A finite element model for simulating second generation high temperature superconducting coils/stacks with large number of turns

Abstract

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.

Iterative multi-scale method for estimation of hysteresis losses and current density in large-scale HTS systems

“…In that publication, a particular attention was paid to the homogenization method [17] and to the further development of the multi-scale method [18,19]. Recently, an efficient FEM model based on the T-A formulation of Maxwell's equations has been discussed in [20,21] for its use in large-scale systems as well. An alternative strategy is the minimum magnetic energy variation (MMEV) method, described in [22,23].…”

Comparison of 2D simulation models to estimate the critical current of a coated superconducting coil

“…In order to simplify the geometry, the racetrack pancake coil is modelled in 2D infinitely long model [12], [19] and the end effect of the two half circles are neglected as illustrated in Fig. 1.…”

“…The current vector potential is calculated in the superconductor, while the magnetic potential is calculated in the whole region. The governing equations in the two regions are described by [11], [12]:…”

“…The introduction of parameter P avoids the direct solution of the nonlinear E-J relationship for the superconductor. In the cross section of each conductor, P is uniformly distributed and is given by (12) where Iz is the transport current of the superconductor, S is the cross section of the superconductor, and Jc(Bx,By) represents the critical current density distribution inside the superconductor. To calculate the magnetic field density, the magnetic vector potential is used and Eq.…”

“…To speed-up the computation time of dynamic problems considering large number of turns, H. Zhang et al [11] and F. Liang et al [12] proposed an efficient transient FEM based on the T-A formulation. In [11] the ac losses of a 5-turn racetrack pancake coil were calculated in 3D and in [12] the ac losses of a 78-turn double pancake racetrack coil and 2000-turn pancake coils in 2D were computed. With the T-A formulation, the thickness of the superconductors is ignored: the superconductor layers are approximated to sheets in 3D and lines in 2D to tackle the high aspect ratio problem.…”