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

In recent years, commercial high-temperature superconductor (HTS) materials have gained 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, therefore 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 of the iterative implementation of the multi-scale method. The multi-scale method itself solves 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 only focus 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.