Generalized Chudnovsky Algorithm for Real-Time PWM Selective Harmonic Elimination/Modulation: Two-Level VSI Example

Abstract

This article presents a novel approach to significantly reducing the mathematical complexity associated with the selective harmonic elimination (SHE), which allows for the real-time implementation of SHE with a reasonable utilization of the computational power of the digital controller. First, the transcendental equations of the optimization problem are converted to a set of algebraic equations using Chebyshev polynomials. Second, the set of algebraic equations is reduced to a single univalent polynomial using generalized Newton's identities. The roots of the polynomial hold a unique solution to the optimization problem. We show that the roots of the univalent polynomial can be solved in real time by direct substitution with no initial guess or iteration. The proposed method is a generalization of a Chudnovsky algorithm; it allows the modulation of the selected harmonics rather than eliminating them. Furthermore, the technique by which the roots of the polynomial are obtained enables one to implement the algorithm in real time with determinate execution time. This article lays the groundwork for presenting the generalized algorithm through a two-level voltage-source inverter drive. More application will follow in the near future.