A coupling method of the superconducting devices modeled by finite element method with the lumped parameters electrical circuit

Abstract

Superconducting devices have been widely studied over these years. Their application can be found in cables for electric power transmission, energy storage systems, magnetic levitation, electric machines, and fault current limiters. The literature presents some formulations to model the superconductors’ behavior using the finite element method (FEM), such as the H, the AV, and the T formulations, among others. Many superconducting devices have been simulated and designed using some of these formulations. However, none method available offers a coupling between an electric power system, simulated using electrical lumped parameters, to the superconducting FEM model. In this context, this work introduces a methodology for coupling superconducting devices in FEM to lumped parameters composing the power system. Here, a case study with a Saturated Iron Core Superconducting Fault Current Limiter was presented to apply the proposed methodology. This research analyzes the influence of the self and external fields in the superconducting coil on its critical current density. Moreover, it investigates the DC-biased coil voltage drop and the superconducting resistance. Besides, the paper presents the simulations of short circuits for various DC currents applied to the superconducting coil. Short-circuit tests were performed for validating the simulation results, and it showed a maximum error of 15% for the compared points.

Essential Material Knowledge and Recent Model Developments for REBCO-Coated Conductors in Electric Power Systems

“…In the present work, the FEM model is coupled to an external circuit and the SCC is then part of an electrical grid modelled as lumped parameters [23]. The recent T-A formulation of the Maxwell equations is used to describe the electromagnetic behavior of the superconductor [55][56][57][58][59].…”

“…For this new formulation, a new method for coupling the superconducting device and the electrical grid considering all the non-linearities present in the system (ferromagnetic and superconductor) has been purposely developed. The initial model was two dimensional (2D) [23] but it was quickly expanded to three dimensions (3D) [60]. These models are presented hereinafter.…”

“…Subsequently, 2D and 3D examples of a simple superconducting coil connected to an external circuit are detailed. In the 2D model, the power losses are computed via two methods for self consistency [23,34,61,62].…”

“…The coupling method proposed in [23] and applied in [6] provides a proper way to consider all the material non-linearities for both the superconductor and the ferromagnetic core (when present) while still allowing an easy coupling with electrical lumped-parameters systems in 2D and 3D. Through the FEM, the electrical parameters of the superconducting device are calculated and passed to the power grid model.…”

“…By essence, it leads to an approximated solution which accuracy depends on the level of geometric details and the fineness of the mesh used to discretize the geometry [22]. Nevertheless, with the advances in computer technology with more powerful products available to the general public alongside the development of numerical computation, a new trend in the modeling of superconducting power components could emerge, combining the sophisticated and accurate FEA with circuit analysis [23]. The main advantage of using FEM-based models to simulate HTS components is the high degree of precision achieved on the local representation of the physics of the superconductor.…”