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Article(id=1210560432008458611, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210560429043085661, articleNumber=null, orderNo=null, doi=10.16790/j.cnki.1009-9239.im.2024.07.011, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1690732800000, receivedDateStr=2023-07-31, revisedDate=1698508800000, revisedDateStr=2023-10-29, acceptedDate=null, acceptedDateStr=null, onlineDate=1766549698115, onlineDateStr=2025-12-24, pubDate=1721404800000, pubDateStr=2024-07-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1766549698115, onlineIssueDateStr=2025-12-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1766549698115, creator=13701087609, updateTime=1766549698115, updator=13701087609, issue=Issue{id=1210560429043085661, tenantId=1146029695717560320, journalId=1149653034449285133, year='2024', volume='57', issue='7', pageStart='1', pageEnd='142', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1766549697408, creator=13701087609, updateTime=1766563951127, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1210620213532430860, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210560429043085661, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1210620213532430861, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210560429043085661, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=84, endPage=93, ext={EN=ArticleExt(id=1210560433530991022, articleId=1210560432008458611, tenantId=1146029695717560320, journalId=1149653034449285133, language=EN, title=Study on electric field distribution characteristics of oil-paper and cross-linked polythylene insulated HVDC cables, columnId=1190369198472794288, journalTitle=Insulating Materials, columnName=Insulation Technology, runingTitle=null, highlight=null, articleAbstract=

DC cable mainly uses oil-paper and crosslinked polyethylene (XLPE) as insulation, and the conductivity characteristics of the two materials are different, which has a significant effect on the electric field distributions in cable. In this paper, a finite element model was established based on the 500 kV typical DC cable structure, and the thermal-electrical coupled simulation analyses were performed on the oil-paper and XLPE insulated cables. The electric field distribution characteristics in the two insulation under different temperatures and temperature drops were studied, and the influences of the conductivity temperature and electric field coefficient on the field strength distribution were analyzed. The conductivity variations of oil-paper and XLPE insulations among the same temperature and field ranges were compared. The results show that the electric field distribution in oil-paper insulation is affected by the insulation temperature difference in the electric field strength range of 10-25 kV/mm and temperature range of 20-90℃, and hardly changes with the insulation temperature under definite temperature difference, while the electric field distribution in XLPE insulation is affected by both insulation temperature and temperature difference. In addition, the overall conductivity of oil-paper insulation is higher than that of XLPE insulation, and its change amplitude with temperature and field strength is larger, which may be the reason why the electric field inversion in oil-paper cable insulation occurs at a lower temperature difference. For the insulating materials used in HVDC cables, the conductivity temperature coefficient should to be controlled small so as to reduce the temperature sensitivity.

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直流电缆主要采用油纸及交联聚乙烯（XLPE）作为绝缘，两类材料的电导率特性不同，对电缆中电场分布的影响不同。本文基于500 kV典型直流电缆结构建立有限元模型，对油纸及XLPE绝缘电缆开展热-电耦合仿真分析，研究了两种绝缘在不同温度及温差下的场强分布特性，分析了绝缘电导率温度系数及电场系数对场强分布的影响，对比了相同温度及场强范围内油纸及XLPE绝缘的电导率变化特性。结果表明：在电场强度为10～25 kV/mm和温度为20～90℃的范围内，油纸绝缘中的电场分布受绝缘温差的影响，在确定温差下几乎不随绝缘温度而变化；而XLPE绝缘中的电场分布同时受绝缘温度和温差的影响。此外，油纸绝缘的电导率整体比XLPE绝缘高，随温度和场强的变化幅度大，这可能是油纸电缆绝缘中电场反转发生在更低温差下的原因。对于高压直流电缆中应用的绝缘材料，应控制电导率温度系数即减小温度敏感性。

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但京民（1995-），男（汉族），湖北孝感人，工程师，主要从事高压输电线路的研究；

刘英（1976-），女（汉族），四川资阳人，教授，博士，主要从事绝缘结构设计和电力电缆工程计算的研究。

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但京民（1995-），男（汉族），湖北孝感人，工程师，主要从事高压输电线路的研究；

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但京民（1995-），男（汉族），湖北孝感人，工程师，主要从事高压输电线路的研究；

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刘英（1976-），女（汉族），四川资阳人，教授，博士，主要从事绝缘结构设计和电力电缆工程计算的研究。

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刘英（1976-），女（汉族），四川资阳人，教授，博士，主要从事绝缘结构设计和电力电缆工程计算的研究。

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tableContent=null), ArticleFig(id=1218111629846298894, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210560432008458611, language=EN, label=Table 1, caption=Dimensions and material parameters of 500 kV DC cable, figureFileSmall=null, figureFileBig=null, tableContent=
结构名称厚度/mm热导率/(W/(m·K))比热容/(J/(kg·K))密度/(kg/m3)
导体57.34003858 700
半导电尼龙带0.60.232 7001 120
半导电屏蔽层2.00.285 72 274.81 120
绝缘层29.00.285 72 3001 200
半导电阻水缓冲带2.00.232 0001 150
合金铅套4.3351281 134
内护套4.40.51 900980
内衬层9.10.231 850910
钢丝铠装6.558.2450778
外护套4.00.231 850910
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500 kV直流电缆尺寸及材料参数

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结构名称厚度/mm热导率/(W/(m·K))比热容/(J/(kg·K))密度/(kg/m3)
导体57.34003858 700
半导电尼龙带0.60.232 7001 120
半导电屏蔽层2.00.285 72 274.81 120
绝缘层29.00.285 72 3001 200
半导电阻水缓冲带2.00.232 0001 150
合金铅套4.3351281 134
内护套4.40.51 900980
内衬层9.10.231 850910
钢丝铠装6.558.2450778
外护套4.00.231 850910
), ArticleFig(id=1218111631289139475, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210560432008458611, language=EN, label=Table 2, caption=Conductivity measurement data of 4258 DC material under different temperature, figureFileSmall=null, figureFileBig=null, tableContent=
场强/(kV/mm)10203040
30℃201054
50℃203.01.91.8
70℃7.02.81.40.9
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不同温度下4258直流料的电导率测量数据

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场强/(kV/mm)10203040
30℃201054
50℃203.01.91.8
70℃7.02.81.40.9
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绝缘温差/℃绝缘内侧温度/℃场强/(kV/mm)不均匀系数
绝缘内侧绝缘外侧
105015.1818.921.110
7015.1918.931.110
9015.2318.891.107
155012.3721.551.271
7012.3921.541270
9012.4221.531.268
20509.8524.731.430
709.8624.671.429
909.8424.661.430
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不同温度及温差下油纸绝缘内外侧场强

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绝缘温差/℃绝缘内侧温度/℃场强/(kV/mm)不均匀系数
绝缘内侧绝缘外侧
105015.1818.921.110
7015.1918.931.110
9015.2318.891.107
155012.3721.551.271
7012.3921.541270
9012.4221.531.268
20509.8524.731.430
709.8624.671.429
909.8424.661.430
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绝缘温差/℃绝缘内侧温度/℃场强/(kV/mm)
绝缘内侧绝缘外侧不均匀系数
105018.716.21.072
7018.915.91.086
9019.115.71.098
155017.916.81.032
7018.216.51.049
9018.516.21.066
205017.117.51.012
7017.517.11.012
9017.916.71.035
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不同温度及温差下XLPE绝缘内外侧场强

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绝缘温差/℃绝缘内侧温度/℃场强/(kV/mm)
绝缘内侧绝缘外侧不均匀系数
105018.716.21.072
7018.915.91.086
9019.115.71.098
155017.916.81.032
7018.216.51.049
9018.516.21.066
205017.117.51.012
7017.517.11.012
9017.916.71.035
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油纸及XLPE绝缘高压直流电缆的电场分布特性研究
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但京民 1 , 李文清 2 , 崔戎舰 1 , 刘英 2 , 李健 1 , 吴高波 1
绝缘材料 | 绝缘技术 2024,57(7): 84-93
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绝缘材料 | 绝缘技术 2024, 57(7): 84-93
油纸及XLPE绝缘高压直流电缆的电场分布特性研究
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但京民1, 李文清2, 崔戎舰1, 刘英2, 李健1, 吴高波1
作者信息
  • 1中国电力工程顾问集团中南电力设计院有限公司,湖北 武汉 430071
  • 2西安交通大学 电气工程学院,陕西 西安 710049

    • 但京民（1995-），男（汉族），湖北孝感人，工程师，主要从事高压输电线路的研究；

    刘英（1976-），女（汉族），四川资阳人，教授，博士，主要从事绝缘结构设计和电力电缆工程计算的研究。

Study on electric field distribution characteristics of oil-paper and cross-linked polythylene insulated HVDC cables
Jingmin DAN1, Wenqing LI2, Rongjian CUI1, Ying LIU2, Jian LI1, Gaobo WU1
Affiliations
  • 1Central Southern China Electric Power Design Institute Co., Ltd. of China Power Engineering Consulting Group, Wuhan 430071, China
  • 2School of Electrical Engineering, Xi′an Jiaotong University, Xi′an 710049, China
出版时间: 2024-07-20 doi: 10.16790/j.cnki.1009-9239.im.2024.07.011
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摘要
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直流电缆主要采用油纸及交联聚乙烯（XLPE）作为绝缘，两类材料的电导率特性不同，对电缆中电场分布的影响不同。本文基于500 kV典型直流电缆结构建立有限元模型，对油纸及XLPE绝缘电缆开展热-电耦合仿真分析，研究了两种绝缘在不同温度及温差下的场强分布特性，分析了绝缘电导率温度系数及电场系数对场强分布的影响，对比了相同温度及场强范围内油纸及XLPE绝缘的电导率变化特性。结果表明：在电场强度为10～25 kV/mm和温度为20～90℃的范围内，油纸绝缘中的电场分布受绝缘温差的影响，在确定温差下几乎不随绝缘温度而变化；而XLPE绝缘中的电场分布同时受绝缘温度和温差的影响。此外，油纸绝缘的电导率整体比XLPE绝缘高，随温度和场强的变化幅度大，这可能是油纸电缆绝缘中电场反转发生在更低温差下的原因。对于高压直流电缆中应用的绝缘材料，应控制电导率温度系数即减小温度敏感性。

高压直流电缆  /  油纸绝缘  /  交联聚乙烯绝缘  /  电场分布  /  绝缘电导率

DC cable mainly uses oil-paper and crosslinked polyethylene (XLPE) as insulation, and the conductivity characteristics of the two materials are different, which has a significant effect on the electric field distributions in cable. In this paper, a finite element model was established based on the 500 kV typical DC cable structure, and the thermal-electrical coupled simulation analyses were performed on the oil-paper and XLPE insulated cables. The electric field distribution characteristics in the two insulation under different temperatures and temperature drops were studied, and the influences of the conductivity temperature and electric field coefficient on the field strength distribution were analyzed. The conductivity variations of oil-paper and XLPE insulations among the same temperature and field ranges were compared. The results show that the electric field distribution in oil-paper insulation is affected by the insulation temperature difference in the electric field strength range of 10-25 kV/mm and temperature range of 20-90℃, and hardly changes with the insulation temperature under definite temperature difference, while the electric field distribution in XLPE insulation is affected by both insulation temperature and temperature difference. In addition, the overall conductivity of oil-paper insulation is higher than that of XLPE insulation, and its change amplitude with temperature and field strength is larger, which may be the reason why the electric field inversion in oil-paper cable insulation occurs at a lower temperature difference. For the insulating materials used in HVDC cables, the conductivity temperature coefficient should to be controlled small so as to reduce the temperature sensitivity.

HVDC cables  /  oil-paper insulation  /  XLPE insulation  /  electric field distribution  /  insulation conductivity
但京民, 李文清, 崔戎舰, 刘英, 李健, 吴高波. 油纸及XLPE绝缘高压直流电缆的电场分布特性研究. 绝缘材料, 2024 , 57 (7) : 84 -93 . DOI: 10.16790/j.cnki.1009-9239.im.2024.07.011
Jingmin DAN, Wenqing LI, Rongjian CUI, Ying LIU, Jian LI, Gaobo WU. Study on electric field distribution characteristics of oil-paper and cross-linked polythylene insulated HVDC cables[J]. Insulating Materials, 2024 , 57 (7) : 84 -93 . DOI: 10.16790/j.cnki.1009-9239.im.2024.07.011
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0 引言
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随着化石能源的短缺和日渐枯竭以及全球气候变化，加大可再生能源利用的呼声日渐高涨[1-2]。发电是可再生能源利用的一种重要方式，但可再生能源一般分布在人烟稀少的地区，离城市、工业区等负荷中心较远，需要通过高压输电线路传输电能[3-4]。直流输电是目前实现远距离、大容量、低损耗、高效率电力传输以及可再生能源发电并网的最佳选择，而高压直流电缆是实现直流输电的关键装备之一[5]。
已投运的超高压直流电缆多采用油纸绝缘，而低压至高压直流电缆较多采用交联聚乙烯（XLPE）绝缘。在电压变化时绝缘中的电场分布取决于材料的电导率，在直流稳态时取决于材料的电阻率，而电导率随温度及场强变化，不同材料的电阻率特性差异大，因此直流电缆的电场分布比较复杂[6-7]。
关于油纸绕包绝缘直流电缆电场分布的研究开始较早。1965年，E OCCHINI等[6]基于5组油纸绝缘试样的电场测试结果建立表征方程，推导了实际电缆在稳态或瞬态下的绝缘场强分布。1975年，C K EOLL[7]指出，不同油纸绝缘的电导率表达式难以统一，这可能对电缆绝缘场强分布的理论分析产生影响。1995年，M J P JEROENSE等[8]考虑温度和场强依赖性，对油纸绝缘电导率公式进行推导，提出了描述离子电导的物理方程；1998年，他进一步计算了油纸绝缘电场从容性分布转为阻性分布时各阶段的场强分布，并建立了场强随时间变化的表达式[9]。2014年，HUANG Z Y等[10-11]以油纸绝缘电缆为例，考虑电缆绝缘场强允许限值，改进了直流电缆的稳态载流量评估技术。
21世纪以来，挤包绝缘直流电缆技术获得较快发展[12]。2008年，C C REDDY等[13]研究指出，直流电压下电缆绝缘几何中心的场强近似等于平均场强，且稳态场强分布曲线都穿过几何中心。2014年，叶信红等[14]设计了250 kV直流交联电缆并计算了稳态场强分布。2016年，李忠华等[15]研究XLPE电缆的暂态电场分布特性，并指出场强幅值与电压极性反转的时间具有强关联性。郑欢等[16]研究了直流叠加冲击电压下XLPE电缆绝缘的暂态电场特性，分析了温度、电导率等对电缆绝缘中暂时态电场的影响。2017年，王雅妮等[17]研究XLPE绝缘温差对电场分布的影响，分析了场强变化趋势。2021年，S KUMARA等[18]应用多种XLPE电导率模型进行绝缘场强分布计算，并分析了结果差异。
从上述研究可以看出，已有的研究多针对某一种电缆绝缘类型，未有在相同条件下针对油纸及XLPE材料的电导率特性及直流电缆绝缘的电场分布进行对比研究及系统分析。基于此，本文采用有限元分析软件COMSOL，在500 kV典型直流电缆结构基础上，建立油纸绝缘及XLPE绝缘电缆模型，仿真研究不同温度及温差下，两种电缆绝缘中的场强分布，为直流电缆的运行参数设计提供理论依据；同时分析绝缘材料电导率温度系数及电场系数对电缆绝缘中场强分布的影响，以及绝缘电导率随温度及场强的变化规律，解释不同直流电缆绝缘中场强分布差异产生的原因，为绝缘材料的选型及开发提供参考。
1 模型建立
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1.1 电缆结构尺寸及材料参数
500 kV直流电缆典型结构如图1所示，采用COMSOL仿真软件建模，电缆的结构尺寸和材料参数如表1所示。为便于在同一尺度下对比油纸绝缘和XLPE绝缘直流电缆电场分布的差异，在研究中保持电缆结构尺寸不变，分别代入油纸绝缘和XLPE绝缘的电导率参数，开展热场耦合下的电场仿真研究。
1.2 场控制方程及边界条件
本文主要讨论不同绝缘温度和温差下电缆绝缘中的电场分布。由于直流电缆绝缘电场分布受电导率控制，而电导率具有温度和场强相关性，因此，这是一个热-电场耦合求解问题。
电场模块控制方程如式（1）～（3）所示。
∇⋅J=0
J=(γ+ε0εr∂∂t)E+Je
E=-∇U
式（1）～（3）中：∇为矢量微分算符；J为电流密度矢量，A/m2；γ为电导率，S/m；ε0为真空介电常数；εr为相对介电常数；t为时间，s；E为电场强度矢量，V/m；Je为外部注入电流密度，A/m2；U为电势，V。
传热模块控制方程如式（4）所示。
ρCp∂θ∂t+ρCpu⋅∇θ=∇⋅(λ∇θ)+Q
式（4）中：ρ为材料密度，kg/m3；Cp为常压热容， J/(kg·K)；θ为温度，K；u为速度矢量，m/s；λ为导热系数，W/(m·K)；Q为热源单位体积发热功率，W/m3[19]。
1.3 绝缘材料的电导率模型
绝缘材料的电导率是决定直流电缆电场分布的关键参数。现有研究中描述电缆绝缘材料电导率的表达式较多，本文选用式（5）和式（6）进行描述[20-23]。式（5）一般用于描述油纸绝缘电缆，为经验公式；式（6）用于描述交联聚乙烯电缆，基于离子跳跃电导机制推导得出。
γT, E=γ0expαT+βE
γT, E=γ1exp-a/T+bE
式（5）～（6）中：T为温度，K；E为电场强度，kV/mm；γ0、γ1分别为设定场强及温度下的初始电导率，S/m；α、a为温度系数；β、b为电场系数，均与材料本身特性有关，反映材料电导率的温度及场强依赖性。
本文根据文献[9]推荐，对于直流电缆油纸绝缘选用的电导率表达式如式（7）所示。
γT, E=1×10-16exp(0.1T+0.03E)
而对于XLPE绝缘，考虑到目前的超高压直流电缆基本都以LE4258作为绝缘料，本文选用北欧4258直流料的测量数据作为拟合电导率依据，如表2所示。
基于表2不同温度和场强下材料片状试样的电导率实测数据，利用式（6）进行拟合，得到XLPE绝缘的电导率表达式如式（8）所示。
γT, E=1.355×10-11exp(-3315/T+6.683×0.01E)
1.4 边界条件设置及网格划分
本文针对绝缘层电场分布特性进行研究，暂不考虑电缆外部实际敷设情况，因此在绝缘屏蔽侧设置恒温边界，以线芯的焦耳热作为电缆中唯一热源，通过线芯中负载电流和绝缘屏蔽温度的配合设置，使绝缘内侧温度和两侧温差达到预设值。同时，将绝缘屏蔽设置为零电位，而额定直流电压施加于线芯，即绝缘承受运行电压，在此条件下开展电场分析。
对已确定结构和材料参数的仿真模型设置电场及热场边界条件后，进行网格划分。根据所需计算精度设置相应网格密度，得到仿真模型的计算网格剖分图如图2所示。
2 绝缘温度及温差对电场的影响分析
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本文通过线芯负载电流和绝缘屏蔽温度的配合设置，实现绝缘内侧温度为50、70、90℃，绝缘两侧温差为10、15、20℃，讨论不同绝缘温度和温差下油纸绝缘和XLPE绝缘电缆中的电场分布。在3个所选择的绝缘内侧温度中，50℃对应实际电缆满负荷运行工况，70℃对应目前XLPE直流电缆设计满负荷运行工况，而90℃用于探索电缆在更高温度下的极限运行特征。所选择的3个绝缘温差值，也是为了涵盖电缆在低、中、高负载率下的不同运行工况。
2.1 油纸绝缘中的电场分布
首先对油纸绝缘直流电缆进行分析。图3(a)展现了绝缘内侧温度固定为70℃、不同绝缘温差下电缆油纸绝缘层中的径向电场分布。从图3(a)可以看出，场强沿半径呈“准线性分布”；不同绝缘温差下的电场分布曲线相交于一点，该交点位于绝缘层径向中点位置，其场强约等于绝缘层平均场强；随着绝缘两侧温差增大，电场分布曲线绕该点呈逆时针旋转。在10℃绝缘温差下，油纸绝缘中已经发生了电场反转的现象，即绝缘径向场强呈内低外高的分布，随着温差增大至15℃和20℃，电场反转现象变得更加显著，绝缘内侧场强持续减小，而外侧场强不断增大，场强不均匀性增加，绝缘中最大场强始终位于绝缘外侧且幅值持续增大。
保持其他条件不变，仅将绝缘内侧温度调整为90℃，电缆油纸绝缘层中的径向电场分布如图3(b)所示。从图3(b)可以看出，该电场分布曲线与图3(a)基本相同，未见显著差异。
由图3已知，在用式（7）表征电导率特性的直流电缆油纸绝缘中，径向电场分布曲线在绝缘内侧温度不同但温差相同情况下高度重合。为进一步确认这个规律，做出不同温差下电缆油纸绝缘径向电场分布图，如图4所示；同时提取不同温度及温差下绝缘内侧及外侧场强，列于表3中，并引入不均匀系数来表征电场分布的不均匀程度，其值为径向最大场强与平均场强的比值。
从图4(a)可以看出，在温差为10℃的条件下，不同内侧温度的绝缘电场分布曲线几乎重合；而温差升高至15℃和20℃时，曲线仍保持高度重合。也就是说，油纸绝缘的径向电场分布在确定的绝缘温差下几乎与温度绝对值无关。这一点可从表3得到进一步证实。
从表3数据可以看出，固定绝缘温差，设置内侧温度分别为50、70、90℃时（也就是绝缘整体温度分别依次增加20℃），绝缘内侧和外侧的场强值变动很小，特别是在温差为20℃时，场强变化未超过0.1 kV/mm。另外，各种情况下，最大场强均出现在绝缘外侧，即径向电场分布已经发生了反转，且随温差增大，最大场强幅值持续增大，在温差为20℃时，最大场强约为24.73 kV/mm。
2.2 XLPE绝缘中的电场分布
保持电缆结构不变，仅将绝缘层替换为XLPE材料，其电导率特性用式（8）表征，设置绝缘内侧温度分别为50、70、90℃、绝缘温差分别为10、15、20℃，开展电场分布的仿真。
图5(a)展示了绝缘内侧温度为70℃、不同绝缘温差下XLPE电缆绝缘层中的径向电场分布。从图5(a)可以看出，场强沿半径仍然呈“准线性分布”；随着绝缘温差的增大，电场分布曲线绕绝缘中点呈现逆时针旋转的规律，这与油纸绝缘中的场强分布特征一致。但是，在绝缘温差由10℃升高至15℃和20℃的过程中，径向电场分布始终为内高外低趋势，虽然随着温差增大绝缘内侧场强持续减小，外侧场强持续增大，但在20℃温差下仍未发生电场反转，电场最大值始终位于绝缘内侧。
保持其他条件不变，将绝缘内侧温度设置为90℃，XLPE电缆绝缘层中的径向电场分布如图5(b)所示。从图5(b)可以看出，该电场分布曲线的变化规律与图5(a)基本相同，且沿径向内高外低的趋势更加明显，电场分布的不均匀程度更显著，在绝缘内侧电场强度幅值也更大。
从图5可以看出，用式（8）表征电导率特性的直流电缆XLPE绝缘径向电场分布同时受到绝缘温度和温差的影响。图6为不同温差下XLPE绝缘中的电场分布特性。从图6可以看出，随着绝缘温差的增大，绝缘内侧场强降低而外侧场强持续升高，电场分布均匀性得到改善；而在确定的温差下，绝缘层整体温度绝对值越高，电场分布曲线越倾斜，绝缘层内侧场强幅值越大。其中仅在绝缘温差为20℃而内侧温度为50℃的情况下，电场分布发生了反转现象，场强最大值转移至绝缘外侧。
为了获得绝缘中最大场强的具体数值，计算出绝缘内侧温度为50、70、90℃、温差为10、15、20℃情况下XLPE绝缘内、外侧的场强值，数据列于表4中。由表4可知，在直流电缆XLPE绝缘中，随着温度和温差的变化，绝缘内侧及外侧的场强值都在相应发生变化；随着绝缘温差从10℃升高至20℃，绝缘中最大场强由19.1 kV/mm下降为17.1 kV/mm，电场不均匀系数由1.098下降至1.012。除绝缘温差为20℃、内侧温度为50℃的情况外，场强最大值均位于绝缘内侧，也就是说，电场分布未发生反转。
2.3 两种绝缘中电场分布对比分析
综合本文中油纸绝缘与XLPE绝缘的电场仿真结果，可以总结得出直流电缆绝缘中的稳态电场分布具有以下基本特征：
（1）径向电场分布接近一条直线；
（2）不同条件下的电场分布曲线相交于一点，该点位于绝缘径向中点，其场强约等于绝缘层平均场强；
（3）随着绝缘两侧温差增大，电场分布曲线绕中点呈逆时针旋转，绝缘内侧场强减小，外侧场强增大。
此外，分别由式（7）和式（8）表征电导率特性的油纸绝缘和XLPE绝缘的径向电场分布又具有各自不同的特征，具体表现如下：
（1）在本文设置的相同条件下，油纸绝缘在温差为10℃时电场已经发生反转，而XLPE绝缘在温差为20℃时才开始发生反转；
（2）油纸绝缘中的电场分布受绝缘温差影响，在温差固定后几乎不随绝缘温度而变化；XLPE绝缘中的电场分布同时受到绝缘温差和温度绝对值的影响。
上述分析表明，两种最常用的直流电缆绝缘材料电导率特性存在显著差异，其中，温度依赖性尤其值得关注。从表3～4中的数据来看，直流电缆绝缘中的电场强度变化范围为10～25 kV/mm，而温度变化范围为30～90℃，相对而言，温度变化范围更大，由其引起的电导率变化必须在可控范围内，以避免绝缘场强的变化超过允许值。
为了在前文基础上更全面地展示绝缘中电场的变化，接下来针对电导率表达式中温度系数及电场系数对电缆绝缘中电场分布的影响展开分析，对油纸绝缘选择满负荷运行工况，设置绝缘内侧温度为70℃，绝缘温差为15℃；对性能更好的XLPE绝缘选择更加苛刻的仿真条件，设置绝缘内侧温度为50℃，绝缘温差为25℃。
3 电导率温度系数及电场系数对绝缘中电场分布的影响分析
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3.1 油纸绝缘
保持电场系数恒定为0.03，设置温度系数为原始值的80%～120%，研究油纸绝缘层中场强分布随温度系数的变化；之后，保持温度系数恒定为0.1，设置电场系数为原始值的50%～200%，研究油纸绝缘层中场强分布随电场系数的变化，结果如图7所示。从图7可以看出，绝缘材料电导率表达式中的电场系数与温度系数变化均会导致油纸绝缘中场强分布曲线斜率发生变化，但两者的影响呈现出相反的趋势。随着电场系数的增大，场强径向分布曲线的斜率减小，场强分布变得更加均匀；而随着温度系数的增大，场强径向分布曲线的斜率增大，场强分布均匀性变差，电场反转现象更为显著。
3.2 XLPE绝缘
XLPE绝缘层中场强分布随温度系数及电场系数的变化规律如图8所示。其中，图8(a)为保持电场系数恒定为6.683×10-2，设置温度系数为原始值的80%～120%得到的结果，而图8(b)为保持温度系数恒定为3 315，设置电场系数为原始值的50%～200%得到的结果。从图8可以看出，XLPE绝缘的径向电场分布曲线随电导率温度系数的增大绕绝缘中占呈逆时针旋转，随电场系数的增大绕绝缘中点呈顺时针旋转，呈现出与电缆油纸绝缘相同的基本规律。因此，降低绝缘材料的温度敏感性、减小电导率温度系数，将有利于抑制电缆在不同负载率下运行时温度大幅变动所带来的绝缘电场分布显著变化、场强幅值增大问题。此外，综合图7和图8还可以看出，增大电导率电场系数对于直流电缆绝缘中场强分布具有改善作用，但其影响小于温度系数，这是由于在直流电缆绝缘中，场强的变化范围通常较温度小，在电导率表达式（如式（7）和式（8））中，场强这一项的整体贡献也比温度项小。
进一步对比前文不同温度及温差下油纸及XLPE绝缘中的电场分布曲线可以发现，直流电缆XLPE绝缘层中的电场分布更接近于交流电缆中的容性分布特征，且在带负载后绝缘中的电场分布更加均匀，有利于电缆绝缘与附件绝缘的匹配设计。此外，对比图7和图8还可以发现，当电导率温度系数发生相同比例的变化时，油纸绝缘和XLPE绝缘的电场变化幅度接近；而当电场系数发生相同比例变化时，XLPE绝缘中的电场变化幅度要明显小于油纸绝缘。也就是说，XLPE绝缘电导率受温度的影响要显著大于场强的影响。为了理解上述特点，针对两种绝缘的电导率特性进行对比分析。
3.3 两种绝缘的电导率特性对比
图9为油纸绝缘和XLPE绝缘的电导率随温度和场强的变化。从图9可以看出，首先，油纸绝缘的电导率整体比XLPE绝缘高；其次，油纸绝缘的电导率随温度和场强的变化更为剧烈，在同等温度和场强变化范围内，油纸绝缘电导率的变化接近4个数量级。相较而言，XLPE绝缘电导率在整个温度和场强变化范围内呈现较为平缓的变化，变化幅度在2个数量级内，显著小于油纸绝缘。这表明目前广泛应用的XLPE绝缘直流料的本征电导率较小，且受温度和场强的影响也较小，在高压直流电缆实际运行过程中，能够为绝缘提供更稳定和优异的电场分布特性，同时可以控制绝缘中的泄漏电流，减小绝缘损耗及发热。
最后，需要补充说明的是，本文针对油纸绝缘和XLPE绝缘的分析都是基于式（7）和式（8）的材料电导率表达式开展的，实际中当电缆采用不同绝缘时，可基于本文分析方法，开展专门研究。此外，本文中的电缆绝缘电场分布特性未考虑空间电荷的影响，而油纸绝缘在直流电压下受空间电荷的影响程度通常要优于XLPE绝缘。
4 结论
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（1）电缆绝缘中径向电场分布接近一条直线；不同条件下电场分布曲线相交于绝缘径向中点，其场强约等于绝缘层平均场强；随着绝缘温差增大，电场分布曲线绕中点呈逆时针旋转，绝缘内侧场强减小，外侧场强增大。
（2）油纸绝缘中电场反转始于10℃温差，而XLPE绝缘在20℃温差才开始发生反转；油纸绝缘中电场分布受绝缘温差的影响，在温差固定后几乎不随绝缘温度而变化；XLPE绝缘中的电场分布同时受绝缘温度和温差的影响。
（3）与油纸绝缘相比，XLPE绝缘直流料的本征电导率低且受温度和场强的影响小，在相同温度及电场变化范围内其电导率变化幅度小，可为直流电缆提供更稳定优异的绝缘电场分布特性，同时减小绝缘中的泄漏电流及损耗。
基金
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  • 中国能源建设集团规划设计有限公司科技项目(GSKJ2-D03-2021)
文献
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2024年第57卷第7期
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doi: 10.16790/j.cnki.1009-9239.im.2024.07.011
  • 接收时间：2023-07-31
  • 首发时间：2025-12-24
  • 出版时间：2024-07-20
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  • 收稿日期：2023-07-31
  • 修回日期：2023-10-29
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中国能源建设集团规划设计有限公司科技项目(GSKJ2-D03-2021)
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    1中国电力工程顾问集团中南电力设计院有限公司,湖北 武汉 430071
    2西安交通大学 电气工程学院,陕西 西安 710049
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2种不同金属材料的力学参数
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Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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