磁链法计算并联细导体段电流分配的误差分析

doi:10.19595/j.cnki.1000-6753.tces.220689

Abstract
Figure/Table
References (0)
Related Citation (15)

Download: PDF (1333 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract

The energy method is complete and self-consistent in calculating the inductance of conductor segments with accurate calculation results. However, integrating the whole field is complicated, and the calculation efficiency could be higher. It is necessary to integrate the conductor area, and the calculation is simple using the magnetic flux method. Therefore it has been widely used in the inductance calculation of conductor segments. However, the method does not satisfy the current continuity law, which leads to calculation errors. Accordingly, the current distribution of parallel conductor segments based on the magnetic flux method also has errors that have yet to be studied in the existing literature.
This paper is specified to parallel filament conductors with single-end injection and single-end outflow, which are common in engineering. The inductance matrices of the parallel filament conductors are extracted by the flux method and the energy method, respectively. The parallel branch currents are derived by the flux method and the energy method. The error formula of parallel branch current by magnetic flux method is obtained. The error is proportional to the actual current and only related to the self-inductance of the parallel conductor and the distance between injection and outflow points. The correctness of the proposed error formula is verified by the current distribution calculation results of the filament conductors with 5 branches and 10 branches in parallel. When the length of the current injection lead is 100 times its radius, the error of the branch current calculated by the magnetic flux method is 12 %.
For parallel filament conductor segments with multi-ended outflow, the influence of distance and length of parallel conductors and the length of the connecting lead on calculation error are studied through systematic theoretical calculation. Regarding the parallel filament conductor segments with multi-ended injection and multi-ended current outflow, the larger the distance between the parallel fine conductors, the weaker the magnetic field coupling and the smaller the mutual inductance. Moreover, the current calculation error of the branch by the flux method decreases, which tends to the current calculation error of a single conductor. The magnetic field coupling of the parallel filament conductor segments with single-ended injection and multi-ended current outflow is between that with single-ended injection and multi-ended outflow model and that with multi-ended injection and multi-ended outflow model. With the increase of lead length, the error of the flux method increases, but its rate gradually decreases, approximately satisfying the logarithmic law. When the distance between parallel conductors is large enough, the current error of the center conductors decreases, and the current error of the edge conductors increases. When the distance between conductors is large enough, the edge conductor current of the flux method is even much larger than the real current.
This paper's theoretical analysis and calculation revise the current distribution results of parallel filament conductors calculated by the magnetic flux method, improve the calculation accuracy without reducing the calculation speed and provide references for engineering applications.

Key words： Parallel filament conductor segments current distribution inductance magnetic flux method energy method

Received: 26 April 2022

PACS:

TM12

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Fu Shi
	Cui Xiang
	Zhan Yongfan

Cite this article:

Fu Shi,Cui Xiang,Zhan Yongfan. Error Analysis of Current Distribution in Parallel Filament Conductor Segments Calculated by Magnetic Flux Method[J]. Transactions of China Electrotechnical Society, 0, (): 230605-230605.

URL:

https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.220689 OR https://dgjsxb.ces-transaction.com/EN/Y0/V/I/230605

[1] 傅实, 邓二平, 赵志斌, 等. 压接型IGBT器件多物理量测试方法综述[J]. 中国电机工程学报, 2020, 40(5): 1587-1605.
Fu Shi, Deng Erping, Zhao Zhibin, et al.Overview of measurement methods of multiple physical parameters in press pack IGBTs[J]. Proceedings of the CSEE, 2020, 40(5): 1587-1605.
[2] Ni Chouwei, Zhao Zhibin, Cui Xiang.Notice of retraction: partial inductance of conductor segments with coulomb gauge in quasi-static field[J]. IEEE Transactions on Electromagnetic Compatibility, 2017, 59(4): 1125-1132.
[3] 周林, 薛飞彪, 司粉妮, 等. Z箍缩等离子体电流分布实验研究[J]. 物理学报, 2012, 61(19): 195207.
Zhou Lin, Xue Feibiao, Si Fenni, et al.Experimental sduty of current distribution in wirearray Zpinch plasma[J]. Acta Physica Sinica, 2012, 61(19): 195207.
[4] Deeney C, Douglas M R, Spielman R B, et al.Enhancement of X-ray power from a ZPinch using nested-wire arrays[J]. Physical Review Letters, 1998, 81(22): 4883-4886.
[5] 叶繁, 薛飞彪, 褚衍运, 等. 双层丝阵Z箍缩电流分配实验研究[J]. 物理学报, 2013, 62(17): 175203.
Ye Fan, Xue Feibiao, Chu Yanyun, et al.Experi- mental study on current division of nested wire array Z pinches[J]. Acta Physica Sinica, 2013, 62(17): 175203.
[6] 丁宁, 张扬, 刘全, 等. 电感分布对双层丝阵Z箍缩内爆动力学模式的影响[J]. 物理学报, 2009, 58(2): 1083-1090.
Ding Ning, Zhang Yang, Liu Quan, et al.Effects of various inductances on the dynamic models of the Z-pinch implosion of nested wire arrays[J]. Acta Physica Sinica, 2009, 58(2): 1083-1090.
[7] 赵屾, 朱鑫磊, 石桓通, 等. 用X-pinch对双丝Z箍缩进行轴向X射线背光照相[J]. 物理学报, 2015, 64(1): 015203.
Zhao Shen, Zhu Xinlei, Shi Huantong, et al.Axial backlighting of two-wire Z-pinch using an X-pinch as an X-ray source[J]. Acta Physica Sinica, 2015, 64(1): 015203.
[8] Davis J, Gondarenko N A, Velikovich A L.Fast commutation of high current in double wire array Z-pinch loads[J]. Applied Physics Letters, 1997, 70(2): 170-172.
[9] Strickler T S, Gilgenbach R M, Johnston M D, et al.Efficient computation of current in multiwire Z-pinch arrays[J]. IEEE Transactions on Plasma Science, 2003, 31(6): 1384-1387.
[10] Grabovskiĭ E V, Zukakishvili G G, Mitrofanov K N, et al.Study of the magnetic fields and soft X-ray emission generated in the implosion of double wire arrays[J]. Plasma Physics Reports, 2006, 32(1): 32-46.
[11] Giuliani J L, Commisso R J.A review of the gas-puff: pinch as an X-ray and neutron source[J]. IEEE Transa- ctions on Plasma Science, 2015, 43(8): 2385-2453.
[12] Ruehli A E.Inductance calculations in a complex integrated circuit environment[J]. IBM Journal of Research and Development, 1972, 16(5): 470-481.
[13] Holloway C L, Kuester E F, Ruehli A E, et al.Partial and internal inductance: two of clayton R. Paul's many passions[J]. IEEE Transactions on Electro- magnetic Compatibility, 2013, 55(4): 600-613.
[14] 倪筹帷. 多导体段的电感参数计算方法[D]. 北京: 华北电力大学, 2018.
[15] 倪筹帷, 赵志斌, 崔翔. 考虑位移电流的部分电感计算方法[J]. 中国电机工程学报, 2017, 37(17): 5181-5187, 5238.
Ni Chouwei, Zhao Zhibin, Cui Xiang.Computing method partial inductance for conductor segments by considering displacement current[J]. Proceedings of the CSEE, 2017, 37(17): 5181-5187, 5238.
[16] 崔翔. 电流连续的细导体段模型的磁场及电感[J]. 物理学报, 2020, 69(3): 034101.
Cui Xiang.Magnetic field and inductance of filament conductor segment model with current continuity[J]. Acta Physica Sinica, 2020, 69(3): 034101.
[17] 金亮, 祝登锋, 杨庆新, 等. 超高压电抗器电感计算灰箱模型与优化[J]. 电工技术学报, 2022, 37(23): 6093-6103.
Jin Liang, Zhu Dengfeng, Yang Qingxin, et al.Grey box model and optimization for inductance calcu- lation of EHV reactors[J]. Transactions of China Electrotechnical Society, 2022, 37(23): 6093-6103.
[18] 刘博, 刘伟志, 董侃, 等. 基于全碳化硅功率组件的变流器母排杂散电感解析计算方法[J]. 电工技术学报, 2021, 36(10): 2105-2114.
Liu Bo, Liu Weizhi, Dong Kan, et al.Analytical calculation method for stray inductance of converter busbar based on full silicon carbide power module[J]. Transactions of China Electrotechnical Society, 2021, 36(10): 2105-2114.
[19] 张春雷, 张辉, 叶佩青, 等. 两相无槽圆筒型永磁同步直线电机电感计算与分析[J]. 电工技术学报, 2021, 36(6): 1159-1168.
Zhang Chunlei, Zhang hui, Ye Peiqing, et al. Inductance analysis of two-phase slotless tubular permanent magnet synchronous linear motor[J]. Transactions of China Electrotechnical Society, 2021, 36(10): 1159-1168.
[20] 李巍, 王浩淞, 陈伟. 永磁同步电机交直轴增量电感计算与测量研究[J]. 电机与控制学报, 2022, 26(12): 19-27.
Li Wei, Wang Haosong, Chen Wei.Research on calculation and measurement of d-axis and q-axis incremental inductance of permanent magnet syn- chronous motor[J]. Transactions of China Electro- technical Society, 2022, 26(12): 19-27.