Computationally Efficient Calculation of PWM-Induced AC Copper Losses in Concentrated Winding Axial Flux Machines

Abstract

This paper presents a computationally efficient methodology for evaluating pulsewidth modulation (PWM)-induced alternating current (AC) copper losses in concentrated winding axial flux permanent magnet (AFPM) machines. The proposed approach combines complex permeability modeling (CPM) with homogenization modeling (HM) of the coil region. The calculation algorithm consists of two sequential steps: AC copper loss evaluation under fundamental current and under PWM-induced harmonics. For the former, time-stepping finite element analysis (FEA) is performed to obtain the magnetic field and current density vectors within the coil domain, and the AC copper loss is calculated in the post-processing stage, similar to conventional iron loss evaluation. For the latter, time-harmonic FEA is employed to incorporate the complex permeability and account for high-frequency effects that cannot be captured in time domain post-processing. To validate the proposed method, two case studies using two-dimensional (2D) and three-dimensional (3D) models are conducted, as full PWM waveform application in a detailed 3D model is computationally infeasible. In addition, a complete machine-level validation under PWM excitation demonstrates good agreement with full FEA. The results confirm that PWM harmonics significantly increase both localized loss density and total AC copper losses by approximately 54% compared to the case neglecting PWM effects. These findings highlight the critical importance of incorporating PWM-induced harmonic effects in loss evaluations to avoid underestimating temperature rise and potential performance degradation in AFPM machines.