A convex relaxation approach for the optimized pulse pattern problem

Lukas Wachter, Orcun Karaca, Georgios Darivianakis, Themistoklis Charalambous

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

1 Citation (Scopus)
8 Downloads (Pure)


Optimized Pulse Patterns (OPPs) are gaining increasing popularity in the power electronics community over the well-studied pulse width modulation due to their inherent ability to provide the switching instances that optimize current harmonic distortions. In particular, the OPP problem minimizes current harmonic distortions under a cardinality constraint on the number of switching instances per fundamental wave period. The OPP problem is, however, non-convex involving both polynomials and trigonometric functions. In the existing literature, the OPP problem is solved using off-the-shelf solvers with local convergence guarantees. To obtain guarantees of global optimality, we employ and extend techniques from polynomial optimization literature and provide a solution with a global convergence guarantee. Specifically, we propose a polynomial approximation to the OPP problem to then utilize well-studied globally convergent convex relaxation hierarchies, namely, semi-definite programming and relative entropy relaxations. The resulting hierarchy is proven to converge to the global optimal solution. Our method exhibits a strong performance for OPP problems up to 50 switching instances per quarter wave.

Original languageEnglish
Title of host publication2021 European Control Conference, ECC 2021
Number of pages6
ISBN (Electronic)978-94-6384-236-5
Publication statusPublished - Jan 2022
MoE publication typeA4 Article in a conference publication
EventEuropean Control Conference - Delft, Netherlands
Duration: 29 Jun 20212 Jul 2021
Conference number: ECC


ConferenceEuropean Control Conference
Abbreviated titleECC


  • Optimized pulse patterns
  • Polynomial optimization
  • Power conversion
  • Pulse width modulation


Dive into the research topics of 'A convex relaxation approach for the optimized pulse pattern problem'. Together they form a unique fingerprint.

Cite this