以四元件模型理解水树生长的电–机械理论
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摘要
为揭示电–机械理论中麦克斯韦应力对水树生长的作用机制,研究了水树生长特性与麦克斯韦应力波形的关系,并运用表征高分子材料力学特性的四元件模型,提出了一种水树生长受麦克斯韦应力影响的可能机制。对交联聚乙烯(XLPE)样本施加3种波形电压,即半波整流电压、正弦交流电压和全波整流电压进行加速水树老化,得到不同波形电压下水树生长特性。实验结果表明:水树长度与电压波形密切相关,半波整流电压下水树最短,正弦交流电压、全波整流电压下水树平均长度分别是前者的1.46、1.86倍。根据实验结果,可得到水树生长特性与相应的麦克斯韦应力波形的关系。通过搭建XLPE材料的四元件模型,建立了3种电压下XLPE材料的形变随麦克斯韦应力变化的曲线,在1个交流电压周期内,半波整流电压下形变最小,全波整流电压下形变最大,正弦交流电压下形变介于前两者之间;形变越大,材料断裂一次所需周期数越小,水树生长速度越快,与水树生长特性一致。因此,结合四元件模型,麦克斯韦应力对水树生长的作用机制得以阐明。
To reveal the mechanism of water tree propagation under Maxwell stress in the electrical-mechanical theory, the relationship between water tree propagation characteristics and Maxwell stress waveforms is investigated. By using a four-element model based on mechanical properties of polymer materials, a possible mechanism is presented to explain the effect of Maxwell stress on water tree propagation. The water tree propagation characteristics are studied by accelerated water tree aging experiments which are performed on XLPE samples by using 3 kinds of voltages like half-wave voltage, sinusoidal voltage, and full-wave voltage. The experimental results show that morphologies and sizes of water tree are dependent on the voltage waveforms. Water tree sizes under half-wave voltages are the shortest. Water tree sizes under full-wave voltage and sinusoidal voltages are 1.46, 1.86 times of the former. According to the experimental results, the relationship between water tree propagation characteristics and their Maxwell stress waveforms is observed. By building a four-element model of XLPE material, the relation curves of XLPE material's deformation and Maxwell stress waveforms under 3 kinds of voltages are obtained. In a cycle of sinusoidal voltage, the deformation under half-wave voltage is the smallest, whereas the deformation is the largest under the full-wave voltage. The deformation under sinusoidal voltage is between them. The larger the XLPE material's deformation is, the fewer the number of cycles is needed for fracture of XLPE material, which leads to higher speed of water tree propagation that is consistent with water tree propagation characteristics. Therefore, by the four-element model, the mechanism of Maxwell stress on water tree propagation is clearly illustrated.
To reveal the mechanism of water tree propagation under Maxwell stress in the electrical-mechanical theory, the relationship between water tree propagation characteristics and Maxwell stress waveforms is investigated. By using a four-element model based on mechanical properties of polymer materials, a possible mechanism is presented to explain the effect of Maxwell stress on water tree propagation. The water tree propagation characteristics are studied by accelerated water tree aging experiments which are performed on XLPE samples by using 3 kinds of voltages like half-wave voltage, sinusoidal voltage, and full-wave voltage. The experimental results show that morphologies and sizes of water tree are dependent on the voltage waveforms. Water tree sizes under half-wave voltages are the shortest. Water tree sizes under full-wave voltage and sinusoidal voltages are 1.46, 1.86 times of the former. According to the experimental results, the relationship between water tree propagation characteristics and their Maxwell stress waveforms is observed. By building a four-element model of XLPE material, the relation curves of XLPE material's deformation and Maxwell stress waveforms under 3 kinds of voltages are obtained. In a cycle of sinusoidal voltage, the deformation under half-wave voltage is the smallest, whereas the deformation is the largest under the full-wave voltage. The deformation under sinusoidal voltage is between them. The larger the XLPE material's deformation is, the fewer the number of cycles is needed for fracture of XLPE material, which leads to higher speed of water tree propagation that is consistent with water tree propagation characteristics. Therefore, by the four-element model, the mechanism of Maxwell stress on water tree propagation is clearly illustrated.
引文
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[14]周凯,杨明亮,陶文彪,等.单一极性直流电压下交联聚乙烯电力电缆水树生长特性[J].高电压技术,2015,41(4):1075-1083.ZHOU Kai,YANG Mingliang,TAO Wenbiao,et al.Propagation characteristics of water trees in XLPE power cables under single polarity DC voltage[J].High Voltage Engineering,2015,41(4):1075-1083.
[15]YAWATA R,UEHARA H,KUDO K,et al.Effects of ions and waveforms on water tree initiation and propagation[C]∥IEEE Conference on Electrical Insulation and Dielectric Phenomena.Montreal,Canada:IEEE,2012:616-619.
[16]何曼君,张红东,陈维孝,等.高分子物理[M].3版.上海:复旦大学出版社,2006:205-246.HE Manjun,ZHANG Hongdong,CHEN Weixiao,et al.Polymer physics[M].3rd ed.Shanghai,China:Fudan University Press,2006:205-246.
[17]RITUMS J E,MATTOZZI A,GEDDE U W,et al.Mechanical properties of high-density polyethylene and crosslinked high-density polyethylene in crude oil and its components[J].Journal of Polymer Science Part B:Polymer Physics,2005,44(4):641-648.
[18]谭洪生.聚烯烃材料:抗冲共聚聚丙烯的结构与高密度聚乙烯导电复合材料的性能[D].杭州:浙江大学,2006.TAN Hongsheng.Polyolefin materials:structure of impact polypropylene copolymer and properties of conductive composites[D].Hangzhou,China:Zhejiang University,2006.
[19]赵威.基于电机械理论的水树老化特性及修复的研究[D].成都:四川大学,2014.ZHAO Wei.Study of the water-tree characteristics based on electro-mechanical theory and rejuvenation for aged XLPE cables[D].Chengdu,China:Sichuan University,2014.
[20]CRINE J P,JOW J.A water treeing model[J].IEEE Transactions on Dielectrics and Electrical Insulation,2005,12(4):801-808.
[21]粟秋硕.XLPE电缆运行故障分析和在线检测研究[D].成都:西南交通大学,2008.SU Qiushuo.XLPE cable operation failure analysis and online detection[D].Chengdu,China:Southwest Jiaotong University,2008.
[22]党智敏,亢婕,屠德民.新型抗水树电缆料的空间电荷和吸水特性的关系[J].电工技术学报,2002,17(6):68-71.DANG Zhimin,KANG Jie,TU Demin.Relationship between the space charge and the property of water absorbing in new cable material of retarding water treeing[J].Transactions of China Electrotechnical Society,2002,17(6):68-71.
[23]BOGGS S,DENSLEY J,KUANG J.Mechanism for impulse conversion of water trees to electrical trees in XLPE[J].IEEE Transactions on Power Delivery,1998,13(2):310-315.
[24]HVIDSTEN S,ILDSTAD E,FAREMO H.Mechanisms causing nonlinear dielectric response of water treed XLPE cables[C]∥IEEEInternational Conference on Conduction and Breakdown in Solid Dielectrics.Vasteras,Sweden:IEEE,1998:73-78.
[25]MEZIANI M,MEKHALDI A,TEGUAR M.Effect of space charge layers on the electric field enhancement at the physical interfaces in power cable insulation[J].IEEE Transactions on Dielectrics and Electrical Insulation,2016,23(6):3725-3733.
[2]ROSS R.Inception and propagation mechanisms of water treeing[J].IEEE Transactions on Dielectrics and Electrical Insulation,1998,5(5):660-680.
[3]ZHOU K,ZHAO W,TAO X.Toward understanding the relationship between insulation recovery and micro structure in water tree degraded XLPE cables[J].IEEE Transactions on Dielectrics and Electrical Insulation,2013,20(6):2135-2142.
[4]党智敏,亢婕,屠德民.新型抗水树聚乙烯绝缘电缆料的研究[J].中国电机工程学报,2002,22(1):8-11.DANG Zhimin,KANG Jie,TU Demin.Study on new cable material of resisting water treeing in polyethylene[J].Proceedings of the CSEE,2002,22(1):8-11.
[5]张洪亮,谢书鸿,尹毅,等.厦门柔直工程±320kV直流电缆绝缘及外护层结构选型与论证[J].高电压技术,2016,42(10):3139-3146.ZHANG Hongliang,XIE Shuhong,YIN Yi,et al.Selection and verification of insulation and sheath structure of±320 k V DC cable for Xiamen Flexible DC Transmission Project[J].High Voltage Engineering,2016,42(10):3139-3146.
[6]HVIDSTEN S,KVANDE S,RYEN A,et al.Severe degradation of the conductor screen of service and laboratory aged medium voltage XLPE insulated cables[J].IEEE Transactions on Dielectrics and Electrical Insulation,2009,16(1):155-161.
[7]周凯,陶文彪,赵威,等.基于蠕变模型的水树老化电缆绝缘自恢复机制[J].中国电机工程学报,2015,35(16):4271-4279.ZHOU Kai,TAO Wenbiao,ZHAO Wei,et al.Insulation self-recovery mechanism of water tree aged cables based on a creep model[J].Proceedings of the CSEE,2015,35(16):4271-4279.
[8]郑晓泉,王金锋,李彦雄.交联聚乙烯中水树枝向电树枝的转化[J].中国电机工程学报,2013,33(22):166-174.ZHENG Xiaoquan,WANG Jinfeng,LI Yanxiong.Transformation of electrical tree from water tree degradation in XLPE[J].Proceedings of the CSEE,2013,33(22):166-174.
[9]ZHOU K,HUANG M,TAO W,et al.A possible water tree initiation mechanism for service-aged XLPE cables:conversion of electrical tree to water tree[J].IEEE Transactions on Dielectrics and Electrical Insulation,2016,23(3):1854-1861.
[10]WANG Z,MARCOLONGO P,LEMBERG J,et al.Mechanical fatigue as a mechanism of water tree propagation in TR-XLPE[J].IEEETransactions on Dielectrics and Electrical Insulation,2012,19(1):321-330.
[11]OHKI Y,ISHIKAWA H,MORITA G,et al.Role of the voltage zero-crossing in the growth of water trees:Effect of superposition method of a high-frequency voltage and a low-frequency voltage[C]∥International Conference on Condition Monitoring and Diagnosis.Beijing,China:IEEE,2008:328-331.
[12]KANEKO D,MAEDA T,ITO T,et al.Role of number of consecutive voltage zero-crossings in propagation of water trees in polyethylene[J].IEEE Transactions on Dielectrics and Electrical Insulation,2004,11(4):708-714.
[13]FUJIMOTO T,UEHARA H,NANBA N.Propagation characteristics of water trees using full and half-cycle rectified voltage waveforms[C]//IEEE Conference on Electrical Insulation and Dielectric Phenomena.Virginia Beach,USA:IEEE,2009:494-497.
[14]周凯,杨明亮,陶文彪,等.单一极性直流电压下交联聚乙烯电力电缆水树生长特性[J].高电压技术,2015,41(4):1075-1083.ZHOU Kai,YANG Mingliang,TAO Wenbiao,et al.Propagation characteristics of water trees in XLPE power cables under single polarity DC voltage[J].High Voltage Engineering,2015,41(4):1075-1083.
[15]YAWATA R,UEHARA H,KUDO K,et al.Effects of ions and waveforms on water tree initiation and propagation[C]∥IEEE Conference on Electrical Insulation and Dielectric Phenomena.Montreal,Canada:IEEE,2012:616-619.
[16]何曼君,张红东,陈维孝,等.高分子物理[M].3版.上海:复旦大学出版社,2006:205-246.HE Manjun,ZHANG Hongdong,CHEN Weixiao,et al.Polymer physics[M].3rd ed.Shanghai,China:Fudan University Press,2006:205-246.
[17]RITUMS J E,MATTOZZI A,GEDDE U W,et al.Mechanical properties of high-density polyethylene and crosslinked high-density polyethylene in crude oil and its components[J].Journal of Polymer Science Part B:Polymer Physics,2005,44(4):641-648.
[18]谭洪生.聚烯烃材料:抗冲共聚聚丙烯的结构与高密度聚乙烯导电复合材料的性能[D].杭州:浙江大学,2006.TAN Hongsheng.Polyolefin materials:structure of impact polypropylene copolymer and properties of conductive composites[D].Hangzhou,China:Zhejiang University,2006.
[19]赵威.基于电机械理论的水树老化特性及修复的研究[D].成都:四川大学,2014.ZHAO Wei.Study of the water-tree characteristics based on electro-mechanical theory and rejuvenation for aged XLPE cables[D].Chengdu,China:Sichuan University,2014.
[20]CRINE J P,JOW J.A water treeing model[J].IEEE Transactions on Dielectrics and Electrical Insulation,2005,12(4):801-808.
[21]粟秋硕.XLPE电缆运行故障分析和在线检测研究[D].成都:西南交通大学,2008.SU Qiushuo.XLPE cable operation failure analysis and online detection[D].Chengdu,China:Southwest Jiaotong University,2008.
[22]党智敏,亢婕,屠德民.新型抗水树电缆料的空间电荷和吸水特性的关系[J].电工技术学报,2002,17(6):68-71.DANG Zhimin,KANG Jie,TU Demin.Relationship between the space charge and the property of water absorbing in new cable material of retarding water treeing[J].Transactions of China Electrotechnical Society,2002,17(6):68-71.
[23]BOGGS S,DENSLEY J,KUANG J.Mechanism for impulse conversion of water trees to electrical trees in XLPE[J].IEEE Transactions on Power Delivery,1998,13(2):310-315.
[24]HVIDSTEN S,ILDSTAD E,FAREMO H.Mechanisms causing nonlinear dielectric response of water treed XLPE cables[C]∥IEEEInternational Conference on Conduction and Breakdown in Solid Dielectrics.Vasteras,Sweden:IEEE,1998:73-78.
[25]MEZIANI M,MEKHALDI A,TEGUAR M.Effect of space charge layers on the electric field enhancement at the physical interfaces in power cable insulation[J].IEEE Transactions on Dielectrics and Electrical Insulation,2016,23(6):3725-3733.