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Several techniques to model high temperature superconductors (HTSs) are used throughout the world. At the same time, the use of superconductors in transportation and magnetic bearings promises an increase in energy efficiency. However, the most widespread simulation technique in the literature, the H-formulation, has not yet been used to simulate superconducting levitation. The goal of this work is to present solutions for the challenges concerning the use of the H-formulation to predict the behavior of superconducting levitators built either with YBCO bulks or stacks of 2G wires. It is worth mentioning the originality of replacing bulks with HTS stacks in this application. In our simulation methodology, the movement between the HTS and the permanent magnet was avoided by restricting the simulation domain to the HTS itself, which can be done by applying appropriate boundary conditions and analytical expressions for the source field. Commercial finite element software was used for the sake of ease of implementation. Simulation results were compared with experimental data, showing good agreement. We conclude that the H-formulation is suitable for problems involving moving objects and is a good alternative to other approaches for simulating superconducting magnetic bearings.

Numerical models for computing the effective critical current of devices made of high-temperature superconducting tapes require the knowledge of the J c (B, θ) dependence, i.e., of the way the critical current density J c depends on the magnetic flux density B and its orientation θ with respect to the tape. In this paper, we present a numerical model based on the critical state with angular field dependence of J c to extract the J c (B, θ) relation from experimental data. The model takes into account the self-field created by the tape, which gives an important contribution when the field applied in the experiments is low. The same model can be also used to compute the effective critical current of devices composed of electromagnetically interacting tapes. In this paper, we consider three examples: two differently current-rated Roebel cables composed of ten strands from REBCO coated conductors and a power cable prototype composed of 22 Bi-2223 tapes. The critical currents computed with the numerical model show good agreement with the measured ones. The simulations reveal also that several parameter sets in J c (B, θ) give an equally good representation of the experimental characterization of the tapes and that the measured I c values of cables are subjected to the influence of experimental conditions, such as I c degradation due to the manufacturing and assembling process and nonuniformity of the tape properties. These two aspects make the determination of a very precise J c (B, θ) expression probably unnecessary, as long as that expression is able to reproduce the main features of the observed angular dependence. The easiness of use of this model, which can be straightforwardly implemented in finite-element programs able to solve static electromagnetic problems, is very attractive both for researchers and device manufactures who want to characterize superconducting tapes and calculate the effective critical current of superconducting devices.

High temperature superconductor Roebel cables are well known for their large current capacity and low AC losses. For this reason they have become attractive candidates for many power applications. The continuous transposition of their strands reduces the coupling losses while ensuring better current sharing among them. However, since Roebel cables have a true 3D structure and are made of several high aspect ratio coated conductors, modelling and simulation of their electromagnetic properties is very challenging. Therefore, a realistic model taking into account the actual layout of the cable is unavoidably a large scale computational problem. In this work, we present a full 3D model of a Roebel cable with 14 strands. The model is based on the H-formulation, widely used for 2D problems. In order to keep the 3D features of the cable (in particular the magnetization currents near the transpositions), no simplifications are made other than the reduction of the modelled length according to the periodicity of the cable structure. The 3D model is used to study the dependence of AC losses on the amplitude of the AC applied magnetic field or transport current. Beyond the importance of simulating the Roebel cable layout, this work represents a further step into achieving 3D simulation of superconducting devices for real applications.