摘要
有触点开关电器在分断电路时将不可避免地产生电弧。该文建立了直动式触头系统开断下的三维电弧模型,将电弧假设为电流折线集合。基于毕奥萨伐尔定律,通过正演分析获得电弧周围测磁平面的磁场分布,并根据磁场反演电弧电流密度分布。为了提高电流重建精度,采用Tikhonov正则化方法求解基于电磁逆问题建立的不适定方程组。考虑到标准Tikhonov正则化方法的最小二乘解由于滤波算子的作用而丢失重建数据的细节使得解过于平滑,采用分数阶Tikhonov正则化方法来提高解的精度,并基于Morozov偏差准则求取正则参数。反演结果表明,通过降低阶数α可减缓滤波算子的收敛速度,提高解向量范数而逼近精确解。同预设值相比,在施加标准差为0.001的测磁干扰下,电弧反演的最大相对误差为21.16%,平均相对误差为8.99%,重建精度高于标准Tikhonov方法与截断奇异值分解法,反演结果能够反映电弧分布趋势。
The switching apparatus with contact will inevitably produce arc when breaking the circuit.In this paper,a three-dimensional arc model of a straight contact system is constructed,that the arc is assumed to be a cluster of broken lines.Based on the Biot-Savart law,the magnetic distribution is measured in-plane around the arc through the forward analysis,thus the arc current density distribution is inversed according to the magnetic field.In order to improve the accuracy of current reconstruction,the Tikhonov regularization method is used to solve the ill-posed equations based on the electromagnetic inverse problem.Considering the approximate solution of the standard Tikhonov regularization method is too smooth because of the loss of the details of the reconstructed data due to the function of the filter operator,the fractional Tikhonov regularization method is adopted to improve the accuracy of the solution,and the Morozov discrepancy criterion is used to obtain the regularization parameter.The inversion result shows that by reducing the order ofαcan slow down the convergence speed of the filtering operator,which will increase the norm of the solution vector to approximate to the exact solution.Under the magnetic interference with a standard deviation of 0.001,the maximum relative error of arc inversion is 21.26%and the mean relative error is 8.99%compared with the preset values,which shows more accuracy than the standard Tikhonov method and truncated singular value decomposition,thus the inversion results can indicate the trend of arc distribution.
作者
赵宏晨
刘晓明
杨滢璇
陈海
杨璐羽
Zhao Hongchen;Liu Xiaoming;Yang Yingxuan;Chen Hai;Yang Luyu(School of Electrical Engineering,Shenyang University of Technology,Shenyang 110870 China;Tianjin Key Laboratory of Advanced Electrical Engineering and Energy Technology,Tianjin Polytechnic University,Tianjin 300387 China;State Grid Liaoning Electric Power Research Institute,Shenyang 110006 China)
出处
《电工技术学报》
EI
CSCD
北大核心
2019年第1期84-91,共8页
Transactions of China Electrotechnical Society
基金
国家自然科学基金面上项目(51777136)
国家电网公司总部科技项目(0711-160TL14711127)资助
