Multiple sets of solutions for harmonic elimination PWM bipolar waveforms: analysis and experimental verification

Multiple sets of solutions for the selective harmonic elimination pulse-width modulation method for inverter control exist. These sets present an independent solution to the same problem but further investigation reveals that certain sets may offer an improved overall harmonic performance. In this paper, a minimization method is discussed as a way to obtain these multiple sets of switching angles. A simple distortion harmonic factor that takes into account the first two most significant harmonics present in the generated waveform is considered in order to evaluate the performance of each set. The bipolar waveform is thoroughly analyzed and two cases are considered; single-phase patterns which eliminate all odd harmonics and three-phase counterparts which eliminate only the nontriplen odd harmonics from the line-to-neutral pattern but such harmonics are naturally eliminated from the line-to-line waveform. Experimental results support the theoretical considerations reported in the paper.

I. Introduction

The elimination of specific harmonics from a given voltage waveform generated by a voltage-source inverter (VSI) using pulse-width modulation (PWM) has been dealt with in numerous papers [1]–[8]. These methods are known in the technical literature as selective harmonic elimination (SHE) or programmed PWM techniques. Originally, such methods presented solutions regarding the angles that eliminate a number of harmonics [1], [2]. The main challenge associated with such techniques is to obtain the analytical solutions of nonlinear transcendental equations that contain trigonometric terms which naturally exhibit multiple solutions [5]. Other methods do exist, such as the sinusoidal PWM (SPWM) based on a comparison of a reference (sinusoidal) waveform with a carrier (triangular) waveform offer a specific well controlled spectrum and bandwidth [9] but the focus of this paper is the SHEPWM one only.