Remote contact-free reconstruction of currents in two-dimensional parallel conductors

Sammanfattning: In this thesis, the theory of the remote contact-free reconstruction of currents in two-dimensional parallel conductors is investigated. The motivation of this study is finding a complement technique to measurement transformers which are the well-established devices to measure currents in power transmission lines. This technique would provide the possibility of measuring currents at different locations of a power system, as well as, at different frequencies. Remote contact-free determination of currents is an electromagnetic inverse source problem in which the currents are reconstructed from the magnetic field data collected by a set of sensors located in the vicinity of the conductors. Since the sensors are not too close to the conductors, the main challenge is the effect of the disturbance fields produced by the external sources in the measurement. In the case that the external sources produce three-dimensional disturbance fields, the magnetic field due to the external sources is expressed as a truncated expansion of the spherical harmonics and both the currents in the conductors and the expansion coefficients are determined by applying the least square method. To overcome the ill-posedness of the problem, the functional to be minimized is augmented by a Tikhonov regularization term that penalizes unphysical solutions introduced by the expansion coefficients. Finally, the problem of selecting a limited number of optimal sensor positions among a set of predetermined sensor positions is considered. Using the relaxation method, this optimization problem is changed to a convex optimization problem which can be readily solved using the CVX package.