Study on AC Copper Losses in an Air-Cored Axial Flux Permanent Magnet Electrical Machine With Flat Wires

In this article, we propose the calculation method of ac copper losses of air-cored axial flux permanent magnet (AFPM) electrical machine with flat wires fed by pulsewidth modulation (PWM) inverters. The ac copper loss due to armature currents in air-cored electrical machines is significant when these machines are driven by PWM inverters. Besides, the exposure of windings to the inhomogeneous alternating rotor magnetic field causes ac copper loss. Analytical formulas are efficient tools to evaluate these losses but few pieces of literature have reported the derivation in such machines. To address this issue, the formulas of aforementioned ac copper losses are derived based on Maxwell's equations and Poynting theorem. As for end windings, the ac copper loss caused by armature current is calculated analytically, while the rotor-induced ac copper loss is calculated by aid of static three-dimensional finite-element analysis (FEA). The interaction of load current and rotor-induced eddy current is also studied. A 12-slot-16-pole air-cored AFPM machine is analyzed with the proposed method, and the analysis is validated by time-transient FEA simulations and prototype experiments. The influence of modulation ratio on ac copper loss due to armature current of the AFPM machine is also discussed.