变压器直流偏磁研究
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摘要
直流偏磁现象是指有直流电流经过中性点流入到电力变压器的绕组中,从而使变压器处于非正常工作状态。引起直流偏磁现象的原因有两种,第一种是在高压直流输电系统中,当采用单极大地回线运行方式或双极不对称运行方式时,大地中回流的直流电流就会流入到中性点接地的变压器绕组；第二种是由于地磁场与太阳等离子风的动态变化相互作用,产生地磁风暴,使地磁场发生变化,这种变化在地球表面产生了电位梯度,就会有低频感应电流流入变压器绕组,由于其频率非常低,可近似认为是直流电流。
直流偏磁下变压器的工作点发生了偏移,其铁芯迅速进入到饱和状态,严重影响其正常工作,产生许多不良后果,如励磁电流幅值明显增大,波形发生严重的畸变,谐波含量增大；变压器铁芯噪声增大,振动加剧；变压器漏磁增加,损耗与温升增大,从而引起金属结构件局部过热；电力系统继电保护装置可能误动作等。总之,直流偏磁现象危害了变压器及电力系统的安全运行,因此,变压器直流偏磁现象备受关注。
本文在深入研究直流偏磁现象物理机理的基础上,对直流偏磁下的变压器进行了实验测量与仿真计算。研究内容如下：
首先,对直流偏磁下的单相变压器、三相三柱变压器和三相五柱变压器提出可行的实验方案,测量直流偏磁下单相变压器和三相变压器的励磁电流及B-H曲线的变化。
其次,首次建立了直流偏磁下单相变压器的传输线模型,模型中,将变压器电路中的微分项离散,并应用J-A铁磁磁滞理论来描述铁芯的饱和以及磁滞效应。涡流损耗用含等值电阻的附加绕组替代,同时考虑绕组铜耗及漏磁等因素,从而使变压器模型得到充分完整的描述。最后利用牛顿-拉夫逊迭代方法,对直流偏磁下的单相变压器进行了时域仿真计算,实现直流偏磁下单相变压器的分析,并与实验获得的数据进行比较,验证该计算模型及计算方法的有效性和正确性。
首次建立了直流偏磁下三相变压器组的传输线模型,并利用牛顿-拉夫逊迭代方法对其进行计算仿真,仿真结果证明所提出的计算模型能够准确的分析三相变压器组的直流偏磁现象。
建立了新的直流偏磁下三相三柱变压器和三相五柱变压器的电路-磁路耦合模型,磁路模型中,考虑了变压器的涡流损耗、铁芯拓扑结构及材料的饱和特性,并将涡流产生的磁动势列入磁路方程,与电路方程进行耦合,并结合铁芯的非线性特征曲线,形成了非线性方程组,通过求解该方程组,最终实现对三相三柱变压器和三相五柱变压器直流偏磁特性的仿真计算,并与实验获得的数据进行比较,从而验证了计算模型能够准确的分析三相三柱变压器和相五柱变压器的直流偏磁现象。
最后,指出了限制直流电流流过变爪器绕组的三种措施：①反向注入电流法,②串联电容法,③串联电阻法,并对这三种措施进行仿真研究。
Direct current (DC) bias phenomenon is that the DC flows into the windings of the transformers through neutral point, which is an abnormal work station. There are two reasons which arose DC bias:One is the monopolar ground circuit operation mode or the bipolar asymmetrically operation mode of the HVDC transmission system. Under this situation, DC will pass by the windings of the transformers through the earthed neutral point. The other is Geomagnetically Induced Current (GIC) which is caused by the interaction of the geomagnetic field and the dynamic movement of the ionic wind. The change of the geomagnetic field produces electric potential gradient, which give rise to low-frequency induction current. It is DC because its frequency is very low.
The work point of the transformer under DC bias will shifts, and its iron will be saturated which affect the normal work of the transformer seriously. This gives rise to lots of bad influence. for example, the peak value of the exciting current increases significantly, and the waveform of the current is seriously distorted with a lot of harmonics; the heavy noise; the serious vibration; the increases of transformer's leakage and losses and temperature build-up; the local heating of metal structures; the malfunction of relay protection devices of electric power system; which endanger the operation safety of the transformers and electric power system. So the DC bias phenomenon of the transformer is concerned.
This paper make a thorough study of the physical mechanism of DC bias. On this basis, the transformer under DC bias is studied by experiment and calculated by simulation. The main research contents are as following:
Firstly, the feasible experiment scheme of the single-phase transformer and the three-phase three-legged transformer and three-phase five-legged transformer under DC bias is proposed. The exciting currents and B-H curve of the transformers under DC bias are measured.
Secondly, this paper proposes a novel transmission-line model (TLM) of the single-phase transformer under DC bias. In the model, the differential terms in transformer circuit model are discretized. The saturation characteristic and hysteresis effect is described on the basis of J-A ferromagnetic hysteresis theory, and the eddy-current losses resulting from the flux paths through legs are replaced by an equivalent resistance. Furthermore, the copper losses and flux leakage of the primary and secondary windings are also included. So the transformer is described sufficiently and completely. At last, the Newton-Raphson technique is chosen to calculate the model. The results compare with the experiment results. That demonstrates the validity of the TLM and effectiveness of analyzing the DC bias phenomenon of the single-phase transformer.
The TLM of the three-phase transformer under DC bias is build. And the Newton-Raphson technique is chosen to calculate the model. The simulation results demonstrate that the TLM can exactly analyze the phenomenon of the three-phase transformer under DC bias.
A novel coupling model of electric circuit and magnetic circuit of the three-phase three-legged transformer and three-phase five-legged transformer under DC bias is built. In the magnetic circuit model, the eddy-current losses, the core topology and the saturation characteristic of the core material are taken into account. The magnetomotive force due to eddy current is given in magnetic circuit equations. By combining an electrical circuit with nonlinear characteristic curve of the core, nonlinear equations can be obtained. A series of mathematic transformation are performed and numerical nonlinear algebraic equations are solved finally. Meanwhile DC bias problem of the three-phase three-legged transformer and three-phase five-legged transformers are analyzed. The simulation results compare with the experiment results. That demonstrate the validity of the coupling models and effectiveness of analyzing the DC bias phenomenon of the three-phase three-legged transformer and three-phase five-legged transformer.
Lastly, this paper introduces several measures of restraining DC bias based on theory analysis.①reverse current method②series-capacitor method③ series-resistanee method. The three measures are studied by simulation.
直流偏磁下变压器的工作点发生了偏移,其铁芯迅速进入到饱和状态,严重影响其正常工作,产生许多不良后果,如励磁电流幅值明显增大,波形发生严重的畸变,谐波含量增大；变压器铁芯噪声增大,振动加剧；变压器漏磁增加,损耗与温升增大,从而引起金属结构件局部过热；电力系统继电保护装置可能误动作等。总之,直流偏磁现象危害了变压器及电力系统的安全运行,因此,变压器直流偏磁现象备受关注。
本文在深入研究直流偏磁现象物理机理的基础上,对直流偏磁下的变压器进行了实验测量与仿真计算。研究内容如下：
首先,对直流偏磁下的单相变压器、三相三柱变压器和三相五柱变压器提出可行的实验方案,测量直流偏磁下单相变压器和三相变压器的励磁电流及B-H曲线的变化。
其次,首次建立了直流偏磁下单相变压器的传输线模型,模型中,将变压器电路中的微分项离散,并应用J-A铁磁磁滞理论来描述铁芯的饱和以及磁滞效应。涡流损耗用含等值电阻的附加绕组替代,同时考虑绕组铜耗及漏磁等因素,从而使变压器模型得到充分完整的描述。最后利用牛顿-拉夫逊迭代方法,对直流偏磁下的单相变压器进行了时域仿真计算,实现直流偏磁下单相变压器的分析,并与实验获得的数据进行比较,验证该计算模型及计算方法的有效性和正确性。
首次建立了直流偏磁下三相变压器组的传输线模型,并利用牛顿-拉夫逊迭代方法对其进行计算仿真,仿真结果证明所提出的计算模型能够准确的分析三相变压器组的直流偏磁现象。
建立了新的直流偏磁下三相三柱变压器和三相五柱变压器的电路-磁路耦合模型,磁路模型中,考虑了变压器的涡流损耗、铁芯拓扑结构及材料的饱和特性,并将涡流产生的磁动势列入磁路方程,与电路方程进行耦合,并结合铁芯的非线性特征曲线,形成了非线性方程组,通过求解该方程组,最终实现对三相三柱变压器和三相五柱变压器直流偏磁特性的仿真计算,并与实验获得的数据进行比较,从而验证了计算模型能够准确的分析三相三柱变压器和相五柱变压器的直流偏磁现象。
最后,指出了限制直流电流流过变爪器绕组的三种措施：①反向注入电流法,②串联电容法,③串联电阻法,并对这三种措施进行仿真研究。
Direct current (DC) bias phenomenon is that the DC flows into the windings of the transformers through neutral point, which is an abnormal work station. There are two reasons which arose DC bias:One is the monopolar ground circuit operation mode or the bipolar asymmetrically operation mode of the HVDC transmission system. Under this situation, DC will pass by the windings of the transformers through the earthed neutral point. The other is Geomagnetically Induced Current (GIC) which is caused by the interaction of the geomagnetic field and the dynamic movement of the ionic wind. The change of the geomagnetic field produces electric potential gradient, which give rise to low-frequency induction current. It is DC because its frequency is very low.
The work point of the transformer under DC bias will shifts, and its iron will be saturated which affect the normal work of the transformer seriously. This gives rise to lots of bad influence. for example, the peak value of the exciting current increases significantly, and the waveform of the current is seriously distorted with a lot of harmonics; the heavy noise; the serious vibration; the increases of transformer's leakage and losses and temperature build-up; the local heating of metal structures; the malfunction of relay protection devices of electric power system; which endanger the operation safety of the transformers and electric power system. So the DC bias phenomenon of the transformer is concerned.
This paper make a thorough study of the physical mechanism of DC bias. On this basis, the transformer under DC bias is studied by experiment and calculated by simulation. The main research contents are as following:
Firstly, the feasible experiment scheme of the single-phase transformer and the three-phase three-legged transformer and three-phase five-legged transformer under DC bias is proposed. The exciting currents and B-H curve of the transformers under DC bias are measured.
Secondly, this paper proposes a novel transmission-line model (TLM) of the single-phase transformer under DC bias. In the model, the differential terms in transformer circuit model are discretized. The saturation characteristic and hysteresis effect is described on the basis of J-A ferromagnetic hysteresis theory, and the eddy-current losses resulting from the flux paths through legs are replaced by an equivalent resistance. Furthermore, the copper losses and flux leakage of the primary and secondary windings are also included. So the transformer is described sufficiently and completely. At last, the Newton-Raphson technique is chosen to calculate the model. The results compare with the experiment results. That demonstrates the validity of the TLM and effectiveness of analyzing the DC bias phenomenon of the single-phase transformer.
The TLM of the three-phase transformer under DC bias is build. And the Newton-Raphson technique is chosen to calculate the model. The simulation results demonstrate that the TLM can exactly analyze the phenomenon of the three-phase transformer under DC bias.
A novel coupling model of electric circuit and magnetic circuit of the three-phase three-legged transformer and three-phase five-legged transformer under DC bias is built. In the magnetic circuit model, the eddy-current losses, the core topology and the saturation characteristic of the core material are taken into account. The magnetomotive force due to eddy current is given in magnetic circuit equations. By combining an electrical circuit with nonlinear characteristic curve of the core, nonlinear equations can be obtained. A series of mathematic transformation are performed and numerical nonlinear algebraic equations are solved finally. Meanwhile DC bias problem of the three-phase three-legged transformer and three-phase five-legged transformers are analyzed. The simulation results compare with the experiment results. That demonstrate the validity of the coupling models and effectiveness of analyzing the DC bias phenomenon of the three-phase three-legged transformer and three-phase five-legged transformer.
Lastly, this paper introduces several measures of restraining DC bias based on theory analysis.①reverse current method②series-capacitor method③ series-resistanee method. The three measures are studied by simulation.
引文
[1]Meliopoulos A P S, Glytsis E N, Cokkinides G J, ct al. Comparison of SS-GIC and MHD-EMP-GIC effects on power systcms[J]. Power Delivery, IEEE Transactions on,1994,9(1):194-207.
[2]Kappenman J G, Albertson V D, Mohan N. Current transformer and relay performance in the presence of geomagnetically-induccd currents[J]. Power Apparatus and Systems, IEEE Transactions on,1981 (3):1078-1088.
[3]Albertson V D, Bozoki B, Feero W E, et al. Geomagnetic disturbance effects on power systems[J]. IEEE transactions on power delivery,1993,8(3):1206-1216.
[4]Towle J N, Prabhakara F S, Ponder J Z. Geomagnetic effects modeling for the PJM interconnection system. I. Earth surface potentials computation[J]. Power Systems, IEEE Transactions on,1992,7(3):949-955.
[5]Meliopoulos A P S, Christoforidis G. Effects of DC ground electrode on converter transformers[J]. Power Delivery, IEEE Transactions on,1989,4(2): 995-1002.
[6]Boteler D H, Shier R M, Watanabe T, et al. Effects of geomagnetically induced currents in the BC hydro 500kV system[J]. Power Delivery, IEEE Transactions on,1989,4(1):818-823.
[7]Picher P, Bolduc E, Dutil A, et al. Study of the acceptable DC current limit in core-form power transformers[J]. Power Delivery, IEEE Transactions on,1997, 12(1):257-265.
[8]薛向党,郭晖,郑云祥,等.在地磁感应电流作用时分析和计算电力变压器特性的一种新方法-时域和频域法[J].电工技术学报.2000,15(2)：1-5.
[9]Albertson V D, Bozoki B, Feero W E, et al. Geomagnetic disturbance effects on power systems[J]. IEEE transactions on power delivery,1993,8(3):1206-1216.
[10]Emanuel A E, Pileggi D J, Levitsky F J. Direct current generation in single-phase residential systems DC effects and permissible levels[J]. Power Apparatus and Systems, IEEE Transactions on,1984 (8):2051-2057.
[11]Boteler D H, Watanabe T, Shier R M, et al. Characteristics of geomagnetically induced currents in the BC Hydro 500kV system[J]. Power Apparatus and Systems, IEEE Transactions on,1982 (6):1447-1456.
[12]Boteler D H. Geomagnetically induced currents:present knowledge and future research[J]. Power Delivery, IEEE Transactions on,1994,9(1):50-58.
[13]Girgis R S, Ko C D. Calculation techniques and results of effects of GIC currents as applied to large power transformers[J]. Power Delivery, IEEE Transactions on,1992,7(2):699-705.
[14]Takasu N, Oshi T, Miyawaki F, et al. An experimental analysis of DC excitation of transformers by geomagnetically induced currents[J]. Power Delivery, IEEE Transactions on,1994,9(2):1173-1182.
[15]Bolduc L, Gaudreau A, Dutil A. Saturation time of transformers under dc excitation[J].Electric Power Systems Research,2000,56(2):95-102.
[16]马为民.换流变压器中直流偏磁电流的计算[J].高电压技术,2004,30(11)：48-49.
[17]蒯狄正,万达,邹云.直流偏磁对变压器的影响[J].中国电力,2004,37(8)：41-43.
[18]李泓志,崔翔,刘东升等.直流偏磁对三相电力变压器的影响[J].电工技术学报,2010(005)：88-96.
[19]姚缨英.大型电力变压器直流偏磁现象的研究[D].沈阳：沈阳工业大学,2000.
[20]李靖宇.换流变压器直流偏磁的试验研究[J].变压器,2005,42(9)：25-28.
[21]李晓萍,文习山,陈慈萱.单相变压器直流偏磁励磁电流仿真分析[J].高电压技术,2005,31(9)：8-10.
[22]李晓萍,文习山,蓝磊等.单相变压器直流偏磁试验与仿真[J].中国电机工程学报,2007,27(9)：33-40.
[23]李晓萍,文习山.三相五柱变压器直流偏磁计算研究[J].中国电机工程学报,2010(1)：127-131.
[24]Lu S, Liu Y. FEM analysis of DC saturation to assess transformer susceptibility to geomagnetically induced currcnts[J]. Power Delivery, IEEE Transactions on, 1993,8(3):1367-1376.
[25]Lu S, Liu Y, De La Ree J. Harmonics generated from a DC biased transformer[J]. Power Delivery, IEEE Transactions on,1993,8(2):725-731.
[26]Tay H C, Swift G W. On the problem of transformer overheating due to geomagnetically induced currents[J]. Power Apparatus and Systems, IEEE Transactions on,1985 (1):212-219.
[27]Takeda,G. Solar Induced Currents and Heating of Metallic Parts[J]. Technical Report Submitted to Manitoba Hydro, Winnipeg, Canada, August,1979.
[28]Albertson V D, Thorson J M, Clayton R E, et al. Solar-induced-currents in power systems:cause and effects[J]. Power Apparatus and Systems, IEEE Transactions on,1973 (2):471-477.
[29]Biro O, Preis K. On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents[J]. Magnetics, IEEE Transactions on, 1989.25(4):3145-3159.
[30]M.V.K.Chari.3D Vector Potential Analysis for Electrical Machinery Field Problcms[J]. IEEE Trans. On Magnetics,1982,18(2):436-446.
[31]Biddlccombe C S, Heighway E, Simkin J, et al. Methods for eddy current computation in three dimensions[J]. Magnetics, IEEE Transactions on,1982, 18(2):492-497.
[32]Kameari A. Three-dimensional eddy current calculation using Unite clement method with-A-V in conductor and Q in vacuum [J]. Magnetics, IEEE Transactions on,1988,24(1):118-121.
[33]Biro O, Preis K, Renhart W, et al. Performance of different vector potential formulations in solving multiply connected 3-D eddy current problems[J]. Magnetics, IEEE Transactions on,1990,26(2):438-441.
[34]G.Drago, P.Girdinio, P.Molfino et al. A Gauged A-V-A-ψFormulation without A.n=0 on Conductor Boundaries[J]. IEEE Trans, on Magnetics.1994, 30(5):2976-2979.
[35]Carpenter C J. Comparison of alternative formulations of 3-dimensional magnetic-field and eddy-current problems at power frequencies[J]. Electrical Engineers, Proceedings of the Institution of,1977,124(11):1026-1034.
[36]Nakata T, Takahashi N, Fujiwara K, et al. Improvements of the method for 3D eddy current analysis[J]. Magnetics, IEEE Transactions on,1988,24(1):94-97.
[37]Kameari A. Calculation of transient 3D eddy current using edge elements[J]. Magnetics, IEEE Transactions on,1990,26(2):466-469.
[38]R.Albanese. A T-Formulation for 3D Finite Element Computation Using Edge Elements[J]. IEEE Trans, on Magnetics,1985,21:2299-2301.
[39]R.Albanese. Solution of 3D Eddy Current Problems by Integral and Differential Methods[J]. IEEE Trans, on Magnetics,1988,24(1):311-314.
[40]Biro O, Preis K. Finite element analysis of 3D eddy currents[J]. Magnetics, IEEE Transactions on,1990,26(2):418-423.
[41]T.Nakata. An Improved Numerical Analysis of Flux Distribution in Anisotropic Materials[J]. IEEE Trans, on Magnetics,1994,30(5):3395-3398.
[42]Labridis D, Dokopoulos P. Calculation of eddy current losses in nonlinear ferromagnetic materials[J]. Magnetics, IEEE Transactions on,1989,25(3): 2665-2669.
[43]Fawzi T, Ahmed M, Burke P. On the use of the impedance boundary conditions in eddy current problems[J]. Magnetics, IEEE Transactions on,1985,21(5): 1835-1840.
[44]Hoole S R H, Weeber K, Hoole NRG. The natural finite element formulation of the impedance boundary condition in shielding structures[J]. Journal of Applied Physics,1988,63(8):3022-3024.
[45]谢德馨,姚缨英.电磁分析中大型稀疏对称线性代数方程组的修正的预处理方法[J].电机与控制,1997,1(2)：98.
[46]Kershaw D S. The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations[J]. Journal of Computational Physics,1978,26(1):43-65.
[47]A.Y.Hannalla, D.C.Macdonald. Numerical analysis of transient Held problems in electrical machines[J]. Proc. IEE,1976,123(9):893-898.
[48]Hannalla A Y, Macdonald D C. Numerical analysis of transient field problems in electrical machines[J]. Electrical Engineers, Proceedings of the Institution of, 1976,123(9):893-898.
[49]Konrad A. The numerical solution of steady-state skin effect problems--An integrodifferential approach[J]. Magnetics, IEEE Transactions on,1981,17(1): 1148-1152.
[50]Nakata T, Takahashi N. Direct finite element analysis of flux and current distributions under specified conditions[J]. Magnetics, IEEE Transactions on, 1982,18(2):325-330.
[51]Nakata T, Takahashi N, Fujiwara K, et al. Finite element analysis of induced currents in axisyminetric multi-conductors connected in parallel to voltage sources[J]. Magnetics, IEEE Transactions on,1990,26(2):968-970.
[52]Strangas E. Coupling the circuit equations to the non-linear time dependent field solution in inverter driven induction motors[J]. Magnetics, IEEE Transactions on, 1985,21(6):2408-2411.
[53]Weiss J, Garg V K. Steady state eddy current analysis in multiply-excited magnetic systems with arbitrary terminal conditions[J]. Magnetics, IEEE Transactions on,1988,24(6):2676-2678.
[54]Tsukerman I A, Konrad A, Eavers J D. A method for circuit connections in time-dependent eddy current problems[J]. Magnetics, IEEE Transactions on, 1992,28(2):1299-1302.
[55]Leonard P J, Rodger D. Voltage forced coils for 3D finite-element electromagnetic models[J]. Magnetics, IEEE Transactions on,1988,24(6): 2579-2581.
[56]Piriou F, Razek A. A non-linear coupled 3D model for magnetic field and electric circuit equations[J]. Magnetics, IEEE Transactions on,1992,28(2):1295-1298.
[57]Bouissou S, Piriou F. Study of 3D formulations to model electromagnetic devices[J]. Magnetics, IEEE Transactions on,1994,30(5):3228-3231.
[58]P.J.Leonard, R.J.Hill-Cottingham, D.Rodger.3D Finite Element Models and External Circhits using the A-y Scheme with Cuts[J]. IEEE Trans, on Magnetics, 1994,30(5):3220-3223.
[59]Wang J S. A nodal analysis approach for 2D and 3D magnetic-circuit coupled problems[J]. Magnetics, IEEE Transactions on,1996,32(3):1074-1077.
[60]Tsukerman I A, Konrad A, Meunier G, et al. Coupled field-circuit problems: trends and accomplishments[J]. Magnetics, IEEE Transactions on,1993,29(2): 1701-1704.
[61]MacBain J. Magnetic field simulation from a voltage source[J], Magnetics, IEEE Transactions on,1983,19(5):2180-2182.
[62]Shi Z W, Rajanathan C B. A method of approach to transient eddy current problems coupled with voltage sources[J]. Magnetics, IEEE Transactions on, 1996,32(3):1082-1085.
[63]Rodger D, Allen N, Lai H C, et al. Calculation of transient 3D eddy currents in nonlinear media verification using a rotational test rig[J]. Magnetics, IEEE Transactions on,1994,30(5):2988-2991.
[64]Leonard P J, Rodger D. Some aspects of two-and three-dimensional transient eddy current modeling using finite elements and single-step time-marching algorithms[J]. IEE Proceedings A (Physical Science, Measurement and Instrumentation, Management and Education, Reviews),1988,135(3):159-166.
[65]Brauer J R, Lee S H, Chen Q M. Adaptive time-stepping in nonlinear transient electromagnetic finite element analysis[J]. Magnetics, IEEE Transactions on, 1997,33(2):1784-1787.
[66]Ho S L, Fu W N, Wong H C. Application of automatic choice of step size for time stepping finite element method to induction motors[J]. Magnetics, IEEE Transactions on,1997,33(2):1370-1373.
[67]Ho S L, Fu W N, Wong H C. An incremental method for studying the steady state performance of induction motors using time stepping Unite element modcl[J]. Magnetics, IEEE Transactions on,1997,33(2):1374-1377.
[68]Mohammed O A, Uler F G. A state space approach and formulation for the solution of nonlinear 3-D transient eddy current problems[J]. Magnetics, IEEE Transactions on,1992,28(2):1111-1114.
[69]Silvester P, Chari M V K. Finite clement solution of saturable magnetic field problems[J]. Power Apparatus and Systems, IEEE Transactions on,1970 (7): 1642-1651.
[70]Biro O, Preis K. On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents[J]. Magnetics, IEEE Transactions on, 1989,25(4):3145-3159.
[71]Chari M V K. Finite-element solution of the eddy-current problem in magnetic struclures[J]. Power Apparatus and Systems, IEEE Transactions on,1974 (1): 62-72.
[72]McWhirter J, Oravec J, Haack R. Computation of magnetostatic fields in three-dimensions based on Fredholm integral equations[J]. Magnetics, IEEE Transactions on,1982,18(2):373-378.
[73]Girgis R S, Scott D J, Yannucci D A, et al. Calculation of Winding Eosses in Shell-Form Transformers for Improved Accuracy and Reliability Part-1: Calculation Procedure and Program Description[J]. Power Delivery, IEEE Transactions on,1987,2(2):398-403.
[74]宫莲,姚若萍等.用等效磁化面电流法求解变压器的三维漏磁场[J].清华大学科学报告,1985.
[75]樊明武,严威利.《电磁场积分方程法》,机械工业出版社,1988.
[76]Turowski J, Turowski M, Kopec M. Method of three-dimensional network solution of leakage field of three-phase transformers[J]. Magnetics, IEEE Transactions on,1990,26(5):2911-2919.
[77]柴建云.大型变压器三维涡流漏磁场计算[D],清华大学,1989.
[78]杨俊友.大型电力器低压引线漏磁场及局部过热研究[D],哈尔滨工业大学,1993.
[79]李岩.大型电力变压器线圈电磁力和局部过热问题研究[D],沈阳工业大学,1995.
[80]谢德馨,汤蕴璆,徐子宏.变压器三维涡流问题的有限元解[J].哈尔滨电工学院学报,1986.
[81]周剑明.电磁场有限元综合模拟方法及大型变压器漏磁场的研究[D].武汉：华中理工大学,1990.
[82]陈家平,电磁场有限元方法及变压器线圈电磁力与振动的研究[D],华中理工大学,1993.
[83]Holland S, O'Conncll G P, Haydock L. Calculating stray losses in power transformers using surface impedance with finite elements[J]. Magnetics, IEEE Transactions on,1992,28(2):1355-1358.
[84]Guerin C, Tanneau G, Meunier G.3D eddy current losses calculation in transformer tanks using the finite element method[J]. Magnetics, IEEE Transactions on,1993,29(2):1419-1422.
[85]Guerin C, Meunier G, Tanneau G. Surface impedance for 3D nonlinear eddy current problems-application to loss computation in transformers[J]. Magnetics, IEEE Transactions on,1996,32(3):808-811.
[86]Esposito N, Musolino A, Raugi M. Equivalent network model for magnetic field and circuital analysis of transformers including hysteresis effects[J]. Magnetics, IEEE Transactions on,1996,32(3):1094-1097.
[87]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,1990.
[88]Haydock L, Holland S A. Transient analysis of power transformers using magnetic and electric equivalent circuits[J]. Magnetics, IEEE Transactions on, 1994,30(5):2996-2999.
[89]Heidrich P, Hanitsch R. Indirectly coupling time-stepping techniques for electro-magnetic systems using quasi Newton-Raphson solvers and on-line field calculations[J]. Magnetics, IEEE Transactions on,1996,32(3):1090-1093.
[90]C.E.Lin, C.L.Cheng C.L.Huang et al. Investigation of Magnetizing Inrush Current in Transformers Part I-Numerical Simulalion[J]. IEEE Trans. On Power Delivery,1993,8(1):246-254.
[91]符杨,蓝之达,陈珩.计及铁芯动态磁化特性的三相变压器励磁涌流的仿真研究[J].变压器,1997,34(9)：4-11.
[92]发海,朱东起.《电机学》.北京：科学出版社,2002：54-56.
[93]钟连宏,陆培均,仇志成,等.直流接地极电流对中性点直接接地变压器影响[J].高电压技术,2003,29(8)：12-13.
[94]解广润.《电力系统接地技术》.北京：水利出版社,1991：95-100.
[95]Koen J, Gaunt C T. Disturbances in the Southern African power network due to geomagnetically induced currenls[J]. Cigre Session paper,2002:36-206.
[96]胡毅,李景录.直流接地极电流对中性点接地变压器的影响[J].变压器,1999,36(1)：15-19.
[97]Annakkage U D, McLaren P G, Dirks E, et al. A current transformer model based on the Jiles-Athcrlon theory of ferromagnetic hysteresis[J]. IEEE Transactions on Power Delivery,2000,15(1):57-61.
[98]Chandrasena W. Development of an improved Low Flcquency Transformer Model for Use in GIC Studies[D]. The University of Manitoba,2003.
[99]皇甫成,魏远航,钟连宏等.基于对偶性原理的三相多芯柱变压器暂态模型[J].中国电机工程学报,2007,27(3)：83-88.
[100]Sadowski N, Batistela N J, Bastos J P A, et al. An inverse Jiles-Atherton model to take into account hysteresis in time-stepping finite-element calculations[J]. IEEE Transactions on Magnetics,2002,38(2):797-800.
[101]Leite J V, Sadowski N, Kuo-Peng P, et al. Inverse Jiles-Atherton vector hysteresis model[J]. IEEE Transactions on Magnetics,2004,40(4):1769-1775.
[102]Peter R.Wilson, J.Neil Ross, Andrew D.Brown, Optimizing the Jiles-Atherton Model of Hysteresis by a Genetic Algorithm[J]. IEEE Trans, on Magnetics,2001, 37(2):989-993.
[103]Dieter Lederer, Hajime Igarashit, ArnulfKost, Toshihisa Honmat. On the Parameter Identification and Application of the Jiles-Atherton Hysteresis Model for Numerical Modeling of Measured Characteristics[J]. IEEE Trans, on Magnetics,1995,35(3):1211-1214
[104]J.V.Leite, N.Sadowski, P.Kllo-Peng,N.J.Batistela, J.P.A. Bastos. The Inverse Jiles-Atherton Model Parameters Identification[J].IEEE Trans, on Magnetics,2003,39 (3):1397-1400.
[105]Wlodarski Z. The Jiles-Atherton model with variable pinning parameter[J]. Magnetics, IEEE Transactions on,2003,39(4):1990-1992.
[106]Jiles D C, Thoelke J B, Devine M K. Numerical determination of hysteresis parameters for the modeling of magnetic properties using the theory of ferromagnetic hysteresis[J]. Magnetics, IEEE Transactions on,1992,28(1):27-35.
[107]Carpenter K H. A differential equation approach to minor loops in the Jiles-Atherton hysteresis model [J]. Magnetics, IEEE Transactions on,1991,27(6): 4404-4406.
[108]Wilcox D.J. Time-domain modeling of power transformers using modal analysis[J]. IEE Proc-Elect Power Appl,1997,144(2):77-84.
[109]Lobry J, Trecat J, Broche C. The transmission line modeling (TLM) method as a new iterative technique in nonlinear 2-D magnetostatics[J]. Magnetics, IEEE Transactions on,1996,32(2):559-566.
[110]Lobry J, Trecat J, Broche C. Symmetry and TLM method in nonlinear magnetostatics[J]. Magnetics, IEEE Transactions on,1996,32(3):702-705.
[111]Im C H, Kim H K, Lee C H, et al. Analysis of the three-phase transformer considering the nonlinear and anisotropic properties using the transmission line modeling method and FEM[J]. Magnetics, IEEE Transactions on,2001,37(5): 3490-3493.
[112]Flack T J. Knight R E. On the domain decomposition and transmission line modelling finite element method for time-domain induction motor analysis[J]. Magnetics, IEEE Transactions on,1999,35(3):1290-1293.
[113]Knight R E, Flack T J. Application of domain decomposition and transmission line modelling techniques to 2D, time-domain, finite element problems[J]. Magnetics, IEEE Transactions on,1999,35(3):1478-1481.
[114]Deblecker O, Lobry J, Broche C. Novel algorithm based on transmission-line modeling in the finite-element method for nonlinear quasi-static field analysis[J]. Magnetics, IEEE Transactions on,2003,39(1):529-538.
[115]Deblecker O, Lobry J, Broche C. Use of transmission-line modelling method in FEM for solution of nonlinear eddy-current problems[J].IEE Proceedings-Science, Measurement and Technology,1998,145(1):31-38.
[116]Lobry J. A new solution technique for open nonlinear magnetostatic problems[J]. Magnetics, IEEE Transactions on,2002.38(2):453-456.
[117]Deblecker O, Lobry J. A new efficient technique for harmonic-balance finite-element analysis of saturated electromagnetic devices[J]. Magnetics, IEEE Transactions on,2006,42(4):535-538.
[118]郭晖,地磁感应电流对电力变压器有害影响及消除方法研究[D].天津大学1998.
[119]蒯狄正,万达,邹云.变压器中性点注入反向抗偏磁直流的应用分析[J].华东电力,2005,33(6)：44-46.
[120J Bolduc L, Granger M, Pare G, et al. Development of a DC current-blocking device for transformer neutrals[J]. Power Delivery, IEEE Transactions on,2005,20(1): 163-168.
[121]薛向党,文剑莹,郑云祥,等.地磁感应电流消除方法初探[J].电力系统自动化,2000,24(4)：58-60.
[122]朱艺颖,蒋卫哦,曾昭华,等.抑制变压器中性点直流电流的措施研究[J].中国电机工程学报,2005,25(13)：1-7.
[123]Eitzmann M A, Walling R A, Sublich M, et al. Alternatives for blocking direct current in AC system neutrals at the Radisson/LG2 compIex[J]. Power Delivery, IEEE Transactions on,1992,7(3):1328-1337.
[124]皇甫成,阮江军,张宁,等.变压器直流偏磁的仿真研究及限制措施[J].高电压技术,2006,32(9)：117-120.
[125]赵杰,黎小林,吕金壮,等.抑制变压器直流偏磁的串接电阻措施[J].电力系统自动化,2006,30(12)：88-91.
[126]马玉龙,肖湘宁,姜旭,等.用于抑制大型电力变压器直流偏磁的接地电阻优化配置[J].电网技术,2006,30(3)：62-65.
[127]Kappenman J G, Norr S R, Sweezy G A, et al. GIC mitigation:a neutral blocking/bypass device to prevent the flow of GIC in power systems[J]. Power Delivery, IEEE Transactions on,1991,6(3):1271-1281.
[2]Kappenman J G, Albertson V D, Mohan N. Current transformer and relay performance in the presence of geomagnetically-induccd currents[J]. Power Apparatus and Systems, IEEE Transactions on,1981 (3):1078-1088.
[3]Albertson V D, Bozoki B, Feero W E, et al. Geomagnetic disturbance effects on power systems[J]. IEEE transactions on power delivery,1993,8(3):1206-1216.
[4]Towle J N, Prabhakara F S, Ponder J Z. Geomagnetic effects modeling for the PJM interconnection system. I. Earth surface potentials computation[J]. Power Systems, IEEE Transactions on,1992,7(3):949-955.
[5]Meliopoulos A P S, Christoforidis G. Effects of DC ground electrode on converter transformers[J]. Power Delivery, IEEE Transactions on,1989,4(2): 995-1002.
[6]Boteler D H, Shier R M, Watanabe T, et al. Effects of geomagnetically induced currents in the BC hydro 500kV system[J]. Power Delivery, IEEE Transactions on,1989,4(1):818-823.
[7]Picher P, Bolduc E, Dutil A, et al. Study of the acceptable DC current limit in core-form power transformers[J]. Power Delivery, IEEE Transactions on,1997, 12(1):257-265.
[8]薛向党,郭晖,郑云祥,等.在地磁感应电流作用时分析和计算电力变压器特性的一种新方法-时域和频域法[J].电工技术学报.2000,15(2)：1-5.
[9]Albertson V D, Bozoki B, Feero W E, et al. Geomagnetic disturbance effects on power systems[J]. IEEE transactions on power delivery,1993,8(3):1206-1216.
[10]Emanuel A E, Pileggi D J, Levitsky F J. Direct current generation in single-phase residential systems DC effects and permissible levels[J]. Power Apparatus and Systems, IEEE Transactions on,1984 (8):2051-2057.
[11]Boteler D H, Watanabe T, Shier R M, et al. Characteristics of geomagnetically induced currents in the BC Hydro 500kV system[J]. Power Apparatus and Systems, IEEE Transactions on,1982 (6):1447-1456.
[12]Boteler D H. Geomagnetically induced currents:present knowledge and future research[J]. Power Delivery, IEEE Transactions on,1994,9(1):50-58.
[13]Girgis R S, Ko C D. Calculation techniques and results of effects of GIC currents as applied to large power transformers[J]. Power Delivery, IEEE Transactions on,1992,7(2):699-705.
[14]Takasu N, Oshi T, Miyawaki F, et al. An experimental analysis of DC excitation of transformers by geomagnetically induced currents[J]. Power Delivery, IEEE Transactions on,1994,9(2):1173-1182.
[15]Bolduc L, Gaudreau A, Dutil A. Saturation time of transformers under dc excitation[J].Electric Power Systems Research,2000,56(2):95-102.
[16]马为民.换流变压器中直流偏磁电流的计算[J].高电压技术,2004,30(11)：48-49.
[17]蒯狄正,万达,邹云.直流偏磁对变压器的影响[J].中国电力,2004,37(8)：41-43.
[18]李泓志,崔翔,刘东升等.直流偏磁对三相电力变压器的影响[J].电工技术学报,2010(005)：88-96.
[19]姚缨英.大型电力变压器直流偏磁现象的研究[D].沈阳：沈阳工业大学,2000.
[20]李靖宇.换流变压器直流偏磁的试验研究[J].变压器,2005,42(9)：25-28.
[21]李晓萍,文习山,陈慈萱.单相变压器直流偏磁励磁电流仿真分析[J].高电压技术,2005,31(9)：8-10.
[22]李晓萍,文习山,蓝磊等.单相变压器直流偏磁试验与仿真[J].中国电机工程学报,2007,27(9)：33-40.
[23]李晓萍,文习山.三相五柱变压器直流偏磁计算研究[J].中国电机工程学报,2010(1)：127-131.
[24]Lu S, Liu Y. FEM analysis of DC saturation to assess transformer susceptibility to geomagnetically induced currcnts[J]. Power Delivery, IEEE Transactions on, 1993,8(3):1367-1376.
[25]Lu S, Liu Y, De La Ree J. Harmonics generated from a DC biased transformer[J]. Power Delivery, IEEE Transactions on,1993,8(2):725-731.
[26]Tay H C, Swift G W. On the problem of transformer overheating due to geomagnetically induced currents[J]. Power Apparatus and Systems, IEEE Transactions on,1985 (1):212-219.
[27]Takeda,G. Solar Induced Currents and Heating of Metallic Parts[J]. Technical Report Submitted to Manitoba Hydro, Winnipeg, Canada, August,1979.
[28]Albertson V D, Thorson J M, Clayton R E, et al. Solar-induced-currents in power systems:cause and effects[J]. Power Apparatus and Systems, IEEE Transactions on,1973 (2):471-477.
[29]Biro O, Preis K. On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents[J]. Magnetics, IEEE Transactions on, 1989.25(4):3145-3159.
[30]M.V.K.Chari.3D Vector Potential Analysis for Electrical Machinery Field Problcms[J]. IEEE Trans. On Magnetics,1982,18(2):436-446.
[31]Biddlccombe C S, Heighway E, Simkin J, et al. Methods for eddy current computation in three dimensions[J]. Magnetics, IEEE Transactions on,1982, 18(2):492-497.
[32]Kameari A. Three-dimensional eddy current calculation using Unite clement method with-A-V in conductor and Q in vacuum [J]. Magnetics, IEEE Transactions on,1988,24(1):118-121.
[33]Biro O, Preis K, Renhart W, et al. Performance of different vector potential formulations in solving multiply connected 3-D eddy current problems[J]. Magnetics, IEEE Transactions on,1990,26(2):438-441.
[34]G.Drago, P.Girdinio, P.Molfino et al. A Gauged A-V-A-ψFormulation without A.n=0 on Conductor Boundaries[J]. IEEE Trans, on Magnetics.1994, 30(5):2976-2979.
[35]Carpenter C J. Comparison of alternative formulations of 3-dimensional magnetic-field and eddy-current problems at power frequencies[J]. Electrical Engineers, Proceedings of the Institution of,1977,124(11):1026-1034.
[36]Nakata T, Takahashi N, Fujiwara K, et al. Improvements of the method for 3D eddy current analysis[J]. Magnetics, IEEE Transactions on,1988,24(1):94-97.
[37]Kameari A. Calculation of transient 3D eddy current using edge elements[J]. Magnetics, IEEE Transactions on,1990,26(2):466-469.
[38]R.Albanese. A T-Formulation for 3D Finite Element Computation Using Edge Elements[J]. IEEE Trans, on Magnetics,1985,21:2299-2301.
[39]R.Albanese. Solution of 3D Eddy Current Problems by Integral and Differential Methods[J]. IEEE Trans, on Magnetics,1988,24(1):311-314.
[40]Biro O, Preis K. Finite element analysis of 3D eddy currents[J]. Magnetics, IEEE Transactions on,1990,26(2):418-423.
[41]T.Nakata. An Improved Numerical Analysis of Flux Distribution in Anisotropic Materials[J]. IEEE Trans, on Magnetics,1994,30(5):3395-3398.
[42]Labridis D, Dokopoulos P. Calculation of eddy current losses in nonlinear ferromagnetic materials[J]. Magnetics, IEEE Transactions on,1989,25(3): 2665-2669.
[43]Fawzi T, Ahmed M, Burke P. On the use of the impedance boundary conditions in eddy current problems[J]. Magnetics, IEEE Transactions on,1985,21(5): 1835-1840.
[44]Hoole S R H, Weeber K, Hoole NRG. The natural finite element formulation of the impedance boundary condition in shielding structures[J]. Journal of Applied Physics,1988,63(8):3022-3024.
[45]谢德馨,姚缨英.电磁分析中大型稀疏对称线性代数方程组的修正的预处理方法[J].电机与控制,1997,1(2)：98.
[46]Kershaw D S. The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations[J]. Journal of Computational Physics,1978,26(1):43-65.
[47]A.Y.Hannalla, D.C.Macdonald. Numerical analysis of transient Held problems in electrical machines[J]. Proc. IEE,1976,123(9):893-898.
[48]Hannalla A Y, Macdonald D C. Numerical analysis of transient field problems in electrical machines[J]. Electrical Engineers, Proceedings of the Institution of, 1976,123(9):893-898.
[49]Konrad A. The numerical solution of steady-state skin effect problems--An integrodifferential approach[J]. Magnetics, IEEE Transactions on,1981,17(1): 1148-1152.
[50]Nakata T, Takahashi N. Direct finite element analysis of flux and current distributions under specified conditions[J]. Magnetics, IEEE Transactions on, 1982,18(2):325-330.
[51]Nakata T, Takahashi N, Fujiwara K, et al. Finite element analysis of induced currents in axisyminetric multi-conductors connected in parallel to voltage sources[J]. Magnetics, IEEE Transactions on,1990,26(2):968-970.
[52]Strangas E. Coupling the circuit equations to the non-linear time dependent field solution in inverter driven induction motors[J]. Magnetics, IEEE Transactions on, 1985,21(6):2408-2411.
[53]Weiss J, Garg V K. Steady state eddy current analysis in multiply-excited magnetic systems with arbitrary terminal conditions[J]. Magnetics, IEEE Transactions on,1988,24(6):2676-2678.
[54]Tsukerman I A, Konrad A, Eavers J D. A method for circuit connections in time-dependent eddy current problems[J]. Magnetics, IEEE Transactions on, 1992,28(2):1299-1302.
[55]Leonard P J, Rodger D. Voltage forced coils for 3D finite-element electromagnetic models[J]. Magnetics, IEEE Transactions on,1988,24(6): 2579-2581.
[56]Piriou F, Razek A. A non-linear coupled 3D model for magnetic field and electric circuit equations[J]. Magnetics, IEEE Transactions on,1992,28(2):1295-1298.
[57]Bouissou S, Piriou F. Study of 3D formulations to model electromagnetic devices[J]. Magnetics, IEEE Transactions on,1994,30(5):3228-3231.
[58]P.J.Leonard, R.J.Hill-Cottingham, D.Rodger.3D Finite Element Models and External Circhits using the A-y Scheme with Cuts[J]. IEEE Trans, on Magnetics, 1994,30(5):3220-3223.
[59]Wang J S. A nodal analysis approach for 2D and 3D magnetic-circuit coupled problems[J]. Magnetics, IEEE Transactions on,1996,32(3):1074-1077.
[60]Tsukerman I A, Konrad A, Meunier G, et al. Coupled field-circuit problems: trends and accomplishments[J]. Magnetics, IEEE Transactions on,1993,29(2): 1701-1704.
[61]MacBain J. Magnetic field simulation from a voltage source[J], Magnetics, IEEE Transactions on,1983,19(5):2180-2182.
[62]Shi Z W, Rajanathan C B. A method of approach to transient eddy current problems coupled with voltage sources[J]. Magnetics, IEEE Transactions on, 1996,32(3):1082-1085.
[63]Rodger D, Allen N, Lai H C, et al. Calculation of transient 3D eddy currents in nonlinear media verification using a rotational test rig[J]. Magnetics, IEEE Transactions on,1994,30(5):2988-2991.
[64]Leonard P J, Rodger D. Some aspects of two-and three-dimensional transient eddy current modeling using finite elements and single-step time-marching algorithms[J]. IEE Proceedings A (Physical Science, Measurement and Instrumentation, Management and Education, Reviews),1988,135(3):159-166.
[65]Brauer J R, Lee S H, Chen Q M. Adaptive time-stepping in nonlinear transient electromagnetic finite element analysis[J]. Magnetics, IEEE Transactions on, 1997,33(2):1784-1787.
[66]Ho S L, Fu W N, Wong H C. Application of automatic choice of step size for time stepping finite element method to induction motors[J]. Magnetics, IEEE Transactions on,1997,33(2):1370-1373.
[67]Ho S L, Fu W N, Wong H C. An incremental method for studying the steady state performance of induction motors using time stepping Unite element modcl[J]. Magnetics, IEEE Transactions on,1997,33(2):1374-1377.
[68]Mohammed O A, Uler F G. A state space approach and formulation for the solution of nonlinear 3-D transient eddy current problems[J]. Magnetics, IEEE Transactions on,1992,28(2):1111-1114.
[69]Silvester P, Chari M V K. Finite clement solution of saturable magnetic field problems[J]. Power Apparatus and Systems, IEEE Transactions on,1970 (7): 1642-1651.
[70]Biro O, Preis K. On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents[J]. Magnetics, IEEE Transactions on, 1989,25(4):3145-3159.
[71]Chari M V K. Finite-element solution of the eddy-current problem in magnetic struclures[J]. Power Apparatus and Systems, IEEE Transactions on,1974 (1): 62-72.
[72]McWhirter J, Oravec J, Haack R. Computation of magnetostatic fields in three-dimensions based on Fredholm integral equations[J]. Magnetics, IEEE Transactions on,1982,18(2):373-378.
[73]Girgis R S, Scott D J, Yannucci D A, et al. Calculation of Winding Eosses in Shell-Form Transformers for Improved Accuracy and Reliability Part-1: Calculation Procedure and Program Description[J]. Power Delivery, IEEE Transactions on,1987,2(2):398-403.
[74]宫莲,姚若萍等.用等效磁化面电流法求解变压器的三维漏磁场[J].清华大学科学报告,1985.
[75]樊明武,严威利.《电磁场积分方程法》,机械工业出版社,1988.
[76]Turowski J, Turowski M, Kopec M. Method of three-dimensional network solution of leakage field of three-phase transformers[J]. Magnetics, IEEE Transactions on,1990,26(5):2911-2919.
[77]柴建云.大型变压器三维涡流漏磁场计算[D],清华大学,1989.
[78]杨俊友.大型电力器低压引线漏磁场及局部过热研究[D],哈尔滨工业大学,1993.
[79]李岩.大型电力变压器线圈电磁力和局部过热问题研究[D],沈阳工业大学,1995.
[80]谢德馨,汤蕴璆,徐子宏.变压器三维涡流问题的有限元解[J].哈尔滨电工学院学报,1986.
[81]周剑明.电磁场有限元综合模拟方法及大型变压器漏磁场的研究[D].武汉：华中理工大学,1990.
[82]陈家平,电磁场有限元方法及变压器线圈电磁力与振动的研究[D],华中理工大学,1993.
[83]Holland S, O'Conncll G P, Haydock L. Calculating stray losses in power transformers using surface impedance with finite elements[J]. Magnetics, IEEE Transactions on,1992,28(2):1355-1358.
[84]Guerin C, Tanneau G, Meunier G.3D eddy current losses calculation in transformer tanks using the finite element method[J]. Magnetics, IEEE Transactions on,1993,29(2):1419-1422.
[85]Guerin C, Meunier G, Tanneau G. Surface impedance for 3D nonlinear eddy current problems-application to loss computation in transformers[J]. Magnetics, IEEE Transactions on,1996,32(3):808-811.
[86]Esposito N, Musolino A, Raugi M. Equivalent network model for magnetic field and circuital analysis of transformers including hysteresis effects[J]. Magnetics, IEEE Transactions on,1996,32(3):1094-1097.
[87]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,1990.
[88]Haydock L, Holland S A. Transient analysis of power transformers using magnetic and electric equivalent circuits[J]. Magnetics, IEEE Transactions on, 1994,30(5):2996-2999.
[89]Heidrich P, Hanitsch R. Indirectly coupling time-stepping techniques for electro-magnetic systems using quasi Newton-Raphson solvers and on-line field calculations[J]. Magnetics, IEEE Transactions on,1996,32(3):1090-1093.
[90]C.E.Lin, C.L.Cheng C.L.Huang et al. Investigation of Magnetizing Inrush Current in Transformers Part I-Numerical Simulalion[J]. IEEE Trans. On Power Delivery,1993,8(1):246-254.
[91]符杨,蓝之达,陈珩.计及铁芯动态磁化特性的三相变压器励磁涌流的仿真研究[J].变压器,1997,34(9)：4-11.
[92]发海,朱东起.《电机学》.北京：科学出版社,2002：54-56.
[93]钟连宏,陆培均,仇志成,等.直流接地极电流对中性点直接接地变压器影响[J].高电压技术,2003,29(8)：12-13.
[94]解广润.《电力系统接地技术》.北京：水利出版社,1991：95-100.
[95]Koen J, Gaunt C T. Disturbances in the Southern African power network due to geomagnetically induced currenls[J]. Cigre Session paper,2002:36-206.
[96]胡毅,李景录.直流接地极电流对中性点接地变压器的影响[J].变压器,1999,36(1)：15-19.
[97]Annakkage U D, McLaren P G, Dirks E, et al. A current transformer model based on the Jiles-Athcrlon theory of ferromagnetic hysteresis[J]. IEEE Transactions on Power Delivery,2000,15(1):57-61.
[98]Chandrasena W. Development of an improved Low Flcquency Transformer Model for Use in GIC Studies[D]. The University of Manitoba,2003.
[99]皇甫成,魏远航,钟连宏等.基于对偶性原理的三相多芯柱变压器暂态模型[J].中国电机工程学报,2007,27(3)：83-88.
[100]Sadowski N, Batistela N J, Bastos J P A, et al. An inverse Jiles-Atherton model to take into account hysteresis in time-stepping finite-element calculations[J]. IEEE Transactions on Magnetics,2002,38(2):797-800.
[101]Leite J V, Sadowski N, Kuo-Peng P, et al. Inverse Jiles-Atherton vector hysteresis model[J]. IEEE Transactions on Magnetics,2004,40(4):1769-1775.
[102]Peter R.Wilson, J.Neil Ross, Andrew D.Brown, Optimizing the Jiles-Atherton Model of Hysteresis by a Genetic Algorithm[J]. IEEE Trans, on Magnetics,2001, 37(2):989-993.
[103]Dieter Lederer, Hajime Igarashit, ArnulfKost, Toshihisa Honmat. On the Parameter Identification and Application of the Jiles-Atherton Hysteresis Model for Numerical Modeling of Measured Characteristics[J]. IEEE Trans, on Magnetics,1995,35(3):1211-1214
[104]J.V.Leite, N.Sadowski, P.Kllo-Peng,N.J.Batistela, J.P.A. Bastos. The Inverse Jiles-Atherton Model Parameters Identification[J].IEEE Trans, on Magnetics,2003,39 (3):1397-1400.
[105]Wlodarski Z. The Jiles-Atherton model with variable pinning parameter[J]. Magnetics, IEEE Transactions on,2003,39(4):1990-1992.
[106]Jiles D C, Thoelke J B, Devine M K. Numerical determination of hysteresis parameters for the modeling of magnetic properties using the theory of ferromagnetic hysteresis[J]. Magnetics, IEEE Transactions on,1992,28(1):27-35.
[107]Carpenter K H. A differential equation approach to minor loops in the Jiles-Atherton hysteresis model [J]. Magnetics, IEEE Transactions on,1991,27(6): 4404-4406.
[108]Wilcox D.J. Time-domain modeling of power transformers using modal analysis[J]. IEE Proc-Elect Power Appl,1997,144(2):77-84.
[109]Lobry J, Trecat J, Broche C. The transmission line modeling (TLM) method as a new iterative technique in nonlinear 2-D magnetostatics[J]. Magnetics, IEEE Transactions on,1996,32(2):559-566.
[110]Lobry J, Trecat J, Broche C. Symmetry and TLM method in nonlinear magnetostatics[J]. Magnetics, IEEE Transactions on,1996,32(3):702-705.
[111]Im C H, Kim H K, Lee C H, et al. Analysis of the three-phase transformer considering the nonlinear and anisotropic properties using the transmission line modeling method and FEM[J]. Magnetics, IEEE Transactions on,2001,37(5): 3490-3493.
[112]Flack T J. Knight R E. On the domain decomposition and transmission line modelling finite element method for time-domain induction motor analysis[J]. Magnetics, IEEE Transactions on,1999,35(3):1290-1293.
[113]Knight R E, Flack T J. Application of domain decomposition and transmission line modelling techniques to 2D, time-domain, finite element problems[J]. Magnetics, IEEE Transactions on,1999,35(3):1478-1481.
[114]Deblecker O, Lobry J, Broche C. Novel algorithm based on transmission-line modeling in the finite-element method for nonlinear quasi-static field analysis[J]. Magnetics, IEEE Transactions on,2003,39(1):529-538.
[115]Deblecker O, Lobry J, Broche C. Use of transmission-line modelling method in FEM for solution of nonlinear eddy-current problems[J].IEE Proceedings-Science, Measurement and Technology,1998,145(1):31-38.
[116]Lobry J. A new solution technique for open nonlinear magnetostatic problems[J]. Magnetics, IEEE Transactions on,2002.38(2):453-456.
[117]Deblecker O, Lobry J. A new efficient technique for harmonic-balance finite-element analysis of saturated electromagnetic devices[J]. Magnetics, IEEE Transactions on,2006,42(4):535-538.
[118]郭晖,地磁感应电流对电力变压器有害影响及消除方法研究[D].天津大学1998.
[119]蒯狄正,万达,邹云.变压器中性点注入反向抗偏磁直流的应用分析[J].华东电力,2005,33(6)：44-46.
[120J Bolduc L, Granger M, Pare G, et al. Development of a DC current-blocking device for transformer neutrals[J]. Power Delivery, IEEE Transactions on,2005,20(1): 163-168.
[121]薛向党,文剑莹,郑云祥,等.地磁感应电流消除方法初探[J].电力系统自动化,2000,24(4)：58-60.
[122]朱艺颖,蒋卫哦,曾昭华,等.抑制变压器中性点直流电流的措施研究[J].中国电机工程学报,2005,25(13)：1-7.
[123]Eitzmann M A, Walling R A, Sublich M, et al. Alternatives for blocking direct current in AC system neutrals at the Radisson/LG2 compIex[J]. Power Delivery, IEEE Transactions on,1992,7(3):1328-1337.
[124]皇甫成,阮江军,张宁,等.变压器直流偏磁的仿真研究及限制措施[J].高电压技术,2006,32(9)：117-120.
[125]赵杰,黎小林,吕金壮,等.抑制变压器直流偏磁的串接电阻措施[J].电力系统自动化,2006,30(12)：88-91.
[126]马玉龙,肖湘宁,姜旭,等.用于抑制大型电力变压器直流偏磁的接地电阻优化配置[J].电网技术,2006,30(3)：62-65.
[127]Kappenman J G, Norr S R, Sweezy G A, et al. GIC mitigation:a neutral blocking/bypass device to prevent the flow of GIC in power systems[J]. Power Delivery, IEEE Transactions on,1991,6(3):1271-1281.