<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.4 20241031//EN" "JATS-journalpublishing1-4.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.4" xml:lang="en">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">sgre</journal-id>
      <journal-title-group>
        <journal-title>Smart Grid and Renewable Energy</journal-title>
      </journal-title-group>
      <issn pub-type="epub">2151-4844</issn>
      <issn pub-type="ppub">2151-481X</issn>
      <publisher>
        <publisher-name>Scientific Research Publishing</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.4236/sgre.2026.175006</article-id>
      <article-id pub-id-type="publisher-id">sgre-151517</article-id>
      <article-categories>
        <subj-group>
          <subject>Article</subject>
        </subj-group>
        <subj-group>
          <subject>Earth</subject>
          <subject>Environmental Sciences</subject>
          <subject>Engineering</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Design and Optimization of a PV-Diesel Hybrid System with Storage for Supplying an Off-Grid Site in Burkina Faso: Integration of a Smart Grid</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <contrib-id contrib-id-type="orcid">0009-0005-4639-7626</contrib-id>
          <name name-style="western">
            <surname>Guengané</surname>
            <given-names>Hassime</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Ouédrogo</surname>
            <given-names>Salifou</given-names>
          </name>
          <xref ref-type="aff" rid="aff2">2</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Bado</surname>
            <given-names>Nébon</given-names>
          </name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Dianda</surname>
            <given-names>Boureima</given-names>
          </name>
          <xref ref-type="aff" rid="aff2">2</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Kam</surname>
            <given-names>Sié</given-names>
          </name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Bathiébo</surname>
            <given-names>Dieudonné Joseph</given-names>
          </name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
      </contrib-group>
      <aff id="aff1"><label>1</label> Multidisciplinary Research Laboratory in Engineering Science (LMRSI)/Ecole Polytechnique de Ouagadougou, Burkina Faso </aff>
      <aff id="aff2"><label>2</label> Renewable Thermal Energies Laboratory (LETRE)/Université Joseph KI-ZERBO, Ouagadougou, Burkina Faso </aff>
      <aff id="aff3"><label>3</label> Centre universitaire de Manga, Manga, Burkina Faso </aff>
      <aff id="aff4"><label>4</label> Institut national de Recherche Scientifiques Appliquées et Technologiques (IRSAT/CNRST), Burkina Faso </aff>
      <author-notes>
        <fn fn-type="conflict" id="fn-conflict">
          <p>We declare that we have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.</p>
        </fn>
      </author-notes>
      <pub-date pub-type="epub">
        <day>27</day>
        <month>05</month>
        <year>2026</year>
      </pub-date>
      <pub-date pub-type="collection">
        <month>05</month>
        <year>2026</year>
      </pub-date>
      <volume>17</volume>
      <issue>05</issue>
      <fpage>105</fpage>
      <lpage>129</lpage>
      <history>
        <date date-type="received">
          <day>09</day>
          <month>04</month>
          <year>2026</year>
        </date>
        <date date-type="accepted">
          <day>24</day>
          <month>05</month>
          <year>2026</year>
        </date>
        <date date-type="published">
          <day>27</day>
          <month>05</month>
          <year>2026</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>© 2026 by the authors and Scientific Research Publishing Inc.</copyright-statement>
        <copyright-year>2026</copyright-year>
        <license license-type="open-access">
          <license-p> This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link> ). </license-p>
        </license>
      </permissions>
      <self-uri content-type="doi" xlink:href="https://doi.org/10.4236/sgre.2026.175006">https://doi.org/10.4236/sgre.2026.175006</self-uri>
      <abstract>
        <p>Burkina Faso has a very low rural electrification rate (7.02 % in 2023), a situation exacerbated by a growing population. This work proposes a decentralized electrification solution. The country possesses significant solar potential (5.5 kWh/m<sup>2</sup>/day), which is harnessed here through a PV-Diesel hybrid mini-power plant equipped with a smart management system (Smart Grid). Designed to supply 100 off-grid households, this plant has the dual objective of facilitating production control and minimizing its cost. Sized to meet an average daily demand of 600 kWh/day, the designed plant integrates PV-Diesel generators, a storage system, an inverter, and a Smart Grid. Implementing the smart grid via the HOMER Pro software enabled the optimization of energy production from each plant component. A study of the influence of the plant’s operational parameters on its performance showed that the size of the energy storage and the PV array reduces the operating time of the diesel generator. Furthermore, the solar fraction is more sensitive to the size of the PV array than to that of the batteries, whose influence becomes negligible beyond three days of autonomy. Five scenarios, obtained by removing one or several components from the initial system, were compared based on the Life Cycle Cost (LCC), the initial investment, and the Operation and Maintenance (O&amp;M) costs over 20 years, while integrating pollutant emission abatement costs. The scenario including the PV-Diesel generators, storage, and the inverter proved to be the best compromise, combining economic optimization with environmental preservation.</p>
      </abstract>
      <kwd-group kwd-group-type="author-generated" xml:lang="en">
        <kwd>Rural Electrification</kwd>
        <kwd>PV-Diesel Hybrid Power Plant</kwd>
        <kwd>Smart Grid</kwd>
        <kwd>Energy Efficiency</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec1">
      <title>1. Introduction</title>
      <p>In Burkina Faso, numerous remote localities remain outside the coverage zone of the national electricity grid. The electrification rate in rural areas increased from 2.9% in 2014 to 7.02% in 2023 [<xref ref-type="bibr" rid="B1">1</xref>]. Internationally, conventional energy sources such as gas, oil, and uranium are diminishing due to widespread diffusion and industrial development in recent years [<xref ref-type="bibr" rid="B2">2</xref>]. However, basic socio-economic development cannot be achieved without a reliable and sustainable energy source. In this context, access to electricity in rural areas is imperative for improving the quality of life of populations and fostering economic progress. The rural electrification process in Burkina Faso is built upon a robust framework, namely electricity cooperatives (COOPELs), which serve as a springboard for promoting and popularizing electricity access. COOPELs align with the same dynamic as the “Electricity for All” program implemented by the Electrification Development Fund (FDE) [<xref ref-type="bibr" rid="B3">3</xref>]. Each COOPEL undertakes the tasks of the National Electricity Company of Burkina (SONABEL) at the local level under the technical supervision of the FDE, ensuring production, transmission, supply, maintenance, and billing. Unfortunately, these cooperatives exhibit limitations in both management and service provision. Indeed, cooperatives are forced to implement rolling blackouts because certain days are heavily loaded, and the capacity of the diesel generators does not cover the needs of subscribers [<xref ref-type="bibr" rid="B4">4</xref>].</p>
      <p>It is evident that efficient and effective management of this energy is necessary. Thus, for the most regular production possible, one solution involves hybridizing different types of sources by exploiting multiple renewable sources in a well-managed, well-coordinated, optimized, and efficient manner. Numerous studies have focused on these hybrid systems to master their operating principles and improve their performance. These primarily include PV-Diesel hybrid systems [<xref ref-type="bibr" rid="B5">5</xref>]-[<xref ref-type="bibr" rid="B8">8</xref>], PV-Wind or Wind-Diesel-Storage hybrid systems, or combinations of all three [<xref ref-type="bibr" rid="B9">9</xref>]-[<xref ref-type="bibr" rid="B13">13</xref>]. The solar-wind-geothermal-diesel combination is also a significant solution according to the results obtained by M. Ismail <italic>et al.</italic>[<xref ref-type="bibr" rid="B14">14</xref>]. This approach requires the integration of automatic and electronic control systems, such as Smart Grids, into energy production and distribution vectors. According to S. Balani [<xref ref-type="bibr" rid="B15">15</xref>], a Smart Grid is the integration of a set comprising an electrical network, a communication network, software, and hardware aimed at monitoring, controlling, and managing energy production, distribution, storage, and consumption. Smart Grids therefore differ from current networks in their aspect, operation, mission, and deployment [<xref ref-type="bibr" rid="B16">16</xref>][<xref ref-type="bibr" rid="B17">17</xref>]. The deployment of smart electrical grids targets several objectives: optimizing the integration of decentralized renewable production, reducing consumption peaks by controlling a portion of consumption to adapt it to production [<xref ref-type="bibr" rid="B18">18</xref>]. The communication architecture of the Smart Grid, according to the NIST, groups together seven (07) domains interconnected via an internet network using communication protocols [<xref ref-type="bibr" rid="B19">19</xref>][<xref ref-type="bibr" rid="B20">20</xref>]. Based on the NIST model, the IEEE proposed an architecture allowing centralized management of surplus energy produced by defining a new domain named Distributed Energy Resources (DER) [<xref ref-type="bibr" rid="B21">21</xref>].</p>
      <p>Smart Grids impact an electrical grid at several levels, including the meter, actuators, switching and storage devices, etc. In this work, we aim to develop an electronic platform integrable into the energy management system of a hybrid power plant, consisting of a Diesel generator set and a Photovoltaic (PV) solar plant with energy storage, intended to supply a village in the Centre-Sud region of Burkina Faso not connected to the national electricity grid. This electricity production management system, integrated into the HOMER Pro simulation software, will consider the possibility that the mini-plant could be connected to the national grid. Ultimately, it will enable us to define the optimal production scenario for each system component while reducing the cost per electrical kWh.</p>
    </sec>
    <sec id="sec2">
      <title>2. Materials and Methods</title>
      <sec id="sec2dot1">
        <title>2.1. Study Area: Yakoungou Site</title>
        <fig id="fig1">
          <label>Figure 1</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId17.jpeg?20260527014015" />
        </fig>
        <p>(Exact geographical coordinates, latitude and longitude—11.8088575, 0.5352355999999999. Altitude—288 meters. Source: <ext-link ext-link-type="uri" xlink:href="https://ms.maptons.com/3152998">https://ms.maptons.com/3152998</ext-link>).</p>
        <p><bold>Figure 1.</bold> View of the study site—Yakoungou locality (Garango, Burkina Faso). </p>
        <p>Yakoungou is a locality constituting Sector 1 of Garango, which is not connected to the national electricity grid. Garango is a department and an urban commune in the province of Boulgou, located approximately twenty kilometers from the city of Tenkodogo (the capital of the Nakambé Region of Burkina Faso). <xref ref-type="fig" rid="fig1">Figure 1</xref> presents a view of the site [<xref ref-type="bibr" rid="B22">22</xref>].</p>
        <p>Geographic coordinates: Latitude: 11.8088575; Longitude: 0.5352355999999999 and Altitude: 288 meters.</p>
        <p>Thus, for the realization of the PV solar field:</p>
        <p>the optimal orientation for the photovoltaic solar panels is due south;according to the findings of Amèdédjihundé H. J. H. [<xref ref-type="bibr" rid="B23">23</xref>], the tilt angle “I” of the solar panels will be set equal to the latitude of the site.</p>
      </sec>
      <sec id="sec2dot2">
        <title>2.2. Data Collection</title>
        <p>In this work, we will primarily use statistical data, standards, and previous studies on rural electrification provided by the National Institute of Statistics and Demography (INSD) of Burkina Faso. A considerable effort was made to develop a data collection form to gather the most plausible data possible on the electrical loads necessary for a meaningful and in-depth analysis.</p>
        <p><bold>Site climatic data</bold></p>
        <fig id="fig2">
          <label>Figure 2</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId19.jpeg?20260527014015" />
        </fig>
        <p><bold>Figure 2.</bold> Monthly averages for global horizontal radiation over 22-years (Jul 1983-Jun 2005).</p>
        <fig id="fig3">
          <label>Figure 3</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId20.jpeg?20260527014015" />
        </fig>
        <p><bold>Figure 3.</bold>Monthly averages air temperature over 30-year period (Jan 1984-Dec 2013).</p>
        <p>Climatic data such as solar radiation and temperature are generated directly by the HOMER Pro software using the input geographic coordinates. <xref ref-type="fig" rid="fig2">Figure 2</xref> presents the monthly averages of global horizontal irradiation per square meter per year, calculated over a 22-year period (July 1983-June 2005) [<xref ref-type="bibr" rid="B24">24</xref>]. <xref ref-type="fig" rid="fig3">Figure 3</xref> presents the monthly averages of ambient air temperature, calculated over 30 years (January 1984-December 2013). The annual averages recorded during these periods are 5.66 kWh. (m<sup>−2</sup>·day) for irradiation and 27.65˚C for ambient temperature, respectively. </p>
        <p><bold>Collection of specific energy data from the population</bold></p>
        <p>The analysis of energy needs takes into account all end-use devices whose operation requires electrical energy. These devices are therefore grouped into three categories:</p>
        <p>households: we consider a population of nearly one thousand (1000) inhabitants, distributed across approximately one hundred households, with an estimated connection rate of 65%. Equations 1 and 2 are used to estimate the total energy consumed.</p>
        <disp-formula id="FD1">
          <label>(1)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>a</mml:mi>
                  <mml:mi>p</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>m</mml:mi>
                  <mml:mi>e</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mn>65</mml:mn>
                </mml:mrow>
                <mml:mrow>
                  <mml:mn>100</mml:mn>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <disp-formula id="FD2">
          <label>(2)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>E</mml:mi>
                <mml:mi>j</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>P</mml:mi>
                <mml:mi>u</mml:mi>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:msub>
                <mml:mi>t</mml:mi>
                <mml:mi>u</mml:mi>
              </mml:msub>
              <mml:mo>+</mml:mo>
              <mml:msub>
                <mml:mi>P</mml:mi>
                <mml:mi>v</mml:mi>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:msub>
                <mml:mi>t</mml:mi>
                <mml:mi>v</mml:mi>
              </mml:msub>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p><italic>E</italic><italic><sub>j</sub></italic>: daily energy in Wh; <italic>P</italic><italic><sub>u</sub></italic>, the power of a device in normal operation (W); <italic>P</italic><italic><sub>v</sub></italic>, the power of a device on standby.</p>
        <p>social Needs: these needs primarily concern requirements for public lighting and electricity supply for the school.economic Activities and On-Site Control System Consumption: economic needs mainly concern the requirements of small and medium-sized industrial activities in the locality. These activities are generally centralized in the market area.<bold>Assessment of the average electrical load demand of the locality</bold></p>
        <p>The collected data enabled the determination of the energy requirements for each activity sector and their hourly profiles. The sectors considered are residential, commercial, and services. <xref ref-type="fig" rid="fig4">Figures 4-7</xref> present, respectively, the profile of the instantaneous power demand over one year, the cumulative power demand per hour over a day, the monthly power demand over a year, and the energy demanded by the loads over a full day. </p>
        <p>It is observed that the load’s energy requirements are highly variable over a 24-hour operating day:</p>
        <p>From 12:00 AM to 4:00 AM, the load demand is low (on the order of approximately 5 kWh). This period generally concerns public lighting.At 5:00 AM, the load begins to increase, evolving to nearly 100 kWh around 9:00 AM. The use of high-power electrical equipment such as grain mills is highly probable during this time.The load starts to decrease again from 10:00 AM to a value of about 20 kWh at noon, due to breaks.</p>
        <fig id="fig4">
          <label>Figure 4</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId25.jpeg?20260527014015" />
        </fig>
        <p><bold>Figu</bold><bold>re 4</bold><bold>.</bold> Instantaneous variation of the power demanded by the loads per day and over one year.</p>
        <fig id="fig5">
          <label>Figure 5</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId26.jpeg?20260527014015" />
        </fig>
        <p><bold>Figure 5</bold><bold>.</bold> Profile of the power demanded by the entire site over the course of a day.</p>
        <fig id="fig6">
          <label>Figure 6</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId27.jpeg?20260527014015" />
        </fig>
        <p><bold>Figure 6</bold><bold>.</bold> Profile of the power demanded per day over the course of a year.</p>
        <p>Note that the cumulative load remains significant between 8:00 AM and 12:00 PM because needs such as those of the school, welding workshops, and grain mills are recorded during this period of the day.</p>
        <p>In the afternoon, demand increases again, reaching a peak at 4:00 PM due to a substantial load consisting of the school, mills, welding workshops, and some household needs.The load then decreases, stabilizing at approximately 20 kWh between 7:00 PM and 1:00 AM, as it essentially consists of household needs and public lighting.</p>
        <fig id="fig7">
          <label>Figure 7</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId28.jpeg?20260527014015" />
        </fig>
        <p><bold>Figure 7</bold><bold>.</bold> Profile of the energy demanded over a full day.</p>
        <p><bold>Table 1</bold> summarizes the values of the power demanded and the corresponding energy over one day of operation for all loads in each defined category.</p>
        <p><bold>Table 1.</bold> Summary of power and energy requirements.</p>
        <table-wrap id="tbl1">
          <label>Table 1</label>
          <table>
            <tbody>
              <tr>
                <td>
                </td>
                <td>Power in normal operation (kW)</td>
                <td>Standby power (kW)</td>
                <td>Daily energy (kWh)</td>
              </tr>
              <tr>
                <td>Social needs</td>
                <td>1.12</td>
                <td>0.162</td>
                <td>5.26</td>
              </tr>
              <tr>
                <td>Social expenses</td>
                <td>2.98</td>
                <td>0.015</td>
                <td>32.205</td>
              </tr>
              <tr>
                <td>Economic activities and self-consumption</td>
                <td>58.080</td>
                <td>0</td>
                <td>515.840</td>
              </tr>
              <tr>
                <td>Total</td>
                <td colspan="2">72.432</td>
                <td>600.645</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
      </sec>
      <sec id="sec2dot3">
        <title>2.3. Mathematical Model of the PV/Diesel Hybrid Power Plant</title>
        <p>2.3.1. Description of the Hybrid System</p>
        <p>The hybrid system under study is composed overall of:</p>
        <p>a photovoltaic (PV) solar generator;a Diesel electric generator;a battery pack;a reversible DC/AC converter that converts direct current and adapts it to supply the DC bus while simultaneously ensuring maximum power point tracking.</p>
        <p>2.3.2. Overall Behavior of the Hybrid System</p>
        <p>The design of a PV/Diesel hybrid system involves determining the optimal values for the peak power of the PV array, the capacity of the batteries, and the power of the Diesel generator. Here, we propose an iterative method for sizing the system’s key parameters.</p>
        <p><bold>Sizing of the PV source</bold></p>
        <p>Usual equations for sizing a PV array:</p>
        <p>Peak power: </p>
        <disp-formula id="FD3">
          <label>(3)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>P</mml:mi>
                <mml:mi>c</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>E</mml:mi>
                    <mml:mrow>
                      <mml:mi>c</mml:mi>
                      <mml:mi>j</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>k</mml:mi>
                    <mml:mi>p</mml:mi>
                  </mml:msub>
                  <mml:mo>×</mml:mo>
                  <mml:msub>
                    <mml:mi>E</mml:mi>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Average cell operating temperature: </p>
        <disp-formula id="FD4">
          <label>(4)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>T</mml:mi>
                <mml:mi>c</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>T</mml:mi>
                <mml:mi>α</mml:mi>
              </mml:msub>
              <mml:mo>+</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>E</mml:mi>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                  <mml:mo>×</mml:mo>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>T</mml:mi>
                        <mml:mrow>
                          <mml:mi>n</mml:mi>
                          <mml:mi>o</mml:mi>
                          <mml:mi>m</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                      <mml:mo>−</mml:mo>
                      <mml:mn>20</mml:mn>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mrow>
                  <mml:mn>7.1</mml:mn>
                  <mml:mo>×</mml:mo>
                  <mml:mn>800</mml:mn>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Maximum number of modules connected in series:</p>
        <disp-formula id="FD5">
          <label>(5)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>m</mml:mi>
                  <mml:mi>s</mml:mi>
                  <mml:mi>max</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>U</mml:mi>
                    <mml:mrow>
                      <mml:mi>e</mml:mi>
                      <mml:mi>c</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>max</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>V</mml:mi>
                    <mml:mrow>
                      <mml:mi>o</mml:mi>
                      <mml:mi>c</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>×</mml:mo>
                  <mml:mn>1.15</mml:mn>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Number of modules connected in parallel:</p>
        <disp-formula id="FD6">
          <label>(6)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>m</mml:mi>
                  <mml:mi>b</mml:mi>
                  <mml:mi>p</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mi>I</mml:mi>
              <mml:mi>N</mml:mi>
              <mml:mi>T</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mi>F</mml:mi>
                  <mml:mi>S</mml:mi>
                  <mml:mo>×</mml:mo>
                  <mml:mfrac>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>c</mml:mi>
                          <mml:mi>j</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mi>i</mml:mi>
                      </mml:msub>
                      <mml:mo>×</mml:mo>
                      <mml:msub>
                        <mml:mi>η</mml:mi>
                        <mml:mi>m</mml:mi>
                      </mml:msub>
                      <mml:mo>×</mml:mo>
                      <mml:msub>
                        <mml:mi>η</mml:mi>
                        <mml:mi>c</mml:mi>
                      </mml:msub>
                      <mml:mo>×</mml:mo>
                      <mml:msub>
                        <mml:mi>S</mml:mi>
                        <mml:mrow>
                          <mml:mi>c</mml:mi>
                          <mml:mi>e</mml:mi>
                          <mml:mi>l</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                      <mml:mo>×</mml:mo>
                      <mml:msub>
                        <mml:mi>N</mml:mi>
                        <mml:mrow>
                          <mml:mi>m</mml:mi>
                          <mml:mi>s</mml:mi>
                          <mml:mi>max</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:mfrac>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Total number of installed modules:</p>
        <disp-formula id="FD7">
          <label>(7)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>t</mml:mi>
                  <mml:mi>m</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>m</mml:mi>
                  <mml:mi>b</mml:mi>
                  <mml:mi>p</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>m</mml:mi>
                  <mml:mi>s</mml:mi>
                  <mml:mi>max</mml:mi>
                </mml:mrow>
              </mml:msub>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Area of the photovoltaic array:</p>
        <disp-formula id="FD8">
          <label>(8)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>S</mml:mi>
                <mml:mrow>
                  <mml:mi>P</mml:mi>
                  <mml:mi>V</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>t</mml:mi>
                  <mml:mi>m</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:msub>
                <mml:mi>S</mml:mi>
                <mml:mrow>
                  <mml:mi>c</mml:mi>
                  <mml:mi>e</mml:mi>
                  <mml:mi>l</mml:mi>
                </mml:mrow>
              </mml:msub>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p><bold>Selection of nominal voltage</bold></p>
        <p>The work of Mohamed El Hacen Jed. [<xref ref-type="bibr" rid="B25">25</xref>] specifies the operating voltage based on the peak power of the PV array. Considering the value of the daily power demand, the operating voltage of the system is 48 V.</p>
        <p><bold>Inverter selection</bold></p>
        <p>The choice of an inverter is based on the system’s operating power, which must be greater than or equal to <inline-formula><mml:math display="inline"><mml:mrow><mml:mi> k </mml:mi><mml:mo> × </mml:mo><mml:msub><mml:mi> P </mml:mi><mml:mrow><mml:mi> o </mml:mi><mml:mi> n </mml:mi><mml:mi> d </mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> to account for current surges during device startup [<xref ref-type="bibr" rid="B26">26</xref>]. Here, <inline-formula><mml:math><mml:math xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi> k </mml:mi><mml:mi></mml:mi></mml:math></mml:math></inline-formula>is a factor between 2 and 3, and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi> P </mml:mi><mml:mrow><mml:mi> o </mml:mi><mml:mi> n </mml:mi><mml:mi> d </mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the nominal power ofan inverter in VA.</p>
        <p>For an isolated site, a stand-alone, bidirectional inverter is required. It must be capable of managing batteries, the generator, and loads, delivering a sinusoidal grid voltage with an overload capacity of approximately 300% (providing short-circuit protection) and a variable power factor [<xref ref-type="bibr" rid="B27">27</xref>].</p>
        <p><bold>Modeling of the system storage capacity</bold></p>
        <p>Nominal capacity of the assembled batteries (Ah):</p>
        <disp-formula id="FD9">
          <label>(9)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:mi>C</mml:mi>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mi>max</mml:mi>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>b</mml:mi>
                          <mml:mi>a</mml:mi>
                          <mml:mi>t</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                      <mml:mo>−</mml:mo>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>G</mml:mi>
                          <mml:mi>E</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                      <mml:mo>−</mml:mo>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>P</mml:mi>
                          <mml:mi>V</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>×</mml:mo>
                  <mml:msub>
                    <mml:mi>n</mml:mi>
                    <mml:mi>j</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>V</mml:mi>
                    <mml:mrow>
                      <mml:mi>b</mml:mi>
                      <mml:mi>a</mml:mi>
                      <mml:mi>t</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>×</mml:mo>
                  <mml:msub>
                    <mml:mi>η</mml:mi>
                    <mml:mrow>
                      <mml:mi>b</mml:mi>
                      <mml:mi>a</mml:mi>
                      <mml:mi>t</mml:mi>
                      <mml:mn>2</mml:mn>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>×</mml:mo>
                  <mml:msub>
                    <mml:mi>η</mml:mi>
                    <mml:mrow>
                      <mml:mi>o</mml:mi>
                      <mml:mi>n</mml:mi>
                      <mml:mi>d</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>×</mml:mo>
                  <mml:mi>P</mml:mi>
                  <mml:mi>D</mml:mi>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Minimum State of Charge threshold (<italic>SOC</italic><sub>min</sub>) at time t:</p>
        <disp-formula id="FD10">
          <label>(10)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:mi>S</mml:mi>
              <mml:mi>O</mml:mi>
              <mml:msub>
                <mml:mi>C</mml:mi>
                <mml:mrow>
                  <mml:mi>min</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>t</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mi>S</mml:mi>
              <mml:mi>O</mml:mi>
              <mml:mi>C</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mi>t</mml:mi>
                  <mml:mo>−</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>+</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>G</mml:mi>
                          <mml:mi>E</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                      <mml:mo>+</mml:mo>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>P</mml:mi>
                          <mml:mi>V</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                      <mml:mo>−</mml:mo>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>b</mml:mi>
                          <mml:mi>a</mml:mi>
                          <mml:mi>t</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>×</mml:mo>
                  <mml:msub>
                    <mml:mi>η</mml:mi>
                    <mml:mrow>
                      <mml:mi>b</mml:mi>
                      <mml:mi>a</mml:mi>
                      <mml:mi>t</mml:mi>
                      <mml:mn>1</mml:mn>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>×</mml:mo>
                  <mml:msub>
                    <mml:mi>η</mml:mi>
                    <mml:mrow>
                      <mml:mi>o</mml:mi>
                      <mml:mi>n</mml:mi>
                      <mml:mi>d</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>V</mml:mi>
                    <mml:mrow>
                      <mml:mi>o</mml:mi>
                      <mml:mi>n</mml:mi>
                      <mml:mi>d</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Maximum State of Charge threshold (<italic>SOC</italic><sub>max</sub>) at time t:</p>
        <disp-formula id="FD11">
          <label>(11)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:mi>S</mml:mi>
              <mml:mi>O</mml:mi>
              <mml:msub>
                <mml:mi>C</mml:mi>
                <mml:mrow>
                  <mml:mi>max</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>t</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mi>S</mml:mi>
              <mml:mi>O</mml:mi>
              <mml:mi>C</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mi>t</mml:mi>
                  <mml:mo>−</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>+</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>G</mml:mi>
                          <mml:mi>E</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                      <mml:mo>+</mml:mo>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>P</mml:mi>
                          <mml:mi>V</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                      <mml:mo>−</mml:mo>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>b</mml:mi>
                          <mml:mi>a</mml:mi>
                          <mml:mi>t</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>V</mml:mi>
                    <mml:mrow>
                      <mml:mi>o</mml:mi>
                      <mml:mi>n</mml:mi>
                      <mml:mi>d</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>×</mml:mo>
                  <mml:msub>
                    <mml:mi>η</mml:mi>
                    <mml:mrow>
                      <mml:mi>b</mml:mi>
                      <mml:mi>a</mml:mi>
                      <mml:mi>t</mml:mi>
                      <mml:mn>2</mml:mn>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>×</mml:mo>
                  <mml:msub>
                    <mml:mi>η</mml:mi>
                    <mml:mrow>
                      <mml:mi>o</mml:mi>
                      <mml:mi>n</mml:mi>
                      <mml:mi>d</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Depth of Discharge (DoD): </p>
        <disp-formula id="FD12">
          <label>(12)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:mi>P</mml:mi>
              <mml:mi>D</mml:mi>
              <mml:mo>=</mml:mo>
              <mml:mn>1</mml:mn>
              <mml:mo>−</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mi>S</mml:mi>
                  <mml:mi>O</mml:mi>
                  <mml:msub>
                    <mml:mi>C</mml:mi>
                    <mml:mrow>
                      <mml:mi>min</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:mi>S</mml:mi>
                  <mml:mi>O</mml:mi>
                  <mml:msub>
                    <mml:mi>C</mml:mi>
                    <mml:mrow>
                      <mml:mi>max</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Constraints on the State of Charge:</p>
        <disp-formula id="FD13">
          <label>(13)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:mi>S</mml:mi>
              <mml:mi>O</mml:mi>
              <mml:msub>
                <mml:mi>C</mml:mi>
                <mml:mrow>
                  <mml:mi>min</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>≤</mml:mo>
              <mml:mi>S</mml:mi>
              <mml:mi>O</mml:mi>
              <mml:mi>C</mml:mi>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>t</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>≤</mml:mo>
              <mml:mi>S</mml:mi>
              <mml:mi>O</mml:mi>
              <mml:msub>
                <mml:mi>C</mml:mi>
                <mml:mrow>
                  <mml:mi>max</mml:mi>
                </mml:mrow>
              </mml:msub>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Number of accumulators (batteries) in series in each branch:</p>
        <disp-formula id="FD14">
          <label>(14)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>a</mml:mi>
                  <mml:mi>s</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>V</mml:mi>
                    <mml:mrow>
                      <mml:mi>o</mml:mi>
                      <mml:mi>n</mml:mi>
                      <mml:mi>d</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>V</mml:mi>
                    <mml:mrow>
                      <mml:mi>b</mml:mi>
                      <mml:mi>a</mml:mi>
                      <mml:mi>t</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Number of parallel branches:</p>
        <disp-formula id="FD15">
          <label>(15)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>b</mml:mi>
                  <mml:mi>p</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mi>C</mml:mi>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>C</mml:mi>
                    <mml:mi>n</mml:mi>
                  </mml:msub>
                  <mml:mo>×</mml:mo>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mi>S</mml:mi>
                      <mml:mi>O</mml:mi>
                      <mml:msub>
                        <mml:mi>C</mml:mi>
                        <mml:mrow>
                          <mml:mi>m</mml:mi>
                          <mml:mi>a</mml:mi>
                          <mml:mi>x</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                      <mml:mo>−</mml:mo>
                      <mml:mi>S</mml:mi>
                      <mml:mi>O</mml:mi>
                      <mml:msub>
                        <mml:mi>C</mml:mi>
                        <mml:mrow>
                          <mml:mi>min</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Total number of accumulators (batteries):</p>
        <disp-formula id="FD16">
          <label>(16)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>T</mml:mi>
                  <mml:mi>b</mml:mi>
                  <mml:mi>a</mml:mi>
                  <mml:mi>t</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>a</mml:mi>
                  <mml:mi>s</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:msub>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>b</mml:mi>
                  <mml:mi>p</mml:mi>
                </mml:mrow>
              </mml:msub>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p><bold>Sizing of the generator set</bold></p>
        <p>Calculation method for sizing the generator set.</p>
        <p>Maximum power:</p>
        <disp-formula id="FD17">
          <label>(17)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>P</mml:mi>
                <mml:mrow>
                  <mml:mi>max</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>P</mml:mi>
                <mml:mi>p</mml:mi>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>f</mml:mi>
                    <mml:mi>p</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>f</mml:mi>
                    <mml:mi>t</mml:mi>
                  </mml:msub>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Power demanded:</p>
        <disp-formula id="FD18">
          <label>(18)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>P</mml:mi>
                <mml:mrow>
                  <mml:mi>a</mml:mi>
                  <mml:mi>p</mml:mi>
                  <mml:mi>p</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>P</mml:mi>
                    <mml:mrow>
                      <mml:mi>max</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:mi>cos</mml:mi>
                  <mml:mi>φ</mml:mi>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Service life [years]:</p>
        <disp-formula id="FD19">
          <label>(19)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>D</mml:mi>
                <mml:mrow>
                  <mml:mi>G</mml:mi>
                  <mml:mi>E</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>T</mml:mi>
                    <mml:mrow>
                      <mml:mi>v</mml:mi>
                      <mml:mi>i</mml:mi>
                      <mml:mi>e</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mn>365</mml:mn>
                      <mml:mo>×</mml:mo>
                      <mml:msub>
                        <mml:mi>T</mml:mi>
                        <mml:mrow>
                          <mml:mi>m</mml:mi>
                          <mml:mi>a</mml:mi>
                          <mml:mi>r</mml:mi>
                          <mml:mi>c</mml:mi>
                          <mml:mi>h</mml:mi>
                          <mml:mi>e</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>Fuel consumed [L]:</p>
        <disp-formula id="FD20">
          <label>(20)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>C</mml:mi>
                <mml:mrow>
                  <mml:mi>v</mml:mi>
                  <mml:mi>o</mml:mi>
                  <mml:mi>l</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>F</mml:mi>
                  <mml:mi>u</mml:mi>
                  <mml:mi>e</mml:mi>
                  <mml:mi>l</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>C</mml:mi>
                <mml:mrow>
                  <mml:mi>F</mml:mi>
                  <mml:mi>u</mml:mi>
                  <mml:mi>e</mml:mi>
                  <mml:mi>l</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mstyle displaystyle="true">
                    <mml:munderover>
                      <mml:mo>∑</mml:mo>
                      <mml:mrow>
                        <mml:mi>i</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mn>0</mml:mn>
                      </mml:mrow>
                      <mml:mrow>
                        <mml:msub>
                          <mml:mi>T</mml:mi>
                          <mml:mrow>
                            <mml:mi>m</mml:mi>
                            <mml:mi>a</mml:mi>
                            <mml:mi>r</mml:mi>
                            <mml:mi>c</mml:mi>
                            <mml:mi>h</mml:mi>
                            <mml:mi>e</mml:mi>
                          </mml:mrow>
                        </mml:msub>
                      </mml:mrow>
                    </mml:munderover>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>P</mml:mi>
                        <mml:mi>i</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:mstyle>
                  <mml:mo>+</mml:mo>
                  <mml:mn>0.1</mml:mn>
                  <mml:mo>×</mml:mo>
                  <mml:msub>
                    <mml:mi>C</mml:mi>
                    <mml:mrow>
                      <mml:mi>b</mml:mi>
                      <mml:mi>a</mml:mi>
                      <mml:mi>t</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
      </sec>
      <sec id="sec2dot4">
        <title>2.4. Configurations of PV/Diesel Systems</title>
        <p>In any hybrid PV/Diesel (DG) energy generation system, the use of an inverter is sometimes necessary for DC/AC conversion. The PV generator can then operate in parallel or alternately with the DG. Three main configurations are distinguished: series, parallel, and switched. Each of these configurations has its own advantages and disadvantages [<xref ref-type="bibr" rid="B23">23</xref>][<xref ref-type="bibr" rid="B28">28</xref>][<xref ref-type="bibr" rid="B29">29</xref>]. The configuration of PV/Diesel systems also depends on the coupling bus. Options include the DC bus, the mixed DC/AC bus, and the AC bus [<xref ref-type="bibr" rid="B26">26</xref>].</p>
        <p>For this study, we opted for the parallel-connected PV/Diesel configuration. The diesel generator is interconnected on the alternating current (AC) bus, while the photovoltaic installation is connected to the direct current (DC) bus. The two buses are connected via a bidirectional electronic converter. The advantage of this configuration is that the converter can operate either as a rectifier, when the generator covers the electrical consumption and contributes to battery charging, or as an inverter, when the load (or part of it) is supplied by the photovoltaic modules and/or the battery. Consequently, the load can be powered by both buses simultaneously.</p>
      </sec>
      <sec id="sec2dot5">
        <title>2.5. HOMER Pro Simulation Software</title>
        <fig id="fig8">
          <label>Figure 8</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId69.jpeg?20260527014019" />
        </fig>
        <p><bold>Figur</bold><bold>e 8</bold><bold>.</bold> Simulation process.</p>
        <p>HOMER Pro (Hybrid Optimization of Multiple Energy Resources) is a modeling and optimization software for decentralized energy systems. It is used to design and analyze autonomous energy systems that incorporate various renewable and non-renewable energy sources, ensuring optimal cost-to-power ratio [<xref ref-type="bibr" rid="B8">8</xref>][<xref ref-type="bibr" rid="B23">23</xref>]. For simulation purposes, input data must be provided. These primarily include the site’s geolocation, the energy demand of the load, and the configuration parameters of the solar PV array, the diesel generator and its fuel, the inverter, and the storage system. The flowchart in <xref ref-type="fig" rid="fig8">Figure 8</xref> summarizes the simulation process using HOMER [<xref ref-type="bibr" rid="B8">8</xref>]<bold>.</bold></p>
      </sec>
      <sec id="sec2dot6">
        <title>2.6. Physical Modeling of the System</title>
        <p>2.6.1. System Architecture</p>
        <p><xref ref-type="fig" rid="fig9">Figure 9</xref> presents the 3D architectural plan of the smart grid power plant, designed using AutoCAD 2025 software. This plan takes into account all the components necessary for the implementation of the system, mainly: the Diesel and PV generators, the storage system, the technical room, the system management unit, and various other secondary components.</p>
        <fig id="fig9">
          <label>Figure 9</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId70.jpeg?20260527014022" />
        </fig>
        <p><bold>Figur</bold><bold>e 9</bold><bold>.</bold> 3D view of control site.</p>
        <fig id="fig10">
          <label>Figure 10</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId71.jpeg?20260527014022" />
        </fig>
        <p><bold>Figure 10</bold><bold>.</bold> System overview diagram.</p>
        <p>The HOMER Pro software provides the block diagram of the power plant shown in <xref ref-type="fig" rid="fig10">Figure 10</xref>.</p>
        <p>2.6.2. Performance Parameters</p>
        <p>The solar fraction<inline-formula><mml:math display="inline"><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mi> f </mml:mi><mml:mi> s </mml:mi></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> and the ratio of renewable energy to load demand <inline-formula><mml:math display="inline"><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mi> K </mml:mi><mml:mrow><mml:mrow><mml:mi> s </mml:mi><mml:mo> / </mml:mo><mml:mi> c </mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> are physical quantities used to characterize the performance of an energy system utilizing renewable sources. Equations (21) and (22) allow for monitoring the evolution of these quantities throughout the system’s operation.</p>
        <disp-formula id="FD21">
          <label>(21)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>f</mml:mi>
                <mml:mi>s</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>E</mml:mi>
                    <mml:mrow>
                      <mml:mi>P</mml:mi>
                      <mml:mi>V</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>−</mml:mo>
                  <mml:msub>
                    <mml:mi>E</mml:mi>
                    <mml:mrow>
                      <mml:mi>p</mml:mi>
                      <mml:mi>e</mml:mi>
                      <mml:mi>r</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>E</mml:mi>
                    <mml:mrow>
                      <mml:mi>P</mml:mi>
                      <mml:mi>V</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>−</mml:mo>
                  <mml:msub>
                    <mml:mi>E</mml:mi>
                    <mml:mrow>
                      <mml:mi>p</mml:mi>
                      <mml:mi>e</mml:mi>
                      <mml:mi>r</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mo>+</mml:mo>
                  <mml:msub>
                    <mml:mi>E</mml:mi>
                    <mml:mrow>
                      <mml:mi>G</mml:mi>
                      <mml:mi>E</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <disp-formula id="FD22">
          <label>(22)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>K</mml:mi>
                <mml:mrow>
                  <mml:mi>s</mml:mi>
                  <mml:mo>/</mml:mo>
                  <mml:mi>c</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>E</mml:mi>
                    <mml:mrow>
                      <mml:mi>P</mml:mi>
                      <mml:mi>V</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>E</mml:mi>
                    <mml:mrow>
                      <mml:mi>c</mml:mi>
                      <mml:mi>j</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>2.6.3. System Optimization</p>
        <p><bold>1)</bold><italic><bold>Energy Constraints</bold></italic></p>
        <p>The primary objective of optimizing the operation of our system is to determine the best scenarios capable of meeting the load demand at all times, at the lowest cost, and in a sustainable manner. The main constraint of this process is to have an efficient and reliable hybrid system. The objective of the constraint management plan here is to maximize the use of renewable energy and to utilize the Diesel generator only when necessary. To achieve this, a number of constraints are imposed:</p>
        <p>Phase 1: The energy produced by the PV array is greater than that demanded by the load <inline-formula><mml:math display="inline"><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mi> E </mml:mi><mml:mrow><mml:mi> c </mml:mi><mml:mi> h </mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow><mml:mo> ≺ </mml:mo><mml:msub><mml:mi> E </mml:mi><mml:mrow><mml:mi> P </mml:mi><mml:mi> V </mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> . The surplus energy is then sent, via the reversible DC/AC converter, to the batteries if the latter have not reached their maximum state of charge <inline-formula><mml:math display="inline"><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:mi> S </mml:mi><mml:mi> O </mml:mi><mml:msub><mml:mi> C </mml:mi><mml:mrow><mml:mi> max </mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> .Phase 2: The energy produced by the PV plant is less than that demanded by the load <inline-formula><mml:math display="inline"><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mi> E </mml:mi><mml:mrow><mml:mi> c </mml:mi><mml:mi> h </mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow><mml:mo> ≻ </mml:mo><mml:msub><mml:mi> E </mml:mi><mml:mrow><mml:mi> P </mml:mi><mml:mi> V </mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> . The energy deficit is compensated for by the batteries, through the reversible DC/AC converter, provided that the state of charge of these batteries has not reached its minimum threshold <inline-formula><mml:math display="inline"><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:mi> S </mml:mi><mml:mi> O </mml:mi><mml:msub><mml:mi> C </mml:mi><mml:mrow><mml:mi> min </mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo> ( </mml:mo><mml:mi> t </mml:mi><mml:mo> ) </mml:mo></mml:mrow></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> .If, during the second phase, the batteries fail to supply the missing energy required by the load, this energy deficit is compensated for by the Diesel generator <inline-formula><mml:math display="inline"><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:msub><mml:mi> E </mml:mi><mml:mrow><mml:mi> G </mml:mi><mml:mi> E </mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> .</p>
        <p>Should the power plant eventually be connected to the public electricity grid, the following scenarios are defined:</p>
        <p>When the electrical energy storage system is charged and production exceeds consumption, the surplus renewable energy will be injected directly into the grid.In the event of a deficit, energy is drawn from the grid to meet the demand.</p>
        <p><bold>2</bold><bold>)</bold><italic><bold>Formulation of the optimization problem</bold></italic></p>
        <p>The developed model is based on the definition of an objective function (cost), or Life Cycle Cost (LCC) [<xref ref-type="bibr" rid="B28">28</xref>][<xref ref-type="bibr" rid="B30">30</xref>], which aims to minimize the production cost. This function takes into account the acquisition, operation, maintenance, and replacement costs of the diesel generator, the photovoltaic array, the storage system, and the reversible DC/AC inverter. It can be written as follows:</p>
        <disp-formula id="FD23">
          <label>(23)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:mi>F</mml:mi>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>D</mml:mi>
                <mml:mrow>
                  <mml:mi>P</mml:mi>
                  <mml:mi>V</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>+</mml:mo>
              <mml:msub>
                <mml:mi>D</mml:mi>
                <mml:mrow>
                  <mml:mi>G</mml:mi>
                  <mml:mi>E</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>+</mml:mo>
              <mml:msub>
                <mml:mi>D</mml:mi>
                <mml:mrow>
                  <mml:mi>B</mml:mi>
                  <mml:mi>A</mml:mi>
                  <mml:mi>T</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>+</mml:mo>
              <mml:msub>
                <mml:mi>D</mml:mi>
                <mml:mrow>
                  <mml:mi>O</mml:mi>
                  <mml:mi>N</mml:mi>
                  <mml:mi>D</mml:mi>
                </mml:mrow>
              </mml:msub>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p><bold>Component sizing of the system</bold></p>
        <p>Based on meteorological data and the energy needs of the population, the HOMER Pro software defines the parameters for each of the essential components of the power plant. These parameters are summarized in <bold>Table</bold><bold>s 2</bold><bold>-</bold><bold>5</bold>.</p>
        <p><bold>The PV array</bold></p>
        <p><bold>Table 2.</bold> PV generator settings.</p>
        <table-wrap id="tbl2">
          <label>Table 2</label>
          <table>
            <tbody>
              <tr>
                <td colspan="7">Generator PV (generic PV system)</td>
              </tr>
              <tr>
                <td>Panel type</td>
                <td>Rated capacity (kW)</td>
                <td>Durating factor (%)</td>
                <td>Lifetime (years)</td>
                <td colspan="3">Cost</td>
              </tr>
              <tr>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>Capacity (kW)</td>
                <td>Capital ($)</td>
                <td>Replacement ($)</td>
              </tr>
              <tr>
                <td>Flat plate</td>
                <td>160</td>
                <td>80</td>
                <td>25</td>
                <td>1</td>
                <td>33,600</td>
                <td>33,600</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <p><bold>Diesel generator</bold></p>
        <p><bold>Table 3.</bold> Diesel generator settings.</p>
        <table-wrap id="tbl3">
          <label>Table 3</label>
          <table>
            <tbody>
              <tr>
                <td colspan="12">Diesel Generator (Cummins 100 kW DSGAA)</td>
              </tr>
              <tr>
                <td colspan="2">Fuel curve</td>
                <td colspan="2">Site specific</td>
                <td colspan="5">Emissions</td>
                <td colspan="3">Cost</td>
              </tr>
              <tr>
                <td>intercept (L/hr)</td>
                <td>slope (L/hr/kW)</td>
                <td>Lifetime (Hours)</td>
                <td>Minimum load ratio (%)</td>
                <td>UnbumedHC(g/L fuel)</td>
                <td>CO(g/Lfuel)</td>
                <td>Particulates (g/L fuel)</td>
                <td>Fuel Sulfur to PM(%)</td>
                <td>
                  NO
                  <sub>x</sub>
                  (g/L fuel)
                </td>
                <td>Initial capital ($)</td>
                <td>Replacement ($)</td>
                <td>Fuel price ($/L)</td>
              </tr>
              <tr>
                <td>5.75</td>
                <td>0.278</td>
                <td>15,000</td>
                <td>30</td>
                <td>0.33</td>
                <td>2.29</td>
                <td>0.24</td>
                <td>2.2</td>
                <td>4.26</td>
                <td>8000</td>
                <td>8000</td>
                <td>1.8</td>
              </tr>
              <tr>
                <td colspan="12">Combustible (Diesel)</td>
              </tr>
              <tr>
                <td colspan="3">Low Heating Value (MJ/kg)</td>
                <td colspan="2">
                  Density (kg/m
                  <sup>3</sup>
                  )
                </td>
                <td colspan="2">Carbon (%)</td>
                <td colspan="2">Sulfur (%)</td>
                <td colspan="3">Cost ($/L)</td>
              </tr>
              <tr>
                <td colspan="3">43.2</td>
                <td colspan="2">820</td>
                <td colspan="2">88</td>
                <td colspan="2">0.4</td>
                <td colspan="3">1.8</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <p><italic><bold>Inverter</bold></italic></p>
        <p><bold>Table 4.</bold> Inverter settings.</p>
        <table-wrap id="tbl4">
          <label>Table 4</label>
          <table>
            <tbody>
              <tr>
                <td colspan="8">Invecter (generic system converter) Si—100K</td>
              </tr>
              <tr>
                <td colspan="2">Inverter Input</td>
                <td colspan="2">
                  <bold>Rectifier Input</bold>
                </td>
                <td colspan="4">
                  <bold>Cost</bold>
                </td>
              </tr>
              <tr>
                <td>Lifetime (years)</td>
                <td>Efficiency (%)</td>
                <td>Relative Capacity (%)</td>
                <td>Efficiency (%)</td>
                <td>Capacity (kW)</td>
                <td>Capital ($)</td>
                <td>Replacement ($)</td>
                <td>O&amp;M ($/year)</td>
              </tr>
              <tr>
                <td>25</td>
                <td>98.7</td>
                <td>100</td>
                <td>98.7</td>
                <td>1</td>
                <td>350</td>
                <td>350</td>
                <td>3</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <p><bold>Storage system</bold></p>
        <p><bold>Table 5.</bold>Storage system settings.</p>
        <table-wrap id="tbl5">
          <label>Table 5</label>
          <table>
            <tbody>
              <tr>
                <td colspan="8">Kenetic Battery Model</td>
                <td colspan="2">Lifetime</td>
                <td colspan="3">Cost</td>
              </tr>
              <tr>
                <td>Nom. Volt.(V)</td>
                <td>Nom. Cap.(kWh)</td>
                <td>Max. Cap. (Ah)</td>
                <td>Cap. Ratio</td>
                <td>Round trip eff. (%)</td>
                <td>Max. Charge Cur. (A)</td>
                <td>Initial SOC (%)</td>
                <td>Min. SOC (%)</td>
                <td>Time (years)</td>
                <td>Throughput</td>
                <td>Cap. (kW)</td>
                <td>Capital ($)</td>
                <td>Rep. ($)</td>
              </tr>
              <tr>
                <td>2</td>
                <td>7.15</td>
                <td>3,570</td>
                <td>0.315</td>
                <td>86</td>
                <td>610</td>
                <td>100</td>
                <td>30</td>
                <td>20</td>
                <td>10118.30</td>
                <td>120</td>
                <td>1619</td>
                <td>1619</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <p><bold>System management strategy (EMS)</bold></p>
        <p>The proposed strategy for managing the available production sources pursues a dual objective: minimizing the operational cost over the system’s lifecycle through optimized operation, while ensuring its long-term viability. This strategy is based on the automation of the start-up and shutdown mechanisms of the diesel generator, enabling activation or deactivation as soon as the required conditions are met, without any human intervention.</p>
        <p>The management system receives, on an hourly basis, input data including solar irradiance, load consumption, battery state-of-charge, generator output, and load demand. These data are used to impose the scheduled output power of the energy sources and the battery, as well as the power imported from or exported to the main grid, should the system be connected to it. Based on the operational constraints, the implemented algorithm intelligently controls the start-up and shutdown of the generator, the charge and discharge cycles of the battery, and the utilization of photovoltaic solar energy. The desired functionalities of the proposed Energy Management System (EMS) are detailed in <xref ref-type="fig" rid="fig11">Figure 11</xref>.</p>
        <fig id="fig11">
          <label>Figure 11</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId92.jpeg?20260527014023" />
        </fig>
        <p><bold>Figure 11.</bold> Schematic diagram of the proposed EMS for the mini smart grid.</p>
        <p>The Energy Management System (EMS) will ensure optimal energy management according to the algorithm shown in <xref ref-type="fig" rid="fig12">Figure 12</xref>.</p>
        <fig id="fig12">
          <label>Figure 12</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId93.jpeg?20260527014023" />
        </fig>
        <p><bold>Figure 12.</bold> EMS management algorithm.</p>
      </sec>
    </sec>
    <sec id="sec3">
      <title>3. Results and Discussions</title>
      <sec id="sec3dot1">
        <title>3.1. Influence of Operating Parameters on System Performance</title>
        <p>To better assess the energy performance of the hybrid system,<xref ref-type="fig" rid="fig13">Figures 13-16</xref> illustrate the evolution of the solar fraction (as defined in Equation (21)), the operating time, and the fuel consumption of the diesel generator over one year of operation, as functions of the PV array area and the battery bank autonomy.</p>
        <fig id="fig13">
          <label>Figure 13</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId94.jpeg?20260527014025" />
        </fig>
        <p><bold>Figure 13.</bold> Effect of energy storage size on the operating parameters of a generator Set.</p>
        <p><xref ref-type="fig" rid="fig13">Figure 13</xref> and <xref ref-type="fig" rid="fig14">Figure 14</xref> show the sensitivity of the diesel generator’s operating parameters—namely the number of start-ups, operating duration, and fuel consumption—to variations in PV array area and battery storage capacity, respectively. It is observed that the operating time, number of start-ups, and fuel consumption decrease more significantly as the storage capacity increases. The same trend is observed with increasing PV array area. Indeed, a larger storage capacity allows the battery bank to meet a greater portion of the energy demand, thereby reducing the frequency of diesel generator starts. This simultaneously explains the reduction in both operating time and fuel consumption. A similar influence is noted for the PV array size: its increase leads to higher PV energy production, which in turn reduces the operating time of the diesel generator.</p>
        <fig id="fig14">
          <label>Figure 14</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId95.jpeg?20260527014025" />
        </fig>
        <p><bold>Figure 14.</bold> Effect of PV array size on the operating parameters of a generator set.</p>
        <fig id="fig15">
          <label>Figure 15</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId96.jpeg?20260527014024" />
        </fig>
        <p><bold>Figure 15.</bold> Evolution of the solar fraction with PV panel surface area for different storage sizes.</p>
        <p>Similarly, an expansion of the PV array area augments solar energy production, further curtailing diesel generator usage.</p>
        <p><xref ref-type="fig" rid="fig15">Figure 15</xref> and <xref ref-type="fig" rid="fig16">Figure 16</xref> respectively show the influence of the PV array size and the battery storage capacity on the solar fraction. It can be observed that the impact of the PV array surface area on the solar fraction is more significant than that observed when varying the size of the energy storage system. Beyond a PV surface area of 300 m<sup>2</sup>, the solar fraction becomes almost insensitive to a storage capacity exceeding 4 days. These findings were predicted by the work of Ludmil Stoyanov [<xref ref-type="bibr" rid="B29">29</xref>] and M. Sidrach de Cardona and L.L. Mora Lopez [<xref ref-type="bibr" rid="B27">27</xref>].</p>
        <fig id="fig16">
          <label>Figure 16</label>
          <graphic xlink:href="https://html.scirp.org/file/6401933-rId97.jpeg?20260527014025" />
        </fig>
        <p><bold>Figure 16.</bold> Influence of battery size for different panel surface areas.</p>
      </sec>
      <sec id="sec3dot2">
        <title>3.2. Economic and Environmental Analysis of the Management System Results</title>
        <p>Five (05) scenarios of the electrical energy production system were studied, each obtained by removing one or more components from the initial system. We primarily consider four (04) costs expressed in US dollars ($): initial capital (IC), operating cost (OC), life-cycle cost (LCC), and cost of energy (COE).</p>
        <p>Scenarios 4 and 5 are by far the least advantageous. They exhibit the highest LCC values, as well as the highest sum of initial capital and operating costs over twenty (20) years. Furthermore, they emit significantly more polluting gases and particles. Undoubtedly, these findings are attributable to the fact that electricity generation in these scenarios requires considerably more generator operating time and, consequently, a large amount of diesel fuel consumed.</p>
        <p>Scenario 2 presents the lowest LCC and initial capital-operating cost combination. Moreover, it is the only scenario that does not include a PV generator. Scenarios 2 and 3 are those utilizing a PV generator and are advantageous.</p>
        <p><bold>Table 6</bold> presents the results obtained from the implementation of the electrical production management system for the various scenarios.</p>
        <p><bold>Table 6</bold><bold>.</bold> Financial details and performance metrics for each scenario.</p>
        <p><bold>Cas 1: PV Generator (40 kW) + Diesel Generator (100 kW) + BAT (120) + Invertler (40 kW)</bold><bold>Cas 2: Diesel Generator (100 kW) + BAT ((120) +</bold><bold>Inverter</bold><bold>(80 kW)</bold><bold>Cas 3: PV Generator (80 kW) + BAT (72) + Inverter (40 kW)</bold><italic><bold>Cas</bold></italic><bold>4:</bold><italic><bold>Diesel Generator</bold></italic><bold>(100 kW)</bold><italic><bold>only</bold></italic><italic><bold>Cas</bold></italic><bold>5: PV Generator (40 kW) +</bold><italic><bold>Diesel Generator</bold></italic><bold>(100 kW) +</bold><italic><bold>Inverter</bold></italic><bold>(20 kW)</bold></p>
        <p>To further our analyses and account for green energy production aspects, we conducted a cross-analysis of the economic and environmental benefits of the three best scenarios and integrated abatement costs. <bold>Table 7</bold> and <bold>Table 8</bold> summarize the results of the environmental impact and abatement costs for Scenarios 1 and 2, respectively. The results show that integrating long-term pollutant emission abatement costs can reduce the economic gap between these two scenarios, but does not eliminate it. Consequently, from a purely economic standpoint, Scenario 2 (Diesel Generator—Storage System—Inverter) remains the most optimal, as it yields the most favorable life-cycle and energy costs. However, given the context of environmental preservation and the consequent need to integrate the concept of green energy into electricity production systems, it is essential to focus more on Scenario 1 (Diesel Generator—PV Generator—Storage System—Inverter). This scenario best reconciles economic optimization with environmental protection.</p>
        <p><bold>Table 7.</bold>Analysis of environmental impact.</p>
        <table-wrap id="tbl6">
          <label>Table 6</label>
          <table>
            <tbody>
              <tr>
                <td rowspan="2">Cas</td>
                <td colspan="2">Energy production (%)</td>
                <td rowspan="2">Fuel Consumption (L/day)</td>
                <td colspan="6">Emissions (kg/an)</td>
              </tr>
              <tr>
                <td>PV</td>
                <td>Diesel</td>
                <td>
                  CO
                  <sub>2</sub>
                </td>
                <td>CO</td>
                <td>Unburned Hydrocarbon</td>
                <td>Fine Particulate Matter</td>
                <td>
                  SO
                  <sub>2</sub>
                </td>
                <td>
                  NO
                  <sub>x</sub>
                </td>
              </tr>
              <tr>
                <td>1</td>
                <td>97</td>
                <td>03</td>
                <td>02.7</td>
                <td>2.607</td>
                <td>2.26</td>
                <td>0.326</td>
                <td>0.237</td>
                <td>6.33</td>
                <td>4.21</td>
              </tr>
              <tr>
                <td>2</td>
                <td>00</td>
                <td>100</td>
                <td>65.9</td>
                <td>63.485</td>
                <td>55</td>
                <td>7.93</td>
                <td>5.77</td>
                <td>154</td>
                <td>102</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <p><bold>Table 8.</bold> Abatement costs for Scenarios 1 and 2.</p>
        <table-wrap id="tbl7">
          <label>Table 7</label>
          <table>
            <tbody>
              <tr>
                <td>
                </td>
                <td>
                  Carbon dioxide (CO
                  <sub>2</sub>
                  )
                </td>
                <td>Carbon monoxide (CO)</td>
                <td>Unburned Hydrocarbon</td>
                <td>Fine Particulate Matter</td>
                <td>
                  Sulfur dioxide(SO
                  <sub>2</sub>
                  )
                </td>
                <td>
                  Nitrogen oxide (NO
                  <sub>x</sub>
                  )
                </td>
                <td>Total Cost ($)</td>
              </tr>
              <tr>
                <td>
                  Abatement Costs ($/kg) [
                  <xref ref-type="bibr" rid="B31">31</xref>
                  ]-[
                  <xref ref-type="bibr" rid="B33">33</xref>
                  ]
                </td>
                <td>0.27</td>
                <td>0.27</td>
                <td>0.156</td>
                <td>0.3</td>
                <td>0.156</td>
                <td>0.189</td>
                <td>-</td>
              </tr>
              <tr>
                <td>Scenario 1 Emissions (kg/an)</td>
                <td>2.61</td>
                <td>2.26</td>
                <td>0.326</td>
                <td>0.237</td>
                <td>6.33</td>
                <td>4.21</td>
                <td>-</td>
              </tr>
              <tr>
                <td>Scenario 2 Emissions (kg/an)</td>
                <td>63.48</td>
                <td>55</td>
                <td>7.93</td>
                <td>5.77</td>
                <td>154</td>
                <td>102</td>
                <td>-</td>
              </tr>
              <tr>
                <td>Scenario 1: 20-Year Abatement Cost ($)</td>
                <td>14.078</td>
                <td>12.204</td>
                <td>1.021</td>
                <td>1.422</td>
                <td>19.825</td>
                <td>15.914</td>
                <td>
                  <bold>64.464</bold>
                </td>
              </tr>
              <tr>
                <td>Scenario 2: 20-Year Abatement Cost ($)</td>
                <td>342.82</td>
                <td>297</td>
                <td>24.837</td>
                <td>34.62</td>
                <td>482.33</td>
                <td>385.56</td>
                <td>
                  <bold>1567.164</bold>
                </td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
      </sec>
    </sec>
    <sec id="sec4">
      <title>4. Conclusions and Perspectives</title>
      <p>In this paper, we have designed and optimized a mini hybrid power plant to meet the daily electrical load of Yakoungou, a village in the Nakambé region of Burkina Faso. Using satellite data and field survey data, we were able to assess energy needs and size the essential components of the system. The study of the power plant’s performance parameters showed that the various energies involved in the operation of this hybrid system depend more on the surface area of the PV modules than on the battery storage capacity. It is not advisable to configure the system with a storage capacity exceeding three days of autonomy, as beyond this value, the impact of increasing storage capacity becomes negligible.</p>
      <p>Using the Energy Management System (EMS) designed and integrated into Homer Pro software, with the collected data as input parameters, we were able to study five scenarios by combining PV and diesel generators, batteries, and the inverter. The execution of the EMS made it possible to control the contribution to energy production of each component of the power plant. For example, by comparing the LCC and the sum of initial capital and operating costs over 20 years, while accounting for abatement costs related to pollutant emissions, it emerges that the scenario combining a diesel generator, PV generator, storage system, and inverter best reconciles economic optimization with environmental protection.</p>
      <p>In terms of perspectives, we believe that implementing the Energy Management System for real-time testing could make it possible to validate the results of this study or, if necessary, improve the management algorithm to account for certain critical situations that may arise during power plant operation, particularly when considering grid connection, which can be a source of network instability.</p>
    </sec>
    <sec id="sec5">
      <title>CRediT Authorship Contribution Statement</title>
      <p><bold>Hassime GUENGANE:</bold> Writing—original draft, data collection, data processing and analysis, visualization, software, investigation, formal analysis.</p>
      <p><bold>Salifou OUEDRAOGO</bold><bold>:</bold> Writing—review &amp; editing, methodology, investigation, analysis of results.</p>
      <p><bold>Nébon BADO:</bold> Writing—review &amp; editing, methodology, investigation, interpretation of results.</p>
      <p><bold>Boureima DIANDA:</bold> Review &amp; editing, supervision, methodology, conceptualization, documentation.</p>
      <p><bold>Sié KAM:</bold> Supervision, methodology, investigation, documentation.</p>
      <p><bold>Dieudonné Joseph BAHIEBO:</bold> Review &amp; editing, supervision, investigation, formal analysis.</p>
      <p><bold>Declaration pertaining to the use of generative AI and AI-assisted technologies in the writing process</bold></p>
      <p>During the preparation of this work, the author(s) used Deep Seek exclusively to enhance the English language quality and improve the readability of the text. Following its use, the content was reviewed and revised as needed. The author(s) assume full responsibility for the final content of the publication.</p>
    </sec>
    <sec id="sec6">
      <title>Nomenclature</title>
      <table-wrap id="tbl8">
        <label>Table 8</label>
        <table>
          <tbody>
            <tr>
              <td>Symbol</td>
              <td>Description</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>c</mml:mi>
                          <mml:mi>j</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Daily energy consumption (Wh/day)</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>K</mml:mi>
                        <mml:mi>p</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>
                Loss coefficient,
                <italic>Kp</italic>
                = 0.50 to 0.70
              </td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>K</mml:mi>
                        <mml:mrow>
                          <mml:mrow>
                            <mml:mi>s</mml:mi>
                            <mml:mo>/</mml:mo>
                            <mml:mi>c</mml:mi>
                          </mml:mrow>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Ratio of renewable energy to load demand</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>f</mml:mi>
                        <mml:mi>s</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Solar fraction</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mi>i</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>
                Daily site irradiation (kWh/m
                <sup>2</sup>
                /day)
              </td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>T</mml:mi>
                        <mml:mi>α</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Ambient temperature (˚C)</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>T</mml:mi>
                        <mml:mrow>
                          <mml:mi>n</mml:mi>
                          <mml:mi>o</mml:mi>
                          <mml:mi>m</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Nominal module operating temperature (˚C)</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>η</mml:mi>
                        <mml:mi>m</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Average module efficiency</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>U</mml:mi>
                        <mml:mrow>
                          <mml:mi>e</mml:mi>
                          <mml:mi>c</mml:mi>
                          <mml:mo>.</mml:mo>
                          <mml:mi>m</mml:mi>
                          <mml:mi>a</mml:mi>
                          <mml:mi>x</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Maximum controller voltage</td>
            </tr>
            <tr>
              <td>1.15</td>
              <td>Reduction coefficient for calculating MPP voltage at 20˚C</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>V</mml:mi>
                        <mml:mrow>
                          <mml:mi>o</mml:mi>
                          <mml:mi>c</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Open-circuit voltage</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:mi>I</mml:mi>
                      <mml:mi>N</mml:mi>
                      <mml:mi>T</mml:mi>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Integer part of the expression in parentheses</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>F</mml:mi>
                        <mml:mi>s</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Safety factor</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>η</mml:mi>
                        <mml:mi>c</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Converter efficiency</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>S</mml:mi>
                        <mml:mrow>
                          <mml:mi>c</mml:mi>
                          <mml:mi>e</mml:mi>
                          <mml:mi>l</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>
                Module surface area (m
                <sup>2</sup>
                )
              </td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>N</mml:mi>
                        <mml:mrow>
                          <mml:mi>m</mml:mi>
                          <mml:mi>s</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Number of modules connected in series</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>G</mml:mi>
                          <mml:mi>E</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Daily energy production of the generator set</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>P</mml:mi>
                          <mml:mi>V</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Daily energy production of the PV array</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>p</mml:mi>
                          <mml:mi>e</mml:mi>
                          <mml:mi>r</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Daily energy loss</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>E</mml:mi>
                        <mml:mrow>
                          <mml:mi>b</mml:mi>
                          <mml:mi>a</mml:mi>
                          <mml:mi>t</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Energy demanded by the load at time 𝑡</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:mi>S</mml:mi>
                      <mml:mi>O</mml:mi>
                      <mml:mi>C</mml:mi>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mi>t</mml:mi>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>
                Battery state of charge at time
                <italic>t</italic>
              </td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:mi>S</mml:mi>
                      <mml:mi>O</mml:mi>
                      <mml:mi>C</mml:mi>
                      <mml:mrow>
                        <mml:mo>(</mml:mo>
                        <mml:mrow>
                          <mml:mi>t</mml:mi>
                          <mml:mo>−</mml:mo>
                          <mml:mn>1</mml:mn>
                        </mml:mrow>
                        <mml:mo>)</mml:mo>
                      </mml:mrow>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>
                Battery state of charge at the previous time (
                <italic>t</italic>
                − 1)
              </td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:mi>S</mml:mi>
                      <mml:mi>O</mml:mi>
                      <mml:msub>
                        <mml:mi>C</mml:mi>
                        <mml:mrow>
                          <mml:mi>min</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>20% of the nominal capacity of the assembled batteries</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:mi>S</mml:mi>
                      <mml:mi>O</mml:mi>
                      <mml:msub>
                        <mml:mi>C</mml:mi>
                        <mml:mrow>
                          <mml:mi>max</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>95% of the nominal capacity of the assembled batteries</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>η</mml:mi>
                        <mml:mrow>
                          <mml:mi>b</mml:mi>
                          <mml:mi>a</mml:mi>
                          <mml:mi>t</mml:mi>
                          <mml:mn>1</mml:mn>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Battery energy efficiency during charging phase</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>η</mml:mi>
                        <mml:mrow>
                          <mml:mi>b</mml:mi>
                          <mml:mi>a</mml:mi>
                          <mml:mi>t</mml:mi>
                          <mml:mn>2</mml:mn>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Battery energy efficiency during discharging phase</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>η</mml:mi>
                        <mml:mrow>
                          <mml:mi>o</mml:mi>
                          <mml:mi>n</mml:mi>
                          <mml:mi>d</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Efficiency of the reversible DC/AC battery converter</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>V</mml:mi>
                        <mml:mrow>
                          <mml:mi>o</mml:mi>
                          <mml:mi>n</mml:mi>
                          <mml:mi>d</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>DC input voltage of the reversible 𝑑𝑐/𝑎𝑐 converter on the battery side (48 V in this study)</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>n</mml:mi>
                        <mml:mi>j</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Number of days of storage (autonomy)</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>R</mml:mi>
                        <mml:mrow>
                          <mml:mi>b</mml:mi>
                          <mml:mi>a</mml:mi>
                          <mml:mi>t</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Battery efficiency (75% - 90%)</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>P</mml:mi>
                        <mml:mi>D</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Depth of discharge</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>V</mml:mi>
                        <mml:mrow>
                          <mml:mi>b</mml:mi>
                          <mml:mi>a</mml:mi>
                          <mml:mi>t</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Battery bank voltage</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>N</mml:mi>
                        <mml:mrow>
                          <mml:mi>a</mml:mi>
                          <mml:mi>s</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Number of batteries in series</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>N</mml:mi>
                        <mml:mrow>
                          <mml:mi>b</mml:mi>
                          <mml:mi>p</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Number of parallel branches</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>T</mml:mi>
                        <mml:mi>n</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Nominal battery voltage</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>C</mml:mi>
                        <mml:mi>n</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>Nominal battery capacity</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>D</mml:mi>
                        <mml:mrow>
                          <mml:mi>P</mml:mi>
                          <mml:mi>V</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>All PV array-related expenses</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>D</mml:mi>
                        <mml:mrow>
                          <mml:mi>G</mml:mi>
                          <mml:mi>E</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>All generator set-related expenses</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>D</mml:mi>
                        <mml:mrow>
                          <mml:mi>B</mml:mi>
                          <mml:mi>A</mml:mi>
                          <mml:mi>T</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>All storage system-related expenses (investment, maintenance, operation, replacement)</td>
            </tr>
            <tr>
              <td>
                <inline-formula>
                  <mml:math display="inline">
                    <mml:mrow>
                      <mml:msub>
                        <mml:mi>D</mml:mi>
                        <mml:mrow>
                          <mml:mi>O</mml:mi>
                          <mml:mi>N</mml:mi>
                          <mml:mi>D</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                    </mml:mrow>
                  </mml:math>
                </inline-formula>
              </td>
              <td>All inverter-related expenses</td>
            </tr>
          </tbody>
        </table>
      </table-wrap>
    </sec>
  </body>
  <back>
    <ref-list>
      <title>References</title>
      <ref id="B1">
        <label>1.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Ripama, T. (2025) Annuaire statistique national 2024: Description chiffrée de la vie socio-économique du Burkina Faso. Institut national de la statistique et de la démographie (INSD). https://www.insd.bf</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Ripama, T.</string-name>
            </person-group>
            <year>2025</year>
            <article-title>Annuaire statistique national 2024: Description chiffrée de la vie socio-économique du Burkina Faso</article-title>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B2">
        <label>2.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Djromadji, K.J. (2022) Étude d’un système hybride pour l’alimentation d’un site isolé et optimisation de la charge: Cas du camp Esker. Mémoire de maitre ès sciences appliquées (M.Sc.A). Université du Québec à Rimouski. https://semaphore.uqar.ca/id/eprint/2045/1/Komlan_Josue_Djromadji_fevrier2022.pdf</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Djromadji, K.J.</string-name>
            </person-group>
            <year>2022</year>
            <article-title>Étude d’un système hybride pour l’alimentation d’un site isolé et optimisation de la charge: Cas du camp Esker</article-title>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B3">
        <label>3.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Karim, K. (2012) Coopératives d’électricité: La touche burkinabè à l’électrification rurale. https://lefaso.net/spip.php?article47721</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Karim, K.</string-name>
            </person-group>
            <year>2012</year>
            <article-title>Coopératives d’électricité: La touche burkinabè à l’électrification rurale</article-title>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B4">
        <label>4.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Dembega, S. and Yelbi, I. (2023.) Les Coopératives d’Électricité (COOPEL) à l’épreuve de l’électrification rurale au Burkina Faso de 2001 à 2023: Du modèle coopératif à l’implication des collectivités territoriales. <italic>Actes du colloque international</italic>: <italic>Le Burkina F</italic><italic>as en Afrique et dans le monde</italic>, 3, 67-88. https://progres.ujkz.gov.bf/home?recherche=DEMBEGA+Salam+et+YELBI+Inoussa.+2023</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Dembega, S.</string-name>
              <string-name>Yelbi, I.</string-name>
            </person-group>
            <year>2023</year>
            <article-title>Les Coopératives d’Électricité (COOPEL) à l’épreuve de l’électrification rurale au Burkina Faso de 2001 à 2023: Du modèle coopératif à l’implication des collectivités territoriales</article-title>
            <source>Actes du colloque international: Le Burkina Fas en Afrique et dans le monde</source>
            <volume>3</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B5">
        <label>5.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Ibrahim, H., Younès, R., Ilinca, A. and Perron, J. (2007) Investigation des générateurs hybrides d’électricité de type éolien-air comprimé. <italic>Revue des Energies Renouvelables</italic>, Numéro spécial CER’07, Oujda, 47-50. https://www.academia.edu/34153092/Investigation_des_g%C3%A9n%C3%A9rateurs_hybrides_d_%C3%A9lectricit%C3%A9_de_type_%C3%A9olien_air_comprim%C3%A9</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Ibrahim, H.</string-name>
              <string-name>Ilinca, A.</string-name>
              <string-name>Perron, J.</string-name>
              <string-name>Renouvelables, N</string-name>
            </person-group>
            <year>2007</year>
            <article-title>Investigation des générateurs hybrides d’électricité de type éolien-air comprimé</article-title>
            <source>Revue des Energies Renouvelables</source>
            <volume>47</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B6">
        <label>6.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Brahim, B.A. (2013) Étude des différentes configurations des systèmes d’énergie hybrides PV/diesel et de leur impact sur le cout de production d’électricité. Master d’ingénierie en eau et environnement, 2iE. http://documentation.2ie-edu.org/cdi2ie/opac_css/doc_num.php?explnum_id=1216</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Brahim, B.A.</string-name>
            </person-group>
            <year>2013</year>
            <article-title>Étude des différentes configurations des systèmes d’énergie hybrides PV/diesel et de leur impact sur le cout de production d’électricité</article-title>
            <source>Master d’ingénierie en eau et environnement</source>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B7">
        <label>7.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Kravtzoff, I. (2015) Optimisation d’un système hybride de génération d’énergie électrique permettant de minimiser la consommation et l’empreinte environnementale. Autre. CentraleSupélec, 2015. Français. https://theses.hal.science/tel-01331563v1</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Kravtzoff, I.</string-name>
            </person-group>
            <year>2015</year>
            <article-title>Optimisation d’un système hybride de génération d’énergie électrique permettant de minimiser la consommation et l’empreinte environnementale</article-title>
            <source>Autre. CentraleSupélec</source>
            <volume>2015</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B8">
        <label>8.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Maoulida, F. (2024) Modélisation et optimisation d’un système hybride de génération d’énergie pour l’habitat rural en Afrique. Energie électrique. Université de Lorraine. Français. https://theses.hal.science/tel-04700340v1</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Maoulida, F.</string-name>
            </person-group>
            <year>2024</year>
            <article-title>Modélisation et optimisation d’un système hybride de génération d’énergie pour l’habitat rural en Afrique</article-title>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B9">
        <label>9.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Beyer, H.G. and Langer, C. (1996) A Method for the Identification of Configurations of Pv/Wind Hybrid Systems for the Reliable Supply of Small Loads. <italic>Solar</italic><italic>Energy</italic>, 57, 381-391. https://doi.org/10.1016/s0038-092x(96)00118-1 <pub-id pub-id-type="doi">10.1016/s0038-092x(96)00118-1</pub-id><ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1016/s0038-092x(96)00118-1">https://doi.org/10.1016/s0038-092x(96)00118-1</ext-link></mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Beyer, H.G.</string-name>
              <string-name>Langer, C.</string-name>
            </person-group>
            <year>1996</year>
            <article-title>A Method for the Identification of Configurations of Pv/Wind Hybrid Systems for the Reliable Supply of Small Loads</article-title>
            <source>Solar Energy</source>
            <volume>57</volume>
            <pub-id pub-id-type="doi">10.1016/s0038-092x(96)00118-1</pub-id>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B10">
        <label>10.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Bhargava, A.K., Garg, H.P. and Agarwal, R.K. (1991) Study of a Hybrid Solar System—Solar Air Heater Combined with Solar Cells. <italic>Energy</italic><italic>Conversion</italic><italic>and</italic><italic>Management</italic>, 31, 471-479. https://doi.org/10.1016/0196-8904(91)90028-h <pub-id pub-id-type="doi">10.1016/0196-8904(91)90028-h</pub-id><ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1016/0196-8904(91)90028-h">https://doi.org/10.1016/0196-8904(91)90028-h</ext-link></mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Bhargava, A.K.</string-name>
              <string-name>Garg, H.P.</string-name>
              <string-name>Agarwal, R.K.</string-name>
            </person-group>
            <year>1991</year>
            <article-title>Study of a Hybrid Solar System—Solar Air Heater Combined with Solar Cells</article-title>
            <source>Energy Conversion and Management</source>
            <volume>8904</volume>
            <issue>91</issue>
            <pub-id pub-id-type="doi">10.1016/0196-8904(91)90028-h</pub-id>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B11">
        <label>11.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Saheb-Koussa, D., Haddadi, M. and Belhamel, M. (2009) Economic and Technical Study of a Hybrid System (wind-Photovoltaic-Diesel) for Rural Electrification in Algeria. <italic>Applied</italic><italic>Energy</italic>, 86, 1024-1030. https://doi.org/10.1016/j.apenergy.2008.10.015 <pub-id pub-id-type="doi">10.1016/j.apenergy.2008.10.015</pub-id><ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1016/j.apenergy.2008.10.015">https://doi.org/10.1016/j.apenergy.2008.10.015</ext-link></mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Saheb-Koussa, D.</string-name>
              <string-name>Haddadi, M.</string-name>
              <string-name>Belhamel, M.</string-name>
            </person-group>
            <year>2009</year>
            <article-title>Economic and Technical Study of a Hybrid System (wind-Photovoltaic-Diesel) for Rural Electrification in Algeria</article-title>
            <source>Applied Energy</source>
            <volume>86</volume>
            <pub-id pub-id-type="doi">10.1016/j.apenergy.2008.10.015</pub-id>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B12">
        <label>12.</label>
        <citation-alternatives>
          <mixed-citation publication-type="thesis">Lopez, M. (2008) Contribution à l’optimisation d’un système de conversion éolien pour une unité de production isolée. PhD Thesis, Université Paris Sud-Paris XI. https://theses.hal.science/tel-00344978v1</mixed-citation>
          <element-citation publication-type="thesis">
            <person-group person-group-type="author">
              <string-name>Lopez, M.</string-name>
              <string-name>Thesis, U</string-name>
            </person-group>
            <year>2008</year>
            <article-title>Contribution à l’optimisation d’un système de conversion éolien pour une unité de production isolée</article-title>
            <source>PhD Thesis</source>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B13">
        <label>13.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Maoulida, F. (2020) Développement d’un système hybride de génération d’énergie en site isolé pour la télécommunication et réalisation d’un régulateur de charge solaire. Mémoire de Master 2, d’Ingénierie en Énergies Renouvelables, Université d’Antananarivo. https://api.pageplace.de/preview/DT0400.9783346210043_A40140617/preview-9783346210043_A40140617.pdf</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Maoulida, F.</string-name>
              <string-name>Renouvelables, U</string-name>
            </person-group>
            <year>2020</year>
            <article-title>Développement d’un système hybride de génération d’énergie en site isolé pour la télécommunication et réalisation d’un régulateur de charge solaire</article-title>
            <source>Mémoire de Master 2</source>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B14">
        <label>14.</label>
        <citation-alternatives>
          <mixed-citation publication-type="confproc">Ismail, M., Alam, A., Masud, A.R., Hussain, M. and Rasheed, H. (2014) Optimal Configuration of Hybrid Renewable Energy System for Remote Areas of Balochistan. 17 <italic>th IEEE International Multi Topic Conference</italic> 2014, Karachi, 8-10 December 2014, 539-544. https://doi.org/10.1109/inmic.2014.7097399 <pub-id pub-id-type="doi">10.1109/inmic.2014.7097399</pub-id><ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1109/inmic.2014.7097399">https://doi.org/10.1109/inmic.2014.7097399</ext-link></mixed-citation>
          <element-citation publication-type="confproc">
            <person-group person-group-type="author">
              <string-name>Ismail, M.</string-name>
              <string-name>Alam, A.</string-name>
              <string-name>Masud, A.R.</string-name>
              <string-name>Hussain, M.</string-name>
              <string-name>Rasheed, H.</string-name>
            </person-group>
            <year>2014</year>
            <article-title>Optimal Configuration of Hybrid Renewable Energy System for Remote Areas of Balochistan</article-title>
            <source>17th IEEE International Multi Topic Conference 2014</source>
            <volume>8</volume>
            <pub-id pub-id-type="doi">10.1109/inmic.2014.7097399</pub-id>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B15">
        <label>15.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Balani, S. (2011) Smart Grid Technologies for Efficiency Improvement of Integrated Industrial Electric System. Theses and Dissertations, University of New Orleans, 155. https://scholarworks.uno.edu/td/115/</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Balani, S.</string-name>
              <string-name>Dissertations, U</string-name>
            </person-group>
            <year>2011</year>
            <article-title>Smart Grid Technologies for Efficiency Improvement of Integrated Industrial Electric System</article-title>
            <source>Theses and Dissertations</source>
            <volume>155</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B16">
        <label>16.</label>
        <citation-alternatives>
          <mixed-citation publication-type="thesis">Mahdi, B. (2016) Gestion de l’énergie d’un système hybride autonome pour application «Smart Grid». Thèse de Doctorat, Université Mohamed Khider-Biskra, République Algérienne Démocratique et Populaire, 135. http://thesis.univ-biskra.dz/2587/</mixed-citation>
          <element-citation publication-type="thesis">
            <person-group person-group-type="author">
              <string-name>Mahdi, B.</string-name>
              <string-name>Doctorat, U</string-name>
              <string-name>Khider-Biskra, R</string-name>
            </person-group>
            <year>2016</year>
            <article-title>Gestion de l’énergie d’un système hybride autonome pour application «Smart Grid»</article-title>
            <source>Thèse de Doctorat</source>
            <volume>135</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B17">
        <label>17.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Hadjsaïd, N. and Sabonnadiere, J.-C. (2015) Des réseaux électriques aux smart grids, Encyclopédie de l’énergie. Ecole Nationale Supérieure de l’Energie, l’Eau et l’Environnement. https://www.encyclopedie-energie.org/wp-content/uploads/2018/09/art073_Nourredine-Hadjsa%C3%AFd_JeanClaude-Sabonnadier_reseaux-electriques-Smartgrids.pdf</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Sabonnadiere, J.</string-name>
            </person-group>
            <year>2015</year>
            <article-title>Des réseaux électriques aux smart grids, Encyclopédie de l’énergie</article-title>
            <source>Ecole Nationale Supérieure de l’Energie</source>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B18">
        <label>18.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Duverger, E. (2019) Réseau électrique intelligent pour les nouveaux usages. Thèse de Doctorat, Université de Perpignan via Domitia, 235. https://theses.hal.science/tel-02460664v1/file/These_Duverger_Emilien_2019.pdf</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Duverger, E.</string-name>
              <string-name>Doctorat, U</string-name>
            </person-group>
            <year>2019</year>
            <article-title>Réseau électrique intelligent pour les nouveaux usages</article-title>
            <source>Thèse de Doctorat</source>
            <volume>235</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B19">
        <label>19.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">U.S. Department of Energy (2016) 6 Charts That Will Make You Optimistic about America’s Clean Energy Future. https://www.energy.gov/articles/6-charts-will-make-you-optimistic-about-america-s-clean-energy-future</mixed-citation>
          <element-citation publication-type="web">
            <year>2016</year>
            <article-title>6 Charts That Will Make You Optimistic about America’s Clean Energy Future</article-title>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B20">
        <label>20.</label>
        <citation-alternatives>
          <mixed-citation publication-type="thesis">Bensaoudi, M.S. and Arar, S.E. (2020) Etude et simulation d’un micro réseau intelligent (microgrid). Mémoire de fin d’étude, Higher School in Applied Sciences, République Algérienne Démocratique et Populaire, 88. https://thesis.essa-tlemcen.dz/bitstream/handle/STDB_UNAM/104/memoire%20MEMOIRE%20apr%C3%A9s%20correction%20nchalah.pdf?sequence=1&amp;isAllowed=y</mixed-citation>
          <element-citation publication-type="thesis">
            <person-group person-group-type="author">
              <string-name>Bensaoudi, M.S.</string-name>
              <string-name>Arar, S.E.</string-name>
              <string-name>Sciences, R</string-name>
            </person-group>
            <year>2020</year>
            <article-title>Etude et simulation d’un micro réseau intelligent (microgrid)</article-title>
            <source>Mémoire de fin d’étude</source>
            <volume>88</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B21">
        <label>21.</label>
        <citation-alternatives>
          <mixed-citation publication-type="thesis">Billami, C. and Mehtari, M. (2021) Régulation et gestion de l’énergie électrique dans un micro-réseau intelligent. Mémoire de fin d’étude, Higher School in Applied Sciences-Tlemcen, 99. https://thesis.essa-tlemcen.dz/handle/STDB_UNAM/231</mixed-citation>
          <element-citation publication-type="thesis">
            <person-group person-group-type="author">
              <string-name>Billami, C.</string-name>
              <string-name>Mehtari, M.</string-name>
            </person-group>
            <year>2021</year>
            <article-title>Régulation et gestion de l’énergie électrique dans un micro-réseau intelligent</article-title>
            <source>Mémoire de fin d’étude</source>
            <volume>99</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B22">
        <label>22.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Wikipedia (2026) Garango (département). https://fr.wikipedia.org/wiki/Garango_(d%C3%A9partement)</mixed-citation>
          <element-citation publication-type="web">
            <year>2026</year>
            <article-title>Garango (département)</article-title>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B23">
        <label>23.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Hounnou, A.H.J. (2019) Dimensionnement optimal d’un système hybride hydroélectrique-photovoltaïque-stockage pour une alimentation rurale isolée. Energie électrique. Thèse de Doctorat, Université Bourgogne Franche-Comté; Université d’Abomey-Calavi (Bénin). https://theses.hal.science/tel-02967644v1</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Hounnou, A.H.J.</string-name>
              <string-name>Doctorat, U</string-name>
            </person-group>
            <year>2019</year>
            <article-title>Dimensionnement optimal d’un système hybride hydroélectrique-photovoltaïque-stockage pour une alimentation rurale isolée</article-title>
            <source>Energie électrique. Thèse de Doctorat</source>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B24">
        <label>24.</label>
        <mixed-citation publication-type="web">NASA Prediction of Worldwide Energy Resource (POWER) Database. https://www.earthdata.nasa.gov/data/projects/power https://power.larc.nasa.gov/</mixed-citation>
      </ref>
      <ref id="B25">
        <label>25.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">El Hacen Jed, M. (2022) Étude de l’évolution de performance d’installations photovoltaïques dans différents environnements par modélisation et analyse expé-rimentale. Autre, Université Paris-Est Créteil Val-de-Marne-Paris 12, Université de Nouakchott. https://theses.hal.science/tel-04886235v1/file/TH2022PA120041.pdf</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Jed, M.</string-name>
              <string-name>Autre, U</string-name>
            </person-group>
            <year>2022</year>
            <article-title>Étude de l’évolution de performance d’installations photovoltaïques dans différents environnements par modélisation et analyse expé-rimentale</article-title>
            <source>Autre</source>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B26">
        <label>26.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Stoyanov, L. (2011) Etude de différentes structures de systèmes hybrides à sources d’énergie renouvelables. Energie électrique, Université Pascal Paoli. https://theses.hal.science/tel-00653412v1</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Stoyanov, L.</string-name>
            </person-group>
            <year>2011</year>
            <article-title>Etude de différentes structures de systèmes hybrides à sources d’énergie renouvelables</article-title>
            <source>Energie électrique</source>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B27">
        <label>27.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Iweh, C.D., Clarence, S.G. and Roger, A.H. (2022) The Optimization of Hybrid Renewables for Rural Electrification: Techniques and the Design Problem. <italic>International</italic><italic>Journal</italic><italic>of</italic><italic>Engineering</italic><italic>Trends</italic><italic>and</italic><italic>Technology</italic>, 70, 222-239. https://doi.org/10.14445/22315381/ijett-v70i9p223 <pub-id pub-id-type="doi">10.14445/22315381/ijett-v70i9p223</pub-id><ext-link ext-link-type="uri" xlink:href="https://doi.org/10.14445/22315381/ijett-v70i9p223">https://doi.org/10.14445/22315381/ijett-v70i9p223</ext-link></mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Iweh, C.D.</string-name>
              <string-name>Clarence, S.G.</string-name>
              <string-name>Roger, A.H.</string-name>
            </person-group>
            <year>2022</year>
            <article-title>The Optimization of Hybrid Renewables for Rural Electrification: Techniques and the Design Problem</article-title>
            <source>International Journal of Engineering Trends and Technology</source>
            <volume>70</volume>
            <pub-id pub-id-type="doi">10.14445/22315381/ijett-v70i9p223</pub-id>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B28">
        <label>28.</label>
        <citation-alternatives>
          <mixed-citation publication-type="confproc">Yamegueu, D. (2012) Expérimentation et optimisation d’un prototype de centrale hybride solaire PV/Diesel sans batteries de stockage: Validation du concept ‘‘Flexy Energy’’. Thèse de Doctorat, Laboratoire Energy solaire et Economie d’Energie LESEE et Laboratoire Procédés, Matériaux et Energie Solaire (PROMES-CNRS). https://theses.fr/2012PERP0001</mixed-citation>
          <element-citation publication-type="confproc">
            <person-group person-group-type="author">
              <string-name>Yamegueu, D.</string-name>
              <string-name>Doctorat, L</string-name>
            </person-group>
            <year>2012</year>
            <article-title>Expérimentation et optimisation d’un prototype de centrale hybride solaire PV/Diesel sans batteries de stockage: Validation du concept ‘‘Flexy Energy’’</article-title>
            <source>Thèse de Doctorat</source>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B29">
        <label>29.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Stoyanov, L., Notton, G. and Lazarov, V.D. (2023) Optimisation des systèmes multi-sources de production d’électricité à énergies renouvelables. <italic>Journal</italic><italic>of</italic><italic>Renewable</italic><italic>Energies</italic>, 10, 1-18. https://doi.org/10.54966/jreen.v10i1.794 <pub-id pub-id-type="doi">10.54966/jreen.v10i1.794</pub-id><ext-link ext-link-type="uri" xlink:href="https://doi.org/10.54966/jreen.v10i1.794">https://doi.org/10.54966/jreen.v10i1.794</ext-link></mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Stoyanov, L.</string-name>
              <string-name>Notton, G.</string-name>
              <string-name>Lazarov, V.D.</string-name>
            </person-group>
            <year>2023</year>
            <article-title>Optimisation des systèmes multi-sources de production d’électricité à énergies renouvelables</article-title>
            <source>Journal of Renewable Energies</source>
            <volume>10</volume>
            <pub-id pub-id-type="doi">10.54966/jreen.v10i1.794</pub-id>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B30">
        <label>30.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Ayaz, R., Ozcanli, A.K., Nakir, I., Bhusal, P. and Unal, A. (2019) Life Cycle Cost Analysis on M1 and M2 Road Class Luminaires Installed in Turkey. <italic>Light</italic><italic>&amp;</italic><italic>Engineering</italic>, 27, 61-70. https://doi.org/10.33383/2018-008 <pub-id pub-id-type="doi">10.33383/2018-008</pub-id><ext-link ext-link-type="uri" xlink:href="https://doi.org/10.33383/2018-008">https://doi.org/10.33383/2018-008</ext-link></mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Ayaz, R.</string-name>
              <string-name>Ozcanli, A.K.</string-name>
              <string-name>Nakir, I.</string-name>
              <string-name>Bhusal, P.</string-name>
              <string-name>Unal, A.</string-name>
            </person-group>
            <year>2019</year>
            <article-title>Life Cycle Cost Analysis on M1 and M2 Road Class Luminaires Installed in Turkey</article-title>
            <source>Light &amp; Engineering</source>
            <volume>27</volume>
            <pub-id pub-id-type="doi">10.33383/2018-008</pub-id>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B31">
        <label>31.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Vidalenc, E., Marchal, D. and Parrouffe, J.-M. (2022) Transition(s) 2050-ensei-gnements énergétiques pour la neutralité carbone. La Revue de l’Énergie n˚ 662. https://www.wec-france.org/les-publications/la-revue-de-lenergie-n662/</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Vidalenc, E.</string-name>
              <string-name>Marchal, D.</string-name>
              <string-name>Parrouffe, J.</string-name>
            </person-group>
            <year>2022</year>
            <article-title>Transition(s) 2050-ensei-gnements énergétiques pour la neutralité carbone</article-title>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B32">
        <label>32.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Criqui, P. (2023) L’évaluation des coûts d’abattement des émissions en France. <italic>Revue</italic><italic>de</italic><italic>l</italic>’ <italic>Energie</italic>, 667, 30-48. https://doi.org/10.3917/ener.667.0030 <pub-id pub-id-type="doi">10.3917/ener.667.0030</pub-id><ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3917/ener.667.0030">https://doi.org/10.3917/ener.667.0030</ext-link></mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Criqui, P.</string-name>
            </person-group>
            <year>2023</year>
            <article-title>L’évaluation des coûts d’abattement des émissions en France</article-title>
            <source>Revue de l’Energie</source>
            <volume>667</volume>
            <pub-id pub-id-type="doi">10.3917/ener.667.0030</pub-id>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B33">
        <label>33.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Meunier, G. and Ponssard, J. (2024) Du bon usage du coût d’abattement dans le contexte de la neutralité carbone en 2050: Principes et application à la mobilité. <italic>Revue</italic><italic>de</italic><italic>l</italic>’ <italic>Energie</italic>, 670, 25-45. https://doi.org/10.3917/ener.670.0025 <pub-id pub-id-type="doi">10.3917/ener.670.0025</pub-id><ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3917/ener.670.0025">https://doi.org/10.3917/ener.670.0025</ext-link></mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Meunier, G.</string-name>
              <string-name>Ponssard, J.</string-name>
            </person-group>
            <year>2024</year>
            <article-title>Du bon usage du coût d’abattement dans le contexte de la neutralité carbone en 2050: Principes et application à la mobilité</article-title>
            <source>Revue de l’Energie</source>
            <volume>670</volume>
            <pub-id pub-id-type="doi">10.3917/ener.670.0025</pub-id>
          </element-citation>
        </citation-alternatives>
      </ref>
    </ref-list>
  </back>
</article>