Sequential homotopy-based computation of multiple solutions for selected harmonic elimination in PWM inverters

The selected harmonic-elimination (HE) method, which is widely used for efficient inverter control, forms the basis of off-line digital PWM modulation techniques in the power electronics field. The method is based on numerical solutions of a set of selected HE equations which are often considered to be impractical to solve. Up to now, any effective method for this subject has not been reported. This paper proposes a systematic method which makes it possible to solve and analyze the equations sequentially by applying a homotopy method and a mathematical induction algorithm even if there are multiple solutions. According to the proposed method, unique HE solutions for single-phase cases and multiple solutions for three-phase cases are computed and reported.