An efficient two dimensional T-A formulation based approach is proposed to calculate the electromagnetic characteristics of tape stacks and coils made of second generation high temperature superconductors. In the approach, a thin strip approximation of the superconductor is used in which the superconducting layer is modeled as a 1-dimensional domain. The formulation is mainly based on the calculation of the current vector potential T in the superconductor layer and the calculation of the magnetic vector potential A in the whole space, which are coupled together in the model. Compared with previous T-based models, the proposed model is innovative in terms of magnetic vector potential A solving, which is achieved by using the differential method, instead of the integral method. To validate the T-A formulation model, it is used to simulate racetrack coils made of second generation high temperature superconducting (2G HTS) tape, and the results are compared with the experimentally obtained data on the AC loss. The results show that the T-A formulation is accurate and efficient in calculating 2G HTS coils, including magnetic field distribution, current density distribution, and AC loss. Finally, the proposed model is used for simulating a 2000 turn coil to demonstrate its effectiveness and efficiency in simulating large-scale 2G HTS coils.

The frequency-dependent critical current of a superconductor strip and Roebel cable has been studied using a 2D finite element simulation. It is shown that the critical current of the superconductor increases with frequency as f 1/n , where n is the exponent of the power law flux creep model. Transport ac loss in a superconductor strip decreases with frequency as f −2/n when the amplitude of the applied ac current is far less than its critical current. However, when the applied current is large and becomes comparable to the critical current, the transport ac loss decreases with frequency as 1/ f . The analytical results are substantiated with available experimental data and the results of a 2D finite element simulation.

A finite element model for a YBCO pancake coil with a magnetic substrate is developed in this paper. An axial symmetrical H formulation and the E-J power law are used to construct the model, with the magnetic substrate considered by introducing an extra time-dependent term in the formula. A pancake coil is made and tested. The measurement of critical current and transport loss is compared to the model result, showing good consistency. The influence of magnetic substrate in the condition of AC and DC current is studied. The AC loss decreases without a magnetic substrate. It is observed that when the applied DC current approaches the critical current the coil turn loss profile changes completely in the presence of magnetic substrate due to the change of magnetic field distribution.

The application of HTS coils for fully HTS machines has become a new research focus. In the stator of an electrical machine, HTS coils are subjected to a combination of an AC applied current and AC external magnetic field. There is a phase shift between the AC current and AC magnetic field. In order to understand and estimate the total AC loss of HTS coils for electrical machines, we designed and performed a calorimetric measurement for a 2G HTS racetrack coil. Our measurement indicates that the total AC loss is greatly influenced by the phase shift between the applied current and the external magnetic field when the magnetic field is perpendicular to the tape surface. When the applied current and the external magnetic field are in phase, the total AC loss is the highest. When there is a 90 degree phase difference, the total AC loss is the lowest. In order to explain this phenomenon, we employ H formulation and finite element method to model the 2G HTS racetrack coil. Our calculation agrees well with experimental measurements. Two parameters are defined to describe the modulation of the total AC loss in terms of phase difference. The calculation further reveals that the influence of phase difference varies with magnetic field direction. The greatest influence of phase difference is in the perpendicular direction. The study provides key information for large-scale 2G HTS applications, e.g. fully HTS machines and superconducting magnetic energy storage, where the total AC loss subjected to both applied currents and external magnetic fields is a critical parameter for the design.

It is widely believed that the second-generation high-temperature superconducting (2G HTS) tapes with magnetic substrates suffer higher transport loss compared to those with non-magnetic substrates. To test this, we prepared two identical coils with magnetic and non-magnetic substrates, respectively. The experimental result was rather surprising that they generated roughly the same amount of transport loss. We used finite element method to understand this result. It is found that, unlike in the single tape where the magnetic field-dependent critical current characteristic can be neglected and the effect of magnetic substrate dominates, the magnetic field-dependent critical current characteristic of 2G tape plays as an equally important role as magnetic substrate in terms of HTS coils.