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

Abstract

In recent years, commercial HTS materials have gained an increasing interest for their use in applications involving large-scale superconductor systems. These systems are typically made from hundreds to thousands of turns of conductors. These applications can range from power engineering devices like power transformers, motors and generators, to commercial and scientific magnets. The available analytical models are restricted to the analysis of individual tapes or relatively simple assemblies, then it is not possible to apply these models to the study of large-scale systems and other simulation tools are required. Due to the large number of turns, the simulations of a whole system can become prohibitive in terms of computing time and load. Therefore, an efficient strategy which does not compromise the accuracy of calculations is needed. Recently, a method, based on a multi-scale approach, showed that the computational load can be lowered by simulating, in detail, only several significant tapes from the system. The main limitation of this approach is the inaccuracy of the estimation of the background magnetic field, this means the field affecting the significant tapes produced by the rest of the tapes and by external sources. To address this issue, we consider the following two complementary strategies. The first strategy consists in the iterative implementation of the multi-scale method. The multi-scale method solves itself a dynamic problem, the iterative implementation proposed here is the iterative application of the multi-scale method, and a dynamic solution is obtained at each iteration. The second strategy is a new interpolation method for current distributions. With respect to conventional interpolation methods, a more realistic current density distribution is then obtained, which allows for a better estimation of the background magnetic field, and consequently, a better estimation of the hysteresis losses. In contrast with previous works, here we do not focus only on the estimation of the hysteresis losses, but also the estimation of the current density distribution is addressed. This new method is flexible enough to simulate different sections of the system with a better level of detail while providing a faster computational speed than other approaches. In order to validate the proposed method, a case study is analyzed via a reference model, which employs the H-formulation of Maxwell's equations and includes all the system's tapes. The comparison, between the reference model and the iterative multi-scale model, shows that the computation time and memory demand are greatly reduced. In addition, a very good agreement with respect to the reference model, both at a local and global scale, is achieved.

Real-time simulation of large-scale HTS systems: multi-scale and homogeneous models using the T–A formulation

“…The multi-scale method, as presented in [20,35], uses two different submodels, single tape and coil. The single tape submodel uses the H formulation and computes the J distribution in the analyzed tapes.…”

“…This method was proposed in [34], with later refinements added in [20]. The last version of the method incorporates an iterative process to improve the accuracy of the current density in the analyzed tapes and, consequently, of the losses [35].…”

Advanced electromagnetic modeling of large-scale high-temperature superconductor systems based on H and T-A formulations

“…The following simultaneous multi-scale models presented below were implemented in a single COM-SOL model, and for convenience just the simpler linear interpolation was used. This is not a major drawback because the ICDF interpolation makes only a marginal contribution to the accuracy of the model [49].…”

Electromagnetic modelling using T‐A formulation for high‐temperature superconductor (RE)Ba 2 Cu 3 O x high field magnets

“…However, these methods cannot do a comprehensive electromagnetic analysis on the HTS, and are also not suitable for complex electromagnetic environments and operations. Finite-element method (FEM) based on H-formulation has been widely applied on the electromagnetic modelling of HTS applications [30][31][32][33], and homogenous Hformulation model has been developed to reduce the computation cost [34,35]. Its governing equation uses magnetic intensity H as solution variable, and the whole model can be built and solved in commercial FEM software Comsol Multi-physics.…”