磁链法计算并联细导体段电流分配的误差分析

Error Analysis of Current Distribution in Parallel Filament Conductor Segments Calculated by Magnetic Flux Method

能量法计算导体段电感的理论完备自洽,计算结果准确,但对全场域的积分复杂,计算效率低。磁链法只需对导体区域积分,计算简单,已广泛应用于导体段电感计算。但现有基于磁链法的电感计算方法因不满足电流连续性定律,计算结果存在误差,因此基于磁链法求得的电感用于计算并联导体段的电流分配也会导致误差,而现有文献尚未对其进行系统研究。该文首先针对工程中常见的电流单端注入单端流出的并联细导体段模型,推导磁链法计算并联支路电流的误差公式,揭示了误差电流正比于真实电流,且只与并联导体组的自感以及总电流注入、流出点的距离有关。该文的理论分析与计算修正了采用磁链法计算的并联细导体电流分配结果,在不降低计算速度的同时提高了计算的准确度,可为工程应用提供参考。

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.