高压直流电缆绝缘二维模型下空间电荷动力学仿真算法研究
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摘要
为实现高压直流电缆绝缘层内部空间电荷输运的数值仿真,结合双极性载流子输运模型,提出基于二维非结构网格的空间电荷输运特性算法。该算法基于对泊松方程与连续方程的迭代求解,其中泊松方程采用有限元法求解,连续方程采用格心离散有限体积法求解。为同时保证电荷密度落在合理区间及二阶计算精度,对绝缘内部电荷密度进行线性重构和限制器控制处理。通过对4mm厚绝缘电缆内部空间电荷二维仿真和电声脉冲法全尺寸测量的结果进行比对,验证了所提算法的准确性和有效性。另外,二维结构空间电荷的仿真结果表明:当电缆长度远大于半径时,除电缆轴向两端区域之外,中部区域空间电荷沿轴向基本均匀分布,因此该条件下中部区域的空间电荷仿真可简化为径向一维模型。但当电缆长度接近半径值或关注电缆端部的空间电荷分布时,空间电荷沿轴向存在明显的不一致性,一维简化模型将不再适用,必须采用二维模型,以提高空间电荷输运仿真结果的准确性。
In order to simulate the space charge behavior in high voltage DC cable insulation, this paper proposed a simulation algorithm for space charge transport based on two dimensional unstructured mesh, which combined with bipolar charge transport model. The algorithm is based on iteratively solving the Poisson equation and charge conservation equation.The finite element method(FEM) is employed to solve the Poisson equation and the finite volume method(FVM) is employed discretizing the charge conservation equation on a cell-centered tessellation. In order to ensure the charge density in a reasonable range and in second-order accuracy, a linear reconstruction with limiter for charge density was adopted in the insulation domain. The comparison results of space charge simulation of 4 mm-thick cable insulation in two dimension and measurement with a full-size space charge system based on pulsed electro-acoustic(PEA) method validate the accuracy and effectiveness of the proposed algorithm. The space charge simulation in two dimension shows that when the cable length is far outweigh that radius, the space charge uniformly distributed along the axial direction apart from both ends. Thus the space charge simulation could modeled in one dimension along radius in such condition. However, the space charge distribution differs obviously along the axial direction at both ends, which suggests the necessity to call for a two dimensional model for simulation of the charge behavior in cable insulation to improve the accuracy.
In order to simulate the space charge behavior in high voltage DC cable insulation, this paper proposed a simulation algorithm for space charge transport based on two dimensional unstructured mesh, which combined with bipolar charge transport model. The algorithm is based on iteratively solving the Poisson equation and charge conservation equation.The finite element method(FEM) is employed to solve the Poisson equation and the finite volume method(FVM) is employed discretizing the charge conservation equation on a cell-centered tessellation. In order to ensure the charge density in a reasonable range and in second-order accuracy, a linear reconstruction with limiter for charge density was adopted in the insulation domain. The comparison results of space charge simulation of 4 mm-thick cable insulation in two dimension and measurement with a full-size space charge system based on pulsed electro-acoustic(PEA) method validate the accuracy and effectiveness of the proposed algorithm. The space charge simulation in two dimension shows that when the cable length is far outweigh that radius, the space charge uniformly distributed along the axial direction apart from both ends. Thus the space charge simulation could modeled in one dimension along radius in such condition. However, the space charge distribution differs obviously along the axial direction at both ends, which suggests the necessity to call for a two dimensional model for simulation of the charge behavior in cable insulation to improve the accuracy.
引文
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[8]Aouabed F,Bayadi A,Rahmani A E,et al.Finite element modelling of electric field and voltage distribution on a silicone insulating surface covered with water droplets[J].IEEE Transactions on Dielectrics and Electrical Insulation,2018,25(2):413-420.
[9]李忠华,陈漳.双层绝缘结构高压直流电缆电场分布仿真[J].高电压技术,2017,43(11):3504-3513.Li Zhonghua,Chen Zhang.Simulation on electric field distribution in HVDC cable with double-layered insulation[J].High Voltage Engineering,2017,43(11):3504-3513(in Chinese).
[10]Li S,Min D,Wang W,et al.Modelling of dielectric breakdown through charge dynamics for polymer nanocomposites[J].IEEE Transactions on Dielectrics and Electrical Insulation,2017,23(6):3476-3485.
[11]Laurent C,Teyssedre G,Roy S L,et al.Charge dynamics and its energetic features in polymeric materials[J].IEEETransactions on Dielectrics and Electrical Insulation,2013,20(2):357-381.
[12]Alison J M,Hill R M.A model for bipolar charge transport,trapping and recombination in degassed crosslinked polyethene[J].Journal of Physics D:Applied Physics,1994,27(6):1291-1299.
[13]Roy S L,Teyssedre G,Laurent C.Charge transport and dissipative processes in insulating polymers:experiments and model[J].IEEE Transactions on Dielectrics and Electrical Insulation,2005,12(4):644-654.
[14]Roy S L,Teyssèdre G,Laurent C.Modelling space charge in a cable geometry[J].IEEE Transactions on Dielectrics and Electrical Insulation,2016,23(4):2361-2367.
[15]Chen G,Zhao J,Li S,et al.Origin of thickness dependent dc electrical breakdown in dielectrics[J].Applied Physics Letters,2012,100(22):2135.
[16]吴建东.低密度聚乙烯纳米复合介质中电荷输运的实验研究和数值模拟[D].上海:上海交通大学,2012.Wu Jiandong.Charge transport investigation in low-density polyethylene/silica nanocomposite based on experiment and numerical simulation[D].Shanghai:Shanghai Jiaotong University,2012(in Chinese).
[17]黄国栋,阮江军,杜志叶,等,改进三维上流元法计算特高压直流线路离子流场[J].中国电机工程学报,2013,33(33):152-159.Huang Guodong,Ruan Jiangjun,Du Zhiye,et al.Improved 3-D upwind FEM for solving ionized field of HVDC transmission lines[J].Proceedings of the CSEE,2013,33(33):152-159(in English).
[18]崔翔,周象贤,卢铁兵.高压直流输电线路离子流场计算方法研究进展[J].中国电机工程学报,2012,32(36):130-141.Cui Xiang,Zhou Xiangxian,Lu Tiebing.Recent progress in the calculation methods of ion flow field of HVDCtransmission lines[J].Proceedings of the CSEE,2012,32(36):130-141(in Chinese).
[19]Jin J.The finite element method in electromagnetics[M].Hoboken:Wiley-IEEE Press,2014:79-102.
[20]王颖,马西奎,邱关源.渐近边界条件在轴对称无界高压静电场计算中的应用[J].高电压技术,1997(1):26-30.Wang Ying,Ma Xikui,Qiu Guanyuan.The application of the asymptotic boundary condition technique in the numerical analysis of axisymmetrical unbounded highvoltage static field[J].High Voltage Engineering,1997(1):26-30(in Chinese).
[21]Barth T,Jespersen D.The design and application of upwind schemes on unstructured meshes[C]//Aiaa Aerospace Sciences Meeting,Reno,Nevada,1989.
[22]Zhang Y,Wu J,Yin Y.A higher-order accurate algorithm based on two-dimensional unstructured mesh for simulation of charge transportation in solid dielectrics[J].IEEE Transactions on Dielectrics and Electrical Insulation,2017,24(5):3165-3172.
[23]兰莉.温度对聚合物绝缘空间电荷行为的影响及数值模型研究[D].上海:上海交通大学,2015.Lan Li.Effect of temperature on space charge distribution and its numerical modeling in polymer insulation[D].Shanghai:Shanghai Jiaotong University,2015(in Chinese).
[24]钱恺羽,张昱,刘德远,等,全尺寸空间电荷测量在水中老化电缆状态评估中的应用[J].高电压技术,2018,44(5):1706-1714.Qian Kaiyu,Zhang Yu,Liu Deyuan,et al.Application of full-size space charge measurement in condition assessment of cables aged in water[J].High Voltage Engineering,2018,44(5):1706-1714(in Chinese).
[25]Liu N,Zhou C,Chen G,et al.Determination of threshold electric field for charge injection in polymeric materials[J].Journal of Applied Physics,2015,106(19):32-44.
[2]Mazzanti G,Marzinotto M.Extruded cables for high voltage direct current transmission:advances in research and development[M].Hoboken:Wiley-IEEE Press,2013:3-4.
[3]Imburgia A,Miceli R,Sanseverino E R,et al.Review of space charge measurement systems:acoustic,thermal and optical methods[J].IEEE Transactions on Dielectrics and Electrical Insulation,2016,23(5):3126-3142.
[4]吴建东,尹毅.周期电场下介质内部空间电荷的检测技术及应用[J].中国电机工程学报,2018,38(5):1572-1581.Wu Jiandong,Yin Yi.Application of space charge detection technology in dielectrics under periodic stress[J].Proceedings of the CSEE,2018,38(5):1572-1581(in Chinese).
[5]Mazzanti G.Space charge measurements in high voltage DC extruded cables in IEEE Standard 1732[J].IEEEElectrical Insulation Magazine,2017,33(4):9-15.
[6]王霞,王陈诚,朱有玉,等,高压直流塑料电缆绝缘用纳米改性交联聚乙烯中的空间电荷特性[J].高电压技术,2015,41(4):1096-1103.Wang Xia,Wang Chencheng,Zhu Youyu,et al.Space charge profiles in XLPE nano dielectrics used for HVDCplastic cable insulation[J].High Voltage Engineering,2015,41(4):1096-1103(in Chinese).
[7]兰莉,吴建东,王雅妮,等,低密度聚乙烯/乙丙橡胶双层介质的界面空间电荷特性[J].中国电机工程学报,2015,35(5):1266-1272.Lan Li,Wu Jiandong,Wang Yani,et al.Space charge property at the interface in low density polyethylene/ethylene propylene rubber double-layered insulation[J].Proceedings of the CSEE,2015,35(5):1266-1272(in Chinese).
[8]Aouabed F,Bayadi A,Rahmani A E,et al.Finite element modelling of electric field and voltage distribution on a silicone insulating surface covered with water droplets[J].IEEE Transactions on Dielectrics and Electrical Insulation,2018,25(2):413-420.
[9]李忠华,陈漳.双层绝缘结构高压直流电缆电场分布仿真[J].高电压技术,2017,43(11):3504-3513.Li Zhonghua,Chen Zhang.Simulation on electric field distribution in HVDC cable with double-layered insulation[J].High Voltage Engineering,2017,43(11):3504-3513(in Chinese).
[10]Li S,Min D,Wang W,et al.Modelling of dielectric breakdown through charge dynamics for polymer nanocomposites[J].IEEE Transactions on Dielectrics and Electrical Insulation,2017,23(6):3476-3485.
[11]Laurent C,Teyssedre G,Roy S L,et al.Charge dynamics and its energetic features in polymeric materials[J].IEEETransactions on Dielectrics and Electrical Insulation,2013,20(2):357-381.
[12]Alison J M,Hill R M.A model for bipolar charge transport,trapping and recombination in degassed crosslinked polyethene[J].Journal of Physics D:Applied Physics,1994,27(6):1291-1299.
[13]Roy S L,Teyssedre G,Laurent C.Charge transport and dissipative processes in insulating polymers:experiments and model[J].IEEE Transactions on Dielectrics and Electrical Insulation,2005,12(4):644-654.
[14]Roy S L,Teyssèdre G,Laurent C.Modelling space charge in a cable geometry[J].IEEE Transactions on Dielectrics and Electrical Insulation,2016,23(4):2361-2367.
[15]Chen G,Zhao J,Li S,et al.Origin of thickness dependent dc electrical breakdown in dielectrics[J].Applied Physics Letters,2012,100(22):2135.
[16]吴建东.低密度聚乙烯纳米复合介质中电荷输运的实验研究和数值模拟[D].上海:上海交通大学,2012.Wu Jiandong.Charge transport investigation in low-density polyethylene/silica nanocomposite based on experiment and numerical simulation[D].Shanghai:Shanghai Jiaotong University,2012(in Chinese).
[17]黄国栋,阮江军,杜志叶,等,改进三维上流元法计算特高压直流线路离子流场[J].中国电机工程学报,2013,33(33):152-159.Huang Guodong,Ruan Jiangjun,Du Zhiye,et al.Improved 3-D upwind FEM for solving ionized field of HVDC transmission lines[J].Proceedings of the CSEE,2013,33(33):152-159(in English).
[18]崔翔,周象贤,卢铁兵.高压直流输电线路离子流场计算方法研究进展[J].中国电机工程学报,2012,32(36):130-141.Cui Xiang,Zhou Xiangxian,Lu Tiebing.Recent progress in the calculation methods of ion flow field of HVDCtransmission lines[J].Proceedings of the CSEE,2012,32(36):130-141(in Chinese).
[19]Jin J.The finite element method in electromagnetics[M].Hoboken:Wiley-IEEE Press,2014:79-102.
[20]王颖,马西奎,邱关源.渐近边界条件在轴对称无界高压静电场计算中的应用[J].高电压技术,1997(1):26-30.Wang Ying,Ma Xikui,Qiu Guanyuan.The application of the asymptotic boundary condition technique in the numerical analysis of axisymmetrical unbounded highvoltage static field[J].High Voltage Engineering,1997(1):26-30(in Chinese).
[21]Barth T,Jespersen D.The design and application of upwind schemes on unstructured meshes[C]//Aiaa Aerospace Sciences Meeting,Reno,Nevada,1989.
[22]Zhang Y,Wu J,Yin Y.A higher-order accurate algorithm based on two-dimensional unstructured mesh for simulation of charge transportation in solid dielectrics[J].IEEE Transactions on Dielectrics and Electrical Insulation,2017,24(5):3165-3172.
[23]兰莉.温度对聚合物绝缘空间电荷行为的影响及数值模型研究[D].上海:上海交通大学,2015.Lan Li.Effect of temperature on space charge distribution and its numerical modeling in polymer insulation[D].Shanghai:Shanghai Jiaotong University,2015(in Chinese).
[24]钱恺羽,张昱,刘德远,等,全尺寸空间电荷测量在水中老化电缆状态评估中的应用[J].高电压技术,2018,44(5):1706-1714.Qian Kaiyu,Zhang Yu,Liu Deyuan,et al.Application of full-size space charge measurement in condition assessment of cables aged in water[J].High Voltage Engineering,2018,44(5):1706-1714(in Chinese).
[25]Liu N,Zhou C,Chen G,et al.Determination of threshold electric field for charge injection in polymeric materials[J].Journal of Applied Physics,2015,106(19):32-44.