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In several cases, substations have become incapable of supporting faults due to short circuit levels increasing. Fault current limiters (FCLs) are a potential solution for this problem. Among several FCL topologies presented in the literature, the saturated Iron-Core Superconducting Fault Current Limiter (SIC-SFCL) has shown promising results in real tests in substations. In this context, this paper presents the impacts of the different kinds of short circuits in the SIC-SFCL device. To reproduce various types of faults, the SIC-SFCL is modeled in a 3D framework considering both ferromagnetic and superconducting non-linearities. Moreover, the proposed 3D FEM model can couple the SIC-SFCL to the electric power system, also representing the electrical grid and the protection systems. For this investigation, the DC-biased superconducting coil's normalized current density and the iron cores' magnetic flux density are examined in light of the different short circuits. The simulations are compared with measurements in a bench prototype, showing a maximum error of 16.5~%. Furthermore, different short circuit types were investigated and compared, which is possible only using a 3D model. The highest limitation occurred in the phase-to-phase short circuit case. In the DC circuit of the SIC-SFCL, the highest transient period has happened in the single-phase short circuit. At last, the phase-to-phase fault presented the highest DC current during the transient.

Funding Information: Financial support was provided by the Swiss National Science Foundation (Grant No. 200021_184940). Funding Information: Networking support provided by the European Cooperation in Science and Technology, COST Action CA19108 (Hi-SCALE) is acknowledged. Funding Information: Supported by Fundação para a Ciência e a Tecnologia, Portugal, with reference UIDB/00066/2020. Funding Information: A part of this work was supported by the Russian National Technology Initiative Foundation (Grant ID 0000000007418QR20002). Funding Information: The research was also supported by the European Synchrotron Radiation Facility (Grant No. MA-2767). Funding Information: This work was supported in part by the New Zealand Ministry of Business, Innovation and Employment (MBIE) by the Strategic Science Investment Fund ‘‘Advanced Energy Technology Platforms’’ under Contract RTVU2004. Funding Information: Y Wang acknowledges support from the National Science Foundation (NSF) Award DMR-2132338. R P Camata and C-C Chen are supported by the FTPP Program funded by NSF EPSCoR RII Track-1 Cooperative Agreement OIA-2148653. C-C Chen also acknowledges support from the NSF Award DMR-2142801. Publisher Copyright: © 2023 The Author(s). Published by IOP Publishing Ltd. This paper presents a roadmap to the application of AI techniques and big data (BD) for different modelling, design, monitoring, manufacturing and operation purposes of different superconducting applications. To help superconductivity researchers, engineers, and manufacturers understand the viability of using AI and BD techniques as future solutions for challenges in superconductivity, a series of short articles are presented to outline some of the potential applications and solutions. These potential futuristic routes and their materials/technologies are considered for a 10-20 yr time-frame. publishersversion published

More than a century after the discovery of superconductors (SCs), numerous studies have been accomplished to take advantage of SCs in physics, power engineering, quantum computing, electronics, communications, aviation, healthcare, and defence-related applications. However, there are still challenges that hinder the full-scale commercialization of SCs, such as the high cost of superconducting wires/tapes, technical issues related to AC losses, the structure of superconducting devices, the complexity and high cost of the cooling systems, the critical temperature, and manufacturing-related issues. In the current century, massive advancements have been achieved in artificial intelligence (AI) techniques by offering disruptive solutions to handle engineering problems. Consequently, AI techniques can be implemented to tackle those challenges facing superconductivity and act as a shortcut towards the full commercialization of SCs and their applications. AI approaches are capable of providing fast, efficient, and accurate solutions for technical, manufacturing, and economic problems with a high level of complexity and nonlinearity in the field of superconductivity. In this paper, the concept of AI and the widely used algorithms are first given. Then a critical topical review is presented for those conducted studies that used AI methods for improvement, design, condition monitoring, fault detection and location of superconducting apparatuses in large-scale power applications, as well as the prediction of critical temperature and the structure of new SCs, and any other related applications. This topical review is presented in three main categories: AI for large-scale superconducting applications, AI for superconducting materials, and AI for the physics of SCs. In addition, the challenges of applying AI techniques to the superconductivity and its applications are given. Finally, future trends on how to integrate AI techniques with superconductivity towards commercialization are discussed.

In recent years, the $H$ formulation of Maxwell's equations has become the de facto standard for simulating the time-dependent electromagnetic behavior of superconducting applications with commercial software. However, there are cases where other formulations are desirable, for example for modeling superconducting turns in electrical machines or situations where the superconductor is better described by the critical state than by a power-law resistivity. In order to accurately and efficiently handle these situations, here we consider two approaches based on the magnetic vector potential: the $T$ - $A$ formulation of Maxwell's equations (with power-law resistivity) and the implementation of a quasi critical state model (QCSM) with a steep $E$ - $J$ relationship limited at $J_{\rm c}$ . In this article, we extend the $T$ - $A$ formulation to thick conductors so that large coils with different coupling scenarios between the turns can be considered. We also discuss the QCSM in terms of its ability to calculate ac losses: in particular, we investigate the dependence of the calculated ac losses on the frequency of the ac excitation and the possibility of using quick one-step (instead of full-cycle) simulations to calculate the ac losses.

Background: Ayurveda is widely practiced in South Asia in the treatment of osteoarthritis (OA). The aim of these secondary data analyses were to identify the most relevant variables for treatment response and group differences between Ayurvedic therapy compared to conventional therapy in knee OA patients. Methods: A total of 151 patients (Ayurveda n = 77, conventional care n = 74) were analyzed according to the intention-to-treat principle in a randomized controlled trial. Different statistical approaches including generalized linear models, a radial basis function (RBF) network, exhausted CHAID, classification and regression trees (CART), and C5.0 with adaptive boosting were applied. Results: The RBF network implicated that the therapy arm and the baseline values of the WOMAC Index subscales might be the most important variables for the significant between-group differences of the WOMAC Index from baseline to 12 weeks in favor of Ayurveda. The intake of nutritional supplements in the Ayurveda group did not seem to be a significant factor in changes in the WOMAC Index. Ayurveda patients with functional limitations > 60 points and pain > 25 points at baseline showed the greatest improvements in the WOMAC Index from baseline to 12 weeks (mean value 107.8 ± 27.4). A C5.0 model with nine predictors had a predictive accuracy of 89.4% for a change in the WOMAC Index after 12 weeks > 10. With adaptive boosting, the accuracy rose to 98%. Conclusions: These secondary analyses suggested that therapeutic effects cannot be explained by the therapies themselves alone, although they were the most important factors in the applied models.

For modelling superconductors, interpolation and analytical formulas are commonly used to consider the relationship between the critical current density and other electromagnetic and physical quantities. However, look-up tables are not available in all modelling and coding environments, and interpolation methods must be manually implemented. Moreover, analytical formulas only approximate real physics of superconductors and, in many cases, lack a high level of accuracy. In this paper, we propose a new approach for addressing this problem involving artificial intelligence (AI) techniques for reconstructing the critical surface of high temperature superconducting (HTS) tapes and predicting their index value known as n-value. Different AI models were proposed and implemented, relying on a public experimental database for electromagnetic specifications of HTS tapes, including artificial neural networks (ANN), eXtreme Gradient Boosting (XGBoost), and kernel ridge regressor (KRR). The ANN model was the most accurate in predicting the critical current of HTS materials, performing goodness of fit very close to 1 and extremely low root mean squared error. The XGBoost model proved to be the fastest method, with training computational times under 1 s; whilst KRR could be used as an alternative solution with intermediate performance.

In large-scale photovoltaic (PV) power plants, the integration of a battery energy storage system (BESS) permits a more flexible operation, allowing the plant to support grid stability. In hybrid PV+BESS plants, the storage system can be integrated by using different power conversion system (PCS) layouts and different charge–discharge strategies. In the AC-coupling layout, the BESS is connected to the ac-side of the system through an additional inverter. In the DC-coupling layout, the BESS is connected to the dc-side, with or without a dedicated dc–dc converter, and no additional inverter is needed. Referring to a 288 MWp PV plant with a 275 MWh BESS, this paper compares the PCS efficiency between AC- and DC-coupling solutions. The power injected into the grid is obtained considering providing primary power-frequency regulation services. A charging and discharging strategy of the BESS is proposed to ensure cyclic battery energy shifting. The power flows in the different components of the system that are obtained under realistic operating conditions, and total energy losses and annual average efficiency are calculated accordingly. Finally, results show a higher efficiency of DC-coupling compared to the AC-coupling layout.

The paper reports the results of the test and modelling activities carried out on large commercial supercapacitor cells at high current. Four commercials cells, with rated capacitance of 3000 F and rated voltage of 2.7 V, are considered. All cells are submitted to consecutive charge/discharge cycles at constant current. A test current in the range 80-130 A is used, which is comparable with the maximum operating current (up to 150 A) that the cells can reach in practical operations. A circuit model of the cells, able to reproduce the most relevant dynamic behavior, with a good compromise between accuracy, simplicity and robustness of the model's parameters, is also developed and validated against the experimental data. It is shown that all the investigated commercial cells are characterized by similar phenomena and comply with the same circuit model. Moreover, it is shown that the circuit parameters of the cells are in the same range and are weakly dependent on the test current. The obtained circuit parameters are accurately reported for all the cells and made fully accessible to users.

The high-Tc superconducting (HTS) dynamo is a promising device that can inject large DC supercurrents into a closed superconducting circuit. This is particularly attractive to energise HTS coils in NMR/MRI magnets and superconducting rotating machines without the need for connection to a power supply via current leads. It is only very recently that quantitatively accurate, predictive models have been developed which are capable of analysing HTS dynamos and explain their underlying physical mechanism. In this work, we propose to use the HTS dynamo as a new benchmark problem for the HTS modelling community. The benchmark geometry consists of a permanent magnet rotating past a stationary HTS coated-conductor wire in the open-circuit configuration, assuming for simplicity the 2D (infinitely long) case. Despite this geometric simplicity the solution is complex, comprising time-varying spatially-inhomogeneous currents and fields throughout the superconducting volume. In this work, this benchmark problem has been implemented using several different methods, including H-formulation-based methods, coupled H-A and T-A formulations, the Minimum Electromagnetic Entropy Production method, and integral equation and volume integral equation-based equivalent circuit methods. Each of these approaches show excellent qualitative and quantitative agreement for the open-circuit equivalent instantaneous voltage and the cumulative time-averaged equivalent voltage, as well as the current density and electric field distributions within the HTS wire at key positions during the magnet transit. A critical analysis and comparison of each of the modelling frameworks is presented, based on the following key metrics: number of mesh elements in the HTS wire, total number of mesh elements in the model, number of degrees of freedom (DOFs), tolerance settings and the approximate time taken per cycle for each model., 22 pages, 7 figures, 2 tables

The volume integral equation method based on the current vector potential approximated by means edge element basis function is a well-established approach for 3-D eddy currents computation. The application of the method is straightforward when simply connected geometries and no connection with external circuits are involved. In this case, in fact, the solving system is easily obtained based on tree–cotree decomposition of the primal graph. However, when multiply connected geometries or external generators are considered, “additional” degrees of freedom, not related to interior cotree edges of the primal graph, need to be identified and involved to assure the consistency of the numerical solution. In this article, the link between the volume integral equation method and the circuit is investigated in detail, and the circuit view is used as a guide for systematically finding the additional degrees of freedom arising in case of multiply connected geometries and/or external circuits. In particular, the dual graph is introduced as the support of the circuit and it is shown that this is the natural frame for taking the topology into account. For multiply connected geometries, the additional degrees of freedom are related to loop currents crossing one only time (or an odd number of times) any cutting surface making the domain simply connected, and are found by applying a minimum path algorithm on the dual graph forming the circuit. In case of conducting domain connected to an external generator, an extended dual graph is introduced for finding the further additional degrees of freedom. This article also researches into the possibility to replace the usual current density of the elements, obtained via facet-element shape functions and exactly matching the current of the faces, with a uniform current density obtained by means of a minimum error procedure and approximately matching the current of the faces. The use of this uniform current density, besides improving the calculation time and the accuracy of the coupling coefficients, also allows the extension of the volume integral equation method to discretizations of the problem domain made of arbitrarily shaped polyhedral elements.

The levitation force between a single grain YBCO cylindrical bulk superconductor and a permanent magnet is investigated. The force measured both in zero field cooling and field cooling condition in the temperature range 20 K - 80 K is reported. The dependence of peak levitation force and power dissipation on the temperature is analyzed and the saturation of the peak force with increasing the critical current of the material is pointed out. A numerical analysis is also carried out for understanding the electrodynamics of the levitation mechanism. Good reproduction of the measured data is obtained and relevant observed phenomena, such as hysteresis of the levitation cycle at high temperature and saturation of the peak force at low temperature, are explained by means of the model. Characterization of the material in terms of critical current density in the field range 0 T - 0.5 T is also obtained by means of the numerical model by means of the fitting of the measured data.

MgB2 material operating at moderate field can conveniently be considered for short-term cost-effective implementation of superconducting magnetic energy storage ( SMES). Due to the intrinsic performance of this material, moderate field operation and cryogen free cooling in the range 10–20 K need to be considered. For investigating the feasibility of MgB2 based SMES technology a 10 kW—2 s system is under development. A small MgB2 coil was developed and tested as the first step of this study. The cooling was obtained by means of a cryogen-free test facility based on a two-stages Gifford–McMahon regenerative heat exchanger. A power conditioning system (PCS) was also developed in order to connect the coil with the power grid. The PCS is based on power mosfet components and consists of two parallel dc/dc boost converters and an inverter connected to a common dc bus at 100 V. Continuous operation of the coil at a charge/discharge rate up to 24 kW can be achieved by means of the PCS. Details of the layout of the coil and the thermal connection with the cryocooler are discussed in this paper. Results of cooling test are reported. Possible SMES operation is also discussed.

This paper investigates the conditions of use and the equivalence of various constitutive laws used to model the electromagnetic behavior of high-temperature superconductors: two versions of the critical state model (CSM), the power law model, and a so-called percolation model. All these models can be used to represent the same superconducting material with some limit of accuracy. The CSM and the power law model are well known in the literature. The percolation model can be seen as a generalization of the power law model that includes also a CSM-like behavior at very low electric fields. The investigation has been carried out for three types of operating conditions: the sudden application of a dc excitation, a pure ac excitation, and combined dc and ac excitations. The equivalence between the different constitutive laws is shown to be a function of the magnitude of the electric fields and of the time scales involved. In the dc case, long time scales and very small electric fields are predominant; thus, the superconductor requires a model that is accurate at low electric fields, such as the percolation model. The losses then arise from the relaxation of the magnetic field in the sample. In the ac case, the power law and percolation models are nearly identical when considering power frequencies, so choosing the simpler power law model is fully acceptable in practice. In addition, the CSM coincidentally provides good predictions of the losses in the power frequency range. In the dc+ac case, when time scales in the range of minutes to hours are considered, it is shown that ac losses dominate over relaxation losses, and the same conclusions as for the ac case apply.

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.

L’invenzione concerne un apparato e un metodo di riscaldamento ad induzione, in particolare per riscaldare manufatti da lavorare di grandi dimensioni comprendenti un materiale magnetico, in particolare per riscaldare manufatti in acciaio di grandi dimensioni.

The connection system of offshore wind parks with the onshore power grid can have a crucial impact on the overall energy yield. The possible (ac and dc) connection systems for offshore wind parks are investigated in detail and compared both in terms of cost and losses. Both conventional copper (Cu) cables and high-temperature superconductor (HTS) cables are considered in the case of dc systems. An offshore wind park with a 360-MW peak power capacity in a 50-km distance from the shore is considered as within this case study. The comparison between the connection systems is carried out in terms of overall energy loss in a full year. The economical comparison is also discussed in detail. It is shown that a hybrid (HTS and Cu) medium-voltage dc connection system with a two-stage dc collector grid followed by an HTS high-voltage dc transmission at ±150 kV offers reduced losses and is cost competitive with respect to ac connection systems based on today's quotation of HTS material. In the near future, as soon as the foreseen reduction in the cost of HTS material is achieved, a full-HTS dc connection system can become the most cost-attractive solution.

The feasibility of an innovative in-depth AC induction heating method for large steel slabs is investigated. Aside from the AC field, which induces the heating currents, a large DC magnetic field is also applied, which brings the material to saturation. Due to saturation, permeability is reduced by orders of magnitude and the penetration depth is drastically increased, thus enabling much faster and more uniform heating. In order to produce the field needed for the saturation of common steel workpieces, lossless DC superconducting magnets need to be employed. A possible layout of an AC induction heater employing magnetic saturation (saturated AC induction heater) is discussed. The conceptual design of the superconducting magnet needed is carried out based on present state-of-the-art superconducting materials. The performance of the saturated AC induction heater is numerically investigated and compared with the case without magnetic saturation.

The design of an interface device for interconnecting a SMES (Superconducting Magnetic Energy Storage) to a LV distribution grid is carried out, in order to demonstrate the feasibility of a SMES for achieving, with the same device, power quality and critical load protection functions. The work is developed inside a three-year research project, called DRYSMES4GRID, funded by the Italian Minister of Economic Development and sees the cooperation of five partners (companies, universities, and research institutes). The aim of the project is to demonstrate the feasibility of the SMES (500 kJ/200 kW) in the short/medium term at competitive cost based on Magnesium Diboride (MgB2). In particular, in this article, after a brief state of art of the SMES applications for the grid, the design and the control logics of the DC/DC chopper for the power modulation of the energy stored in the SMES and of the threephase AC/DC inverter are shown. The activities are mainly based on digital simulations to evaluate the performances of this device in a LV distribution grid in presence of linear and non-linear loads, considering in particular the peak shaving function, while the device is connected to the mains, and the islanding operation condition after the detection of a voltage dip.

A three-year research project, called DRYSMES4GRID, was recently funded by the Italian Minister of Economic Development, Italy. The project, which involves five Italian partners (companies, universities, and research institutes), is aimed to demonstrate the feasibility of cost-competitive SMES based on magnesium diboride (MgB2) with a cryogen-free cooling by means of the manufacturing and the testing of a demonstrator with an objective rating of 500 kJ/200 kW. This rating is deemed suitable for disclosing the critical technological aspects of all components in view of practical applications. A further goal of the project is the assessment of the technical and economic benefits that the SMES can bring to real-world electric grids. The general outline and technical objectives of the project are presented in this paper. Preliminary design assumptions and results concerning the MgB2 coil and the power condition system are also discussed. © 2018 IEEE.

Intrinsically stable magnetic levitation between superconductors and permanent magnets can be exploited in a variety of applications of great technical interest in the field of transportation (rail transportation), energy (flywheels) and industry. In this contribution, we present a new model for the calculation of levitation forces between superconducting bulks and permanent magnet, based on the $H$-formulation of Maxwell's equations coupled with an Arbitrary Lagrangian-Eulerian formulation. The model uses a moving mesh that adapts at each time step based on the time-change of the distance between a superconductor bulk and a permanent magnet. The model is validated against a fixed mesh model (recently in turn validated against experiments) that uses an analytical approach for calculating the magnetic field generated by the moving permanent magnet. Then, it is used to analyze the magnetic field dynamics both in field-cooled and zero-field-cooled conditions and successively used to test different configurations of permanent magnets and to compare them in terms of levitation forces. The easiness of implementation of this model and its flexibility in handling different geometries, material properties, and application scenarios make the model an attractive tool for the analysis and optimization of magnetic levitation-based applications.

Objective Ayurveda is commonly used in South Asia to treat knee osteoarthritis (OA). We aimed to evaluate the effectiveness of Ayurvedic treatment compared to conventional conservative care in patients with knee OA. Method According to American College of Rheumatology (ACR) criteria knee OA patients were included in a multicenter randomized, controlled, open-label trial and treated in 2 hospital clinics and 2 private outpatient clinics in Germany. Participants received either a multi-modal Ayurvedic treatment or multi-modal conventional care with 15 treatments over 12 weeks respectively. Primary outcome was the change on the Western Ontario and McMaster University Osteoarthritis (WOMAC) Index after 12 weeks. Secondary outcomes included WOMAC subscales; the pain disability index and a pain experience scale, numeric rating scales for pain and sleep quality, quality-of-life and mood, rescue medication use, and safety issues. Results One hundred fifty-one participants (Ayurveda n = 77, conventional care n = 74) were included. Changes of the WOMAC Index from baseline to 12 weeks were more pronounced in the Ayurveda group (mean difference 61.0 [95%CI: 52.4;69.6]) than in the conventional group (32.0 [95%CI: 21.4;42.6]) resulting in a significant between-group difference (p < 0.001) and a clinically relevant effect size (Cohen's d 0.68 [95% CI:0.35;1.01]). Similar trends were observed for all secondary outcomes at week 12. Effects were sustained at follow-ups after 6 and 12 months. Conclusion Results suggest that Ayurvedic treatment is beneficial in reducing knee OA symptoms. Further studies should be conducted to confirm the magnitude of the effect and to clarify the role of different treatment components and non-specific effects. Registration at clinicaltrials.gov (NCT01225133; initial release 10/06/2010).

Introduction In the Indian medical system of Ayurveda, health results from the balanced interplay between three functional principles or doṣa – Vāta , Pitta , and Kapha – that regulate psychophysical functions. The relative proportion of the three doṣa in an individual determines the person's psychophysical constitution, Prakŗti . The aim of this pilot study was to jointly assess individuals’ Prakŗti and personality and emotional traits, investigating convergences and divergences between the two classification approaches. Method Data were collected among 391 adult participants through the following self-assessment instruments: Questionnaire on Doṣa Prakŗti AyurVeda (QDAV), specifically developed in this study to evaluate Prakŗti ; Big Five Inventory (BFI) to assess personality; Positive Affect Negative Affect Schedule (PANAS), to evaluate emotional profile; Short Form Health Survey (SF-36), to measure perceived health. Participants’ Prakŗti profile was identified first through QDAV and subsequently through its implemented version QDAV-R. Individuals characterized by predominant Vāta , Pitta , or Kapha Prakŗti ( N = 173) were selected for subsequent analyses. Personality, emotional profile, and perceived health were compared across these groups through nonparametric procedures. Results QDAV-R allowed for effectively classifying participants according to their Prakŗti . Personality, emotional and health features reported by Vāta , Pitta , and Kapha participants were consistent with the corresponding descriptions provided in the Ayurveda literature. Discussion Findings suggest that Prakŗti classification can be fruitfully integrated into diagnostic and treatment protocols in healthcare and psychotherapy. These results can inform future studies, aimed at combining psychophysical measures derived from different knowledge traditions within an authentically integrated and person-centered approach to health and well-being.

An innovative linear levitating system based on MgB 2 bulks produced by the reactive liquid infiltration method is designed and built. Details of the system are presented. The levitation performance is also evaluated by means of previous experimental data. The linear levitating system consists of four MgB 2 arc-shaped tiles lodged inside a double-shell Dewar sliding on a guide made of Nd-Fe-B permanent magnets. The magnets on the guide are properly arranged in a flux shaper configuration in order to produce maximum stiffness. Each MgB 2 bulk has a curvature radius of 165 mm (arc length of 200 mm), thickness of 10 mm, and width of 70 mm. The system is cooled by means of a solid nitrogen heat sink. Helium gas supply to a heat exchanger is used in order to cool down the MgB 2 slabs and the nitrogen at a temperature in the range of 20-30 K. When the flow of helium gas is interrupted, the temperature of the solid nitrogen remains below 39 K for half an hour. During this time interval, levitation measurements can be performed. Experimental verification of the cooling concept has been carried out successfully.

In recent years, numerical models have become popular and powerful tools to investigate the electromagnetic behavior of superconductors. One domain where this advances are most necessary is the 3D modeling of the electromagnetic behavior of superconductors. For this purpose, a benchmark problem consisting of superconducting cube subjected to an AC magnetic field perpendicular to one of its faces has been recently defined and successfully solved. In this work, a situation more relevant for applications is investigated: a superconducting parallelepiped bulk with the magnetic field parallel to two of its faces and making an angle with the other one without and with a further constraint on the possible directions of the current. The latter constraint can be used to model the magnetization of a stack of high-temperature superconductor tapes, which are electrically insulated in one direction. For the present study three different numerical approaches are used: the Minimum Electro-Magnetic Entropy Production (MEMEP) method, the $H$-formulation of Maxwell's equations and the Volume Integral Method (VIM) for 3D eddy currents computation. The results in terms of current density profiles and energy dissipation are compared, and the differences in the two situations of unconstrained and constrained current flow are pointed out. In addition, various technical issues related to the 3D modeling of superconductors are discussed and information about the computational effort required by each model is provided. This works constitutes a concrete result of the collaborative effort taking place within the HTS numerical modeling community and will hopefully serve as a stepping stone for future joint investigations.

Purpose This study aims to investigate the feasibility of saturated AC heating of magnetic metals. In AC heating of magnetic steel below the Curie temperature, because of the high magnetic permeability, the penetration depth is in the order of 1-6 mm at 50 Hz. Surface heating is then obtained, in practice, if large slabs are processed. The necessity to provide the required surface-to-core temperature uniformity (about 25°C) at the end of the heating process, avoiding excessive thermal stresses which can lead to cracks, thus implies a long heating time. Design/methodology/approach The penetration depth can be increased if the material is brought to saturation by applying an external DC magnetic field, and a faster in-depth heating can be obtained. The DC saturating field can be produced with no losses over large volumes by means of superconducting (SC) coils. Findings The feasibility of in-depth induction heating of a 200 × 1,000 × 5,000 mm magnetic steel slab with an applied 2 T DC saturating field is numerically investigated. The results show that the use of a DC saturating field leads to shorter processes which fulfil the heating objectives. Practical implications A DC saturating field cannot be produced by means of copper coils because of the large amount of material and the unaffordable power required. However, this field can effectively be produced by means of SC magnets based on state-of-the-art materials. Originality/value Superconductivity may be the enabling technology for fast and efficient induction heating of magnetic steel slabs if the increase in productivity can balance the additional costs due to the SC magnet.

High Temperature Superconductors (HTS) are advanced materials, which allow the development of evices with unachieved performance, as well as new functionalities. Further advantages are a drastic increase in efficiency from the materials’ zero (DC) to near zero (AC) resistivity, increased device compactness from the significantly larger current-carrying capability and the possibility of longer device lifespans. Numerical modelling is an essential tool for the design and optimisation of practical HTS devices and for improving understanding of the fundamental properties of HTS materials. The modelling of HTS materials must incorporate very complex behavior due to extreme nonlinearity and hysteresis, strong anisotropy, temperature dependence, relaxation and the high aspect ratio and complex composite structure of practical wires and tapes. Such complex behaviour raises new challenges in the development of reliable modelling tools and requires a specialised research effort to effectively deal with these problems. Hence, a series of international workshops dedicated to the numerical modelling of HTS has been organized since 2010 with the support of the HTS modelling workgroup [1]. The aim is to stimulate discussion and collaboration among experts in order to produce advances in modelling methods and tools needed for the development of HTS science and technology. Previous highly successful editions were held in Lausanne, Cambridge, Barcelona and Bratislava. The 5th International Workshop on Numerical Modelling of HTS was held in Bologna, Italy, on 15–17 June 2016. The workshop received 71 abstracts submitted for presentation and was attended by 92 registered participants. Submitted abstracts were rated by the workshop’s International Scientific Committee and organized over 37 oral presentations and 34 poster presentations. The top-rated contributions were invited to submit a full-length research manuscript for possible publication in Superconductor Science and Technology after the standard peer review process. The selected papers accepted for publication are collected in this special Focus on Numerical Modelling of HTS. The main topics covered by the focus issue are described as follows, where only papers appearing in the special issue are cited

The impact of fault current limiter (FCL) devices on safety and power quality of distribution networks is quantitatively investigated. The thermal let-through caused by actual short-circuit current waveforms rather than the rms value of the symmetric component is introduced to assess the impact of the fault. Situations of vulnerability caused by a very high short-circuit current for distribution networks supplied by large power transformers, especially if operating at a lower voltage, are discussed. Concerning power quality, the possibility of restricting, by means of an FCL, the area affected by voltage dips due to a polyphase fault, thus avoiding the propagation of the disturbance to all customers, is investigated. The impact of the FCL on dispersed generation (DG) is also looked into. In particular, the possible use of FCL for avoiding unwanted trips of protection due to the DG is discussed. Finally, the possibility of interconnecting, by means of an FCL, two distribution networks without risking excessive vulnerability in the event of a fault is discussed, and the increased performance of such interconnected networks in terms of maximum permissible disturbing power is quantitatively assessed.

Modern electric power systems are becoming more and more complex in order to meet new needs. Nowadays a high power quality is mandatory and there is the need to integrate increasing amounts of on-site generation. All this translates in more sophisticated electric network with intrinsically high short circuit rate. This network is vulnerable in case of fault and special protection apparatus and procedures needs to be developed in order to avoid costly or even irreversible damage. A superconducting fault current limiter (SFCL) is a device with a negligible impedance in normal operating conditions that reliably switches to a high impedance state in case of extra-current. Such a device is able to increase the short circuit power of an electric network and to contemporarily eliminate the hazard during the fault. It can be regarded as a key component for future electric power systems. In this paper the state of the art of superconducting fault current limiters mature for applications is briefly resumed and the potential impact of this device on the paradigm of design and operation of power systems is analyzed. In particular the use of the FCL as a mean to allow more interconnection of MV bus-bars as well an increased immunity with respect to the voltage disturbances induced by critical customer is discussed. The possibility to integrate more distributed generation in the distribution grid is also considered.

The levitation performance of a magnetic bearing, based on 48 mm inner diameter, 3mm thickness and 80 mm height, MgB2 tube is experimentally investigated. A numerical model is developed and validated against the experimental results in order to compare different rotor geometries and to investigate the temperature behaviour of the system. Investigation of the effect of the hysteresis on practical superconducting bearings is also carried out by means of the model.

A magnetization-based formulation of the volume integral equations method for 3-D magnetostatics is discussed. The magnetization of each element is related, via the constitutive law of the material, to the average magnetic flux density within the element rather than to the value at the center as is usually done. This assumption leads to more accurate distribution of magnetization and allows a faster convergence of the solution. Moreover, it leads to more symmetric matrix of the coefficients and reduces the numerical instability due to looping patterns of magnetization, which is inherent to integral methods. The formulation is made effective by the use of a hybrid numerical and analytical approach, which allows for the fast and accurate calculation of the coefficients. The proposed model is validated and compared with the usual model both for saturable and linear material with high susceptibility.

The experimental investigation of the levitation force between a Permanent magnet (PM) and MgB2 disk prepared by means of the Reactive Mg Liquid Infiltration is presented. Both FC and ZFC levitation in the temperature range from 21 K to 37 K are considered. The long term behavior of the levitation force is also investigated. A numerical model is developed in order to investigate the electrodynamics of levitation. The hysteretic behavior of the levitation force is related to the dynamic of current penetration inside the MgB2 disk by means of the numerical model.

A novel energy storage system based on a SMES cooled by cryogenic fuel is being developed at the Dept. of Electrical Engineering of the University of Bologna. The system represents an alternative solution with respect to nowadays battery packs for the storage of electrical energy with large specific power. The device may find suitable application on board of road vehicles fed by liquid hydrogen with hybrid power-train (internal combustion engine and electric motor/generation), where a cryogenic tank is already present and no additional cryogenic costs are needed. The housing of the SMES inside the tank used for fuel storage, allows the exploitation of the thermal power required for the continuous evaporation of fuel for feeding the engine to remove the AC losses from the magnet, thus avoiding the need of externally supplied cooling power. In this paper both the design of the magnet and its operation in combination with electronic converter and electric motor/generator during charge/discharge cycles are discussed. Moreover the ongoing activity for the development of a laboratory-scale prototype using MgB2 superconductor is presented.

We have analyzed the characteristics of dc-induction heating of aluminium billets both numerically and experimentally and developed a numerical model for the calculation of the power and temperature distributions inside the billet during the heating. We validated the model by comparison with the experimental results from a laboratory-scale prototype using permanent magnets. We studied the heating process of a real scale system by means of the model, taking into account the weakening of the mechanical properties during the heating. We provide an example of design of an industrial scale dc induction heater.