<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">EPE</journal-id><journal-title-group><journal-title>Energy and Power Engineering</journal-title></journal-title-group><issn pub-type="epub">1949-243X</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/epe.2017.94B072</article-id><article-id pub-id-type="publisher-id">EPE-75334</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Engineering</subject></subj-group></article-categories><title-group><article-title>
 
 
  The Research of Connection between Degree of Polymerization and Frequency Domain Dielectric Spectroscopy Characteristics during Oil-Paper Insulation Aging
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Danyu</surname><given-names>Jiang</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Guangning</surname><given-names>Wu</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Xian</surname><given-names>Yang</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Qingkai</surname><given-names>Hao</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib></contrib-group><aff id="aff1"><addr-line>ASchool of Electrical Engineering College, Southwest Jiaotong University, Chengdu, China</addr-line></aff><aff id="aff2"><addr-line>Electric Power Research Institute of Guangdong Power Grid Corporation, Guangzhou, China</addr-line></aff><pub-date pub-type="epub"><day>06</day><month>04</month><year>2017</year></pub-date><volume>09</volume><issue>04</issue><fpage>667</fpage><lpage>674</lpage><history><date date-type="received"><day>March</day>	<month>9,</month>	<year>2017</year></date><date date-type="rev-recd"><day>Accepted:</day>	<month>March</month>	<year>30,</year>	</date><date date-type="accepted"><day>April</day>	<month>6,</month>	<year>2017</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p>
 
 
   
   In order to study the linkage effects between degree of polymerization and frequency domain dielectric spectroscopy characteristics of oil-paper insulation, the frequency domain dielectric response test platform of oil-paper insulation is set up. Complex permittivity of oil-paper insulation respectively composed by new or aged oil and insulation paper with different DP are tested, and complex permittivity of oil-paper insulation respectively composed by insulation respectively composed by new oil and insulation paper with different DP and low or high moisture content are tested. The test results are analyzed, and the analysis results show that the degree of polymerization of insulation paper has an influence on complex permittivity of oil-paper insulation though influencing the distribution of moisture and acids between oil and paper. 
  
 
</p></abstract><kwd-group><kwd>Degree of Polymerization</kwd><kwd> Oil-Paper Insulation</kwd><kwd> Frequency  Domain Dielectric Spectroscopy</kwd><kwd> Moisture</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>1. Introduction</title><p>As the promotion of transmission voltage, oil-immersed power transformers in power systems become more and more important. Oil-paper insulation is an oil immersion major component of the internal insulation of power transformers in the transformer. The effect of thermal stress on the long-term operation of the device can lead oil-paper insulation to the decline of its insulation performance [<xref ref-type="bibr" rid="scirp.75334-ref1">1</xref>]. The faults caused by transformer insulation performance degradation accounts for about 80% of the total faults, and aging of oil paper insulation failures accounts for a large proportion. Therefore, accurate diagnosis of oil paper insulation aging degree has very important practical significance [<xref ref-type="bibr" rid="scirp.75334-ref2">2</xref>].</p><p>Frequency domain dielectric spectroscopy (FDS) is an non-destructive diagnostic method. When FDS was introduced to insulation fault diagnosis for power transformers, it was received wide attention of scholars. Compared with the chemical analysis, FDS is an accurate and reliable method to determine the moisture content of the paper insulation and insulation oil conductivity [<xref ref-type="bibr" rid="scirp.75334-ref3">3</xref>].</p><p>Oil-paper insulation aging process is easy to produce water and acid [<xref ref-type="bibr" rid="scirp.75334-ref4">4</xref>]. Heat insulating paper, electrical, mechanical, aging water and acid synergistic can decrease the degree of polymerization of transformer when operation time increases. The decline in the degree of insulation paper is not recoverable, and the insulation performance of the insulation paper can also be reduced [<xref ref-type="bibr" rid="scirp.75334-ref5">5</xref>]. So, this paper study the influence of DP on frequency domain dielectric spectroscopy characteristics of oil-paper insulation and the mechanisms, and frequency domain dielectric response test platform of oil- paper insulation is set up.</p></sec><sec id="s2"><title>2. FDS Principle and Experiment</title><sec id="s2_1"><title>2.1. FDS Principle</title><p>Variable voltage U(t) across the capacitor plates produce a uniform electric field E(t) = U(t)/d between the plates, where d is the distance between two plates [<xref ref-type="bibr" rid="scirp.75334-ref6">6</xref>]. The electric potential of the electrodes D(t) is composed of the instantaneous contribution of vacuum e<sub>0</sub>E(t) and the polarization response of inertia delay P(t),</p><disp-formula id="scirp.75334-formula516"><label>(1)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/75334x2.png"  xlink:type="simple"/></disp-formula><p>The full current density is known by Maxwell equation</p><disp-formula id="scirp.75334-formula517"><label>(2)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/75334x3.png"  xlink:type="simple"/></disp-formula><p>where s<sub>0</sub> is DC conductivity, Fourier transform of (2)</p><disp-formula id="scirp.75334-formula518"><label>(3)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/75334x4.png"  xlink:type="simple"/></disp-formula><disp-formula id="scirp.75334-formula519"><label>(4)</label><graphic position="anchor" xlink:href="http://html.scirp.org/file/75334x5.png"  xlink:type="simple"/></disp-formula><p>where <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/75334x6.png" xlink:type="simple"/></inline-formula> and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/75334x7.png" xlink:type="simple"/></inline-formula> are the real and imaginary parts of repolarization coefficient, <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/75334x8.png" xlink:type="simple"/></inline-formula>and <inline-formula><inline-graphic xlink:href="http://html.scirp.org/file/75334x9.png" xlink:type="simple"/></inline-formula> are the real and imaginary parts of the complex permittivity .</p></sec><sec id="s2_2"><title>2.2. FDS Experiment</title><p>The template is used to format your paper and style the text. All margins, column widths, line spaces, and text fonts are prescribed; please do not alter them. You may note peculiarities. For example, the head margin in this template measures proportionately more than is customary. This measurement and others are deliberate, using specifications that anticipate your paper as one part of the entire journals, and not as an independent document. Please do not revise any of the current designations.</p><p>Experimental materials used in this paper are transformer insulation paper and mineral insulating oil, details of materials shown in <xref ref-type="table" rid="table1">Table 1</xref>.</p><p>According to <xref ref-type="table" rid="table1">Table 1</xref>, different degree of polymerization of insulation paper can be obtained. Measuring the degree of polymerization of insulating paper is reference for GB 1548-2004. In order to reduce the measurement error, three samples are measured, and the average value of the degree of polymerization of three samples is used as the degree of polymerization. (<xref ref-type="table" rid="table2">Table 2</xref>) Because small molecule acid has a great impact on frequency domain dielectric response characteristics of oil paper insulation [<xref ref-type="bibr" rid="scirp.75334-ref7">7</xref>], so this paper use the small molecule acid――Formic acid. Test principle diagram and test apparatus are shown in <xref ref-type="fig" rid="fig1">Figure 1</xref>.</p><fig-group id="fig1"><label><xref ref-type="fig" rid="fig1">Figure 1</xref></label><caption><title> Experimental schematic and setup.</title></caption><fig id ="fig1_1"><label></label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/75334x10.png"/></fig><fig id ="fig1_2"><label></label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/75334x11.png"/></fig></fig-group><table-wrap id="table1" ><label><xref ref-type="table" rid="table1">Table 1</xref></label><caption><title> The material information</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Material</th><th align="center" valign="middle" >Material Type</th><th align="center" valign="middle" >Moisture content (%)</th><th align="center" valign="middle" >Degree of polymerization</th></tr></thead><tr><td align="center" valign="middle" >Insulating paper</td><td align="center" valign="middle" >0.3 mm Thick kraft paper</td><td align="center" valign="middle" >6.5</td><td align="center" valign="middle" >1131</td></tr><tr><td align="center" valign="middle" >Insulating oil</td><td align="center" valign="middle" >25# naphthenic oil</td><td align="center" valign="middle" >17.9 &#215; 10<sup>−4</sup></td><td align="center" valign="middle" >-</td></tr></tbody></table></table-wrap><table-wrap id="table2" ><label><xref ref-type="table" rid="table2">Table 2</xref></label><caption><title> Pre-conditional process of paper with different DP</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >DP</th><th align="center" valign="middle" >Pre-conditional process</th></tr></thead><tr><td align="center" valign="middle" >1131</td><td align="center" valign="middle" >100˚C/50 Pa/2 d</td></tr><tr><td align="center" valign="middle" >775</td><td align="center" valign="middle" >100˚C/50 Pa/20 d</td></tr><tr><td align="center" valign="middle" >326</td><td align="center" valign="middle" >150˚C/50 Pa/35 d</td></tr></tbody></table></table-wrap></sec></sec><sec id="s3"><title>3. Experimental Result Analysis</title><sec id="s3_1"><title>3.1. Analysis of Frequency Domain Dielectric Spectrum of New Insulation Oil and Insulation Paper</title><p>Define abbreviations and acronyms the first time they are used in the text, even after they have been defined in the abstract. Abbreviations such as IEEE, SI, MKS, CGS, sc, dc, and rms do not have to be defined. Do not use abbreviations in the title or heads unless they are unavoidable.</p><p><xref ref-type="fig" rid="fig2">Figure 2</xref> shows complex permittivity measurement curve. The degree of polymerization are 1131, 775, 326 of insulating paper which is composed of new insulation oil. Compared with different polymerization degree of insulation, the influence on complex permittivity of the real and imaginary parts is very small.</p></sec><sec id="s3_2"><title>3.2. Analysis of Frequency Domain Dielectric Spectrum of Small Molecule Acid-Containing Oil Paper Insulation and DP</title><p>Put different degree of polymerization of the insulating paper in a high initial small molecule acid content (acid value 0.3 mg KOH/g) insulation oil, the balance distribution of the small molecule acid is shown in <xref ref-type="table" rid="table3">Table 3</xref>.</p><fig id="fig2"  position="float"><label><xref ref-type="fig" rid="fig2">Figure 2</xref></label><caption><title> Complex permittivity ofnew oil-paperwith different DP</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/75334x12.png"/></fig><table-wrap id="table3" ><label><xref ref-type="table" rid="table3">Table 3</xref></label><caption><title> Distribution of acid between oil and paper with different DP</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >DP</th><th align="center" valign="middle" >Acid in oil (mg KOH/g)</th><th align="center" valign="middle" >Acid in oil (mgKOH/g)</th><th align="center" valign="middle" >Ratio of paper and oleic acid value</th></tr></thead><tr><td align="center" valign="middle" >1131</td><td align="center" valign="middle" >0.063</td><td align="center" valign="middle" >4.74</td><td align="center" valign="middle" >75.2</td></tr><tr><td align="center" valign="middle" >775</td><td align="center" valign="middle" >0.041</td><td align="center" valign="middle" >5.18</td><td align="center" valign="middle" >126.3</td></tr><tr><td align="center" valign="middle" >326</td><td align="center" valign="middle" >0.048</td><td align="center" valign="middle" >5.04</td><td align="center" valign="middle" >105</td></tr></tbody></table></table-wrap><p><xref ref-type="fig" rid="fig3">Figure 3</xref> shows the complex permittivity testing curves of different polymerization degree of insulation paper with high initial small molecule acid content (0.3 mg KOH/g) insulation oil composition of oil paper insulation. Compared with the real and imaginary parts of the complex permittivity, when the insulating oil initial small molecule acid content is relatively high, the decrease of DP of insulating paper make different influence on complex permittivity of the real and imaginary parts. It is mainly reflected in the low frequency region. With the decrease of the degree of insulation paper, the amplitude of the complex permittivity and imaginary part of the dielectric constant increase, and the rate of the curve decrease.</p></sec><sec id="s3_3"><title>3.3. Analysis of Frequency Domain Dielectric Spectrum of Insulation Paper with Aging Insulation Oil</title><p><xref ref-type="fig" rid="fig4">Figure 4</xref> shows the colour of new oil, 15 days- aged oil and 20 days-aged oil in experiment. The rightmost oil sample has been aged for 20 days whose moisture is 150 ppm and acid content is 0.12 mg KOH/g. <xref ref-type="table" rid="table4">Table 4</xref> shows the moisture and acid equilibrium distribution between 20 days aged oil and paper with different DP whose initial moisture content is 2%.</p><fig id="fig3"  position="float"><label><xref ref-type="fig" rid="fig3">Figure 3</xref></label><caption><title> Complex permittivity of oil with high initial light acid content-paper with different DP</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/75334x13.png"/></fig><table-wrap id="table4" ><label><xref ref-type="table" rid="table4">Table 4</xref></label><caption><title> Distribution of moisture and acids between oil and paper in group of aged oil and insulation paper with different DP</title></caption><table><tbody><thead><tr><th align="center" valign="middle"  rowspan="2"  >DP</th><th align="center" valign="middle"  colspan="2"  >Insulating oil</th><th align="center" valign="middle"  colspan="2"  >Insulating paper</th></tr></thead><tr><td align="center" valign="middle" >Water content/ppm</td><td align="center" valign="middle" >Acid value (mgKOH/g)</td><td align="center" valign="middle" >Water content/ppm</td><td align="center" valign="middle" >Acid value (mgKOH/g)</td></tr><tr><td align="center" valign="middle" >1131</td><td align="center" valign="middle" >42</td><td align="center" valign="middle" >0.0957</td><td align="center" valign="middle" >22160</td><td align="center" valign="middle" >0.486</td></tr><tr><td align="center" valign="middle" >775</td><td align="center" valign="middle" >54</td><td align="center" valign="middle" >0.0926</td><td align="center" valign="middle" >21920</td><td align="center" valign="middle" >0.548</td></tr><tr><td align="center" valign="middle" >326</td><td align="center" valign="middle" >81</td><td align="center" valign="middle" >0.0931</td><td align="center" valign="middle" >21380</td><td align="center" valign="middle" >0.558</td></tr></tbody></table></table-wrap><fig-group id="fig4"><label><xref ref-type="fig" rid="fig4">Figure 4</xref></label><caption><title> Color contrast figure of aged and new oil.</title></caption><fig id ="fig4_1"><label></label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/75334x14.png"/></fig><fig id ="fig4_2"><label></label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/75334x15.png"/></fig><fig id ="fig4_3"><label></label><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/75334x16.png"/></fig></fig-group><p><xref ref-type="fig" rid="fig5">Figure 5</xref> shows the complex permittivity of oil-paper with different DP from experiment. With the decrease of DP, the real and imaginary part of complex permittivity tend to increase in the whole texting frequency range, and the increasing width is larger in low frequency range which make the real and imaginary part decrease more precipitously in low frequency along with the increase of frequency. The acid contained in the aged insulating oil is mainly macromolecular acid, and it would not draw manifest effect on FDS property of oil-paper system. Due to the aging of insulating oils and different polymerization degree of insulation paper initial contain a certain amount of moisture, when different degree of polymerization of insulating paper cause the same initial moisture content, it influence oil paper insulation frequency domain dielectric spectrum characteristics. The impact test results similar to <xref ref-type="fig" rid="fig3">Figure 3</xref>, which shows that interpretation is reasonable.</p></sec></sec><sec id="s4"><title>4. Conclusions</title><p>1) When insulating oil of small molecule acid content is high, the decreases of DP of insulating paper have a great impact on paper insulation complex permittivity, and the impact of the low frequency region is mainly reflected in the test.</p><p>2) For light acids, the decreasing of DP has an influence on Complex permittivity of oil-paper insulation only when oil-paper insulation has high light acid content, and the influence is mainly manifested in the low frequency area of the test. For moisture, the decreasing of DP has already affected Complex permittivity of oil-paper insulation largely when oil-paper insulation has low moisture content, and the impact is mainly manifested in the low frequency area of the test. While the moisture content is higher, the impact is manifested clearly in all frequency area of the test.</p><p>3) The degree of polymerization of insulation paper has an influence on complex permittivity of oil-paper insulation though influencing the distribution of moisture and acids between oil and paper.</p><fig id="fig5"  position="float"><label><xref ref-type="fig" rid="fig5">Figure 5</xref></label><caption><title> Complex permittivity of aged oil-paperwith different DP</title></caption><graphic mimetype="image"   position="float"  xlink:type="simple"  xlink:href="http://html.scirp.org/file/75334x17.png"/></fig><p>4) When the frequency domain dielectric spectroscopy is used to diagnose the moisture or acids content in oil-paper insulation, it should be considered that the effect of DP on the distribution of moisture and acids between oil and insulation paper has an impact on the frequency domain dielectric spectroscopy characteristics of oil-paper insulation.</p></sec><sec id="s5"><title>Acknowledgements</title><p>The authors would like to thank National Natural Science Foundation of China for supporting this project.</p></sec><sec id="s6"><title>Cite this paper</title><p>Jiang, D.Y., Wu, G.N., Yang, X. and Hao, Q.K. (2017) The Research of Connection between Degree of Polymerization and Frequency Domain Di- electric Spectroscopy Characteristics during Oil-Paper Insulation Aging. Energy and Power Engineering, 9, 667-674. https://doi.org/10.4236/epe.2017.94B072</p></sec></body><back><ref-list><title>References</title><ref id="scirp.75334-ref1"><label>1</label><mixed-citation publication-type="other" xlink:type="simple">Gobi, K., Supramaniam, Hussien, Z. F., Aizam, M. (2008) Application of Frequency Domain Spectroscopy (FDS) in Assessing Dry-ness And Ageing State of Transformer Insulation Systems. IEEE International Conference on Power and Energy, 55–56, 2008.</mixed-citation></ref><ref id="scirp.75334-ref2"><label>2</label><mixed-citation publication-type="other" xlink:type="simple">Gielniak, C., Ekanaykake, K., Walczak (2005) Dielectric Responses of New and Aged Transformer Pressboard in Dry and Wet States. 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