A double Fourier analysis development of THD for PWM inverters: A theoretical method for motor loss minimization

Many papers have been written analyzing losses in AC machines and also losses in inverters. A much smaller number of papers are available which discuss the combined loss effect of AC machines operated by inverters. In those papers, either experimental results or finite element analysis are used to investigate these loss effects. To develop a better understanding of the means by which these losses occur, and more importantly how they could then be minimized, a theoretical basis for this study is hereby presented in this paper. This paper presents an accurate theory from which calculations of traction motor losses, due to PWM power inverter harmonics, could be made. The relationships among harmonic amplitude, modulation index and frequency are demonstrated and compared in 3D graphs for SPWM operation, which is commonly used in hybrid electric vehicles (HEV). Double Fourier analysis is used to theoretically decompose the output voltage and current of the SPWM inverter to each harmonic component. Finally, the total harmonic distortion (THD), which is the cause of the harmonic losses, versus modulation index will be summarized. Close agreement was found to exist between these theoretical results, simulation, and the experimental results of others.