基于混合法的油浸式变压器二维瞬态温度场仿真
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摘要
温升是影响油浸式变压器正常运行的重要因素,为了得到变压器的温度场分布,提出一种基于混合方法的多物理场计算方法。对于油浸式变压器流体场和温度场的强耦合问题,混合方法考虑了温度对媒质物性参数的影响,采用迎风有限体积法和迎风有限元法依次计算流体场和温度场,即流体场和温度场依次循环求解,最终得到油浸式变压器启动过程瞬态温度场和稳态温度场。为了验证文中算法的有效性,采用换流变压器二维简化模型,分别采用文中方法和多物理场仿真软件Comsol计算了常温下的稳态温度场,计算结果验证了混合方法的准确性和有效性。在验证文中算法有效性的基础上,利用该方法分析了换流变压器常温环境下启动过程的瞬态温度场分布,分析结果可为工程提供参考。
The temperature rise of oil-immersed power transformer is a vital factor that affects its performance. In this paper,a multi-physical field calculation method based on hybrid method is presented for obtaining the temperature distribution in the power transformer. In view of the strong coupling between thermal and fluid field, the influence of the temperature on the physical parameters of the material is considered by the proposed hybrid method. The velocity distribution is calculated firstly by solving the governing equation of fluid field used the upwind finite volume method. Then, the upwind finite element method is used to obtain the temperature distribution of thermal field. The fluid and thermal field are solved iteratively, and finally, the transient and the steady-state temperature field of the transformer are obtained during its starting period. To verify the validity of the proposed method, a two-dimensional simplified model of converter transformer has been adopted. The proposed multi-physical field method is applied to calculate the steady-state temperature distribution of converter transformer under ambient temperature, and the result of the proposed method is compared with software Comosol. It shows that the thermal distribution computed by the proposed method is in very good agreement with the results calculated by the commercial software Comosol,which proves the accuracy and validity of the proposed method. Based on the validity of the proposed algorithm, the transient temperature distribution of converter transformer during its starting period is analyzed under ambient temperature. The analysis results can be provided as references for engineering practice.
The temperature rise of oil-immersed power transformer is a vital factor that affects its performance. In this paper,a multi-physical field calculation method based on hybrid method is presented for obtaining the temperature distribution in the power transformer. In view of the strong coupling between thermal and fluid field, the influence of the temperature on the physical parameters of the material is considered by the proposed hybrid method. The velocity distribution is calculated firstly by solving the governing equation of fluid field used the upwind finite volume method. Then, the upwind finite element method is used to obtain the temperature distribution of thermal field. The fluid and thermal field are solved iteratively, and finally, the transient and the steady-state temperature field of the transformer are obtained during its starting period. To verify the validity of the proposed method, a two-dimensional simplified model of converter transformer has been adopted. The proposed multi-physical field method is applied to calculate the steady-state temperature distribution of converter transformer under ambient temperature, and the result of the proposed method is compared with software Comosol. It shows that the thermal distribution computed by the proposed method is in very good agreement with the results calculated by the commercial software Comosol,which proves the accuracy and validity of the proposed method. Based on the validity of the proposed algorithm, the transient temperature distribution of converter transformer during its starting period is analyzed under ambient temperature. The analysis results can be provided as references for engineering practice.
引文
[1]陈庆国,侯帅,池明赫,等.换流变压器出线装置电场分布与绝缘结构优化[J].高电压技术,2013,12(39):2859-2868.CHEN Qingguo, HOU Shuai.CHI Minghe, et al. Electric field distribution in convertor transformer outlet device and its insulation structure optimization[J]. High Voltage Engineering,2013,12(39):2859-2868.
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[5] LIAO C, RUAN J, LIU C, et al. 3-D coupled electromagnetic-fluid-thermal analysis of oil-immersed triangular wound core transformer[J]. IEEE Transactions on Magnetics, 2014, 50(11):1-4.
[6] EBENEZER M, RAMACHANDRALAL R M, PILLAI SARASAMMA C N. Study and analysis of the effect of harmonics on the hot spot temperature of a distribution transformer using finite-volume method[J]. Electric Power Components and Systems, 2015, 43(20):2251-2261.
[7]朱海兵,李晓健,吴奕,等.变压器温度场分布的热流耦合分析[J].南京工程学院学报(自然科学版),2015,13(3):74-78.ZHU Haibing, LI Xiaojian, WU Yi, et al. Thermal-fluid coupled field analysis for temperature distribution in the power transformer[J]. Journal of Nanjing Engineering College(Natural Science Edition), 2015,13(3):74-78.
[8] JEONG G Y, JANG S P, LEE H Y, et al. Magnetic-thermal-fluidic analysis for cooling performance of magnetic nanofluids comparing with transformer oil and air by using fully coupled finite element method[J]. IEEE Transactions on Magnetics,2013,49(5):1865-1868.
[9]兰贞波,文武,阮江军,等.基于有限元法的干式变压器多物理场分析计算[J].高压电器,2015,51(8):107-113.LAN Zhenbo, WEN Wu, RUAN Jiangjun, et al. Analysis of multi-physical field in ventilated dry-type transformer with FEM method[J]. High Voltage Apparatus, 2015, 51(8):107-113.
[10] XIE B, LI S, IKEBATA A, et al. A multi-moment finite volume method for incompressible navier-stokes equations on unstructured grids:Volume-average/point-value formulation[J]. Journal of Computational Physics, 2014(277):138-162.
[11]岳国良,王永强,何杰,等.基于FVM的大型油浸式变压器风机控制策略研究[J].高压电器,2016, 52(7):116-122.YUE Guoliang, WANG Yongqiang, HE Jie, et al. Research of strategies based on FVM for large oil-immersed power transformer's fan control[J]. High Voltage Apparatus, 2016,52(7):116-122.
[12]熊英,关晖,吴锤结.基于有限体积法的非结构网格大涡模拟离散方法研究[J].应用数学和力学,2016,37(11):1129-1144.XIONG Ying, GUAN Hui, WU Chuijie. Large eddy simulation based on finite volume method of unstructured grid simulation discrete method research[J]. Journal of AppliedMathematics and Mechanics, 2016,37(11):1129-1144.
[13]柳思源,刘韩生,董瑜.考虑迎风性的高精度水击数值模拟[J].人民黄河,2015, 37(11):107-109.LIU Siyuan, LIU Hansheng, DONG Yu. Considering the wind resistance of high precision numerical simulation[J].Water Hammer The People of the Yellow River, 2015,37(11):107-109.
[14] ETEIBA M B, AZIZ M M A, SHAZLY J H. Heat conduction problems in gas cooled-insulated power transformers solved by the finite-element method[J]. IEEE Transactions on Power Delivery, 2008, 23(3):1457-1463.
[15] PREIS K,BIRO 0, BUCHGRABER G,et al. Thermalelectromagnetic coupling in the finite-element simulation of power transformers[J]. IEEE Transactions on Magnetics,2006, 42(4):999-1002.
[16] ALLAHBAKHSHI M, AKBARI M. Heat analysis of the power transformer bushings using the finite element method[J]. Applied Thermal Engineering, 2016,100(1):714-720.
[17] J00 H W, LEE C H, RHO J S, et al. Analysis of temperature rise for piezoelectric transformer using finite-element method[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2006, 53(8):1449-1457.
[18]李立毅,黄旭珍,寇宝泉,等.基于有限元法的圆筒型直线电机温度场数值计算[J].电工技术学报,2013,28(2):132-138.LI Liyi, HUANG Xuzhen, KOU Baoquan, et al. Numerical calculation of temperature field for tubular linear motor based on finite element method[J]. Transactions of China Electrotechnical Society, 2013,28(2):132-138.
[19] HENDRIANA D, BATHE K J. On upwind methods for parabolic finite elements in incompressible flows[J]. International Journal for Numerical Methods in Engineering,2000,47(3):317-340.
[20] BROOKS A N, HUGHES T J. Streamline upwind/petrovgalerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[J]. Computer methods in applied mechanics and engineering, 1982,32(1):199-259.
[21] ZIENKIEWICZ O C,TAYLOR R L,NITHIARASU P. The finite element method for fluid dynamics[M]. 6th edition.Burlington, MA:Butterworth-Heinemann,2005:28-50.
[22]景崇友,王建民,陈志伟,等.换流变压器绕组瞬态漏磁场与谐波损耗的分析[J].变压器,2007,44(4):1-4.JING Chongyou, WANG Jianmin, CHEN Zhiwei, et al.analysis of transient leakage field and harmonic losses inwindings of converter transformers[J]. Transformer, 2007,44(4):1-4.
[23]刘旸.大型换流变压器损耗分析与计算[D].哈尔滨:哈尔滨理工大学,2010.LIU Yang. Analysis and calculation of loss in giant convert-er transformer[D]. Harbin:Harbin University of Science and Technology, 2010.
[24]孔庆奕,程志光,李悦宁.取向硅钢片在不同环境温度下的磁特性[J].高电压技术,2014, 40(9):2743-2749.KONG Qingyi CHENG Zhiguang, LI Yuening. Magnetic properties of oriented silicon steel sheet under different ambient temperatures[J]. High Voltage Engineering, 2014,40(9):2743-2749.
[25]韩芳旭.换流变压器谐波损耗及热问题的计算与分析[D].沈阳:沈阳工业大学,2011.HAN Fangxu. Calculation and analysis of harmonic loss and thermal problems on converter transformer[D]. Shenyang:Shenyang University of Technology, 2011.
[26]汤寒松.一种NS方程上风有限元[J].长沙:长沙交通学院学报,1987,23(2):10.TANG Hansong. A NS equation upwind finite element method[J]. Transactions of Changsha Communication College, 1987,23(2):10.
[27]刘国坚,王丰华.树脂浇注干式变压器温度场分布的计算分析[J].高压电器,2016, 52(8):83-89.LIU Guojian, WANG Fenghua. Temperature field calculation and analysis of cast-resin dry-type transformers[J]. High Voltage Apparatus, 2016, 52(8):83-89.
[28]王建军,陆明万,张雄.流体力学Petrov-Galerkin有限元法研究进展[J].计算力学学报,1998,15(4):495-502.WANG Jianjun, LU Mingwan, ZHANG Xiong. Research progress of fluid mechanics Petrov-Galerkin finite element method[J]. Chinese Journal of Computational mechanics,1998,15(4):495-502.
[2]周孝信,陈树勇,鲁宗相.电网和电网技术发展的回顾与展望—试论三代电网[J].中国电机工程学报,2013,33(22):1-11.ZHOU Xiaoxin, CHEN Shuyong,LU Zongxiang. Review and prospect for power system development and related technologies:A concept of three generation power systems[J].Proceedings of the CSEE,2013,33(22):1-11.
[3]刘振亚.全球能源互联网[M].北京:中国电力出版社,2015:272-273.LIU Zhenya. Global energy internet[M]. Beijing:China Electric Power Press,2015:272-273.
[4]王永强,马伦,律方成,等.基于有限差分和有限体积法相结合的油浸式变压器三维温度场计算[J].高电压技术,2014, 40(10):3179-3185.WANG Yongqiang, MA Lun, LYU Fangcheng, et al. Calculation of 3D temperature field of oil immersed transformer by the combination of the finite element and finite volume method[J]. High Voltage Engineering,2014,40(10):3179-3185.
[5] LIAO C, RUAN J, LIU C, et al. 3-D coupled electromagnetic-fluid-thermal analysis of oil-immersed triangular wound core transformer[J]. IEEE Transactions on Magnetics, 2014, 50(11):1-4.
[6] EBENEZER M, RAMACHANDRALAL R M, PILLAI SARASAMMA C N. Study and analysis of the effect of harmonics on the hot spot temperature of a distribution transformer using finite-volume method[J]. Electric Power Components and Systems, 2015, 43(20):2251-2261.
[7]朱海兵,李晓健,吴奕,等.变压器温度场分布的热流耦合分析[J].南京工程学院学报(自然科学版),2015,13(3):74-78.ZHU Haibing, LI Xiaojian, WU Yi, et al. Thermal-fluid coupled field analysis for temperature distribution in the power transformer[J]. Journal of Nanjing Engineering College(Natural Science Edition), 2015,13(3):74-78.
[8] JEONG G Y, JANG S P, LEE H Y, et al. Magnetic-thermal-fluidic analysis for cooling performance of magnetic nanofluids comparing with transformer oil and air by using fully coupled finite element method[J]. IEEE Transactions on Magnetics,2013,49(5):1865-1868.
[9]兰贞波,文武,阮江军,等.基于有限元法的干式变压器多物理场分析计算[J].高压电器,2015,51(8):107-113.LAN Zhenbo, WEN Wu, RUAN Jiangjun, et al. Analysis of multi-physical field in ventilated dry-type transformer with FEM method[J]. High Voltage Apparatus, 2015, 51(8):107-113.
[10] XIE B, LI S, IKEBATA A, et al. A multi-moment finite volume method for incompressible navier-stokes equations on unstructured grids:Volume-average/point-value formulation[J]. Journal of Computational Physics, 2014(277):138-162.
[11]岳国良,王永强,何杰,等.基于FVM的大型油浸式变压器风机控制策略研究[J].高压电器,2016, 52(7):116-122.YUE Guoliang, WANG Yongqiang, HE Jie, et al. Research of strategies based on FVM for large oil-immersed power transformer's fan control[J]. High Voltage Apparatus, 2016,52(7):116-122.
[12]熊英,关晖,吴锤结.基于有限体积法的非结构网格大涡模拟离散方法研究[J].应用数学和力学,2016,37(11):1129-1144.XIONG Ying, GUAN Hui, WU Chuijie. Large eddy simulation based on finite volume method of unstructured grid simulation discrete method research[J]. Journal of AppliedMathematics and Mechanics, 2016,37(11):1129-1144.
[13]柳思源,刘韩生,董瑜.考虑迎风性的高精度水击数值模拟[J].人民黄河,2015, 37(11):107-109.LIU Siyuan, LIU Hansheng, DONG Yu. Considering the wind resistance of high precision numerical simulation[J].Water Hammer The People of the Yellow River, 2015,37(11):107-109.
[14] ETEIBA M B, AZIZ M M A, SHAZLY J H. Heat conduction problems in gas cooled-insulated power transformers solved by the finite-element method[J]. IEEE Transactions on Power Delivery, 2008, 23(3):1457-1463.
[15] PREIS K,BIRO 0, BUCHGRABER G,et al. Thermalelectromagnetic coupling in the finite-element simulation of power transformers[J]. IEEE Transactions on Magnetics,2006, 42(4):999-1002.
[16] ALLAHBAKHSHI M, AKBARI M. Heat analysis of the power transformer bushings using the finite element method[J]. Applied Thermal Engineering, 2016,100(1):714-720.
[17] J00 H W, LEE C H, RHO J S, et al. Analysis of temperature rise for piezoelectric transformer using finite-element method[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2006, 53(8):1449-1457.
[18]李立毅,黄旭珍,寇宝泉,等.基于有限元法的圆筒型直线电机温度场数值计算[J].电工技术学报,2013,28(2):132-138.LI Liyi, HUANG Xuzhen, KOU Baoquan, et al. Numerical calculation of temperature field for tubular linear motor based on finite element method[J]. Transactions of China Electrotechnical Society, 2013,28(2):132-138.
[19] HENDRIANA D, BATHE K J. On upwind methods for parabolic finite elements in incompressible flows[J]. International Journal for Numerical Methods in Engineering,2000,47(3):317-340.
[20] BROOKS A N, HUGHES T J. Streamline upwind/petrovgalerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations[J]. Computer methods in applied mechanics and engineering, 1982,32(1):199-259.
[21] ZIENKIEWICZ O C,TAYLOR R L,NITHIARASU P. The finite element method for fluid dynamics[M]. 6th edition.Burlington, MA:Butterworth-Heinemann,2005:28-50.
[22]景崇友,王建民,陈志伟,等.换流变压器绕组瞬态漏磁场与谐波损耗的分析[J].变压器,2007,44(4):1-4.JING Chongyou, WANG Jianmin, CHEN Zhiwei, et al.analysis of transient leakage field and harmonic losses inwindings of converter transformers[J]. Transformer, 2007,44(4):1-4.
[23]刘旸.大型换流变压器损耗分析与计算[D].哈尔滨:哈尔滨理工大学,2010.LIU Yang. Analysis and calculation of loss in giant convert-er transformer[D]. Harbin:Harbin University of Science and Technology, 2010.
[24]孔庆奕,程志光,李悦宁.取向硅钢片在不同环境温度下的磁特性[J].高电压技术,2014, 40(9):2743-2749.KONG Qingyi CHENG Zhiguang, LI Yuening. Magnetic properties of oriented silicon steel sheet under different ambient temperatures[J]. High Voltage Engineering, 2014,40(9):2743-2749.
[25]韩芳旭.换流变压器谐波损耗及热问题的计算与分析[D].沈阳:沈阳工业大学,2011.HAN Fangxu. Calculation and analysis of harmonic loss and thermal problems on converter transformer[D]. Shenyang:Shenyang University of Technology, 2011.
[26]汤寒松.一种NS方程上风有限元[J].长沙:长沙交通学院学报,1987,23(2):10.TANG Hansong. A NS equation upwind finite element method[J]. Transactions of Changsha Communication College, 1987,23(2):10.
[27]刘国坚,王丰华.树脂浇注干式变压器温度场分布的计算分析[J].高压电器,2016, 52(8):83-89.LIU Guojian, WANG Fenghua. Temperature field calculation and analysis of cast-resin dry-type transformers[J]. High Voltage Apparatus, 2016, 52(8):83-89.
[28]王建军,陆明万,张雄.流体力学Petrov-Galerkin有限元法研究进展[J].计算力学学报,1998,15(4):495-502.WANG Jianjun, LU Mingwan, ZHANG Xiong. Research progress of fluid mechanics Petrov-Galerkin finite element method[J]. Chinese Journal of Computational mechanics,1998,15(4):495-502.