Analytic formulation and optimization of weighted total harmonic distortion in single-phase staircase modulated multilevel inverters

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3 Scopus citations


Weighted total harmonic distortion (WTHD) is an important performance merit, representing either current or voltage quality of voltage source inverters. Unlike general (non-weighted) THD, which can be evaluated using a closed-form analytic time-domain expression, WTHD is typically calculated using approximate frequency-domain numerical approaches. The paper reveals a novel analytic WTHD expression for output voltage of Staircase Modulated (SCM) single-phase Multi-Level Inverters (MLI). The proposed formula, valid for SCM MLI of arbitrary topology with any number and parity of voltage levels, is a function of all switching angles (SA) only and may thus be easily implemented in common symbolic/numeric computing software. Due to its analytical nature, the WTHD expression yields highly accurate results, eliminating the risk of round-off and underestimation errors, associated with conventional frequency-based numerical approaches. Furthermore, based on the proposed formula, Optimal Minimization of WTHD was carried out for accurate calculation of optimum SA, yielding minimum WTHD for desired modulation index. Eight sets of high-resolution (1171 samples per level) look-up tables, linking desired modulation index to optimum SA values, were generated. A downloadable file, containing MATLAB coded WTHD functions and the eight look-up tables, are provided as a shortened URL. In order to verify the proposed expression, analytic WTHD values are compared with results obtained in previous works. In addition, the methodology was validated utilizing Processor-in-Loop simulation of 7 and 8 level SCM MLI.

Original languageEnglish
Article number117470
StatePublished - 15 May 2020


  • Multilevel inverters
  • Optimization
  • Staircase modulation
  • Weighted total harmonic distortion

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Pollution
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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