# Optimization Design and Control of Six-Phase Switched
## 3 Surrogate Modeling Method  
### Sample Data Collection  
The size definition of the prototype is shown in Figure 4, in which the pole arc coefficients of the stator and the rotor, and the inner and outer diameters of the stator and rotor are fixed values. Define the yoke width ratio \(\lambda_{\text{hcs}}=h_{\text{cs}}/b_{\text{ps}}\), the stator slot area \(S\) can be expressed as  
\[S=\frac{\pi}{48}{\left(\left(D_{\text{S}}-2b_{\text{ps}}h_{\text{cs}}\right)^ {2}-{D_{\text{si}}}^{2}\right)}-{\lambda_{\text{hcs}}}{b_{\text{ps}}}^{2} \tag{7}\]  
Once the number of turns of each phase is fixed, the resistance of each phase changes with the width of the stator yoke under the condition of the same slot fill factor. Thus, the resistance of each phase is set as dynamic resistance, which can be represented by  
\[r_{\text{sp}}=\frac{4N_{\text{ph}}^{2}\rho\left(I_{\text{a}}+b_{\text{ps}} \right)}{k_{\text{u}}S} \tag{8}\]  
where \(\rho\) is the resistivity and \(k_{\text{u}}\) is the slot fill factor.  
It can be concluded from (7) and (8) that the resistance of each phase is related to the optimized parameter \(\lambda_{\text{hcs}}\). The relevant parameters of the motor are shown in Table 1, and the optimization variables are shown in Table 2. It should be noted that the angle position control (APC) is taken as the control method. Thus, the turn-on angle and the conduction width are the control parameters for further optimization. In this paper, the simulation \(0^{\circ}\) is defined as the position where the stator teeth of phase A is aligned with the centerline of the rotor teeth (the y-axis position shown in Figure 4).  
It could be found in our recent work [26] that \(\lambda_{\text{hcs}}\) exhibits a great influence on the saturation degree and too small values will cause the current distortion. Moreover, the slot fill factor will be reduced with the enlargement of \(\lambda_{\text{hcs}}\); thus, the range of \(\lambda_{\text{hcs}}\) is determined as [0.8, 1]. For the turn-on angle of phase A, as the aligned position is defined as \(0^{\circ}\), the unaligned position is \(18^{\circ}\), where \(18^{\circ}\) is half of the rotation period. For SRMs, it is acknowledged that the turn-on angle should be set in advance before the unaligned position to possibly generate more power. Based on our design experience, the turn-on angle could be set around 50 electrical degrees (corresponding to \(5^{\circ}\)) ahead of the unaligned position, and the conduction angle could be 160 electrical degrees (corresponding to \(16^{\circ}\)) to avoid the negative torque. Thus, the range of the turn-on angle of phase A and its conduction width could be set around \(13^{\circ}\) and \(16^{\circ}\), respectively. Since the phases of SRMs are excited sequentially, the turn-on angle range of phase B is added \(6^{\circ}\) (rotation period divided by the phase number) to the basis of phase A.  
According to the previous analysis, the saturation of the stator yoke leads to the asymmetry of the phase currents, which intensifies the torque ripple of the system; therefore, this paper selects the average torque \(T\) (Nm), the torque ripple \(T_{\text{rip}}\), and the difference between the RMS value of the two adjacent phase current (represented by \(I^{*}\)) are set as the optimization objectives, where \(I^{*}\) is generally expressed as  
\[I^{*}=\left|\frac{I_{\text{Brms}}-I_{\text{Crms}}}{I_{\text{Brms}}}\right| \cdot 100\% \tag{9}\]  
where \(I_{\text{Brms}}\) and \(I_{\text{Crms}}\) represent the RMS values of currents of phases B and C, respectively.