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Article(id=1222482834179216021, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1222482826851771163, articleNumber=null, orderNo=null, doi=10.16790/j.cnki.1009-9239.im.2021.02.016, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1587744000000, receivedDateStr=2020-04-25, revisedDate=1593878400000, revisedDateStr=2020-07-05, acceptedDate=null, acceptedDateStr=null, onlineDate=1769392220301, onlineDateStr=2026-01-26, pubDate=1613750400000, pubDateStr=2021-02-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1769392220301, onlineIssueDateStr=2026-01-26, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1769392220301, creator=13041195026, updateTime=1769392220301, updator=13041195026, issue=Issue{id=1222482826851771163, tenantId=1146029695717560320, journalId=1149653034449285133, year='2021', volume='54', issue='2', pageStart='1', pageEnd='106', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1769392218554, creator=13041195026, updateTime=1770971669597, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1229107524746670183, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1222482826851771163, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1229107524750864488, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1222482826851771163, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=92, endPage=100, ext={EN=ArticleExt(id=1222482834594452145, articleId=1222482834179216021, tenantId=1146029695717560320, journalId=1149653034449285133, language=EN, title=Power Frequency Breakdown Characteristics and Lifetime Model of 500 kV XLPE Submarine Cable Insulation Material under Electro-thermal Stress, columnId=1190369066675179686, journalTitle=Insulating Materials, columnName=Material Research, runingTitle=null, highlight=null, articleAbstract=

In order to deeply grasp the breakdown characteristics of AC 500 kV cross-linked polyethylene (XLPE) submarine cable insulation materials under electrical-thermal stress and establish an electrical-thermal combined lifetime model, we conducted electrical-thermal breakdown experiments on the XLPE material at 25, 40, 55, 70℃ under step stress firstly. The AC electric strength and voltage duration time were analyzed by Weibull distribution to obtain the equivalent AC electric strength and voltage duration time at different temperatures. Then the FALLOU, SIMONI, CRINE models were established by multiple linear regression method, and their error was analyzed. Finally, an E-T lifetime model for the AC 500 kV XLPE material was constructed. The results show that at the same temperature, the equivalent electric strength decreases with the increase of voltage duration time of each voltage stage. At the same voltage duration time of each stage, with the increase of temperature, the equivalent AC electric strength and voltage duration time both firstly increase and then decrease. The analysis on the electrical-thermal lifetime models indicate that the fitting error of FALLOU, SIMONI, CRINE models is large, and their fitting goodness do not meet the accuracy requirements. An improved electric-thermal combined ageing lifetime model is obtained by using stepwise regression to calculate the significance and correlation between electric-thermal variables and lifetime, and the error analysis show that it has better fitting accuracy.

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为深入掌握交流500 kV交联聚乙烯（XLPE）海缆绝缘材料在电-热应力下的工频击穿特性并建立电-热联合寿命模型，本研究首先对500 kV海缆主绝缘进行25、40、55、70℃步进应力下的电-热联合绝缘击穿试验，对电气强度和耐压时间进行Weibull统计分析，获得不同温度下等效电气强度和等效耐压时间的变化规律。然后，通过多元线性回归建立FALLOU、SIMONI和CRINE模型并进行误差分析。最后，研究构建适用于该交流500 kV XLPE材料的E-T耦合参数模型。结果表明：在相同温度下，随着每级电压持续时间的增加，等效电气强度逐渐降低；在每级电压持续时间相同时，随着温度的升高，等效电气强度和电压持续时间均呈现先上升后下降的趋势。对电-热联合老化模型的分析表明，3种模型拟合误差较大，拟合优度不满足精度要求。本研究通过利用逐步回归计算电-热变量与寿命的显著性与相关性，获得改进的电-热联合老化寿命模型，误差分析显示改进模型具有较好的拟合精度。

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刘智谦（1995-），男（汉族），江苏泰州人，硕士生，主要从事电气设备绝缘在线监测与故障诊断的研究；

郝建（1984-），男（汉族），河北衡水人，副教授，主要从事新型绝缘材料研发及其性能表征的研究。

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2南京南瑞继保电气有限公司，江苏 南京 211102, bio={"content":"

刘智谦（1995-），男（汉族），江苏泰州人，硕士生，主要从事电气设备绝缘在线监测与故障诊断的研究；

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刘智谦（1995-），男（汉族），江苏泰州人，硕士生，主要从事电气设备绝缘在线监测与故障诊断的研究；

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郝建（1984-），男（汉族），河北衡水人，副教授，主要从事新型绝缘材料研发及其性能表征的研究。

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郝建（1984-），男（汉族），河北衡水人，副教授，主要从事新型绝缘材料研发及其性能表征的研究。

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figureFileBig=null, tableContent=

温度

/℃

Δt/s等效电气强度等效击穿时间
α/(kV/mm)βα/sβ
256059.0719.651 204.9919.36
12057.3919.982 407.8312.13
24055.8030.404 719.3516.37
48053.1014.878 405.059.38
406060.3118.341 212.1113.54
12058.7220.122 543.6214.32
24057.9929.184 875.4212.37
48054.9612.788 657.948.46
556063.2017.961 293.6418.24
12058.4437.012 402.8419.10
24056.7345.864 600.8116.88
48055.1224.149 114.0912.50
706051.7520.761 128.725.27
12049.159.272 220.136.02
24045.4010.053 642.376.16
48040.6015.966 162.928.75
), ArticleFig(id=1222974151434953219, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1222482834179216021, language=CN, label=表1, caption=

不同温度和电场强度下的寿命统计

, figureFileSmall=null, figureFileBig=null, tableContent=

温度

/℃

Δt/s等效电气强度等效击穿时间
α/(kV/mm)βα/sβ
256059.0719.651 204.9919.36
12057.3919.982 407.8312.13
24055.8030.404 719.3516.37
48053.1014.878 405.059.38
406060.3118.341 212.1113.54
12058.7220.122 543.6214.32
24057.9929.184 875.4212.37
48054.9612.788 657.948.46
556063.2017.961 293.6418.24
12058.4437.012 402.8419.10
24056.7345.864 600.8116.88
48055.1224.149 114.0912.50
706051.7520.761 128.725.27
12049.159.272 220.136.02
24045.4010.053 642.376.16
48040.6015.966 162.928.75
), ArticleFig(id=1222974151510450693, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1222482834179216021, language=EN, label=Tab.2, caption=Estimated parameters of FALLOU, SIMONI, and CRINE models, figureFileSmall=null, figureFileBig=null, tableContent=
模型参数估计值95% 置信区间
FALLOUA1-120.73-215.16-26.30
A22.250.533.97
B144 507.1212 805.5976 208.66
B2-777.08-1 351.77-202.40
SIMONIA1-498.75-875.71-121.79
A2175 311.8848 622.13302 001.64
B1125.1531.04219.26
B2-43 297.18-74 893.32-11 701.04
CRINEA14 116.071 962.036 270.11
A2-608.69-927.42-289.96
B1-187 445.7-287 317.1-87 574.31
B2-59.96-84.75-35.16
), ArticleFig(id=1222974151577559559, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1222482834179216021, language=CN, label=表2, caption=

FALLOU, SIMONI, CRINE模型的参数估计

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模型参数估计值95% 置信区间
FALLOUA1-120.73-215.16-26.30
A22.250.533.97
B144 507.1212 805.5976 208.66
B2-777.08-1 351.77-202.40
SIMONIA1-498.75-875.71-121.79
A2175 311.8848 622.13302 001.64
B1125.1531.04219.26
B2-43 297.18-74 893.32-11 701.04
CRINEA14 116.071 962.036 270.11
A2-608.69-927.42-289.96
B1-187 445.7-287 317.1-87 574.31
B2-59.96-84.75-35.16
), ArticleFig(id=1222974151648862729, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1222482834179216021, language=EN, label=Tab.3, caption=The fitting goodness of FALLOU, SIMONI, CRINE models, figureFileSmall=null, figureFileBig=null, tableContent=
模型判定系数R2F统计量观测值检验P值
FAIIOU0.568 15.262 10.015 1
SIMONI0.563 95.171 30.015 9
CRINE0.699 99.326 90.001 8
), ArticleFig(id=1222974151707582987, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1222482834179216021, language=CN, label=表3, caption=

FALLOU、SIMONI、 CRINE模型拟合优度

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模型判定系数R2F统计量观测值检验P值
FAIIOU0.568 15.262 10.015 1
SIMONI0.563 95.171 30.015 9
CRINE0.699 99.326 90.001 8
), ArticleFig(id=1222974151770497549, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1222482834179216021, language=EN, label=Tab.4, caption=Results of stepwise regression, figureFileSmall=null, figureFileBig=null, tableContent=
参数组合判定系数R2

F统计量

观测值

检验P值
E, T, 1/T, E/T, lnT, lnE/T0.9319.811.1×10-4
E, T, 1/T, E/T, lnT0.9223.862.9×10-5
T, 1/T, E/T, lnT, lnE/T0.8712.894.3×10-4
E, T, 1/T, E/T, lnE/T0.8713.263.8×10-4
), ArticleFig(id=1222974151850189327, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1222482834179216021, language=CN, label=表4, caption=

逐步回归参数组合与拟合优度分析

, figureFileSmall=null, figureFileBig=null, tableContent=
参数组合判定系数R2

F统计量

观测值

检验P值
E, T, 1/T, E/T, lnT, lnE/T0.9319.811.1×10-4
E, T, 1/T, E/T, lnT0.9223.862.9×10-5
T, 1/T, E/T, lnT, lnE/T0.8712.894.3×10-4
E, T, 1/T, E/T, lnE/T0.8713.263.8×10-4
), ArticleFig(id=1222974151934075409, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1222482834179216021, language=EN, label=Tab.5, caption=Estimated parameters of E-T coupling model, figureFileSmall=null, figureFileBig=null, tableContent=
参数估计值95%置信区间
A1-27.83-50.60-5.06
A21.240.322.16
A32 679 720.84381 597.304 977 844.38
A4-479.69-782.64-176.75
A517 197.642 701.6731 693.61
), ArticleFig(id=1222974152001184275, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1222482834179216021, language=CN, label=表5, caption=

E-T耦合模型参数估计

, figureFileSmall=null, figureFileBig=null, tableContent=
参数估计值95%置信区间
A1-27.83-50.60-5.06
A21.240.322.16
A32 679 720.84381 597.304 977 844.38
A4-479.69-782.64-176.75
A517 197.642 701.6731 693.61
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交流500 kV XLPE海缆绝缘材料在电-热联合应力下的工频击穿特性与寿命模型
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刘智谦 1, 2 , 戴锡泽 1 , 郝建 1 , 高震 3 , 李捍平 3 , 郑新龙 3
绝缘材料 | 材料研究 2021,54(2): 92-100
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绝缘材料 | 材料研究 2021, 54(2): 92-100
交流500 kV XLPE海缆绝缘材料在电-热联合应力下的工频击穿特性与寿命模型
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刘智谦1, 2, 戴锡泽1, 郝建1, 高震3, 李捍平3, 郑新龙3
作者信息
  • 1重庆大学 输配电装备及系统安全与新技术国家重点实验室，重庆 400044
  • 2南京南瑞继保电气有限公司，江苏 南京 211102
  • 3国网浙江省电力有限公司舟山供电公司，浙江 舟山 316021

    • 刘智谦（1995-），男（汉族），江苏泰州人，硕士生，主要从事电气设备绝缘在线监测与故障诊断的研究；

    郝建（1984-），男（汉族），河北衡水人，副教授，主要从事新型绝缘材料研发及其性能表征的研究。

Power Frequency Breakdown Characteristics and Lifetime Model of 500 kV XLPE Submarine Cable Insulation Material under Electro-thermal Stress
Zhiqian LIU1, 2, Xize DAI1, Jian HAO1, Zhen GAO3, Hanping LI3, Xinlong ZHENG3
Affiliations
  • 1State Key Laboratory of Power Transmission Equipment & System Security and New Technology Chongqing University, Chongqing 400044, China
  • 2NR Electric Co., Ltd., Nanjing 211102, China
  • 3State Grid Zhoushan Power Supply Company, State Grid Zhejiang Electric Power Co., Ltd., Zhoushan 316021, China
出版时间: 2021-02-20 doi: 10.16790/j.cnki.1009-9239.im.2021.02.016
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摘要
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为深入掌握交流500 kV交联聚乙烯（XLPE）海缆绝缘材料在电-热应力下的工频击穿特性并建立电-热联合寿命模型，本研究首先对500 kV海缆主绝缘进行25、40、55、70℃步进应力下的电-热联合绝缘击穿试验，对电气强度和耐压时间进行Weibull统计分析，获得不同温度下等效电气强度和等效耐压时间的变化规律。然后，通过多元线性回归建立FALLOU、SIMONI和CRINE模型并进行误差分析。最后，研究构建适用于该交流500 kV XLPE材料的E-T耦合参数模型。结果表明：在相同温度下，随着每级电压持续时间的增加，等效电气强度逐渐降低；在每级电压持续时间相同时，随着温度的升高，等效电气强度和电压持续时间均呈现先上升后下降的趋势。对电-热联合老化模型的分析表明，3种模型拟合误差较大，拟合优度不满足精度要求。本研究通过利用逐步回归计算电-热变量与寿命的显著性与相关性，获得改进的电-热联合老化寿命模型，误差分析显示改进模型具有较好的拟合精度。

海底电缆  /  交联聚乙烯  /  步进应力  /  绝缘性能  /  电-热联合绝缘寿命模型

In order to deeply grasp the breakdown characteristics of AC 500 kV cross-linked polyethylene (XLPE) submarine cable insulation materials under electrical-thermal stress and establish an electrical-thermal combined lifetime model, we conducted electrical-thermal breakdown experiments on the XLPE material at 25, 40, 55, 70℃ under step stress firstly. The AC electric strength and voltage duration time were analyzed by Weibull distribution to obtain the equivalent AC electric strength and voltage duration time at different temperatures. Then the FALLOU, SIMONI, CRINE models were established by multiple linear regression method, and their error was analyzed. Finally, an E-T lifetime model for the AC 500 kV XLPE material was constructed. The results show that at the same temperature, the equivalent electric strength decreases with the increase of voltage duration time of each voltage stage. At the same voltage duration time of each stage, with the increase of temperature, the equivalent AC electric strength and voltage duration time both firstly increase and then decrease. The analysis on the electrical-thermal lifetime models indicate that the fitting error of FALLOU, SIMONI, CRINE models is large, and their fitting goodness do not meet the accuracy requirements. An improved electric-thermal combined ageing lifetime model is obtained by using stepwise regression to calculate the significance and correlation between electric-thermal variables and lifetime, and the error analysis show that it has better fitting accuracy.

submarine cable  /  cross-linked polyethylene (XLPE)  /  step stress  /  insulation properties  /  lifetime model
刘智谦, 戴锡泽, 郝建, 高震, 李捍平, 郑新龙. 交流500 kV XLPE海缆绝缘材料在电-热联合应力下的工频击穿特性与寿命模型. 绝缘材料, 2021 , 54 (2) : 92 -100 . DOI: 10.16790/j.cnki.1009-9239.im.2021.02.016
Zhiqian LIU, Xize DAI, Jian HAO, Zhen GAO, Hanping LI, Xinlong ZHENG. Power Frequency Breakdown Characteristics and Lifetime Model of 500 kV XLPE Submarine Cable Insulation Material under Electro-thermal Stress[J]. Insulating Materials, 2021 , 54 (2) : 92 -100 . DOI: 10.16790/j.cnki.1009-9239.im.2021.02.016
正文
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0 引言
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我国将建设“海洋强国”作为国家发展战略，海底电缆作为海洋输电与基建的必要组件，得到了长足发展[1]。自1988年起我国开始海缆工程建设，发展至今，电压等级不断提升，传输距离不断增长。2019年1月，我国自主研发的世界首条500 kV交联聚乙烯（XLPE）海缆在舟山500 kV联网输变电工程敷设完成。在海底电缆服役过程中，绝缘本体在热、电、机械等应力作用下会出现老化的现象[2-3]。随着老化的发展，XLPE绝缘材料的绝缘性能下降，最终以电击穿的形式体现出来[4]。因此，需要对XLPE材料在电热条件下的击穿特性与寿命模型进行研究，深入掌握该种材料的绝缘性能，保障海缆的运行安全。
通过击穿测试结合Weibull统计方法可以表征材料的性能，也可以用于材料寿命模型的构建[5-6]。击穿试验分为短时击穿和长期耐压试验两种。短时击穿可以直观地反映材料的绝缘性能。S GRZYBOWSKI等[7]通过对XLPE电缆在交直流和脉冲电场下的击穿特性分析发现脉动电场对缺陷敏感；金天雄等[8]通过不同老化程度XLPE样品的短时击穿特性分析老化对样品绝缘性能的影响。长期耐压试验主要用于分析材料的寿命特性。试验分为恒定应力和步进应力两种加压方式，其中，步进应力方法效率高，通过极大似然估计法等可以实现恒定应力与步进应力试验结果的转换，从试验的结果与效率来看，步进应力下的电老化试验更能满足测试要求[9]。
绝缘材料的寿命模型分为单因素和多因素，单因素老化模型中通过击穿电场和耐压时间建立电老化反幂模型[10]；多因素老化模型综合考虑电、热、机械应力，将两种及以上应力因素形成寿命模型参量。当多种内外部因素共同作用时，绝缘材料的寿命与单一因素作用时具有明显差异，即多种因素产生的老化并非单一因素老化的代数和[11]。电和热是最常见的两种老化因子，目前研究主要集中于电-热联合应力寿命模型[12]。20世纪90年代，P PALONIEMI等[13]提出了基于指数关系的FALLOU模型，G C MONTANARI等[14]提出了概率模型，J P CRINE等[15]提出了基于物理参量的CRINE模型。另外，在结合反幂模型和阈值电场后L SIMONI[16]和T S RAMU[17]分别提出了SIMONI模型和RUMA模型。国内学者在此基础上将寿命模型推广修正，使之适用于多种材料。杨丽君等[18-20]对变压器油纸绝缘进行电-热联合加速老化试验，建立FALLOU、SIMONI和CRINE模型并进行拟合优度分析，发现FALLOU模型适合油纸绝缘材料的寿命分析。朱健[21]研究了聚酰亚胺材料的多因素寿命模型，对3层复合薄膜结构进行电-热联合老化寿命预测，发现SIMONI模型的拟合优度最高。梁韵[22]考虑电、热、水分等耦合条件，将水分参量耦合到模型，建立涉及水分的多因素XLPE材料寿命模型。
以上研究成果均在电-热应力作用下构建绝缘材料寿命模型，以FALLOU、SIMONI和CRINE模型为构造寿命模型的基础，结合材料本身绝缘特性对模型进行优化。对于交流500 kV XLPE材料，目前尚无在步进应力条件下对其绝缘特性和寿命模型的研究。电缆制造业缺乏500 kV XLPE海底电缆绝缘材料的行业标准与规范。本研究首先对交流500 kV XLPE海缆绝缘材料进行步进应力下的电-热联合老化试验，获得不同测试温度和电压步长下XLPE绝缘样品在电-热应力下的电气强度和电压持续时间，并对其进行双参量Weibull统计分析，分析XLPE绝缘材料在不同温度和电压步长下的击穿特性；然后分别构建500 kV XLPE海缆绝缘材料的FALLOU、SIMONI和CRINE模型，拟合模型参数，评估拟合优度；最后提出适用于500 kV XLPE海缆绝缘材料寿命评估的改进模型。
1 试验
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1.1 试验样品及处理
本研究选用某电缆厂生产的交流500 kV XLPE海底电缆绝缘层作为原材料制备试样。将该海底电缆绝缘层利用电缆切片机切成厚度为（0.5±0.05） mm的片状试样，然后进行48 h脱气干燥处理，并用酒精清除表面的灰尘和其他污物。
1.2 步进应力下电-热联合击穿试验
步进应力下电-热联合击穿试验通过电压击穿试验仪（HCDJC-100 kV）进行，测试系统如图1所示。采用油浴控制试验环境温度。考虑到电缆满载运行温度不超过90℃、材料玻璃化转变温度等因素，确定试验温度为25、40、55、70℃。试验采用板-板电极，电极直径为25 mm。步进应力试验需设置起始电压U0，升压时间步长Δt和升压电压步长ΔU。从效率考虑，起始电压选取短时击穿电压的40%，在预试验中获得试验样品的短时电气强度为70 kV/mm，因此起始电压U0设为10 kV。升压速度为500 V/s，升压电压步长ΔU为1 kV。计时从试验电压上升开始，直至样品击穿，记录样品击穿所用时间和击穿电压。逐步升压法选择60、120、240、480 s作为Δt进行试验。由于样品的击穿失效时间具有分散性，本研究选择9个样品进行重复试验并进行Weibull统计分析，得到相同试验温度、Δt条件下的XLPE绝缘样品的等效电气强度E和等效电压持续时间t。
1.3 步进应力下电-热联合试验Weibull分析方法
本研究选择两参数Weibull分布模型用于XLPE绝缘介质击穿电压和耐压时间的统计。两参数Weibull分布模型的失效分布函数如式（1）所示。
Ft, α, β=1-exp-tαβ
式（1）中：t为试验变量，通常为试验获得的电气强度或击穿时间，随着t的增大，失效概率增加；α>0，α为尺度参数，即概率为63.2%时的t值，通常取该参数为样品的击穿电压或寿命；β>0，β为形状参数，代表分散性。通过获得的试验数据样本可对失效分布函数中的α、β进行估计，进而确定Weibull分布模型。本研究数据样本为完整数据，经验分布函数 Fn(ti)的取值由式（2）计算获得。
Fnti=i-0.3n+0.4×100%
式（2）中：i代表测试样本次序；n为样本数量。
2 试验结果及分析
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2.1 步进应力下电-热联合老化试验Weibull分析
将25、40、55、70℃下不同Δt的试验结果进行Weibull统计分析，结果如图2所示，图2中横坐标为电气强度或电压持续时间；纵坐标为失效率，即击穿的可能性；坐标点为试验测试结果，即通过经验分布函数计算获得的电气强度或电压持续时间对应的失效概率。曲线为拟合线，该线根据实测点计算获得，其斜率与实测结果的分散程度有关。从图2可知，在25℃和40℃，当Δt为120 s和240 s时，电气强度分布曲线相交，即在较低温度条件下，120 s和240 s两个每级电压持续时间未能在击穿电压上出现明显变化，说明材料在较低温度下性能保持稳定；70℃下4个Δt对应的4条电气强度分布曲线出现明显区分，说明较高温度下材料性能下降明显。表1是25、40、55、70℃下不同Δt试验结果Weilbull参数统计表。从表1可知，随着Δt增大，等效电气强度逐渐降低，在70℃下等效电气强度下降更明显；在相同Δt下，随着温度的升高，等效电气强度和等效击穿时间均呈现先略微上升后下降的趋势。
图3为试验温度、Δt与电压持续时间的关系图。从图3可知，电压持续时间随着温度升高呈现低温段（25～55℃）略微增加，高温段（55～70℃）减少的变化趋势。因此，在同一电压持续时间下，55℃的等效电气强度和电压持续时间最大；以55℃为阈值温度，电气强度呈现出随温度升高先略微上升后下降的趋势。
2.2 多因素老化寿命评估模型及误差分析
将试验温度转换为绝对温度，将步进应力下电-热联合老化试验经Weibull统计分析后的5个温度对应4个Δt的等效电气强度和电压持续时间视作材料的电气强度和耐压寿命，对寿命取对数，获得电气强度-温度-寿命对数关系图，结果如图4所示。从图4可以看出，随着温度和电气强度的变化，寿命呈现出两点明显特征。第1个特征是在低温区间（298～328 K），随着温度升高，寿命维持恒定甚至有所增加。在低温（298～313 K）、低电气强度（20～30 kV/mm）条件下，寿命维持稳定，图像有明显的平台区。第2个特征是在高温区间（328～343 K），随着温度和电气强度的升高，寿命迅速减少。在高温（343 K）、高电气强度（40～60 kV/mm）条件下，电-热应力联合作用使得寿命下降速度大幅增加，即使在对数坐标下，寿命依旧呈现显著非线性的减少趋势。
利用表1获得的等效电气强度E和等效击穿时间L（视作寿命），通过多元线性回归的方式获得该交流500 kV XLPE绝缘材料的多因素老化寿命模型。FALLOU模型由单应力指数模型推导而来，表达式如式（3）所示。
L=expA1+A2E+B1+B2ET
式（3）中：A1、A2、B1、B2均为常数；L为寿命；E为加速老化试验电场；T为试验的绝对温度。对式（3）两边取对数，得式（4）。
lnL=A1+A2E+B1+B2ET
SIMONI模型将绝缘老化状态与某种与绝缘失效有关的属性p进行关联性分析，将p随老化时间而变化的函数关系F(p)作为老化量的表征，表达式如式（5）所示。
L=L0exp-BΔ1TEE0-N
式（5）中：L0为温度为T0及电场为E0时的绝缘寿命；Δ（1/T）=1/T0-1/T；N=n-bΔ（1/T），为电压寿命指数n在热应力作用下的修正；B和b为常数，由试验结果确定。对式（5）两边取对数，得式（6）。
lnL=A1+A2/T+B1lnE+B2lnE/T
CRINE模型考虑老化过程中的理化变化，用化学反应速率表征老化过程，使模型具有物理意义，表达式如式（7）所示。
L=hkTexpΔWkTcscheλEkT
式（7）中：ΔW为自由能；λ为电子散射距离；e为参与老化过程的粒子电荷数；h为普朗克常量；k为玻尔兹曼常量；T为试验温度；E为电气强度。
CRINE模型为物理模型，区别于传统唯象模型，因此难以与单一应力作用下的寿命模型产生一定关联性。另外，在较高电气强度下，满足eλE<<kT，则CRINE模型如式（8）所示。
L=hkTexpΔW-eλEkT
代入相关参数，对式（8）两边取对数，得式（9）。
lnL=A1+A2ln1/T+B1/T+B2E/T
对于FALLOU模型，将E、1/T和E/T视作自变量，lnL视作因变量，利用多元线性回归方法计算出A1、A2、B1、B2参数（A1、A2、B1、B2为系数，不具备物理意义），得到FALLOU模型的表达如式（10）所示，寿命图如图5所示；同理，对于SIMONI模型，将1/T、1/E和lnE/T视作自变量，lnL视作因变量，获得SIMONI模型如式（11）所示，寿命图如图6所示；对于CRINE模型，将ln(1/T)、1/T和E/T视作自变量，lnL视作因变量，获得CRINE模型如式（12）所示，寿命图如图7所示。表2为3种模型的拟合参数和95%置信区间对应的参数范围。
lnL=-120.73+2.25E+44507.12T-777ET
lnL=-498.75+175311T+125.15lnE-43297lnET
lnL=4116+608.69ln1T-187445.71T-59.96ET
表3为FALLOU、SIMONI、CRINE模型的拟合优度参数，包括判定系数R2、F统计量观测值和检验P值。一般拟合优度要求判定系数大于0.9，F统计量观测值大于F分布对应参数，检验P值小于0.05。比较3种模型拟合优度参数可知，3种模型均不满足拟合优度要求。对比图4～7发现，实际情况下在较宽温度范围内，XLPE样品寿命随温度升高而先略微增加后迅速减少，而FALLOU模型和SIMONI模型作为唯象模型，均仅考虑寿命随温度升高而减少[9]，并未考虑低温情况下寿命随温度升高有所增加的现象；CRINE模型作为物理模型，E-T参量耦合的关系由物理关系推导分析，模型刻画出寿命从低温低场强向高温高场强过程中先略有增加再迅速减少的变化，但仍旧未能满足拟合优度要求。
2.3 多因素老化寿命评估新模型及误差分析
针对3种经典寿命模型在低温部分拟合效果较差的问题，本部分充分考虑温度与电场之间的耦合关系，增加电场与温度的耦合参量，并利用逐步回归修正模型参量，获得拟合优度较高的改进唯象模型。逐步回归后的模型将保留具有显著性且相关性较低的变量，剔除不显著变量以确保最后得到的自变量集是最优的。在拟合过程中，应明确模型变量最少，拟合优度相对最高的原则。
从图4所示试验结果分析，新寿命模型应在原有模型的基础上，表达出寿命在低温段略微增加，高温段加速减少的变化规律。式（13）为FALLOU模型的推导过程，该模型以反幂模型为基础，系数a和b由热应力作用决定。反幂模型是表示电应力作用的方程，将系数a和b代入反幂模型可得FALLOU模型，FALLOU模型是热应力、电应力和电热应力耦合3部分影响的叠加。因此，FALLOU模型同时考虑3部分应力的影响，耦合关系清晰明确，本文以FALLOU模型为基础，构建新寿命模型。从实验结果可知，寿命的变化与温度影响有显著关系，即在新寿命模型构建过程中，应着重对热应力部分进行改进。
lnL=a+bEa=a1+a2/Tb=b1+b2/T→lnL=a1+a2/T+b1+b2/TE
根据对数关系表达可知寿命模型基本表达式如式（14）所示，为包含6个变量的对数形式的隐函数。
FE, T, 1/T, E/T, lnT, lnET=lnL
式（14）中：E、1/T、E/T为FALLOU模型变量；T、lnT、lnE/T为温度参量和电热应力的耦合参量，变量显著性通过逐步回归检验，获得与寿命具有显著性关系的变量。表4为不同参量组合拟合优度表，分析可知E、T、1/T、E/T、lnT与寿命关系显著，关系式如式（15）所示。
lnL=C+A1T+A2E+A3T+A4ET+A5lnT
式（16）为新模型的推导过程，热应力作用是导致材料寿命变化的主要原因，热应力部分导致变量1/T、lnT增加，其中函数（a2/T+a3T）调节低温部分上升趋势变化，函数lnT调节高温部分非线性迅速降低的变化。
lnL=a+bEa=a1+a2/T+a3T+a4lnTb=b1+b2/T⇒lnL=a1+a2/T+a3T+a4lnT+b1+b2/TE
表5为E-T耦合模型参数和95%置信区间对应的参数范围，拟合函数如式（17）所示。E-T耦合模型寿命图如图8所示。
lnL=-98646.4-27.83T+1.24E+2679720T-479ET+17197lnT
以实际XLPE绝缘样品的Weibull特征寿命为基准值，对比分析3种典型电-热联合寿命模型的预测精度，计算式如式（18）所示。
Error=I拟合值-I实际值/I拟合值×100%
式（18）中：I拟合值是拟合公式在对应温度和电气强度下的寿命；I实际值是试验获得的寿命值。图9为4种模型与实际测试值的误差分析。
从图9可知，FALLOU、SIMONI、CRINE模型的预测误差在40%以上，难以满足寿命预测精度要求；E-T耦合模型的拟合误差相对于上述3种模型的拟合精度有了较大改善。
3 结论
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在25、40、55、70℃下进行Δt为60、120、240、480 s步进应力电-热联合工频击穿试验，并分析多因素老化模型，主要结论如下:
（1）随着温度升高，XLPE样品的电气强度与电压持续时间在低温阶段（25～55℃）呈现缓慢上升变化，在高温阶段（55～70℃）迅速下降；电气强度和电压持续时间在55℃达到最大值。
（2）利用FALLOU、SIMONI和CRINE模型构建了交流500 kV XLPE海缆绝缘材料寿命模型的模型参数，分析表明拟合优度均无法达到R2≥0.9的拟合精度要求，说明3种电-热联合老化模型不适用评估该种绝缘材料在电-热应力下的寿命。
（3）提出了交流500 kV XLPE海缆绝缘材料在电-热联合应力作用下的E-T耦合模型，模型利用逐步回归的方法实现变量组合的最优化，使模型拟合精度最优，变量相关性最低。误差分析显示新模型的拟合优度R2≥0.93，评估误差优于FALLOU、SIMONI和CRINE模型。
基金
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  • 国家电网公司科技项目(52110417000N)
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doi: 10.16790/j.cnki.1009-9239.im.2021.02.016
  • 接收时间：2020-04-25
  • 首发时间：2026-01-26
  • 出版时间：2021-02-20
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  • 收稿日期：2020-04-25
  • 修回日期：2020-07-05
基金
国家电网公司科技项目(52110417000N)
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    1重庆大学 输配电装备及系统安全与新技术国家重点实验室，重庆 400044
    2南京南瑞继保电气有限公司，江苏 南京 211102
    3国网浙江省电力有限公司舟山供电公司，浙江 舟山 316021
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