Explicit reconstruction of line-currents and their positions in a two-dimensional parallel conductor structure

TL;DR

This paper presents an explicit Green identity-based algorithm for reconstructing the positions and currents of multiple long parallel conductors in a 2D setting, with applications to power line measurements, addressing stability issues and measurement uncertainties.

Contribution

It introduces a novel explicit reconstruction method using Green identities that can handle multiple conductors and improve stability in power line current reconstruction.

Findings

Algorithm successfully reconstructs multiple conductors' positions and currents.

Numerical simulations demonstrate robustness against measurement errors.

Stability decreases as the number of conductors increases.

Abstract

The magnetic inverse source problem of reconstructing the positions and currents of very long parallel conductors is considered in a two-dimensional situation, with applications to power line measurements. The input data is the magnetic field on a contour surrounding the conductors to be reconstructed. Using a scalar-vector Green identity, an explicit reconstruction algorithm is derived. The numerical implementation of the algorithm is described and simulation results are presented, demonstrating the influences from numerical errors and uncertainties in measurement data. The algorithm can handle an arbitrary number of conductors, but stability problems associated with the illposedness accelerate with increasing number of conductors. Mathematically, the Green identity approach removes the influence of external disturbances and thus have potential usefulness in current reconstruction for determining optimal sensor positions and how to process measurement data.