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<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">1264157</article-id>
<article-id pub-id-type="doi">10.3389/fenrg.2024.1264157</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>Power quality improvement using a 31-level multi-level inverter with bio-inspired optimization approach</article-title>
<alt-title alt-title-type="left-running-head">Praveena and Sathishkumar</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fenrg.2024.1264157">10.3389/fenrg.2024.1264157</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Praveena</surname>
<given-names>A.</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/1970058/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Sathishkumar</surname>
<given-names>K.</given-names>
</name>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/86435/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
</contrib>
</contrib-group>
<aff>
<institution>School of Electrical Engineering</institution>, <institution>Vellore Institute of Technology</institution>, <addr-line>Vellore</addr-line>, <country>India</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/79324/overview">Chee Wei Tan</ext-link>, University of Technology Malaysia, Malaysia</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/507713/overview">Minh Quan Duong</ext-link>, The University of Danang, Vietnam</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1566843/overview">Norjulia Mohamad Nordin</ext-link>, University of Technology Malaysia, Malaysia</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: K. Sathishkumar, <email>kansathh21@yahoo.co.in</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>19</day>
<month>03</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="collection">
<year>2024</year>
</pub-date>
<volume>12</volume>
<elocation-id>1264157</elocation-id>
<history>
<date date-type="received">
<day>20</day>
<month>07</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>22</day>
<month>01</month>
<year>2024</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2024 Praveena and Sathishkumar.</copyright-statement>
<copyright-year>2024</copyright-year>
<copyright-holder>Praveena and Sathishkumar</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>In recent years, the power quality (PQ) improvements have been explored through various approaches. The employment of electronic devices with renewable energy sources has expanded the harmonics level of voltage and current. Due to harmonics, the PQ of a specific electrical system gets affected. At critical load conditions, the traditional PQ mitigation approaches fail to develop the performance of the system. Therefore, in this work, the Spider Monkey Optimization convolutional neural network (SM-CNN)-based 31-level multilevel inverter (MLI) is used. This method balances the reactive power demands and enhances real power in the grid-tied photovoltaic (PV) system. The maximum power point tracking (MPPT) algorithm depending on radial basis function neural networks (RBFNNs) is used to maximize PV power. For strengthening the voltage level of the PV and to generate higher DC voltage with a minimized switching loss, an integrated boost fly back converter (IBFC) is introduced. The presented technique is implemented in the MATLAB/Simulink platform to figure out the estimation of PQ issues. The suggested MLI lessens the total harmonic distortion (THD) value to 2.45% with an improved power factor.</p>
</abstract>
<kwd-group>
<kwd>photovoltaic system</kwd>
<kwd>multilevel inverter</kwd>
<kwd>Spider Monkey Optimization convolutional neural network</kwd>
<kwd>radial basis function neural network-MPPT</kwd>
<kwd>integrated boost-flyback converter</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Sustainable Energy Systems</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<title>1 Introduction</title>
<p>In developing technologies, the issue of power electronic devices has shown a greater surge because of the exploitation in real-time applications. Generally, several types of controllers are used to mitigate different power quality (PQ) issues (<xref ref-type="bibr" rid="B3">Babu et al., 2020a</xref>). The rapid consolidation of photovoltaics (PV) is mostly based on improvements in PQ and global radiation technology (<xref ref-type="bibr" rid="B23">Ray et al., 2018</xref>). Power is converted from DC to AC by use of an inverter and a distribution system. The majority of voltage and current distortion has an impact on the system&#x2019;s performance when it is linked to the grid. As a result of highly volatile devices coupled with an increase in the demand for nonlinear loads, the effectiveness of the system and the power network with regard to PQ is also affected (<xref ref-type="bibr" rid="B5">Badoni et al., 2021</xref>).</p>
<p>The unique functions of the PQ impact are consumers and utility equipment. By including renewable energy sources (RES) in the grid, the PQ of the system might be increased. Based on the coupled RES and nonlinear loads, the negative impacts on the system&#x2019;s PQ are improved in this case. A renewable energy source contributes to the amount of reactive power on the line, and the associated harmonics are determined by nonlinear loads on the grid (<xref ref-type="bibr" rid="B4">Babu et al., 2020b</xref>; <xref ref-type="bibr" rid="B11">Golla et al., 2021</xref>; <xref ref-type="bibr" rid="B22">Ray et al., 2021</xref>). Many other RES-based technologies have been created during the last few years. Some of those sources are becoming more affordable very quickly, and others are widely recognized as low-cost options for grid-related applications (<xref ref-type="bibr" rid="B20">Rajesh et al., 2021</xref>).</p>
<p>The output voltage of boost-type converters can be boosted above the input voltage. Nevertheless, because of the internal losses, output voltage, and current stresses suffered by semiconductors, they present a gain restriction (<xref ref-type="bibr" rid="B28">Spiazzi et al., 2010</xref>). A high-frequency transformer connected to a flyback converter can be used as a way to receive significantly more voltage. However, because of the energy stored by the converter in its leakage inductance, when blocking voltage is present, the power main switch frequently shows a high reverse voltage (<xref ref-type="bibr" rid="B9">Chen et al., 2015</xref>; <xref ref-type="bibr" rid="B27">Shitole et al., 2017</xref>).</p>
<p>As a result, using integrated converters is necessary for the purpose of increasing costs and lowering efficiency. Moreover, during commutations, high conversion exposes the diode output to maximum voltage peaks. Furthermore, conventional converters have a limited duty ratio but can increase the output voltage. Furthermore, output voltage and switching stress are also both close. As a result, the given output voltage is considered the duty cycle with a lower value, increasing the converter&#x2019;s efficiency (<xref ref-type="bibr" rid="B12">Hu et al., 2014</xref>; <xref ref-type="bibr" rid="B18">Pathy et al., 2016</xref>; <xref ref-type="bibr" rid="B25">Shen and Chiu, 2016</xref>; <xref ref-type="bibr" rid="B6">Banaei et al., 2019</xref>). Therefore, in order to overcome the above issues, the integrated boost-flyback converter (IBFC) is used in this study. The proposed IBFC effectively stabilizes the PV output voltage.</p>
<p>The maximum power extraction method is a main consideration in PV system electricity generation for improving the effectiveness of non-uniform solar irradiance and shading. Overall, numerous control techniques for a grid-coordinated PV system have been proposed (<xref ref-type="bibr" rid="B7">Bouselham et al., 2017</xref>). The most commonly used MPPT algorithms in both huge and small-sized PV applications are fuzzy logic control, perturb and observe (P&#x26;O), and incremental conductance. It is a difficult task to maintain synchronization, reliability, and overall system behavior in the grid connection (<xref ref-type="bibr" rid="B8">Chandra and Gaur, 2020</xref>; <xref ref-type="bibr" rid="B19">Prasad et al., 2021</xref>). As a consequence, an efficient control mechanism is required to control PQ issues in a PV system. Thus, the effective RBFNN-MPPT is employed to separate more power from the PV system.</p>
<p>Domestic and industrial appliances have seen enormous growth over the past few years. Power systems with defects that cause damage produce their elements as an outcome of the overheating process (<xref ref-type="bibr" rid="B14">Kumar et al., 2018</xref>; <xref ref-type="bibr" rid="B10">Dhanamjayulu et al., 2019</xref>; <xref ref-type="bibr" rid="B13">Khare et al., 2020</xref>; <xref ref-type="bibr" rid="B16">Lal and Thankachan, 2021</xref>). Additionally, there are certain common problems in these power systems, such as harmonic distortion, voltage sag, transient, and spikes (<xref ref-type="bibr" rid="B2">Arjunagi and Patil, 2021</xref>; <xref ref-type="bibr" rid="B17">Parida et al., 2021</xref>; <xref ref-type="bibr" rid="B21">Ramasamy and Perumal, 2021</xref>; <xref ref-type="bibr" rid="B1">Aarthi et al., 2023</xref>). With the help of Spider Monkey optimization CNN, MLI tackles the aforementioned issues and provides a high output voltage. The power quality should be considered to improve the performance based on renewable energy using DC&#x2013;DC converters, and bridge controllers are used to optimize the energy (<xref ref-type="bibr" rid="B15">Kumar et al., 2012</xref>; <xref ref-type="bibr" rid="B26">Shimi et al., 2013</xref>).</p>
<p>By the main considerations of various problems, the power quality disturbances are classified by using neural network classifiers, but they mostly conflict massive distortions that occur and fail to improve the performance of power quality (<xref ref-type="bibr" rid="B24">Saravanakumar and Saravana kumar, 2023</xref>). However, in some cases, the new learning algorithms are used based on the deep learning system by concerning power quality systems [29]. The CNN model makes deforming scaling learning techniques to classify the distortion, but learning weights are mitigated to adjust the bias weight of power quality elements to improve the performance.</p>
<p>In this paper, the efficient RBFNN-based MPPT is deployed for improving the performance of the grid-tied PV system from PQ issues. The IBFC is used to boost the level of voltage in the PV system. By using the SM-CNN control approach for 31-level MLI, the PQ is successfully improved, and this inverter takes parallel processing PQ difficulties to easily manage the power consumption. Hence, the suggested approach is used to provide the system with enhanced PQ and a reduced THD of 2.45%.</p>
</sec>
<sec id="s2">
<title>2 Proposed system</title>
<p>The block diagram of the suggested methodology is demonstrated in <xref ref-type="fig" rid="F1">Figure 1</xref>. The grid coordinated with the solar system consists of the PV array, IBFC, 31-level MLI, and LC filter.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Block diagram of suggested Methodology.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g001.tif"/>
</fig>
<p>For applying the RBFNN-based MPPT algorithm, the highest power is extracted from the PV system, and it is also utilized to strengthen the power conversion efficiency in the solar panel. A single PV panel produces a limited amount of electricity, necessitating the use of a large number of PV panels. The boost-flyback converter is integrated to circumvent this problem, which in turn produces a stable output. The MLI converts the power, in the form of DC into AC, and it is transformed into the grid (i.e., load). The enhanced output from the converter is fed into a 31-level MLI that enhances the PQ and minimizes the lower-order harmonics, with the assistance of SM-CNN.</p>
</sec>
<sec id="s3">
<title>3 Proposed system modeling</title>
<sec id="s3-1">
<title>3.1 Modeling of the PV system</title>
<p>The majority of PV arrays include an inverter to transform DC into alternating current, which may be used to power loads like motors, lights, and other appliances. The individual components of a PV array are normally connected in parallel after the modules are typically connected in series to achieve the necessary voltages. The corresponding circuit diagram for a PV cell is shown in <xref ref-type="fig" rid="F2">Figure 2</xref>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Circuit diagram for PV cell.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g002.tif"/>
</fig>
<p>A current source in parallel with a diode models an ideal. Nevertheless, no solar cell is perfect, so shunt and series resistances are included in the model, as illustrated in the PV cell schematic above. <inline-formula id="inf1">
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</sec>
<sec id="s3-2">
<title>3.2 Model of the radial basis function neural network-based MPPT technique</title>
<p>
<xref ref-type="fig" rid="F3">Figure 3</xref> demonstrates the architecture for the RBFNN-based MPPT algorithm. The proposed RBFNN-MPPT is a three-layer network with a hidden layer, input layer, and output layer.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>RBFNN-based MPPT algorithm.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g003.tif"/>
</fig>
<p>It is an algorithm for supervised learning, which is employed to train multi-layer activation functions. When a specific set of inputs (power) is applied to the RBFNN-based MPPT technique, it produces the expected output (duty cycle) by fine-tuning its weights. Using PV module power and converter duty cycle as input variables and irradiance variations as the output variables, the RBFNN is trained. The parameters used in the RBFNN training are listed in <xref ref-type="table" rid="T1">Table 1</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Parameter specification.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Parameter</th>
<th align="left">RBFNN</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Input data</td>
<td align="left">Power and PV</td>
</tr>
<tr>
<td align="left">Target data</td>
<td align="left">Duty cycle, D</td>
</tr>
<tr>
<td align="left">Training function</td>
<td align="left">&#x201c;trainlm&#x201d;</td>
</tr>
<tr>
<td align="left">Hidden layer function</td>
<td align="left">Radial basis &#x201c;radbas&#x201d;</td>
</tr>
<tr>
<td align="left">MSE performance</td>
<td align="left">0.0121</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Steps for the RBFNN</p>
<p>
<statement content-type="step" id="Step_1">
<label>Step 1:</label>
<p>Generation&#x2009;of&#x2009;random&#x2009;weights&#x2009;to&#x2009;small&#x2009;random&#x2009;values&#x2009;to&#x2009;make&#x2009;sure&#x2009;t&#x2009;hat&#x2009;the&#x2009;network&#x2009;is unsaturated&#x2009;by&#x2009;large&#x2009;weight&#x2009;value.</p>
</statement>
</p>
<p>
<statement content-type="step" id="Step_2">
<label>Step 2:</label>
<p>A&#x2009;training&#x2009;pair&#x2009;from&#x2009;the&#x2009;training&#x2009;set&#x2009;is&#x2009;selected</p>
</statement>
</p>
<p>
<statement content-type="step" id="Step_3">
<label>Step 3:</label>
<p>The&#x2009;input&#x2009;vector&#x2009;to&#x2009;the&#x2009;network&#x2009;input&#x2009;is&#x2009;applied</p>
</statement>
</p>
<p>
<statement content-type="step" id="Step_4">
<label>Step 4:</label>
<p>The&#x2009;network&#x2009;output&#x2009;is&#x2009;calculated</p>
</statement>
</p>
<p>
<statement content-type="step" id="Step_5">
<label>Step 5:</label>
<p>Error&#x2009;is&#x2009;computed&#x2009;as&#x2009;the&#x2009;subtraction&#x2009;between&#x2009;the&#x2009;network&#x2009;output&#x2009;and&#x2009;desired&#x2009;output.</p>
</statement>
</p>
<p>
<statement content-type="step" id="Step_6">
<label>Step&#x2009;6:</label>
<p>Network&#x2009;weights&#x2009;are&#x2009;adjusted&#x2009;in&#x2009;order&#x2009;to&#x2009;minimize&#x2009;the&#x2009;error.</p>
</statement>
</p>
<p>
<statement content-type="step" id="Step_7">
<label>Step&#x2009;7:</label>
<p>Return&#x2009;to steps&#x2009;2-6&#x2009;for&#x2009;the individual&#x2009;input-output&#x2009;pair&#x2009;of&#x2009;the training&#x2009;set&#x2009;until&#x2009;the&#x2009;error&#x2009;for&#x2009;the&#x2009;whole&#x2009;system&#x2009;is&#x2009;tolerabley.</p>
<p>The RBFNN&#x2019;s hidden layer has unique activation functions including Gaussian, multi-quadratics, and inverse multiquadratics. When compared to the traditional BPNN, the RBFNN is a better activation function with reduced distance from function establishments.</p>
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</p>
</statement>
</p>
<sec id="s3-2-1">
<title>3.2.1 Performance testing</title>
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<p>
<xref ref-type="table" rid="T2">Table 2</xref> represents the parameter specification for RBFNN MPPT techniques. The highest power attained from the PV system is enhanced with the advisable IBFC, which is employed to convert the PV output voltage into an AC form with higher efficiency and low switching losses.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Modes of operation.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Mode</th>
<th align="left">Conducting switches and diode</th>
<th align="left">Output voltage</th>
<th align="left">Mode</th>
<th align="left">Conducting switches and diode</th>
<th align="left">Output voltage</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">1</td>
<td align="left">S1, D2, D3, D4, T1, and T2</td>
<td align="left">6 V</td>
<td align="left">1</td>
<td align="left">S1, D2, D3, D4, T3, and T4</td>
<td align="left">-6 V</td>
</tr>
<tr>
<td align="left">2</td>
<td align="left">S2, D1, D3, D4, T1, and T2</td>
<td align="left">12 V</td>
<td align="left">2</td>
<td align="left">S2, D1, D3, D4, T3, and T4</td>
<td align="left">&#x2212;12 V</td>
</tr>
<tr>
<td align="left">3</td>
<td align="left">S1, S2, D3, D4, T1, and T2</td>
<td align="left">18 V</td>
<td align="left">3</td>
<td align="left">S1, S2, D3, D4, T3, and T4</td>
<td align="left">&#x2212;18 V</td>
</tr>
<tr>
<td align="left">4</td>
<td align="left">S3, D1, D2, D4, T1, and T2</td>
<td align="left">24 V</td>
<td align="left">4</td>
<td align="left">S3, D1, D2, D4, T3, and T4</td>
<td align="left">&#x2212;24 V</td>
</tr>
<tr>
<td align="left">5</td>
<td align="left">S1, S3, D2, D4, T1, and T2</td>
<td align="left">30 V</td>
<td align="left">5</td>
<td align="left">S1, S3, D2, D4, T3, and T4</td>
<td align="left">&#x2212;30 V</td>
</tr>
<tr>
<td align="left">6</td>
<td align="left">S2, S3, D1, D4, T1, and T2</td>
<td align="left">36 V</td>
<td align="left">6</td>
<td align="left">S2, S3, D1, D4, T3, and T4</td>
<td align="left">&#x2212;36 V</td>
</tr>
<tr>
<td align="left">7</td>
<td align="left">S<sub>1</sub>, S<sub>2</sub>, S<sub>3</sub>, D<sub>4</sub>, T<sub>1</sub>, and T<sub>2</sub>
</td>
<td align="left">42 V</td>
<td align="left">7</td>
<td align="left">S1, S2, S3, D4, T3, and T4</td>
<td align="left">&#x2212;42 V</td>
</tr>
<tr>
<td align="left">8</td>
<td align="left">S4, D1, D2, D3, T1, and T2</td>
<td align="left">48 V</td>
<td align="left">8</td>
<td align="left">S4, D1, D2, D3, T3, and T4</td>
<td align="left">&#x2212;48 V</td>
</tr>
<tr>
<td align="left">9</td>
<td align="left">S1, S4, D2, D3, T1, and T2</td>
<td align="left">54 V</td>
<td align="left">9</td>
<td align="left">S1, S4, D2, D3, T3, and T4</td>
<td align="left">&#x2212;54 V</td>
</tr>
<tr>
<td align="left">10</td>
<td align="left">S2, S4, D1, D3, T1, and T2</td>
<td align="left">60 V</td>
<td align="left">10</td>
<td align="left">S2, S4, D1, D3, T3, and T4</td>
<td align="left">&#x2212;60 V</td>
</tr>
<tr>
<td align="left">11</td>
<td align="left">S1, S2, S, D3, T1, and T<sub>2</sub>
</td>
<td align="left">66 V</td>
<td align="left">11</td>
<td align="left">S1, S2, S4, D3, T3, and T4</td>
<td align="left">&#x2212;66V</td>
</tr>
<tr>
<td align="left">12</td>
<td align="left">S3, S4, D1, D2, T1, and T2</td>
<td align="left">72 V</td>
<td align="left">12</td>
<td align="left">S3, S4, D1, D2, T3, and T4</td>
<td align="left">&#x2212;72 V</td>
</tr>
<tr>
<td align="left">13</td>
<td align="left">S1, S3, S4, D2, T1, and T2</td>
<td align="left">78</td>
<td align="left">13</td>
<td align="left">S1, S3, S4, D2, T3, and T4</td>
<td align="left">&#x2212;78 V</td>
</tr>
<tr>
<td align="left">14</td>
<td align="left">S2, S3, S4, D1, T1, and T2</td>
<td align="left">84 V</td>
<td align="left">14</td>
<td align="left">S2, S3, S4, D1, T3, and T4</td>
<td align="left">&#x2212;84 V</td>
</tr>
<tr>
<td align="left">15</td>
<td align="left">S1, S2, S3, S4, T1, and T2</td>
<td align="left">90 V</td>
<td align="left">15</td>
<td align="left">S1, S2, S3, S4, T3, and T4</td>
<td align="left">&#x2212;90 V</td>
</tr>
</tbody>
</table>
</table-wrap>
<sec id="s3-2-1-1">
<title>3.2.1.1 Modeling OF IBFC</title>
<p>
<xref ref-type="fig" rid="F1">Figure 1</xref> shows that the IBFC shares the power IGBT switch and the inductor to integrate a boost and flyback converter.</p>
<p>
<inline-graphic xlink:href="fenrg-12-1264157-fx1.tif"/>
</p>
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</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> runs continuously and stays above 0 throughout a switching cycle in the continuous conduction mode (CCM). The operation of the IBFC can be divided into stages.</p>
</sec>
<sec id="s3-2-1-2">
<title>3.2.1.2 Stage 1</title>
<p>While <inline-formula id="inf43">
<mml:math id="m49">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>W</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is activated, <inline-formula id="inf44">
<mml:math id="m50">
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf45">
<mml:math id="m51">
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are reverse-biased. <inline-formula id="inf46">
<mml:math id="m52">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is used to power the linked inductor&#x2019;s primary winding, <inline-formula id="inf47">
<mml:math id="m53">
<mml:mrow>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>m</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> increases linearly, and <inline-formula id="inf48">
<mml:math id="m54">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> stores the energy. The linked inductor&#x2019;s primary and secondary currents, <inline-formula id="inf49">
<mml:math id="m55">
<mml:mrow>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf50">
<mml:math id="m56">
<mml:mrow>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, respectively, are both 0 since D2 is reverse-biased. The load resistance, <inline-formula id="inf51">
<mml:math id="m57">
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, discharges <inline-formula id="inf52">
<mml:math id="m58">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf53">
<mml:math id="m59">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> throughout this time, supplying the load current<bold>.</bold>
</p>
</sec>
<sec id="s3-2-1-3">
<title>3.2.1.3 Stage 2</title>
<p>
<xref ref-type="fig" rid="F4">Figure 4</xref> when <inline-formula id="inf54">
<mml:math id="m60">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>W</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is disabled, <inline-formula id="inf55">
<mml:math id="m61">
<mml:mrow>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>m</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> continues to flow in the same direction by compelling <inline-formula id="inf56">
<mml:math id="m62">
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf57">
<mml:math id="m63">
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> to conduct. During this time, the energy held in <inline-formula id="inf58">
<mml:math id="m64">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is released to charge <inline-formula id="inf59">
<mml:math id="m65">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf60">
<mml:math id="m66">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> as <inline-formula id="inf61">
<mml:math id="m67">
<mml:mrow>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>m</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> linearly diminishes<bold>.</bold>
</p> <fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>IBFC.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g004.tif"/>
</fig>
<p>With the use of this approximation, the current waveform analysis and device ratings, such as <inline-formula id="inf62">
<mml:math id="m68">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>W</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, are made easier.</p>
<p>The following equation represents the voltage gain of the IBFC as follows:<disp-formula id="e7">
<mml:math id="m69">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>O</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>n</mml:mi>
<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>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
<disp-formula id="e8">
<mml:math id="m70">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>O</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>n</mml:mi>
<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:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
</p>
<p>where <inline-formula id="inf63">
<mml:math id="m71">
<mml:mrow>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the duty cycle of the <inline-formula id="inf64">
<mml:math id="m72">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>W</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf65">
<mml:math id="m73">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the linked inductor&#x2019;s turn ratio. By modifying the duty ratio <inline-formula id="inf66">
<mml:math id="m74">
<mml:mrow>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> of the switch, the average output voltage of the IBFC is changed.</p>
</sec>
</sec>
<sec id="s3-2-2">
<title>3.2.2 Modeling of the 31-level MLI</title>
<p>Asymmetric semiconductor devices using the same voltage sources and quantity can also produce high output levels when compared to their symmetric counterparts. The MLI structure, constructed with an H-bridge inverter circuit defined as the polarity generation circuit and an asymmetric fundamental circuit called as the level generator unit, is illustrated in <xref ref-type="fig" rid="F5">Figure 5</xref>. Switches in the polarity generation circuit, especially contrasted to other switches in the level generation unit, are under more stress<bold>.</bold>
</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Proposed MLI.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g005.tif"/>
</fig>
<p>The circuit contains an equal number of driver circuits and IGBTs as all of its semiconductor switching components are positioned in the same direction. The switching losses in a multilevel inverter circuit depend on three different parameters: switching frequency, current, and blocking voltage. The locations of each and every switch in the level generation unit are displayed in <xref ref-type="table" rid="T3">Table 3</xref>. A total of 15 levels are generated using the level generation units <inline-formula id="inf67">
<mml:math id="m75">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and the polarity generation units <inline-formula id="inf68">
<mml:math id="m76">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf69">
<mml:math id="m77">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Switching OFF <inline-formula id="inf70">
<mml:math id="m78">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> results in the 0 level. Half cycles, both positive and negative, are also symmetrical.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Design parameter.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Parameter</th>
<th align="center">Specification</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td colspan="2" align="center">Solar PV system</td>
</tr>
<tr>
<td align="center">Series-connected solar PV cells</td>
<td align="center">
<inline-formula id="inf71">
<mml:math id="m79">
<mml:mrow>
<mml:mn>36</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="center">Open circuit voltage</td>
<td align="center">
<inline-formula id="inf72">
<mml:math id="m80">
<mml:mrow>
<mml:mn>12</mml:mn>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="center">Short circuit current</td>
<td align="center">
<inline-formula id="inf73">
<mml:math id="m81">
<mml:mrow>
<mml:mn>8.33</mml:mn>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="center">Peak power</td>
<td align="center">10 <inline-formula id="inf74">
<mml:math id="m82">
<mml:mrow>
<mml:mi>K</mml:mi>
<mml:mi>W</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and 10 panels</td>
</tr>
<tr>
<td colspan="2" align="center">Integrated boost-flyback</td>
</tr>
<tr>
<td align="center">
<inline-formula id="inf75">
<mml:math id="m83">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#x26;</mml:mo>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">
<inline-formula id="inf76">
<mml:math id="m84">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>350</mml:mn>
<mml:mi>u</mml:mi>
<mml:mi>H</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>&#x2a;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>350</mml:mn>
<mml:mi>u</mml:mi>
<mml:mi>H</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>2</mml:mn>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="center">&#x2022; <inline-formula id="inf77">
<mml:math id="m85">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#x26;</mml:mo>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">&#x2022; <inline-formula id="inf78">
<mml:math id="m86">
<mml:mrow>
<mml:mn>47</mml:mn>
<mml:mi>u</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="center">&#x2022; <inline-formula id="inf79">
<mml:math id="m87">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mo>&#x26;</mml:mo>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:mi>o</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">&#x2022; <inline-formula id="inf80">
<mml:math id="m88">
<mml:mrow>
<mml:mn>180</mml:mn>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="center">&#x2022; <inline-formula id="inf81">
<mml:math id="m89">
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">&#x2022; <inline-formula id="inf82">
<mml:math id="m90">
<mml:mrow>
<mml:mn>470</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>u</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>As an illustration, the switches <inline-formula id="inf83">
<mml:math id="m91">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are turned ON, and state 3 of the diodes <inline-formula id="inf84">
<mml:math id="m92">
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf85">
<mml:math id="m93">
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are forward-biased. In the positive half-cycle, <inline-formula id="inf86">
<mml:math id="m94">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>O</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is obtained. This method is repeated for each additional state to achieve the output voltage values.</p>
<p>In a positive cycle, the H-bridge inverter&#x2019;s switches <inline-formula id="inf87">
<mml:math id="m95">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf88">
<mml:math id="m96">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are turned <inline-formula id="inf89">
<mml:math id="m97">
<mml:mrow>
<mml:mi>O</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, while <inline-formula id="inf90">
<mml:math id="m98">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf91">
<mml:math id="m99">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are turned <inline-formula id="inf92">
<mml:math id="m100">
<mml:mrow>
<mml:mi>O</mml:mi>
<mml:mi>F</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. <inline-formula id="inf93">
<mml:math id="m101">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf94">
<mml:math id="m102">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2002;</mml:mtext>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are turned <inline-formula id="inf95">
<mml:math id="m103">
<mml:mrow>
<mml:mi>O</mml:mi>
<mml:mi>F</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, while <inline-formula id="inf96">
<mml:math id="m104">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf97">
<mml:math id="m105">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are turned <inline-formula id="inf98">
<mml:math id="m106">
<mml:mrow>
<mml:mi>O</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> during the negative cycle. The following <xref ref-type="table" rid="T3">Table 3</xref> demonstrates the 31-MLI&#x2019;s method of operation.</p>
<p>The circuit is going to operate in mode 1, and the amplitude of 6 V will now be linked to the grid through the inverter switches <inline-formula id="inf99">
<mml:math id="m107">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf100">
<mml:math id="m108">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> during the positive half-cycle when the switches <inline-formula id="inf101">
<mml:math id="m109">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf102">
<mml:math id="m110">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf103">
<mml:math id="m111">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf104">
<mml:math id="m112">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> of the multiplier are switched <inline-formula id="inf105">
<mml:math id="m113">
<mml:mrow>
<mml:mi>O</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. The circuit will transition to mode 2, and the output voltage of 12 V will be accessible at the inverter output when switches <inline-formula id="inf106">
<mml:math id="m114">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf107">
<mml:math id="m115">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> <inline-formula id="inf108">
<mml:math id="m116">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf109">
<mml:math id="m117">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are turned <inline-formula id="inf110">
<mml:math id="m118">
<mml:mrow>
<mml:mi>O</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. Similarly, by turning on the switches <inline-formula id="inf111">
<mml:math id="m119">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf112">
<mml:math id="m120">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf113">
<mml:math id="m121">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> of the multiplier cell in mode 3, the output of 18 V will be made available. The switches are activated in this order until all 15 modes have been used. For negative cycles, the same switching sequence is repeated<bold>.</bold>
</p>
</sec>
<sec id="s3-2-3">
<title>3.2.3 SM optimized CNN</title>
<sec id="s3-2-3-1">
<title>3.2.3.1 CNN</title>
<p>The CNN classifier efficiently differentiates the harmonics with the help of the features including standard deviation, mean, entropy, energy, and log-entropy. The feedforward network of the CNN basically has three layers, such as maximum, pooling, and convolutional layers, which are fully connected. The CNN architecture is illustrated in <xref ref-type="fig" rid="F5">Figure 5</xref>.</p>
<p>The backpropagation method is used to train the parameters. The factor of two values is down-sampled by pooling layers, which is regarded as the down-sampling layer, and the maximum value of the convolutional layer is sent to the next layer. The number of training samples and times is reduced by this proposed strategy. These samples are carried on to the following layer, which is fully connected and has multiple hidden layers. Weights are used to connect the hidden and output layers, the final output classifier layer, and the pooled samples to a fully connected network. The forward and backpropagation are the two steps of the training process, where forward propagation provides the actual input data and backpropagation updates the training parameters.</p>
<p>Using all of the input coefficients has a negative influence on the classification accuracy every time. As a result, the chosen coefficients mean <inline-formula id="inf114">
<mml:math id="m122">
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
</inline-formula>, standard deviation <inline-formula id="inf115">
<mml:math id="m123">
<mml:mrow>
<mml:mfenced open="(" close="" separators="|">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
</inline-formula>), energy (<inline-formula id="inf116">
<mml:math id="m124">
<mml:mrow>
<mml:mfenced open="" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
</inline-formula>, entropy (<inline-formula id="inf117">
<mml:math id="m125">
<mml:mrow>
<mml:mfenced open="" close=")" separators="|">
<mml:mrow>
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
</inline-formula>, and log-energy entropy <inline-formula id="inf118">
<mml:math id="m126">
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>E</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
</inline-formula> are eliminated to reduce complexity and improve classification accuracy. The primary component expressions are described as follows:</p>
<p>Mean<disp-formula id="e9">
<mml:math id="m127">
<mml:mrow>
<mml:msub>
<mml:mi>M</mml:mi>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mstyle displaystyle="true">
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>N</mml:mi>
</mml:msubsup>
</mml:mstyle>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>
</p>
<p>Energy<disp-formula id="e10">
<mml:math id="m128">
<mml:mrow>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>N</mml:mi>
</mml:msubsup>
</mml:mstyle>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mfenced open="|" close="|" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>
</p>
<p>Standard deviation<disp-formula id="e11">
<mml:math id="m129">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mstyle displaystyle="true">
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>N</mml:mi>
</mml:msubsup>
</mml:mstyle>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:msup>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>
</p>
<p>Entropy<disp-formula id="e12">
<mml:math id="m130">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mstyle displaystyle="true">
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>N</mml:mi>
</mml:msubsup>
</mml:mstyle>
<mml:msup>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>log</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msup>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>
</p>
<p>Log-energy entropy<disp-formula id="e13">
<mml:math id="m131">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>E</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>N</mml:mi>
</mml:msubsup>
</mml:mstyle>
<mml:mrow>
<mml:mi>log</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msup>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(13)</label>
</disp-formula>
</p>
<p>In this paper, the reference and real signals are transmitted to the CNN classifier to reduce the harmonics and provide reference power to the PWM generator that produces gating pulses for the 31-level MLI. Furthermore, the CNN has to be optimized to enhance the control performance of the MLI.</p>
</sec>
</sec>
</sec>
</sec>
<sec id="s4">
<title>4 SMO algorithm</title>
<p>The SMO methodology is a metaheuristic method that uses fission and fusion swarm intelligence for foraging. This algorithm is inspired from the behavior of spider monkey. The following are six iterative collaborative phases, and the SMO method relies on trial and error.</p>
<sec id="s4-1">
<title>4.1 Initializing</title>
<p>The SMO initializes each <inline-formula id="inf119">
<mml:math id="m132">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mi>p</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> using Eq. <xref ref-type="disp-formula" rid="e14">14</xref>
<disp-formula id="e14">
<mml:math id="m133">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>U</mml:mi>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(14)</label>
</disp-formula>
</p>
<p>where <inline-formula id="inf120">
<mml:math id="m134">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the <inline-formula id="inf121">
<mml:math id="m135">
<mml:mrow>
<mml:mi>q</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dimension&#x2019;s <inline-formula id="inf122">
<mml:math id="m136">
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> for random, the upper and lower bounds of <inline-formula id="inf123">
<mml:math id="m137">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mi>p</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> of <inline-formula id="inf124">
<mml:math id="m138">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf125">
<mml:math id="m139">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in the <inline-formula id="inf126">
<mml:math id="m140">
<mml:mrow>
<mml:mi>q</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> direction, respectively. The number of <inline-formula id="inf127">
<mml:math id="m141">
<mml:mrow>
<mml:mi>U</mml:mi>
<mml:mi>R</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is between [0, 1], with a uniform distribution.</p>
</sec>
<sec id="s4-2">
<title>4.2 Local leader phase)</title>
<p>
<inline-formula id="inf128">
<mml:math id="m142">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> includes the historical occurrences of local group members and leaders to shift the place. If the new position value is higher than the past one, the <inline-formula id="inf129">
<mml:math id="m143">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> location of the <inline-formula id="inf130">
<mml:math id="m144">
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> local group is updated.<disp-formula id="e15">
<mml:math id="m145">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>w</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>U</mml:mi>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>U</mml:mi>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(15)</label>
</disp-formula>
</p>
<p>The local group <inline-formula id="inf131">
<mml:math id="m146">
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> of the <inline-formula id="inf132">
<mml:math id="m147">
<mml:mrow>
<mml:mi>q</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dimension is selected for <inline-formula id="inf133">
<mml:math id="m148">
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. <inline-formula id="inf134">
<mml:math id="m149">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is random and is represented as <inline-formula id="inf135">
<mml:math id="m150">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, such that <inline-formula id="inf136">
<mml:math id="m151">
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. <inline-formula id="inf137">
<mml:math id="m152">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the <inline-formula id="inf138">
<mml:math id="m153">
<mml:mrow>
<mml:mi>q</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dimension of the <inline-formula id="inf139">
<mml:math id="m154">
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> local group leader location.</p>
</sec>
<sec id="s4-3">
<title>4.3 Global leader phase</title>
<p>Following LLP, the GLP is initiated to update the location. Equation <xref ref-type="disp-formula" rid="e16">16</xref> provides the location update as follows:<disp-formula id="e16">
<mml:math id="m155">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>w</mml:mi>
<mml:mi>p</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>U</mml:mi>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>U</mml:mi>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>p</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(16)</label>
</disp-formula>
</p>
<p>where <inline-formula id="inf140">
<mml:math id="m156">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>l</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the <inline-formula id="inf141">
<mml:math id="m157">
<mml:mrow>
<mml:mi>q</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> dimension of the GLP and <inline-formula id="inf142">
<mml:math id="m158">
<mml:mrow>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is a randomly chosen index between <inline-formula id="inf143">
<mml:math id="m159">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
</sec>
<sec id="s4-4">
<title>4.4 Global leader learning phase</title>
<p>By utilizing the strategy of greedy selection, GLL is updated. The new SM depends on the country with the fittest people in the world. If updates are discovered, the global limit count (GLC) is increased and the value of the global leader is applied to the optimum setting.</p>
</sec>
<sec id="s4-5">
<title>4.5 Local leader learning phase</title>
<p>The <inline-formula id="inf144">
<mml:math id="m160">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> location is updated with the position of the local leader for optimal fitness in a specific group. The ideal location is given to the local leader. If no updates are found, an increment of 1 is applied to the limit count.</p>
</sec>
<sec id="s4-6">
<title>4.6 Local leader decision phase</title>
<p>When a local leader does not update its location or outdated from global and local leaders depending on <inline-formula id="inf145">
<mml:math id="m161">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> using Eq. <xref ref-type="disp-formula" rid="e17">17</xref>, the candidates of the local group change the position at a random step 1.<disp-formula id="e17">
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</p>
</sec>
<sec id="s4-7">
<title>4.7 Global leader decision phase</title>
<p>In accordance with GLD, the population is split into smaller groups. For the global leader limit, the location value is unchanged. The dividing process starts after there are as many groups (MG) as possible. For the newly created group, a local leader is selected during each cycle. It does not modify its position until the allowable maximum is reached, at which point it tries to merge all of the permitted groups into a single group. The maximum number of permitted groups is established.</p>
</sec>
<sec id="s4-8">
<title>4.8 Gaussian mutation</title>
<p>In complex iterative optimization situations, the SMO approach is imprisoned in the local best value. The algorithm solution value does not vary throughout the iteration. This approach leaves the location of the local optimum, adds GM and random perturbation, and then extends to execute the algorithm in order to enhance the algorithm probability and algorithm deficiency. Equation <xref ref-type="disp-formula" rid="e18">18</xref> provides the formula for the Gaussian mutation.<disp-formula id="e18">
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<label>(18)</label>
</disp-formula>
</p>
<p>where <italic>rand</italic> represents a random number between [0, 1], and <inline-formula id="inf146">
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</p>
<p>where <inline-formula id="inf147">
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</inline-formula> stands for the mean value. With the support of SMO, the CNN parameters are optimally tuned for the generation of improved THD and unity power factor.</p>
</sec>
</sec>
<sec sec-type="results|discussion" id="s5">
<title>5 Results and Discussion</title>
<p>This proposed work aimed at the improvement of an efficient spider monkey optimization CNN, which is deployed to improve the PQ in the grid-tied PV system. In addition, the RBFFN-based MPPT algorithm is employed to track the highest power from the PV system. The suggested control technique is verified using the MATLAB platform. <xref ref-type="table" rid="T4">Table 4</xref> represents the parameter specification for the proposed system.</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Efficiency analysis.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Analysis</th>
<th colspan="4" align="center">Methods</th>
</tr>
<tr>
<th align="left">P &#x26; O controller (<xref ref-type="bibr" rid="B15">Kumar et al., 2012</xref>)</th>
<th align="left">MPPT scheme (<xref ref-type="bibr" rid="B26">Shimi et al., 2013</xref>)</th>
<th align="left">CS-HHO-based MPPT scheme</th>
<th align="left">RBFNN-MPPT</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Total input power (W)</td>
<td align="left">162.56</td>
<td align="left">162.51</td>
<td align="left">162.59</td>
<td align="left">162.63</td>
</tr>
<tr>
<td align="left">Output power (W)</td>
<td align="left">156.73</td>
<td align="left">155.71</td>
<td align="left">157.12</td>
<td align="left">159.65</td>
</tr>
<tr>
<td align="left">Efficiency (%)</td>
<td align="left">96.40%</td>
<td align="left">95.21%</td>
<td align="left">96.81%</td>
<td align="left">97.2%</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>A temperature variation of 0.1 s is introduced, as shown in <xref ref-type="fig" rid="F6">Figure 6A</xref>, to calculate the efficiency of the suggested technique in handling the intermittent nature of the PV system. At this same moment, the temperature suddenly increases from 25&#xb0;C to 35&#xb0;C. Similar to how temperature varies, <xref ref-type="fig" rid="F6">Figure 6B</xref> shows that solar irradiation varies from 800&#xa0;W/sq.m to 1000&#xa0;W/sq.m.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>CNN Architecture.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g006.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F7">Figure 7</xref> displays the solar panel voltage and currents as a variation in temperature. Due to operating conditions, the voltage is suddenly increased from 58 V to 72 V; similarly, the current increases to 15 A, afterward, the current remains constant at 0.1 s.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>
<bold>(A)</bold> Temperature and <bold>(B)</bold> irradiation waveforms for the solar panel.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g007.tif"/>
</fig>
<p>The waveform that represents the voltage output of the IBFC is presented in <xref ref-type="fig" rid="F8">Figure 8A</xref>. From that waveform, the voltage of 300 V is achieved at 0.2&#xa0;s, and <xref ref-type="fig" rid="F8">Figure 8B</xref> shows output current variations until 0.1&#xa0;s, after which the stable value of 2.5 A is maintained.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>
<bold>(A)</bold> Voltage and <bold>(B)</bold> current waveforms for the solar panel.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g008.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F9">Figure 9</xref> illustrates that the input DC voltage is obtained from the integrated boost-flyback converter. VDC1 and VDC2 with the constant value of 15 V and 16 V, respectively, are maintained. Likewise, <xref ref-type="fig" rid="F10">Figure 10</xref> shows the DC voltage VDC3 and VDC4 with the stable value of 52 V and 102 V are maintained.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>
<bold>(A)</bold> Voltage and <bold>(B)</bold> current output of IBFC.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g009.tif"/>
</fig>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Input <bold>(A)</bold> VDC1 &#x0026; <bold>(B)</bold> VDC2 waveform.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g010.tif"/>
</fig>
<p>
<inline-graphic xlink:href="fenrg-12-1264157-fx2.tif"/>
</p>
<p>
<xref ref-type="fig" rid="F10">Figure 10</xref> shows the load RMS voltage waveform. From that graph, the load RMS voltage 175 V is accomplished at 0.02s.</p>
<p>From the waveform representation shown in <xref ref-type="fig" rid="F11">Figure 11</xref>, it is noted that a constant voltage of 230 V is supplied to the grid. Similarly, the grid current value of 4 A is maintained.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Input <bold>(A)</bold> VDC3 &#x0026; <bold>(B)</bold> VDC4 waveforms.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g011.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F12">Figure 12</xref> depicts the waveforms that represent the reactive and real power of grid 1. At 0.03&#xa0;s, the magnitude of real power stabilizes at 520&#xa0;W, and the minimized reactive power is achieved.</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Grids: <bold>(A)</bold> voltage and <bold>(B)</bold> current.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g012.tif"/>
</fig>
<p>
<inline-graphic xlink:href="fenrg-12-1264157-fx3.tif"/>
</p>
<p>The waveform of the power factor is shown in <xref ref-type="fig" rid="F13">Figure 13</xref>. Thus, a power factor of 1 is attained, denoting that the suggested system operates with efficiency and dependability.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Real and reactive power waveforms.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g013.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F14">Figure 14</xref> shows the output current and voltage waveform of the 31-level MLI. Here, the voltage of 220 V is maintained as shown in <xref ref-type="fig" rid="F14">Figure 14A,</xref> and the load current of 4.5 A is achieved, as shown in <xref ref-type="fig" rid="F14">Figure 14B</xref>.</p>
<fig id="F14" position="float">
<label>FIGURE 14</label>
<caption>
<p>31-level output <bold>(A)</bold> voltage and <bold>(B)</bold> load current waveforms.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g014.tif"/>
</fig>
<p>
<inline-graphic xlink:href="fenrg-12-1264157-fx4.tif"/>
</p>
<p>
<xref ref-type="fig" rid="F15">Figure 15</xref> indicates the proposed IBFC converter&#x2019;s THD value as 2.45%, which has very low harmonics when compared to that of other approaches.</p>
<fig id="F15" position="float">
<label>FIGURE 15</label>
<caption>
<p>THD waveform.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g015.tif"/>
</fig>
<p>
<xref ref-type="table" rid="T5">Table 5</xref> compares several power tracking methods, and <xref ref-type="fig" rid="F16">Figure 16</xref> shows the corresponding graphs with similar comparisons. As the RBFNN-based MPPT efficiency is 98.80%, <xref ref-type="table" rid="T5">Table 5</xref> and <xref ref-type="fig" rid="F17">Figure 17</xref> demonstrate the various measures, including mean, median, and standard deviation. The considered factors strongly show that the suggested method outperforms the existing methods in terms of the considered factors.</p>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Statistical analysis.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Methods</th>
<th align="left">ANN</th>
<th align="left">CS-RNN</th>
<th align="left">SM-CNN</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Mean</td>
<td align="left">1.5625</td>
<td align="left">0.5136</td>
<td align="left">0.4342</td>
</tr>
<tr>
<td align="left">Median</td>
<td align="left">1.8500</td>
<td align="left">0.2175</td>
<td align="left">0.1702</td>
</tr>
<tr>
<td align="left">Standard deviation</td>
<td align="left">0.9254</td>
<td align="left">0.4102</td>
<td align="left">0.3152</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F16" position="float">
<label>FIGURE 16</label>
<caption>
<p>Efficiency analysis.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g016.tif"/>
</fig>
<fig id="F17" position="float">
<label>FIGURE 17</label>
<caption>
<p>Statistical analysis.</p>
</caption>
<graphic xlink:href="fenrg-12-1264157-g017.tif"/>
</fig>
</sec>
<sec sec-type="conclusion" id="s6">
<title>6 Conclusion</title>
<p>We conclude that the proposed system improves high performance to achieve efficiency. The MLIs have been heavily used to improve the PQ of PV systems. The requirement for a large number of components, increased standing voltage, and high harmonic content in the output cause a significant impact on the efficiency of a standard MLI. In this work, a control approach called Spider Monkey Optimization CNN is used with an appropriate level of inverter (31 level) to lessen PQ problems to solve the mitigations. The integrated boost-flyback converter is employed, in order to stabilize the output voltage of the PV panel to achieve the performance. Intended for separating the highest power from the solar PV system, the RBFNN-based MPPT technique is used, and this achieves an efficiency of 97.2%, which is the highest efficiency compared to that of other control methods. The proposed MLI is produced with an enhanced power factor and a lower THD value of 2.45%, and the influence of harmonics is also negligible.</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>PA: writing&#x2013;original draft. SK: writing&#x2013;original draft.</p>
</sec>
<sec sec-type="funding-information" id="s9">
<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="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>
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