Analytical calculation of Permanent Magnet Flux Linkage and Winding Inductance of Mover Permanent Magnet Double Salient Reluctance Linear Machines

Aiming at the nonlinear problem of permanent magnet flux linkage and winding inductance function in the mover permanent magnet double salient reluctance linear machine (MPM-DSRLM), which makes it impossible to establish an accurate mathematical model with a simple algorithm, an analytical method is studied to calculate air gap magnetic field by using the Schwarz-Christoffel (SC) mapping and combine single excitation flux linkage method and integral of the air gap magnetic field to calculate PM flux linkage, winding self-inductance and mutual inductance parameters. In the case of ignoring the saturation of iron core, the PM of MPM - DSRLM is firstly equivalent to line current. Then, the two-dimensional conformal transformation models for PM single excitation and winding current single excitation are established respectively. The air gap magnetic field on the surface of stator tooth is calculated through the SC Toolbox, and it's integrated to get the phase winding flux. Finally, according to the three-phase flux linkage equation, the PM flux linkage, the winding self-inductance and mutual inductance parameters are derived. By comparing the analytical calculation results with the two-dimensional finite element simulation results, it is found that the waveform trend and value of two methods are in good agreement, which makes the mathematical modeling of MPM-DSRLM more simplified and accurate.