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<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">1400651</article-id>
<article-id pub-id-type="doi">10.3389/fenrg.2024.1400651</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Energy Research</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Cost-effective high-gain DC-DC converter for elevator drives using photovoltaic power and switched reluctance motors</article-title>
<alt-title alt-title-type="left-running-head">Baskaran 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.2024.1400651">10.3389/fenrg.2024.1400651</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Baskaran</surname>
<given-names>J.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
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<contrib contrib-type="author">
<name>
<surname>Naghapushanam</surname>
<given-names>Manimaran</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
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<contrib contrib-type="author">
<name>
<surname>Ganapathy</surname>
<given-names>Mahalakshmi</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
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<contrib contrib-type="author">
<name>
<surname>Meena</surname>
<given-names>P.</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
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<contrib contrib-type="author">
<name>
<surname>Meena</surname>
<given-names>V. P.</given-names>
</name>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
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<contrib contrib-type="author" corresp="yes">
<name>
<surname>Azar</surname>
<given-names>Ahmad Taher</given-names>
</name>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
</xref>
<xref ref-type="aff" rid="aff7">
<sup>7</sup>
</xref>
<xref ref-type="aff" rid="aff8">
<sup>8</sup>
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<contrib contrib-type="author" corresp="yes">
<name>
<surname>Hameed</surname>
<given-names>Ibrahim A.</given-names>
</name>
<xref ref-type="aff" rid="aff9">
<sup>9</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
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<aff id="aff1">
<sup>1</sup>
<institution>Department of Electrical and Electronics Engineering</institution>, <institution>PSG Institute of Technology and Applied Research</institution>, <addr-line>Coimbatore</addr-line>, <country>India</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Department of Electrical and Electronics Engineering</institution>, <institution>Adhiparasakthi Engineering College</institution>, <addr-line>Melmaruvathur</addr-line>, <addr-line>Tamil Nadu</addr-line>, <country>India</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Department of Electrical and Electronics Engineering</institution>, <institution>Agni College of Technology</institution>, <addr-line>Chennai</addr-line>, <addr-line>Tamil Nadu</addr-line>, <country>India</country>
</aff>
<aff id="aff4">
<sup>4</sup>
<institution>Department of Electrical Engineering</institution>, <institution>Indian Institute of Technology Jodhpur</institution>, <addr-line>Jodhpur</addr-line>, <addr-line>Rajasthan</addr-line>, <country>India</country>
</aff>
<aff id="aff5">
<sup>5</sup>
<institution>Department of Electrical and Electronics Engineering</institution>, <institution>Amrita School of Engineering</institution>, <addr-line>Bengaluru</addr-line>, <country>India</country>
</aff>
<aff id="aff6">
<sup>6</sup>
<institution>College of Computer and Information Sciences</institution>, <institution>Prince Sultan University</institution>, <addr-line>Riyadh</addr-line>, <country>Saudi Arabia</country>
</aff>
<aff id="aff7">
<sup>7</sup>
<institution>Automated Systems and Soft Computing Lab (ASSCL)</institution>, <institution>Prince Sultan University</institution>, <addr-line>Riyadh</addr-line>, <country>Saudi Arabia</country>
</aff>
<aff id="aff8">
<sup>8</sup>
<institution>Faculty of Computers and Artificial Intelligence</institution>, <institution>Benha University</institution>, <addr-line>Benha</addr-line>, <country>Egypt</country>
</aff>
<aff id="aff9">
<sup>9</sup>
<institution>Department of ICT and Natural Sciences</institution>, <institution>Norwegian University of Science and Technology</institution>, <addr-line>Alesund</addr-line>, <country>Norway</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/1882335/overview">Praveen Kumar Balachandran</ext-link>, Vardhaman College of Engineering, India</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/2663506/overview">Devakirubakaran S.</ext-link>, SRM Institute of Science and Technology, India</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/654824/overview">Prince Winston D.</ext-link>, Kamaraj College of Engineering &#x26; Technology, India</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Ahmad Taher Azar, <email>aazar@psu.edu.sa</email>; Ibrahim A. Hameed, <email>ibib@ntnu.no</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>06</day>
<month>05</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="collection">
<year>2024</year>
</pub-date>
<volume>12</volume>
<elocation-id>1400651</elocation-id>
<history>
<date date-type="received">
<day>13</day>
<month>03</month>
<year>2024</year>
</date>
<date date-type="accepted">
<day>18</day>
<month>04</month>
<year>2024</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2024 Baskaran, Naghapushanam, Ganapathy, Meena, Meena, Azar and Hameed.</copyright-statement>
<copyright-year>2024</copyright-year>
<copyright-holder>Baskaran, Naghapushanam, Ganapathy, Meena, Meena, Azar and Hameed</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>Low-cost photovoltaic-powered elevators (PVPEs) have gained ever-increasing attention in the last few years for their advantages in terms of renewable energy and low maintenance costs after installation. In this paper, four high-step-up DC-DC converters for low-voltage sources such as solar photovoltaic, fuel cells, and battery banks are proposed. Their performances are evaluated in terms of optimal capability and high reliability. Among the four proposed architectures, the bootstrap converter is selected for its ability to restrict losses and other redundant parameters. The proposed converter drives the inverter-driven switched reluctance motor (SRM) assembly through a directly coupled method, which eliminates the need for battery banks while aiding in cost reduction. The prototype model is implemented, and results are validated, showing promising performance and thus being very efficacious for application to low-cost PVPEs.</p>
</abstract>
<kwd-group>
<kwd>photovoltaic systems</kwd>
<kwd>SRM</kwd>
<kwd>DC-DC boost converters</kwd>
<kwd>multilevel-inverter</kwd>
<kwd>continuous conduction mode</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Solar Energy</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>The photovoltaic-powered elevator (PVPE) promises to be the invention of the next few years due to its several advantages and characteristics. It is pollution-free and needs less maintenance after installation. It does not need any fuel to be powered up, and its source of power is renewable, clean, and environmentally friendly. The source of power is renewable, clean, and environmentally friendly. It is estimated that in (<xref ref-type="bibr" rid="B9">Cronshaw, 2015</xref>) the solar-powered apparatus is going to play the most significant role in human life. As of now, the most important equipment is motors, which utilize non-renewable energy as the main source. We are badly in need of an alternate energy source that would be renewable and reliable&#x2014;none other than solar PV systems.</p>
<p>One easier way of making electrical energy available during calamities is solar energy. Nevertheless, the solar-powered system available traditionally is too expensive, and most of the energy is lost in conversion. If a few steps were taken to minimize these aspects, then this kind of energy would become a cheaper and maintenance-free system for several years (<xref ref-type="bibr" rid="B6">Caracas et al., 2013</xref>; <xref ref-type="bibr" rid="B26">Meghni et al., 2017</xref>). In (<xref ref-type="bibr" rid="B32">Raghavendra et al., 2019</xref>), the authors propose a unique converter for solar water-pumping assemblies that do not require a battery (<xref ref-type="bibr" rid="B1">Antonello et al., 2016</xref>; <xref ref-type="bibr" rid="B32">Raghavendra et al., 2019</xref>; <xref ref-type="bibr" rid="B24">Meena and Singh, 2023b</xref>; <xref ref-type="bibr" rid="B11">Fekik et al., 2023</xref>; <xref ref-type="bibr" rid="B38">Thanikanti et al., 2023</xref>). Then, new high-voltage-boosting converters are designed in (<xref ref-type="bibr" rid="B14">Hwu et al., 2012</xref>; <xref ref-type="bibr" rid="B13">Hwu and Yau, 2013</xref>).</p>
<p>When sunlight intensity crosses 1000 <italic>W</italic>/<italic>m</italic>
<sup>2</sup>, which is roughly equivalent to midday in summer in Germany, for example, or when solar irradiation approaches 1000 <italic>W</italic>/<italic>m</italic>
<sup>2</sup> at lower temperatures, a module&#x2019;s real power may rise above its nominal power (<xref ref-type="bibr" rid="B36">Sontake and Kalamkar, 2016</xref>).Two popular configurations usually employed for PV-powered systems are (i) battery-coupled and (ii) direct-coupled methods. The former approach uses the battery to increase supply over a longer period by acting as a constant voltage source for the system. But for elevators, the longer utilization period will be only during the day, when the Sun shines brightly. Though battery utilization aids in some aspects, it has its own drawbacks, as discussed below. The batteries minimize the performance of the system as the voltage is decided by the battery and not by the solar panel. Therefore, when the Sun&#x2019;s luminosity is high, the nominal power can exceed 1000 <italic>W</italic>/<italic>m</italic>
<sup>2</sup> (roughly during midday), but the battery lays an obstacle to the maximum utilization of power by the system. Furthermore, the batteries have a 2-year life duration when compared to the PV module&#x2019;s life span of 20 years. In addition, the cost of battery maintenance and replacement is significant. As a result, the total efficiency of the system is diminished, while the PVPE system installation cost is increased. As a result, the battery-coupled system is not employed (<xref ref-type="bibr" rid="B10">Eker, 2005</xref>; <xref ref-type="bibr" rid="B21">Meah et al., 2008</xref>; <xref ref-type="bibr" rid="B8">Chunting et al., 2010</xref>; <xref ref-type="bibr" rid="B39">Tschanz et al., 2010</xref>; <xref ref-type="bibr" rid="B40">Vitorino et al., 2010</xref>; <xref ref-type="bibr" rid="B20">Malla et al., 2011</xref>; <xref ref-type="bibr" rid="B25">Meena and Singh, 2022</xref>; <xref ref-type="bibr" rid="B2">Arun et al., 2024</xref>; <xref ref-type="bibr" rid="B15">Jagan et al., 2024</xref>).</p>
<p>In (<xref ref-type="bibr" rid="B18">Lee et al., 2000</xref>), interleaved operation of two or more boost converters is presented in this study for high-power applications to increase output power and reduce output ripple (<xref ref-type="bibr" rid="B18">Lee et al., 2000</xref>; <xref ref-type="bibr" rid="B17">Kengne et al., 2023</xref>). Two structures, a switched-capacitor (SC)-based boost converter and a two-level inverter, are connected in cascade in this article (<xref ref-type="bibr" rid="B3">Axelrod et al., 2005</xref>). To meet safety standards and make maximum use of the PV-generated power, a recent research trend in residential power generation systems is to adopt the PV parallel connected configuration rather than the series-connected design (<xref ref-type="bibr" rid="B19">Li and He, 2010</xref>; <xref ref-type="bibr" rid="B27">Meghni et al., 2018</xref>; <xref ref-type="bibr" rid="B31">Radwan et al., 2018</xref>; <xref ref-type="bibr" rid="B37">Suresh et al., 2019</xref>; <xref ref-type="bibr" rid="B35">Sethuraman et al., 2020</xref>). This work includes thorough mathematical analysis, detailed converter design, parameter analysis and comparison with other existing converters, and a new hardware prototype with expanded hardware results (<xref ref-type="bibr" rid="B34">Sathyan et al., 2015</xref>; <xref ref-type="bibr" rid="B29">Periyanayagam et al., 2020</xref>; <xref ref-type="bibr" rid="B16">Kalaiarasi et al., 2021</xref>; <xref ref-type="bibr" rid="B23">Meena and Singh, 2023a</xref>; <xref ref-type="bibr" rid="B33">Reddy et al., 2023</xref>; <xref ref-type="bibr" rid="B22">Meena et al., 2024</xref>; <xref ref-type="bibr" rid="B4">Bharatiraja et al., 2016a</xref>; <xref ref-type="bibr" rid="B5">Bharatiraja et al., 2016b</xref>). From the analyses made above, it is evident that an efficient and low-cost PVPE can be set up if a suitable boost converter is designed while still minimizing the conduction and switching losses for improved performance.</p>
<p>In this paper, we propose a detailed study of four high-step-up boost converters. Then, the most suitable topology is chosen after a careful analysis of the simulation results. In <xref ref-type="fig" rid="F1">Figure 1</xref>, the overall block diagram of the proposed system is shown for better understanding of the proposed topology. The design of four types of high-step-up bootstrap converters and a multilevel inverter energizing the switched reluctance motor (SRM) according to the prevailing necessity are considered the main contributions of the work claimed in this research. The cost-reducing factor has already been discussed adequately.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Block diagram of the proposed system.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g001.tif"/>
</fig>
<p>The rest of this paper is organized as follows: The <xref ref-type="sec" rid="s2">Section 2</xref> elaborates on the design and selection part of the optimal bootstrap DC-DC converter and its reliable features. The multilevel-inverter-fed SRM drive is designed to provide a dynamic speed response during source variations as well as load surges in the <xref ref-type="sec" rid="s3">Section 3</xref>. <xref ref-type="sec" rid="s4">Section 4</xref> shows the photovoltaic supply comparison with and without the maximum power point tracking (MPPT) controller that excites the DC-DC converter. Numerical results and hardware implementation are depicted in <xref ref-type="sec" rid="s5">Section 5</xref>, while the paper&#x2019;s conclusions and justifications are briefly highlighted in <xref ref-type="sec" rid="s6">Section 6</xref>.</p>
</sec>
<sec id="s2">
<title>2 Selection of the DC-DC converters</title>
<p>There are two types of converters available for modifying the power obtained from the solar cells, which are meant for consumer-friendly use. The first is an inverter, which converts the DC into AC at the desired frequency to supply AC appliances. The other one is a DC-to dc converter, which already possesses numerous applications via DC motors for solar water pumping systems and other emerging areas like solar-powered electrical vehicles. In this proposed system, the preferred PVPE is driven by SRM; therefore, we have opted for designing a suitable boost converter and PWM inverter. As a result, various boost converters, starting from the basic conventional converter to newly proposed topologies like interleaved converters, quadruple converters, hybrid interleaved-quadruple converters, and finally bootstrap converters, were designed and simulated in this paper. The results were compared to choose the best converter according to the motor requirements.</p>
<sec id="s2-1">
<title>2.1 Bootstrap converters</title>
<p>This converter consists of bootstrap capacitors and two boost inductors that allow the converter to work appropriately. The three switches are operated in a fashion where only half bridge and one low side gate drive are triggered. The bootstrap converter simulation circuit is shown in <xref ref-type="fig" rid="F2">Figure 2</xref>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>The proposed bootstrap converter.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g002.tif"/>
</fig>
</sec>
<sec id="s2-2">
<title>2.2 Operating modes of the converter</title>
<p>Mode 1, <xref ref-type="fig" rid="F3">Figure 3</xref>: When switches <italic>S</italic>
<sub>1</sub> and <italic>S</italic>
<sub>3</sub> are turned on, the capacitor <italic>C</italic>
<sub>
<italic>b</italic>
</sub> is immediately charged and the inductors are magnetized because the diode <italic>D</italic>
<sub>0</sub> is reverse biased due to the <italic>S</italic>
<sub>3</sub> switch being turned on.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Continuous conduction Mode-1.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g003.tif"/>
</fig>
<p>The output capacitor will provide electricity to the load during this time. The voltage across <italic>L</italic>
<sub>1</sub> and <italic>L</italic>
<sub>2</sub> in this mode can be expressed as<disp-formula id="equ1">
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<mml:mo>&#x2212;</mml:mo>
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<mml:mo>&#x2212;</mml:mo>
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<mml:mi>N</mml:mi>
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<mml:mo>&#x3d;</mml:mo>
<mml:msub>
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</mml:math>
</disp-formula>Mode 2, <xref ref-type="fig" rid="F4">Figure 4</xref>: When switch <italic>S</italic>
<sub>2</sub> is activated, the capacitor <italic>C</italic>
<sub>
<italic>b</italic>
</sub> is instantaneously charged to the input voltage. The input voltage, together with the energy stored in <italic>C</italic>
<sub>
<italic>e</italic>
</sub>, <italic>L</italic>
<sub>1</sub> &#x26; <italic>L</italic>
<sub>2</sub> feeds the load, causing <italic>C</italic>
<sub>0</sub> to be energized and <italic>C</italic>
<sub>
<italic>e</italic>
</sub> discharged, <italic>L</italic>
<sub>1</sub>, <italic>L</italic>
<sub>2</sub> to be demagnetized.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Continuous conduction Mode-2.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g004.tif"/>
</fig>
<p>So <italic>V</italic>
<sub>0</sub> in this mode can be expressed as<disp-formula id="equ3">
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</mml:mrow>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>O</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
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</mml:math>
</disp-formula>
<disp-formula id="equ4">
<mml:math id="m4">
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mn>2</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>O</mml:mi>
<mml:mi>F</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mn>2</mml:mn>
<mml:mo>&#x2212;</mml:mo>
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<mml:mi>N</mml:mi>
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</mml:msub>
</mml:math>
</disp-formula>
</p>
<p>The converter is operated in continuous conduction mode; the waveform is shown in <xref ref-type="fig" rid="F5">Figure 5</xref>.The voltage conversion ratio in the continuous conduction mode is given by<disp-formula id="equ5">
<mml:math id="m5">
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
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</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
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</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:math>
</disp-formula>The output response of the converter and the switching pulses are shown in <xref ref-type="fig" rid="F6">Figures 6</xref>, <xref ref-type="fig" rid="F7">7</xref>. The input voltage of the converter is 24 V, the output voltage is 72 V, and the switching frequency is 5 kHz. <xref ref-type="table" rid="T1">Table 1</xref> shows the comparison of the parameters and the responses of each boost converter. The best-suited converter for the SPWP is selected and implemented in the prototype.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Continuous conduction mode waveform of the converter.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g005.tif"/>
</fig>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Simulation output of a bootstrap converter.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g006.tif"/>
</fig>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Switching pulses of the bootstrap converter.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g007.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Comparison of the results and other factors to deduce the best converter.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Types of boost converter</th>
<th align="center">Input voltage</th>
<th align="center">Output Voltage</th>
<th align="center">Output current</th>
<th align="center">No. Of inductors used</th>
<th align="center">No. Of capacitors used</th>
<th align="center">No. Of switches used</th>
<th align="center">Voltage gain</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Conventional</td>
<td align="left">12</td>
<td align="left">24</td>
<td align="left">0.7</td>
<td align="left">1</td>
<td align="left">1</td>
<td align="left">1</td>
<td align="left">2</td>
</tr>
<tr>
<td align="left">Interleaved</td>
<td align="left">20</td>
<td align="left">148</td>
<td align="left">2.5</td>
<td align="left">3</td>
<td align="left">1</td>
<td align="left">2</td>
<td align="left">7.5</td>
</tr>
<tr>
<td align="left">Voltage Quadruple</td>
<td align="left">24</td>
<td align="left">94</td>
<td align="left">1.8</td>
<td align="left">3</td>
<td align="left">3</td>
<td align="left">2</td>
<td align="left">3.9</td>
</tr>
<tr>
<td align="left">Hybrid</td>
<td align="left">24</td>
<td align="left">407</td>
<td align="left">14.2</td>
<td align="left">6</td>
<td align="left">3</td>
<td align="left">5</td>
<td align="left">16.9</td>
</tr>
<tr>
<td align="left">Bootstrap</td>
<td align="left">24</td>
<td align="left">72</td>
<td align="left">2.5</td>
<td align="left">2</td>
<td align="left">2</td>
<td align="left">3</td>
<td align="left">3</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Taking into consideration the input voltage and output voltage, the gain is highest in a hybrid converter. And then, bearing in mind the current limitations due to some saturation facts of SRM, we turn on the interleaved and bootstrap converters. However, a few primary parameters, like the number of inductors, capacitors, and switches that would be able to avoid bulkiness, offer a better power factor, and have low switching losses, can be taken into account when picking a suitable converter among the two. Thus, we chose the bootstrap converter with two inductors, two capacitors, and 3 MOSFET switches, which can offer three times the input voltage with maximum compatibility.</p>
</sec>
</sec>
<sec id="s3">
<title>3 Multilevel-inverter fed SRM drive operating principle</title>
<p>The multilevel-inverter-fed SRM drive is designed to provide a dynamic speed response during source variations as well as load surges in this section. <xref ref-type="fig" rid="F8">Figure 8</xref> illustrates the energy flow diagram of the proposed multilevel inverter topology (Phase A) at various levels. When the DC supply is given to the circuit, all three capacitors <italic>C</italic>1, <italic>C</italic>2 and <italic>C</italic>3 get charged. The DC voltage across the capacitors is equally divided, i.e.,<disp-formula id="e1">
<mml:math id="m6">
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
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</mml:mrow>
</mml:mfrac>
</mml:math>
<label>(1)</label>
</disp-formula>
</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Energy Flow diagram of the seven level switched capacitor based symmetric multilevel inverter (SCBSMLI) at <bold>(A)</bold> Positive First level <bold>(B)</bold> Positive Second Level <bold>(C)</bold> Positive Third Level <bold>(D)</bold> Negative First Level <bold>(E)</bold> Negative Second Level <bold>(F)</bold> Negative Third Level.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g008.tif"/>
</fig>
<p>To attain the first level in the positive cycle, the switches <italic>SA</italic> and <italic>X</italic>1 are excited, and the energy flows through <italic>C</italic>1 &#x2212; <italic>D</italic>1 &#x2212; <italic>X</italic>1 &#x2212; <italic>D</italic>3 &#x2212; <italic>RL</italic> &#x2212; <italic>SA</italic> &#x2212; <italic>C</italic>1. For the second level, the current flows through <italic>C</italic>2 &#x2212; <italic>D</italic>5 &#x2212; <italic>X</italic>2 &#x2212; <italic>D</italic>7 &#x2212; <italic>SA</italic> &#x2212; <italic>C</italic>1 &#x2212; <italic>C</italic>2 and <italic>C</italic>3 &#x2212; <italic>SC</italic> &#x2212; <italic>RL</italic> &#x2212; <italic>SA</italic> &#x2212; <italic>C</italic>1 &#x2212; <italic>C</italic>2 &#x2212; <italic>C</italic>3 for the third level. In the negative cycle, for the first level, the current flows from <italic>C</italic>3 &#x2212; <italic>SD</italic> &#x2212; <italic>RL</italic> &#x2212; <italic>D</italic>6 &#x2212; <italic>X</italic>2 &#x2212; <italic>D</italic>8 &#x2212; <italic>C</italic>1, for the second level, the current flows from <italic>C</italic>2 &#x2212; <italic>C</italic>1 &#x2212; <italic>SD</italic> &#x2212; <italic>RL</italic> &#x2212; <italic>D</italic>2 &#x2212; <italic>X</italic>1 &#x2212; <italic>D</italic>4 &#x2212; <italic>C</italic>2; and <italic>C</italic>1 &#x2212; <italic>C</italic>2 &#x2212; <italic>C</italic>3 &#x2212; <italic>SD</italic> &#x2212; <italic>RL</italic> &#x2212; <italic>SB</italic> &#x2212; <italic>C</italic>1.</p>
<p>In terms of the switching conditions provided in <xref ref-type="table" rid="T2">Table 2</xref>, the gating pulses for each switch are graphed in <xref ref-type="fig" rid="F9">Figure 9</xref>. In one full cycle of operation, the seven-level output is divided into 16 regions with respect to the firing angle (<italic>&#x3b1;</italic>
<sub>
<italic>n</italic>
</sub>). For a seven-level switched capacitor-based symmetric multilevel inverter (SCBSMLI), the three positive half cycle levels are triggered at <italic>&#x3b1;</italic>
<sub>1</sub>, <italic>&#x3b1;</italic>
<sub>2</sub>, and <italic>&#x3b1;</italic>
<sub>3</sub>, which lie between 0 and <italic>&#x3c0;</italic>/2, and the negative half cycle levels are triggered at <italic>&#x3b1;</italic>
<sub>9</sub> (&#x3d;<italic>&#x3c0;</italic> &#x2b; <italic>&#x3b1;</italic>
<sub>1</sub>), <italic>&#x3b1;</italic>
<sub>10</sub> (&#x3d;<italic>&#x3c0;</italic> &#x2b; <italic>&#x3b1;</italic>
<sub>2</sub>), and <inline-formula id="inf1">
<mml:math id="m7">
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
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</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close="">
<mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>&#x3c0;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
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</mml:mrow>
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</inline-formula>, which lies between <italic>&#x3c0;</italic> and 3<italic>&#x3c0;</italic>/2. The zero level occurs during <italic>&#x3b1;</italic>
<sub>0</sub> (&#x3d;0) to <italic>&#x3b1;</italic>
<sub>1</sub>, <italic>&#x3b1;</italic>
<sub>7</sub> to <italic>&#x3b1;</italic>
<sub>9</sub>, and <italic>&#x3b1;</italic>
<sub>15</sub> to <italic>&#x3b1;</italic>
<sub>16</sub> (&#x3d;2<italic>&#x3c0;</italic>).</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Switching Conditions of seven level SCBSMLI.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Level</th>
<th align="center">SA</th>
<th align="center">SB</th>
<th align="center">SC</th>
<th align="center">SD</th>
<th align="center">X1</th>
<th align="center">X2</th>
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<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Gate pulses of switches SA, SB, SC, SD, X1 and X2.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g009.tif"/>
</fig>
<p>The switches are turned on in the following regions:<disp-formula id="equ6">
<mml:math id="m14">
<mml:mi>S</mml:mi>
<mml:mi>A</mml:mi>
<mml:mo>:</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
</disp-formula>
<disp-formula id="equ7">
<mml:math id="m15">
<mml:mi>S</mml:mi>
<mml:mi>B</mml:mi>
<mml:mo>:</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>11</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>13</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
</disp-formula>
<disp-formula id="equ8">
<mml:math id="m16">
<mml:mi>S</mml:mi>
<mml:mi>C</mml:mi>
<mml:mo>:</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
</disp-formula>
<disp-formula id="equ9">
<mml:math id="m17">
<mml:mi>S</mml:mi>
<mml:mi>D</mml:mi>
<mml:mo>:</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>9</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
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<mml:mrow>
<mml:mn>15</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
</disp-formula>
<disp-formula id="e2">
<mml:math id="m18">
<mml:mi>X</mml:mi>
<mml:mn>1</mml:mn>
<mml:mo>:</mml:mo>
<mml:mfenced open="{" close="">
<mml:mrow>
<mml:mtable class="cases">
<mml:mtr>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
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<mml:mrow>
<mml:mn>2</mml:mn>
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<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>7</mml:mn>
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<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>11</mml:mn>
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<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
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<mml:mrow>
<mml:mn>13</mml:mn>
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</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
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<mml:mrow>
<mml:mn>14</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:math>
<label>(2)</label>
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<disp-formula id="e3">
<mml:math id="m19">
<mml:mi>X</mml:mi>
<mml:mn>2</mml:mn>
<mml:mo>:</mml:mo>
<mml:mfenced open="{" close="">
<mml:mrow>
<mml:mtable class="cases">
<mml:mtr>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
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</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
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<mml:mrow>
<mml:mn>6</mml:mn>
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<mml:mspace width="1em"/>
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</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>9</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
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<mml:mrow>
<mml:mn>10</mml:mn>
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</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>14</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>15</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:math>
<label>(3)</label>
</disp-formula>The above switching conditions (2) and (3) are rewritten in the term of <italic>&#x3b1;</italic>
<sub>1</sub>, <italic>&#x3b1;</italic>
<sub>2</sub> and <italic>&#x3b1;</italic>
<sub>3</sub>
<disp-formula id="equ10">
<mml:math id="m20">
<mml:mi>S</mml:mi>
<mml:mi>A</mml:mi>
<mml:mo>:</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
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<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
</disp-formula>
<disp-formula id="equ11">
<mml:math id="m21">
<mml:mi>S</mml:mi>
<mml:mi>B</mml:mi>
<mml:mo>:</mml:mo>
<mml:mi>&#x3c0;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
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<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
</disp-formula>
<disp-formula id="equ12">
<mml:math id="m22">
<mml:mi>S</mml:mi>
<mml:mi>C</mml:mi>
<mml:mo>:</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
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<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
</disp-formula>
<disp-formula id="equ13">
<mml:math id="m23">
<mml:mi>S</mml:mi>
<mml:mi>D</mml:mi>
<mml:mo>:</mml:mo>
<mml:mi>&#x3c0;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
</disp-formula>
<disp-formula id="e4">
<mml:math id="m24">
<mml:mi>X</mml:mi>
<mml:mn>1</mml:mn>
<mml:mo>:</mml:mo>
<mml:mfenced open="{" close="">
<mml:mrow>
<mml:mtable class="cases">
<mml:mtr>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
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<mml:mspace width="1em"/>
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</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:mfrac>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:mi>&#x3c0;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c0;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:mfrac>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:math>
<label>(4)</label>
</disp-formula>
<disp-formula id="e5">
<mml:math id="m25">
<mml:mi>X</mml:mi>
<mml:mn>2</mml:mn>
<mml:mo>:</mml:mo>
<mml:mfenced open="{" close="">
<mml:mrow>
<mml:mtable class="cases">
<mml:mtr>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
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<mml:mtr>
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<mml:mrow>
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<mml:mrow>
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<mml:mrow>
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<mml:mspace width="1em"/>
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</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:mi>&#x3c0;</mml:mi>
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<mml:mrow>
<mml:mn>1</mml:mn>
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</mml:msub>
<mml:mo>&#x3c;</mml:mo>
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<mml:mrow>
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</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
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<mml:mrow>
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</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
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<mml:mrow>
<mml:mn>2</mml:mn>
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</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
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<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
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</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:math>
<label>(5)</label>
</disp-formula>
</p>
<p>From the above (4) and (5), the AC output voltage of the SCBSMLI is calculated using the Fourier Half Sine series as given in the (6), since the desired output is ultimately as<disp-formula id="e6">
<mml:math id="m26">
<mml:mi>f</mml:mi>
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<mml:mrow>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
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</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mfenced open="{" close="">
<mml:mrow>
<mml:mtable class="cases">
<mml:mtr>
<mml:mtd columnalign="left">
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<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
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</mml:msub>
<mml:mo>,</mml:mo>
<mml:mspace width="0.3333em"/>
<mml:mspace width="0.3333em"/>
<mml:mspace width="0.3333em"/>
<mml:mspace width="0.3333em"/>
<mml:mi>i</mml:mi>
<mml:mi>f</mml:mi>
<mml:mspace width="0.3333em"/>
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<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
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<mml:mrow>
<mml:mn>1</mml:mn>
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</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
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<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
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</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
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<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
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</mml:msub>
<mml:mo>,</mml:mo>
<mml:mspace width="0.3333em"/>
<mml:mspace width="0.3333em"/>
<mml:mspace width="0.3333em"/>
<mml:mspace width="0.3333em"/>
<mml:mi>i</mml:mi>
<mml:mi>f</mml:mi>
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<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
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<mml:mrow>
<mml:mn>2</mml:mn>
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</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c0;</mml:mi>
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<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
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</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mn>3</mml:mn>
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</mml:msub>
<mml:mo>,</mml:mo>
<mml:mspace width="0.3333em"/>
<mml:mspace width="0.3333em"/>
<mml:mspace width="0.3333em"/>
<mml:mspace width="0.3333em"/>
<mml:mi>i</mml:mi>
<mml:mi>f</mml:mi>
<mml:mspace width="0.3333em"/>
<mml:mspace width="0.3333em"/>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:mi>&#x3c0;</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mspace width="1em"/>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:math>
<label>(6)</label>
</disp-formula>
<disp-formula id="e7">
<mml:math id="m27">
<mml:mi>f</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x221e;</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:msub>
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi>s</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
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</mml:mfenced>
</mml:math>
<label>(7)</label>
</disp-formula>where<disp-formula id="e8">
<mml:math id="m28">
<mml:msub>
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:msubsup>
<mml:mrow>
<mml:mo>&#x222b;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mi>f</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3c9;</mml:mi>
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</mml:mfenced>
<mml:mi>s</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
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</mml:mfenced>
<mml:mi>d</mml:mi>
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<mml:mrow>
<mml:mi>&#x3c9;</mml:mi>
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</mml:mfenced>
</mml:math>
<label>(8)</label>
</disp-formula>writing (8) in terms of voltage<disp-formula id="e9">
<mml:math id="m29">
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:msubsup>
<mml:mrow>
<mml:mo>&#x222b;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi>s</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mi>d</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
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</mml:mfenced>
</mml:math>
<label>(9)</label>
</disp-formula>Substituting (5) in <xref ref-type="disp-formula" rid="e8">(8)</xref>
<disp-formula id="e10">
<mml:math id="m30">
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mtable class="matrix">
<mml:mtr>
<mml:mtd columnalign="center">
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mfenced open="[" close="">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mo>&#x222b;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msubsup>
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi>s</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mrow>
<mml:mo>&#x222b;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msubsup>
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi>s</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x2b;</mml:mo>
</mml:mrow>
</mml:mfenced>
<mml:mspace width="0.3333em"/>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="center">
<mml:mfenced open="" close="]">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mo>&#x222b;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msubsup>
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi>s</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3c9;</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:math>
<label>(10)</label>
</disp-formula>Substituting (2) in <xref ref-type="disp-formula" rid="e9">(9)</xref>
<disp-formula id="e11">
<mml:math id="m31">
<mml:msub>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mtable class="matrix">
<mml:mtr>
<mml:mtd columnalign="center">
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mfenced open="[" close="">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mo>&#x222b;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
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<label>(11)</label>
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<label>(12)</label>
</disp-formula>
</p>
<p>Integrating and simplifying (10) using trigonometric functions, the AC output voltage is for seven-level SCBSMLI given as<disp-formula id="e13">
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<label>(13)</label>
</disp-formula>DC machine-like performance can be achieved for a permanent magnet synchronous motor (PMSM) drive when vector-control or field-oriented control (FOC) is used to achieve decoupling control. It is mentioned that the vector-control decouples the excitation component (<italic>i</italic>
<sub>
<italic>d</italic>
</sub>) and torque segment (<italic>i</italic>
<sub>
<italic>q</italic>
</sub>) in PMSM by applying the instant space-vector hypothesis (<xref ref-type="bibr" rid="B30">Pillay and Krishnan, 1989</xref>; <xref ref-type="bibr" rid="B4">Bharatiraja et al., 2016a</xref>; <xref ref-type="bibr" rid="B5">Bharatiraja et al., 2016b</xref>). A high-precision and servo-controlled industrial robot driven by PMSM-Direct Torque Control utilizing composite active vectors is designed in (<xref ref-type="bibr" rid="B41">Yuan et al., 2019</xref>). The conceptual framework of antecedents to trends on permanent magnet synchronous generators for wind energy conversion systems has been briefed in (<xref ref-type="bibr" rid="B7">Chokkalingham et al., 2018</xref>; <xref ref-type="bibr" rid="B28">Padmanathan et al., 2019</xref>; <xref ref-type="bibr" rid="B12">Fekik et al., 2021</xref>).</p>
<p>The PMSM-PUMP drive comprises five primary parts: the PMSM, inverter, control unit, temperature sensor, and pump as load. The schematic representation of the drive system is shown in <xref ref-type="fig" rid="F10">Figure 10</xref>. The inverter receives DC supply from the PV panel with a constant-voltage MPPT controller. Thus, the pump receives constant voltage during the day even when fluctuations are experienced in the Sun&#x2019;s radiance insolation.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Schematic-representation of the PMSM-PUMP drive system.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g010.tif"/>
</fig>
</sec>
<sec id="s4">
<title>4 MPPT controller</title>
<p>The proposed system is simulated, and the results are compared with the system simulated without MPPT. The MPPT-controlled bootstrap converter drives the SVM inverter to run the PMSM-PUMP assembly block diagram, as shown in <xref ref-type="fig" rid="F11">Figure 11</xref>. The comparison between the proposed system without MPPT and with MPPT is done after introducing a step change in the insolation from 1,000 to 950, as exhibited in <xref ref-type="fig" rid="F12">Figure 12</xref>.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Block diagram of bootstrap converter and SVM inverter with MPPT controller.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g011.tif"/>
</fig>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Response of the proposed system with and without MPPT.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g012.tif"/>
</fig>
<p>Following the insolation graph, the other parameters like <italic>V</italic>
<sub>
<italic>pv</italic>
</sub>, <italic>P</italic>
<sub>
<italic>pv</italic>
</sub>, <italic>V</italic>
<sub>
<italic>out</italic>
</sub>, and speed of the motor are obtained and compared with the system without MPPT to show the superiority of the proposed system.</p>
<p>A comparison of output voltage and motor speed with and without MPPT is delineated in <xref ref-type="table" rid="T3">Table 3</xref>. By using the MPPT controller, the output voltage is enhanced from 385V to 415V, and motor speed is also enhanced from 1200 RPM to 1415 RPM. The panel voltage and power also seem to be improved in the MPPT-controlled system.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Comparison of output voltage and motor speed with and without MPPT.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">CASE</th>
<th align="center">VPV</th>
<th align="center">PPV (W)</th>
<th align="center">
<italic>V</italic>
<sub>
<italic>o</italic>
</sub>
</th>
<th align="center">N (RPM) (rpm)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Without MPPT</td>
<td align="center">122 V</td>
<td align="center">591</td>
<td align="center">385 V</td>
<td align="center">1,200</td>
</tr>
<tr>
<td align="center">With MPPT</td>
<td align="center">119 V</td>
<td align="center">640</td>
<td align="center">415 V</td>
<td align="center">1,415</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>From <xref ref-type="table" rid="T3">Table 3</xref>, it is evident that the system with MPPT is showing better results than the system without MPPT. Also, the desired values are obtained, and the response is stable for the system with the MPPT technique.</p>
</sec>
<sec id="s5">
<title>5 Experimental setup &#x26; results</title>
<p>Thus, after the design of the proposed system, the implementation of the prototype model is carried out. Its results are validated with the proposed topology, and the challenges of implementation are summarized. <xref ref-type="fig" rid="F13">Figure 13</xref> shows the hardware setup of the proposed topology. The bootstrap converter is designed, and its output is shown in the DSO. The solar panel supplies the DC voltage for the bootstrap converter, and the constant voltage MPPT technique is employed to offer the required output as per the motor ratings. The motor speed response is converted into serial input, and then it is sent to the COM-8 port of the computer, where it is displayed on the monitor. The hardware parameters of the bootstrap are given in <xref ref-type="table" rid="T4">Table 4</xref>.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Hardware of the proposed topology.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g013.tif"/>
</fig>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Hardware parameters of bootstrap converter.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">S. No.</th>
<th align="center">Parameters</th>
<th align="center">Value</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">1</td>
<td align="center">Power rating</td>
<td align="center" style=";">100 <italic>W</italic>
</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">Input voltage</td>
<td align="center" style=";">24 <italic>V</italic>
</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">Switching frequency</td>
<td align="center" style=";">195 <italic>KHz</italic>
</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">Output voltage</td>
<td align="center" style=";">200 <italic>V</italic>
</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">Inductors</td>
<td align="center" style=";">170 <italic>&#x3bc;F</italic>
</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">Bootstrap capacitor, <italic>C</italic>
<sub>1</sub>
</td>
<td align="center" style=";">100 <italic>&#x3bc;F</italic>
</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">Output capacitors, <italic>C</italic>
<sub>3</sub>
</td>
<td align="center" style=";">60 <italic>&#x3bc;F</italic>
</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">Load resistance</td>
<td align="center" style=";">400 &#x3a9;</td>
</tr>
<tr>
<td align="center">9</td>
<td align="center">Capacitor, <italic>C</italic>
<sub>2</sub>
</td>
<td align="center" style=";">200 <italic>&#x3bc;F</italic>
</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<xref ref-type="fig" rid="F14">Figure 14</xref> shows the output of the bootstrap converter from the hardware implemented for the purpose of giving constant dc voltage equal to 23.7 V and current of 142 mA to the inverter which drives the SRM. Then <xref ref-type="fig" rid="F15">Figure 15</xref> gives the speed response of the SRM to deliver a constant speed to the ELEVATOR load even if any disturbance occurs.</p>
<fig id="F14" position="float">
<label>FIGURE 14</label>
<caption>
<p>Output of the bootstrap converter from the hardware implemented.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g014.tif"/>
</fig>
<fig id="F15" position="float">
<label>FIGURE 15</label>
<caption>
<p>The speed response of the SRM with constant speed to the pump with load disturbance.</p>
</caption>
<graphic xlink:href="fenrg-12-1400651-g015.tif"/>
</fig>
</sec>
<sec id="s6">
<title>6 Conclusion and future works</title>
<p>This work has introduced four architectures of DC-DC converters for possible application in low-cost PVPEs. Results and comparisons from simulations show that the proposed bootstrap converter provides an enhanced output and small voltage pressure on the switches. In the projected topology, only two inductors are used for high-voltage output applications. In different operations, the converter just handles two duty ratios. Thus, we can minimize the overall cost of the solar-powered water elevator system by reducing processes like battery installation, maintenance, and further switching losses due to the DC-AC alteration stage. The direct DC-DC boost converter coupled configuration might also provide additional cost reduction. In our solution, the SRM is used as the drive for the elevator. The speed response of the SRM is guarded by a multilevel inverter controller, which ensures the stability of the whole system. The bootstrap converter supplying DC to the inverter that excites the SRM to drive the prototype is finally implemented.</p>
<p>Future work will focus on refining the proposed bootstrap converter architecture to optimize its efficiency and performance further. Additionally, research will explore integrating advanced control strategies to enhance the overall stability and reliability of the solar-powered water elevator system.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s7">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s8">
<title>Author contributions</title>
<p>JB: Conceptualization, Formal Analysis, Methodology, Resources, Software, Writing&#x2013;original draft, Writing&#x2013;review and editing. MN: Conceptualization, Formal Analysis, Methodology, Resources, Software, Writing&#x2013;original draft, Writing&#x2013;review and editing. MG: Conceptualization, Formal Analysis, Methodology, Resources, Software, Writing&#x2013;original draft, Writing&#x2013;review and editing. PM: Conceptualization, Formal Analysis, Methodology, Resources, Software, Writing&#x2013;original draft, Writing&#x2013;review and editing. VM: Conceptualization, Formal Analysis, Methodology, Resources, Software, Writing&#x2013;original draft, Writing&#x2013;review and editing. ATA: Conceptualization, Formal Analysis, Investigation, Methodology, Validation, Writing&#x2013;original draft, Writing&#x2013;review and editing. IH: Formal Analysis, Funding acquisition, Investigation, Methodology, Resources, Validation, Writing&#x2013;review and editing.</p>
</sec>
<sec sec-type="funding-information" id="s9">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. This research was funded by the Norwegian University of Science and Technology.</p>
</sec>
<ack>
<p>The authors would like to acknowledge the support of the Norwegian University of Science and Technology for paying the Article Processing Charges (APC) of this publication. This research is supported by Automated Systems and Soft Computing Lab (ASSCL), Prince Sultan University, Riyadh, Saudi Arabia. The authors would like to thank Prince Sultan University, Riyadh, Saudi Arabia for their support.</p>
</ack>
<sec sec-type="COI-statement" id="s10">
<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="s11">
<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>
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