Bounding the Minimal Current Harmonic Distortion in Optimal Modulation of Single-Phase Power Converters

TL;DR

This paper introduces a novel control-theoretic approach to optimize pulse patterns in single-phase power converters, effectively minimizing current harmonic distortion through convex relaxation techniques.

Contribution

It reformulates the OPP design as a hybrid optimal control problem, enabling scalable convex relaxations to find lower bounds on harmonic distortion.

Findings

Hierarchy of semidefinite programs effectively bounds harmonic distortion

Method scales subquadratically with system complexity

Numerical results validate the approach's effectiveness

Abstract

Optimal pulse patterns (OPPs) are a modulation technique in which a switching signal is computed offline through an optimization process that accounts for selected performance criteria, such as current harmonic distortion. The optimization determines both the switching angles (i.e., switching times) and the pattern structure (i.e., the sequence of voltage levels). This optimization task is a challenging mixed-integer nonconvex problem, involving integer-valued voltage levels and trigono metric nonlinearities in both the objective and the constraints. We address this challenge by reinterpreting OPP design as a periodic mode-selecting optimal control problem of a hybrid system, where selecting angles and levels corresponds to choosing jump times in a transition graph. This time-domain formulation enables the direct use of convex-relaxation techniques from optimal control, producing a hierarchy of semidefinite programs that lower-bound the minimal achievable harmonic distortion and scale subquadratically with the number of converter levels and switching angles. Numerical results demonstrate the effectiveness of the proposed approachs