高速电力机车主变压器三维油箱损耗分析及温度场计算
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摘要
虽然电力机车主变压器在原理上与普通电力变压器没有太大的差别，但是电力机车主变压器是高漏抗、多绕组变压器，当采用饼式、分裂式绕组时，由于横向漏磁场大，因此油箱的损耗也高。若不采取措施，较大的损耗会使金属构件局部过热，因此，精确的计算油箱损耗非常必要，但传统的计算方法是根据普通变压器的经验公式进行估算，对高漏抗变压器来说，误差较大，且无法准确估算局部过热点，因此需要采用更为准确的有限元数值计算方法。本文引入大型通用有限元软件-ANSYS软件，较系统分析了与研究内容相关的似稳电磁场的基本理论，以及有限元法的基本原理，其中重点介绍了边单元的概念与特点。采用ANSYS软件的边单元法，建立了高速电力机车主变压器油箱三维漏磁场模型，在此基础上较准确地计算出油箱损耗，并与二维计算结果进行了比较，结果表明：三维分析的结果更加准确，而涡流密度分布图为变压器油箱采取更好的屏蔽措施提供了直观的参考；建立了变压器油箱屏蔽的优化模型并采用子问题近似优化算法对油箱屏蔽尺寸进行了优化，在限制最大涡流密度的条件下，使油箱屏蔽体积最小，重量最轻。结果表明：优化后变压器油箱涡流密度分布更加均匀，总损耗降低了4％，但是体积却增加不多，能够为工程实际所接受；最后，建立了变压器油箱三维温度场的有限元模型，按照磁-热弱耦合方法，获得了优化前后油箱稳态温度场的分布，找到了油箱最热点的温升，证明了油箱屏蔽结构是合理的。
Although there is no much difference in theory between electric locomotive main transformer and normal power transformer, electric locomotive main transformer is high leakage reactance and multi-winding one. The transverse leakage magnetic field is intensive when adopting cake and interleave windings, so the losses in tank is high. If no measurements have been taken, the tank wall may have local hot-spot which can deteriorate the transformer performance. It is necessary to calculate accurately the loss in the tank and estimate temperature rise of the hot-spot. The conventional calculating method is to estimate the loss in the tank according to empirical formula of normal transformer. It may have relatively large error for transformer made of high leakage reactance and cannot estimate the local hot-spot accurately, so more accurate finite element method (FEM) is needed. The large universal finite element software -ANSYS is introduced in this paper. The principal theory of quasi-static magnetic filed and ratio
nale of FEM relative to the research is presented systematically, in which edge element method is emphatically discussed. 3-D leakage magnetic field model of high-speed electric locomotive main transformer tank is built using edge element method and accurate tank loss is calculated compared with 2-D analysis model. Result shows 3-D model is more accurate and eddy density distribution pattern provides intuitionistic help for taking better shielding measures. The tank shielding optimization model is presented by limiting maximum eddy density in tank and minimizing shielding volume. Optimization result through subproblem approximation optimization technique indicates eddy current density more uniformly distributed in tank and total losses decrease 4%, but shielding volume adds little, which can be accepted by practical engineering. 3-D steady state temperature field model of transformer tank is built and the local hot-spots and temperature rises before and after optimization are obtained using magneto-thermal w
eak coupling method. Results verify the rationality of tank shielding structure.
Although there is no much difference in theory between electric locomotive main transformer and normal power transformer, electric locomotive main transformer is high leakage reactance and multi-winding one. The transverse leakage magnetic field is intensive when adopting cake and interleave windings, so the losses in tank is high. If no measurements have been taken, the tank wall may have local hot-spot which can deteriorate the transformer performance. It is necessary to calculate accurately the loss in the tank and estimate temperature rise of the hot-spot. The conventional calculating method is to estimate the loss in the tank according to empirical formula of normal transformer. It may have relatively large error for transformer made of high leakage reactance and cannot estimate the local hot-spot accurately, so more accurate finite element method (FEM) is needed. The large universal finite element software -ANSYS is introduced in this paper. The principal theory of quasi-static magnetic filed and ratio
nale of FEM relative to the research is presented systematically, in which edge element method is emphatically discussed. 3-D leakage magnetic field model of high-speed electric locomotive main transformer tank is built using edge element method and accurate tank loss is calculated compared with 2-D analysis model. Result shows 3-D model is more accurate and eddy density distribution pattern provides intuitionistic help for taking better shielding measures. The tank shielding optimization model is presented by limiting maximum eddy density in tank and minimizing shielding volume. Optimization result through subproblem approximation optimization technique indicates eddy current density more uniformly distributed in tank and total losses decrease 4%, but shielding volume adds little, which can be accepted by practical engineering. 3-D steady state temperature field model of transformer tank is built and the local hot-spots and temperature rises before and after optimization are obtained using magneto-thermal w
eak coupling method. Results verify the rationality of tank shielding structure.
引文
[1] P. P. Silvester, Finite Elements for Electrical Engineers, Cambridge University Press, 1990
[2] M. Plonus, Applied electromagnetics, McGraw. Hill, 1978
[3] Y.Inui et al., Effects of Tank and Tank Shields on Magnetic Fields and Stray Losses in Transformer Windings, IEEE Paper C73.101.7, 1973
[4] S. Isaka et al., FEA of Eddy Currents in Transformer Parallel Conductors, IEEE PAS-104, No.10, pp. 2731-2737, 1985
[5] M. A. Coulson, The Development of 3D Electronicmagnetic Solvers for Industrial Design, IEEE MAG.21, 1985
[6] Z.Valkovic, Calculation of Losses in Three Phase Transformer Tanks, IEE Proc. Vol.127, No.1, pp.20-25, 1980
[7] R.S.Girgis, Calculation of Winding Losses in Shell. Form Transformers for Improved Accuracy and Reliability, IEEE PWRD.2, No.2, PP.398-410, 1987
[8] 宫莲等．用等效磁化面电流求解变压器三维漏磁场．清华大学科技报告，1985
[9] 柴建云．大型变压器三维涡流漏磁场计算．清华大学年博士学位论文，1989
[10] 谢德馨等．变压器三维涡流问题有限元解．哈尔滨电工学院学报．1986，2
[11] D.A. Koppiklar, S.V. Kulkarni, P.N. Srinivas, Evaluation of flitch losses in power transformers, IEEE. Transaction on Mags. Vol. 14, No.3, pp. 996-1001. July 1999
[12] Vlatko Cingoski, Akihiro Namera, Kazufumi Kaneda et al, Analysis of Magneto. Thermal Coupled Problem Involving Moving Eddy. Current Conductors, IEEE. Transaction on Mags. Vol. 32, No. 3, pp. 1042-1045, May 1996
[13] Kazuhiro Muramatsu, Norio Takahashi and Takayuki Mimura, Magneto Thermal Fluid Analysis Taking Account of Natural Convection Using Semi-Lagrange Coordinate System, IEEE Trans. on Mags. Vol.35, No.3, pp.1670-1673, May 1999
[14] 何庆宁．交流传动电力机车主变压器计算分析：硕士学位论文．长沙：湖南大学，2001
[15] 胡之光．电机电磁场的分析与计算，北京：机械工业出版社，1982
[16] 汤蕴谬．电机内的电磁场(第二版)．北京：科学出版社．1998年1月
[17] 金建铭．电磁场有限元方法．西安：西安电子科技大学出版社，1998
[18] 张榴晨，徐松，有限元法在电磁计算中的应用．北京：中国铁道出版社，1996
[19] J.P.Webb, Edge Elements and What They can do for You, IEEE Trans. on Mags., Vol.29, No.2, pp.1460-1465, March 1993
[20] Gerrit Mur, Edge element,their Advantages and their Disadvantages, IEEE Trans. on Mags. Vol.30, No.5, pp.3552-3557, September 1994
[21] Cristian Golovanov, Yves Marechal and Gerard Meunier, 3D Edge Element based Formulation coupled to Electric Circuits, IEEE Trans. on Mags. Vol.34, No.5, pp.3162-3165, September 1998
[22] Akihisa kameari, Calculation of Transient 3D Eddy Current Using Edge elements, IEEE Trans. on Mags. Vol.26, No.2, pp.466-469, March 1990
[23] J.A.A. Santos, J.P.A.Bastos, N.Sadowski, Using Laplace's Equation for Defining Magnetizing Current Densities for 3D Analysis with Edge Element, IEEE Trans. on Mags. Vol.35, No.3, pp.1179-1182, May 1999
[24] Biro, O., Preis, K., Magele, C., enhart, W., ichter, K. R., Vrist, G., "Numerical Analysis of 3D Magnetostatic Fields", IEEE Transaction on Magnetics, Vol. 27, No. 5, pp. 3798-3803, 1991
[25] Gyimesi, M. and Ostergaard, D., "Non.Conforming Hexahedral Edge Elements for Magnetic Analysis", (ANSYS, Inc. internal development), submitted to COMPUMAG, Rio, 1997
[26] Preis, K., Bardi, I., Biro, O., Magele, C., Vrisk G., and ichter, K. R., "DifferentFinite Element Formulations of 3..D Magnetostatic Fields", IEEE Transactions on Magnetics, Vol. 28, No. 2, pp. 1056-1059, 1992
[27] Gyimesi, Miklos and Ostergaard, Dale, "Mixed Shape Non..Conforming Edge Elements", CEFC '98, Tucson, AZ, 1998
[28] Ostergaard, Dale and Gyimesi, Miklos, "Analysis of Benchmark Problem, TEAM20 with Various Formulations", Proceedings of the TEAM Workshop, COMPUMAG Rio, pp. 18-20, 1997
[29] Ostergaard, Dale and Gyimesi, Miklos, "Magnetic Corner: Accurate Force Computations", Analysis Solutions, Vol. 1, Issue 2, pp. 10-11, 1997-98
[30] Nedelec, J.C., "Mixed Finite Elements in R~3", Numerical Methods, Vol.35, pp.315-341, 1980
[31] Van Welij, J.S., "Calculation of Eddy Currents in Terms of H on hexahedra", IEEE Transactions on Magnetics, Vol. 18, pp. 431-435, 1982
[32] Kameari, A., "Calculation of Transient 3D Eddy Current Using Edge Elements", IEEE Transacions on Magnetics, Vol. 26, pp. 466-469, 1990
[33] Jin, J., The Finite Element Method in Electromagnetics, John Wiley and Sons, Inc., New York, 1993
[34] Christophe Guerin, Gerard Tanneau, Gerard Meunier, 3D Current Losses Calculation in Transformer Tanks Using the Finite Element Method, IEEE Trans. on Mags. Vol.29, No.2, pp. 1419-1422, March 1993
[35] Yoshihiro Kawase, Takuya Mori and Tomohiro Ota, Magnetic Field Analysis of Coupling Transformer for Electric Vehicle Using 3.D Finite Element Method, IEEE Trans. on Mags. Vol.34, No.5, pp.3186-3189, September 1998
[36] E.E.Kriezis, Stvros M.Panas, Eddy Currents: Theory and Applications,Proceedings of the IEEE, Vol. 80, No. 10, pp. 1559-1581, October 1992
[37] (?)静秋，徐子宏．三相电力变压器短路电抗的数值分析．哈尔滨电工学院学报，1991，14(1)：19-25
[38] С. Б. 瓦修京斯基著，崔立君、杜恩田等译．变压器的理论与计算．机械工业出版社．1983年7月
[39] 沈阳变压器研究所，变压器(内部资料)．第一机械工业部科学技术情报研究所，1981年2月．
[40] 陈保林．最优化理论与算法．北京：请华大学出版社，1989
[41] Makoto Horii, Norio Takahashi, 3-D Optimization of Design Variables in x-, y- and z-Direction of Transformer Tank Shield Model, IEEE Trans. on Mags. Vol.37, No.5, pp.3631-3634, September 2001
[42] Norio Takahashi, Testsuro Kitamura, Makoto Horii, et al. Optimal Design of Tank Shield Model of Transformer, IEEE Trans. on Mags. Vol.36, No.4, pp. 1089-1093, July 2000
[43] Yoshihiro Kawase, Takayuki Ichihashi, Heat Analysis of Thermal Overload Relays Using 3.D Finite Element Method, IEEE Trans. on Mags. Vol.35, No.3, pp.1658-1661, May 1999
[44] 张新波，许承千．电机三维温度场的综合分析．电工技术杂志，2000，3：3-5
[45] 辜成林．电力变压器铁心磁场、损耗和温度场的理论与计算．武汉：华中理工大学出版社，1993
[46] 李伟力，付敏，周封等．基于流体相似理论和三维有限元法计算大中型异步电动机的定子三维温度场，中国电机工程学报，2000，2(5)：14-17
[47] 钱滨江，伍贻文，常家芳等．传热学简明手册．北京：高等教育出版社，1983
[48] 杨世铭．传热学．北京：人民教育出版社，1981
[49] Kay Hameyer, Johan Driesen, Herbert De Gersem and Ronnie Belmans, The Classification of Coupled Field Problems, IEEE Trans. on Mags. Vol.35, No.3, pp.1618-1621, May 1999
[50] 路长柏，朱英浩．电力变压器计算．哈尔滨：黑龙江科学技术出版社，1986
[51] 余德浩，计算数学与科学工程计算及其在中国的若干发展．数学进展，2002，31(1)：1-6
[52] D.Rodger and H.C.Lai, A Surface Impedance Method for 3D Time Transient Problem, IEEE Trans. on Mags. Vol.35, No.3, pp.1369.1371, May 1999
[53] S.A.Holland, L.Haydock, Calculating Stray Losses in Power Transformers Using Surface Impedance with Finite Elements, IEEE Trans. on Mags. Vol.28, No.2, pp. 1355-1358, March 1992
[54] Christophe Guerin, Gerard Meunier, Surface Impedance for 3D Nonlinear Eddy Current Problems Application to Loss Computation in Transformer, IEEE Trans. on Vol.32, No.3, pp.808-811, May 1996
[2] M. Plonus, Applied electromagnetics, McGraw. Hill, 1978
[3] Y.Inui et al., Effects of Tank and Tank Shields on Magnetic Fields and Stray Losses in Transformer Windings, IEEE Paper C73.101.7, 1973
[4] S. Isaka et al., FEA of Eddy Currents in Transformer Parallel Conductors, IEEE PAS-104, No.10, pp. 2731-2737, 1985
[5] M. A. Coulson, The Development of 3D Electronicmagnetic Solvers for Industrial Design, IEEE MAG.21, 1985
[6] Z.Valkovic, Calculation of Losses in Three Phase Transformer Tanks, IEE Proc. Vol.127, No.1, pp.20-25, 1980
[7] R.S.Girgis, Calculation of Winding Losses in Shell. Form Transformers for Improved Accuracy and Reliability, IEEE PWRD.2, No.2, PP.398-410, 1987
[8] 宫莲等．用等效磁化面电流求解变压器三维漏磁场．清华大学科技报告，1985
[9] 柴建云．大型变压器三维涡流漏磁场计算．清华大学年博士学位论文，1989
[10] 谢德馨等．变压器三维涡流问题有限元解．哈尔滨电工学院学报．1986，2
[11] D.A. Koppiklar, S.V. Kulkarni, P.N. Srinivas, Evaluation of flitch losses in power transformers, IEEE. Transaction on Mags. Vol. 14, No.3, pp. 996-1001. July 1999
[12] Vlatko Cingoski, Akihiro Namera, Kazufumi Kaneda et al, Analysis of Magneto. Thermal Coupled Problem Involving Moving Eddy. Current Conductors, IEEE. Transaction on Mags. Vol. 32, No. 3, pp. 1042-1045, May 1996
[13] Kazuhiro Muramatsu, Norio Takahashi and Takayuki Mimura, Magneto Thermal Fluid Analysis Taking Account of Natural Convection Using Semi-Lagrange Coordinate System, IEEE Trans. on Mags. Vol.35, No.3, pp.1670-1673, May 1999
[14] 何庆宁．交流传动电力机车主变压器计算分析：硕士学位论文．长沙：湖南大学，2001
[15] 胡之光．电机电磁场的分析与计算，北京：机械工业出版社，1982
[16] 汤蕴谬．电机内的电磁场(第二版)．北京：科学出版社．1998年1月
[17] 金建铭．电磁场有限元方法．西安：西安电子科技大学出版社，1998
[18] 张榴晨，徐松，有限元法在电磁计算中的应用．北京：中国铁道出版社，1996
[19] J.P.Webb, Edge Elements and What They can do for You, IEEE Trans. on Mags., Vol.29, No.2, pp.1460-1465, March 1993
[20] Gerrit Mur, Edge element,their Advantages and their Disadvantages, IEEE Trans. on Mags. Vol.30, No.5, pp.3552-3557, September 1994
[21] Cristian Golovanov, Yves Marechal and Gerard Meunier, 3D Edge Element based Formulation coupled to Electric Circuits, IEEE Trans. on Mags. Vol.34, No.5, pp.3162-3165, September 1998
[22] Akihisa kameari, Calculation of Transient 3D Eddy Current Using Edge elements, IEEE Trans. on Mags. Vol.26, No.2, pp.466-469, March 1990
[23] J.A.A. Santos, J.P.A.Bastos, N.Sadowski, Using Laplace's Equation for Defining Magnetizing Current Densities for 3D Analysis with Edge Element, IEEE Trans. on Mags. Vol.35, No.3, pp.1179-1182, May 1999
[24] Biro, O., Preis, K., Magele, C., enhart, W., ichter, K. R., Vrist, G., "Numerical Analysis of 3D Magnetostatic Fields", IEEE Transaction on Magnetics, Vol. 27, No. 5, pp. 3798-3803, 1991
[25] Gyimesi, M. and Ostergaard, D., "Non.Conforming Hexahedral Edge Elements for Magnetic Analysis", (ANSYS, Inc. internal development), submitted to COMPUMAG, Rio, 1997
[26] Preis, K., Bardi, I., Biro, O., Magele, C., Vrisk G., and ichter, K. R., "DifferentFinite Element Formulations of 3..D Magnetostatic Fields", IEEE Transactions on Magnetics, Vol. 28, No. 2, pp. 1056-1059, 1992
[27] Gyimesi, Miklos and Ostergaard, Dale, "Mixed Shape Non..Conforming Edge Elements", CEFC '98, Tucson, AZ, 1998
[28] Ostergaard, Dale and Gyimesi, Miklos, "Analysis of Benchmark Problem, TEAM20 with Various Formulations", Proceedings of the TEAM Workshop, COMPUMAG Rio, pp. 18-20, 1997
[29] Ostergaard, Dale and Gyimesi, Miklos, "Magnetic Corner: Accurate Force Computations", Analysis Solutions, Vol. 1, Issue 2, pp. 10-11, 1997-98
[30] Nedelec, J.C., "Mixed Finite Elements in R~3", Numerical Methods, Vol.35, pp.315-341, 1980
[31] Van Welij, J.S., "Calculation of Eddy Currents in Terms of H on hexahedra", IEEE Transactions on Magnetics, Vol. 18, pp. 431-435, 1982
[32] Kameari, A., "Calculation of Transient 3D Eddy Current Using Edge Elements", IEEE Transacions on Magnetics, Vol. 26, pp. 466-469, 1990
[33] Jin, J., The Finite Element Method in Electromagnetics, John Wiley and Sons, Inc., New York, 1993
[34] Christophe Guerin, Gerard Tanneau, Gerard Meunier, 3D Current Losses Calculation in Transformer Tanks Using the Finite Element Method, IEEE Trans. on Mags. Vol.29, No.2, pp. 1419-1422, March 1993
[35] Yoshihiro Kawase, Takuya Mori and Tomohiro Ota, Magnetic Field Analysis of Coupling Transformer for Electric Vehicle Using 3.D Finite Element Method, IEEE Trans. on Mags. Vol.34, No.5, pp.3186-3189, September 1998
[36] E.E.Kriezis, Stvros M.Panas, Eddy Currents: Theory and Applications,Proceedings of the IEEE, Vol. 80, No. 10, pp. 1559-1581, October 1992
[37] (?)静秋，徐子宏．三相电力变压器短路电抗的数值分析．哈尔滨电工学院学报，1991，14(1)：19-25
[38] С. Б. 瓦修京斯基著，崔立君、杜恩田等译．变压器的理论与计算．机械工业出版社．1983年7月
[39] 沈阳变压器研究所，变压器(内部资料)．第一机械工业部科学技术情报研究所，1981年2月．
[40] 陈保林．最优化理论与算法．北京：请华大学出版社，1989
[41] Makoto Horii, Norio Takahashi, 3-D Optimization of Design Variables in x-, y- and z-Direction of Transformer Tank Shield Model, IEEE Trans. on Mags. Vol.37, No.5, pp.3631-3634, September 2001
[42] Norio Takahashi, Testsuro Kitamura, Makoto Horii, et al. Optimal Design of Tank Shield Model of Transformer, IEEE Trans. on Mags. Vol.36, No.4, pp. 1089-1093, July 2000
[43] Yoshihiro Kawase, Takayuki Ichihashi, Heat Analysis of Thermal Overload Relays Using 3.D Finite Element Method, IEEE Trans. on Mags. Vol.35, No.3, pp.1658-1661, May 1999
[44] 张新波，许承千．电机三维温度场的综合分析．电工技术杂志，2000，3：3-5
[45] 辜成林．电力变压器铁心磁场、损耗和温度场的理论与计算．武汉：华中理工大学出版社，1993
[46] 李伟力，付敏，周封等．基于流体相似理论和三维有限元法计算大中型异步电动机的定子三维温度场，中国电机工程学报，2000，2(5)：14-17
[47] 钱滨江，伍贻文，常家芳等．传热学简明手册．北京：高等教育出版社，1983
[48] 杨世铭．传热学．北京：人民教育出版社，1981
[49] Kay Hameyer, Johan Driesen, Herbert De Gersem and Ronnie Belmans, The Classification of Coupled Field Problems, IEEE Trans. on Mags. Vol.35, No.3, pp.1618-1621, May 1999
[50] 路长柏，朱英浩．电力变压器计算．哈尔滨：黑龙江科学技术出版社，1986
[51] 余德浩，计算数学与科学工程计算及其在中国的若干发展．数学进展，2002，31(1)：1-6
[52] D.Rodger and H.C.Lai, A Surface Impedance Method for 3D Time Transient Problem, IEEE Trans. on Mags. Vol.35, No.3, pp.1369.1371, May 1999
[53] S.A.Holland, L.Haydock, Calculating Stray Losses in Power Transformers Using Surface Impedance with Finite Elements, IEEE Trans. on Mags. Vol.28, No.2, pp. 1355-1358, March 1992
[54] Christophe Guerin, Gerard Meunier, Surface Impedance for 3D Nonlinear Eddy Current Problems Application to Loss Computation in Transformer, IEEE Trans. on Vol.32, No.3, pp.808-811, May 1996