正多边离散环路磁场积分问题分析

Analysis of magnetic field integral along regular polygonal discrete loop

摘要:

为解决直通光路型光学电流互感器抗外磁场干扰能力差的问题,提出一种零和御磁技术解决方法．在分析离散环路磁场积分的基础上,对离散安培环路定律及其数学模型进行探讨,并具体研究了正多边离散环路S^m模型和S^m正分布的mS^m模型等两类离散环路磁场积分模型．结果表明:S^m模型存在2m个零和P点,干扰电流位于零和P点时对S^m模型的磁场积分结果的贡献为零;mS^m模型中任意两个S^m位置互换时其原点与零和P点互换．据此提出了S^m模型的零和定理和mS^m模型的互易定理,离散安培环路定律与零和定理、互易定理一起形成了正多边离散环路磁场积分理论体系．研究结果为光学电流互感器的零和御磁技术奠定了理论基础．

Abstract:

This paper proposed a zero-sum magnetic field integral technology to minimize the crosstalk effect in straight light path optical current transducer. The discrete Ampere’s law was proposed and studied based on analyzing of the magnetic field integral along a discrete loop, and its mathematical model was established. The S^m model of regular polygonal discrete loop and the mS^m model of S^m regular distribution were discussed. The results showed that the S^m model possessed 2m zero-sum points, and the currents which placed on the zero-sum points did not contribute to the magnetic field integral result of S^m model. The origin point interchanged with the zero-sum point when any two S^m models of the mS^m model switched places. Based on that conclusion, the zero-sum theorem of S^m model and the reciprocal theorem of mS^m model were proposed. The discrete Ampere’s law, the zero-sum theorem of S^m model and the reciprocal theorem of mS^m model together made up the theory system of magnetic field integral along regular polygonal discrete loop, which still met the Ampere’s law.