Modeling of Permanent Magnet Machines Using Field Reconstruction Method
Permanent magnet synchronous machine (PMSM) is becoming more prevalent in industry applications due to its high power and torque density. The magnetic field distribution in the airgap of the motor is critical in predicting the performance, as well as implementing optimal design and control. Conventional methods to calculate the magnetic field include analytical lumped model, equivalent magnetic circuit (EMC) method, and finite element analysis (FEA) method. However, they have their limitation in terms of accuracy and computation time. Field reconstruction method was recently proposed for modeling of a surface mounted permanent magnet synchronous motor (SPMSM). It provides a fast method to reconstruct the magnetic field distribution with both high computation efficiency and good accuracy. However, due to the partial saturation effect in interior permanent magnet synchronous machine (IPMSM), conventional FRM method cannot be directly applied for modeling of IPMSM. An extended FRM (EFRM) is proposed to overcome the issue of partial saturation and slotting effect in IPMSM. Conformal mapping (CM) was recently proposed to calculate the magnetic field analytically. In general, CM is to map the complicated air gap structure into a simplified structure such as a rectangle or an annulus, in which the analytical solution of the magnetic field is readily available. The analytical solution of the magnetic field in simplified geometry is then transferred back to obtain the magnetic field distribution in original air gap geometry. Also, the effect of stator slots can be modeled with an equivalent permeability. As such original stator slots are transfomed into a slotless structure. This greatly simplifies the process of CM. What’s more, considering the equivalent permeability method would simplify the stator slot to a slotless structure which would greatly reduce the time to build the basis functions in EFRM. The combination of EFRM and CM would be an effective method to model IPMSM. In summary, CM shows a great advantage in achieving high calculation efficiency in modeling of PMSM though the accuracy is limited by only the saturation effects. The application of EFRM is extended to calculate the core loss and to estimate the average torque in PMSM. FEA simulation and experiments are conducted to verify the effectiveness of the proposed methods.