Computation of self-field hysteresis losses in conductors with helicoidal structure using a 2D finite element method

Abstract

It is well known that twisting current-carrying conductors helps to reduce their coupling losses. However, the impact of twisting on self-field hysteresis losses has not been as extensively investigated as that on the reduction of coupling losses. This is mostly because the reduction of coupling losses has been an important issue to tackle in the past, and it is not possible to consider twisting within the classical two-dimensional (2D) approaches for the computation of self-field hysteresis losses. Recently, numerical codes considering the effect of twisting in continuous symmetries have appeared. For general three-dimensional (3D) simulations, one issue is that no robust, widely accepted and easy to obtain model for expressing the relationship between the current density and the electric field is available. On the other hand, we can consider that in these helicoidal structures currents flow only along the helicoidal trajectories. This approach allows one to use the scalar power-law for superconductor resistivity and makes the eddy current approach to a solution of a hysteresis loss problem feasible. In this paper we use the finite element method to solve the eddy current model in helicoidal structures in 2D domains utilizing the helicoidal symmetry. The developed tool uses the full 3D geometry but allows discretization which takes advantage of the helicoidal symmetry to reduce the computational domain to a 2D one. We utilize in this tool the non-linear power law for modelling the resistivity in the superconducting regions and study how the self-field losses are influenced by the twisting of a 10-filament wire. Additionally, in the case of high aspect ratio tapes, we compare the results computed with the new tool and a one-dimensional program based on the integral equation method and developed for simulating single layer power cables made of ReBCO coated conductors. Finally, we discuss modelling issues and present open questions related to helicoidal structures and AC-loss computations in three dimensions.