Current-THD minimization in multilevel inverters with variable DC ratios utilizing a generic closed-form analytic formulation of line-voltage WTHD

Eli Barbie, Alon Kuperman, Dmitry Baimel

Research output: Contribution to journalArticlepeer-review


This article presents a generic approach to load-current THD minimization in hard-switched Staircase Modulation (SCM) based three-phase (3ɸ) Multilevel Inverters (MLI) with either fixed or variable DC source Ratios (DCR). First, a computer-aided closed-form analytical formulation of Weighted THD (WTHD) applied directly to line-voltage waveforms is derived using Maple software and then verified against numerically-obtained results of previous works. The proposed symbolic analysis of Weighted Line-voltage THD (WLTHD) applies to 3ɸ-MLIs of any topology with Equal Voltage Steps (EVS) or Unequal Voltage Steps (UVS), and any number of voltage levels count (N), either odd or even. Such an analytical approach eliminates the risk of underestimation errors associated with numerical methods. The proposed closed-form WLTHD expression is then utilized for optimal minimization of current-THD in 3ɸ inductive loads with unconnected neutral. This is achieved by introducing a generic UVS-based Optimal Minimization of WLTHD (OMWLTHD), which calculates the optimum Phase Switching Angles (PSA) and the supply DC-Ratios (DCR), given any desired Modulation Index (MI), thus ensuring minimum current-THD across the entire linear MI range. The revealed OMWLTHD approach is fully validated by both digital simulations and controller plus hardware-in-loop (C-HIL) based experiments, using 7-, 8-, and even 13-level 3ɸ-MLIs of both EVS and UVS configurations. Furthermore, to reveal the impact of WLTHD minimization on actual load current-THD, the MLIs were loaded by a Resistive-Inductive-EMF (RLE) load, as well as a 3ɸ squirrel cage induction motor, thus representing a wide range of possible loads, such as motors and ac grids. The conclusive verification results have shown that in the case of 3-wire inductive loads with a power factor up to 0.95, the proposed UVS-based WLTHD optimization is more beneficial for current-THD minimization over other harmonic distortion quantifying parameters, as WLTHD presents the strongest correlation to actual load current THD when tested against any other parameter such as phase and line THD or WTHD. The revealed improvement in current THD was even more pronounced for UVS-based SCM compared to traditional EVS-based SCM. Additionally, MATLAB and Maple source files of the proposed WLTHD formulations and Excel-based pre-calculated optimum PSA and DCR sets for different values of N are provided as downloadable links to further enhance the contribution of the article.

Original languageEnglish
Pages (from-to)211-239
Number of pages29
JournalAEJ - Alexandria Engineering Journal
StatePublished - 1 Mar 2023


  • Current-THD
  • Line-voltage
  • Minimization
  • Optimization
  • Staircase modulation
  • Three-phase multi-level inverters
  • Unequal DC ratios
  • Weighted THD

ASJC Scopus subject areas

  • Engineering (all)


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