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The purpose of this paper is to develop a rapid and realistic modelling approach for the design and characterization of high temperature superconducting (HTS) coils and windings carrying DC currents. Indeed, the strong dependence of the electromagnetic properties of such materials on the magnetic field makes the design and characterization of HTS systems a delicate operation where local quantities have to be evaluated.

A volume integral modelling approach has been developed taking into account the electric nonlinearity of the HTS material which is represented by power law. The variations of the characteristic quantities of the HTS (critical current density and power law exponent) with the magnetic flux density are also taken into account by using Kim’s law. The volume integral modelling allows to model only the active parts of the system and thus to overcome the difficulties linked to the multiscale dimensions.

The model has been tested in a case study in which simulation results were compared to measurements and to finite element analysis. A good agreement was found which validates the model as a rapid and efficient tool for HTS coils and windings design and modelling.

HTS coils are important elements of emerging superconducting devices which require a high level of reliability, such as generators or motors. The proposed approach is interesting to speed up the design and optimization procedures of such systems.

Advanced structures of the basic elements have been used in the volume integral modelling, which results in a considerable gain in computation time and in memory-space saving while keeping a high level of precision and realism of the modelling, which has been verified experimentally.

This paper seeks to describe an approach to multi‐objective optimization problems (MOOPs) based on game theory (GT) and to provide a comparison with the more standard Pareto approach on a real design problem.

The GT is first briefly presented, then a possible recasting of MOOPs in terms of GT is described, where players from GT are associated with single objectives and strategies to the choice of degrees of freedom. A comparison with the Pareto approach is performed on the optimized design of a superconducting synchronous generator.

It was shown that the GT can be applied to the optimized design of real world devices, with results that present a different viewpoint on the problem, yet with device performance comparable with those obtained by standard approaches.

Only the Nash approach to non‐cooperative games has been applied; the conditions for the solution found using GT to belong to the Pareto front have not been fully explored.

Designers and engineers interested in optimal design are presented with a new design technique able to get a balance among conflicting partial objectives, that can also be used to select among different possible designs obtained in other ways (e.g. using the Pareto front approach).

The paper demonstrates the possibility of using GT in the design of real world electromagnetic devices, with reference to the optimal shape design of a high temperature superconducting single‐phase synchronous generator.

A saturated iron core superconducting fault current limiter (SISFCL) has an important role to play in the present-day power system, providing effective protection against electrical faults and thus ensuring an uninterrupted supply of electricity to the consumers. Previous mathematical models developed to describe the SISFCL use a simple flux density-magnetic field intensity curve representing the ferromagnetic core. As the magnetic state of the core affects the efficient working of the device, this paper aims to present a novel approach in the mathematical modeling of the device with the inclusion of hysteresis.

The Jiles–Atherton’s hysteresis model is utilized to develop the mathematical model of the limiter. The model is numerically solved using MATLAB. To support the validity of model, finite element model (FEM) with similar specifications was simulated.

Response of the limiter based on the developed mathematical model is in close agreement with the FEM simulations. To illustrate the effect of the hysteresis, the responses are compared by using three different hysteresis characteristics. Harmonic analysis is performed and comparison is carried out utilizing fast Fourier transform and continuous wavelet transform. It is observed that the core with narrower hysteresis characteristic not only produces a better current suppression but also creates a higher voltage drop across the DC source. It also injects more harmonics in the system under fault condition.

Inclusion of hysteresis in the mathematical model presents a more realistic approach in the transient analysis of the device. The paper provides an essential insight into the effect of the core hysteresis characteristic on the device performance.

The purpose of this paper is to propose a hybrid driving system that couples a motor and flywheel energy storage (FES) for a megawatt-scale superconducting direct current (DC) induction heater. Previous studies have proven that a superconducting DC induction heater has great advantages in relation to its energy efficiency and heating quality. In this heater, a motor rotates an aluminium billet in a DC magnetic field and the induced eddy current causes it to be heated. When the aluminium billet begins to rotate, a high peak load torque appears at a low rotation speed. Therefore, driving the billet economically has been a great challenge when designing the driving system, which is the focus of this paper.

A hybrid driving system based on FES is designed to provide extra torque when the peak load torque occurs at a low rotation speed, which allows the successful start-up of the aluminium billet and the operation of the motor at its rated capacity. The mechanical structure of this hybrid driving system is introduced. A simulation model was constructed using Matlab/Simulink and the dynamic start-up process is analysed. The influence of the flywheel’s inertia and required minimum engagement speed are investigated.

The results of this paper show that the hybrid driving system that couples FES and a motor can successfully be used to start the aluminium billet rotating. The flywheel’s inertia and engagement speed are the most important parameters. The inertia of the flywheel decreases with an increase in its engagement speed.

The cost of the driving system is significantly reduced, which is very important in relation to the commercial potential of this apparatus.

A novel start-up strategy for driving the aluminium billet of a superconducting DC induction heater at low speed is proposed based on FES.

This paper aims to develop a new quasi-three dimensional (3D) analytical model devoted to the study of nonlinear transient magneto-thermal coupled problems in permanent magnet (PM) transverse flux induction heating device (TFIHD).

The presented work is based on analytical development of strongly coupled problem, including electromagnetic and thermal boundary problems. The electromagnetic problem is first solved by using the separation variables method to evaluate the induced currents in the nonmagnetic plate and the resulting power density loss distribution. The plate temperature profile is then obtained thanks to strong involvement of this magnetic model in a new analytical thermal model combining the separation of variables method and the Green’s functions transient regime analysis method. The coupled model is then used in a simulation procedure of the magneto-thermal process allowing taking into account the workpiece electrothermal nonlinear properties. The developed coupled model is validated by computing the performances of the studied PM TFIHD and comparing them to those obtained by finite element simulations.

An efficient transient quasi-3D magneto-thermal analytical model is developed allowing rapid analysis of PM induction heating for core heating of parallelepiped parts. The developed model also allows fast and accurate simulations of nonlinear and transient three dimensional (3D) magneto-thermal phenomena for planar induction heaters.

The developed quasi-3D magneto-thermal analytical model is limited to design induction heating devices of planar structure with PM inductors.

A new transient quasi-3D magneto-thermal analytical model accounts for non-linearity and edge effect and helps to fast study and fast design of linear permanent magnet induction heating device.

To analyse the heating process of an aluminum billet rotating in a static magnetic field produced by superconducting coils.

The idea is to force the billet to rotate in a static magnetic field produced by a DC superconducting magnet. Since, a static superconducting magnet has no losses, the efficiency of the system is the efficiency of the motor used. In order to evaluate the temperature distribution arising from the field profile produced by a given coil configuration, a numerical model, based on an equivalent electric network with temperature‐dependent parameters, is used.

The main heating parameters, i.e. heating time, total power injected and temperature difference, are evaluated for different values of angular velocity and magnetic field. The field profile suitable to meet the specifics of an industrial heating process in terms of temperature homogeneity and heating time is determined. Starting form this profile the layout of the magnet is arrived at and some considerations on the operating condition of the superconducting windings are reported.

The mechanical stress in the billet due to weight, centrifugal effects, applied torque and resonance is examined by taking into account the weakening of the material properties with the increase of temperature and the practical limits of the heating process are evaluated.

DC induction heating of aluminum billet using superconducting magnets can be done fulfilling the specifics of the industrial processes.

A high‐efficiency induction heater for aluminum billets using superconducting coils in a novel scheme is investigated.

Electrical characteristics of transformer oil (TO) have been studied during normal and thermal aging conditions. In this paper, breakdown voltage (BDV), partial discharge (PD), heat transfer results and the physical mechanisms considering the impact of varying the diameter of Al₂O₃ nanoparticles (NPs) have been investigated. Different quantities of the two sizes of Al₂O₃ were added to the oil using a two-step method to determine the positive effect of NPs on the electrical and thermal properties of TO. Finally, the physical mechanisms related to the obtained experimental results have been performed.

The implementation of nanoparticles in this paper was provided by US Research Nanomaterials, Inc., USA. The provided Al₂O₃ NPs have an average particle size of 20–80 nm and a specific surface area of 138 and 58 m²/g, respectively, which have a purity of over 99%. Thermal aging has been done. The IEC 60156 standard has been implemented to calculate the BDV, and a 500-mL volume test cell (Apar TO 1020) has been used. PD test is performed according to Standard IEC 60343, and a JDEVS-PDMA 300 device was used for this test.

BDV tests indicate that 20 nm Al₂O₃ is more effective at improving BDV than 80 nm Al₂O₃, with an improvement of 113% compared to 99% for the latter. The analysis of Weibull probability at BDV indicates that 20 nm Al₂O₃ performs better, with improvements of 141%, 125% and 112% at probabilities of 1, 10 and 50%, respectively. The results of the PD tests using the PDPR pattern also show that 20 nm Al₂O₃ is superior. For the heat transfer test, 0.05 g/L of both diameters were used to ensure fair conditions, and again, the advantage was with 20 nm Al₂O₃ (23% vs 18%).

The effect of Al₂O₃ NP diameter (20 and 80 nm) on various properties of virgin and aged TO has been investigated experimentally in this paper to examine the effect of proposed NP on electrical improvement of TO.

The purpose of this paper is to analyze the influence of different types of winding configurations on the distribution of leakage field and branch currents for a 330-kVA high-temperature superconducting (HTS) transformer winding.

A three-dimensional electromagnetic model coupled with a circuit model validated by an experiment is developed to calculate the leakage field and current uniformity under four different types of secondary winding configurations. The four types of gaps between secondary windings are uniform gap, arithmetic progression (AP) gap, six sections with three different gaps and eight sections with four different gaps. A coefficient named as uneven degree is used to define the current nonuniformity.

The simulation results show that the currents and leakage field of double pancakes (DPs) on both sides are larger than those of the other DPs, and the currents of several middle DPs are smaller than the average rated current with an ISOB gap and larger than the average rated current with an IBOS gap. For any one of the four types of winding configurations, the type with the ISOB gap can prohibit the current nonuniformity more effectively, whereas the IBOS gap can decrease the leakage field more. The AP with the ISOB gap is a wise choice for decreasing the uneven degree and leakage field.

There is an optimal winding configuration for decreasing the leakage field and uneven degree of branch currents. The results and numerical model are very useful for the design of a HTS transformer.

The leakage field distribution and branch currents nonuniformity for 25 parallel DPs are investigated and optimized.

The purpose of the paper is to provide a comparison of first‐ and second‐order two dimensional finite element models for evaluating the electromagnetic properties and calculating AC loss in high‐temperature superconductor (HTS) coated conductors.

The models are based on the two‐dimensional (2D) H formulation, which is based on directly solving the magnetic field components in 2D. Two models – one with a minimum symmetric triangular mesh and one with a single‐layer square mesh – are compared based on different types of mesh elements: first‐order (Lagrange – linear) and second‐order (Lagrange – quadratic) mesh elements, and edge elements.

The number and type of mesh elements are critically important to obtain the minimum level of discretization to achieve accurate results. Artificially increasing the superconductor layer and choosing a minimum symmetric mesh with triangular edge elements can provide a sufficiently accurate estimation of the hysteretic superconductor loss for a transport current.

This paper describes how the selection of mesh type and number of elements affects the computation speed and convergence properties of the finite element model using two different types of meshing. It offers an insight into the different factors modelers must consider when modeling HTS coated conductors and the methods that may be applied when extending the model to complex device geometries, such as wound coils.

The purpose of this study is to investigate a novel rotor design model to improve the technical performance of a superconducting synchronous generator.

Superconducting synchronous generators with a modular rotating cryostat for a single coil of the superconducting winding instead of an old-style single cryostat in which all rotor components are cold are briefly discussed. Subsequently, a new method of cryostat arrangement in the magnetic system of a rotor is considered. Different options were compared for the cryostat placement. The advantages of the novel rotor design model are noted.

In the novel rotor design model, the leakage coefficient of the excitation winding decreases, and the air gap magnetic flux increases, which will save on a superconductor material.

For the purposes of this investigation, a finite element study of flux distribution in the cross section of a superconducting synchronous generator with a 10 MW rating at 10 rpm was conducted, and the magnetic fluxes and air gap flux densities were obtained for different modes. For direct-drive superconducting synchronous generators with distributed winding and different pole numbers, the calculations of magnetic fluxes were carried out by calculating the magnetic conductivities.

A new method of the cryostat arrangement in the magnetic system of a rotor has been classified as an invention and was protected by a patent. This paper is directly applicable to the field of superconducting synchronous generators.