure 10 show that the harmonics increased obviously as the DC bias current increased. Although the DC bias current brought distortion to all the current waveform, the cause of these current distortions was not the same. The harmonics magnitudes of excitation current and the high voltage side current showed an identical tendency. The even harmonics occurred due to the DC bias current, especially the second harmonic, which turned into the biggest harmonic component. The occurrence of even harmonics caused the distortion of the waveform of the excitation current and high voltage side current. Whereas the middle and low voltage side current showed identical tendency, the DC bias effects on even harmonic was small, the main reason for distortion of the common and low voltage current was the odd harmonics. The winding current at each side of the RSM with load under various DC bias are shown in Figure 11. As can be seen from figure, the distortion of the waveform increased obviously as the DC bias current increased. The distortion occurred when DC bias current flowed into the windings and the distortion showed the same tendency as the excitation current, which mainly occurred in the first half cycle, the current maximum was located close to the moment of a quarter. Besides, the middle and low voltage side current seemed less affected by the DC bias, whereas the high voltage side current waveform showed an obvious distortion. The total harmonic distortion (THD) was utilized to present the distortion degree of current under DC bias current, which is defined as the ratio of the root mean square (RMS) amplitude of a set of higher harmonic frequencies to the fundamental [8], expressed by  
\[\mathrm{THD}=\frac{\sqrt{{I_{2}}^{2}{I_{3}}^{2}{I_{4}}^{2}+\ldots}}{{I_{1}}} \tag{3}\]  
The THD of the current at each side are shown in Figure 12. The excitation and high voltage wingding current were less tolerant of DC bias current, the distortion degree increased obviously as the DC bias current increased, whereas, the current of the middle and low voltage side remained almost the same under DC bias current. The no-load loss and the active power at rated operation were measured by a power analyzer, as shown in Figure 13. The DC bias current caused a significant increase in no-load loss. Therefore, active power of each side decreased as the DC bias current increased. \begin{table}
\begin{tabular}{c c c} \hline
**RSM** & **Ratio of 2 nd to 1 st** & **UHV** \\ \hline
0 & 0 & 0 \\
1 & 0.91277 & 2.6862 \\
2 & 0.94365 & 6.013 \\
3 & 0.95092 & 7.5070 \\
4 & 0.9524 & 7.9731 \\
5 & 0.95144 & 8.2497 \\ \hline \end{tabular}
\end{table} 
Table 3: Equivalent relationship of DC bias current of RSM to UHV. Figure 10: Magnitudes of harmonics of each winding current under various DC bias current. (**a**) series winding current. (**b**) common winding current. (**c**) low voltage winding current.