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Article(id=1209927806570590701, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1209927804129514029, articleNumber=null, orderNo=null, doi=10.16790/j.cnki.1009-9239.im.2024.04.017, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1684339200000, receivedDateStr=2023-05-18, revisedDate=1690300800000, revisedDateStr=2023-07-26, acceptedDate=null, acceptedDateStr=null, onlineDate=1766398868457, onlineDateStr=2025-12-22, pubDate=1713542400000, pubDateStr=2024-04-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1766398868457, onlineIssueDateStr=2025-12-22, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1766398868457, creator=13701087609, updateTime=1766398868457, updator=13701087609, issue=Issue{id=1209927804129514029, tenantId=1146029695717560320, journalId=1149653034449285133, year='2024', volume='57', issue='4', pageStart='1', pageEnd='129', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1766398867876, creator=13701087609, updateTime=1766563872818, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1210619885072282300, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1209927804129514029, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1210619885072282301, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1209927804129514029, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=122, endPage=129, ext={EN=ArticleExt(id=1209927806788694511, articleId=1209927806570590701, tenantId=1146029695717560320, journalId=1149653034449285133, language=EN, title=Study on transient temperature distribution of defects in XLPE cables based on electromagnetic-thermal coupling, columnId=1192878364340924664, journalTitle=Insulating Materials, columnName=Test and Analysis, runingTitle=null, highlight=null, articleAbstract=

In view of three common defects of 10 kV cables, three-dimensional cable defect models were established and conducted electromagnetic-thermal coupled temperature field analysis to study the transient temperature models of three defective cables. The effects of different operating currents and laying conditions on the temperature of three defective cables were analyzed. The results show that the harm of defects on the cable ranked from high to low is metal tip defect, air gap defect, and scratch defect. Under the same current carrying capacity, the temperature at the metal tip defect is higher than that at the other two defects. It is determined that the heat dissipation effect of tunnel laying is the best when the cable has defects. The internal temperature of the cable without defects decreases gradually from the core to outer sheath in the radial direction, and the internal temperature field of the cable is distorted under the action of defects. The fitting coefficients between core temperature and outer sheath temperature of the defective cable, and the fitting coefficients between temperature at the defect and the core temperature of cable are both close to 1. The simulation fitting results provide theoretical support for the judgment and identification of cable defects.

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针对10 kV电缆常见的3种缺陷，本文建立了三维电缆缺陷模型并进行电磁-热耦合温度场分析，研究3种缺陷电缆的暂态温度模型，分析不同工作电流与不同敷设条件对3种缺陷电缆温度的影响。结果表明：缺陷对电缆的危害从大到小排序依次为金属尖端缺陷、气隙缺陷、划痕缺陷；在相同载流量的情况下，金属尖端缺陷处温度高于其他两种缺陷处温度；确定了电缆在出现缺陷时隧道敷设的散热效果最好；无缺陷试样电缆内部温度从线芯至外护套沿径向逐渐降低，在缺陷的作用下电缆内部温度场发生畸变；缺陷电缆线芯温度与外护套温度的拟合系数、电缆缺陷处温度与电缆线芯温度的拟合系数均接近1。仿真拟合结果为电缆缺陷的判断与识别提供了理论支撑。

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马志鹏（1988-），男（汉族），重庆人，讲师，主要研究方向为电气设备状态监测。
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陈新岗（1968-），男（汉族），重庆人，教授，主要研究方向为电气设备状态监测、智能发变电运行与控制、信号采集与信号处理。

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陈新岗（1968-），男（汉族），重庆人，教授，主要研究方向为电气设备状态监测、智能发变电运行与控制、信号采集与信号处理。

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陈新岗（1968-），男（汉族），重庆人，教授，主要研究方向为电气设备状态监测、智能发变电运行与控制、信号采集与信号处理。

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结构名称参数值/mm
线芯外径11.9
半导体屏蔽厚度1.0
主绝缘层厚度5.9
金属屏蔽层厚度1.0
外护层厚度4.6
电缆总外径47.0
), ArticleFig(id=1217486449151230135, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1209927806570590701, language=CN, label=表1, caption=

电缆本体建模参数

, figureFileSmall=null, figureFileBig=null, tableContent=
结构名称参数值/mm
线芯外径11.9
半导体屏蔽厚度1.0
主绝缘层厚度5.9
金属屏蔽层厚度1.0
外护层厚度4.6
电缆总外径47.0
), ArticleFig(id=1217486449222533304, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1209927806570590701, language=EN, label=Tab.2, caption=Material parameters for the calculation of electromagnetic field of the cable body, figureFileSmall=null, figureFileBig=null, tableContent=
材料相对介电常数相对磁导率电阻率/(Ω·m)
铜1.0×10411.754×10-8
半导电体10010.167
XLPE2.410.58×108
空气111×1015
), ArticleFig(id=1217486449310613690, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1209927806570590701, language=CN, label=表2, caption=

用于计算电缆本体电磁场的材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
材料相对介电常数相对磁导率电阻率/(Ω·m)
铜1.0×10411.754×10-8
半导电体10010.167
XLPE2.410.58×108
空气111×1015
), ArticleFig(id=1217486449394499772, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1209927806570590701, language=EN, label=Tab.3, caption=Material parameters for the calculation of temperature field of the cable body, figureFileSmall=null, figureFileBig=null, tableContent=
材料导热系数/(W/(m·K))密度/(kg/m3)比热容/(J/(kg·K))
铜4018 921385
半导电体0.51 0551 407
XLPE0.2891 2002 250
空气0.0231.291 000
), ArticleFig(id=1217486449495163069, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1209927806570590701, language=CN, label=表3, caption=

用于计算电缆本体温度场的材料参数

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材料导热系数/(W/(m·K))密度/(kg/m3)比热容/(J/(kg·K))
铜4018 921385
半导电体0.51 0551 407
XLPE0.2891 2002 250
空气0.0231.291 000
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缺陷类型仿真温度/℃试验温度/℃误差/℃
金属尖端缺陷35.936.80.9
气隙缺陷31.632.40.8
划痕缺陷41.241.60.4
), ArticleFig(id=1217486449654546625, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1209927806570590701, language=CN, label=表4, caption=

试验与仿真数据对比

, figureFileSmall=null, figureFileBig=null, tableContent=
缺陷类型仿真温度/℃试验温度/℃误差/℃
金属尖端缺陷35.936.80.9
气隙缺陷31.632.40.8
划痕缺陷41.241.60.4
), ArticleFig(id=1217486449730044099, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1209927806570590701, language=EN, label=Tab.5, caption=Fitting data of wire core temperature and defect temperature, figureFileSmall=null, figureFileBig=null, tableContent=
缺陷类型拟合方程R2
金属尖端缺陷Ta=0.82+0.94Tc0.999 94
气隙缺陷Ta=1.61+0.87Tc0.988 52
划痕缺陷Ta=10.30+0.396Tc0.999 39
), ArticleFig(id=1217486451013501125, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1209927806570590701, language=CN, label=表5, caption=

线芯温度与缺陷温度拟合数据

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缺陷类型拟合方程R2
金属尖端缺陷Ta=0.82+0.94Tc0.999 94
气隙缺陷Ta=1.61+0.87Tc0.988 52
划痕缺陷Ta=10.30+0.396Tc0.999 39
), ArticleFig(id=1217486451097387207, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1209927806570590701, language=EN, label=Tab.6, caption=Fitting data of wire core temperature and outer sheath temperature of cable, figureFileSmall=null, figureFileBig=null, tableContent=
缺陷类型拟合方程R2
金属尖端缺陷Td =0.264 52+13.6Tc0.979
气隙缺陷Td=0.374 45+10.2 Tc0.988
划痕缺陷Td=0.233 72+17.9Tc0.990
), ArticleFig(id=1217486451181273289, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1209927806570590701, language=CN, label=表6, caption=

线芯温度与外护套温度拟合数据

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缺陷类型拟合方程R2
金属尖端缺陷Td =0.264 52+13.6Tc0.979
气隙缺陷Td=0.374 45+10.2 Tc0.988
划痕缺陷Td=0.233 72+17.9Tc0.990
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基于电磁-热耦合的XLPE电缆缺陷暂态温度分布研究
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陈新岗 1, 2 , 宋欣 1 , 马志鹏 1, 2 , 谭世耀 1 , 范益杰 1 , 李宁一 1 , 黄宇杨 1 , 邹政廷 1
绝缘材料 | 测试与分析 2024,57(4): 122-129
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绝缘材料 | 测试与分析 2024, 57(4): 122-129
基于电磁-热耦合的XLPE电缆缺陷暂态温度分布研究
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陈新岗1, 2, 宋欣1, 马志鹏1, 2, 谭世耀1, 范益杰1, 李宁一1, 黄宇杨1, 邹政廷1
作者信息
  • 1重庆理工大学 电气与电子工程学院,重庆 400054
  • 2重庆市能源互联网工程技术研究中心,重庆 400054

    • 陈新岗（1968-），男（汉族），重庆人，教授，主要研究方向为电气设备状态监测、智能发变电运行与控制、信号采集与信号处理。

通讯作者:

马志鹏（1988-），男（汉族），重庆人，讲师，主要研究方向为电气设备状态监测。
Study on transient temperature distribution of defects in XLPE cables based on electromagnetic-thermal coupling
Xingang CHEN1, 2, Xin SONG1, Zhipeng MA1, 2, Shiyao TAN1, Yijie FAN1, Ningyi LI1, Yuyang HUANG1, Zhengting ZHOU1
Affiliations
  • 1School of Electrical and Electronic Engineering, Chongqing University of Technology, Chongqing 400054, China
  • 2Chongqing Energy Internet Engineering Technology Research Center, Chongqing 400054, China
出版时间: 2024-04-20 doi: 10.16790/j.cnki.1009-9239.im.2024.04.017
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摘要
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针对10 kV电缆常见的3种缺陷，本文建立了三维电缆缺陷模型并进行电磁-热耦合温度场分析，研究3种缺陷电缆的暂态温度模型，分析不同工作电流与不同敷设条件对3种缺陷电缆温度的影响。结果表明：缺陷对电缆的危害从大到小排序依次为金属尖端缺陷、气隙缺陷、划痕缺陷；在相同载流量的情况下，金属尖端缺陷处温度高于其他两种缺陷处温度；确定了电缆在出现缺陷时隧道敷设的散热效果最好；无缺陷试样电缆内部温度从线芯至外护套沿径向逐渐降低，在缺陷的作用下电缆内部温度场发生畸变；缺陷电缆线芯温度与外护套温度的拟合系数、电缆缺陷处温度与电缆线芯温度的拟合系数均接近1。仿真拟合结果为电缆缺陷的判断与识别提供了理论支撑。

电磁热耦合  /  缺陷模型  /  敷设方式  /  拟合分析  /  有限元分析

In view of three common defects of 10 kV cables, three-dimensional cable defect models were established and conducted electromagnetic-thermal coupled temperature field analysis to study the transient temperature models of three defective cables. The effects of different operating currents and laying conditions on the temperature of three defective cables were analyzed. The results show that the harm of defects on the cable ranked from high to low is metal tip defect, air gap defect, and scratch defect. Under the same current carrying capacity, the temperature at the metal tip defect is higher than that at the other two defects. It is determined that the heat dissipation effect of tunnel laying is the best when the cable has defects. The internal temperature of the cable without defects decreases gradually from the core to outer sheath in the radial direction, and the internal temperature field of the cable is distorted under the action of defects. The fitting coefficients between core temperature and outer sheath temperature of the defective cable, and the fitting coefficients between temperature at the defect and the core temperature of cable are both close to 1. The simulation fitting results provide theoretical support for the judgment and identification of cable defects.

electromagnetic thermal coupling  /  defect model  /  laying method  /  fitting analysis  /  finite element analysis
陈新岗, 宋欣, 马志鹏, 谭世耀, 范益杰, 李宁一, 黄宇杨, 邹政廷. 基于电磁-热耦合的XLPE电缆缺陷暂态温度分布研究. 绝缘材料, 2024 , 57 (4) : 122 -129 . DOI: 10.16790/j.cnki.1009-9239.im.2024.04.017
Xingang CHEN, Xin SONG, Zhipeng MA, Shiyao TAN, Yijie FAN, Ningyi LI, Yuyang HUANG, Zhengting ZHOU. Study on transient temperature distribution of defects in XLPE cables based on electromagnetic-thermal coupling[J]. Insulating Materials, 2024 , 57 (4) : 122 -129 . DOI: 10.16790/j.cnki.1009-9239.im.2024.04.017
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0 引言
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城市电力系统采用大量的地下电缆作为输配电骨架，据统计，截至2022年，我国地下电缆敷设长度已突破250万公里[1-3]。环境中的潮湿、机械应力和运维工作中的过载、安装保养不当等因素都将加速地下电缆绝缘缺陷的产生[4-5]。对于运行电压等级达到10 kV的城市配电电缆而言，其早期出现绝缘缺陷时无明显状态变化，但高电压的长期作用会加剧绝缘老化进而导致电缆发生爆炸与火灾[6]。为了预防绝缘缺陷引发的相关事故，需对其开展深入研究。已有研究成果表明，缺陷处的温度分布规律与缺陷受运行条件影响的演化机理具有明确关联。因此，对配电电缆缺陷处的温度开展研究，是获取其早期缺陷信息的必要手段，对于电缆绝缘事故的预防与控制具有重要意义。当前针对缺陷处温度分布规律的研究主要从两个方面展开。
一方面为基于数值计算的有限元仿真研究，针对辐射、对流、导热3种传热方式施加微分方程来描述热量的传递规律，并通过有限元法解析温度模型得到温度分布的数值。文献[7]通过有限元方法计算电缆典型缺陷的径向温度场，然后通过电缆外护套温度分布来内推电缆内部热导率模型，从而判断电缆缺陷类型，但该研究没有考虑电缆实际敷设条件对缺陷温度造成的影响。文献[8-10]对电缆气隙缺陷进行有限元温度场计算，分析气隙缺陷对温度分布的影响规律，但在进行有限元计算时没有考虑温度对电导率的影响，使得计算精度不高。文献[11]建立了电缆气隙受潮情况下的有限元模型，研究了不同受潮程度的气隙缺陷对电缆温度的影响，发现在受潮情况下气隙缺陷处温度达到击穿临界值，但该研究没有考虑电磁损耗与电缆温度的耦合关系。
另一方面为基于IEC标准的电路解析法研究，根据电路和热路的相似性建立等效电路求解温度模型。文献[12]通过Runge-Kutta法在经典热路模型的基础上得到双路电缆暂态温度值，再通过Levenberg-Marquardt优化算法对电缆暂态温度值进行非线性拟合得到暂态温度分布模型。文献[13]利用经典热路模型计算电缆外护套动态温度，将其作为Elman神经网络输入，计算出线芯的动态温度。但热路法无法准确模拟电缆缺陷并计算电缆缺陷下的温度暂态模型。文献[14-15]将电缆本体与敷设环境进行分成建模，计算了电缆外部环境的等效热阻与热容，完善了模型参数，最终提高了热路法的精度，但增加了计算时间。
针对上述研究现状，本文在Comsol仿真软件中以电缆运行时线芯产生的焦耳热为主要热源，电缆介质损耗和涡流损耗为次要热源，建立并完善暂态温度模型。在该模型中对3种常见电缆缺陷展开研究，分析缺陷、工作电流对电缆温度的影响，获取含不同缺陷的电缆在不同工作条件下的三维暂态温度分布规律。
1 电缆暂态温度模型计算原理
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通过试验制造常见的电缆缺陷后再测得电缆在不同工况下的三维轴向温度分布较为复杂，因此本文采用有限元Comsol Multiphysics软件建立传热模型，计算缺陷电缆暂态温度分布。
1.1 电磁热数学模型
根据能量守恒定律和傅里叶传热定律，电缆本体传热和空气环境的三维传热控制方程可表示为式（1）。
pC∂T∂t-∂∂x(λx∂T∂x)-∂∂y(λy∂T∂y)-∂∂z(λz∂T∂z)-Qin=0
式（1）中：p代表电缆密度；C代表电缆比热容；t为传热时间；T为温度变量；λx、λy、λz分别代表电缆三维坐标x、y、z轴向热导率；Qin代表电缆内部热源产生的焦耳热，可分为电缆线芯热电效应产生的焦耳热和在交流电场下产生的绝缘介质损耗。电缆线芯热电效应产生的焦耳热为主要热源（Q），由线芯铜质材料导热系数K和工作电流I所决定如式（2）所示。
Q=KI2
电缆绝缘在交流电场下产生的绝缘介质损耗pc如式（3）所示。
pc=ωC1U2tanδ
式（3）中：ω表示角频率；U表示电缆主绝缘上的电压；C1为电缆绝缘常数；δ表示绝缘介质损耗角。
为了提高计算效率，对电缆的电磁场模型做出简化：①电缆运行在50 Hz工频下，且位移电流忽略不计；②场域中无自由电荷。
基于上述简化，引入矢量磁电位A简化电磁耦合的计算复杂度。对于外加激励存在的电流区，其矢量磁位的控制方程如式（4）所示[16-17]。
(∇×1μ∇)A=-Js+JωσA
式（4）中：μ表示材料磁导率；A表示矢量磁位；J表示电流密度；σ表示材料电导率；Js表示外加电流密度。
1.2 多物理场耦合计算
当对电缆施加工频电流时，电缆温升会影响电缆线芯电导率，而电导率的改变会影响电磁损耗和电磁场的变化，耦合关系如图1所示。其中电缆线芯的电导率与温度关系如式（5）所示。
σ=σ201+α(T-20)
式（5）中：σ为电缆线芯的电导率；T为实时温度；σ20为20℃下电缆线芯的电导率。
电缆线芯电导率与电磁场中电磁损耗的关系如式（6）～（7）所示。
pa=∫VJEdV
J=σE
式6）～（7）中：pa表示电磁损耗；E表示电场强度；V表示电缆体积。
由式（5）～（7）可知，随着电缆温度的上升，电导率逐渐下降，从而使电磁损耗减小，通过不断迭代计算电缆线芯电导率反馈到电缆暂态温度模型中，建立电磁-热耦合关系。
2 电缆缺陷模型的构建
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2.1 电缆缺陷模型构建
XLPE电缆缺陷形成原因主要有外力破坏、电缆制造、电缆敷设3大类型，本文以8.7/15kV YJV 1×400型电缆为研究对象，对其构建三维电缆仿真模型，如图2所示，其主要由线芯、半导体屏蔽层、主绝缘层、金属屏蔽层、外护套组成。
分析其常见缺陷形成原因，共设计3种缺陷[18]：
（1）绝缘内部气隙缺陷：电缆主绝缘在挤出工艺中混入气泡记为气隙缺陷，在仿真模型中此缺陷设计为直径为2 mm的球形气隙。
（2）金属尖端缺陷：金属线芯由铜线绞合制造而成，在此过程中可能会产生附着在线芯上的金属尖刺，此缺陷设计为半径为0.6 mm、高度为2 mm、曲率半径为1.031 mm的圆锥缺陷。
（3）划痕缺陷：电缆在安装时受外力破坏，在主绝缘边缘产生划痕缺陷，在模型中设计尺寸为2 mm×0.2 mm×0.2 mm的划痕缺陷模型。
通过Comsol对电缆常见的3种缺陷建模，如图3所示。
2.2 电缆材料物性参数
电缆有限元数值计算涉及电磁场和温度场，电磁-热耦合计算所涉及的材料物性参数如表1～3所示。
2.3 电缆几何模型网格划分
为了提高迭代计算速度和精度，加强计算过程收敛性，对于梯度变化较大的区域（电缆半导体屏蔽层和金属屏蔽层）采用Comsol默认的四面体网格手动调节网格密度来提高温度分布的精度，对于线芯、绝缘层、空气域采用自适应密度调节来加快计算速度，电缆整体网格分布如图4所示。
3 电缆缺陷模型的暂态仿真分析
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3.1 电缆缺陷模型构建
对8.7/15kV YJV 1×400型单芯电缆进行仿真模型构建，根据IEC 60502-2023，在有限元仿真中分别设置电缆的载流量与所处环境温度为720 A与25℃，电缆不同材料物性参数按照表2进行设置。
在电磁-热耦合物理场下，电缆金属尖端缺陷温度分布如图5所示。从图5可以看出，半导体层与XLPE主绝缘的界面上出现金属尖端缺陷，使得缺陷周围等温线分布不均匀，在缺陷周围等温线出现明显不规则形状差异，且在金属尖端处温度分布发生明显畸变。
电缆气隙缺陷温度分布如图6所示，由于电缆绝缘层的气隙导致电场发生突变[19-21]，使得热量积聚在缺陷周围，进而导致局部温升。划痕缺陷位于电缆外护套层，其温度分布如图7所示，相对于前两种缺陷，温度变化较小。
通过探针提取了3种缺陷暂态温度对比数据，结果如图8～10所示。从图8可以看出，无缺陷试样在2.2 h时达到78.15℃后趋于热稳定，而电缆金属尖端缺陷在2.1 h达到85.33℃后趋于热稳定。对比图8～10可知，由于金属尖端缺陷导致应力更加集中且使缺陷表面产生局部放电，加剧了温升与老化[14-15]，因此在3种缺陷中温度变化最大。
从图9可以看出，气隙缺陷温升相对于金属尖端缺陷的变化幅度更小，气隙缺陷在2 h达到68.32℃后趋于热稳定，而相同位置无缺陷试样在2.75 h达到73.52℃后趋于热稳定。
从图10可以看出，电缆划痕缺陷在4 h达到37.56℃后趋于热稳定，无缺陷试样达到热稳定时温度为36.10℃，相对于其他两种缺陷温度变化最小。
3.2 不同工况下的电缆缺陷暂态温度模型分析
在环境温度相同的条件下，通过Comsol有限元计算，分析不同电缆缺陷中的不同载流量对电缆线芯温度的影响，得到电缆金属尖端缺陷、划痕缺陷、气隙缺陷暂态温升随时间的变化规律，如图11～13所示。从图11～13可以看出，随着载流量的增加，划痕缺陷处温升相比其他两种缺陷更为缓慢且未达到90℃的临界值。金属尖端缺陷温升最快，在相同载流量下金属尖端缺陷温度高于气隙缺陷温度。在电缆超负荷运行时，金属尖端缺陷相较于气隙缺陷温度更易达到临界值，对电缆损害更严重。
3.3 不同敷设条件下电缆缺陷暂态温度模型分析
通过Comsol仿真模拟电缆在直埋敷设、隧道敷设、管道敷设[22-23]3种不同敷设条件下的温度，对3种敷设方式下的缺陷电缆设定载流量为720 A，表面辐射率为5.6，环境温度取气候温度平均值25℃，设置空气导热系数为0.7 W/(m·K)。管道敷设采用PVC材质套管，设置其导热系数为0.142 W/(m·K)。直埋敷设设置深度为1 m，回填沙土导热系数取值为0.142 W/(m·K)。考虑到隧道中金属支架与电缆接触面积小，因此在模型中不考虑金属支架。
3种电缆缺陷在不同敷设方式下的温度仿真结果如图14～16所示。从图14可以看出，电缆金属尖端缺陷在3种不同的敷设方式下温度存在明显差异。隧道敷设条件下线芯温度为85.4℃，缺陷处温度为82.3℃；管道敷设下线芯到达热稳定时的温度为88.4℃，缺陷处温度为85.7℃；直埋敷设下线芯温度为92.6℃，缺陷处温度为88.6℃。其他两种缺陷温度分布规律与金属尖端缺陷相似。按散热能力排序从大到小依次为隧道敷设、管道敷设、直埋敷设。在地下敷设电缆时，应当选择散热效果最好的隧道敷设。
3.4 验证仿真有效性
为了验证仿真模型的有效性，以图3所示的3种缺陷模型按1∶1制备实物缺陷电缆，利用红外测温技术对缺陷电缆外护套的温度进行测量。图17为缺陷电缆连接大电流发生器的原理图，大电流发生器型号为TT-SIQ-4000A，其升流器容量为24 kVA，输入电压为380 V，最大输出电流为4 kA。选用10 m的8.7/15 kV YJV 1×400型XLPE电缆通过螺栓与大电流发生器的金属电极连接，试验环境为25.2℃。
通过转动升流器转盘，对缺陷电缆施加600 A的工频电流，待缺陷电缆温度到达热稳定后使用FLUKE红外成像仪对电缆外护套测温，3种缺陷电缆的热成像结果如图18所示。由图18可知，在施加600 A工频电流4 h后，缺陷电缆温度到达热稳定，将试验数据列于表4并与仿真模型数据进行对比。由表4可知，试验数据略高于仿真数据，但与仿真数据误差较小，验证了三维XLPE缺陷电缆暂态温度分布模型的有效性。分析误差原因主要有：①构建模型尺寸与试验真实尺寸存在误差。②试验环境自然对流换热系数与仿真设置的有所不同。
3.5 拟合分析
电缆温度同时受线芯发热和缺陷引起的局部发热的影响[24]。通过拟合公式，对电缆温度进行监测可以初步判定电缆状态，需对以下参数进行数据拟合分析。
（1）分析电缆缺陷温度与线芯温度的关系并进行拟合，结果如图19所示。从图19可以看出，线芯温度与各缺陷处的温度呈线性分布。进一步分析得到如表5所示数据，Tc表示线芯温度，Ta表示缺陷处温度。从表5可以看出，R2数值接近于1，说明缺陷处温度与线芯温度拟合关系准确度高。当金属尖端缺陷处温度每上升10℃时，线芯温度上升约10℃；气隙缺陷处温度上升10℃，线芯温度上升约10℃；划痕缺陷温度上升10℃，线芯温度上升约14℃。金属尖端缺陷、气隙缺陷和划痕缺陷分别位于电缆线芯、电缆主绝缘和电缆绝缘界面上，主绝缘的导热系数低，热量不易向外扩散，因此位置越靠近外护套的缺陷温升越大，对应的电缆线芯温升值也越大。
（2）分析缺陷电缆线芯温度与外护套温度的关系并进行拟合，结果如图20所示，拟合方程如表6所示，其中Td表示外护套温度。从图20与表6可以看出，电缆出现缺陷情况下，线芯温度与外护套温度拟合曲线也趋于线性关系。R2数值接近于1，且拟合曲线上升速率从大到小依次为划痕缺陷、金属尖端缺陷、气隙缺陷，这是因为划痕缺陷位置在外护套表面，使外护套绝缘层耐热性减弱，而金属尖端缺陷由于其材料热导率远大于气隙，传热速率大于气隙缺陷。由于缺陷破坏了电缆绝缘，使得电缆线芯的热源在缺陷处不规则向外传播，同时绝缘的破坏也使得电场发生畸变[25-27]。在多场耦合的条件下，不同缺陷的线芯与外护套温度线性拟合也不相同。当电缆局部温度异常升高时，可以及时采取措施进行维修或更换，以避免发生故障。
4 结论
收起
（1）在相同工作环境下，金属尖端缺陷对线芯温度的影响大于气隙缺陷与划痕缺陷的影响，3种电缆缺陷的最大载流量（线芯温度为90℃时）不同。当电缆高负荷时，金属尖端缺陷相比其他缺陷温度温升更快。
（2）针对10 kV XLPE电缆，通过Comsol建立3种常见敷设条件模型，计算得到暂态温度分布。不同敷设条件下同一缺陷电缆温度不同，按散热能力排序从大到小依次为隧道敷设、管道敷设、直埋敷设。
（3）根据上述电缆参数拟合关系，通过监测电缆外护套温度可以计算得到线芯温度与缺陷温度，对于电缆故障判断与识别提供了理论支持。
基金
收起
  • 重庆市教育委员会科学技术研究项目(KJZDK202101103)
  • 重庆理工大学科研启动基金项目(2021ZDZ016)
  • 重庆理工大学研究生教育高质量发展行动计划资助项目(gzlcx20233126)
文献
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2024年第57卷第4期
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doi: 10.16790/j.cnki.1009-9239.im.2024.04.017
  • 接收时间：2023-05-18
  • 首发时间：2025-12-22
  • 出版时间：2024-04-20
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  • 收稿日期：2023-05-18
  • 修回日期：2023-07-26
基金
重庆市教育委员会科学技术研究项目(KJZDK202101103)
重庆理工大学科研启动基金项目(2021ZDZ016)
重庆理工大学研究生教育高质量发展行动计划资助项目(gzlcx20233126)
作者信息
    1重庆理工大学 电气与电子工程学院,重庆 400054
    2重庆市能源互联网工程技术研究中心,重庆 400054

通讯作者:

马志鹏（1988-），男（汉族），重庆人，讲师，主要研究方向为电气设备状态监测。
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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
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光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
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