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Article(id=1210227965850423989, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210227961236681448, articleNumber=null, orderNo=null, doi=10.16790/j.cnki.1009-9239.im.2022.01.004, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1611504000000, receivedDateStr=2021-01-25, revisedDate=1614787200000, revisedDateStr=2021-03-04, acceptedDate=null, acceptedDateStr=null, onlineDate=1766470432007, onlineDateStr=2025-12-23, pubDate=1642608000000, pubDateStr=2022-01-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1766470432007, onlineIssueDateStr=2025-12-23, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1766470432007, creator=13701087609, updateTime=1766470432007, updator=13701087609, issue=Issue{id=1210227961236681448, tenantId=1146029695717560320, journalId=1149653034449285133, year='2022', volume='55', issue='1', pageStart='1', pageEnd='112', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1766470430907, creator=13701087609, updateTime=1766562962621, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1210616067429364090, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210227961236681448, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1210616067429364091, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210227961236681448, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=24, endPage=31, ext={EN=ArticleExt(id=1210227966097887930, articleId=1210227965850423989, tenantId=1146029695717560320, journalId=1149653034449285133, language=EN, title=Simulation Study on Growth Characteristics of Electrical Tree in Two-dimensional Microsheet Composite by Orientation Regulating, columnId=1190369066675179686, journalTitle=Insulating Materials, columnName=Material Research, runingTitle=null, highlight=null, articleAbstract=

In order to obtain the influence of orientation angle of two-dimensional microsheet on the growth characteristics of electrical tree in composite dielectrics, on the basis of WZ breakdown model of fractal media, we studied the growth and fractal dimension characteristics of electrical tree under different microsheet orientation angles, growth probability index, and discharge threshold voltage. The change of electric field caused by the change of two-dimensional microsheet orientation angle was analyzed, and the influence mechanism of microsheet on the growth of electrical tree was explained. The results show that when the microsheet is oriented perpendicular to the electric field, the electrical tree has the largest fractal dimension and is most difficult to breakdown. With the decrease of the angle formed by microsheet and electric field direction, both the fractal dimension and breakdown time of electrical tree decrease. With the increase of the growth probability index or threshold voltage, the fractal dimension of electrical tree decreases, and the influence on the electrical tree fractal dimension in microcomposite dielectrics with different orientation angles increases. When the orientation angle of microsheet is perpendicular to the electric field, the electric field distribution is relatively uniform. With the increase of microsheet orientation angle, the electric field concentrates at the both ends of microsheet, and the closer the adjacent microsheet, the more concentration the electric field.

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为得到二维微米片取向角度对复合电介质中电树枝生长特性的影响规律，基于分形介质的WZ模型，研究了不同微米片取向角度、生长概率指数、放电阈值电压下，电树枝的生长和分形维数特性。分析了二维微米片取向角度变化引起电场强度变化的原因，并解释了微米片对电树枝生长的影响机制。结果表明：当微米片沿垂直于电场方向取向时，电树枝的分形维数最大，且最不容易击穿。随着微米片与电场方向形成的夹角减小，电树枝的分形维数和击穿时间均减小。随着生长概率指数或阈值电压增大，电树枝的分形维数减小，且对不同取向角度微米复合电介质中电树枝分形维数的影响增大。当微米片取向角度为垂直于电场方向时，电场分布相对比较均匀，随微米片取向角度增大，电场集中在微米片两端，且相邻微米片越接近的地方场强越集中。

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周远翔（1966-），男（汉族），福建莆田人，教授，主要从事高电压与绝缘技术教学与科研工作。

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周远翔（1966-），男（汉族），福建莆田人，教授，主要从事高电压与绝缘技术教学与科研工作。

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周远翔（1966-），男（汉族），福建莆田人，教授，主要从事高电压与绝缘技术教学与科研工作。

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unstructuredReference=谷琛,严萍,邵涛,等.基于分形理论的电介质放电仿真计算[J].高电压技术,2006,32(1):1-4., articleTitle=基于分形理论的电介质放电仿真计算, refAbstract=null)], funds=[Fund(id=1210913941673341735, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210227965850423989, awardId=51977186, language=CN, fundingSource=国家自然科学基金资助项目(51977186), fundOrder=null, country=null), Fund(id=1210913941761422123, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210227965850423989, awardId=3204044, language=CN, fundingSource=北京市自然科学基金资助项目(3204044), fundOrder=null, country=null), Fund(id=1210913941832725292, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210227965850423989, awardId=LAPS20006, language=CN, fundingSource=新能源电力系统国家重点实验室开放课题资助项目(LAPS20006), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1210913933704163808, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210227965850423989, xref=1, 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language=EN, label=Tab.1, caption=Fractal dimension and breakdown times of different micro-composite dielectrics, figureFileSmall=null, figureFileBig=null, tableContent=
材料类型分形维数D击穿时间tb/h
AP样品1.364 73.360 0
AR样品1.411 55.210 0
A0样品1.456 97.420 0
A30样品1.382 53.580 0
A60样品1.351 63.110 0
), ArticleFig(id=1210913941195191069, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210227965850423989, language=CN, label=表1, caption=

不同微米复合电介质的分形维数和击穿时间

, figureFileSmall=null, figureFileBig=null, tableContent=
材料类型分形维数D击穿时间tb/h
AP样品1.364 73.360 0
AR样品1.411 55.210 0
A0样品1.456 97.420 0
A30样品1.382 53.580 0
A60样品1.351 63.110 0
), ArticleFig(id=1210913941341991711, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210227965850423989, language=EN, label=Tab.2, caption=Maximum electric field strength in different micro-composite dielectrics, figureFileSmall=null, figureFileBig=null, tableContent=
材料类型最大电场强度/(×107V/m)
AR样品2.450 0
A0样品2.217 2
A30样品2.451 3
A60样品2.544 5
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不同微米复合电介质中的最大电场强度

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材料类型最大电场强度/(×107V/m)
AR样品2.450 0
A0样品2.217 2
A30样品2.451 3
A60样品2.544 5
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二维微米片复合材料取向调控电树枝生长特性的仿真研究
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周远翔 1, 2 , 胡德雄 1 , 张云霄 2 , 张灵 2 , 滕陈源 2 , 黄猛 3
绝缘材料 | 材料研究 2022,55(1): 24-31
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绝缘材料 | 材料研究 2022, 55(1): 24-31
二维微米片复合材料取向调控电树枝生长特性的仿真研究
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周远翔1, 2, 胡德雄1, 张云霄2, 张灵2, 滕陈源2, 黄猛3
作者信息
  • 1新疆大学 电气工程学院 电力系统及大型发电设备安全控制和仿真国家重点实验室风光储分室， 新疆 乌鲁木齐 830047
  • 2清华大学 电机工程与应用电子技术系 电力系统及大型发电设备安全控制和仿真国家重点实验室，北京 100084
  • 3华北电力大学 新能源电力系统国家重点实验室，北京 102206

    • 周远翔（1966-），男（汉族），福建莆田人，教授，主要从事高电压与绝缘技术教学与科研工作。

Simulation Study on Growth Characteristics of Electrical Tree in Two-dimensional Microsheet Composite by Orientation Regulating
Yuanxiang ZHOU1, 2, Dexiong HU1, Yunxiao ZHANG2, Ling ZHANG2, Chenyuan TENG2, Meng HUANG3
Affiliations
  • 1The Wind Solar Storage Division of State Key Lab of Control and Simulation of Power System and Generation Equipment, School of Electrical Engineering, Xinjiang University, Urumqi 830047, China
  • 2State Key Lab of Control and Simulation of Power System and Generation Equipment, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China
  • 3State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China
出版时间: 2022-01-20 doi: 10.16790/j.cnki.1009-9239.im.2022.01.004
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摘要
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为得到二维微米片取向角度对复合电介质中电树枝生长特性的影响规律，基于分形介质的WZ模型，研究了不同微米片取向角度、生长概率指数、放电阈值电压下，电树枝的生长和分形维数特性。分析了二维微米片取向角度变化引起电场强度变化的原因，并解释了微米片对电树枝生长的影响机制。结果表明：当微米片沿垂直于电场方向取向时，电树枝的分形维数最大，且最不容易击穿。随着微米片与电场方向形成的夹角减小，电树枝的分形维数和击穿时间均减小。随着生长概率指数或阈值电压增大，电树枝的分形维数减小，且对不同取向角度微米复合电介质中电树枝分形维数的影响增大。当微米片取向角度为垂直于电场方向时，电场分布相对比较均匀，随微米片取向角度增大，电场集中在微米片两端，且相邻微米片越接近的地方场强越集中。

WZ模型  /  二维微米片  /  电树枝  /  取向角度  /  电场分布

In order to obtain the influence of orientation angle of two-dimensional microsheet on the growth characteristics of electrical tree in composite dielectrics, on the basis of WZ breakdown model of fractal media, we studied the growth and fractal dimension characteristics of electrical tree under different microsheet orientation angles, growth probability index, and discharge threshold voltage. The change of electric field caused by the change of two-dimensional microsheet orientation angle was analyzed, and the influence mechanism of microsheet on the growth of electrical tree was explained. The results show that when the microsheet is oriented perpendicular to the electric field, the electrical tree has the largest fractal dimension and is most difficult to breakdown. With the decrease of the angle formed by microsheet and electric field direction, both the fractal dimension and breakdown time of electrical tree decrease. With the increase of the growth probability index or threshold voltage, the fractal dimension of electrical tree decreases, and the influence on the electrical tree fractal dimension in microcomposite dielectrics with different orientation angles increases. When the orientation angle of microsheet is perpendicular to the electric field, the electric field distribution is relatively uniform. With the increase of microsheet orientation angle, the electric field concentrates at the both ends of microsheet, and the closer the adjacent microsheet, the more concentration the electric field.

WZ model  /  two-dimensional microsheet  /  electrical tree  /  orientation angle  /  electric field distribution
周远翔, 胡德雄, 张云霄, 张灵, 滕陈源, 黄猛. 二维微米片复合材料取向调控电树枝生长特性的仿真研究. 绝缘材料, 2022 , 55 (1) : 24 -31 . DOI: 10.16790/j.cnki.1009-9239.im.2022.01.004
Yuanxiang ZHOU, Dexiong HU, Yunxiao ZHANG, Ling ZHANG, Chenyuan TENG, Meng HUANG. Simulation Study on Growth Characteristics of Electrical Tree in Two-dimensional Microsheet Composite by Orientation Regulating[J]. Insulating Materials, 2022 , 55 (1) : 24 -31 . DOI: 10.16790/j.cnki.1009-9239.im.2022.01.004
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0 引言
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电力电缆输电具有受外界影响小、供电可靠性高、土地资源利用率高等优点，成为了城市电网增容改造、大规模新能源并网消纳等的重要电力传输方式[1-3]。随着我国电力工业的飞速发展，电网电压等级和输送容量日益增加，对电缆的绝缘可靠性提出了更大的挑战。电树枝老化是聚合物材料中常见的老化方式之一，已被证实为电力电缆绝缘破坏的重要方式[4-5]。研究表明，电压、温度等对电树枝老化特性有显著影响，电树枝老化问题成为了制约电力电缆向更高电压、大容量发展的瓶颈之一[6-7]。
如何提高电缆绝缘材料的耐电树枝老化性能是研究的热点，目前抑制电树枝老化的方法主要包括：①改进电缆结构，均匀化电缆绝缘层电场分布；②电缆绝缘材料超净化处理；③改进电缆材料配方，例如添加电压稳定剂和无机微米颗粒等[8]。自1994年英国学者T J LEWIS首次提出纳米电介质以来[9]，电介质材料的纳米改性技术被认为是未来提高绝缘材料电气性能最有可能取得突破进展的研究方向[10]。针对抑制绝缘材料中的电树枝老化现象，国内外学者利用纳米改性技术进行了相关研究，主要以交联聚乙烯（cross-linked polyethylene，XLPE）、环氧树脂（epoxy resin，ER）、硅橡胶（silicone rubber，SIR）等绝缘材料为基体，通过向基体中掺杂SiO2[11-13]、ZnO[14-15]、Al2O3[14-16]等球状纳米颗粒，发现纳米颗粒的引入能够有效提升电树枝的起始电压，并抑制电树枝生长。
然而，研究同样发现，要实现较为有效的抑制电树枝效果，往往需要添加较高质量分数的球状纳米颗粒[17]，这主要是由于低添加量下球状纳米颗粒对电树枝生长路径的阻挡有限。ZHU M X等[18]提出添加片层状纳米粒子并对纳米片进行取向排列，可实现在较低添加量下，提高纳米填料阻挡电树枝生长的效果。杨丽君等[19]发现经电场诱导后的低密度聚乙烯/蒙脱土材料与诱导前相比具有更高的起树电压和更低的电树枝引发率。MA T T等[20]发现在硅橡胶中添加质量分数为1.0%的未取向蒙脱土能够使电树枝长度减小33.3%，而仅添加质量分数为0.5%的取向蒙脱土就能达到相同的效果。可以看到所添加粒子的取向状态对绝缘材料中电树枝的生长特性有显著的影响。与纳米片相比，由于微米片具有更大的阻挡面积，因此可以利用微米片取向排列来提高复合材料阻挡电树枝生长的效果，然而针对微米片取向相关的调控机制仍未明晰。
目前的研究多是通过添加不同粒径、含量的粒子去进行实验分析，试错成本高，而仿真作为实验的一种有效补充方法，可为实验开展提供较好的理论指导。本研究利用分形介质击穿模型中的WZ模型，选择针-板电极，建立不同取向角度的微米复合电介质模型，仿真分析微米片取向角度、生长概率指数、放电阈值电压对微米复合电介质中电树枝分形维数和生长特性的影响规律。结合有限元分析，分析不同取向角度微米复合电介质中的电场分布特性，进而讨论微米片取向角度对电树枝生长特性的影响机制，以期为后续粒子选型、材料制备等试验方面提供理论指导。
1 仿真实验
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1.1 电极结构
本研究搭建了二维针-板电极模型结构，如图1所示。其中，每一小格边长为5 μm，不考虑针电极外形和材料的影响，将针电极视为1条线段。在针电极上加入上极板，设置上极板与针电极的电势φ=1，下极板为地电极电势φ=0。
1.2 WZ模型
WZ模型是电树枝模拟中最常用的模型之一，H J WIESMANN等[21]在NPW模型的基础上新引入了放电阈值场强Ec和电树通道内部结构电场Es两个参数，建立了WZ模型。WZ模型认为，电介质击穿存在一个阈值场强Ec，只有当待发展点的场强大于Ec时，该点才可以成为电树点，并且电树通道内部并不是等电势的。WZ模型中放电的发展服从概率分布P(i)，如式（1）所示。
P(i)=(|Ei'-Ei|-Ec)η∑(|Ei'-Ei|-Ec)η
式（1）中：Ei′为可能发展的放电点的场强；Ei为与可能发展点连接的电树点场强；Ec为放电发展的阈值场强。
WZ模型的参数有两个，电场强度E和放电生长概率指数η。生长概率指数η是反映电树枝生长受电场分布影响程度的关键参数之一，电树枝是在生长概率最大点处生长，这点将电树枝生长的决定性过程变成随机过程，给出统计意义上的分支可能性。当生长概率指数η变化时，电树枝的分形维数D会随之变化，证实了这一点。
目前，有学者已经利用WZ模型仿真模拟了交流电压下不同局放量[22]、不同针尖曲率半径以及不同针板间距下[23]对应的电树枝形态，研究发现实验得到的电树枝形态及其分布特性与利用WZ模型进行仿真模拟得到的结果较为相似，进一步说明了WZ模型应用于交流电压下电树枝生长特性的仿真研究是具备一定合理性的。
1.3 仿真步骤
（1） 电位计算
由于在仿真中电树枝的发展是步进式的，且是等步长的，因此可以将电场分布计算简化为电势分布计算。坐标为（i，j）节点的电势φi,j由二维离散后的拉普拉斯方程求出，如式（2）所示。
φi,j=1/4(φi, j-1+φi-1, j+φi, j+1+φi+1, j)
结合初始边界条件，通过多次迭代可得到整个电介质中的电势分布情况。
（2） 计算待发展点成为电树点的概率
引入一个判断过程，若待发展点与电树点之间的电压差大于放电阈值电压，由公式（1）求出发展概率，否则该待发展点成为电树点的概率为0。
（3） 计算分形维数D
设r为单位长度，N(r)为以rD为单位的测量值，其可由D的定义求得，如式（3）所示[24]。
N(r)∝r-D⇒D=limr→0lnN(r)/ln(1/r)
因为本模型选用针-板电极结构，由数个二维小方格构成，设上下极板的距离为s，则单位长度r=1/s，电树枝所占的总格数N与s服从指数关系，如式（4）所示。
N∝r-D⇒N∝sD
当s远大于r时，由式（3）可求得分形维数D，如式（5）所示。
D=limr→0lnN/lns
此时结束运行，具体仿真流程如图2所示。
1.4 不同取向角度微米复合电介质仿真
将WZ模型应用于填充不同取向角度微米复合电介质中，构建微米片垂直于电场方向排列（即微米片呈0°排列）的对象，且以微米片中心点为基准，沿逆时针分别旋转30°和60°，构建不同取向角度的微米片排列对象。将未填充微米片和填充的微米片呈0°、30°、60°及未取向的复合电介质分别编号为AP、A0、A30、A60、AR。
整个仿真区域横向长度为1 000 µm，纵向宽度为500 µm，微米片的长度为100 µm，宽度为5 µm。其中基体和微米片所用的材料分别是环氧树脂（ER）和氮化硼（boron nitride，BN），相对介电常数分别为3.6和5.0，体积电阻率分别为1016 Ω·cm和1018 Ω·cm。
2 仿真结果与讨论
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2.1 不同运行时间下电树枝的生长情况
仿真得到30、60、150 min时刻AP样品和A0样品中电树枝的生长情况，如图3所示。定义电树枝最远点到上极板的垂直距离为电树枝的长度，可得到AP样品在30、60、150 min时刻电树枝的长度分别为300、350、425 μm，而A0样品的电树枝长度分别为240、280、375 μm。可见A0样品中电树枝的长度在不同时刻均小于AP样品，说明引入垂直于电场方向定向排列的微米片可以有效抑制电树枝发展。这是因为与AP样品相比，A0中微米片的引入作为屏障阻碍了电树枝朝纵向生长，如图3(b)所示，电树枝在遇到A0中微米片时分为两个支路并且趋于横向生长，使得电树枝的宽度增加，长度减小，从而延缓了电树枝到达地电极的时间，所以在相同时刻A0样品中电树枝的长度要小于AP样品。
2.2 微米片取向角度对电树枝生长特性的影响
粒子的形状和分布会影响复合电介质的性能[25]，因此仿真研究不同取向角度的微米片对电树枝生长特性的影响，电树枝从针尖处发展到地电极的生长情况如图4所示。由图4(a)可以看到，AP样品中横向生长的电树枝分支较少。引入未取向微米片后，由于微米片具有较好的阻隔作用，电树枝在遇到微米片时，需要绕开微米片进行生长，因此增加了电树枝生长路径的长度，如图4(b)所示。从图4(c)～(e)可以看到，当电树枝遇到A0样品中定向排列的微米片时，电树枝的生长路径明显地被分裂为2个主通道，并且形成了许多朝横向生长的小分支。
为定量分析图4中不同取向角度微米复合电介质中电树枝生长通道的变化规律，研究并记录了电树枝从针尖处发展到地电极时的分形维数D和所需要的时间tb。在相同条件下，将每种材料仿真3次的结果求平均值，结果如表1所示。
分形维数D是反映电树枝曲直和密集程度的一个重要参数，D越大说明电树枝的结构越复杂，分支较多；击穿时间tb是体现电介质耐电树性能的一个重要指标，tb越大说明材料的耐电树性能越好。从表1可以看出，分形维数D的排列顺序为D（A0）>D（AR）>D（A30）>D（AP）>D（A60），击穿时间tb的排列顺序与之相对应。其中A0样品的分形维数D比AP样品的大6.76%，A0样品的击穿时间tb比AP样品的增长120.83%。
随着微米片取向角度的增大，电树枝的分形维数D和击穿时间tb均减小，其中A30样品的tb仅比AP样品的大6.55%，说明A30样品中取向角度为30°的微米片对提升复合电介质的耐电树性能不显著。当微米片取向角度增大到60°时，A60样品的分形维数D和击穿时间tb均小于AP样品，说明A60样品的耐电树性能不如AP样品。这是因为随着微米片取向角度的增大，微米片沿平行于电场的方向转动，微米片取向角度越接近平行于电场的方向，微米片会形成一个抑制电树枝朝横向生长的通道，使得微米片阻挡电树枝生长的有效面积减小，导致微米片阻挡电树枝生长的效果变差，甚至不如未添加微米片的样品。
2.3 生长概率指数对电树枝生长特性的影响
在WZ模型中，电树枝的生长并不是直接取决于局部场强，而是在满足成为电树枝的条件下往发展概率最大的地方生长。生长概率指数η影响着各个点的生长概率，因此本研究选取η=0.5、1.0、1.5，仿真在不同η下AP样品和A0样品中电树枝的生长情况，结果如图5所示。从图5可以看出，η的值越小，电树枝越密集且分支越多。这是因为η的值越小，电树枝的生长对局部场强的依赖性越小，电树枝就越密集[26]。极端情况下，当η=0时，电树枝的生长与电介质中的电场分布情况无关，电树枝可以朝任意方向生长。η的值越大，电树枝的生长对局部场强的依赖性就大，电树枝会朝场强最大的方向发展，即发展的方向比较固定，电树枝的分支减少。
生长概率指数η对不同取向角度微米复合电介质电树枝分形维数D和击穿时间tb的影响如图6所示。从图6可以看出，无论η取值如何，分形维数D的排列顺序均为D（A0）>D（AR）>D（A30）>D（AP）>D（A60），击穿时间tb的变化规律与之相对应。当η=0.5、1.0、1.5时，各复合电介质的分形维数D相差分别为2.12%～4.92%、2.29%～5.38%、3.03%～6.17%，可见随着η增大，各复合电介质的分形维数D差距增大。这也是因为η越大，电树枝的生长受复合电介质内部局部场强的影响越大。
2.4 阈值电压对电树枝生长特性的影响
WZ模型中电介质击穿存在一个阈值电压，且只有施加的电压超过放电阈值电压，电介质内部才可能出现放电，因此阈值电压是反映电介质内部绝缘水平的一个重要参数。为简化计算，令KC为放电阈值电压和外施电压的比值，用KC来反映阈值电压的大小[27]。图7为阈值电压对电树枝特性的影响。由图7可以看到，当KC=0.01时，AP和A0样品中的电树枝比较密集，分支较多，随着KC增大，电树枝的分支显著变少。这是因为阈值电压越高，电介质中符合电树枝发展条件的待发展点数量越少[27]。
阈值电压对不同取向角度微米复合电介质中电树枝分形维数D的影响如图8所示。从图8可以看出，当KC=0.04时，分形维数D最大为1.324 1，最小为1.219 1，各复合电介质的分形维数D相差1.03%～6.81%；当KC=0.03时，分形维数D最大为1.419 7，最小为1.264 6，各复合电介质的分形维数D相差3.03%～6.16%。这说明在电介质内部绝缘水平较好的情况下，添加不同取向角度的微米片对电树枝形态的影响比较大。这是由于KC越大，电介质中符合电树枝发展条件的待发展点数量越少，即电介质内部中缺陷点的数量就越少，此时不同取向角度微米片对电树枝生长形态的影响起主导作用。当KC越小，例如在KC=0.01时，分形维数D最大为1.430 0，最小为1.376 3，各复合电介质的分形维数D相差仅为1.19%～3.90%，这说明在电介质内部绝缘水平较差的情况下，添加不同取向角度的微米片对电树枝形态的影响较小。这是由于KC的值越小，电介质中符合电树枝发展条件的待发展点数量越多，即电介质内部中缺陷点的数量越多，此时缺陷对电树枝生长形态的影响起主导作用，而引入不同取向角度的微米片对电树枝生长形态的影响有限。
2.5 不同类型微米复合电介质的电场分布
微米复合电介质中的电场分布情况是影响电树枝生长的一个关键因素，利用有限元分析COMSOL软件计算不同取向微米复合电介质中的电场分布情况，结果如图9所示。
BN微米片的相对介电常数高于ER基体材料，因此引入微米片会导致材料内部电场畸变。如图9(a)所示，当微米片取向角度为0°时，A0样品中微米片周围的电场分布相对比较均匀，如表2所示，最大电场强度为2.217 2×107 V/m。一方面，主要是A0样品中取向角度为0°的BN微米片阻挡电树枝生长的有效面积最大，延长了电树枝到达地电极之前的生长长度，从而延缓了电树枝到达地电极导致绝缘失效的时间。杨丽君等[19]通过在聚乙烯中添加取向后的蒙脱土纳米片，同样发现当纳米片取向角度为0°时，电树枝结构较为紧密，且生长缓慢。另一方面，均匀的电场不容易使得电树枝进一步发展。
随着微米片取向角度增大，其阻挡电树枝生长的有效面积随之减小，从图9(b)～(c)发现电场主要集中在BN微米片的两端，且A30和A60样品的最大电场强度均大于A0样品，因此A30和A60样品的耐电树枝性能均不如A0样品。同时发现相邻微米片越接近的地方场强越集中，A60样品中相邻两个微米片之间的距离要比A30样品中的小，使得A60样品中的最大电场强度大于A30样品，并且A60微米片阻挡电树枝的有效面积小于A30微米片，因此A60样品的耐电树枝性能不如A30样品。
当微米片未取向时，仿真发现AR样品的耐电树枝性能优于AP样品。为验证该仿真结果，在实验室中以ER为基体，掺杂粒径为10 µm未取向的BN微米片，施加电压频率为8 kV、2 kHz作为电树枝的生长电压，研究电树枝的生长情况，结果如图10所示。从图10可以看出，在1 min时刻，ER材料中电树枝形态明显为树枝状，并且生长规模较大，而在BN/ER复合材料中电树枝形态则较为短小，电树枝通道颜色变深。经统计，ER材料和BN/ER复合材料的电树枝长度分别为534.75 µm和344.37 µm，与ER材料相比，BN/ER复合材料中的电树枝长度缩短了35.6%，从而验证了引入未取向的二维微米片阻挡电树枝生长的效果优于未添加的。
3 结论
收起
（1）当微米片取向角度为垂直于电场方向时，电树枝的分形维数和击穿时间最大，微米复合电介质的耐电树枝性能最好；随着微米片与电场方向所形成的夹角减小，电树枝的分形维数和击穿时间均减小，耐电树枝性能变差。
（2）随着生长概率指数或阈值电压增大，电树枝分支减少、分形维数减小，并且对不同取向角度微米复合电介质中电树枝分形维数的影响增大。
（3）当微米片取向角度为垂直于电场方向时，电场分布相对比较均匀，随微米片取向角度增大，电场集中在微米片两端，且相邻微米片越接近的地方场强越集中。
基金
收起
  • 国家自然科学基金资助项目(51977186)
  • 北京市自然科学基金资助项目(3204044)
  • 新能源电力系统国家重点实验室开放课题资助项目(LAPS20006)
文献
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2022年第55卷第1期
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doi: 10.16790/j.cnki.1009-9239.im.2022.01.004
  • 接收时间：2021-01-25
  • 首发时间：2025-12-23
  • 出版时间：2022-01-20
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  • 收稿日期：2021-01-25
  • 修回日期：2021-03-04
基金
国家自然科学基金资助项目(51977186)
北京市自然科学基金资助项目(3204044)
新能源电力系统国家重点实验室开放课题资助项目(LAPS20006)
作者信息
    1新疆大学 电气工程学院 电力系统及大型发电设备安全控制和仿真国家重点实验室风光储分室， 新疆 乌鲁木齐 830047
    2清华大学 电机工程与应用电子技术系 电力系统及大型发电设备安全控制和仿真国家重点实验室，北京 100084
    3华北电力大学 新能源电力系统国家重点实验室，北京 102206
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