Numerical simulation is an effective tool for predicting the electromagnetic behavior of superconductors. Recently, a finite element method-based model coupling the T-A formulation with an electrical circuit has been proposed: the model presents the superconducting constituent as a global voltage parameter in the electrical circuit. This allows assessing the overall behavior of complex high-temperature superconductor (HTS) systems involving multiple power items, while keeping a high degree of precision on the presentation of local effects. In this work, the applicability of this model has been extended to large-scale HTS applications with hundreds or thousands of tapes by referring to two widely recognized methodologies, multi-scale and homogenization, to improve the computation efficiency. Based on the two approaches, three different models were developed and their effectiveness was assessed using the case study of a 1000 turn cylindrical HTS coil charged by a DC voltage source. The comparison of the calculated global circuit parameters, local field distributions, losses, and computation time proves that the computation efficiency can be improved with respect to a model simulating all HTS tapes, without compromising accuracy. The results indicate that the developed models can therefore be efficient tools to design and optimize large-scale HTS devices used in electrical machines and power grids. It is also found that the inductance of an HTS coil is varied according to the transport current and can be even higher than that of a normal conductor coil with the same geometry. We attribute this result to the superconductor’s non-uniform current distribution and relaxation effect during the dynamic process.

Numerical models based on the finite-element method are popular tools for investigating the macroscopic electromagnetic behavior of high-temperature superconductor (HTS) applications. This article explains how to use the $T$-$A$ formulation in COMSOL Multiphysics for modeling HTS coils in 2-D with different coupling scenarios between the turns. First we consider a racetrack coil wound from one piece of superconducting tape. Then, we consider a coil obtained by winding a cable composed of different HTS tapes. In the latter case, the tape turns are either electrically connected along their entire length or just at the two ends of the coil: in the model, these two different types of electrical connection are implemented with the help of the electrical circuit module. The current density distributions and the ac losses of the coils in the different coupling scenarios are compared and discussed. The limits of applicability of the presented approach are pointed out. The model is developed for the straight section of racetrack coils, but can be easily adapted to axisymmetric geometries.

The short-circuit levels have increased considerably in transmission and distribution systems in the last years. Fault current limiter (FCL) devices are a potential solution to this problem. Among several FCL topologies, this group has good experience in the use of superconducting fault current limiters (SFCL) to reduce the electrical current during short-circuits. The literature also presents studies of the saturated iron core superconducting fault current limiter (SIC-SFCL) topology employing mathematical modeling and prototypes design. Some of them have shown promising results, including the construction of pilot prototypes in medium and high voltage substations. The SIC-SFCL simulation studies presented optimal topologies that reduce the amount of ferromagnetic material used in the core and represent well the behavior of this limiter. The finite element method and the finite element analysis are suitable to model the SIC-SFCL. However, a more detailed study focusing on the optimization of the DC bias superconducting coil of the SIC-SFCL has not been presented in the literature yet. In this context, this work proposes a multi-objective optimization method using the Nelder–Mead algorithm to find an optimal geometry for the superconducting coil. In this optimization, the objectives functions are: to maximize the critical current density in the high-temperature superconductor (HTS), minimize the voltage drop in the copper winding, minimize the current through the DC biased superconducting winding, and minimize the price of the HTS superconducting winding. Before implementing the multi-objective optimization algorithm, we have tested a non-superconducting saturated iron core prototype and used the results to validate the simulation models. After that, we have replaced the DC copper winding with an HTS coil in the simulations and initiate the optimization process. Results show that constructing the DC bias superconducting coil using the minimum possible fill factor might not be the best choice.

Power systems are becoming more interconnected and complex. The distributed generation expands and spreads across the grids, reducing the distance between the load and the generation. In addition, several substations are aging after decades of operation and their equipment struggle to sustain the ever increasing fault levels. In this context, the fault current limiter (FCL) arrived as a solution to mitigate this problem. Considering the FCL devices, the resistive superconducting FCL (R-SFCL) is the most mature technology with potential to be produced in mass scale, due to its ability to quickly change its impedance during a fault current and its high current density capacity. In this paper, a novel R-SFCL topology is presented, which has an unique design that allows a compact size and the possibility of modulated assembly. These characteristics enable setups for various voltage and current levels. One advantage of this topology is the compromise between volume and high heat exchange that can reduce the recovery time under load. One bench prototype was modeled using the thermal–electrical analogy implemented in ATPDraw, tested in two different labs. Tests were performed at faults levels of 12 kA peak , 5 kA rms and 2.7 kA rms for 137 V. Measured and simulated results were compared, resulting in a relative error of less than 12%. Two contributions can be highlighted: the new design of the R-SFCL and the inclusion in the convection heat exchange model curves for the heating (during the quench) and cooling (after fault), which allows to predict the recovery under load.

The manufacturing of commercial REBCO tapes, REBCO referring to Rare-earth barium copper oxide, has matured enough to lead to a variety of applications ranging from scientific instruments to electric power systems. In particular, its large current density with a high n index and low hysteresis losses make it a strong candidate for specific applications relying on the dependence of its resistance on current. Despite its advantages, there are still issues that remain to be addressed, such as the scarcity of experimental data for the basic characteristics of the superconductor over a wide range of temperature and applied magnetic field, the inhomogeneity of these characteristics along the conductor length, as well as the anisotropy of the critical current and n index with respect to the direction of the applied magnetic field. To better utilize the technology, it is therefore sensible to understand the relevancy of these issues so that one could simulate as accurately as possible the physics of the superconductor, at least the dynamics that may impact the correct operation of the superconducting device. There are different levels of modelling to achieve such a goal that can either focus on the performance of the superconductor itself, or on the whole device. The present work addresses some of the latest developments in the modelling of commercial REBCO tapes in power systems with a particular focus on the thermoelectric behavior of superconducting devices connected to external circuits. Two very different approaches corresponding to two different scales in the modelling of superconducting devices are presented: (1) analysis using equivalent models and lumped parameters to study the thermoelectric response of superconducting devices as a whole, (2) Finite Element Analysis (FEA) to compute distributed fields such as current density, magnetic flux density and local losses in tapes. In this context, this paper reviews both approaches and gives a broad variety of examples to show their practical applications in electric power systems. Firstly, they show the relevance of the technology in power systems engineering. Secondly, they allow inferring the necessary level of model details to optimize the operation of superconducting power devices in power grids. This level of details relies completely on the knowledge of some basic measurable properties of superconducting tapes (critical current and n index) and their cooling conditions.

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.