Analytical Calculation of Harmonics and Harmonic Losses in Five-Phase Carrier-Based PWM Voltage Source Inverters

Abstract

The main purpose of this paper is to analyze a five-phase Voltage Source Inverter (VSI) that is operated with the Pulse Width Modulation (PWM) switching technique. Double Fourier integral (DFI) analysis has been used to extract the harmonics of the line-to-line voltages. Moreover, the harmonic current ripple has been calculated for an effective inductive five-phase load with a regular pentagon connection. Correspondingly, a new closed-form solution for calculating the harmonic losses in five-phase VSIs has been derived. In addition, a new equation for the weighted total harmonic distortion (WTHD) index has been extracted for five-phase VSIs. To validate the suggested analytical solutions (i.e., harmonic losses and WTHD equations), the results are compared with the DFI calculation method and the method of applying the fast Fourier transform (FFT) to a simulated waveform. The results show that the proposed analytical method has high accuracy and requires less mathematical effort, especially at high-frequency ratio values. Finally, the study includes simulation results and the implementation of an experimental setup.

Keywords

• Closed-form solution
• five-phase inverter
• Fourier transform
• harmonic distortion
• harmonic loss
• PWM modulation