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An Improved Problem Formulation for THD Minimization of Multilevel Inverters

An Improved Problem Formulation for THD Minimization of Multilevel Inverters Multilevel inverters (MLIs) generate a staircase sine wave. Switching angles at which the staircase output steps up/down determine modulation index (MI) and total harmonic distortion (THD). Hence, the optimal switching angles are of great interest that ensures a specific MI while minimizing THD. Several methods in the literature use weighted bi-objective optimization where two parts of the objective function consider MI and THD. This approach is affected by heuristically assigned weights to the parts of the objective function. The issue can be circumvented by imposing a predefined limit on MI error. However, the MI error is still nonzero that leads to sub-optimal results. In this work, the problem of finding the optimal switching angles is formulated as minimization of THD subjected to the constraint of ensuring a specific value of MI. A symmetric staircase sine wave having 2k+1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$2k+1$$\end{document} levels is described by k switching angles. Hence, the previous works consider the objective function in k dimensional space. However, this work considers THD minimization with k-1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k-1$$\end{document} switching angles while the kth switching angle is calculated for the true value of desired MI. The proposed approach is applied to 7–15-level MLIs resulting in 5.2%, 3.94%, 2.28%, 1.92% and 1.47% THD, respectively. Compared to the results reported in the literature, the proposed approach results in a lower THD and ensures compliance of IEEE-519 standard at several instances where the other approaches fail. The computational results are validated through simulations and hardware implementation. Realization of true MI, reduction in the search space dimensions and minimization of THD below the previously reported results are major contributions of this work. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Arabian Journal for Science and Engineering Springer Journals

An Improved Problem Formulation for THD Minimization of Multilevel Inverters

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Springer Journals
Copyright
Copyright © King Fahd University of Petroleum & Minerals 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
2193-567X
eISSN
2191-4281
DOI
10.1007/s13369-023-07867-w
Publisher site
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Abstract

Multilevel inverters (MLIs) generate a staircase sine wave. Switching angles at which the staircase output steps up/down determine modulation index (MI) and total harmonic distortion (THD). Hence, the optimal switching angles are of great interest that ensures a specific MI while minimizing THD. Several methods in the literature use weighted bi-objective optimization where two parts of the objective function consider MI and THD. This approach is affected by heuristically assigned weights to the parts of the objective function. The issue can be circumvented by imposing a predefined limit on MI error. However, the MI error is still nonzero that leads to sub-optimal results. In this work, the problem of finding the optimal switching angles is formulated as minimization of THD subjected to the constraint of ensuring a specific value of MI. A symmetric staircase sine wave having 2k+1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$2k+1$$\end{document} levels is described by k switching angles. Hence, the previous works consider the objective function in k dimensional space. However, this work considers THD minimization with k-1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k-1$$\end{document} switching angles while the kth switching angle is calculated for the true value of desired MI. The proposed approach is applied to 7–15-level MLIs resulting in 5.2%, 3.94%, 2.28%, 1.92% and 1.47% THD, respectively. Compared to the results reported in the literature, the proposed approach results in a lower THD and ensures compliance of IEEE-519 standard at several instances where the other approaches fail. The computational results are validated through simulations and hardware implementation. Realization of true MI, reduction in the search space dimensions and minimization of THD below the previously reported results are major contributions of this work.

Journal

Arabian Journal for Science and Engineering – Springer Journals

Published: Nov 1, 2023

Keywords: THD minimization; Genetic algorithms (GA); Multilevel inverters; Optimal switching angles for MLIs

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