Calculation of the local current density in high-temperature superconducting insulated rare earth–barium–copper oxide coils using a volume integral formulation and its contribution to coil protection

Abstract

High-temperature superconducting materials have remarkable current-carrying capabilities, even when operated under high magnetic fields. Since long rare earth-barium-copper oxide (REBCO)-coated conductors are now available (thanks to improvements in the fabrication process) this material has become an attractive option for high field magnet applications. However, such extreme operating conditions require an efficient quench protection system to prevent the coil from developing damaging hot spots, which greatly depends on the winding used. We focus here on the protection of insulated HTS coils against thermal runaways that can locally destroy the magnet. We developed a transient two-dimensional (2D) axisymmetric model using a volume integral formulation based on generalization of the partial element equivalent circuit method to compute the local current density distribution inside REBCO-insulated coils and account for local performance variations. Indeed, the most interesting property of integral methods is the requirement that only active regions are meshed, which leads to a significant reduction in the size of the problem. The formulation is introduced for general 3D cases and its adaptation to 2D axisymmetric problems is detailed. The formulation has been validated thanks to a bulk magnetization benchmark, the results of which (obtained with the finite element method) were compared with our integral formulation solution. The model has also been compared with experimental data obtained on a double pancake coil. The objective is to study the effects of magnetization on the transient voltage due to dynamic current distribution when ramping up the magnet so as to be able to determine some key parameters associated with coil protection. Such an approach is developed on a small-scale test case and the transient behaviours observed are discussed.

12 T Insulated REBCO Magnet Used as 1 MJ SMES: Protection Strategies and Preliminary Assembly Tests

“…As such, it rapidly decays to zero during a current plateau (stabilization of the current density distribution). This phenomenon, first observed in [4], has been modelled and studied in detail [5,13]. This drift forces us to perform a dynamic signal compensation.…”

“…For future, larger assemblies, the signals will have to be treated automatically, taking into account the transient components of the signals as well as the voltage peaks due to winding movements. Modeling efforts have been made in this direction [5,13].…”

Time constant of the transverse-field demagnetization of superconducting stacks of tapes

“…For infinitely long problems (2D), J becomes a scalar, further reducing the number of degrees of freedom compared to FEM methods in the H formulation. In this sense, MEMEP has many features in common with integral methods [33][34][35]. A difference is that MEMEP, as other variational methods, minimizes a functional to find the current density; being also able to take any E(J) relations into account, including the multivalued E(J) relation of the Critical State Model [30,31,36,37].…”

Chebyshev spectral method for superconductivity problems

“…The obtained results demonstrate an approximately linear convergence to the stack problem solution with an increase of the inner coil radius. Except for the work [9], where the coil with r 1 /a ≈ 1 has been considered, usually, r 1 /a > 10, see [10][11][12]. For such coils, even if not the Bean model but a more realistic field-dependent current voltage relation is employed, solution of the corresponding stack problem can, probably, serve as an accurate approximation.…”

“…To be more specific about computing the integrals for magnetic field calculation, we note that, using the Gauss-Chebyshev quadrature (9) with the roots of T N chosen as its knots, we obtain…”