This paper presents a dynamic modeling method for a 3-phase mutually coupled switched reluctance machine (MCSRM) considering spatial harmonics, and saturation. The conventional modeling methods of MCSRMs are based on 3D look-up tables (LUTs), where the phase flux linkages are considered as state variables. These 3D LUTs describe the phase currents with respect to phase flux linkages, and rotor position. The 3D LUTs represent two $dq$ quadrants, and are obtained from finite element analysis (FEA) by multi-phase excitation where the excitation currents cover two quadrants in the $dq$ synchronous reference frame. The LUTs used in the proposed method represent the phase current, and electro-magnetic torque as vectors. The magnitude, and the angle of these vectors are represented by the sine, and cosine Fourier coefficients. Hence, rotor position is not an input to the LUTs, and the proposed method uses 2D LUTs. Additionally, the flux linkages in the four $dq$ quadrants possess symmetry for MCSRMs. Therefore, LUTs corresponding to only one $dq$ quadrant are required. The single-quadrant based LUTs reduces the number of FEA steps, and the size of the LUTs by 50% compared to the two-quadrant LUT based models. Finally, the proposed method is validated using FEA, and experiments for a 12/8 MCSRM.

中文翻译：

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单相三相互耦开关磁阻电机的动态矢量建模 dq-象限查询表

本文提出了一种考虑空间谐波和饱和度的三相互耦开关磁阻电机（MCSRM）的动态建模方法。MCSRM的常规建模方法基于3D查找表（LUT），其中相通量链接被视为状态变量。这些3D LUT描述了与相磁链有关的相电流以及转子位置。3D LUT代表两个$ dq $ 象限，是通过多相激励从有限元分析（FEA）获得的，其中激励电流覆盖了两个象限。 $ dq $同步参考帧。提出的方法中使用的LUT将相电流和电磁转矩表示为矢量。这些向量的大小和角度由正弦和余弦傅立叶系数表示。因此，转子位置不是LUT的输入，建议的方法使用2D LUT。此外，四个中的磁链$ dq $象限具有MCSRM的对称性。因此，LUT仅对应一个$ dq $象限是必需的。与基于两象限的LUT的模型相比，基于单象限的LUT减少了FEA步骤的数量，并且LUT的大小减少了50％。最后，使用有限元分析验证了所提出的方法，并针对12/8 MCSRM进行了实验。