Simulation study of current sharing in a liquid Helium-cooled three-tape REBCO cable with defects: influence of effective electrical and thermal conductivities and thermal boundary conditions

Current sharing is a critical self-protecting mechanism for no-insulation coils and multi-strand cables made from REBCO coated conductors. Typically, the primary variable considered vital for current sharing is the inter-strand resistance, with surface contact resistance between superconducting wires or tapes often making a significant contribution. However, thermal conductance is also known to be an important, albeit secondary, factor for cables made from low-temperature superconductors. In this work, we demonstrate that the importance of thermal variables is even greater for current sharing in REBCO, including the effective thermal conductance within the cable and the cable’s thermal boundary condition.

We focus on finite element method (FEM) modeling of current sharing behavior in a three-layer REBCO cable with defects, where the defect density is set at one defect per 3 cm of cable. A current sharing metric (CSM) is defined as the ratio of achievable current (Ia) before thermal runaway occurs to the cable’s nominal critical current (Ic). Our simulations indicate that the CSM (Ia/Ic) increases with decreasing inter-strand contact resistance, encompassing both inter-strand electrical contact resistance (ICR) and inter-strand thermal contact resistance (ITR). We then analyze current sharing in two different initial states: equilibrium and transient. In the equilibrium state, the cable has pre-existing defects before excitation, potentially due to underlying conductor inhomogeneities or defects induced during cable formation or magnet winding. In this case, current sharing is well-distributed along the cable. In the transient state, the defect forms during service — that is, the cable is already carrying its operating current when the defect arises. Here, current sharing is limited to a region near the defective area, resulting in a lower CSM compared to the equilibrium state given the same inter-strand contact properties. Finally, we explored current sharing in the equilibrium state across a series of specific cases with varying sets of ICR and ITR. Through simulations of 40 different cases, we developed an analytic expression describing the correlation between current sharing and the inter-strand contact properties, providing a predictive framework for understanding current sharing behavior in REBCO cables.