Dynamic Vector Modeling of Three-Phase Mutually Coupled Switched Reluctance Machines With Single dq-Quadrant Look-up Tables

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.