# Optimization Design and Control of Six-Phase Switched
## 2 The Phenomenon of Current Asymmetry  
### Asymmetric Current Phenomenon  
In the traditional SRMs with an odd number of phases, such as the three-phase 6/4 and the five-phase 10/8 SRMs, the magnetic poles are alternately arranged at NS when the windings are connected in the forward direction. The polarities between two stator teeth of one phase are opposite; thus, a flux loop is generated between the two stator teeth, the interphase coupling can be ignored, and the magnetic field distribution is symmetric.  
For the SRMs with an even number of phases, a six-phase 12/10 SRM is taken as an investigated example to illustrate the asymmetric current phenomenon, as shown in Figure 1. The relevant main parameters of the motor are presented in Table 1. When the winding arrangement is the NS alternative shown in Figure 1a, the polarities between the two stator teeth of each phase are the same. For example, the polarities of the teeth A\({}_{1}\) and A\({}_{2}\) are both N polar; therefore, flux loops with the adjacent phases will be generated when the motor is excited, resulting in a large coupling between the adjacent phases. Meanwhile, the magnetic field distributions are the same when two adjacent phases are simultaneously excited, such as phases A and B or phases B and C, as shown in Figure 1a. In addition, when the decoupling winding arrangement is applied, such as the NNSS alternative shown in Figure 1b, the polarities of the two stator poles in each phase are opposite. Under this situation, if two adjacent phases are excited simultaneously, flux loops with different distances will be generated, as presented in Figure 1b. For instance, a long flux path is formed when phases A and B are simultaneously excited, as shown by the red dotted line in Figure 1b. While a quite shorter one is formed when phases B and C are simultaneously excited, as shown by the green dotted line in Figure 1b; therefore, the magnetic field distribution is asymmetric when the NNSS alternative winding arrangement is adopted for the six-phase SRM.  
Figure 2 shows the current and torque waveforms achieved by the finite-element models (FEMs) when the investigated six-phase SRM with NNSS alternative connection. It can be found that the current waveforms of phases A, C, and E are similar, and so are the other three phases. The maximum current values in phases A, C, and E are greater than the remaining three phases. It should be noted that, as presented in Figure 2, torques at points 1 and 3 are the maximum torques corresponding to the maximum current positions, and torques at points 2 and 4 are the minimum values at the intersection of the phase currents. Since the current value in phase A is generally greater than that with the same position of phase B, as a result, the torques at points 1 and 2 are larger than those at points 3 and 4, respectively; therefore, it can be concluded that the asymmetry of the phase currents aggravates the torque ripple of the system.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline Stator poles & 12 & Stator tooth width (\(b_{\text{ps}}\)/mm) & 5.6 \\ Rotor poles & 10 & Rated speed (r/min) & 3000 \\ Stator outer diameter (\(D_{\text{s}}\)/mm) & 80 & Rated voltage/V & 24 \\ Rotor outer diameter (\(D_{\text{a}}\)/mm) & 47.4 & Stack length (\(l_{\text{a}}\)/mm) & 70 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main parameters of six-phase SRM.  
Figure 1: Magnetic poles and flux distribution in a six-phase SRM under winding connections with (**a**) NS alternative and (**b**) NNSS alternative.  
Figure 2: Current and torque waveforms of the investigated six-phase SRM under NNSS alternative winding connection.