Numerical Electromagnetic Modeling of HTS Power Transmission Cables

This Ph.D. thesis consists of two successive phases. The objective of the first phase was to develop a fast and accurate numerical model to solve the electromagnetic problem of helically wound thin tape conductors. This method must be applicable to find current distribution and AC losses in High Temperature Superconducting (HTS) power transmission cables made of coated tapes. In the second phase of the project, the developed model was used to perform parametric analysis of the AC loss behavior of single layer HTS cables with different design schemes and design parameters. The main objective of this phase was focused on the minimization of AC losses in HTS cables either by searching for optimal designs parameters or alternative design schemes. In the latest generation of HTS power cables, superconducting coated tapes are the conductors of choice. The thickness of the superconducting layer of these tapes is around 1 to 2 μm, and depending on the application, their width varies from 4 to 12 mm. In the cable design, such tapes are helically wound around cylindrical formers in single or multi-layer arrangements. The complicated geometry of the tapes as well as the non-linear resistivity of their superconducting layer, make the accurate solution of the electromagnetic problem of HTS cables quite challenging. During the first phase of this thesis, we introduced a numerical method to compute current and field distribution in helically wound thin tape conductors when one or many of them are arranged in a symmetrical manner. According to the symmetry arguments associated with the geometry of the problem, and neglecting the thickness of the tapes, the real 3-D problem of helically wound tapes could be reduced to a computationally small 1-D problem whose domain lies along the half-width of any of the constituting tapes. The low frequency version of the eddy current equation, as the governing equation of the problem, is discretized over this reduced dimension study domain. To establish a direct relationship between the current density and the vector potential in the problem formulation, the solution of the Biot-Savart integral to find the magnetic vector potential of helically wound current sheets is used.