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Article(id=1210590157967856457, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210590152548807015, articleNumber=null, orderNo=null, doi=10.16790/j.cnki.1009-9239.im.2024.09.016, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1693584000000, receivedDateStr=2023-09-02, revisedDate=1698681600000, revisedDateStr=2023-10-31, acceptedDate=null, acceptedDateStr=null, onlineDate=1766556785337, onlineDateStr=2025-12-24, pubDate=1726761600000, pubDateStr=2024-09-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1766556785337, onlineIssueDateStr=2025-12-24, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1766556785337, creator=13701087609, updateTime=1766556785337, updator=13701087609, issue=Issue{id=1210590152548807015, tenantId=1146029695717560320, journalId=1149653034449285133, year='2024', volume='57', issue='9', pageStart='1', pageEnd='165', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1766556784044, creator=13701087609, updateTime=1766563998200, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1210620410958312217, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210590152548807015, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1210620410958312218, tenantId=1146029695717560320, journalId=1149653034449285133, issueId=1210590152548807015, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=149, endPage=157, ext={EN=ArticleExt(id=1210590159247119190, articleId=1210590157967856457, tenantId=1146029695717560320, journalId=1149653034449285133, language=EN, title=Research on thermal effect and section mechanical properties of submarine cable based on finite element simulation, columnId=1192878364340924664, journalTitle=Insulating Materials, columnName=Test and Analysis, runingTitle=null, highlight=null, articleAbstract=

Submarine cable is a transmission component of high-voltage power, and the heat generated during the operation of submarine cable will cause the structural temperature rise and expand. Under the constraint of each layer, the submarine cable will produce large thermal stress and deformation, which will cause structural damage. In addition, the increase of temperature will lead to the decrease of elastic modulus of the polymer material inside the submarine cable, resulting in the change of mechanical properties of the submarine cable section. Therefore, it is necessary to study the stress and deformation caused by thermal expansion during the operation of submarine cables, and analyze the influence of temperature on the mechanical properties of submarine cables. In this paper, based on an offshore wind power project, a finite element model of submarine cable-soil was established in finite element software ABAQUS, and the temperature field distribution under steady-state current carrying capacity was obtained. Based on the results of temperature field, the thermal stress and thermal deformation of the submarine cable were calculated by the thermal-mechanical coupling method, and the change of mechanical properties of the submarine cable section under the action of temperature was analyzed. The results show that the highest temperature appears in the copper conductor during the operation of submarine cable, and the outer coating layer has the lowest temperature. With the copper conductor as the center, the temperature drop gradient along the inside radial direction is small, and the temperature drop gradient along the outside radial direction is large. The thermal stress is mainly concentrated in the metal structure, and the maximum deformation occurs in the steel wire armor. When the copper conductor and the optical fiber are located at the top of the cross section, the displacement is the largest, and the displacement is the smallest at the bottom. After considering the influence of temperature, the stress of copper conductor and optical fiber will increase, while the tensile and torsional stiffness of submarine cable will decrease, and the reduction of inverse torsional stiffness is greater than that of clockwise torsional stiffness.

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海缆作为高压电力的传输构件，运行过程中产生的热量会引起结构温度升高及膨胀。受各层约束作用，海缆将产生较大的热应力与变形，进而引起结构损坏。此外，温度升高会导致海缆内部高分子材料弹性模量降低，导致海缆截面力学性能的改变。因此有必要研究海缆运行过程中因热膨胀引起的应力和变形，分析温度对海缆截面力学性能的影响。本文以某海上风电工程为依托，基于有限元软件ABAQUS建立了海缆-土体整体有限元模型，获得了稳态载流量下的温度场分布；基于温度场结果，采用热力耦合方法计算了海缆的热应力和热变形，并分析了温度作用下海缆截面力学性能的改变。结果表明：海缆运行时最高温度出现在铜导体中，外被层温度最低，以铜导体为中心，沿径向往内侧温度变化梯度较小，往外侧温度变化梯度较大；热应力主要集中在金属结构中，最大变形出现在钢丝铠装层中，当铜导体与光纤位于截面顶部时位移最大，位于底部时位移最小；考虑温度影响后，铜导体与光纤的应力会增大，同时海缆的拉伸与扭转刚度会降低，且逆扭转刚度的降低程度大于顺扭转刚度。

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朱海飞（1982-），男（汉族），湖南武冈人，高级工程师，主要研究方向为海上风力发电技术及应用研究；

王向坤（2000-），男（汉族），山西晋城人，硕士生，研究方向为海上风电基础研究。

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朱海飞（1982-），男（汉族），湖南武冈人，高级工程师，主要研究方向为海上风力发电技术及应用研究；

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朱海飞（1982-），男（汉族），湖南武冈人，高级工程师，主要研究方向为海上风力发电技术及应用研究；

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3Zhejiang East China Engineering Consulting Co., Ltd., Hangzhou 311100, China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1218262760786412034, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, authorId=1218262760585085435, language=CN, stringName=韩大伟, firstName=大伟, middleName=null, lastName=韩, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=2, 3, address=2中国电建集团华东勘测设计研究院有限公司,浙江 杭州 311122
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王向坤（2000-），男（汉族），山西晋城人，硕士生，研究方向为海上风电基础研究。

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王向坤（2000-），男（汉族），山西晋城人，硕士生，研究方向为海上风电基础研究。

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Experimental study on tensile and elastic modulus of polypropylene plastic plate at different temperatures[J]. Experimental Technique and Testing Machine, 2005(3):20,35., articleTitle=Experimental study on tensile and elastic modulus of polypropylene plastic plate at different temperatures, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1218262759842693575, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, xref=1, ext=[AuthorCompanyExt(id=1218262759872053705, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, companyId=1218262759842693575, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1Shandong Energy New Energy (Dongying) Co., Ltd., Dongying 250014, China), AuthorCompanyExt(id=1218262759897219534, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, companyId=1218262759842693575, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, 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country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=4State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan 430072, China), AuthorCompanyExt(id=1218262760211792357, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, companyId=1218262760199209445, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=4武汉大学 水资源工程与调度全国重点实验室,湖北 武汉 430072)])], figs=[ArticleFig(id=1218262764183798362, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=EN, label=Fig.1, caption=Schematic diagram of submarine cable laying, figureFileSmall=ZjyINjpIJM+Yittg3RWY9A==, figureFileBig=67973EcKiElF9V7gfQlTJQ==, tableContent=null), ArticleFig(id=1218262764292850271, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=CN, label=图1, 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tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=CN, label=图13, caption=顺扭矩荷载作用下铜导体与光纤应力变化曲线, figureFileSmall=jZmwb7DX4pMKl8tDst0FTw==, figureFileBig=XxXfO+vGI64oMVJPCtSFOw==, tableContent=null), ArticleFig(id=1218262767874785965, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=EN, label=Fig 14, caption=Stress curves of copper conductor and optical fiber under inverse torque load, figureFileSmall=VCVbQXvJAuRTmJ8LDWHllQ==, figureFileBig=He1zXt5eWdCYeOh9cZD38w==, tableContent=null), ArticleFig(id=1218262767967060656, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=CN, label=图14, caption=逆扭矩荷载作用下铜导体与光纤应力变化曲线, figureFileSmall=VCVbQXvJAuRTmJ8LDWHllQ==, figureFileBig=He1zXt5eWdCYeOh9cZD38w==, tableContent=null), ArticleFig(id=1218262768042558127, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=EN, label=Fig.15, caption=Torque-angular strain curves of submarine cable, figureFileSmall=poJlSbsL11ab7B9CYKypmw==, figureFileBig=4L+Pqcpu/L52aPmV+dvwLw==, tableContent=null), ArticleFig(id=1218262768118055602, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=CN, label=图15, caption=扭矩-角应变关系曲线, figureFileSmall=poJlSbsL11ab7B9CYKypmw==, figureFileBig=4L+Pqcpu/L52aPmV+dvwLw==, tableContent=null), ArticleFig(id=1218262768273244850, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=EN, label=Table 1, caption=Structure size and material heat transfer characteristic parameters of each layer of submarine cable, figureFileSmall=null, figureFileBig=null, tableContent=
结构名称厚度/mm外径/mm导热系数/(W/(m·K))比热容/(J/(kg·K))
阻水铜导体—35.6400385
绝缘层11.658.80.29390
铅护套976.835.3129
半导电护套688.80.292 300
单模光纤—17.80.29434
钢管实体4.727.246448
光纤护套2.532.20.292 300
填充层—2120.171 900
钢丝铠装层1023246448
PP外被层5.22420.171 900
), ArticleFig(id=1218262768365519540, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=CN, label=表1, caption=

海缆各层结构尺寸及材料传热特性参数

, figureFileSmall=null, figureFileBig=null, tableContent=
结构名称厚度/mm外径/mm导热系数/(W/(m·K))比热容/(J/(kg·K))
阻水铜导体—35.6400385
绝缘层11.658.80.29390
铅护套976.835.3129
半导电护套688.80.292 300
单模光纤—17.80.29434
钢管实体4.727.246448
光纤护套2.532.20.292 300
填充层—2120.171 900
钢丝铠装层1023246448
PP外被层5.22420.171 900
), ArticleFig(id=1218262768449405622, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=EN, label=Table 2, caption=Mechanical property parameters of submarine cable and soil, figureFileSmall=null, figureFileBig=null, tableContent=
结构名称热膨胀系数/(10-6·K-1)密度/(kg/m3)弹性模量/GPa泊松比
阻水铜导体16.48 7001260.34
绝缘层150930E1(T)0.41
铅护套3011 340160.44
聚乙烯护套2209350.250.30
单模光纤2.42 20373.10.27
钢管实体127 8502000.30
光纤聚乙烯内护套2209350.250.30
填充层1609460.320.46
钢丝铠装层127 8502000.30
外被层160946E2(T)0.41
土体502 0200.040.30
), ArticleFig(id=1218262768529097400, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=CN, label=表2, caption=

海缆与土体力学性能参数

, figureFileSmall=null, figureFileBig=null, tableContent=
结构名称热膨胀系数/(10-6·K-1)密度/(kg/m3)弹性模量/GPa泊松比
阻水铜导体16.48 7001260.34
绝缘层150930E1(T)0.41
铅护套3011 340160.44
聚乙烯护套2209350.250.30
单模光纤2.42 20373.10.27
钢管实体127 8502000.30
光纤聚乙烯内护套2209350.250.30
填充层1609460.320.46
钢丝铠装层127 8502000.30
外被层160946E2(T)0.41
土体502 0200.040.30
), ArticleFig(id=1218262768612983483, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=EN, label=Table 3, caption=Variation of elastic modulus of outer coating with temperature, figureFileSmall=null, figureFileBig=null, tableContent=
温度/℃01020304050607080
弹性模量/GPa1.151.050.920.720.610.490.430.370.29
), ArticleFig(id=1218262768692675262, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=CN, label=表3, caption=

外被层弹性模量随温度的变化

, figureFileSmall=null, figureFileBig=null, tableContent=
温度/℃01020304050607080
弹性模量/GPa1.151.050.920.720.610.490.430.370.29
), ArticleFig(id=1218262768768172737, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=EN, label=Table 4, caption=Bearing ratio of main structural layers of the submarine cable under tensile loading, figureFileSmall=null, figureFileBig=null, tableContent=
拉力/kN不考虑温度影响考虑温度影响
铜导体铠装钢丝绝缘外被层铜导体铠装钢丝绝缘外被层
109.8250.240.1981.19310.1251.010.0270.595
2012.5756.540.1821.14113.0157.520.0260.584
3015.6461.320.1701.09616.5262.210.0250.578
4018.1266.510.1671.07219.0167.260.0240.568
5019.8871.210.1641.05020.3272.390.0200.551
), ArticleFig(id=1218262768831087300, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=CN, label=表4, caption=

拉伸荷载作用下海缆主要结构层承载比

, figureFileSmall=null, figureFileBig=null, tableContent=
拉力/kN不考虑温度影响考虑温度影响
铜导体铠装钢丝绝缘外被层铜导体铠装钢丝绝缘外被层
109.8250.240.1981.19310.1251.010.0270.595
2012.5756.540.1821.14113.0157.520.0260.584
3015.6461.320.1701.09616.5262.210.0250.578
4018.1266.510.1671.07219.0167.260.0240.568
5019.8871.210.1641.05020.3272.390.0200.551
), ArticleFig(id=1218262768914973383, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=EN, label=Table 5, caption=Bearing ratio of the main structural layers of submarine cable under clockwise torque, figureFileSmall=null, figureFileBig=null, tableContent=
扭矩/(kN·m)不考虑温度影响考虑温度影响
铜导体钢丝铠装层绝缘层外被层铜导体钢丝铠装层绝缘层外被层
14.70353.110.13810.125.78555.000.0267.181
29.34557.050.1186.07610.0258.020.0235.264
312.0366.830.1065.19713.2167.340.0223.682
414.0373.920.1023.59414.4574.210.0212.887
515.1176.210.0973.01415.8177.050.0202.148
), ArticleFig(id=1218262769015636681, tenantId=1146029695717560320, journalId=1149653034449285133, articleId=1210590157967856457, language=CN, label=表5, caption=

顺扭矩作用下海缆主要结构层承载比

, figureFileSmall=null, figureFileBig=null, tableContent=
扭矩/(kN·m)不考虑温度影响考虑温度影响
铜导体钢丝铠装层绝缘层外被层铜导体钢丝铠装层绝缘层外被层
14.70353.110.13810.125.78555.000.0267.181
29.34557.050.1186.07610.0258.020.0235.264
312.0366.830.1065.19713.2167.340.0223.682
414.0373.920.1023.59414.4574.210.0212.887
515.1176.210.0973.01415.8177.050.0202.148
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扭矩/(kN·m)不考虑温度影响考虑温度影响
铜导体钢丝铠装层绝缘层外被层铜导体钢丝铠装层绝缘层外被层
15.14449.440.10311.4526.46451.540.0198.101
26.16550.950.1018.7688.12452.550.0186.524
37.96552.970.0997.0128.91254.140.0185.017
48.91454.540.0986.1149.83455.580.0184.008
510.01257.820.0975.01210.7658.980.0183.521
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逆扭矩作用下海缆主要结构层承载比

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扭矩/(kN·m)不考虑温度影响考虑温度影响
铜导体钢丝铠装层绝缘层外被层铜导体钢丝铠装层绝缘层外被层
15.14449.440.10311.4526.46451.540.0198.101
26.16550.950.1018.7688.12452.550.0186.524
37.96552.970.0997.0128.91254.140.0185.017
48.91454.540.0986.1149.83455.580.0184.008
510.01257.820.0975.01210.7658.980.0183.521
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基于有限元仿真的海缆热效应与截面力学性能研究
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朱海飞 1 , 韩大伟 2, 3 , 王向坤 4 , 夏志胜 1 , 巩凡 1
绝缘材料 | 测试与分析 2024,57(9): 149-157
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绝缘材料 | 测试与分析 2024, 57(9): 149-157
基于有限元仿真的海缆热效应与截面力学性能研究
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朱海飞1, 韩大伟2, 3, 王向坤4, 夏志胜1, 巩凡1
作者信息
  • 1山能新能源(东营)有限公司,山东 东营 250014
  • 2中国电建集团华东勘测设计研究院有限公司,浙江 杭州 311122
  • 3浙江华东工程咨询有限公司,浙江 杭州 311100
  • 4武汉大学 水资源工程与调度全国重点实验室,湖北 武汉 430072

    • 朱海飞（1982-），男（汉族），湖南武冈人，高级工程师，主要研究方向为海上风力发电技术及应用研究；

    王向坤（2000-），男（汉族），山西晋城人，硕士生，研究方向为海上风电基础研究。

Research on thermal effect and section mechanical properties of submarine cable based on finite element simulation
Haifei ZHU1, Dawei HAN2, 3, Xiangkun WANG4, Zhisheng XIA1, Fan GONG1
Affiliations
  • 1Shandong Energy New Energy (Dongying) Co., Ltd., Dongying 250014, China
  • 2PowerChina Huadong Engineering Corporation Limited, Hangzhou 311122, China
  • 3Zhejiang East China Engineering Consulting Co., Ltd., Hangzhou 311100, China
  • 4State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan 430072, China
出版时间: 2024-09-20 doi: 10.16790/j.cnki.1009-9239.im.2024.09.016
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摘要
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海缆作为高压电力的传输构件，运行过程中产生的热量会引起结构温度升高及膨胀。受各层约束作用，海缆将产生较大的热应力与变形，进而引起结构损坏。此外，温度升高会导致海缆内部高分子材料弹性模量降低，导致海缆截面力学性能的改变。因此有必要研究海缆运行过程中因热膨胀引起的应力和变形，分析温度对海缆截面力学性能的影响。本文以某海上风电工程为依托，基于有限元软件ABAQUS建立了海缆-土体整体有限元模型，获得了稳态载流量下的温度场分布；基于温度场结果，采用热力耦合方法计算了海缆的热应力和热变形，并分析了温度作用下海缆截面力学性能的改变。结果表明：海缆运行时最高温度出现在铜导体中，外被层温度最低，以铜导体为中心，沿径向往内侧温度变化梯度较小，往外侧温度变化梯度较大；热应力主要集中在金属结构中，最大变形出现在钢丝铠装层中，当铜导体与光纤位于截面顶部时位移最大，位于底部时位移最小；考虑温度影响后，铜导体与光纤的应力会增大，同时海缆的拉伸与扭转刚度会降低，且逆扭转刚度的降低程度大于顺扭转刚度。

海缆  /  有限元  /  热力耦合  /  应力  /  截面力学性能

Submarine cable is a transmission component of high-voltage power, and the heat generated during the operation of submarine cable will cause the structural temperature rise and expand. Under the constraint of each layer, the submarine cable will produce large thermal stress and deformation, which will cause structural damage. In addition, the increase of temperature will lead to the decrease of elastic modulus of the polymer material inside the submarine cable, resulting in the change of mechanical properties of the submarine cable section. Therefore, it is necessary to study the stress and deformation caused by thermal expansion during the operation of submarine cables, and analyze the influence of temperature on the mechanical properties of submarine cables. In this paper, based on an offshore wind power project, a finite element model of submarine cable-soil was established in finite element software ABAQUS, and the temperature field distribution under steady-state current carrying capacity was obtained. Based on the results of temperature field, the thermal stress and thermal deformation of the submarine cable were calculated by the thermal-mechanical coupling method, and the change of mechanical properties of the submarine cable section under the action of temperature was analyzed. The results show that the highest temperature appears in the copper conductor during the operation of submarine cable, and the outer coating layer has the lowest temperature. With the copper conductor as the center, the temperature drop gradient along the inside radial direction is small, and the temperature drop gradient along the outside radial direction is large. The thermal stress is mainly concentrated in the metal structure, and the maximum deformation occurs in the steel wire armor. When the copper conductor and the optical fiber are located at the top of the cross section, the displacement is the largest, and the displacement is the smallest at the bottom. After considering the influence of temperature, the stress of copper conductor and optical fiber will increase, while the tensile and torsional stiffness of submarine cable will decrease, and the reduction of inverse torsional stiffness is greater than that of clockwise torsional stiffness.

submarine cables  /  finite element  /  thermal coupling  /  stress  /  section mechanical properties
朱海飞, 韩大伟, 王向坤, 夏志胜, 巩凡. 基于有限元仿真的海缆热效应与截面力学性能研究. 绝缘材料, 2024 , 57 (9) : 149 -157 . DOI: 10.16790/j.cnki.1009-9239.im.2024.09.016
Haifei ZHU, Dawei HAN, Xiangkun WANG, Zhisheng XIA, Fan GONG. Research on thermal effect and section mechanical properties of submarine cable based on finite element simulation[J]. Insulating Materials, 2024 , 57 (9) : 149 -157 . DOI: 10.16790/j.cnki.1009-9239.im.2024.09.016
正文
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0 引言
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海缆作为连接海上风电场与陆上变电站的电力传输介质，在海上风电工程中发挥着重要作用[1]。在海缆运行时其内部会产生大量的热[2]，导致结构温度升高及膨胀。但由于层间结构的相互约束，膨胀受到限制，导致各层结构产生较大的热应力和变形，进而引起海缆结构的损坏。此外，海缆内部的高分子材料，如绝缘层、外被层，其弹性模量会随温度的升高而降低，影响海缆的力学性能。因此，研究海缆结构运行时的温度场分布、热应力与变形及截面力学性能的变化，有利于提高海缆的运行可靠性，降低事故发生率。
目前，已有大量学者利用解析方法和有限元方法计算海缆的温度场及载流量。吕安强等[3]基于热路模型推导出光纤与导体的温度关系方程，并建立有限元模型进行验证。林钰等[4]根据电-热-流耦合理论建立三芯海缆埋设和敷设两种方式下的有限元模型，分析其温度场和载流量。张皓等[5]依据IEC 60287及有限元方法计算典型敷设环境下的海缆载流量，对比分析了影响三芯电缆温度场的因素。
根据海缆温度场分布，可以计算海缆的热效应以及截面力学性能的变化。李盛翀等[6]基于有限元热力耦合模型分析了高压大截面电缆在高温作用下各层结构的应力和变形。M A HAMDAN等[7]采用有限元方法分析了交流三芯海缆内部的热应力，研究影响护套塑性应变的关键参数。李兢[8]采用有限元方法对海缆轴向拉伸刚度进行分析，并与解析法对比，结果证明有限元法的优势及有效性。罗强[9]分析了脐带缆在温度作用下拉伸、弯曲及扭转等刚度的变化，结果表明温度会不同程度降低电缆的力学刚度。
从以上研究可知，目前关于海缆热效应的研究均未考虑埋设状态下海缆与海底土壤间的相互作用；此外，对考虑温度效应的海缆截面力学性能研究较少。因此，本文以渤海某风电工程项目为依托，建立了海缆-土体整体的有限元模型，获得稳态载流量下的温度场分布；基于温度场的结果，采用热力耦合方法计算海缆的应力与变形，分析了钢丝铠装层、铜导体和单模光纤等主要结构的仿真结果，并探究温度作用下海缆截面力学性能的变化，以期为海缆结构热效应及力学性能的研究提供参考。
1 工程背景与海缆结构
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1.1 工程背景
渤海某海上风电工程的规划装机容量为399.5 MW，场址面积为70.4 km2，机组单机容量为8.5 MW。风电机组发出电能经海上升压站升压后，通过HYJQDF41-F-127型220 kV三芯光纤复合海缆接入陆上集控中心，该海缆埋设深度为2 m，如图1所示。
1.2 海缆剖面结构
220 kV三芯光纤复合海缆由铜导体线芯、光纤单元及铠装层等组成，其结构剖面如图2所示。其中铜导体线芯由铜导体、绝缘屏蔽和XLPE绝缘等组成，光纤单元由单模光纤、钢管和铠装钢丝等组成，外部保护材料包括钢丝铠装和PP外被层等。
1.3 海缆绞合层结构
海缆内部结构复杂，铜导体线芯、铠装钢丝和光纤单元均以绞合方式布置，节距为2 m，如图3所示，其他部分均为非绞合层[10]。
2 海缆温度场仿真分析
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2.1 有限元模型
为降低仿真模型的计算难度，对海缆结构适当简化。忽略尺寸较薄的半导电阻水带，将传热系数接近的绝缘屏蔽、XLPE绝缘和导体屏蔽合并，统称为绝缘层；将光纤单元中的单模光纤和钢管合并，称为单模光纤；将光纤外部的铠装钢丝简化为钢管实体结构；将厚度较薄的PP内垫层与填充结构合并，统称为填充层。合并后各结构尺寸及热学特性见表1。
海缆模型轴向长度为2.5 m，并定义轴向长度方向为Z轴正方向，竖直向上为Y轴正方向，X轴方向由右手螺旋法则确定，绞合结构的绞合方向为顺时针方向。目前已有研究表明光电复合海缆对海土温度的影响范围在1.5 m左右[11]，因此土壤模型尺寸选取为4 m×4 m×2.5 m。整体模型采用C3D8R实体单元，网格划分如图4～5所示。
对于220 kV三芯光纤复合交流电缆，其运行过程中的总损耗包括导体损耗、绝缘介质损耗、金属护套损耗和铠装钢丝损耗，将IEC 60287-1-1:2006[12]所求得的各损耗除以各自结构的截面积，所得的产热率作为热荷载施加于结构中，并将模型下边界土体设为第一类边界条件[13]，深层土壤温度为15℃，土壤的左右前后边界、海缆的轴向截面为第二类边界条件[13]，法向热流密度为0 W/m2，模型土壤的上边界为第三类边界条件[13]，环境温度为15℃，对流换热系数取200 W/(m2·K)，土壤导热系数为1 W/(m·K)。
2.2 温度场仿真结果
交联聚乙烯海缆的最高运行温度为90℃[14]，为获取稳态载流量下海缆内部温度场的分布，以导体温度为90℃反推对应的载流量。当模型施加电流为587.58 A时，导体温度达到了最高允许温度90℃。依据文献[14]中载流量相关计算公式可算得理论稳态载流量为561.18 A，与有限元结果的相对误差为4.70%，由此证明了有限元模型的准确性。
稳态载流量下温度场分布如图6所示。从图6可以看出，当施加587.58 A的负荷电流时，导体温度最高为90℃，外被层温度最低为61.84℃，且其右侧温度高于左侧，三条线芯交汇处温度为87.12℃。
为分析海缆内部温度分布，选取从海缆截面中心穿过铜导体中心最后到外被层的径向路径，提取路径上各点的温度，如图7所示。由图7可知，温度分布以铜导体为中心，沿径向往内的温度变化梯度较小，内侧填充层、半导电护套、铅护套中的温度基本一致，内侧绝缘层沿径向往内的温差为2.84℃；以铜导体为中心，沿径向往外的温度变化梯度较大，外侧绝缘层中温差为3.84℃，外侧半导电护套中温差为6.05℃，外侧填充层中温差为11.81℃，钢丝铠装层中温差较小，外被层中温差为5.12℃。出现上述现象的原因是金属结构中的导热系数较大，易于传热，温度具有一致性；而高分子材料如绝缘层等，导热系数较小，不易于传热，导致结构中会产生温差。同时由于三芯海缆呈现“品”字形排布，各相铜导体产生的热量在海缆中心点处交汇，且散热受限，进而导致铜导体与海缆中心点间的温差较小。
3 海缆热效应与力学性能分析
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海缆由金属和高分子材料组成，各部分材料与土体的力学性能参数见表2。其中，绝缘和外被层通常为高分子材料，其弹性模量（E）与温度（T）分别满足式（1）及表3所示的关系[15-16]。对于其他温度下的弹性模量，外被层（PP）采用线性插值的方法获取，绝缘层（XLPE）则通过式（1）获取。
E(T)=0.027T2-4.64T+232
3.1 热效应分析
3.1.1 有限元模型
海缆运行时产生的热量会导致各结构中存在热膨胀，进而在温度升高时结构内部产生热应变。由于海缆的构造特点，各层结构会彼此约束且温度存在差异，导致应变无法释放，进而产生热应力。因此每个单元的应变是由应力引起的应变与温度变化所产生的热应变的叠加，因此结构中的任意节点，存在如式（2）所示平衡方程[6]。
dσth=Kdδ
式（2）中：dσth为所选结点的温度荷载增量，见式（3）；K为结点刚度矩阵，由式（4）计算；dδ为结点形变增量。
dσth=∫BTCdTdV
K=∫BTDBdV
式（3）～（4）中：B为形变δ与应变ε的转换矩阵，关系见式（5）；V为体积；C为温度矩阵，通过式（6）计算；D为弹性矩阵，由弹性模量与泊松比决定。
dε=Bdδ
C=D(α+∂D-1∂Tσ)
式（5）～（6）中：α为热膨胀系数向量。
采用热力耦合的方法，将温度场结果作为预定义场加入到海缆结构模型中，因此，热力耦合网格划分情况与温度场相同。由于海缆结构内涉及较多的接触，为保证计算精度，采用显示动力分析方法，并选用该分析模块中的自动接触算法。对土体底部施加固定约束，四周面施加法向约束，土体顶部为自由面，同时对海缆端面施加轴向位移约束。
3.1.2 热效应结果
海缆在埋设状态下，外围土体会约束其热膨胀，图8为海缆外被层表面接触应力云图。由图8可知，海缆外被层与土体并非全部接触，仅为部分区域接触，最大接触应力为56.7 MPa。图9为海缆内部结构应力云图。由图9可知，海缆热应力分布不均匀，应力承受部件集中在金属部件中；受端部效应的影响，铜导体、钢丝铠装层及单模光纤在端部存在应力集中，端部应力大于中间部位，其中铜导体最大应力为195.2 MPa，钢丝铠装层最大应力为158.88 MPa，单模光纤最大应力为40.92 MPa。图10为海缆内部各结构的合位移云图，即各个分位移合成的总位移。由图10可知，钢丝铠装层位移最大，为3.78 mm，出现在端面处，除去端面效应后中间部位的位移比较均匀，表现为顶部钢丝位移大于底部位移；铜导体与单模光纤的位移大小与其位置有关，当铜导体与单模光纤位于截面顶部时，位移最大，位于截面底部时，位移最小，从截面顶部到底部，铜导体与单模光纤的位移呈现出逐渐减小的趋势。
3.2 海缆力学性能分析
3.2.1 拉伸性能分析
固定海缆的一端，将另一端耦合至一点。图11展示了不同拉伸荷载下，在考虑温度影响及不考虑温度影响下铜导体与光纤的应力分布。由图11可知，无论是否考虑温度影响，铜导体与光纤的应力变化趋势相近，最大应力出现在结构端部；考虑温度影响时，应力极值会略微增大，且作用荷载越大，其增大的程度更高。这是因为温度升高使得高分子材料弹性模量降低，导致结构在承受相同荷载时，应力水平提高。
海缆在考虑温度影响及不考虑温度影响下拉力与轴向应变的关系如图12所示。提取图12中曲线的斜率即为拉伸刚度，可得不考虑温度影响时海缆的拉伸刚度为360 MN，考虑温度影响时的拉伸刚度为311 MN，降低了13.6%。考虑温度影响时绝缘层弹性模量平均降低了约85.9%，外被层弹性模量平均降低了约56.5%，而拉伸刚度只降低了13.6%。为分析其原因，提取不同拉伸荷载作用下海缆内部主要结构层的承载情况如表4所示。由表4可知，在拉伸荷载作用下，钢丝铠装层和铜导体是海缆的主要承载构件，而绝缘层及外被层的承载比较小，其对结构拉伸刚度的贡献较小。因此，考虑温度影响后，结构拉伸刚度的降低程度也相对较低。
3.2.2 扭转性能分析
扭转分为顺扭转与逆扭转，图13和图14分别为不同顺逆扭矩下，海缆在考虑温度影响及不考虑温度影响下铜导体与光纤的应力分布。由图13～14可知，无论是否考虑温度影响，铜导体与光纤的应力变化趋势相近；考虑温度影响时，应力的数值会略微增大，且作用荷载越大，其增大的程度更高。这同样是因为温度的升高使得高分子材料的弹性模量降低，导致结构在承受相同荷载时，应力水平提高。
海缆在考虑温度影响及不考虑温度影响下扭矩与角应变关系如图15所示。提取图15中曲线的斜率即为扭转刚度，可得不考虑温度影响时海缆的顺扭转刚度为366 kN·m2，考虑温度影响时的顺扭转刚度为349 kN·m2，降低了4.6%；不考虑温度影响时海缆的逆扭转刚度为292 kN·m2，考虑温度影响时的逆扭转刚度为258 kN·m2，降低了11.6%。同样提取不同顺逆扭矩作用下海缆内部主要结构层的承载情况，如表5和表6所示。由表5～6可知，顺逆扭矩作用下钢丝铠装层和铜导体仍是主要的承载构件，而绝缘层及外被层的承载比仍较小，对结构扭转刚度的贡献较小。因此，考虑温度影响后，结构扭转刚度的降低程度同样也相对较低，但由于顺扭矩的方向与钢丝铠装层绞合方向相同，该方向扭矩的作用使得钢丝铠装层处于张紧的状态，进而造成钢丝铠装层的承载比逆扭矩时高，最终导致海缆顺扭转刚度较逆扭转刚度大，且其降低程度较逆扭转刚度小。
4 结论
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本文依托渤海某海上风电工程，以220 kV三芯光纤复合海缆作为研究对象，基于有限元软件ABAQUS，建立了海缆-土体整体有限元模型，对埋设海缆在运行时的温度场分布及热效应情况进行分析，并探究了海缆在温度作用下截面力学性能的变化，得到如下结论：
（1）针对埋设方式的海缆，在稳态载流量下，温度分布以铜导体为中心扩展，沿径向往内侧的温度变化梯度较小，往外侧的温降梯度较大。
（2）海缆中的热应力主要集中在金属结构中，受端部效应影响，海缆在端部存在应力集中；钢丝铠装层端面中的位移最大，当铜导体与单模光纤位于截面顶部时位移最大，位于截面底部时位移最小。
（3）在拉伸荷载作用下，铜导体和钢丝铠装层是海缆的主要承载构件，而绝缘层和外被层的承载比较小。由于绝缘层与外被层对结构拉伸刚度的贡献较小，因此与不考虑温度影响相比，考虑温度影响后，海缆截面拉伸力学性能稍有下降，约下降了13.6%。
（4）在顺逆扭矩荷载作用下，铜导体和钢丝铠装层仍是海缆的主要承载构件，而绝缘层和外被层的承载比仍较小。由于顺扭矩作用下钢丝铠装层的承载比逆扭矩时高，导致该结构的顺扭转刚度较逆扭转刚度大，且考虑温度影响后，其顺扭转刚度的降低程度（4.6%）较逆扭转刚度降低程度（11.6%）低。
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doi: 10.16790/j.cnki.1009-9239.im.2024.09.016
  • 接收时间：2023-09-02
  • 首发时间：2025-12-24
  • 出版时间：2024-09-20
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  • 收稿日期：2023-09-02
  • 修回日期：2023-10-31
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    1山能新能源(东营)有限公司,山东 东营 250014
    2中国电建集团华东勘测设计研究院有限公司,浙江 杭州 311122
    3浙江华东工程咨询有限公司,浙江 杭州 311100
    4武汉大学 水资源工程与调度全国重点实验室,湖北 武汉 430072
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2种不同金属材料的力学参数
科
Family		 属数
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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