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This study presents a novel method for fast calculating the eddy current losses (ECLs) caused by pulse‐width modulation (PWM) harmonic voltages in the permanent magnets (PMs) of surface‐mounted PM synchronous machines (SPMSMs) with distributed windings or concentrated windings. Based on the small‐signal models of the SPMSMs, the functional relationships between the high‐frequency harmonic voltages (HFHVs) in the rotor reference frame and the corresponding ECLs are investigated with the time‐harmonic finite element analysis (THFEA). Instead of using complex analytical PM ECL models, the relationships are directly established with some numerical methods, such as the Gauss quadrature and the piecewise cubic Hermite interpolation method, based on the results from THFEA. With the functional relationships, the total PM ECL caused by all the HFHVs is simply calculated by summing the ECL generated by each harmonic component in the spectra of the PWM voltage in the rotor reference frame. Both two‐ and three‐dimensional (2D and 3D) models of the SPMSMs are calculated. Besides, to further reduce the needed steps of 3D THFEA, an equivalent 2D THFEA method using modified PM conductivities under different‐axis HFHV excitations is proposed. The merits of the proposed method are validated by comparing with the traditional time‐stepping finite element method. [ABSTRACT FROM AUTHOR]

Normal calculation of the carrier harmonic iron losses (CHILs) brought by the pulse width modulated (PWM) voltage source inverter in interior permanent magnet synchronous motors by the time‐stepping finite‐element analysis (TSFEA) with short time steps is very time‐consuming. In this study, a novel method for fast calculation is proposed, where a combination of the frozen differential reluctivity tensor method and the time‐harmonic finite‐element analysis is proposed to investigate the relationship between PWM voltage harmonics and the corresponding CHILs, with which the CHILs in stator and rotor are fast‐calculated with the voltage harmonics in stator and rotor reference frames, respectively. Besides, the eddy current reaction effect in electrical steel sheets on the CHILs at high frequency is considered by an analytical method and validated with the TSFEA. The results reveal that eight parameters are recommended to calculate the CHILs at different operating conditions, which vary with the fundamental current. Consequently, the CHIL map over the entire operating conditions can be fast‐calculated using the analytical spectra of the PWM voltages. Experiment on a specimen is conducted to validate the accuracy of the proposed method, which shows it depends on whether the equivalent differential permeability of the silicon steel can be accurately modelled. [ABSTRACT FROM AUTHOR]

A method for fast calculating the high-frequency harmonic loss (HFHL) in the permanent magnet (PM) of interior PM synchronous machine under the pulsewidth modulated voltage source inverter supply is proposed. The combination of the frozen differential reluctivity tensor method and the linear frequency finite-element analysis (FEA) is proposed to investigate the relationship between the high-frequency harmonic voltages (HFHVs) in the rotor reference frame and the flux density variations in the PM, which is described quantitatively with the proposed analytical model using several dimensionless parameters. Then, the PM HFHLs are calculated analytically with the models using the flux density variations as input. The relative errors between the HFHLs calculated analytically and those obtained from the time-stepping FEA are within 15% at eight arbitrary working conditions. The proposed method can be used to calculate the PM HFHL in both two- and three-dimensional cases, which is testified with the experiment. Quadratic polynomial is used to fit the relationship between the dimensionless parameters and the fundamental currents. With the fitted polynomial and the analytical spectra of the HFHVs obtained from the double Fourier integration method, the PM HFHL map over entire working range can be calculated in one hour. [ABSTRACT FROM AUTHOR]

A new method for fast calculating the permanent magnet (PM) eddy current losses (ECLs) in interior PM synchronous machine caused by the high-frequency harmonic voltages (HFHVs) under pulsewidth modulation (PWM) voltage source inverter supply is proposed, by which time-consuming transient finite element analysis (FEA) is eliminated and the influence of the axial segmentation on the PM ECLs can be taken into consideration. The combination of the fixed differential permeability method and the linear frequency FEA is proposed to investigate the relationship between arbitrary HFHV and the corresponding PM ECL at different load conditions. The analytical model proposed in the previous published paper is used to describe this relationship quantitatively. Finally, the total PM ECLs at different load conditions can be calculated based on the fast Fourier transform results of the input PWM voltages. The relative errors between the total losses obtained with the proposed method and those with time-stepping FEA are within 21% at four typical load conditions, and the proposed method can reduce the computation time for one load condition to few minutes considering arbitrary PM axial segmentation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]