Multilevel Selective Harmonic Modulation by Duality

TL;DR

This paper presents a novel optimal control approach using duality and penalization techniques to design multilevel staircase control signals for selective harmonic modulation in power electronics, enhancing converter performance.

Contribution

It introduces a duality-based optimal control method with a special penalization to generate multilevel controls with staircase structure, addressing SHM constraints.

Findings

Effective control signals with desired harmonic properties

Improved power converter performance

Novel penalization technique for control design

Abstract

We address the Selective Harmonic Modulation (SHM) problem in power electronic engineering, consisting in designing a multilevel staircase control signal with some prescribed frequencies to improve the performances of a converter. In this work, SHM is addressed through an optimal control methodology based on duality, in which the admissible controls are piece-wise constant functions, taking values only in a given finite set. To fulfill this constraint, the cornerstone of our approach is the introduction of a special penalization in the cost functional, in the form of a piece-wise affine approximation of a parabola. In this manner, we build optimal multilevel controls having the desired staircase structure.