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

Abstract

The emergence of second-generation high temperature superconducting tapes has favored the development of large-scale superconductor systems. The mathematical models capable of estimating electromagnetic quantities in superconductors have evolved from simple analytical models to complex numerical models. The available analytical models are limited to the analysis of single wires or infinite arrays that, in general, do not represent actual devices in real applications. The numerical models based on finite element method using the H formulation of the Maxwell's equations are useful for the analysis of medium-size systems, but their application in large-scale systems is problematic due to the excessive computational cost in terms of memory and computation time. Then it is necessary to devise new strategies to make the computation more efficient. The homogenization and the multi-scale methods have successfully simplified the description of the systems allowing the study of large-scale systems. Also, efficient calculations have been recently achieved using the T-A formulation. In the present work, we propose a series of adaptations to the multi-scale and homogenization methods so that they can be efficiently used in conjunction with the T-A formulation to compute the distribution of current density and hysteresis losses in the superconducting layer of superconducting tapes. The computation time and the amount of memory are substantially reduced up to a point that it is possible to achieve real-time simulations of HTS large-scale systems under slow ramping cycles of practical importance on personal computers.

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

“…As in the case of the H formulation, the selection of the elements used in the FEM matters. Two kind of elements are required, Lagrange second-order elements are used to approximate A and Lagrange first-order elements for T. These specific choices avoid spurious solutions, as justified in [50].…”

“…The case study used in this work is the same racetrack coil presented in [13,50]. This coil has ten pancakes, each consisting of 200 turns, bringing a total number of turns equal to 2000.…”

T-A Formulation for the Design and AC Loss Calculation of a Superconducting Generator for a 10 MW Wind Turbine

“…This formulation of Maxwell's equations was introduced in [23] and it has been used for modelling several superconducting devices [24], [25], [26]. In this approach, the magnetic vector potential A is computed in the entire geometry as:…”

“…The above mentioned integral can be further reduced by assuming a 1D element, which yields the following expression [25]:…”

The Application of a CMR-B-Scalar Sensor for the Investigation of the Electromagnetic Acceleration of Type II Superconductors

“…In the past decade, due to developments in software and computing power, the modelling of the electrodynamic behavior of type II superconductors has become less restrictive, and good agreements between experiments and simulations have been achieved when investigating superconductor magnetization [ 20 , 21 ] and magnetic levitation [ 22 , 23 , 24 ]. Various eddy current problem formulations have been proposed, suited to handle different superconductor application scenarios or to improve computation times [ 25 , 26 , 27 , 28 , 29 ].…”