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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Phys.</journal-id>
<journal-title>Frontiers in Physics</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Phys.</abbrev-journal-title>
<issn pub-type="epub">2296-424X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1595410</article-id>
<article-id pub-id-type="doi">10.3389/fphy.2025.1595410</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Physics</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Aging monitoring and fault positioning for zinc oxide surge arresters based on the fifth harmonic of the leakage current</article-title>
<alt-title alt-title-type="left-running-head">Lu et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fphy.2025.1595410">10.3389/fphy.2025.1595410</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Lu</surname>
<given-names>Yongling</given-names>
</name>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/3006264/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Xue</surname>
<given-names>Zhitong</given-names>
</name>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Guo</surname>
<given-names>Jiahao</given-names>
</name>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Chenyu</given-names>
</name>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Liu</surname>
<given-names>Jian</given-names>
</name>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Xiao</surname>
<given-names>Xiaolong</given-names>
</name>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Sun</surname>
<given-names>Jian</given-names>
</name>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
</contrib-group>
<aff>
<institution>State Grid Jiangsu Electric Power Research Institute Co., Ltd.</institution>, <addr-line>Nanjing</addr-line>, <addr-line>Jiangsu</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1468735/overview">Qiuqin Sun</ext-link>, Hunan University, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2426761/overview">Bystr&#xed;k Doln&#xed;k</ext-link>, Technical University of Ko&#x161;ice, Slovakia</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2618420/overview">Yanhui Wei</ext-link>, Qingdao University of Science and Technology, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3021705/overview">Anil Khopkar</ext-link>, Electrical Research And Development Association (ERDA), India</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Yongling Lu, <email>1395500274@qq.com</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>10</day>
<month>07</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>13</volume>
<elocation-id>1595410</elocation-id>
<history>
<date date-type="received">
<day>18</day>
<month>03</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>28</day>
<month>05</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Lu, Xue, Guo, Zhang, Liu, Xiao and Sun.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Lu, Xue, Guo, Zhang, Liu, Xiao and Sun</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Current techniques for aging monitoring and fault positioning for zinc oxide surge arresters usually use the third harmonic of the leakage resistive current. However, harmonic interference in the power grid voltage greatly affects the third harmonic, resulting in poor monitoring and positioning effects. Therefore, based on the harmonic characteristics of the resistive current, this article adopts the fifth harmonic of the leakage current as a novel monitoring indicator for zinc oxide surge arresters. In addition, it builds an aging experimental platform for zinc oxide surge arresters with voltage harmonic interference. An improved displacement current method and a fast Fourier transform algorithm are used to extract current harmonic features, and the percentage changes in features and harmonic sensitivity are introduced to analyze the fifth harmonic characteristics. A monitoring threshold and positioning scheme is proposed. The results show that the fifth harmonic exhibits high sensitivity to faults, with smaller changes in harmonic sensitivity and characteristic percentage, stronger resistance to harmonic interference. Furthermore, it is more suitable for aging monitoring and fault positioning for zinc oxide surge arresters than existing third harmonic analysis methods.</p>
</abstract>
<kwd-group>
<kwd>leakage current</kwd>
<kwd>third harmonic of resistive current</kwd>
<kwd>fifth harmonic of the resistive current</kwd>
<kwd>aging monitoring and positioning zinc oxide surge arresters</kwd>
<kwd>aging monitoring and positioning</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Interdisciplinary Physics</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Zinc oxide surge arresters are extensively used to protect electrical systems from transient overvoltage caused by severe lightning strikes and grid switching operations [<xref ref-type="bibr" rid="B1">1</xref>]. However, the aging of valve discs of arresters typically leads to increased conductivity. Moreover, in severe cases, internal flashovers and arrester explosions can severely disrupt the normal operation of zinc oxide surge arresters [<xref ref-type="bibr" rid="B2">2</xref>&#x2013;<xref ref-type="bibr" rid="B5">5</xref>]. Arrester failure warrants immediate localization and replacement by operators to prevent interference with other electrical equipment in the grid [<xref ref-type="bibr" rid="B6">6</xref>]. Therefore, it is crucial to investigate aging monitoring and fault positioning for zinc oxide surge arresters.</p>
<p>Several methods, including residual voltage method [<xref ref-type="bibr" rid="B7">7</xref>], power loss measurement [<xref ref-type="bibr" rid="B8">8</xref>], leakage current measurement [<xref ref-type="bibr" rid="B9">9</xref>], capacitive current compensation [<xref ref-type="bibr" rid="B10">10</xref>], and harmonic analysis [<xref ref-type="bibr" rid="B11">11</xref>], have been proposed for monitoring the aging and fault conditions of zinc oxide surge arresters. Leakage current measurement is the most widely adopted for arrester condition assessment owing to its convenience and high accuracy [<xref ref-type="bibr" rid="B12">12</xref>]. Arrester failure can cause a significant surge in the total leakage current, exhibiting noticeable distortion in the waveform [<xref ref-type="bibr" rid="B13">13</xref>, <xref ref-type="bibr" rid="B14">14</xref>]. The total leakage current is the vector sum of the resistive component <italic>i</italic>
<sub>R</sub> and the capacitive component <italic>i</italic>
<sub>C</sub>, as shown in <xref ref-type="fig" rid="F1">Figure 1</xref>. The resistive leakage current is influenced by the applied voltage, fault characteristics, and ambient temperature. In addition, it exhibits high sensitivity to arrester faults and degradation [<xref ref-type="bibr" rid="B15">15</xref>, <xref ref-type="bibr" rid="B16">16</xref>]. Since the variation in the third harmonic of the resistive current is more pronounced than that of the fundamental wave, it can be used for diagnosing arrester fault conditions [<xref ref-type="bibr" rid="B17">17</xref>]. However, the third harmonic of the resistive current is also affected by harmonics in the grid voltage, especially the third harmonic of the voltage, which significantly impacts the third harmonic of the resistive current [<xref ref-type="bibr" rid="B18">18</xref>, <xref ref-type="bibr" rid="B19">19</xref>]. This interference prevents the precise reflection of arrester fault conditions. Therefore, a new monitoring indicator that is robust against voltage harmonic interference is necessary.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Equivalent circuit model of zinc oxide surge arresters.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g001.tif"/>
</fig>
<p>Recently, Wang et al. [<xref ref-type="bibr" rid="B20">20</xref>] from the China Electric Power Research Institute investigated the variation trends in resistive current and harmonics under system voltage harmonics, particularly noting the significant effect it had on the third harmonic, and proposed an integrated online monitoring device for arresters. Qi et al. [<xref ref-type="bibr" rid="B21">21</xref>] from Wuhan University of Technology proposed a waveform distortion correction method based on measured voltage waveforms to eliminate the effect of high-order voltage harmonics on resistive current and identified the true value of the leakage current. Additionally, Khodsuz and Mirzaie [<xref ref-type="bibr" rid="B22">22</xref>] from Brno University of Technology proposed a technique for eliminating the effect of voltage third harmonics on the resistive leakage current based on grid voltage analysis. However, these studies rely on measuring grid voltage harmonics, which not only increases the measurement and computational burden but also is not conducive to the reliability and effectiveness of fault monitoring and positioning for online arresters.</p>
<p>To address these challenges, this study proposes the fifth harmonic of the resistive leakage current as a new indicator for aging monitoring and fault positioning for zinc oxide surge arresters. First, an aging experimental platform was established for zinc oxide surge arresters, with harmonic components added to the applied voltage to simulate grid voltage harmonic interference. Second, the resistive leakage current was extracted using an improved displacement current method, and the harmonic components of the resistive current were determined using the fast Fourier transform (FFT) algorithm. Finally, the variations in characteristic quantities under voltage harmonic interference and aging faults were investigated to evaluate the robustness of the fifth harmonic against voltage harmonics and its effectiveness and reliability for aging monitoring. A monitoring and positioning scheme is also proposed. This methodology is specifically designed for aging monitoring and fault localization in zinc oxide surge arresters, enabling real-time degradation assessment and facilitating cost-effective operation and maintenance through predictive condition-based strategies.</p>
</sec>
<sec id="s2">
<title>2 Construction of the aging experimental platform for zinc oxide surge arresters</title>
<p>In the experiment, a variable low-voltage power supply of 0&#x2013;240 V was employed. Two experimental schemes were designed. In Scheme I, a pure sinusoidal voltage was applied. But during experimental validation, the inherent nonlinearities of zinc oxide surge arresters and power transformers introduced harmonic distortions. Post-FFT analysis revealed a measured THD of 1.26%, with harmonic voltage components quantified as follows: third harmonic (<italic>V</italic>
<sub>3rd</sub>) at 0.907%, fifth harmonic (<italic>V</italic>
<sub>5th</sub>) at 0.454%, seventh harmonic (<italic>V</italic>
<sub>7th</sub>) at 0.305%, ninth harmonic (<italic>V</italic>
<sub>9th</sub>) at 0.239%, and eleventh harmonic (<italic>V</italic>
<sub>11th</sub>) at 0.126%,as shown in <xref ref-type="fig" rid="F2">Figure 2a</xref>. In Scheme II, a voltage with a total harmonic distortion of 5% was applied to simulate the harmonic impact in power grids. The harmonic contents of the applied voltage included 3.6% third harmonic (<italic>V</italic>
<sub>3rd</sub>), 1.8% fifth harmonic (<italic>V</italic>
<sub>5th</sub>), 1.21% seventh harmonic (<italic>V</italic>
<sub>7th</sub>), 0.95% ninth harmonic (<italic>V</italic>
<sub>9th</sub>), and 0.5% eleventh harmonic (<italic>V</italic>
<sub>11th</sub>), as shown in <xref ref-type="fig" rid="F2">Figure 2b</xref>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>
<bold>(a)</bold> Harmonic content of the applied voltage for Scheme 1; <bold>(b)</bold> Harmonic content of the applied voltage for Scheme 2.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g002.tif"/>
</fig>
<p>Two zinc oxide surge arresters were selected for the experiment: one in a normal condition and the other in a severely aged and faulty condition. The normal condition refers to pristine, unused arresters post-manufacturing, while the aged condition corresponds to units that have been in continuous operation at Yancheng Substation, Jiangsu Province for a decade. The parameters of the arresters are listed in <xref ref-type="table" rid="T1">Table 1</xref>. An experimental circuit was constructed using a variable low-voltage power supply, voltage regulator, transformer, capacitive voltage divider, and high-precision current sensor, as shown in <xref ref-type="fig" rid="F3">Figure 3</xref>, The capacitive voltage divider (FLDFR-150 kV) serves as a critical component for measuring the applied voltage. The accompanying display meter can display the magnitude and waveform of this voltage and transmit the waveform to a computer for FFT analysis to validate harmonic injection levels, and the value of the protective resistor is 10 k&#x3a9;. The arresters were subjected to voltages ranging from 70 to 120 kV using the variable low-voltage power supply and a step-up transformer, the parameters of the transformer are listed in <xref ref-type="table" rid="T2">Table 2</xref>. The applied voltage was monitored using a capacitive voltage divider, and its harmonic components were obtained using the FFT algorithm. The total leakage current was extracted using a high-precision current sensor (CM1A H00), and measure the total leakage current using a high-speed oscilloscope (HDO6054).</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Parameters of zinc oxide surge arresters.</p>
</caption>
<table>
<tbody valign="top">
<tr>
<td align="center">Rated voltage</td>
<td align="center">110 kV</td>
</tr>
<tr>
<td align="center">Continuous operating voltage</td>
<td align="center">94 kV</td>
</tr>
<tr>
<td align="center">Temporary overvoltage</td>
<td align="center">130 kV</td>
</tr>
<tr>
<td align="center">DC reference voltage</td>
<td align="center">180 kV</td>
</tr>
<tr>
<td align="center">Nominal discharge current</td>
<td align="center">10 kA</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Experimental principle diagram.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g003.tif"/>
</fig>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Parameters of transformer.</p>
</caption>
<table>
<tbody valign="top">
<tr>
<td align="center">Voltage rating</td>
<td align="center">240 V/150 kV</td>
</tr>
<tr>
<td align="center">Rated Current</td>
<td align="center">1 A</td>
</tr>
<tr>
<td align="center">Frequency</td>
<td align="center">50 Hz</td>
</tr>
<tr>
<td align="center">Rated Power</td>
<td align="center">150 kVA</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3">
<title>3 Harmonic feature extraction of the leakage current in zinc oxide surge arresters</title>
<p>The low-voltage power supply was adjusted to subject the arresters to voltages ranging from 70 to 120 kV through the step-up transformer. The input voltage and total leakage current were measured.</p>
<p>An improved displacement current method was employed to extract the resistive leakage current, as shown in the Simulink model in <xref ref-type="fig" rid="F4">Figure 4</xref>. A zero-crossing detector was used to determine the phase of the current waveform, and a frequency detector was used to determine the frequency of the total leakage current. A new waveform was obtained by introducing a quarter-cycle delay to the total leakage current waveform, which was then added to the original total leakage current waveform to generate a composite waveform. The peak time of the composite waveform and that of the capacitive current component were determined using a peak time detector. The capacitive current waveform was generated based on the known frequency, peak time, and peak value. The resistive leakage current (<italic>I</italic>
<sub>R</sub>) was ultimately extracted by subtracting the capacitive current component (<italic>I</italic>
<sub>C</sub>) from the total leakage current.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Simulink model of improved shift current method.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g004.tif"/>
</fig>
<p>The FFT was used to determine the third harmonic (<italic>I</italic>
<sub>R3rd</sub>) and fifth harmonic (<italic>I</italic>
<sub>R5th</sub>) of the resistive leakage current. Experiments were conducted on both normal and aged arresters under the two schemes, and the total leakage current (<italic>I</italic>
<sub>T</sub>), resistive leakage current (<italic>I</italic>
<sub>R</sub>), and their harmonics (<italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub>) were measured and recorded. The overall process is shown in <xref ref-type="fig" rid="F5">Figure 5</xref>.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Overall flowchart of the harmonic extraction.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g005.tif"/>
</fig>
</sec>
<sec id="s4">
<title>4 Characteristic analysis of <italic>I</italic>
<sub>R5th</sub>
</title>
<sec id="s4-1">
<title>4.1 Analysis of the anti-voltage harmonic interference capability of <italic>I</italic>
<sub>R5th</sub>
</title>
<p>Under both Scheme I and Scheme II conditions, the arresters were subjected to voltages ranging from 70 to 120 kV, the voltage waveform is shown in <xref ref-type="fig" rid="F6">Figure 6</xref>, Scheme I exhibits a standard sinusoidal voltage profile, while Scheme II demonstrates noticeable waveform distortion following the intentional introduction of harmonic components.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Applied voltage waveform.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g006.tif"/>
</fig>
<p>The current waveform of the transformer&#x2019;s high-voltage side output is shown in <xref ref-type="fig" rid="F7">Figure 7</xref>. It is noteworthy that these waveforms directly represent the total leakage current of the surge arresters. Scheme I corresponds to the total leakage current under sinusoidal voltage conditions, whereas Scheme II reflects the leakage current under harmonic-distorted voltage conditions. The peak values of the total leakage current (<italic>I</italic>
<sub>T</sub>) were measured, as shown in <xref ref-type="table" rid="T3">Table 3</xref>. The resistive leakage current (<italic>I</italic>
<sub>R</sub>) was extracted from the total leakage current using the improved displacement current method, and its peak value was recorded, as shown in <xref ref-type="table" rid="T3">Table 3</xref>. It can be observed from <xref ref-type="table" rid="T3">Tables 3</xref>, <xref ref-type="table" rid="T4">4</xref> that, due to the addition of voltage harmonics in Scheme II, the total leakage current increased by 9.3 &#xb5;A, and the resistive current increased by 11.5 &#xb5;A under the rated voltage. The percentage changes in I<sub>T</sub> and its <italic>I</italic>
<sub>R</sub> under Scheme II are shown in <xref ref-type="fig" rid="F8">Figure 8</xref>. Under the rated voltage, the percentage increase in <italic>I</italic>
<sub>T</sub> was 0.63%, while the percentage increase in <italic>I</italic>
<sub>R</sub> was 1.32%. This indicates that the peak value of <italic>I</italic>
<sub>R</sub> increased more significantly than that of <italic>I</italic>
<sub>T</sub> due to voltage harmonics, as <italic>I</italic>
<sub>R</sub> is more sensitive to changes in voltage harmonics.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Total leakage current waveform.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g007.tif"/>
</fig>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Total leakage current <italic>I</italic>
<sub>T</sub> for two schemes.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Applied voltage (kV)</th>
<th align="center">Scheme I <italic>I</italic>
<sub>T</sub> (&#xb5;A)</th>
<th align="center">Scheme II <italic>I</italic>
<sub>T</sub> (&#xb5;A)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">70</td>
<td align="center">826.9</td>
<td align="center">827.4</td>
</tr>
<tr>
<td align="center">80</td>
<td align="center">946.8</td>
<td align="center">948.5</td>
</tr>
<tr>
<td align="center">90</td>
<td align="center">1,115</td>
<td align="center">1,117.2</td>
</tr>
<tr>
<td align="center">94</td>
<td align="center">1,168.5</td>
<td align="center">1,171.4</td>
</tr>
<tr>
<td align="center">98</td>
<td align="center">1,237.4</td>
<td align="center">1,241.8</td>
</tr>
<tr>
<td align="center">100</td>
<td align="center">1,289.8</td>
<td align="center">1,295.7</td>
</tr>
<tr>
<td align="center">110</td>
<td align="center">1,475.6</td>
<td align="center">1,484.9</td>
</tr>
<tr>
<td align="center">120</td>
<td align="center">2,395.2</td>
<td align="center">2,425.5</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Resistive leakage current <italic>I</italic>
<sub>R</sub> for two schemes.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Applied voltage (kV)</th>
<th align="center">Scheme I <italic>I</italic>
<sub>R</sub> (&#xb5;A)</th>
<th align="center">Scheme II <italic>I</italic>
<sub>R</sub> (&#xb5;A)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">70</td>
<td align="center">320.2</td>
<td align="center">320.5</td>
</tr>
<tr>
<td align="center">80</td>
<td align="center">389.9</td>
<td align="center">390.7</td>
</tr>
<tr>
<td align="center">90</td>
<td align="center">543.5</td>
<td align="center">544.8</td>
</tr>
<tr>
<td align="center">94</td>
<td align="center">595.3</td>
<td align="center">597.5</td>
</tr>
<tr>
<td align="center">98</td>
<td align="center">641.2</td>
<td align="center">643.9</td>
</tr>
<tr>
<td align="center">100</td>
<td align="center">706.0</td>
<td align="center">712.2</td>
</tr>
<tr>
<td align="center">110</td>
<td align="center">870.4</td>
<td align="center">881.9</td>
</tr>
<tr>
<td align="center">120</td>
<td align="center">2019.6</td>
<td align="center">2061.7</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>
<italic>I</italic>
<sub>T</sub> and <italic>I</italic>
<sub>R</sub> percentage changes.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g008.tif"/>
</fig>
<p>The peak amplitudes of <italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> were calculated using the FFT algorithm, as shown in <xref ref-type="table" rid="T5">Table 5</xref>. In Scheme I, the amplitude and nonlinearity of the resistive current varied with the applied voltage, and harmonic components were present in the resistive current. In Scheme II, the peaks of both <italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> increased with the introduction of voltage harmonics. Under the rated voltage, the increases were 10.7 &#xb5;A and 2.9 &#xb5;A, respectively. When the percentage weight of <italic>V</italic>
<sub>3rd</sub> was nearly twice that of <italic>V</italic>
<sub>5th</sub>, the increase in the <italic>I</italic>
<sub>R3rd</sub> peak was 3.7 times that of <italic>I</italic>
<sub>R5th</sub>. This indicates that the increase in I<sub>R3rd</sub> due to V<sub>3rd</sub> is more significant than the increase in <italic>I</italic>
<sub>R5th</sub> due to <italic>V</italic>
<sub>5th</sub>.</p>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Peak amplitudes of <italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub>.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Applied voltage (kV)</th>
<th colspan="2" align="center">
<italic>I</italic>
<sub>R3rd</sub> peak amplitude (&#xb5;A)</th>
<th colspan="2" align="center">
<italic>I</italic>
<sub>R5th</sub> peak amplitude (&#xb5;A)</th>
</tr>
<tr>
<th align="center">Scheme I</th>
<th align="center">Scheme II</th>
<th align="center">Scheme I</th>
<th align="center">Scheme II</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">70</td>
<td align="center">54.80</td>
<td align="center">55.10</td>
<td align="center">17.70</td>
<td align="center">17.80</td>
</tr>
<tr>
<td align="center">80</td>
<td align="center">70.20</td>
<td align="center">70.70</td>
<td align="center">31.80</td>
<td align="center">32.00</td>
</tr>
<tr>
<td align="center">90</td>
<td align="center">99.10</td>
<td align="center">100.60</td>
<td align="center">48.10</td>
<td align="center">48.30</td>
</tr>
<tr>
<td align="center">94</td>
<td align="center">121.80</td>
<td align="center">124.60</td>
<td align="center">55.20</td>
<td align="center">55.70</td>
</tr>
<tr>
<td align="center">98</td>
<td align="center">143.50</td>
<td align="center">147.40</td>
<td align="center">64.50</td>
<td align="center">65.20</td>
</tr>
<tr>
<td align="center">100</td>
<td align="center">163.90</td>
<td align="center">169.10</td>
<td align="center">75.60</td>
<td align="center">76.60</td>
</tr>
<tr>
<td align="center">110</td>
<td align="center">241.00</td>
<td align="center">249.90</td>
<td align="center">110.40</td>
<td align="center">112.00</td>
</tr>
<tr>
<td align="center">120</td>
<td align="center">525.60</td>
<td align="center">550.20</td>
<td align="center">259.30</td>
<td align="center">265.90</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s4-2">
<title>4.2 Analysis of the effectiveness of <italic>I</italic>
<sub>R5th</sub> for aging monitoring</title>
<p>Under both Scheme I and Scheme II conditions, the applied voltage was different, and the <italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> of both normal and severely aged arresters were measured and calculated, as shown in <xref ref-type="fig" rid="F9">Figures 9</xref>, <xref ref-type="fig" rid="F10">10</xref>, and the data for <xref ref-type="fig" rid="F9">Figure 9</xref> is shown in <xref ref-type="table" rid="T5">Table 5</xref>, and the data for <xref ref-type="fig" rid="F10">Figure 10</xref> is shown in <xref ref-type="table" rid="T6">Table 6</xref>. Under voltage harmonic interference, both current harmonics increased, but the change in <italic>I</italic>
<sub>R3rd</sub> was significant, while <italic>I</italic>
<sub>R5th</sub> remained relatively stable.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>
<italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> peak values of surge arresters in normal state.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g009.tif"/>
</fig>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>
<italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> peak values of surge arresters in aging fault condition.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g010.tif"/>
</fig>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>Peak amplitudes of <italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub>.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Applied voltage (kV)</th>
<th colspan="2" align="center">
<italic>I</italic>
<sub>R3rd</sub> peak amplitude (&#xb5;A)</th>
<th colspan="2" align="center">
<italic>I</italic>
<sub>R5th</sub> peak amplitude (&#xb5;A)</th>
</tr>
<tr>
<th align="center">Scheme I</th>
<th align="center">Scheme II</th>
<th align="center">Scheme I</th>
<th align="center">Scheme II</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">70</td>
<td align="center">79.80</td>
<td align="center">81.00</td>
<td align="center">26.4</td>
<td align="center">26.6</td>
</tr>
<tr>
<td align="center">80</td>
<td align="center">115.60</td>
<td align="center">117.40</td>
<td align="center">55.9</td>
<td align="center">56.5</td>
</tr>
<tr>
<td align="center">90</td>
<td align="center">169.50</td>
<td align="center">173.30</td>
<td align="center">77.8</td>
<td align="center">78.9</td>
</tr>
<tr>
<td align="center">94</td>
<td align="center">197.20</td>
<td align="center">202.00</td>
<td align="center">94.5</td>
<td align="center">96.5</td>
</tr>
<tr>
<td align="center">98</td>
<td align="center">213.50</td>
<td align="center">221.10</td>
<td align="center">106.0</td>
<td align="center">108.4</td>
</tr>
<tr>
<td align="center">100</td>
<td align="center">240.30</td>
<td align="center">249.70</td>
<td align="center">113.3</td>
<td align="center">115.9</td>
</tr>
<tr>
<td align="center">110</td>
<td align="center">345.00</td>
<td align="center">366.40</td>
<td align="center">162.1</td>
<td align="center">165.9</td>
</tr>
<tr>
<td align="center">120</td>
<td align="center">880.10</td>
<td align="center">936.50</td>
<td align="center">458.9</td>
<td align="center">472.2</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Comparing the data obtained in Scheme I, as shown in <xref ref-type="fig" rid="F11">Figure 11</xref>, it is evident that both <italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> increased for the aged arresters compared to the normal condition, indicating that both harmonics can serve as indicators of aging and fault condition in zinc oxide surge arresters.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>
<italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> peak values in normal and aging fault conditions.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g011.tif"/>
</fig>
<p>The percentage changes in the peaks of <italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> under harmonic interference were calculated for both types of arresters, as shown in <xref ref-type="fig" rid="F12">Figure 12</xref>; <xref ref-type="table" rid="T7">Table 7</xref>. The percentage increase was more prominent in <italic>I</italic>
<sub>R3rd</sub> than in <italic>I</italic>
<sub>R5th</sub>. Although the percentage weight of <italic>V</italic>
<sub>3rd</sub> was nearly twice that of <italic>V</italic>
<sub>5th</sub> in Scheme II, the increase in the peak of <italic>I</italic>
<sub>R3rd</sub> was 2.55 and 2.65 times higher than that of <italic>I</italic>
<sub>R5th</sub> for the normal and aged arresters, respectively, under the rated voltage. This indicates that the impact of <italic>V</italic>
<sub>3rd</sub> on the peak of <italic>I</italic>
<sub>R3rd</sub> is greater than that of <italic>V</italic>
<sub>
<italic>5th</italic>
</sub> on the peak of <italic>I</italic>
<sub>R5th</sub>. This is attributed to the nonlinearity of zinc oxide surge arresters, leading to a more significant increase in <italic>I</italic>
<sub>R3rd</sub>. Additionally, the percentage increase in the aged arresters was higher than that in the normal arresters, validating the monitoring effectiveness of <italic>I</italic>
<sub>R5th</sub>. Therefore, it can replace <italic>I</italic>
<sub>R3rd</sub> as a new monitoring indicator.</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Percentage changes in <italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> in normal and aging fault conditions under harmonic interference.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g012.tif"/>
</fig>
<table-wrap id="T7" position="float">
<label>TABLE 7</label>
<caption>
<p>Data analysis of normal and aging fault conditions under harmonic interference.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Condition of arresters</th>
<th align="left">
<italic>I</italic>
<sub>R3rd</sub> percentage variation</th>
<th align="left">
<italic>I</italic>
<sub>R5th</sub> percentage variation</th>
<th align="left">Percentage ratio</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Normal condition</td>
<td align="center">3.69</td>
<td align="center">1.45</td>
<td align="center">2.55</td>
</tr>
<tr>
<td align="left">Aging fault condition</td>
<td align="center">6.20</td>
<td align="center">2.34</td>
<td align="center">2.65</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s4-3">
<title>4.3 Sensitivity analysis of <italic>I</italic>
<sub>R5th</sub> harmonics</title>
<p>In Scheme I, the peaks of <italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> were extracted independently of voltage harmonics. Therefore, the changes in the peaks of <italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> were compared by changing the magnitude of the applied voltage to verify the potential of <italic>I</italic>
<sub>R5th</sub> as a standard for aging fault assessment in zinc oxide surge arresters.</p>
<p>In Scheme II, the peaks of <italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> were influenced by voltage harmonics. The changes in the peaks of <italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub> under the influence of <italic>V</italic>
<sub>3rd</sub> and <italic>V</italic>
<sub>5th</sub> were analyzed, and the percentage changes in the characteristic quantities were calculated and normalized by the percentage changes in the voltage harmonics. The average values were used to derive the sensitivity <italic>S</italic> expression:<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:mi mathvariant="normal">S</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mi>N</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>N</mml:mi>
<mml:mo>&#x2013;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>z</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>z</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>z</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
</p>
<p>Using <xref ref-type="disp-formula" rid="e1">Equation 1</xref>, the harmonic sensitivity <italic>S</italic> of the total leakage current <italic>I</italic>
<sub>T</sub>, <italic>I</italic>
<sub>R3rd</sub>, and <italic>I</italic>
<sub>R5th</sub> was calculated, as shown in <xref ref-type="table" rid="T8">Table 8</xref>. The results indicate that the harmonic sensitivity of <italic>I</italic>
<sub>R5th</sub> is lower than that of the other characteristic quantities. This suggests that, under voltage conditions with total harmonic interference, the value of <italic>I</italic>
<sub>R5th</sub> is less affected and provides high reliability for monitoring both the normal and aging fault conditions of arresters.</p>
<table-wrap id="T8" position="float">
<label>TABLE 8</label>
<caption>
<p>Harmonic sensitivity analysis.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Feature parameter category</th>
<th align="center">Harmonic sensitivity <italic>S</italic>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Total leakage current <italic>I</italic>
<sub>T</sub>
</td>
<td align="center">0.1793</td>
</tr>
<tr>
<td align="center">
<italic>I</italic>
<sub>R3rd</sub>
</td>
<td align="center">0.5157</td>
</tr>
<tr>
<td align="center">
<italic>I</italic>
<sub>R5th</sub>
</td>
<td align="center">0.1356</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s5">
<title>5 Aging monitoring and fault positioning for zinc oxide surge arresters</title>
<p>Based on the relationship between the resistive current harmonics (<italic>I</italic>
<sub>R3rd</sub> and <italic>I</italic>
<sub>R5th</sub>) and the applied voltage, threshold values for identifying the aging fault conditions of zinc oxide surge arresters were established, as shown in <xref ref-type="table" rid="T9">Table 9</xref>. The data provenance has been explicitly substantiated through statistical derivation from extensive experimental measurements, which systematically validates the threshold robustness.</p>
<table-wrap id="T9" position="float">
<label>TABLE 9</label>
<caption>
<p>
<italic>I</italic>
<sub>R5th</sub> threshold judgment criteria for aging faults of zinc oxide surge arresters.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Applied voltage</th>
<th align="center">
<italic>I</italic>
<sub>R5th</sub>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">90 kV &#x3c; U &#x2264; 98 kV</td>
<td align="center">&#x3e;75 &#xb5;A</td>
</tr>
<tr>
<td align="center">98 kV &#x3c; U &#x2264; 110 kV</td>
<td align="center">&#x3e;110 &#xb5;A</td>
</tr>
<tr>
<td align="center">110 kV &#x3c; U</td>
<td align="center">&#x3e;300 &#xb5;A</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<italic>I</italic>
<sub>R5th</sub> is proposed as a new indicator for fault diagnosis of arresters. The leakage current of the zinc oxide surge arresters is detected using a zero-flux high-precision current sensor. After FFT analysis and analog-to-digital signal processing, the data can be transmitted wirelessly for online monitoring. When the monitored value of <italic>I</italic>
<sub>R5th</sub> exceeds the aforementioned threshold, an alert is triggered. Combined with a GPS positioning system, the location of the faulty arresters can be accurately obtained. The principle of the monitoring and positioning method is shown in <xref ref-type="fig" rid="F13">Figure 13</xref>.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Schematic diagram of monitoring and positioning method for zinc oxide surge arresters.</p>
</caption>
<graphic xlink:href="fphy-13-1595410-g013.tif"/>
</fig>
</sec>
<sec sec-type="conclusion" id="s6">
<title>6 Conclusion</title>
<p>This study proposes a novel method for aging monitoring and fault positioning for zinc oxide surge arresters based on the fifth harmonic of the resistive leakage current (<italic>I</italic>
<sub>R5th</sub>). Initially, an aging experimental platform was established for zinc oxide surge arresters, and experiments were conducted with a voltage harmonic control group. Subsequently, the leakage current harmonic characteristics were extracted using an improved displacement current method and fast Fourier transform algorithm. The characteristics of <italic>I</italic>
<sub>R5th</sub> were analyzed through the percentage change in the feature and harmonic sensitivity analysis. Finally, by integrating high-precision current sensor technology with GPS positioning, a principle method for applying <italic>I</italic>
<sub>R5th</sub> to the fault monitoring and positioning for zinc oxide surge arresters was proposed. The following conclusions can be drawn:<list list-type="simple">
<list-item>
<p>&#x2022; Under voltage harmonic interference, when the percentage weight of <italic>V</italic>
<sub>3rd</sub> is nearly twice as that of <italic>V</italic>
<sub>5th</sub>, the peak increase in <italic>I</italic>
<sub>R3rd</sub> is 3.7 times that of <italic>I</italic>
<sub>R5th</sub>, indicating that <italic>I</italic>
<sub>
<italic>R5th</italic>
</sub> has a stronger resistance to voltage harmonic interference.</p>
</list-item>
<list-item>
<p>&#x2022;<italic>I</italic>
<sub>R5th</sub> exhibits similar sensitivity to aging faults as <italic>I</italic>
<sub>R3rd</sub>. However, under aging fault conditions, the percentage change in and harmonic sensitivity of <italic>I</italic>
<sub>R5th</sub> are lower than those of <italic>I</italic>
<sub>R3rd</sub>, showing improved data reliability. Therefore, <italic>I</italic>
<sub>R5th</sub> is more suitable for aging monitoring and fault positioning for zinc oxide surge arresters.</p>
</list-item>
</list>
</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s7">
<title>Data availability statement</title>
<p>The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.</p>
</sec>
<sec sec-type="author-contributions" id="s8">
<title>Author contributions</title>
<p>YL: Writing &#x2013; original draft, Writing &#x2013; review and editing. ZX: Writing &#x2013; original draft, Writing &#x2013; review and editing. JG: Writing &#x2013; original draft, Writing &#x2013; review and editing. CZ: Writing &#x2013; original draft, Writing &#x2013; review and editing. JL: Writing &#x2013; original draft, Writing &#x2013; review and editing. XX: Writing &#x2013; original draft, Writing &#x2013; review and editing. JS: Writing &#x2013; original draft, Writing &#x2013; review and editing.</p>
</sec>
<sec sec-type="funding-information" id="s9">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research and/or publication of this article.</p>
</sec>
<sec sec-type="COI-statement" id="s10">
<title>Conflict of interest</title>
<p>Authors YL, ZX, JG, CZ, JL, XX, and JS were employed by State Grid Jiangsu Electric Power Research Institute Co., Ltd.</p>
<p>This work was supported by the Project of State Grid Jiangsu Electric Power Co., Ltd. Science and Technology Funding in China (J2024068). The funder had the following involvement in the study: In terms of research design, the funder provided necessary space for experimental equipment, and during the paper writing phase, the funder offered necessary revision suggestions.</p>
</sec>
<sec sec-type="ai-statement" id="s11">
<title>Generative AI statement</title>
<p>The authors declare that no Generative AI was used in the creation of this manuscript.</p>
</sec>
<sec sec-type="disclaimer" id="s12">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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