An accurate and efficient 3D steady-state model for simulating the voltage–current characteristics of HTS coils

Abstract The voltage–current ( U – I ) characteristic of high-temperature superconducting (HTS) coils is a key reference for predicting the critical current ( I c ) and the n -value, both essential parameters in coil design. Accurate and efficient simulation of the U – I curve is therefore critical, especially for coils wound with second-generation coated conductors, where strong anisotropy and complex electromagnetic behavior pose significant challenges for conventional numerical methods. This work presents a three-dimensional steady-state model for efficient and accurate simulation of HTS coil U – I characteristics. Assuming a uniform current density distribution, the magnetic flux density is calculated using the vector potential method. The anisotropic dependence of the critical current density on the local magnetic field is incorporated to determine the electric field distribution, and the average electric field and voltage are obtained through volume integration. The model is validated against both experimental measurements and other numerical models. Compared to the measured data, simulation errors remain within 0.9%–11%, and relative errors against the extensively benchmarked H-formulation model are within 0.1%–3%, while achieving at least an order of magnitude improvement in computational speed. Furthermore, the model shows improved accuracy and efficiency as the number of coil turns and pancakes increases. In I c determination, the model demonstrates both enhanced computational accuracy and equivalent efficiency compared to conventional load-line methods. In addition, it matches the accuracy of the state-of-the-art homogenized self-consistent model while reducing computation time by 64%. Leveraging the model, this work examines the effects of external magnetic fields and non-uniform temperature distributions on the U – I characteristics of HTS coils, and uncovers the underlying physics governing I c improvement in coils with stepped cross-sections. This research establishes a powerful computational tool for optimizing the electromagnetic design of superconducting coils.