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

TL;DR

This work tackles the problem of bounding the minimal current harmonic distortion (TDD) for optimal pulse patterns in single‑phase, multi‑level power converters. It recasts OPP design as a periodic mode‑selecting optimal control problem of a hybrid system and applies the moment–SOS convex relaxation to obtain SDP lower bounds that scale subquadratically with the number of levels and switching angles. The approach yields provable lower bounds on TDD and demonstrates tightness via numerical recovery of feasible pulse patterns, outperforming traditional SHE methods in several scenarios. The results offer a scalable, time‑domain framework for guaranteed‑lower‑bound OPP design with practical relevance to grid‑connected converters and motor drives.

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

Figures (18)

• Figure 1: Equivalent circuit of the considered power electronic system
• Figure 2: Single-phase voltage-source converter with three output voltage levels and four active switches
• Figure 3: Example of patterns with (from top to bottom) FW, HW, and QW symmetries
• Figure 4: Transition graph for $N=3, k=4$
• Figure 5: Representations of a pulse pattern for $N=3, k=4$.