Real-Time Implementation of Selective Harmonic Elimination with Seamless Dynamic Performance

Abstract

This paper presents a novel approach to significantly reducing the mathematical complexity that is 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 set 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 the unique solution to the optimization problem. It is shown that the root of the univalent polynomial can be solved in real-time by direct substitution with no initial guess or iteration. The proposed implementation method reduces the computational effort required by the controller and features improved transient response during a step change in the modulation index, the switching frequency, and the fundamental frequency without being subjected to the transient current spikes of the conventional SHE methods.