Selective Harmonic Control: A General Problem Formulation and Selected Solutions

TLDR

Selective harmonic elimination/control has been widely studied, but the common quarter‑wave symmetry assumption limits the solution space and can lead to sub‑optimal harmonic distributions. The authors propose a more general formulation that removes the quarter‑wave symmetry constraint for two classes of the m‑level, n‑harmonic control problem. They detail the special cases of two‑ and three‑level harmonic elimination and provide representative solutions for each control problem. This approach yields new solutions that were previously unattainable with quarter‑wave symmetric techniques.

Abstract

Selective harmonic elimination/control has been a widely researched alternative to traditional pulse-width modulation techniques. Previous and current work has made fundamental assumptions that enforce output waveform quarter-wave symmetry, presumably in order to reduce the complexity of the resulting equations. However, the quarter-wave symmetric assumption is not strictly necessary. It restricts the solution space, which can result in sub-optimal solutions with regards to the uncontrolled harmonic distribution. A more general formulation is proposed, removing the quarter-wave symmetry constraint for two classes of the m-level, n-harmonic harmonic control problem. The special cases of two- and three-level harmonic elimination are presented in detail along with representative solutions for each harmonic control problem. New solutions previously unattainable based on quarter-wave symmetric techniques are identified.