<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing DTD v2.3 20070202//EN" "journalpublishing.dtd">
<article article-type="review-article" dtd-version="2.3" xml:lang="EN" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">
<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Energy Res.</journal-id>
<journal-title>Frontiers in Energy Research</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Energy Res.</abbrev-journal-title>
<issn pub-type="epub">2296-598X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1396149</article-id>
<article-id pub-id-type="doi">10.3389/fenrg.2024.1396149</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Energy Research</subject>
<subj-group>
<subject>Review</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>A structural review on reduced switch count and hybrid multilevel inverters</article-title>
<alt-title alt-title-type="left-running-head">Mosepele et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fenrg.2024.1396149">10.3389/fenrg.2024.1396149</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Mosepele</surname>
<given-names>Boikhutso</given-names>
</name>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2664632/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/project-administration/"/>
<role content-type="https://credit.niso.org/contributor-roles/resources/"/>
<role content-type="https://credit.niso.org/contributor-roles/visualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Samikannu</surname>
<given-names>Ravi</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/1207012/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/supervision/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Amuhaya</surname>
<given-names>Lilian</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/2601795/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/supervision/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
</contrib-group>
<aff>
<institution>Department of Electrical and Communications Systems Engineering</institution>, <institution>Botswana International University of Science and Technology</institution>, <addr-line>Palapye</addr-line>, <country>Botswana</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/997751/overview">Terence O&#x2019;Donnell</ext-link>, University College Dublin, Ireland</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/78481/overview">Fateh Krim</ext-link>, University Ferhat Abbas of Setif, Algeria</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1017564/overview">Fei Li</ext-link>, Hefei University of Technology, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Boikhutso Mosepele, <email>morobana@gmail.com</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>09</day>
<month>07</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="collection">
<year>2024</year>
</pub-date>
<volume>12</volume>
<elocation-id>1396149</elocation-id>
<history>
<date date-type="received">
<day>05</day>
<month>03</month>
<year>2024</year>
</date>
<date date-type="accepted">
<day>11</day>
<month>06</month>
<year>2024</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2024 Mosepele, Samikannu and Amuhaya.</copyright-statement>
<copyright-year>2024</copyright-year>
<copyright-holder>Mosepele, Samikannu and Amuhaya</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Classical multilevel inverter (MLI) topologies have gained widespread interest in industry and academia because of the improved qualities they offer over their two-level counterparts. MLIs are characterized by reduced Total Harmonic Distortion (THD) and high power conversion efficiency. Classical MLI topologies, however, are not without drawbacks; generally, they require many components as the number of output waveform levels is increased, resulting in high cost and complex implementation. Furthermore, MLIs based on flying capacitors have issues with capacitor voltage balancing and high inrush currents. As a result, this has prompted researchers to develop reduced component count (RCC) or reduced switch count (RSC) and hybrid topologies to achieve high power quality, but at reduced cost and complexity in comparison to classical MLI topologies. This article evaluates the merits and demerits of recently proposed reduced switch count and hybrid topologies, identifies challenges and opportunities, and proposes further research and development for the improvement of multilevel inverters. This review paper will be helpful to those conducting research in the field of MLI technology.</p>
</abstract>
<kwd-group>
<kwd>hybrid topologies</kwd>
<kwd>multilevel inverters</kwd>
<kwd>photovoltaic systems</kwd>
<kwd>reduced switch count topology</kwd>
<kwd>renewable energy</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Process and Energy Systems Engineering</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Society is more than ever compelled to efficiently utilize existing energy resources while also incorporating Renewable Energy Sources (RES) into the energy infrastructure. This move is aimed to reduce Greenhouse Gases (GHG) emissions, comb the imminent climate crisis, and meet the increasing demand for electricity around the world. This energy demand has promoted the development of alternative sources such as wind turbines, tidal energy generation, Photovoltaic (PV), and green hydrogen energy systems (<xref ref-type="bibr" rid="B5">Ashok Kumar et al., 2021</xref>). PV systems are becoming cost-competitive against conventional thermal power generation systems and will be a major source of electrical power in the future (<xref ref-type="bibr" rid="B63">Ullah et al., 2020</xref>).</p>
<p>Power inverters are a crucial component of photovoltaic systems. They are responsible for increasing the input voltage and converting the DC power to AC power that can be connected to the grid or used in standalone systems. Typically, inverters have multiple stages of conversion, where the first stage is a DC-DC converter that increases the input voltage and performs Maximum Power Point Tracking (MPPT). The final stage of the inverter chain is the DC-AC converter. In some cases, the photovoltaic system may require transformers for galvanic isolation.</p>
<p>Power quality is a crucial aspect of power inverters. Ideally, inverters should produce a pure sinusoidal waveform, but this is not always possible in real-life applications (<xref ref-type="bibr" rid="B17">Cherkaoui Jaouad et al., 2022</xref>). To achieve high power output power quality, 2-level inverters must be switched at high frequencies, resulting in decreased conversion efficiencies (<xref ref-type="bibr" rid="B35">Kabalc&#x131;, 2021</xref>). However, the introduction of multilevel inverters has led to cost reduction, lower Total Harmonic Distortion (THD), and improved efficiency (<xref ref-type="bibr" rid="B64">Vakacharla et al., 2020</xref>).</p>
<p>Improvements on the inverters can be attributed to two factors, the development of new topologies and control methods that incorporated innovations and modernization in semiconductor and computing technologies. With MLI, high voltage inverters that were previously unfeasible with 2-level inverters due to power rating constraints on semiconductor switches can now be implemented (<xref ref-type="bibr" rid="B36">Kala and Arora, 2017</xref>). MLIs offer several other benefits over 2-level inverters, such as reduced rate voltage change over the change in time (dV/dt), lower common-mode voltages, and elimination of the need for bulky output filters (<xref ref-type="bibr" rid="B53">Rodriguez et al., 2009</xref>; <xref ref-type="bibr" rid="B23">Dhanamjayulu et al., 2022a</xref>; <xref ref-type="bibr" rid="B6">Atar et al., 2023</xref>).</p>
<p>Multilevel inverters offer many advantages, but they also have some drawbacks. The cost of the many switching devices and passive components necessary for MLIs can be a limiting factor in their potential applications. This article discusses the research that is being done in academia and industry to develop new reduced switch count and hybrid multilevel inverter topologies. These topologies aim to achieve high output power quality and improved efficiency with reduced switch counts and low complexity. It is important that topologies proposed as reduced switch count types do not come at the expense of increased complexity or use of multiple voltage sources. To assess the features and benefits of new advanced topologies, several key parameters are taken into consideration: total harmonic distortion, component count, efficiency, and complexity (<xref ref-type="bibr" rid="B11">Bhaskar et al., 2020</xref>; <xref ref-type="bibr" rid="B56">Sedaghati et al., 2022</xref>; <xref ref-type="bibr" rid="B60">St&#xf6;ttner et al., 2022</xref>; <xref ref-type="bibr" rid="B67">Wikipedia, 2024</xref>). <xref ref-type="fig" rid="F1">Figure 1</xref> shows the classification of multilevel inverters. They may be categorized into single source, multiple source, resonant, and reduced switch count inverters. Only reduced switch count types and their improvement types or hybrids will be reviewed in this article and are highlighted in blue in the figure.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Classification of MLI topologies based on supply and topological structure.</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g001.tif"/>
</fig>
<p>Research in multilevel inverters is an ever-evolving endeavor, and newer topologies that bring better performance are always contributed to the body of knowledge. In (<xref ref-type="bibr" rid="B46">Mehta and Puri, 2022</xref>), a review of reduced component MLI topologies classified as symmetric, asymmetric, and hybrid configurations was presented (<xref ref-type="bibr" rid="B13">Bughneda et al., 2021</xref>), reviewed photovoltaic systems and highlighted promising use cases of MLI in such systems (<xref ref-type="bibr" rid="B8">Barros et al., 2022</xref>), looked at modular multilevel inverters, their submodules, and modulation techniques, and (<xref ref-type="bibr" rid="B31">Jana et al., 2017</xref>) reviews multilevel topologies with a focus on soft-switched topologies. A recent review publication (<xref ref-type="bibr" rid="B66">Vinay Kumar and GowriManohar, 2023</xref>), reviewed and classified RSCs in asymmetric and symmetric topological structures, and compared their performance merits. The authors observed superior characteristics in asymmetrical structures in terms of higher efficiency, better switch utilization, and low THD. This review article takes a different approach not only to review topologies and their operations, advantages, and disadvantages but also to identify research opportunities for further development.</p>
<p>The paper is structured as follows. <xref ref-type="sec" rid="s2">Section 2</xref> presents a topological review of classical MLIs, discusses their advantages, and disadvantages, and highlights the motivation to move towards reduced switch count and hybrid MLIs; <xref ref-type="sec" rid="s3">Section 3</xref> provides an overview of modulation techniques that can be applied to MLI, <xref ref-type="sec" rid="s4">Section 4</xref> presents an analysis of recently proposed reduced switch count inverters and hybrid multilevel inverters, <xref ref-type="sec" rid="s5">Section 5</xref> summarizes the advantages and disadvantages of the reviewed topologies, and suggests potential research opportunities for further development, and <xref ref-type="sec" rid="s6">Section 6</xref> of the paper summarizes the conclusions and observations that were made during the review process.</p>
</sec>
<sec id="s2">
<title>2 Classical multilevel topologies</title>
<p>The neutral-point clamped (NPC), cascaded h-bridge (CHB), and flying-capacitor (FC) MLIs were the first invented MLI topologies and are referred to as classical topologies. Coverage of the fundamental topologies is done extensively in other publications, (<xref ref-type="bibr" rid="B2">Abd Halim et al., 2016</xref>; <xref ref-type="bibr" rid="B19">Choudhury et al., 2021</xref>; <xref ref-type="bibr" rid="B7">Barnawi et al., 2023</xref>), and a summary is presented in this article for brevity. The CHB requires the least number of components among the three, as shown in <xref ref-type="fig" rid="F2">Figure 2</xref>; <xref ref-type="table" rid="T1">Table 1</xref>, the reason for its widespread adoption in industrial applications. The main drawback of CHB MLI is the requirement for independent voltage sources, the provision of which is often achieved with expensive transformers. Asymmetric configurations of the CHB have the advantage of generating many voltage levels with fewer power sources and components, although this comes at a loss of redundancy, fault tolerance, and modularity (<xref ref-type="bibr" rid="B54">Rotella et al., 2006</xref>; <xref ref-type="bibr" rid="B9">Barzegarkhoo et al., 2016</xref>; <xref ref-type="bibr" rid="B37">Kannan et al., 2017</xref>; <xref ref-type="bibr" rid="B14">Busarello et al., 2018</xref>; <xref ref-type="bibr" rid="B41">Kumar Gupta and Bhatnagar, 2018</xref>; <xref ref-type="bibr" rid="B18">Chitra and Valluvan, 2020</xref>; <xref ref-type="bibr" rid="B49">Odeh et al., 2021</xref>). The resulting implementations have increased cost and complexity. FC MLIs have capacitor voltage balancing problems and high inrush currents. The NPC has the highest number of components. The issue with NPCs is the voltage balancing of the DC link capacitors at the input as the number of levels increases, which can cause undesirable transients that can damage the switching devices if not properly managed (<xref ref-type="bibr" rid="B3">Ahmad et al., 2024</xref>; <xref ref-type="bibr" rid="B39">Kieferndorf et al., 2000</xref>; <xref ref-type="bibr" rid="B24">Es-Saadi et al., 2018</xref>; <xref ref-type="bibr" rid="B25">Ghani et al., 2023</xref>). When the FC is compared to the NPC, the FC requires half the number of flying capacitors and clamping diodes compared to the NPC, resulting in a significant reduction in component count and cost. Additionally, the FC offers redundancy in configurations to generate zero output voltage, which can be valuable for optimization purposes (<xref ref-type="bibr" rid="B16">Chang-xin et al., 2009</xref>; <xref ref-type="bibr" rid="B12">Bressan et al., 2019</xref>; <xref ref-type="bibr" rid="B28">Humayun et al., 2020</xref>; <xref ref-type="bibr" rid="B43">Laamiri et al., 2017</xref>; <xref ref-type="bibr" rid="B65">Vincotech, 2024</xref>). In summary, all three have the benefit of generating low THD waveforms but in general, require many components to generate at high levels. A quantitative summary of component count for the three topologies is shown in <xref ref-type="table" rid="T1">Table 1</xref> on the basis of the number of sources (N<sub>DC</sub>), number of switches (N<sub>SW</sub>), number of diodes (N<sub>D</sub>), and number of capacitors (N<sub>C</sub>). A qualitative summary is presented in <xref ref-type="table" rid="T2">Table 2</xref>, summarizing the merits and demerits of each topology. Great effort is directed toward developing multilevel inverters to enhance the level count while using fewer components.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Number of components <italic>versus</italic> number of output levels in classical topologies.</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g002.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Comparison of classical MLIs on number of DC sources and numbers of different components.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Topology</th>
<th align="center">N<sub>DC</sub>
</th>
<th align="center">N<sub>SW</sub>
</th>
<th align="center">N<sub>D</sub>
</th>
<th align="center">N<sub>C</sub>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">CHB MLI</td>
<td align="center">
<inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mi mathvariant="normal">L</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">
<inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#x2219;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mi mathvariant="normal">L</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0</td>
<td align="center">0</td>
</tr>
<tr>
<td align="center">NPC MLI</td>
<td align="center">1</td>
<td align="center">
<inline-formula id="inf3">
<mml:math id="m3">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#x2219;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mi mathvariant="normal">L</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">
<inline-formula id="inf4">
<mml:math id="m4">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mi mathvariant="normal">L</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2219;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mi mathvariant="normal">L</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0</td>
</tr>
<tr>
<td align="center">FCMLI</td>
<td align="center">1</td>
<td align="center">
<inline-formula id="inf5">
<mml:math id="m5">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#x2219;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mi mathvariant="normal">L</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0</td>
<td align="center">
<inline-formula id="inf6">
<mml:math id="m6">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mi mathvariant="normal">L</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2219;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mi mathvariant="normal">L</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Qualitative comparison of classical MLIs.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Topology</th>
<th align="center">Features and merits</th>
<th align="center">Demerits</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">CHB</td>
<td align="left">&#x2022; High modularity<break/>&#x2022; Minimum component count<break/>&#x2022; Asymmetrical configuration yields high voltage levels with fewer components</td>
<td align="left">&#x2022; Requires many isolated DC sources<break/>&#x2022; Modularity lost with asymmetrical configurations</td>
</tr>
<tr>
<td align="left">NPC</td>
<td align="left">&#x2022; Single voltage source<break/>&#x2022; Low voltage stress</td>
<td align="left">&#x2022; No modularity<break/>&#x2022; Many diodes are required</td>
</tr>
<tr>
<td align="left">FC</td>
<td align="left">&#x2022; Single voltage source<break/>&#x2022; Inherent capacitor charge balancing</td>
<td align="left">&#x2022; Many capacitors are required<break/>&#x2022; Capacitor charge imbalance issues</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3">
<title>3 Multilevel modulation techniques</title>
<p>Multilevel inverters need specific switching patterns to achieve the desired output voltage. Various techniques have emerged over time to control the topologies, and modulation techniques are an advanced field on their own. These techniques can be categorized on the basis of switching frequency into high-frequency and low-frequency techniques. Although there are many modulation techniques available, here we present a summary of some of the commonly used ones found in the literature (<xref ref-type="bibr" rid="B41">Kumar Gupta and Bhatnagar, 2018</xref>).</p>
<sec id="s3-1">
<title>3.1 High-frequency techniques</title>
<p>High-frequency pulse width modulation (HFPWM) techniques include space-vector pulse width modulation (SVPWM) and multi-carrier PWM. SVPWM is less popular due to its high complexity for many-level MLI. Multi-carrier methods, as the name suggests, make use of multiple carriers of triangular or sawtooth waveforms. The frequency, amplitude, phase of each carrier, and delay between carriers can be adjusted to improve performance. With all this freedom present, many multi-carrier methods have been proposed. An N-level inverter requires N-1 carrier signals. The methods include phase deposition PWM(PD-PWM): here all carrier signals are in phase and level-shifted; phase opposition disposition PWM(POD-PWM): with this technique, carrier signals above and below zero reference are shifted by 180&#xb0;; phase shift PWM(PS-PWM): here all the carrier signals are shifted at some angle which determines the performance of modulation; variable frequency carrier bands PWM(VFCB-PWM): for this technique, all the carriers can assume different frequencies; carrier overlapping PWM(CO-PWM): for this modulation scheme, the carrier signals overlap each other; and alternate phase opposition disposition (APOD-PWM): in this scheme, the carrier signals are alternatingly phase shifted by 180&#xb0;. The modulation method we choose has a significant impact on the inverter THD performance. In (<xref ref-type="bibr" rid="B50">Oghorada et al., 2019</xref>), the authors investigated the use of PS-PWM, PD-PWM, and two proposed modulation methods on a 5L-FCMLI. In (<xref ref-type="bibr" rid="B26">Harin et al., 2017</xref>), a simulation comparison of different modulation techniques is carried out on a 3Linverter and the results showed that PD-PWM generated waveforms with the least THD.</p>
</sec>
<sec id="s3-2">
<title>3.2 Low-frequency techniques</title>
<p>Space vector control (SVCPWM) calculates the switching times based on a space vector representation of the reference voltage together with the possible switching states (<xref ref-type="bibr" rid="B45">Mayorga et al., 2021</xref>). In (<xref ref-type="bibr" rid="B44">Lewicki et al., 2023</xref>), a new SVPWM algorithm with DC link voltage balancing capability is proposed for a three-phase 7-level CHB system. It was demonstrated to increase control of DC link voltages compared to other methods. In (<xref ref-type="bibr" rid="B32">Jayakumar et al., 2021</xref>), the authors review SVCPWM control technique in conventional 2-level and 3-level NPC and compare it to multiple carrier techniques presented in the previous section. SVC is demonstrated to provide better DC-link voltage balancing, common mode voltage reduction, better THD, and switching loss reduction.</p>
<p>The nearest-level control method, also known as staircase modulation in some publications, is an important technique for high voltage inverters. However, if it is used for low voltage level inverters, it produces low order harmonics that are difficult to filter (<xref ref-type="bibr" rid="B40">Kumar et al., 2022</xref>). In (<xref ref-type="bibr" rid="B52">Ramu et al., 2022</xref>), an evaluation of LSPWM, PSPWM, and NLC is carried out on RSCMLI. Nearest-level control demonstrated the highest efficiency due to reduced switching losses at low switching frequencies. In (<xref ref-type="bibr" rid="B15">Busarello et al., 2019</xref>), a clear understanding of NLC is presented for an ACHB MLI, with calculations for the power distribution between CHB cells. It is argued that asymmetric MLIs benefit greatly from NLC for their high efficiency.</p>
</sec>
<sec id="s3-3">
<title>3.3 Hybrid modulation techniques</title>
<p>Hybrid modulation combines carrier-based high-frequency modulations and fundamental-frequency modulation strategies (<xref ref-type="bibr" rid="B61">Tamilvani and Valluvan, 2012</xref>). For the same reason that hybrid multilevel inverters inherit good characteristics from the individual topologies, hybrid modulation seeks to marry the benefits of each. The outcome is reduced switching losses and high-power quality, two competing merits in multilevel inverters. Fundamental frequency signals generate a square wave to establish the main part of the reference signal. The square wave is then subtracted from the reference signal, creating the difference reference signal which is compared against the high-frequency carrier signal for the generation of drive signals for other switches. An additional benefit is the reduced number of required carrier signals and hence reduced computational requirement. The hybrid modulation is applied to provide high-voltage fundamental-frequency and low-voltage high-frequency switching operations resulting in reduced switching losses. In (<xref ref-type="bibr" rid="B34">Jiang et al., 2017</xref>), carrier-based PWM is combined with SVPWM for a 3-level NPC, resulting in increased efficiency.</p>
</sec>
</sec>
<sec id="s4">
<title>4 Reduced switch count and hybrid multilevel inverter topologies</title>
<p>In the work of Thakre et al. (<xref ref-type="bibr" rid="B62">Thakre et al., 2022</xref>), the authors developed a topology as shown in <xref ref-type="fig" rid="F3">Figure 3</xref>, that can accommodate symmetric and asymmetric voltage sources to improve the level count. The basic module of the topology consists of two unidirectional switches, two free-wheeling diodes, and two isolated voltage sources and can generate 3 voltage levels. Its ability to generate enhanced level count is overshadowed by the many voltage sources, which make it a cost-sensitive topology. The polarity inversion full bridge driving the output limits application to low and medium-voltage applications.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Proposed multilevel module-based 11-level MLI in [<xref ref-type="bibr" rid="B62">Thakre et al. (2022)</xref>].</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g003.tif"/>
</fig>
<p>
<xref ref-type="bibr" rid="B4">Ahmed et al. (2018)</xref>, proposed a reversed source half-bridge multilevel inverter, eliminating the need for a dedicated polarity generator. It is usually custom to employ a full-bridge front end for this specific purpose of polarity generation, however, the front end in this case requires switches of high voltage blocking capability vis-a-vis the level generation switches and will only be limited to low voltage applications. To eliminate the full bridge front-end, the authors developed the topology as shown in <xref ref-type="fig" rid="F4">Figure 4</xref>, that inherits simple cascaded half-bridge modules. Cascaded half-bridges cannot generate negative voltages, and to solve this, the authors implemented another half-bridge module with a negative polarity voltage equal to all the other cascaded positive modules combined. Intermediate voltage levels are generated through subtractive operations. The control complexity is low, and the asymmetric nature allows for low frequency modulation to enhance efficiency. Nevertheless, the negative half bridge limits its application to low-voltage applications and the many power sources can increase the cost.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Cascaded half-bridge MLI (<xref ref-type="bibr" rid="B4">Ahmed et al., 2018</xref>).</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g004.tif"/>
</fig>
<p>In their paper <xref ref-type="bibr" rid="B29">Islam et al. (2023)</xref> proposed a five-level voltage-boosting switched capacitor MLI as shown in <xref ref-type="fig" rid="F5">Figure 5</xref>. This structure consists of seven switches, 3 diodes, and 2 capacitors that act as virtual voltage sources. The topology uses a full-bridge frontend for polarity inversion, which makes it highly modular and extensible for high-voltage applications, although that comes at the expense of many voltage sources. The capacitor voltage balancing is inherent and allows for simple control. The switch utilization is low for this topology.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Switched capacitor MLI (<xref ref-type="bibr" rid="B29">Islam et al., 2023</xref>).</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g005.tif"/>
</fig>
<p>A switched series-parallel source multilevel inverter is proposed in (51) with a single DC source and 2 switched capacitors. Using capacitors in a topology to replace voltage sources helps to reduce the overall component count in a system. The inverter as shown in <xref ref-type="fig" rid="F6">Figure 6</xref>, generates a 7-level output waveform and inherently balanced capacitor voltages. The excellent merit of the topology is the boosting capability, which additionally eliminates the need for boost converters, especially in renewable energy systems. The topology is highly modular and can be extended either by adding more switched capacitor units in series or cascading through the outer full bridge. The switch S2 has the highest conduction loss compared to other switches. This unbalanced nature will lead to reliability issues. Another downside of the topology is that the number of carrier signals used is tied to the voltage gain. This requires increased computational capability when extending and is costly. Fundamental-frequency modulation may erode the capacitor balancing capability and therefore not appropriate. Hybrid modulation can be explored to try to reduce the quantity of carrier signals.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Series-parallel capacitor source proposed in [<xref ref-type="bibr" rid="B33">Jena et al. (2023)</xref>].</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g006.tif"/>
</fig>
<p>A 31-level topology is presented in (52) to enhance output level count and shown in <xref ref-type="fig" rid="F7">Figure 7</xref> with asymmetric input voltage sources. The level generation circuits are innovative; however, the structure requires isolated voltage sources, in this case, provided using a high-frequency link which makes it unattractive cost-wise. As with all asymmetric topologies, the level count is enhanced. Generally, the component count is reduced on the level generation side but taking into account the high-frequency link and its associated components the prices will be compounded. The topology is complex, considering all the design variables including the design and sizing of the high-frequency transformer. It makes up for the demerits with high efficiency associated with low-frequency modulated asymmetric structure.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>High-frequency magnetic-linked source-switched MLI in [<xref ref-type="bibr" rid="B30">Islam et al. (2020)</xref>].</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g007.tif"/>
</fig>
<p>In (53), the authors present a novel high-frequency linked series switched-source MLI shown in <xref ref-type="fig" rid="F8">Figure 8</xref>. It distinguishes itself from the topology in (52) by using the high-frequency transformer to generate only the low-voltage sources in an asymmetric configuration. The main voltage input to the inverter is supplied directly from the voltage source, hence the lack of complete galvanic isolation. The center-tapped secondary winding output allows for an enhanced level generation with the switched rectifier circuits, however, the many rectifiers involved considerably reduce the efficiency to a reported 95%. The topology still retains many components and the output full-bridge limits it to low to medium-voltage applications. However, cascading allows the system to be built to higher voltages, albeit costly considering the transformers.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>High-frequency link switched rectifier MLI (<xref ref-type="bibr" rid="B27">Hatas et al., 2023</xref>).</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g008.tif"/>
</fig>
<p>In (54), a novel 13-level switched capacitor MLI with a voltage gain of six is proposed and is depicted here in <xref ref-type="fig" rid="F9">Figure 9</xref>. The topology combines a switched capacitor series-parallel unit and an L-type unit for extending to high levels and gain. The topology benefits from a high number of complementary switching pairs, reducing the cost of drivers. The high gain is an advantage, especially for photovoltaic applications where the requirements for a boost converter are eliminated. However, the carrier signal requirement is twice the gain, making the control complex. The topology has inherent capacitor voltage balancing, an additional feature for reducing complexity. The structure could benefit from decoupling the charging of C1 and C2 in parallel, charge them independently and benefit from enhanced voltage gain and still retain the extensibility offered by the L-type unit. Furthermore, all the capacitors are charged in series with the voltage source and the addition of a series inductor can help with limiting the initial inrush currents.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>13-level SC with series-parallel and L-type units (<xref ref-type="bibr" rid="B21">Deng et al., 2023</xref>).</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g009.tif"/>
</fig>
<p>In (55), a series-connected switched-source configuration with an auxiliary module and polarity changing full bridge is proposed. The topology was designed with hybrid modulation in mind from the onset and is shown in <xref ref-type="fig" rid="F10">Figure 10</xref>. The switched sources are dedicated to the level generation, switched at low frequency, and the auxiliary modules, are switched at carrier signal frequency to smoothen the output waveform. The zero level is generated by the polarity changing full-bridge. All voltage sources must be equal to avoid short-circuiting through the body diodes. For this reason, it cannot accommodate asymmetric configurations. The voltage sources can be connected in parallel to share the load equally. One major benefit is that if the auxiliary module source is chosen to be half of the series sources, the number of levels generated is doubled. The topology generates a high number of levels with very few switches but requires isolated voltage sources even for the minimal configuration. Because the polarity is generated through the full bridge, it is limited to low to medium voltage applications. Even though possible to cascade, it would prove expensive. The topology benefits from a high number of complementary switches, reducing the cost of drivers drastically.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>9-level series-connected switched-source MLI (<xref ref-type="bibr" rid="B10">Bassi and Salam, 2019</xref>).</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g010.tif"/>
</fig>
<p>
<xref ref-type="bibr" rid="B42">Kumari et al. (2023)</xref>, proposed a 5-level extendible topology as shown in <xref ref-type="fig" rid="F11">Figure 11</xref>. Its simple structure and inherent capacitor voltage balancing reduce the complexity of control. The design has retained a full bridge end, making it highly modular and extensible for higher voltage applications. For single source applications, it will only be limited to low-voltage applications. Its low gain makes it unattractive for photovoltaic applications requiring high gains. The topology has inherent voltage balancing capability. A single discharging state is always followed by two charging states, giving it a good capacitor voltage balancing capability and making it suitable for high-current applications.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>MLI switched capacitor with reduced switch count (<xref ref-type="bibr" rid="B42">Kumari et al., 2023</xref>).</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g011.tif"/>
</fig>
<p>In reference (<xref ref-type="bibr" rid="B38">Khan et al., 2022</xref>), a new topology of switched-capacitor is presented as shown in <xref ref-type="fig" rid="F12">Figure 12</xref>. The topology and switching patterns implemented for it are designed to achieve inherent self-balancing of capacitor voltages, eliminating the need for auxiliary circuits and reducing the control complexity. The authors solve the issue of high inrush currents by incorporating a series inductor and implementing a precharge soft-start modulation scheme. The quasi-resonant recharging operations reduce losses considerably, a big advantage as low-loss capacitor charging or resonant charging in multilevel inverters is a current topic. With the inclusion of the pre-charge soft start, the control complexity has increased.</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Single-phase 5-level SC MLI (<xref ref-type="bibr" rid="B38">Khan et al., 2022</xref>).</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g012.tif"/>
</fig>
<p>Sheik Tanzim et al. (<xref ref-type="bibr" rid="B47">Meraj et al., 2021</xref>), proposed a novel hybrid T-type inverter, a hybridization of a T-type, and a cross-switched MLI shown in <xref ref-type="fig" rid="F13">Figure 13</xref>. The multisource structure allows for asymmetric configurations for increased level generation. The structure is extensible although the requirement for many isolated voltage sources is a drawback, and complexity is greatly increased. The cross-connected voltage sources require higher voltage blocking devices, a variation that will increase costs. Notwithstanding, the topology uses low-frequency switching, resulting in good efficiency results. The main drawback of this topology is the many different voltage sources.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Hybrid T-type multilevel inverter (<xref ref-type="bibr" rid="B47">Meraj et al., 2021</xref>).</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g013.tif"/>
</fig>
<p>
<xref ref-type="bibr" rid="B22">Dhanamjayulu et al. (2022b)</xref>, have proposed a novel 35-level asymmetric inverter applicable to renewable energy and electric mobility systems, comprising of eight unidirectional switches, 2 bidirectional switches, and five voltage sources. The inverter is shown in <xref ref-type="fig" rid="F14">Figure 14</xref>. All asymmetrical topologies have the advantage of producing many levels with fewer components, but this topology contains a high number of voltage sources. The topology has four bidirectional switches designated as S1, S2, S6 and S12. The topology lacks extensibility and is limited to low to medium-voltage applications. As each of the voltage sources is of a different size, power distribution, and handling is unbalanced and varied. It is suited to battery systems where isolated power sources are readily available. The reported efficiency of the inverter is 93.37%, a comparatively poor performance figure in general, owing to the many switches present.</p>
<fig id="F14" position="float">
<label>FIGURE 14</label>
<caption>
<p>35-level inverter in [<xref ref-type="bibr" rid="B22">Dhanamjayulu et al. (2022b)</xref>].</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g014.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F15">Figure 15</xref> illustrates the 17-level asymmetric polygon-type asymmetric 17-level RSC MLI proposein (<xref ref-type="bibr" rid="B55">Samadaei et al., 2019</xref>). The topology is constructed with 2 voltage sources and 2 switched capacitors. One source has voltage V<sub>dc</sub> while the second has 3V<sub>dc</sub>, with the same scaling for the capacitor sources. The topology employs the NLC modulation technique that results in low switching losses. The switching states and the corresponding output voltages are presented in Table 14. The 1Vdc source is used to charge the 1Vdc capacitor, and the same is true for the 3Vdc source and capacitor. The inherent capacitor charging is achieved through careful planning of the switching paths. Both capacitors are charged one after the other within one window at the 0Vdc output voltage and their charging paths are created as follows: to charge the 1Vdc capacitor, switches S<sub>1</sub>, S<sub>2</sub>, S<sub>4</sub>, S<sub>8,</sub> and S<sub>11</sub> are engaged; and to charge the 3Vdc capacitor, switches S<sub>4</sub>, S<sub>5</sub>, S<sub>6</sub>, S<sub>7</sub> and S<sub>11</sub> are switched ON. The sizing of the capacitors is such that it charges with sufficient charge to last all switching states within one-half of a single fundamental cycle. With such a long discharging period and a single short window for charging capacitors, high voltage ripples will be present. Very large and expensive capacitors will be necessary to keep voltage ripples to a minimum.</p>
<fig id="F15" position="float">
<label>FIGURE 15</label>
<caption>
<p>Polygon-type MLI proposed in [<xref ref-type="bibr" rid="B55">Samadaei et al. (2019)</xref>].</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g015.tif"/>
</fig>
<p>Srivivasan et al. proposed switch-ladder MLI (SLMLI) shown in <xref ref-type="fig" rid="F16">Figure 16</xref> (<xref ref-type="bibr" rid="B59">Srinivasan et al., 2021</xref>). The structure generates an output voltage of 81 levels. The output voltage levels can be increased by increasing the number of DC sources within the cell or through cascading modules or stages with fixed DC sources. The latter will use fewer switching devices compared to the former when increasing MLI voltage levels. In the presented topology. V<sub>1</sub> &#x3d; V<sub>dc</sub>, V<sub>2</sub>&#x3d;(z&#x2b;2) &#x2a; V<sub>dc</sub>, V<sub>3</sub>&#x3d;(4z) &#x2a;V<sub>1</sub>, V<sub>4</sub>&#x3d;(z&#x2b;2) &#x2a;V<sub>3</sub>. Negative output values are generated by the polarity inversion full bridge. The nearest-level modulation technique was employed and achieved low THD values. The topology can generate a high number of levels, however the modules use four voltage sources and cascading the modules increases the cost and complexity even further.</p>
<fig id="F16" position="float">
<label>FIGURE 16</label>
<caption>
<p>Switch-ladder MLI in [<xref ref-type="bibr" rid="B59">Srinivasan et al. (2021)</xref>].</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g016.tif"/>
</fig>
<p>In (62) an asymmetric H-6 topology is proposed and depicted in <xref ref-type="fig" rid="F17">Figure 17</xref>. The structure uses an H-6 inverter with a string of isolated DC sources on either side of the H-6 cell. The DC sources are controlled by the outer switches for level generation and the center switches S<sub>H1</sub>-S<sub>H6</sub> are used for polarity inversion. The level generation switches operate at high PWM frequencies while the H-bridge switches operate at fundamental frequency to reduce the switching loss. Asymmetric voltage sources can be chosen for the DC source values yielding a high number of output levels. This is a highly complex topology and requires isolated voltage sources. In practical terms, obtaining different voltage ratios with photovoltaic systems or fuel cells can make the implementation expensive. It is suitable for battery operated inverters.</p>
<fig id="F17" position="float">
<label>FIGURE 17</label>
<caption>
<p>Hybrid H-6 MLI proposed in [<xref ref-type="bibr" rid="B51">Radhakrishnan et al. (2024)</xref>].</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g017.tif"/>
</fig>
<p>Siddique et al. proposed in (63) a new design of 11-level active neutral-point clamped (ANPC) inverter with high gain for photovoltaic applications. <xref ref-type="fig" rid="F18">Figure 18</xref> shows the inverter topology, consisting of a single voltage source, two switched capacitors, and 12 switching devices. Of the 12 switches, S<sub>1</sub>, S<sub>2</sub>, S<sub>5</sub>, S<sub>8</sub>, S<sub>9,</sub> and S<sub>10</sub> have voltage ratings of the input DC source, S<sub>3</sub> and S<sub>4</sub> have half the DC source rating, switched S<sub>6</sub>, S<sub>7</sub>, S<sub>11</sub> and S<sub>12</sub> have voltage ratings twice the DC source voltage. The variability in the switch rating makes the inverter design complicated. Since the topology has a voltage gain of 2.5, it is well suited for use in photovoltaic systems and eliminates the need for a separate boost converter. The switch utilization, however, is low.</p>
<fig id="F18" position="float">
<label>FIGURE 18</label>
<caption>
<p>9-level SC proposed in [<xref ref-type="bibr" rid="B20">Daula Siddique et al. (2022)</xref>].</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g018.tif"/>
</fig>
<p>In (64), a 9-level SC inverter with voltage boost and capacitor self-balancing capability is proposed and shown in <xref ref-type="fig" rid="F19">Figure 19</xref>. It consists of two switched capacitors, C1 and C2. C1 is charged to the input voltage and C2 is charged to 2Vin, through a series connection of C1 and the input voltage source. The topology is capable of switching at fundamental frequency, leading to efficient implementation. Having a gain of four eliminates the need for boost converter for photovoltaic applications. The topology&#x2019;s main drawback is that it retains many switches. It boasts inherent capacitor voltage balancing but suffers from high inrush currents at startup.</p>
<fig id="F19" position="float">
<label>FIGURE 19</label>
<caption>
<p>11-level ANPC proposed in [<xref ref-type="bibr" rid="B57">Samadaei et al. (2019)</xref>].</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g019.tif"/>
</fig>
<p>In (65), a modified 7-level packed U-cell (PUC) inverter with voltage gain is presented and shown in <xref ref-type="fig" rid="F20">Figure 20</xref>. The traditional 7-level PUC has a single voltage source V<sub>dc</sub> and a capacitor source clamped to V<sub>dc</sub>/3. The downside of this topology is the requirement for external closed-loop control for capacitor voltage balancing. The complexity is high. To solve the issue of voltage balancing, a PUC5 was invented along with a novel modulation method with inherent voltage balancing in (<xref ref-type="bibr" rid="B1">Abarzadeh et al., 2019</xref>). Both the PUC7 and the PUC5 are attractive with their low switch counts, but they lack voltage gain and as such not suitable for where voltage boosting is required as so in photovoltaic systems. The generic PUC is extensible but requires many voltage sources because the level generation is done for the most part by subtraction of voltage sources. In the modified PUC presented here, the capacitor is replaced by a voltage source with reversed polarity, and this allows the generation of higher voltage amplitude through the additive series connection of V<sub>1</sub> and V<sub>2</sub>. In the case of modified PUC, V<sub>1</sub> &#x3d; 2V<sub>2</sub>, and the output voltages that are generated are 0, &#xb1;V<sub>dc</sub>, &#xb1;2V<sub>dc</sub>, &#xb1;3V<sub>dc</sub>. The requirement for more than one voltage source is a disadvantage for this topology. An opportunity presents itself to explore a PUC7 with inherent voltage balancing and will be mentioned in the following section.</p>
<fig id="F20" position="float">
<label>FIGURE 20</label>
<caption>
<p>Modified 7-level PUC (<xref ref-type="bibr" rid="B57">Shojaei et al., 2019</xref>).</p>
</caption>
<graphic xlink:href="fenrg-12-1396149-g020.tif"/>
</fig>
</sec>
<sec sec-type="discussion" id="s5">
<title>5 Discussion</title>
<p>
<xref ref-type="table" rid="T3">Table 3</xref> summarizes the features, and points out the merits, and demerits of the reviewed MLI topologies. <xref ref-type="table" rid="T4">Table 4</xref> shows a comparative analysis of the different topologies on the basis of the number of levels generated (N<sub>L</sub>), number of switches (N<sub>SW</sub>), number of diodes (N<sub>D</sub>), number of magnetic transformers or inductors (N<sub>TR/IND</sub>), the ratio of levels to the total number of components (N<sub>L</sub>/N<sub>COMP</sub>), and lastly a statement of the whether the reported topology employes asymmetric sources or not.It is crucial to understand that the overall cost of MLIs increase with a rise in the number of components, voltage sources and the complexity involved to implement the modulation strategies. The review looked at recently proposed inverters categorized as reduced switch count topologies. While galvanic isolation can be mandatory, the trend is in favor of nonisolated topologies as they are cost-effective. The topologies reported in (<xref ref-type="bibr" rid="B4">Ahmed et al., 2018</xref>; <xref ref-type="bibr" rid="B55">Samadaei et al., 2019</xref>; <xref ref-type="bibr" rid="B30">Islam et al., 2020</xref>; <xref ref-type="bibr" rid="B47">Meraj et al., 2021</xref>; <xref ref-type="bibr" rid="B59">Srinivasan et al., 2021</xref>; <xref ref-type="bibr" rid="B22">Dhanamjayulu et al., 2022b</xref>; <xref ref-type="bibr" rid="B62">Thakre et al., 2022</xref>; <xref ref-type="bibr" rid="B27">Hatas et al., 2023</xref>; <xref ref-type="bibr" rid="B51">Radhakrishnan et al., 2024</xref>) benefit from the use of asymmetric configurations to achieve high switch utilization or generate a high number of levels. This comes at the expense of a loss of modularity, which is highly desired to extend topologies for high voltage applications. The aforementioned topologies, utilizing multiple active voltage sources, present with high complexities as it is not the case that isolated voltage source are readily available. The cost of implementing multiple voltage sources is likely to be prohibitive. Single voltage source topologies utilizing capacitors to achieve voltage gain and level generation are attracting more attention from industry because or their low cost and manageable complexities. Many switched capacitor topologies are proposed, as those reviewed in this article, (<xref ref-type="bibr" rid="B38">Khan et al., 2022</xref>; <xref ref-type="bibr" rid="B21">Deng et al., 2023</xref>; <xref ref-type="bibr" rid="B29">Islam et al., 2023</xref>; <xref ref-type="bibr" rid="B33">Jena et al., 2023</xref>; <xref ref-type="bibr" rid="B42">Kumari et al., 2023</xref>), and increased research in this domain will lead to more optimal designs. Single source switched-capacitor topologies are favourable. In developing many-level SC topologies, soft-charging of capacitors becomes ever more important to be incorporated in inverters beyond five levels or single capacitor.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Summarized features, merits, and demerits of reviewed topologies.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Ref.</th>
<th align="center">Type</th>
<th align="left">Features and merits</th>
<th align="left">Demerits</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">
<xref ref-type="bibr" rid="B62">Thakre et al. (2022)</xref>
</td>
<td align="center">Multilevel Module-based MLI</td>
<td align="left">&#x2022; Asymmetry to reduce switch count and increase level count</td>
<td align="left">&#x2022; Requires isolated sources<break/>&#x2022; Full-bridge limits application to low to medium-voltage</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B4">Ahmed et al. (2018)</xref>
</td>
<td align="center">Cascaded Half-Bridge<break/>MLI</td>
<td align="left">&#x2022; High switch utilization and benefits from asymmetrical sources to generate high level count</td>
<td align="left">&#x2022; Requires isolated sources<break/>&#x2022; Limited modularity<break/>&#x2022; High blocking voltage devices required for some switches</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B29">Islam et al. (2023)</xref>
</td>
<td align="center">Reversing Voltage<break/>Switched Capacitor MLI</td>
<td align="left">&#x2022; Single voltage source<break/>&#x2022; Inherent capacitor voltage balancing</td>
<td align="left">&#x2022; Low switch utilization</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B33">Jena et al. (2023)</xref>
</td>
<td align="center">Series-Parallel<break/>Capacitor MLI</td>
<td align="left">&#x2022; Single voltage source reduces cost<break/>&#x2022; Extensible by adding more series-parallel capacitor units</td>
<td align="left">&#x2022; High number of carrier signals required<break/>&#x2022; Unbalanced switch load</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B30">Islam et al. (2020)</xref>
</td>
<td align="center">High Frequecy Link<break/>Series connected switched source</td>
<td align="left">&#x2022; High level generation with fewer components</td>
<td align="left">&#x2022; Transformer carries high cost<break/>&#x2022; Isolation transformer can introduce more losses<break/>&#x2022; High complexity</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B27">Hatas et al. (2023)</xref>
</td>
<td align="center">Hybrid HFL switched source<break/>MLI</td>
<td align="left">&#x2022; Adjustable single DC source</td>
<td align="left">&#x2022; High cost on transformer<break/>&#x2022; Boost converter increases complexity<break/>&#x2022; Many rectifiers</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B21">Deng et al. (2023)</xref>
</td>
<td align="center">Switched Series-parallel<break/>SCMLI</td>
<td align="left">&#x2022; High gain SC MLI eliminating the requirement for boost converter<break/>&#x2022; Extensible<break/>&#x2022; Inherent capacitor voltage balancing</td>
<td align="left">&#x2022; High complexity from using many carrier signals</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B10">Bassi and Salam (2019)</xref>
</td>
<td align="center">Series-connected switched-source<break/>MLI</td>
<td align="left">&#x2022; Highly modular<break/>&#x2022; Can double the level count by halving the auxiliary module voltage</td>
<td align="left">&#x2022; Many isolated voltage sources<break/>&#x2022; Low switch utilization for symmetric sources<break/>&#x2022; Limited by full-bridge to low voltage applications</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B42">Kumari et al. (2023)</xref>
</td>
<td align="center">Reversing Voltage<break/>SCMLI</td>
<td align="left">&#x2022; Single voltage source<break/>&#x2022; Inherent capacitor balancing</td>
<td align="left">&#x2022; Simple and low switch utilization</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B38">Khan et al. (2022)</xref>
</td>
<td align="center">Reversing voltage SCMLI</td>
<td align="left">&#x2022; Switched capacitor MLI with inherent voltage balancing and soft start to eliminate initial inrush capacitor charging current<break/>&#x2022; High efficiency and very good power quality<break/>&#x2022; Single active voltage loss</td>
<td align="left">&#x2022; Two modes of control: pre-charge soft start and steady-state control increases control complexity</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B47">Meraj et al. (2021)</xref>
</td>
<td align="center">T-Type<break/>Hybrid</td>
<td align="left">&#x2022; Hybridized T-Type and cross-switched MLI.<break/>&#x2022; Asymmetric and symmetric configurations</td>
<td align="left">&#x2022; Many isolated active sources at different voltage levels<break/>&#x2022; High control complexity</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B22">Dhanamjayulu et al. (2022b)</xref>
</td>
<td align="center">Series-connected switched source</td>
<td align="left">&#x2022; Asymmetrical voltage sources to generate many voltage levels<break/>&#x2022; Fundamental frequency modulation</td>
<td align="left">&#x2022; Many isolated active voltage sources increase cost<break/>&#x2022; High complexity</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B55">Samadaei et al. (2019)</xref>
</td>
<td align="center">Polygon type<break/>MLI</td>
<td align="left">&#x2022; High switch utilization<break/>&#x2022; Inherent voltage balancing<break/>&#x2022; NLC modulation for reduced switching losses</td>
<td align="left">&#x2022; Isolated active power sources required</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B59">Srinivasan et al. (2021)</xref>
</td>
<td align="center">Switched-source<break/>MLI</td>
<td align="left">&#x2022; 81-level ladder MLI with reduced switch count<break/>&#x2022; Modular structure<break/>&#x2022; NLC modulation for reduced switching losses</td>
<td align="left">&#x2022; Isolated active voltage sources required</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B51">Radhakrishnan et al. (2024)</xref>
</td>
<td align="center">Hybrid H-6<break/>Switched-source<break/>MLI</td>
<td align="left">&#x2022; High switch utilization because of asymmetric configuration<break/>&#x2022; Asymmetric configuration of DC sources for an increased number of levels</td>
<td align="left">&#x2022; Isolated active sources required<break/>&#x2022; High complexity</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B20">Daula Siddique et al. (2022)</xref>
</td>
<td align="center">Active NPC (Improved)</td>
<td align="left">&#x2022; High gain for PV applications<break/>&#x2022; Inherent capacitor voltage balancing</td>
<td align="left">&#x2022; High voltage blocking switches required<break/>&#x2022; Low switch utilization</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B48">Mustafa et al. (2023)</xref>
</td>
<td align="center">Hybrid Reversing Voltage<break/>MLI</td>
<td align="left">&#x2022; High gain of 4<break/>&#x2022; Inherent capacitor voltage balancing</td>
<td align="left">&#x2022; Switches of different voltage ratings<break/>&#x2022; High switch count<break/>&#x2022; Low voltage applications</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B57">Shojaei et al. (2019)</xref>
</td>
<td align="center">PUC7 (Modified)</td>
<td align="left">&#x2022; Inherits high switch utilization from the traditional PUC topology<break/>&#x2022; Reversed voltage source to achieve voltage gain</td>
<td align="left">&#x2022; Isolated DC sources required</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Comparison of presented topologies based on component counts and switch utilization.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Ref.</th>
<th align="center">N<sub>L</sub>
</th>
<th align="center">N<sub>SW</sub>
</th>
<th align="center">N<sub>D</sub>
</th>
<th align="center">N<sub>C</sub>
</th>
<th align="center">N<sub>TR/IND</sub>
</th>
<th align="center">N<sub>DC</sub>
</th>
<th align="center">N<sub>L</sub>/N<sub>comp</sub>
</th>
<th align="center">Asymmetric</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">
<xref ref-type="bibr" rid="B62">Thakre et al. (2022)</xref>
</td>
<td align="center">11</td>
<td align="center">8</td>
<td align="center">4</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">5</td>
<td align="center">0.78</td>
<td align="center">yes</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B4">Ahmed et al. (2018)</xref>
</td>
<td align="center">7</td>
<td align="center">6</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">3</td>
<td align="center">1.16</td>
<td align="center">yes</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B29">Islam et al. (2023)</xref>
</td>
<td align="center">5</td>
<td align="center">7</td>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0.45</td>
<td align="center">no</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B33">Jena et al. (2023)</xref>
</td>
<td align="center">5</td>
<td align="center">5</td>
<td align="center">4</td>
<td align="center">2</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0.45</td>
<td align="center">no</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B30">Islam et al. (2020)</xref>
</td>
<td align="center">9</td>
<td align="center">13</td>
<td align="center">4</td>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">4</td>
<td align="center">0.4</td>
<td align="center">yes</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B27">Hatas et al. (2023)</xref>
</td>
<td align="center">17</td>
<td align="center">13</td>
<td align="center">5</td>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0.73</td>
<td align="center">yes</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B21">Deng et al. (2023)</xref>
</td>
<td align="center">13</td>
<td align="center">12</td>
<td align="center">2</td>
<td align="center">3</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0.76</td>
<td align="center">no</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B10">Bassi and Salam (2019)</xref>
</td>
<td align="center">13</td>
<td align="center">12</td>
<td align="center">5</td>
<td align="center">4</td>
<td align="center">0</td>
<td align="center">2</td>
<td align="center">0.62</td>
<td align="center">no</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B42">Kumari et al. (2023)</xref>
</td>
<td align="center">5</td>
<td align="center">6</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0.625</td>
<td align="center">no</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B38">Khan et al. (2022)</xref>
</td>
<td align="center">5</td>
<td align="center">7</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0.5</td>
<td align="center">no</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B47">Meraj et al. (2021)</xref>
</td>
<td align="center">11</td>
<td align="center">12</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">5</td>
<td align="center">0.92</td>
<td align="center">yes</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B22">Dhanamjayulu et al. (2022b)</xref>
</td>
<td align="center">35</td>
<td align="center">14</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">5</td>
<td align="center">2.5</td>
<td align="center">yes</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B55">Samadaei et al. (2019)</xref>
</td>
<td align="center">17</td>
<td align="center">18</td>
<td align="center">0</td>
<td align="center">2</td>
<td align="center">0</td>
<td align="center">2</td>
<td align="center">0.85</td>
<td align="center">yes</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B59">Srinivasan et al. (2021)</xref>
</td>
<td align="center">81</td>
<td align="center">12</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">8</td>
<td align="center">6.75</td>
<td align="center">yes</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B51">Radhakrishnan et al. (2024)</xref>
</td>
<td align="center">25</td>
<td align="center">13</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">4</td>
<td align="center">1.92</td>
<td align="center">yes</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B20">Daula Siddique et al. (2022)</xref>
</td>
<td align="center">11</td>
<td align="center">12</td>
<td align="center">0</td>
<td align="center">4</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0.68</td>
<td align="center">no</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B48">Mustafa et al. (2023)</xref>
</td>
<td align="center">9</td>
<td align="center">11</td>
<td align="center">1</td>
<td align="center">2</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0.64</td>
<td align="center">no</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B57">Shojaei et al. (2019)</xref>
</td>
<td align="center">7</td>
<td align="center">6</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">2</td>
<td align="center">1.16</td>
<td align="center">yes</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The focus of the review work was to identify opportunities for further development in multilevel inverter research. Insightful observations are made from the work presented in the paper.<list list-type="simple">
<list-item>
<p>&#x2043; Asymmetry is used extensively in the development of new reduced switch count topologies and its superiority is documented in the mentioned review article (<xref ref-type="bibr" rid="B66">Vinay Kumar and GowriManohar, 2023</xref>). Although it helps to generate more levels with a small number of switches as in the asymmetric CHB, and as evidenced from Table 20, the technique still retains the requirement for isolated active sources. The asymmetry in voltage sources is used in SC topologies such as (<xref ref-type="bibr" rid="B55">Samadaei et al., 2019</xref>) and others of the same type. It will be noticed that such topologies only use the additive operations possible for asymmetric topologies, to the exclusion of subtractive operations as in [56]. Including the subtraction of asymmetric voltage sources has the potential to generate more levels, especially in switched capacitor topologies, eliminating the need for isolated DC sources, and development in this direction can yield positive outcomes.</p>
</list-item>
<list-item>
<p>&#x2043; (<xref ref-type="bibr" rid="B38">Khan et al., 2022</xref>) incorporates soft charging for the single boost capacitor, resulting in reduced losses during capacitor charging. SC topologies with more than one capacitor level, such as in (<xref ref-type="bibr" rid="B21">Deng et al., 2023</xref>), do not employ any soft charging. Although the voltage ripples may be low by design, the more levels there are in the topology, the more losses we can expect from hard charging of these capacitors. The topologies can benefit from including soft charging for all switched capacitors involved. Development in this area can yield higher efficiency and elimination of deleterious high-inrush capacitor currents.</p>
</list-item>
<list-item>
<p>&#x2043; Resonant charging is widely adopted for SC converters (<xref ref-type="bibr" rid="B68">Zhu et al., 2021</xref>; <xref ref-type="bibr" rid="B69">Zhu et al., 2023</xref>), and this is possible because they have a fixed voltage transfer ratio and are usually operated with a fixed duty cycle. On the contrary, SC multilevel inverters have a sinusoidal variable instantaneous voltage transfer ratio (or variable duty cycle), and this makes achieving fully soft charging challenging. The frequent mismatch resulting from the change in duty cycle in HFPWM will equate to power loss during capacitor charging, as shown in Eq. <xref ref-type="disp-formula" rid="e1">1</xref>. NLC modulation is based on comparison of the reference signal to constant values, and the output waveform only switches to the next voltage level if the comparison yields above a midpoint threshold. Because the modulation is carried out at low frequency, the output voltage level is held for considerably longer time compared to HFPWM and presents an opportunity to explore resonant switched capacitor charging. If achieved, this can result in highly efficient SC multilevel inverters.</p>
</list-item>
</list>
<disp-formula id="e1">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mtext>loss</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>&#x394;</mml:mo>
<mml:msup>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:msub>
<mml:mi mathvariant="normal">f</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
<list list-type="simple">
<list-item>
<p>&#x2043; Many SC MLIs have the capacitors charged to multiples of the source voltage, translating to the use of larger capacitors as the gain and output power capacity of the inverter is increased. This results in the use of expensive capacitors. Charging the capacitors to a fraction of the source voltage will result in the use of smaller, low voltage and less costly capacitors. However, this will require voltage clamping or other voltage charge control mechanisms which can be costly. The benefits can be weighed against the cost, depending on the target application. In (45), it was demonstrated that power processing for an asymmetric configuration of {1:2:6} in the asymmetric CHB is 4.2% for the first source, 15.8% for the second source and 80% for the third voltage source. Effectively, the first two voltage sources are primarily for waveform quality improvement. If we assign the first two sources to be capacitors, then we can expect to use smaller and low voltage capacitors. Low power processing can lead to more efficient inverters. Furthermore, because the capacitor will not be isolated, it will be possible to retain modularity, which is lost in the asymmetric CHB.</p>
</list-item>
<list-item>
<p>&#x2043; An interesting research opportunity is to experiment the development of a PUC7 with inherent capacitor voltage balancing and voltage gain. Eliminating the requirement for auxiliary circuits or an additional voltage source. The combinations of a sensor-less self-balancing PUC5 in (66) and reversal of the second voltage source, the capacitor in this case, (<xref ref-type="bibr" rid="B57">Shojaei et al., 2019</xref>), could yield a PUC7 with a gain of 1.5. This however may require 2 additional cross switches in the middle cell. Other high level implementations of the PUC employ sophisticated model-predictive modulation method and sensors such as the hybrid PUC in (<xref ref-type="bibr" rid="B58">Sorto-Ventura et al., 2020</xref>) are unattractive for industrial use because of the high complexity.</p>
</list-item>
</list>
</p>
</sec>
<sec sec-type="conclusion" id="s6">
<title>6 Conclusion</title>
<p>The focus of this work was to review reduced switch count and hybridized improvement types and identify challenges and opportunities to conduct research and development to improve multilevel inverters. The merits and drawbacks of classical topologies have been reviewed and presented as the primary motivation for the advancement and development of new reduced switch count and hybrid multilevel inverters. It is observed that even in the recent topologies, there still exist some challenges and opportunities for further development of multilevel inverters. The use of asymmetry has been a crucial technique in reducing the number of switches, and topologies with the highest output level count to the number of switches are asymmetric. However, asymmetric topologies have increased cost and complexity as they require many isolated active voltage sources. Elimination of additional active sources prompts the use of switched capacitors that employ the full set of operations applicable to asymmetric MLIs, addition, and subtraction of voltage sources. This remains unexplored in SC topologies and has the potential to achieve a high switch utilization as it does in isolated voltage source topologies. The problem of high inrush currents in multi-capacitor SC inverters still needs to be resolved with the developmemt of new topologies involving many capacitors. Resonant charging of capacitors in multilevel converters remains a challenge because of the high-frequency variable voltage transfer ratio. Fundamental frequency-modulated topologies present an opportunity to explore the resonant charging of the switched capacitors. The authors intend to explore the opportunities presented in this review article for further research and development and hope it to be helpful to other researchers as well.</p>
</sec>
</body>
<back>
<sec id="s7">
<title>Author contributions</title>
<p>BM: Conceptualization, Investigation, Project administration, Resources, Visualization, Writing&#x2013;original draft, Writing&#x2013;review and editing. RS: Supervision, Writing&#x2013;review and editing. LA: Supervision, Writing&#x2013;review and editing.</p>
</sec>
<sec sec-type="funding-information" id="s8">
<title>Funding</title>
<p>The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article.</p>
</sec>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s10">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<ref-list>
<title>References</title>
<ref id="B1">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Abarzadeh</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Vahedi</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Al-Haddad</surname>
<given-names>K.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>Fast sensor-less voltage balancing and capacitor size reduction in PUC5 converter using novel modulation method</article-title>. <source>IEEE Trans. Industrial Inf.</source> <volume>15</volume>, <fpage>4394</fpage>&#x2013;<lpage>4406</lpage>. <pub-id pub-id-type="doi">10.1109/TII.2019.2893739</pub-id>
</citation>
</ref>
<ref id="B2">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Abd Halim</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Ganeson</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Azri</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Tengku Azam</surname>
<given-names>T. N. A.</given-names>
</name>
</person-group> (<year>2016</year>). <article-title>Review of multilevel inverter topologies and its applications</article-title>. <source>J. Telecommun. Electron. Comput. Eng. (JTEC)</source>. <comment>Available at: <ext-link ext-link-type="uri" xlink:href="https://jtec.utem.edu.my/jtec/article/view/1278">https://jtec.utem.edu.my/jtec/article/view/1278</ext-link>.</comment>
</citation>
</ref>
<ref id="B3">
<citation citation-type="web">
<person-group person-group-type="author">
<name>
<surname>Ahmad</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Khan</surname>
<given-names>J. A.</given-names>
</name>
<name>
<surname>Khan</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Izaz</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Hayat</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Ali</surname>
<given-names>L.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>Designing of different high efficiency diode clamped multilevel inverters and their performance analysis</article-title>. <comment>Available at: <ext-link ext-link-type="uri" xlink:href="https://core.ac.uk/download/234685392.pdf">https://core.ac.uk/download/234685392.pdf</ext-link> (Accessed February 1, 2024)</comment>.</citation>
</ref>
<ref id="B4">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ahmed</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Sheir</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Orabi</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Asymmetric cascaded half-bridge multilevel inverter without polarity changer</article-title>. <source>Alexandria Eng. J.</source> <volume>57</volume>, <fpage>2415</fpage>&#x2013;<lpage>2426</lpage>. <pub-id pub-id-type="doi">10.1016/j.aej.2017.08.018</pub-id>
</citation>
</ref>
<ref id="B5">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Ashok Kumar</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Albert Alexander</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Rajendran</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2021</year>). in <source>Power electronic converters for solar photovoltaic systems</source>. Editors <person-group person-group-type="editor">
<name>
<surname>Ashok Kumar</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Albert Alexander</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Rajendran</surname>
<given-names>M.</given-names>
</name>
</person-group> (<publisher-name>Academic Press</publisher-name>) <fpage>xvii</fpage>&#x2013;<lpage>xviii</lpage>. <pub-id pub-id-type="doi">10.1016/B978-0-12-822730-5.02001-8</pub-id>
</citation>
</ref>
<ref id="B6">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Atar</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Balci</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Kayabasi</surname>
<given-names>A.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>Determination of output current THD of multilevel inverter by ANN</article-title>. <source>Measurement</source> <volume>210</volume>, <fpage>112525</fpage>. <pub-id pub-id-type="doi">10.1016/j.measurement.2023.112525</pub-id>
</citation>
</ref>
<ref id="B7">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Barnawi</surname>
<given-names>A. B.</given-names>
</name>
<name>
<surname>Alfifi</surname>
<given-names>A. R. A.</given-names>
</name>
<name>
<surname>Elbarbary</surname>
<given-names>Z. M. S.</given-names>
</name>
<name>
<surname>Alqahtani</surname>
<given-names>S. F.</given-names>
</name>
<name>
<surname>Shaik</surname>
<given-names>I. M.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>Review of multilevel inverter for high-power applications</article-title>. <source>Front. Eng. Built Environ.</source> <volume>4</volume>, <fpage>77</fpage>&#x2013;<lpage>89</lpage>. <pub-id pub-id-type="doi">10.1108/FEBE-05-2023-0020</pub-id>
</citation>
</ref>
<ref id="B8">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Barros</surname>
<given-names>L. A. M.</given-names>
</name>
<name>
<surname>Martins</surname>
<given-names>A. P.</given-names>
</name>
<name>
<surname>Pinto</surname>
<given-names>J. G.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>A comprehensive review on modular multilevel converters, submodule topologies, and modulation techniques</article-title>. <source>Energies</source> <volume>15</volume>, <fpage>1078</fpage>. <pub-id pub-id-type="doi">10.3390/en15031078</pub-id>
</citation>
</ref>
<ref id="B9">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Barzegarkhoo</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Vosoughi</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Zamiri</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>Kojabadi</surname>
<given-names>H. M.</given-names>
</name>
<name>
<surname>Chang</surname>
<given-names>L.</given-names>
</name>
</person-group> (<year>2016</year>). <article-title>A cascaded modular multilevel inverter topology using novel series basic units with a reduced number of power electronic elements</article-title>. <source>J. Power Electron.</source> <volume>16</volume>, <fpage>2139</fpage>&#x2013;<lpage>2149</lpage>. <pub-id pub-id-type="doi">10.6113/JPE.2016.16.6.2139</pub-id>
</citation>
</ref>
<ref id="B10">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Bassi</surname>
<given-names>H. M.</given-names>
</name>
<name>
<surname>Salam</surname>
<given-names>Z.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>A new hybrid multilevel inverter topology with reduced switch count and dc voltage sources</article-title>. <source>Energies, MDPI</source> <volume>12</volume>, <fpage>977</fpage>. <pub-id pub-id-type="doi">10.3390/en12060977</pub-id>
</citation>
</ref>
<ref id="B11">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Bhaskar</surname>
<given-names>M. S.</given-names>
</name>
<name>
<surname>Meraj</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Iqbal</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Ben-Brahim</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Padmanaban</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Abu-Rub</surname>
<given-names>H.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>E<sup>K</sup>&#x3b8; multilevel inverter - a minimal switch novel configuration for higher number of output voltage levels</article-title>. <source>IET Power Electron.</source> <volume>13</volume>, <fpage>2804</fpage>&#x2013;<lpage>2815</lpage>. <pub-id pub-id-type="doi">10.1049/iet-pel.2019.0945</pub-id>
</citation>
</ref>
<ref id="B12">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Bressan</surname>
<given-names>M. V.</given-names>
</name>
<name>
<surname>Rech</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Batschauer</surname>
<given-names>A. L.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>Design of flying capacitors for n-level FC and n-level SMC</article-title>. <source>Int. J. Electr. Power Energy Syst.</source> <volume>113</volume>, <fpage>220</fpage>&#x2013;<lpage>228</lpage>. <pub-id pub-id-type="doi">10.1016/j.ijepes.2019.05.030</pub-id>
</citation>
</ref>
<ref id="B13">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Bughneda</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Salem</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Richelli</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Ishak</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Alatai</surname>
<given-names>S.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Review of multilevel inverters for PV energy system applications</article-title>. <source>Energies</source> <volume>14</volume>, <fpage>1585</fpage>. <pub-id pub-id-type="doi">10.3390/en14061585</pub-id>
</citation>
</ref>
<ref id="B14">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Busarello</surname>
<given-names>T. D. C.</given-names>
</name>
<name>
<surname>De Sousa Marcondes Reuter</surname>
<given-names>A. L.</given-names>
</name>
<name>
<surname>P&#xe9;res</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Godoy Sim&#xf5;es</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Understanding the staircase modulation strategy and its application in asymmetric cascaded H-bridge multilevel inverter</article-title>. <source>IEEE Ind. Appl. Soc. Annu. Meet.</source> <pub-id pub-id-type="doi">10.1109/IAS.2018.8544721</pub-id>
</citation>
</ref>
<ref id="B15">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Busarello</surname>
<given-names>T. D. C.</given-names>
</name>
<name>
<surname>De Sousa Marcondes Reuter</surname>
<given-names>A. L.</given-names>
</name>
<name>
<surname>Peres</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Simoes</surname>
<given-names>M. G.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>Understanding the staircase modulation strategy and its application in both isolated and grid-connected asymmetric cascaded H-bridge multilevel inverters</article-title>. <source>IEEE Trans. Industry Appl.</source> <volume>55</volume>, <fpage>5371</fpage>&#x2013;<lpage>5382</lpage>. <pub-id pub-id-type="doi">10.1109/TIA.2019.2927189</pub-id>
</citation>
</ref>
<ref id="B16">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Chang-xin</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Li-ping</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Tai-xu</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Cheng-bao</surname>
<given-names>C.</given-names>
</name>
</person-group> (<year>2009</year>). <article-title>Flying capacitor multilevel inverters with novel PWM method</article-title>. <source>Procedia Earth Planet. Sci.</source> <volume>1</volume>, <fpage>1554</fpage>&#x2013;<lpage>1560</lpage>. <pub-id pub-id-type="doi">10.1016/j.proeps.2009.09.240</pub-id>
</citation>
</ref>
<ref id="B17">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Cherkaoui Jaouad</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Chaikhy</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Belhora</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Hajjaji</surname>
<given-names>A.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>Comparison between two levels and multi-level (NPC and Cascad) inverters</article-title>. <source>Mater. Today; Proc.</source> <volume>66</volume>, <fpage>162</fpage>&#x2013;<lpage>180</lpage>. <pub-id pub-id-type="doi">10.1016/j.matpr.2022.04.338</pub-id>
</citation>
</ref>
<ref id="B18">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Chitra</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Valluvan</surname>
<given-names>K. R.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Design and implementation of cascaded H-Bridge multilevel inverter using FPGA with multiple carrier phase disposition modulation scheme</article-title>. <source>Microprocess. Microsystems</source> <volume>76</volume>, <fpage>103108</fpage>. <pub-id pub-id-type="doi">10.1016/j.micpro.2020.103108</pub-id>
</citation>
</ref>
<ref id="B19">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Choudhury</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Bajaj</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Dash</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Kamel</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Jurado</surname>
<given-names>F.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Multilevel inverter: a survey on classical and advanced topologies, control schemes, applications to power system and future prospects</article-title>. <source>Energies</source> <volume>14</volume>, <fpage>5773</fpage>. <pub-id pub-id-type="doi">10.3390/en14185773</pub-id>
</citation>
</ref>
<ref id="B20">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Daula Siddique</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Prathap Reddy</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Iqbal</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Sarwar</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Ahmed Memon</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Dahri</surname>
<given-names>K.</given-names>
</name>
<etal/>
</person-group> (<year>2022</year>). <article-title>A new design of active NPC converter topology with higher voltage gain for solar PV applications</article-title>. <source>Sustain. Energy Technol. Assessments</source> <volume>54</volume>, <fpage>102850</fpage>. <pub-id pub-id-type="doi">10.1016/j.seta.2022.102850</pub-id>
</citation>
</ref>
<ref id="B21">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Deng</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Duan</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Ye</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>A multilevel switched capacitor inverter with reduced components and self-balance</article-title>. <source>Appl. Sci. MPDI</source> <volume>13</volume>, <fpage>8955</fpage>. <pub-id pub-id-type="doi">10.3390/app13158955</pub-id>
</citation>
</ref>
<ref id="B22">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Dhanamjayulu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Rudravaram</surname>
<given-names>V.</given-names>
</name>
<name>
<surname>Sanjeevikumar</surname>
<given-names>P.</given-names>
</name>
</person-group> (<year>2022b</year>). <article-title>Design and implementation of a novel 35-level inverter topology with reduced switch count</article-title>. <source>Electr. Power Syst. Res.</source> <volume>212</volume>, <fpage>108641</fpage>. <pub-id pub-id-type="doi">10.1016/j.epsr.2022.108641</pub-id>
</citation>
</ref>
<ref id="B23">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Dhanamjayulu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Sanjeevikumar</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Muyeen</surname>
<given-names>S. M.</given-names>
</name>
</person-group> (<year>2022a</year>). <article-title>A structural overview on transformer and transformer-less multi level inverters for renewable energy applications</article-title>. <source>Energy Rep.</source> <volume>8</volume>, <fpage>10299</fpage>&#x2013;<lpage>10333</lpage>. <pub-id pub-id-type="doi">10.1016/j.egyr.2022.07.166</pub-id>
</citation>
</ref>
<ref id="B24">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Es-Saadi</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Khafallah</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Chaikhy</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Brik</surname>
<given-names>A. A.</given-names>
</name>
<name>
<surname>Khoukh</surname>
<given-names>A.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Using the five-level NPC inverter to improve the FOC control of the asynchronous machine</article-title>. <source>IEEE Xplore</source>. <pub-id pub-id-type="doi">10.1109/IRSEC.2017.8477356</pub-id>
</citation>
</ref>
<ref id="B25">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ghani</surname>
<given-names>A. A.</given-names>
</name>
<name>
<surname>Ahmed</surname>
<given-names>Q. S.</given-names>
</name>
<name>
<surname>Ihsan</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>S.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>Design of three-level NPC AC/DC bidirectional converter using model predictive controller for DC bus voltage stability of subway</article-title>. <source>Eng. Proc.</source> <volume>46</volume>(<issue>1</issue>), <fpage>37</fpage>. <pub-id pub-id-type="doi">10.3390/engproc2023046037</pub-id>
</citation>
</ref>
<ref id="B26">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Harin</surname>
<given-names>M. M.</given-names>
</name>
<name>
<surname>Vanitha</surname>
<given-names>V.</given-names>
</name>
<name>
<surname>Jayakumar</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>Comparison of PWM techniques for a three level modular multilevel inverter</article-title>. <source>Energy Procedia</source> <volume>117</volume>, <fpage>666</fpage>&#x2013;<lpage>673</lpage>. <pub-id pub-id-type="doi">10.1016/j.egypro.2017.05.180</pub-id>
</citation>
</ref>
<ref id="B27">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hatas</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Almali</surname>
<given-names>M. N.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>Design and control of a novel topology for multilevel inverters using high frequency link</article-title>. <source>Electr. Power Syst. Res. Elsevier</source> <volume>221</volume>, <fpage>109458</fpage>. <pub-id pub-id-type="doi">10.1016/j.epsr.2023.109458</pub-id>
</citation>
</ref>
<ref id="B28">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Humayun</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Khan</surname>
<given-names>M. M.</given-names>
</name>
<name>
<surname>Muhammad</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>W.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Evaluation of symmetric flying capacitor multilevel inverter for grid-connected application</article-title>. <source>Int. J. Electr. Power Energy Syst.</source> <volume>115</volume>, <fpage>105430</fpage>. <pub-id pub-id-type="doi">10.1016/j.ijepes.2019.105430</pub-id>
</citation>
</ref>
<ref id="B29">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Islam</surname>
<given-names>M. T.</given-names>
</name>
<name>
<surname>Alam</surname>
<given-names>M. A.</given-names>
</name>
<name>
<surname>Lipu</surname>
<given-names>M. S. H.</given-names>
</name>
<name>
<surname>Hasan</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Meraj</surname>
<given-names>S. T.</given-names>
</name>
<name>
<surname>Masrur</surname>
<given-names>H.</given-names>
</name>
<etal/>
</person-group> (<year>2023</year>). <article-title>A single DC source five-level switched capacitor inverter for grid-integrated solar photovoltaic system: modeling and performance investigation</article-title>. <source>Sustainability</source> <volume>15</volume>, <fpage>8405</fpage>. <pub-id pub-id-type="doi">10.3390/su15108405</pub-id>
</citation>
</ref>
<ref id="B30">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Islam</surname>
<given-names>M. T.</given-names>
</name>
<name>
<surname>Islam</surname>
<given-names>M. R.</given-names>
</name>
<name>
<surname>Muttaqi</surname>
<given-names>K. M.</given-names>
</name>
</person-group> (<year>2020</year>). <source>A novel high frequency magnetic linked reduced switch multilevel inverter for solar photovoltaic systems</source>. <publisher-loc>Hobart, Australia</publisher-loc>: <publisher-name>Australasian Universities Power Engineering Conference AUPEC</publisher-name>. <comment>Available at: <ext-link ext-link-type="uri" xlink:href="https://ieeexplore.ieee.org/document/9344497">https://ieeexplore.ieee.org/document/9344497</ext-link> (Accessed February 11, 2024)</comment>.</citation>
</ref>
<ref id="B31">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Jana</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Saha</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Das Bhattacharya</surname>
<given-names>K.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>A review of inverter topologies for single-phase grid-connected photovoltaic systems</article-title>. <source>Renew. Sustain. Energy Rev. Elsevier</source> <volume>72</volume>, <fpage>1256</fpage>&#x2013;<lpage>1270</lpage>. <pub-id pub-id-type="doi">10.1016/j.rser.2016.10.049</pub-id>
</citation>
</ref>
<ref id="B32">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Jayakumar</surname>
<given-names>V.</given-names>
</name>
<name>
<surname>Chokkalingam</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Lange Munda</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>A comprehensive review on space vector modulation techniques for neutral point clamped multi-level inverters</article-title>. <source>IEEE Access</source> <volume>9</volume>, <fpage>112104</fpage>&#x2013;<lpage>112144</lpage>. <pub-id pub-id-type="doi">10.1109/ACCESS.2021.3100346</pub-id>
</citation>
</ref>
<ref id="B33">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Jena</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Kumar</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Hemanth Kumar</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Janardhan</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Singh</surname>
<given-names>A. R.</given-names>
</name>
<name>
<surname>Naidoo</surname>
<given-names>R.</given-names>
</name>
<etal/>
</person-group> (<year>2023</year>). <article-title>A single DC source generalized switched capacitors multilevel inverter with minimal component count</article-title>. <source>Compon. Count</source> <volume>2023</volume>, <fpage>1</fpage>&#x2013;<lpage>12</lpage>. <pub-id pub-id-type="doi">10.1155/2023/3945160</pub-id>
</citation>
</ref>
<ref id="B34">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Jiang</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Gao</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>L.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>A hybrid modulation strategy with reduced switching losses and neutral point potential balance for three-level NPC inverter</article-title>. <source>J. Electr. Eng. Technoly, Korea Sci.</source> <volume>12</volume>, <fpage>738</fpage>&#x2013;<lpage>750</lpage>. <pub-id pub-id-type="doi">10.5370/JEET.2017.12.2.738</pub-id>
</citation>
</ref>
<ref id="B35">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Kabalc&#x131;</surname>
<given-names>E.</given-names>
</name>
</person-group> (<year>2021</year>). <source>Multilevel inverters: introduction and emergent topologies</source>. <publisher-name>Academic Press</publisher-name>, <fpage>2</fpage>&#x2013;<lpage>28</lpage>.</citation>
</ref>
<ref id="B36">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kala</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Arora</surname>
<given-names>S.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>A comprehensive study of classical and hybrid multilevel inverter topologies for renewable energy applications</article-title>. <source>Renew. Sustain. Energy Rev.</source> <volume>76</volume>, <fpage>905</fpage>&#x2013;<lpage>931</lpage>. <pub-id pub-id-type="doi">10.1016/j.rser.2017.02.008</pub-id>
</citation>
</ref>
<ref id="B37">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kannan</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Mohanty</surname>
<given-names>N. K.</given-names>
</name>
<name>
<surname>Selvarasu</surname>
<given-names>R.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>A new topology for cascaded H-bridge multilevel inverter with PI and Fuzzy control</article-title>. <source>Energy Procedia</source> <volume>117</volume>, <fpage>917</fpage>&#x2013;<lpage>926</lpage>. <pub-id pub-id-type="doi">10.1016/j.egypro.2017.05.211</pub-id>
</citation>
</ref>
<ref id="B38">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Khan</surname>
<given-names>M. N. H.</given-names>
</name>
<name>
<surname>Barzegarkhoo</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Siwakoti</surname>
<given-names>Y. P.</given-names>
</name>
<name>
<surname>Khan</surname>
<given-names>S. A.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Blaabjerg</surname>
<given-names>F.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>A new switched-capacitor multilevel inverter with soft start and quasi resonant charging capabilities</article-title>. <source>Int. J. Electr. Power and Energy Syst.</source> <volume>135</volume>, <fpage>107412</fpage>. <pub-id pub-id-type="doi">10.1016/j.ijepes.2021.107412</pub-id>
</citation>
</ref>
<ref id="B39">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kieferndorf</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Basler</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Fabian</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Coccia</surname>
<given-names>A.</given-names>
</name>
</person-group> (<year>2000</year>). <article-title>The five-level converter</article-title>. <source>ABB</source>. <comment>Available at: <ext-link ext-link-type="uri" xlink:href="https://library.e.abb.com/public/8c65d75ced8b80d6c1257988005b5c69/41-46%201m127_ENG_72dpi.pdf">https://library.e.abb.com/public/8c65d75ced8b80d6c1257988005b5c69/41-46%201m127_ENG_72dpi.pdf</ext-link> (Accessed February 1, 2024)</comment>.</citation>
</ref>
<ref id="B40">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kumar</surname>
<given-names>K. B.</given-names>
</name>
<name>
<surname>Bhanuchandar</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Vamshy</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Gurunath</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Mohandas</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Palle</surname>
<given-names>K.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>A nearest level control technique for an asymmetric source configuration of multi-level inverter topology</article-title>. <source>Int. J. Eng. Sci. Technoly</source> <volume>14</volume>, <fpage>1</fpage>&#x2013;<lpage>9</lpage>. <pub-id pub-id-type="doi">10.4314/ijest.v14i3.1S</pub-id>
</citation>
</ref>
<ref id="B41">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Kumar Gupta</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Bhatnagar</surname>
<given-names>P.</given-names>
</name>
</person-group> (<year>2018</year>). <source>Multilevel inverters-conventional and emerging topologies and their control</source>. <publisher-name>Academic Press</publisher-name>.</citation>
</ref>
<ref id="B42">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kumari</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Gopal</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Kumar Dhaked</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Panda</surname>
<given-names>K. P.</given-names>
</name>
<name>
<surname>Vijaya Kumar</surname>
<given-names>Y. N.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>A single source five-level switched-capacitor based multilevel inverter with reduced device count</article-title>. <source>e-Prime-Advances Electr. Eng. Electron. Energy, Elsevier</source> <volume>5</volume>, <fpage>100235</fpage>. <pub-id pub-id-type="doi">10.1016/j.prime.2023.100235</pub-id>
</citation>
</ref>
<ref id="B43">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Laamiri</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Ghanes</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Amet</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Santomenna</surname>
<given-names>G.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>Direct control strategy for a three phase eight-level flying-capacitor inverter</article-title>. <source>IFAC-PapersOnLine</source> <volume>50</volume>, <fpage>15786</fpage>&#x2013;<lpage>15791</lpage>. <pub-id pub-id-type="doi">10.1016/j.ifacol.2017.08.2315</pub-id>
</citation>
</ref>
<ref id="B44">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Lewicki</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Odeh</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Morawiec</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>Space vector pulsewidth modulation strategy for multilevel cascaded H-bridge inverter with DC-link voltage balancing ability</article-title>. <source>IEEE Trans. Industrial Electron.</source> <volume>70</volume>, <fpage>1161</fpage>&#x2013;<lpage>1170</lpage>. <pub-id pub-id-type="doi">10.1109/TIE.2022.3158005</pub-id>
</citation>
</ref>
<ref id="B45">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Mayorga</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Roncero-Clemente</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Llor</surname>
<given-names>A. M.</given-names>
</name>
<name>
<surname>Husev</surname>
<given-names>O.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>A simple space vector modulation method with DC-link voltage balancing and reduced common-mode voltage strategy for a three-level T-type quasi-Z source inverter</article-title>. <source>IEEE Access</source> <volume>9</volume>, <fpage>82747</fpage>&#x2013;<lpage>82760</lpage>. <pub-id pub-id-type="doi">10.1109/ACCESS.2021.3087035</pub-id>
</citation>
</ref>
<ref id="B46">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Mehta</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Puri</surname>
<given-names>V.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>A review of different multi-level inverter topologies for grid integration of solar photovoltaic system</article-title>. <source>Renew. Energy Focus</source> <volume>43</volume>, <fpage>263</fpage>&#x2013;<lpage>276</lpage>. <pub-id pub-id-type="doi">10.1016/j.ref.2022.10.002</pub-id>
</citation>
</ref>
<ref id="B47">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Meraj</surname>
<given-names>S. T.</given-names>
</name>
<name>
<surname>Yahaya</surname>
<given-names>N. Z.</given-names>
</name>
<name>
<surname>Hasan</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Masaoud</surname>
<given-names>A.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>A hybrid T-type (HT-type) multilevel inverter with reduced components</article-title>. <source>Ain Shams Eng. J.</source> <volume>12</volume>, <fpage>1959</fpage>&#x2013;<lpage>1971</lpage>. <pub-id pub-id-type="doi">10.1016/j.asej.2020.12.010</pub-id>
</citation>
</ref>
<ref id="B48">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Mustafa</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Sarwar</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Tariq</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Ahmad</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Mahmoud</surname>
<given-names>H. A.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>Development and control of a switched capacitor multilevel inverter</article-title>. <source>Energies</source> <volume>16</volume>, <fpage>4269</fpage>. <pub-id pub-id-type="doi">10.3390/en16114269</pub-id>
</citation>
</ref>
<ref id="B49">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Odeh</surname>
<given-names>C. I.</given-names>
</name>
<name>
<surname>Lewicki</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Morawiec</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2021</year>). &#x201c;<article-title>A single-carrier-based pulse-width modulation template for cascaded H-bridge multilevel inverters</article-title>,&#x201d; in <source>IEEE access</source>. <pub-id pub-id-type="doi">10.1109/ACCESS.2021.3065743</pub-id>
</citation>
</ref>
<ref id="B50">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Oghorada</surname>
<given-names>O. J. K.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Esan</surname>
<given-names>B. A.</given-names>
</name>
<name>
<surname>Dickson</surname>
<given-names>E.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>Carrier-based sinusoidal pulse-width modulation techniques for flying capacitor modular multi-level cascaded converter</article-title>. <source>Heliyon</source> <volume>5</volume>, <fpage>e03022</fpage>. <pub-id pub-id-type="doi">10.1016/j.heliyon.2019.e03022</pub-id>
</citation>
</ref>
<ref id="B51">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Radhakrishnan</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Arasan</surname>
<given-names>E. S.</given-names>
</name>
<name>
<surname>Ramalingam</surname>
<given-names>B. C.</given-names>
</name>
<name>
<surname>Chandrasekaran</surname>
<given-names>K.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>A new asymmetric H-6 structured multilevel inverter with reduced power components</article-title>. <source>Symmetry</source> <volume>16</volume>, <fpage>72</fpage>. <pub-id pub-id-type="doi">10.3390/sym16010072</pub-id>
</citation>
</ref>
<ref id="B52">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ramu</surname>
<given-names>V.</given-names>
</name>
<name>
<surname>Satish Kumar</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Srinivas</surname>
<given-names>G. N.</given-names>
</name>
<name>
<surname>Lspwm</surname>
<given-names>PSPWM</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>LSPWM, PSPWM and NLCPWM on multilevel inverters with reduced number of switches</article-title>. <source>Mater. Today Proc.</source> <volume>54</volume>, <fpage>710</fpage>&#x2013;<lpage>727</lpage>. <comment>Available from</comment>. <pub-id pub-id-type="doi">10.1016/j.matpr.2021.10.410</pub-id>
</citation>
</ref>
<ref id="B53">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Rodriguez</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Franquelo</surname>
<given-names>L. G.</given-names>
</name>
<name>
<surname>Kouro</surname>
<given-names>S. L.</given-names>
</name>
<name>
<surname>Jos&#xc9;</surname>
<given-names>I. P.</given-names>
</name>
<name>
<surname>Prats</surname>
<given-names>R. C.</given-names>
</name>
<name>
<surname>Perez</surname>
<given-names>M. M.</given-names>
</name>
<etal/>
</person-group> (<year>2009</year>). &#x201c;<article-title>Multilevel converters: an enabling technology for high-power applications</article-title>,&#x201d; in <source>Proceedings of the IEEE</source>, <fpage>1786</fpage>&#x2013;<lpage>1817</lpage>. <pub-id pub-id-type="doi">10.1109/JPROC.2009.2030235</pub-id>
</citation>
</ref>
<ref id="B54">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Rotella</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Pe&#xf1;ailillo</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Pereda</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Dixon</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2006</year>). <source>PWM method to eliminate power sources in a nonredundant 27-level inverter for machine drive applications</source>. <publisher-loc>Montreal</publisher-loc>: <publisher-name>IEEE International Symposium on Industrial Electronics</publisher-name>. <pub-id pub-id-type="doi">10.1109/ISIE.2006.295789</pub-id>
</citation>
</ref>
<ref id="B55">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Samadaei</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>Kaviani</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Iranian</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Pouresmaeil</surname>
<given-names>E.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>The P-type module with virtual dc links to increase levels in multilevel inverters</article-title>. <source>Electronics</source> <volume>8</volume>, <fpage>1460</fpage>. <comment>Available from</comment>. <pub-id pub-id-type="doi">10.3390/electronics8121460</pub-id>
</citation>
</ref>
<ref id="B56">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Sedaghati</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Horrillo-Quintero</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>S&#xe1;nchez-S&#xe1;inz</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Fern&#xe1;ndez-Ram&#xed;rez</surname>
<given-names>L. M.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>Staircase modulation improvement to balance output power of stages of cascade H-bridge multilevel inverter</article-title>. <source>Comput. Electr. Eng.</source> <volume>103</volume>, <fpage>108331</fpage>. <comment>Available from</comment>. <pub-id pub-id-type="doi">10.1016/j.compeleceng.2022.108331</pub-id>
</citation>
</ref>
<ref id="B57">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shojaei</surname>
<given-names>A. A.</given-names>
</name>
<name>
<surname>Najafi</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Vahedi</surname>
<given-names>H.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>Standalone operation of modified seven-level packed U-cell (MPUC) single-phase inverter</article-title>. <source>Electronics</source> <volume>8</volume>, <fpage>268</fpage>. <pub-id pub-id-type="doi">10.3390/electronics8030268</pub-id>
</citation>
</ref>
<ref id="B58">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Sorto-Ventura</surname>
<given-names>K. R.</given-names>
</name>
<name>
<surname>Abarzadeh</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Al-Haddad</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Dessaint</surname>
<given-names>L. A.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>23-level single DC source hybrid PUC (H-PUC) converter topology with reduced number of components: real-time implementation with model predictive control</article-title>. <source>IEEE Open J. Industrial Electron. Soc.</source> <volume>1</volume>, <fpage>127</fpage>&#x2013;<lpage>137</lpage>. <comment>Available from</comment>. <pub-id pub-id-type="doi">10.1109/OJIES.2020.3007989</pub-id>
</citation>
</ref>
<ref id="B59">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Srinivasan</surname>
<given-names>G. K.</given-names>
</name>
<name>
<surname>Rivera</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Loganathan</surname>
<given-names>V.</given-names>
</name>
<name>
<surname>Ravikumar</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Mohan</surname>
<given-names>B.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Trends and challenges in multi-level inverter with reduced switches</article-title>. <source>Electronics</source> <volume>10</volume>, <fpage>368</fpage>. <comment>Available from</comment>. <pub-id pub-id-type="doi">10.3390/electronics10040368</pub-id>
</citation>
</ref>
<ref id="B60">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>St&#xf6;ttner</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Hanzl</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Endisch</surname>
<given-names>C.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>Extensive investigation of symmetrical and asymmetrical cascaded multilevel inverters for electric vehicle applications</article-title>. <source>Electr. Power Syst. Res.</source> <volume>209</volume>, <fpage>108009</fpage>. <comment>Available from</comment>. <pub-id pub-id-type="doi">10.1016/j.epsr.2022.108009</pub-id>
</citation>
</ref>
<ref id="B61">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Tamilvani</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Valluvan</surname>
<given-names>K. R.</given-names>
</name>
</person-group> (<year>2012</year>). <article-title>Hybrid modulation technique for cascaded multilevel inverter for high power and high quality applications in</article-title>. <source>Renew. Energy Syst.</source> <comment>Available at: <ext-link ext-link-type="uri" xlink:href="http://www.irphouse.com/ijeee/ijeev5n1_6.pdf">http://www.irphouse.com/ijeee/ijeev5n1_6.pdf</ext-link> (Accessed February 11, 2024)</comment>.</citation>
</ref>
<ref id="B62">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Thakre</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Mohanty</surname>
<given-names>K. B.</given-names>
</name>
<name>
<surname>Kommukuri</surname>
<given-names>V. S.</given-names>
</name>
<name>
<surname>Chatterjee</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Nigam</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Gupta</surname>
<given-names>S. K.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>Modified cascaded multilevel inverter for renewable energy systems with less number of unidirectional switches</article-title>. <source>Energy Rep. Elsevier</source> <volume>8</volume>, <fpage>5296</fpage>&#x2013;<lpage>5304</lpage>. <comment>Available from</comment>. <pub-id pub-id-type="doi">10.1016/j.egyr.2022.03.167</pub-id>
</citation>
</ref>
<ref id="B63">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ullah</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Haidar</surname>
<given-names>A. M. A.</given-names>
</name>
<name>
<surname>Hoole</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Zen</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Ahfock</surname>
<given-names>T.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>The current state of Distributed Renewable Generation, challenges of interconnection and opportunities for energy conversion based DC microgrids</article-title>. <source>J. Clean. Prod.</source> <volume>273</volume>, <fpage>122777</fpage>. <pub-id pub-id-type="doi">10.1016/j.jclepro.2020.122777</pub-id>
</citation>
</ref>
<ref id="B64">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Vakacharla</surname>
<given-names>V. R.</given-names>
</name>
<name>
<surname>Gnana</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Xuewei</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Narasimaharaju</surname>
<given-names>B. L.</given-names>
</name>
<name>
<surname>Bhukya</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Banerjee</surname>
<given-names>A.</given-names>
</name>
<etal/>
</person-group> (<year>2020</year>). <article-title>State-of-the-art power electronics systems for solar-to-grid integration</article-title>. <source>Sol. Energy</source> <volume>210</volume>, <fpage>128</fpage>&#x2013;<lpage>148</lpage>. <comment>Available from</comment>. <pub-id pub-id-type="doi">10.1016/j.solener.2020.06.105</pub-id>
</citation>
</ref>
<ref id="B65">
<citation citation-type="web">
<person-group person-group-type="author">
<name>
<surname>Vincotech</surname>
<given-names>F.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>Capacitor inverter the advantages and operation of flying capacitor inverter</article-title>. <comment>Available at: <ext-link ext-link-type="uri" xlink:href="https://www.vincotech.com/fileadmin/user_upload/content_media/documents/pdf/support-documents/technical-papers/Vincotech_TP_Solar_The_Advantages_and_Operation_of_Flying_Capacitor_Inverter_2020.pdf">https://www.vincotech.com/fileadmin/user_upload/content_media/documents/pdf/support-documents/technical-papers/Vincotech_TP_Solar_The_Advantages_and_Operation_of_Flying_Capacitor_Inverter_2020.pdf</ext-link> (Accessed February 11, 2024)</comment>.</citation>
</ref>
<ref id="B66">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Vinay Kumar</surname>
<given-names>N. V.</given-names>
</name>
<name>
<surname>GowriManohar</surname>
<given-names>T.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>A comprehensive survey on reduced switch count multilevel inverter topologies and modulation techniques</article-title>. <source>J. Electr. Syst. Inf.</source> <volume>10</volume>, <fpage>3</fpage>. <comment>Available from</comment>. <pub-id pub-id-type="doi">10.1186/s43067-023-00071-8</pub-id>
</citation>
</ref>
<ref id="B67">
<citation citation-type="web">
<collab>Wikipedia</collab> (<year>2024</year>). <article-title>Total harmonic distortion</article-title>. <comment>Available at: <ext-link ext-link-type="uri" xlink:href="https://en.wikipedia.org/wiki/Total_harmonic_distortion">https://en.wikipedia.org/wiki/Total_harmonic_distortion</ext-link> (Accessed April 4, 2024)</comment>.</citation>
</ref>
<ref id="B68">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Zhu</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Ye</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Pilawa-Podgurski</surname>
<given-names>R. C. N.</given-names>
</name>
</person-group> (<year>2021</year>). &#x201c;<article-title>Modeling and analysis of resonant switched-capacitor converters with finite terminal capacitances</article-title>,&#x201d; in <source>2021 IEEE 22nd workshop on control and modelling of power electronics (COMPEL)</source>, <comment>Available from</comment>. <pub-id pub-id-type="doi">10.1109/COMPEL52922.2021.9646020</pub-id>
</citation>
</ref>
<ref id="B69">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhu</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Ye</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Pilawa-Podgurski</surname>
<given-names>R. C. N.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>Modeling and analysis of switched-capacitor converters with finite terminal capacitances</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>39</volume>, <fpage>6640</fpage>&#x2013;<lpage>6653</lpage>. <pub-id pub-id-type="doi">10.1109/TPEL.2023.3313562</pub-id>
</citation>
</ref>
</ref-list>
</back>
</article>