Analytical Expression for Line Voltage THD of Three‐Phase Staircase Modulated Multilevel Inverters

Eli Barbie, Dmitry Baimel, Alon Kuperman

Research output: Contribution to journalArticlepeer-review


In this article, a simple closed‐form analytical expression for the line‐voltage total harmonic distortion (LTHD) of three‐phase staircase‐modulated (SCM) multilevel inverters (MLI) is proposed. The revealed expression is valid for any conventional MLI topology with arbitrary number and parity of voltage levels. The proposed formulation is presented as an analytic function of the number of voltage levels (N) and the phase switching angles (PSA); thus, it is suited to MLIs of equal voltage source supply and of any topology. This function may be employed for accurate LTHD calculation and optimization. The results are verified against LTHD calculations and optimizations, obtained numerically from previous works. Both processor in loop (PIL)‐ and controller + hardware in loop (C‐HIL)‐based real‐time experimental validations are included as well. A downloadable file containing the Maple and MATLAB functions of the proposed expression are also provided.

Original languageEnglish
Article number364
JournalElectronics (Switzerland)
Issue number3
StatePublished - 1 Feb 2022


  • Line‐voltage
  • Multilevel inverters
  • Optimization
  • Staircase modulation
  • THD

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Hardware and Architecture
  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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