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.

Computational Modelling of Russia's First 2G-HTS Triaxial Cable

“…In Figure 1, it is to be noted that the thickness of the superconducting layer within the SuperOx tape has been increased by a factor of 50. This allows to overcome the numerical difficulties that can be caused by the large aspect ratio of the 2G-HTS tapes, whilst maintaining the integrability of the physical quantities by renormalizing the critical current density J c as it is customarily done in the numerical modelling of 2G-HTS tapes [22,23,29]. Likewise, as none of the other layers composing the SuperOx tapes are known to be magnetic nor carry any of the transport current which is to flow only on the superconducting layer, these can be assumed to have the same electrically insulating and non-magnetic properties of the so-called "air" domain, what allows to neglect also the occurrence of eddy currents.…”

3D FEM Modelling of CORC Commercial Cables with Bean's like magnetization currents and its AC-Losses Behaviour

“…However, these approaches neglect the hysteresis losses caused by the twist pitch angle, i.e., by the non-perpendicularity of the derived magnetic field and the local profiles of current density along the entire length of tapes and cable, hence leading to unreliable results in terms of the AC losses specially at short twist pitch lengths. However, as mentioned above this difference can be overcome within a 2D model, by empirically adding the self-field hysteresis loss caused by the spiral structure of the wound tapes [18]. Albeit, this method neglects the thickness of the HTS tapes and assume an infinitely thin film structure for the superconducting tapes.…”

3D Modelling and Validation of the Optimal Pitch in Commercial CORC Cables

“…By using symmetry conditions at the full 3D geometry whose approaches can render to computations over a 2D domain, these drawbacks can be addressed. Assuming that the current only flows along the 2D domains following the helicoidal trajectories, a scalar power-law for the resistivity of the superconductor makes the eddy current approach feasible for the solution of the 3D CORC ® cable but within a 2D formulation for the electromagnetic variables [15]. Similarly, by neglecting any significant hysteretic process across the thickness of the 2G-HTS tapes, i.e., by assuming infinitely thin superconducting tapes where all relevant pinning dynamics manifest only at their surface, 3D geommetry models such as the ones based on the so-called T-A formulation result in the computational modelling of 2D domains [16].…”