铁心材料饱和磁化强度的偏差对求解变压器涌流的影响（英文）
|
摘要
铁磁材料在深度饱和时的磁化曲线是准确计算涌流的前提,而测量的磁化曲线一般不能满足涌流计算的需求。这是因为制作测量深度饱和磁化曲线的装置是很难完成的,而且目前也没有相关的标准。因此,通常基于已测量的数据和磁化原理用方程来大致拟合深度饱和时的磁化曲线。在本文中,磁化曲线通过二次和三次函数(Akima插值法)延拓,并且利用三次函数延拓的曲线更接近可用的测量结果。饱和磁化强度M_s是形成深度饱和磁化曲线的关键参数。本文讨论了M_s对磁化曲线的影响,用非线性暂态的有限元方法分析了M_s对求解变压器涌流的影响。当M_s减小时,磁化曲线下降,动态磁导率下降,因此电流将在一定电压下增加。当电压约为额定电压的1.38倍时,由M_s引起的电流误差最大。研究表明,M_s的5%的偏差会导致涌流计算结果产生66%的偏差。尽管通过测量获得硅钢片的高精度M_s不是一件容易的事情,但应该设法降低其误差,以使得仿真变压器过电压工况时有较高的精度。
The measured magnetizing curve usually fails to meet the requirements of inrush current simulation. Since there are no standards for measuring magnetizing curve by measurement devices, it is usually expressed approximately by a function. In this paper, the magnetizing curves are extended by quadratic and cubic functions(Akima interpolation method), where the cubic function is closer to the available measurement results. Saturation magnetization M_s is a key quantity in forming magnetizing curve in deep saturation. The influences of Ms on the magnetizing curve and the solution of transformer current were analyzed by the nonlinear transient finite element method. When M_s decreases, the magnetizing curve as well as the dynamic permeability goes down, the current hence increases under a certain voltage. When the voltage is about 1.38 times the rated voltage, the errors of the current caused by M_s are maximum. The results show that an error of 5% of Ms can cause an error of 66% of the current solution. Although it is not easy to get high accurate Ms for silicon steel sheet by measurement, its error should be managed to reduce to obtain the relatively high accuracy of the over-voltage operation simulation.
The measured magnetizing curve usually fails to meet the requirements of inrush current simulation. Since there are no standards for measuring magnetizing curve by measurement devices, it is usually expressed approximately by a function. In this paper, the magnetizing curves are extended by quadratic and cubic functions(Akima interpolation method), where the cubic function is closer to the available measurement results. Saturation magnetization M_s is a key quantity in forming magnetizing curve in deep saturation. The influences of Ms on the magnetizing curve and the solution of transformer current were analyzed by the nonlinear transient finite element method. When M_s decreases, the magnetizing curve as well as the dynamic permeability goes down, the current hence increases under a certain voltage. When the voltage is about 1.38 times the rated voltage, the errors of the current caused by M_s are maximum. The results show that an error of 5% of Ms can cause an error of 66% of the current solution. Although it is not easy to get high accurate Ms for silicon steel sheet by measurement, its error should be managed to reduce to obtain the relatively high accuracy of the over-voltage operation simulation.
引文
[1]Specification of individual materials-cold-rolled nonoriented electrical steel strip and sheet delivered in the fully-processed state[S].IEC Standard,60404-8-4,1998.
[2]IEC 60404-2-1996 Magnetic materials-Part 2:Methods of measurement of the magnetic properties of electrical steel sheet and strip by means of an Epstein frame[S].1996.
[3]Otome D,Nakano M,Takahashi N.Development of measurement system of magnetic properties at high flux density using novel single-sheet tester[J].IEEETransactions on Magnetics,2009,45(10):3889-3892.
[4]Qu Qing Chang.Precise magnetic properties measurement on electrical sheet steels under deep saturation[J].IEEE Transactions on Magnetics,1984,20(5):1717-1719.
[5]Hofmann M,Kahraman D,Herzog H G,et al.Numerical determination of the effective magnetic path length of a single-sheet tester[J].IEEE Transactions on Magnetics,2014,50(2):7023004.
[6]Cheng Z G,Takahashi N,Forghani B.Electromagnetic and thermal field modeling and application in electrical engineering[M].Beijing:Science Press,2009.
[7]Knight A M,Dorrell D G.Improving the torque prediction of saturated automotive drive machines by accurate representation of saturated curves[J].IEEETransactions on Magnetics,2012,48(11):4630-4633.
[8]He Xiaoqing,Liu Shuping,Li Panhong,et al.Eliminating the single-phase transformer inrush current based on pre-magnetizing[J].Power System Protection and Control,2014,42(17):120-124.
[9]Yao Dongxiao,Deng Maojun,Ni Chuankun,et al.Transformer's multi-side inrush current generation mechanism and its influence on the differential protection's fast action zone[J].Power System Protection and Control,2016,44(5):36-41.
[10]Hurt D,Li S,Amann A.Versatile SQUID susceptometer with multiple measurement modes[J].IEEETransactions on Magnetics,2013,49(7):3541-3544.
[11]Li S,Hurt D,Toth M,et al.A low background magneto-optic probe for high sensitivity SQUIDsusceptometer[J].IEEE Transactions on Magnetics,2014,50(11):1-4.
[12]Zhao Xiaojun,Li Lin,Cheng Zhiguang,et al.Analysis of magnetizing characteristic of laminated core based on the DC-biasing experiment[J].Transactions of China Electrotechnical Society,2011,26(1):8-13.
[13]Vakilian M,Degeneff R C.A method for modeling nonlinear core characteristics of transformers during transients[J].IEEE Transactions on Power Delivery,1994,9(4):1916-1925.
[14]Rioual M,Guillot Y,Crepy C.Determination of the saturated inductance of transformers by analytical formulae,comparison with an electromagnetic field calculation approach and validation by on-site tests[C]//IEEE Power Tech Conference,Bucharest,Romania,2009:1-6.
[15]Chi Qingguang,Zhang Yanli,Ren Yajun,et al.Improvement on rotational loss model and measurement of local loss in the iron core[J].Power System Protection and Control,2018,33(17):3951-3957.
[16]Qiao Ji,Xu Zhiwei,Zou Jun,et al.A high-accuracy iterative method of characteristics without deutsch assumption for calculating ion-flow field of HVDCoverhead lines[J].Transactions of China Electrotechnical Society,2018,33(19):4419-4425.
[17]Zhang Pengfei,Zou Jun,Wu Xiaogang,et al.A fast and precise method for calculating dynamic inductance of common mode chock[J].Transactions of China Electrotechnical Society,2018,33(19):4458-4466.
[18]Chen Bin,Li Lin,Zhao Zhibin.Calculation of highpower high-frequency transformer's copper loss and magnetic core loss in dual-active-bridge DC-DCconverter[J].Transactions of China Electrotechnical Society,2017,32(22):124-133.
[19]Zhang Yanli,Peng Zhihua,Xie Dexin,et al.Effect of different magnetization curves on simulation for transformer core loss under DC bias[J].Transactions of China Electrotechnical Society,2014,29(5):43-47.
[20]Chen Junquan,Wang Dong,Chen Zhihua,et al.Review of precise modeling technology of electrical soft magnetic material applied in vessel equipment[J].Transactions of China Electrotechnical Society,2017,32(22):167-175.
[21]Shao Wenquan,Qiao Ni,Wang Jianbo.A novel algorithm of identifying inrush current based on waveform cross-correlation coefficient[J].Power System Protection and Control,2015,43(23):15-20.
[2]IEC 60404-2-1996 Magnetic materials-Part 2:Methods of measurement of the magnetic properties of electrical steel sheet and strip by means of an Epstein frame[S].1996.
[3]Otome D,Nakano M,Takahashi N.Development of measurement system of magnetic properties at high flux density using novel single-sheet tester[J].IEEETransactions on Magnetics,2009,45(10):3889-3892.
[4]Qu Qing Chang.Precise magnetic properties measurement on electrical sheet steels under deep saturation[J].IEEE Transactions on Magnetics,1984,20(5):1717-1719.
[5]Hofmann M,Kahraman D,Herzog H G,et al.Numerical determination of the effective magnetic path length of a single-sheet tester[J].IEEE Transactions on Magnetics,2014,50(2):7023004.
[6]Cheng Z G,Takahashi N,Forghani B.Electromagnetic and thermal field modeling and application in electrical engineering[M].Beijing:Science Press,2009.
[7]Knight A M,Dorrell D G.Improving the torque prediction of saturated automotive drive machines by accurate representation of saturated curves[J].IEEETransactions on Magnetics,2012,48(11):4630-4633.
[8]He Xiaoqing,Liu Shuping,Li Panhong,et al.Eliminating the single-phase transformer inrush current based on pre-magnetizing[J].Power System Protection and Control,2014,42(17):120-124.
[9]Yao Dongxiao,Deng Maojun,Ni Chuankun,et al.Transformer's multi-side inrush current generation mechanism and its influence on the differential protection's fast action zone[J].Power System Protection and Control,2016,44(5):36-41.
[10]Hurt D,Li S,Amann A.Versatile SQUID susceptometer with multiple measurement modes[J].IEEETransactions on Magnetics,2013,49(7):3541-3544.
[11]Li S,Hurt D,Toth M,et al.A low background magneto-optic probe for high sensitivity SQUIDsusceptometer[J].IEEE Transactions on Magnetics,2014,50(11):1-4.
[12]Zhao Xiaojun,Li Lin,Cheng Zhiguang,et al.Analysis of magnetizing characteristic of laminated core based on the DC-biasing experiment[J].Transactions of China Electrotechnical Society,2011,26(1):8-13.
[13]Vakilian M,Degeneff R C.A method for modeling nonlinear core characteristics of transformers during transients[J].IEEE Transactions on Power Delivery,1994,9(4):1916-1925.
[14]Rioual M,Guillot Y,Crepy C.Determination of the saturated inductance of transformers by analytical formulae,comparison with an electromagnetic field calculation approach and validation by on-site tests[C]//IEEE Power Tech Conference,Bucharest,Romania,2009:1-6.
[15]Chi Qingguang,Zhang Yanli,Ren Yajun,et al.Improvement on rotational loss model and measurement of local loss in the iron core[J].Power System Protection and Control,2018,33(17):3951-3957.
[16]Qiao Ji,Xu Zhiwei,Zou Jun,et al.A high-accuracy iterative method of characteristics without deutsch assumption for calculating ion-flow field of HVDCoverhead lines[J].Transactions of China Electrotechnical Society,2018,33(19):4419-4425.
[17]Zhang Pengfei,Zou Jun,Wu Xiaogang,et al.A fast and precise method for calculating dynamic inductance of common mode chock[J].Transactions of China Electrotechnical Society,2018,33(19):4458-4466.
[18]Chen Bin,Li Lin,Zhao Zhibin.Calculation of highpower high-frequency transformer's copper loss and magnetic core loss in dual-active-bridge DC-DCconverter[J].Transactions of China Electrotechnical Society,2017,32(22):124-133.
[19]Zhang Yanli,Peng Zhihua,Xie Dexin,et al.Effect of different magnetization curves on simulation for transformer core loss under DC bias[J].Transactions of China Electrotechnical Society,2014,29(5):43-47.
[20]Chen Junquan,Wang Dong,Chen Zhihua,et al.Review of precise modeling technology of electrical soft magnetic material applied in vessel equipment[J].Transactions of China Electrotechnical Society,2017,32(22):167-175.
[21]Shao Wenquan,Qiao Ni,Wang Jianbo.A novel algorithm of identifying inrush current based on waveform cross-correlation coefficient[J].Power System Protection and Control,2015,43(23):15-20.