Application of Multi-Population Genetic Algorithm and Truncated Singular Value Decomposition in Switching Arc Inversion

doi:10.11985/2018.06.003

Abstract

Abstract:

By using the corresponding relationship between the current and the space magnetic field, the arc is regarded as a set of multiple current lines with variable arc diameters. Based on Biot-Savart’s law, the magnetic field distribution of combined arc streamlines in space is obtained by forward analysis. To simplify the complexity of the problem, the research only considers the phase of the arc not entering the splitter plates, and the multi-population genetic algorithm(MPGA) is used to optimize the objective function for solving the nonlinear equations of the electromagnetic inverse problem to determine the space position of the arc. On the basis of the above, the truncated singular value decomposition(TSVD) method is used to inverse the arc current distribution, with the regularization parameters obtained by the GCV criterion. The inversion results will contribute to understand the physical characteristics of the switch arc.

Key words: Switching arc inverse problem, ill-posed, MPGA, TSVD, GCV criterion

CLC Number:

TM501

Zhao Hongchen,Wang Gang,Liu Xiaoming. Application of Multi-Population Genetic Algorithm and Truncated Singular Value Decomposition in Switching Arc Inversion[J]. Journal of Electrical Engineering, 2018, 13(6): 14-19.

Figures/Tables 10

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Tab

References 20

[1]	赵宏晨 . 基于电磁特性分析的开关电弧反演研究[D]. 沈阳:沈阳工业大学, 2015.
[2]	冷雪, 刘莉, 刘晓明 , 等. 高压SF₆断路器不同开断条件下混沌特性分析[J]. 电气工程学报, 2015,10(11):27-32.
	Leng Xue, Liu Li, Liu Xiaoming , et al. Chaotic characteristics analysis of high voltage SF₆ circuit breaker under different breaking conditions[J]. Journal of Electrical Engineering, 2015,10(11):27-32.
[3]	王伟宗, 吴翊, 荣命哲 , 等. 空气开关电弧仿真技术及其应用的研究[J]. 低压电器, 2010(5):7-11.
	Wang Weizong, Wu Yi, Rong Mingzhe , et al. Research on the simulation technology and application of the air switch arc[J]. Low Voltage Electrical Apparatus, 2010(5):7-11.
[4]	Yang Fei, Rong Mingzhe, Wu Yi , et al. Numerical analysis of the influence of splitter-plate erosion on an air arc in the quenching chamber of a low-voltage circuit breaker[J]. Journal of Physics D: Applied Physics. 2010,43:1-12.
[5]	蔡彬, 陈德桂, 吴锐 , 等. 开关柜内部故障电弧的在线检测与保护装置[J]. 电工技术学报, 2005,20(10):83-87.
	Cai Bin, Chen Degui, Wu Rui , et al. Online detecting and protection system for internal faults arc in swithgear[J]. Transactions of China Electrotechnical Society, 2005,20(10):83-87.
[6]	丁心志, 刘柱揆, 严跃 , 等. 电弧光光谱成分特性及其应用分析[J]. 电气工程学报, 2015,10(5):75-81.
	Ding Xinzhi, Liu Zhukui, Yan Yue , et al. Analysis of characteristics and application for arc spectral components[J]. Journal of Electrical Engineering, 2015,10(5):75-81.
[7]	Brdys C, Toumazet J P, Velleaud G , et al. Study of the low-voltage electric breaking arc restrike by means of an inverse method[J]. IEEE Transactions on Plasma Science, 1999,27(2):595-603. doi: 10.1109/27.772291
[8]	Debellut E, Gary F, Cajal D , et al. Study of re-strike phenomenon in a low-voltage breaking device by means of the magnetic camera[J]. Journal of Physics D: Applied Physics, 2001,34:1665-1674. doi: 10.1088/0022-3727/34/11/317
[9]	Brdys C, Toumazet J P, Laurent A , et al. Optical and magnetic diagnostics of the electric arc dynamics in a low voltage circuit breaker[J]. Measurement Science and Technology, 2002,13:1146-1153. doi: 10.1088/0957-0233/13/7/324
[10]	Toumazet J P, Brdys C, Laurent A , et al. Combined use of an inverse method and a voltage measurement: estimation of the arc column volume and its variations[J]. Measurement Science and Technology, 2005,16:1525-1533. doi: 10.1088/0957-0233/16/7/015
[11]	张鹏飞, 张国钢, 杨博宇 , 等. 空气开关电弧电流密度分布的智能反演方法研究[J]. 中国电机工程学报, 2013,33(33):160-168.
	Zhang Guogang, Zhang Pengfei, Yang Boyu , et al. Investigations on intelligent inversion methods of current density distribution of electrical arc in air[J]. Proceedings of the CSEE, 2013,33(33):160-168.
[12]	Zhang Pengfei, Zhang Guogang, Dong Jinlong , et al. Non-intrusive magneto-optic detecting system for investigations of air switching arcs[J]. Plasma Science and Technology, 2014,16(7):661-668. doi: 10.1088/1009-0630/16/7/06
[13]	Luca G, Luca D R, Daniele P, et al. Current identification in vacuum circuit breakers by inverting magnetic field data[C]. International Conference on Electric Power Equipment-Switching Technology, Xi’an, China, 2011: 65-68.
[14]	Luca G, Daniele P, Luca D R . Current density reconstruction in vacuum arcs by inverting magnetic field data[J]. IEEE Transaction on Magnetics, 2012,48(8):2324-2333. doi: 10.1109/TMAG.2012.2192287
[15]	Dong Jinlong, Zhang Guogang, Zhang Zhiqiang , et al. Inverse problem solution and regularization parameter selection for current distribution reconstruction in switching arcs by inverting magnetic fields[J]. Mathematical Problems in Engineering, 2018: 1-11.
[16]	赵宏晨, 刘晓明, 李龙女 . 采用遗传算法的低压开关电弧反演[J]. 高压电器, 2017,53(4):25-30.
	Zhao Hongchen, Liu Xiaoming, Li Longnv . Arc inversion with genetic algorithm for low voltage switch[J]. High Voltage Apparatus, 2017,53(4):25-30.
[17]	林阳, 赵欢, 丁汉 . 基于多种群遗传算法的一般机器人逆运动学求解[J]. 机械工程学报, 2017,53(3):1-8.
	Lin Yang, Zhao Huan, Ding Han , et al. Solution of inverse kinematics for general robot manipulators based on multiple population genetic algorithm[J]. Journal of Mechanical Engineering, 2017,53(3):1-8.
[18]	叶满园, 周琪琦, 蔡鸿 , 等. 基于多种群遗传算法的多电平逆变器多波段SHEPWM技术[J]. 电工技术学报, 2015,30(16):111-119.
	Ye Manyuan, Zhou Qiqi, Cai Hong , et al. Multiple population genetic algorithm based on multi-band SHEPWM control technology for multi-level inverter[J]. Transactions of China Electrotechnical Society, 2015,30(16):111-119.
[19]	Hansen P C, O’Leary D P . The use of the L-curve in the regularization of discrete ill-posed problems[J]. SIAM Journal of Scientific Computing, 1993,14(6):1487-1503. doi: 10.1137/0914086
[20]	马超, 华宏星 . 一种基于新的正则化技术的冲击载荷识别法[J]. 振动与冲击, 2015,34(12):164-168.
	Ma Chao, Hua Hongxing . Impact force identification based on improved regularization technique[J]. Journal of Vibration and Shock, 2015,34(12):164-168.

电流线标号	最小二乘法(%)	截断奇异值分解法(%)
1	8.01	1.14
2	28.99	2.77
3	30.85	3.28
4	39.83	6.56
5	31.89	6.01