Electrical machines employing superconductors are attractive solutions in a variety of application domains. Numerical models are powerful and necessary tools to optimize their design and predict their performance. The electromagnetic modeling of superconductors by finite-element method (FEM) is usually based on a power-law resistivity for their electrical behavior. The implementation of such constitutive law in conventional models of electrical machines is quite problematic: the magnetic vector potential directly gives the electric field and requires using a power-law depending on it. This power-law is a non-bounded function that can generate enormous uneven values in low electric field regions that can destroy the reliability of solutions. The method proposed here consists in separating the model of an electrical machine in two parts, where the magnetic field is calculated with the most appropriate formulation: the H-formulation in the part containing the superconductors and the A-formulation in the part containing conventional conductors (and possibly permanent magnets). The main goal of this work is to determine and to correctly apply the continuity conditions on the boundary separating the two regions. Depending on the location of such boundary - in the fixed or rotating part of the machine - the conditions that one needs to apply are different. In addition, the application of those conditions requires the use of Lagrange multipliers satisfying the field transforms of the electromagnetic quantities in the two reference systems, the fixed and the rotating one. In this article, several exemplary cases for the possible configurations are presented. In order to emphasize and capture the essential point of this modeling strategy, the discussed examples are rather simple. Nevertheless, they constitute a solid starting point for modeling more complex and realistic devices.

Superconducting cables have been proven in a variety of pilot projects and utility installations, demonstrating several of their advantages, including compact size and low energy losses, which can make the technology economically attractive for certain applications. It is clear though that different applications impose different requirements and challenges, but also opportunities for the cables. An interesting application is high-power DC transfer at medium voltage (MVDC). The high-current capability of the superconductor allows for a reduction in voltage while maintaining or increasing the power transfer level. In this way, one MVDC superconducting cable can replace one or more conventional high-voltage DC cables. In the European project Superconducting cables for sustainable energy transition (SCARLET), two types of MVDC cables will be developed, one based on HTS and one on MgB ₂ materials. Additionally, protection requirements will be considered, including the development of a modular DC fault current limiter for 10 kA. A main motivation for the development is the elimination of costly high-voltage converter stations when going from high to medium voltage, e.g., for offshore wind power plants. Another feature is the combined hydrogen and electricity transmission from generation sites to industry or mobility end users. This paper describes the superconducting MVDC cable concept as well as the main challenges and research needed to develop and type test the cables.

This paper analyses the current distribution in no-insulation (NI) coils in a layer-wound configuration. The investigation aims at comparing the electrical characteristic of two coils wound from the same BSCCO tape, with or without electrical insulation between turns. Both coils are characterized by a very similar geometry, with the same number of turns and layers. Both coils, cooled in liquid nitrogen bath, are charged until the tape critical current is exceeded. To interpret the measurements and analyze the current distribution within the winding, a lumped-parameter equivalent electrical circuit is developed and solved numerically in a time-varying regime. The model results are compared with the signals acquired through voltage taps soldered at the same locations in both coils. Finally, the model is applied to investigate the impact of the transverse contact resistance and to estimate the most stressed locations of the coil during charging, in terms of power produced by Joule effect.

The first Italian Superconducting Fault Current Limiter 9 kV/3.4 MVA was developed and lab tested by Ricerca sul Sistema Energetico S.p.A. and then installed in the Milan distribution grid belonging to A2A Reti Elettriche S.p.A. This resistive-type SFCL device was operational since March 2012 and hence has been field tested for more than two years, providing a large amount of experimental data with a significant experience gaining. Some preliminary results were already presented; however, this paper reports on the main outcomes of the field testing activity including the effective short-circuit current limitation provided by this SFCL prototype during a severe real three-phase short-circuit event in the Milan distribution grid. The SFCL device showed to behave as expected, promptly limiting the short-circuit current by a factor of about 2. This is the first SFCL limiting action in Italy and one of the very first worldwide. Further to this first successful installation, the hosting utility A2A agreed to install in the same substation a new SFCL device protecting four different feeders, therefore implying a SFCL upgrading up to 15.6 MVA. Therefore, this paper also anticipates the key steps towards the development of the upgraded SFCL prototype to be commissioned in early 2015.

In prevision of an expansion in the installed power and the progressive increase in electrification toward energy transition, high-efficiency electric grids are required. In this process, superconducting power cables could play an important role as they can be installed either to realize new lines or to replace existing infrastructures, potentially reducing the costs and the environmental impact compared to conventional solutions. The technical-economic convenience of the superconducting choice depends on the design parameters of the line, such as the voltage and power levels and the line length. For each condition, the configuration of the cable and its cooling system must be optimized while complying with a number of electrical and geometrical constraints. Identifying a priori the optimal cable configuration is not trivial, as the numerous variables involved are mutually dependent. This article describes a novel tool developed to quantify technical-economic aspects of superconducting cables, allowing the user to freely select the operating conditions for a generic electric line. The tool adopts a genetic algorithm to solve a constrained minimization problem for a multivariable function, returning the cable configuration characterized by the lowest costs. For this study, ac concentric cables realized with high temperature superconductors are selected, but the approach described can easily be adapted to other types of cable. By means of suitable simplifying hypotheses, the equations used to size the cable components and their corresponding costs, estimate the thermal inputs and describe the cryogen flows are introduced as parametric equations. Finally, the results of a detailed study on the impact of the relevant parameters on the cable design and costs is provided.

So far, the No-insulation (NI) technology using High Temperature Superconducting (HTS) materials has been limited to magnetic and power devices involving slow charging rates, generally avoiding AC applications, due to the onset of transverse currents. However, the limits of applicability are not well defined and few quantitative comparisons between insulated and NI coils under time-varying regimes have been presented. A proper analysis of the AC losses under these conditions is important to assess the possible use of NI windings for fast-charging or AC devices. This paper focuses on the layer-wound configuration of NI coils, less studied in the literature than the pancake-wound configuration. The investigation aims at comparing the behavior of two coils wound from the same tape, with or without electrical insulation between turns. The two coils are characterized by a very similar geometry, with the same number of turns and layers. The AC losses are assessed by adopting appropriate experimental setups in two different laboratories. Charge-discharge tests are performed with different ramp-rates up to a peak current with a triangular or trapezoidal waveform, determining the electrodynamic losses during these current cycles. Furthermore, the windings are supplied with sinusoidal currents of different amplitude and frequency, pointing out the differences in terms of AC losses between the two coil configurations.