Calculation of PM Eddy Current Loss in IPM Machine Under PWM VSI Supply With Combined 2-D FE and Analytical Method

A hybrid method combining 2-D finite-element (FE) method and analytical model is proposed for permanent magnet (PM) eddy current loss calculation in interior PM machines under pulsewidth modulation (PWM) voltage source inverter (VSI) supply, in which the PM eddy current reaction effect and PM axial segmentation are taken into consideration. First, the 2-D time-stepping (TS) FE analysis results considering and neglecting PM eddy current under PWM VSI supply are compared so that the cause of PM eddy current loss, the increase of high-order armature current components due to PM eddy current effect, and the decrease of the high-order components in average flux density due to leakage flux are revealed. Second, an analytical model for PM eddy current loss calculation using voltage input is deduced with the average flux density as input and a leakage flux factor is introduced in the model to meet the real case in PM machine. Moreover, the 3-D frequency FE analysis is used to verify the derived model. Third, the ratio between the average flux density and the imposed flux density is defined as a key parameter to reflect the PM eddy current reaction effect quantitatively, for both 2-D and 3-D cases. A functional relationship is established to describe the variation of the average flux density with and without considering the PM eddy current, where the parameter is obtained with nonlinear fitting of the 2-D FEA results. At last, the calculation procedure of the hybrid method is presented and a flux-concentrating field-modulated PM machine is taken as an example for calculation. The results are verified by an FE analysis. The proposed method is more efficient compared with the 3-D TS FE method while maintaining rather good accuracy.