Search

Within the German project ENSYSTROB a 3-phase resistive fault current limiter for medium voltage applications (12 kV, 533 Arms) was designed, built, tested and installed in the grid for a one year’s field test. The superconducting modules are made of YBCO coated conductors and replace the modules of an already successfully tested limiter on the basis of BSCCO 2212 bulk material. The components are multifilar spirals equipped with pairs of 12 mm wide YBCO tapes. The single components were characterized with respect to critical current, AC losses and limitation behavior under all possible operation conditions. The finally mounted limiter was successfully tested with respect to high voltage and limitation according to the standards of the customer. It is now installed and operating in its field test location. Finally we give a first comparison of both materials with respect to the different operational aspects.

The adaptive resistivity method is a special algorithm that allows approaching the Bean critical state by an iterative adjustment of the material’s resistivity and can be quite easily implemented in commercially available finite-element codes. Its main advantage is that the critical-state model does not depend on time (or frequency of the applied loads) so that the critical-state description is uniquely determined by the field profiles at the peak value of the applied loads. We proved its validity in the simulation of complex superconducting systems comparing its results either with analytical descriptions, where they exist, or the well-known edge-element model based on direct magnetic field formulation.

Nikaitchuq is an oil field on the North Slope of Alaska that has been developed with more than 60 extended-reach wells having 6,000-ft to 18,000-ft-long horizontal sections. The main reservoir interval in Nikaitchuq corresponds to a shelfal lobe composed of two main sand bodies, encased in structural depressions. The development scheme consists of waterflood line drive with horizontal producers and water injection wells located side by side. The majority of the development wells were designed with a single horizontal trajectory undulating between the two main sands bodies in counter phase with the related water injectors. To be successful, such challenging well design requires accurate geological modeling, effective geosteering capabilities, and sensible well data acquisition. The objective of the approach here described is to correctly reconstruct the reservoir geometry by integrating numerous data and information coming from such long horizontal wells. However, data and information that have originated from different sources have different levels of accuracy. A thorough data quality assessment is a mandatory step in any data integration exercise. Hence, all information available in each horizontalwell section was reviewed in detail and cross-examined. Bed boundary mapping data interpretation via different inversion processes and log and image interpretations (such as gamma ray, neutron density, resistivity, density images, deep azimuthal electromagnetic data) were compared, validated, and integrated in the 3D geological model to perform a very precise reconstruction of reservoir internal geometry. Such accuracy in modeling was not only aimed at enhancing the precision of volumes in place and resource estimates, but it was also a prerequisite for the successful drilling of the subsequent wells during the field development. The novelty of the approach consisted in the integration of density image logs, bed boundary mapping data, and resistivity modeling results to derive accurate information on the reservoir geometry at a scale useful for 3D modeling. This use of data goes beyond common practices.

In the past few years the Roebel technique has been established as a method for cabling of coated conductor tapes to achieve high current carrying capabilities for low ac-loss applications. We have successfully developed Roebel cables consisting of up to 50 tapes and with current carrying capabilities up to 2.6 kA (77 K, self-field). However, for applications like busbars or fusion magnets current carrying capabilities of more than 10 kA are required. Such high current carrying capabilities cannot be reached by a simple scale-up with additional tapes. We present a concept for Coated Conductor Rutherford Cables (CCRCs) for currents exceeding 10 kA using Roebel subcables as strands. The first steps towards a short subsize CCRC demonstrator cable with electrical and mechanical characterization of commercial coated conductor tapes, strands and a first Roebel strand have been performed and will be discussed.

A new German government funded project for a resistive fault current limiter has started in September 2009 (ENSYSTROB) and is presented. The consortium includes partners from industry, research centers and utilities. It aims the construction of a 3-phase medium voltage current limiter (12 kV, 800 A) for the protection of the domestic supply in a power plant. A special feature of this application is the presence of large in-rush currents (4100 Ap for 50 ms, 1800 A for 15 s). The superconducting components are bifilar pancake coils consisting of pairs of YBCO-tapes in face to back configuration. Successful limitation experiments on prototype components with prospective currents in the whole range are shown. Also the stability with respect to high voltage could be demonstrated. The AC-losses under normal operation are shown, by simulation and experiment, to be smaller than the heat input of the current leads. The current limiting components are compared with similar elements based on BSCCO 2212 bulk material (Nexans SuperConductors).

In this paper we present a new model for computing the current density and field distributions in superconductors by means of a finite element (FE) periodic space-time (PST) formulation. By considering the time as a space dimension, and considering periodic excitations for the applied field or transport current, we can use a static model to solve this time dependent problem. This approach has the potential to overcome one of the major problems of FE modeling of superconductors: the length of simulations, even for relatively simple cases. In this paper we show our first results for different cases of superconductors with AC magnetic fields and currents. Results are compared with those of standard time-dependent methods and analytical solutions.

In order to successfully integrate superconducting fault current limiters (SFCL) into electric power system networks, accurate and fast simulation models are needed. This led us to develop a generic electric circuit model of an inductive SFCL, which we implemented in the EMTP-RV software. The selected SFCL is of shielded-core type, i.e. a HTS hollow cylinder surrounds the central leg of a magnetic core, and is located inside a primary copper winding, generating an AC magnetic field proportional to the line current. The model accounts for the highly nonlinear flux diffusion phenomenon across the superconducting cylinder, governed by the Maxwell equations and the non-linear E-J relationship of HTS materials. The computational efficiency and simplicity of this model resides in a judicious 1-D approximation of the geometry, together with the use of an equivalent electric circuit that reproduces accurately the actual magnetic behavior for the flux density (B) inside the walls of the HTS cylinder. The HTS properties are not restricted to the simple power law model, but instead, any resistivity function depending on J, B and T can be used and inserted directly in the model through a non-linear resistance appearing in the equivalent circuit.

In this paper, we investigate the influence of various numerical parameters on the precision and the speed of ac loss computations in high-temperature superconductors using the finite-element method. The case considered here is an infinite slab subjected to an external ac magnetic field. This problem can be modeled by a 1-D partial differential equation (diffusion equation). This relatively simple case allowed investigating the influence of the various parameters in a reasonable time. The findings of this work can be used as a starting point for optimizing the numerical settings of more complex models. As the main results, it is shown that choosing first-order elements for approximating the flux density ( B) is the most stable option, and that using high order adaptive time-stepping methods provides good accuracy and fast simulations. A new and simple self-check test for validating the computed ac losses is also proposed. Finally, a detailed analysis about the behavior of the numerical solution near flux/current fronts is provided.

Coated conductors are very promising for the design of novel and efficient resistive Fault Current Limiters (FCLs). However, a detailed knowledge about their thermal and electromagnetic behaviors in the presence of over- critical currents is crucial for their improvement. In this context, we performed finite element magneto-thermal modeling of coated conductors under over-critical current on several geometries. Accordingly, we have investigated the influence of the physical properties of stabilizer and substrate on the thermal stability to improve the HTS-FCL design. All simulations were performed using COMSOL Multiphysics, a commercial finite element package, which has a built-in coupling between the thermal and electrical equations, allowing us to compute both quantities simultaneously during the solving process. Our results allow us to determine the current threshold to achieve thermal stability of HTS fault current limiters made with coated conductors.

We have considered a three-phase concentric high- T c superconducting (HTS)-cable with a copper shield neutral wire in a three-phase system. An equivalent circuit model describing the cable by the global quantities current and voltage has been developed, by which the effects of design parameters such as material, layer radii and pitch length can be investigated. The equivalent circuit consists of a nonlinear resistance, a hysteretic inductance (to model HTS), and an inductance (to model mutual inductances). The equivalent circuit is here extended with a by-pass resistance that models the silver matrix of the HTS tape. This enables to consider over-critical currents (i.e. beyond hysteresis saturation), whereby extra care must be taken for the numerical simulations. We have considered a design of fixed radii and have optimized the pitch length of each layer in order to have equal reactances for all phases.

Several AC power applications of YBCO-coated conductors (CCs) involve superconducting tapes wound in coils. In such a configuration the superconducting tape is arranged as closely packed turns, which strongly interact due to the generated magnetic field. This has a strong influence on the AC losses, which are different from those of an isolated tape, and need to be precisely quantified in order to predict and reduce the refrigeration requirements of applications. In this paper we experimentally evaluate the transport AC losses in a pancake coil composed of 25 turns of superconducting tape. We describe in detail the measuring technique utilized, pointing out the issues in this kind of measurement. We also present preliminary results of AC loss computation by finite-element modelling.

Time-resolved magneto-optical imaging measurements show that an ac current enables the vortex matter in YBa2Cu3O7-x thin films to reorganize into two coexisting steady states of driven vortex motion with different characteristics: a quasi-static disordered glassy state in the sample interior and a dynamic state of plastic motion near the edges. Finite-element calculations consistent with the critical state model show good agreement with the measured field profiles in the quasi-static state but predict a larger hysteretic behavior in the dynamic state.

In superconducting coils tapes are often closely packed in a configuration similar to a ldquoz-stackrdquo, which strongly influences the AC losses with respect to when tapes can be considered as separate objects: losses are reduced in the presence of externally applied AC magnetic field, but are increased in the presence of AC transport current. In this paper, we quantify the magnitude of the tape interaction and the AC losses of these two cases, both experimentally and by means of finite-element method simulations. We also discuss the experimental issues arisen with the utilized AC loss measurement technique.

In this paper we present initial results on growing YBCO/IBAD-MgO/YBCO stacks. Amorphous Y2O3 layers, deposited by sol-gel, are used to level the YBCO surface. Since the YBCO films prepared by pulsed laser deposition are relatively rough, preparing a smooth surface on top of YBCO for IBAD texturing is a major challenge for this structure. For all substrates studied-polished and unpolished metal tape and YBCO - we were able to reduce the roughness of the substrate using the sol-gel layer, with multiple coatings being more effective. First it is demonstrated that high quality YBCO films can be deposited on sol-gel-Y2O3/IBAD-MgO templates. Second it is shown that the sol-gel and the IBAD process do not affect the superconducting properties of the underlying YBCO film. Finally, a superconducting YBCO bilayer stack is demonstrated. Improvements in the properties of the top YBCO layer is expected when the surface roughness is reduced further for deposition of subsequent IBAD-textured layers. This new technology should enable novel designs of coated conductors for reduced AC losses and increased Je.

In this paper we present a new 2D numerical model for AC loss computation in high-temperature superconductors, based on the use of edge finite elements. These elements are curl conforming by construction and involve the continuity of the tangential component of the magnetic field between adjacent elements. In this way they do not require the imposition of the zero divergence of the magnetic field at each time step, which, with standard nodal elements, increases the null space of the matrix and the risks of divergence of the algorithm. The model, implemented in the software package COMSOL, uses the two magnetic field components as state variables. It has been tested for computing the losses of YBCO coated conductor tapes in two cases of practical interest, which cannot be investigated by analytical models.

First experimental observations of the ferromagnetic shielding effect in high-Tc superconducting coated conductors were carried out. Experimental results were compared to simulations calling upon finite-element calculations based on the H-formulation of Maxwell equations to model superconducting strips with ferromagnetic shields. Samples of copper-stabilized coated conductors were electroplated with nickel shields and afterwards characterized. Both externally applied oscillating transverse magnetic fields as well as transport currents were studied. Having observed promising gains with respect to the reduction of ac losses in both cases, we further investigated the potential of ferromagnetic shielding. The numerical model was able to reproduce and also predict experimental results very well and will serve as an indispensable tool to determine the potential of soft ferromagnetic materials to significantly reduce hysteretic losses., Comment: 4 pages, 3 figures, 1 table

Numerical models are powerful tools to predict the electromagnetic behavior of superconductors. In recent years, a variety of models have been successfully developed to simulate high-temperature-superconducting (HTS) coated conductor tapes. While the models work well for the simulation of individual tapes or relatively small assemblies, their direct applicability to devices involving hundreds or thousands of tapes, as for example coils used in electrical machines, is questionable. Indeed the simulation time and memory requirement can quickly become prohibitive. In this article, we develop and compare two different models for simulating realistic HTS devices composed of a large number of tapes: 1) the homogenized model simulates the coil using an equivalent anisotropic homogeneous bulk with specifically developed current constraints to account for the fact that each turn carries the same current; 2) the multi-scale model parallelizes and reduces the computational problem by simulating only several individual tapes at significant positions of the coil's cross-section using appropriate boundary conditions to account for the field generated by the neighboring turns. Both methods are used to simulate a coil made of 2000 tapes, and compared against the widely used H-formulation finite element model that includes all the tapes. Both approaches allow speeding-up simulations of large number of HTS tapes by 1-3 orders of magnitudes, while keeping a good accuracy of the results. Such models could be used to design and optimize large-scale HTS devices., 17 pages, 11 figures

In order to transport sufficiently high current, high-temperature superconductor (HTS) tapes are assembled in cable structures of different forms. In such cables, the tapes are tightly packed and have a strong electromagnetic interaction. In particular, the generated self-field is quite substantial and can give an important contribution in reducing the maximum current the cable can effectively carry. In order to be able to predict the critical current of said cable structures, a static numerical model has been recently proposed. In this contribution, we present in detail the implementation of such models in different programming environments, including finite-element-based and general numerical analysis programs, both commercial an open-source. A comparison of the accuracy and calculation speed of the different implementations of the model is carried out for the case of a Roebel cable. The model is also used to evaluate the importance of choosing a very accurate description of the angular Jc(B) dependence of the superconductor as input for the material's property. The numerical codes, which are open-source, are made freely available to interested users., Comment: The accompanying models descried in this work are available for free download at the HTS modeling workgroup under http://www.htsmodelling.com/?p=917

The design of a high-temperature superconducting (HTS) Superconducting Magnetic Energy Storage (SMES) coil with solenoidal and toroidal geometry is carried out based on a commercially available second-generation HTS conductor. An SMES system of practical interest (1 MW/5 s) is considered. The comparison between ideal toroidal and solenoidal geometry is first discussed, and the criteria used for choosing the geometrical parameters of the coils' bore are explained. The design of the real coil is then carried out, and the final amount of conductor needed is compared. A preliminary comparison of the two coils in terms of ac loss during one charge and discharge cycle is also discussed.

This paper presents a new numerical model for computing the current density, field distributions and AC losses in superconductors. The model, based on the direct magnetic field H formulation without the use of vector and scalar potentials (which are used in conventional formulations), relies on first-order edge finite elements. These elements are by construction curl conforming and therefore suitable to satisfy the continuity of the tangential component of magnetic field across adjacent elements, with no need for explicitly imposing the condition . This allows the overcoming of one of the major problems of standard nodal elements with potential formulation: in the case of strong discontinuities or nonlinearities of the physical properties of the materials and/or in presence of sharp corners in the conductors' geometry, the discontinuities of the potentials' derivatives are unnatural and without smoothing artifices the convergence of the algorithm is put at risk. In this work we present in detail the model for two-dimensional geometries and we test it by comparing the numerical results with the predictions of analytical solutions for simple geometries. We use it successively for investigating cases of practical interest involving more complex configurations, where the interaction between adjacent tapes is important. In particular we discuss the results of AC losses in superconducting windings.

Investigation of AC loss under simultaneous action of transport AC and external AC field is of prime importance for reliable prediction of dissipation in electric power devices like motors/generators, transformers and transmission cables. The experimental rig allowing to perform AC loss measurement in such conditions on short (10 cm) samples of tapes from hightemperature superconductor Bi-2223/Ag has been designed and tested. Both the electrical and thermal method have been incorporated, allowing to combine better sensitivity of former one and a higher reliability of the latter one. Our main aim is to see how the AC loss depends on the phase shift between the current and the field. Such a shift could acquire rather different values in various applications. While in transformer winding, the maximum phase shift at full load will probably not exceed a few degrees, in a three phases transmission cable in tri-axial configuration it is around 120°. Therefore we explored the whole range of phase shifts from 0 to 360°. Surprisingly, the maxima of dissipation do not coincide with zero shift as expected from qualitative considerations.

In this paper, we present a new numerical model, in which both the thermal and the electromagnetic aspects of the over-critical current regime of HTS materials are taken into account. The electromagnetic and thermal equations have been implemented in finite-element-method (FEM) software in order to obtain a novel, closer to reality model for investigating the behaviour of the superconductor when the current exceeds $I_{c}$. This model has been applied for studying the behaviour of strip lines of an YBCO/Au FCL with a sapphire substrate. Simulations with currents largely exceeding $I_{c}$ have been performed, showing that the total current limitation occurs only when the temperature dependence of the electrical parameters is taken into consideration. Such modelling can replace experiments with currents far exceeding $I_{c}$ which may damage or destroy the studied sample or HTS device.

Investigation of ac loss under the simultaneous action of the transport ac current and the external ac magnetic field is of prime importance for the reliable prediction of dissipation in electric power devices such as motors/generators, transformers and transmission cables. An experimental rig allowing us to perform ac loss measurements in such conditions, on short (10 cm) tape samples of high-temperature superconductor Bi-2223/Ag, was designed and tested. Both the electromagnetic and thermal methods were incorporated, allowing us to combine the better sensitivity of the former and the higher reliability of the latter. Our main aim was to see how the ac loss depends on the phase shift between the transport current and the external magnetic field. Such a shift could have different values in various applications. While in a transformer winding, the maximum phase shift at full load will probably not exceed a few degrees, in a three phase transmission cable in tri-axial configuration it is around 120°. Therefore, we explored the whole range of phase shifts from 0 to 360°. Surprisingly, the maxima of dissipation did not coincide with zero shift as expected from qualitative considerations.

YBCO coated conductors (CCs) are being developed with extremely high dc critical currents, which should allow their extensive use in power applications. However, the CCs manufactured at present have unacceptably high energy losses in ac magnetic fields applied perpendicular to the CC face. This magnetic ac loss can be significantly reduced if the superconductor is divided into parallel electromagnetically decoupled filaments. Simply cutting the YBCO into filaments does not achieve this, as the filaments remain coupled. In this paper we present a new technique for obtaining decoupled filaments. This is achieved by cutting the superconductor into parallel filaments plus introducing periodic transverse cross-cuts. The cross-cuts allow the magnetic flux to penetrate between the filaments and thus decouples them. The continuity of the current path is maintained by means of normal metal 'bridges' across the cross-cuts. We present data demonstrating that at power frequencies five cross-cuts every metre are sufficient to decouple the filaments. We also show that it is straightforward to produce normal metal bridges whose Ohmic losses due to the transport current are sufficiently low that the overall losses of a CC carrying ac or dc transport currents in applied ac magnetic fields are reduced to manageable levels. In a specific example, the losses of a CC in a 20 mT, 60 Hz magnetic field carrying 100 A ac transport current were reduced by nearly two orders of magnitude. Numerical simulations based on the finite-element method have been also performed and confirm some of the experimental results. We also indicate how this technique may be further improved.

The magnetic field profile on the surface of Bi-2223/Ag tapes has been dynamically measured across the width of the samples. The experimental technique uses a Hall-probe array with 7 sensors connected to a multiple channel lock-in amplifier especially programmed for fast and synchronous data acquisition measurements. The speed of the system is high enough to measure real-time profiles with 7 probes and 50 Hz sine current through the sample. A numerical method to estimate the current distribution inside the tapes using the measured field profile data is proposed. The inverse problem has been solved using certain assumptions on the current distribution in the superconductor. Validation of the results has been done by comparison with finite element method simulations.

The performance of HTS devices is strongly influenced by local values of the current and field distributions. In this paper, we investigate the influence of the magnetic field and the geometrical configuration on the loss behavior of a 200 kVA FCL prototype, composed by Bi-2223/Ag tapes wound around a cylindrical support. The investigation is performed by means of finite element computations, with the use of an axisymmetric 2D A-V formulation for taking into account the cylindrical geometry. The electrical behavior of the superconductor is described by means of a B-dependent E-J power-law relation, derived from experimental measurements with a field of different orientation. Several geometrical configurations are analyzed and compared, in order to find the ones with the lowest AC loss.

Geometrical aspects of the design of fault current limiters (FCL) have a great impact on their performances. Recently, the University of Geneva have made certain optimizations by splitting the FCL into many small dissipative lengths in order to achieve a distributed transition along the device. For this paper, we have performed new 3D finite element method (FEM) simulations for studying the behavior of strip lines of a YBCO/Au FCL in an AC nominal use (sinusoidal current at industrial frequency) up to 3 I/sub c/. The very large aspect ratio of the device needs a particular attention to the modeling and meshing process. The numerical results show that presence of sharp corners can influence the performance of the device. Due to the high value of the electric field in these areas, the local losses are much higher than in the case of smooth corners, and this may lead to burning and cracking the wafer. Irreversible damage experiments have confirmed these locations. In this paper we proposed new geometries, taking into account the length of the connecting path and the corners optimization in order to decrease the risk of very high localized losses in the meander.

To reach large current carrying capability and mechanical flexibility, superconducting cables consist of many single conductors connected in parallel. Distribution of ac current into these parallel paths is controlled by their impedances, which often are not identical. We have found that, even in the case of a cable model made from straight Bi-2223 tapes placed in just one single layer, the nonuniformity of contact resistances causes a dispersion in the amplitudes and phases of ACs in individual tapes. Two models, one analytical and other a Finite Element Model, were used to predict the influence of phase shifts on ac loss and its measurement by an electrical method. Due to phase shifts of local magnetic fields, the purely inductive component of voltage taken by an arbitrary pair of taps is not exactly out-of-phase regarding the total cable current. Then, its product with the cable current is evaluated as a false loss-contributing component. Fortunately, with the use of voltage taps and wires regularly distributed around the cable, true value of ac loss can be recovered.

In this paper, the effects of the magnetic self-field on the transport properties of a multilayer high-T/sub c/ superconducting (HTS) cable are investigated by means of two-dimensional finite-element method (FEM) simulations. Analyzed is a three-layer HTS cable, but the developed methods can be used for a different number of layers. The superconductor is described by the nonlinear power-law relation E=E/sub c/(J/J/sub c/)/sup n/, where the parameters J/sub c/ and n depend on the magnetic field experienced by the material. This dependence decreases the global transport capacity of the superconductor, enhancing its AC losses. It is shown that, especially at high transport currents, the AC losses are considerably higher than in the case where the dependence on the magnetic field is neglected. A simple electrical model, considering the cable from macroscopic point of view, has been proposed for finding the optimal winding pitches, leading to a uniform current repartition. The use of this electrical model allows to overcome the difficulties of direct three-dimensional FEM computations. In addition, the rapidity of solutions by the electric model gives the possibility of testing quickly many geometrical configurations in order to find the ones leading to an even current repartition. This optimization process would not be possible with detailed FEM simulations.

In this work, a model of a multi-layer high-Tc superconducting (HTS) cable that computes the current distribution across layers as well as the AC loss is presented. Analyzed is the case of a four-layer cable, but the developed method can be applied to a cable with an arbitrary number of layers. The cable is modelled by an equivalent circuit consisting of the following elements: nonlinear resitances, linear self and mutual inductances, as well as nonlinear, hysteretic inductances. The first take into account the typical current-voltage relation for superconductors, the second introduce coupling among the layers and depend on the geometrical parameters of the cable, the third describe the hysteretic behaviour of superconductors. In the presented analysis, the geometrical dimensions of the cable are fixed, except for the pitch length and the winding orientation of the layers. These free parameters are varied in order to partition the current across the layers such that the AC loss in the superconductor is minimized. The presented model allows to evaluate rapidly the current distribution across the different layers and to compute the corresponding AC loss. The rapidity of the computation allows calculating the losses for many different configurations within a reasonable time. The model has so firstly been used for finding the pitch lengths giving an optimal current distribution across the layers and for computing the corresponding AC loss. Secondly, the model has been refined taking into account the effects of the magnetic self-field, which, especially at high currents, can sensibly reduce the transport capacity of the cable, in particular in the outer layers.

For describing the E-J relation of high-Tc superconductors (HTS) in power applications, where the applied current I is generally limited by Ic, the critical state model, a piecewise linear generalization, or a simple power-law of the type E=Ec(J/Jc)^n are most often used. The power-law cannot be used for modelling the E-J relation with I>>I_c due to the unbound exponential increase of the electric field for currents above Ic, while in reality the non-linear HTS resistivity is limited by its normal state value. This paper presents a modified E-J model for describing the V-I characteristic of HTS tapes with applied currents largely exceeding Ic. This model is based on the power-law in combination with a parallel metallic branch and has a limited resistivity - the HTS one in the normal state. It can be used for black-box modelling of superconductors in a unlimited current range, as well as for numerical modelling of superconducting devices, which can be operated at currents far exceeding Ic; for example fault-current limiters or cables with over-critical current excursions. The model has been tested in a simple numerical implementation and the modified power-law has been implemented in finite element method simulations. It is shown that for bulk material with currents above 1.3-2Ic$ (depending on the n-value), the usual power-law results in excessive AC loss estimation.

The current repartition inside a HTS cable is very important for determining its AC losses and can be influenced by the uniformity of several parameters, either linked to the physical properties of the individual tapes (critical current Ic and power index n) or due to the manufacturing process (contact resistance). This work investigates the importance of the non-uniformity of these parameters for a manufactured 16-tape straight superconducting cable by means of finite element method (FEM) simulations. The utilized non-linear E-J model includes the anisotropic dependence of the critical current density and the power index on the local magnetic field. It is shown that the non-uniformity of the cable parameters influences the behaviour of the individual tapes, but not that of the whole cable. The utilized FEM model has been validated by a comparison with electrical measurements of the cable AC losses, as well as with the results of another simpler numerical model, which considers the cable from the macroscopic point of view.

The finite element method has been employed in order to simulate the behavior of a HTS cable for transport current applications. The E-J model includes an anisotropic dependence of the critical current density J/sub c/ and power index n on the local magnetic field, whose magnitude is nonnegligible and determines the effective critical current of the cable. The cable consists of four electrically insulated layers, each of them composed by 20 superconducting tapes, providing a total critical current of about 4 kA. In order to obtain a uniform repartition of the current among the layers, a sufficiently high contact resistance has been inserted in the electric circuit. The ac losses and the field distribution have been computed. A comparison is also made with a simple electric model of a HTS cable.

Different measurement techniques have demonstrated that due to better alignment during the manufacturing process, the central filaments in multifilamentary Bi-2223 tapes have higher critical current density than the outer filaments. A numerical model of non-twisted tapes has been used in Finite-Element-Method simulations. The model incorporates non-uniform lateral Jc distribution in accordance with direct Ic measurements, made along the width of a Bi-2223 tape. Two types of simulations are performed on 7 and 19-filamentary tapes with applied transport current – one with constant Jc in all filaments, and another with a Jc(x) dependence. The current distribution and AC loss in each filament are numerically calculated and compared. It is demonstrated that the current density distribution and power dissipation vary considerably in the different filaments, which is due to the position of the filament with respect to the edge of the tape and the different Jc values along the width.

Different finite-element method (FEM) formulations have been developed in order to model the electromagnetic behavior of type-II superconductors. This paper presents a comparison between simulations with A-V formulation models implemented in two FEM software packages (FLUX2D and FLUX3D) and a numerical method based on analytical model for superconductors in applied magnetic field. These models can be used for superconductors with complex geometry and power-law current-voltage characteristics. Simulated is a 37-filamentary tape with applied transport current in self-field and alternating current (ac) magnetic field parallel to the wide side of the tape. A good agreement is found between the ac-loss and current distributions obtained with the different models.

The estimation of the critical current (I c) and AC losses of high-temperature superconductor devices through modeling and simulation requires the knowledge of the critical current density (J c) of the superconducting material. This J c is in general not constant and depends both on the magnitude (B loc) and the direction (θ, relative to the tape) of the local magnetic flux density. In principle, J c(B loc,θ) can be obtained from the experimentally measured critical current I c(B a,θ), where B a is the magnitude of the applied magnetic field. However, for applications where the superconducting materials experience a local field that is close to the self-field of an isolated conductor, obtaining J c(B loc,θ) from I c(B a,θ) is not a trivial task. It is necessary to solve an inverse problem to correct for the contribution derived from the self–field. The methods presented in the literature comprise a series of approaches dealing with different degrees of mathematical regularization to fit the parameters of preconceived nonlinear formulas by means of brute force or optimization methods. In this contribution, we present a parameter-free method that provides excellent reproduction of experimental data and requires no human interaction or preconception of the J c dependence with respect to the magnetic field. In particular, it allows going from the experimental data to a ready-to-run J c(B loc,θ) model in a few minutes.

International audience

Roebel cables made of high temperature superconducting (HTS) coated conductors can carry high currents with a compact design and reduced ac losses. Therefore, they are good candidates for manufacturing coils for HTS applications such as motors and generators. In this paper, we present the experimental dc and ac characterization of several coils assembled from a 5-m-long Roebel cable built at Karlsruhe Institute of Technology, which differ in the number of turns and turn-to-turn spacing. Our experiments, which are supported by finite-element-method calculations, show that a more tightly wound Roebel coil, despite having a lower critical (and therefore operating) current, can produce a higher magnetic field than a loosely wound one. For a given magnetic field produced at the coil's center, all the coils have similar ac losses, with the exception of the most loosely wound one, which has much higher losses due to the relatively large current needed to produce the desired field. The experiments presented in this paper are carried out on the geometry of pancake coils made of Roebel cables, but they are exemplary of a more general strategy, based on coupling experiments and numerical simulations, that can be used to optimize the coil design, with respect to different parameters, such as tape quantity, size, or ac loss, the relative importance of which is dictated by the specific application.

Energy applications employing high-temperature superconductors (HTS), such as motors/generators, transformers, transmission lines and fault current limiters, are usually operated in the alternate current (AC) regime. In order to be efficient, the HTS devices need to have a sufficiently low value of AC loss, in addition to the necessary current-carrying capacity. Most applications are operated with currents beyond the current capacity of single conductors and consequently require cabled conductor solutions with much higher current carrying capacity, from a few kA to up to 20-30 kA for large hydro-generators. A century ago, in 1914, Ludwig Roebel invented a low-loss cable design for copper cables, which was successively named after him. The main idea behind Roebel cables is to separate the current in different strands and to provide a full transposition of the strands along the cable direction. Nowadays, these cables are commonly used in the stator of large generators. Based on the same design concept of their conventional material counterparts, HTS Roebel cables from REBCO coated conductors were first manufactured at the Karlsruhe Institute of Technology (KIT) and have been successively developed in a number of varieties that provide all the required technical features such as fully transposed strands, high transport currents and low AC losses, yet retaining enough flexibility for a specific cable design. In the past few years a large number of scientific papers have been published on the concept, manufacturing and characterization of such cables. Times are therefore mature for a review of those results. The goal is to provide an overview and a succinct and easy-to-consult guide for users, developers, and manufacturers of this kind of HTS cables.

Cables made of MgB 2 superconductors are currently explored as a viable solution for transporting high electrical power in the AC regime. In order to be competitive against the DC solution, the cables need to have an acceptable level of AC losses. In this contribution, we discuss the main aspects relevant for designing a cable with a sufficiently low AC loss level. To this end, we perform finite-element-method (FEM) simulations to determine the current and field distributions and calculate the AC losses of such cable configuration. For current capacities of 2–5 kA (peak), power cables are assembled from a relatively small number of MgB 2 strands. The performance of such cables strongly depends on the current and field distributions, which are in turn influenced by the number and the arrangement of the superconducting components and also by the magnetic properties of supporting materials. Numerical simulations can help to test different cable configurations and provide important insights for optimizing the cable’s design. The numerical model includes the field dependence of the superconductor’s critical current density J c ( B ) as well as the non-linear properties of magnetic materials.

In this paper we develop a method based on the critical state for calculating the current and field distributions and the AC losses in a cable made of curved thin superconducting tapes. The method also includes the possibility of considering spatial variation of the critical current density, which may be the result of the manufacturing process. For example, rare-earth based coated conductors are known to have a decrease of the transport properties in near the edges of the tape: this influences the way current and field penetrate in the sample and, consequently, the AC losses. We demonstrate that curved tapes arranged on a cylindrical former behave as an infinite horizontal stack of straight tapes, and we compare the AC losses in a variety of working conditions, both without and with the lateral dependence of the critical current density. This model and subsequent similar approaches can be of interest for various applications of coated conductors, including power cables and conductor-on-round-core (CORC) cables.

International audience

The current–voltage (I–V) curve is the basic characteristic of a superconducting wire or tape. Measuring I–V curves is generally problematic when samples have poor stabilization. Soldering voltage taps to an active part of the conductor affects the effectiveness of the local cooling and/or can be difficult to do in certain devices such as fault current limiters and cables where the tapes are closely packed. In order to overcome these problems, voltage taps can be placed outside the active area of the superconductor. We proved both by simulations and experiments that this arrangement leads to the same results as the standard four point method and it provides more detailed information for sample protection. The same arrangement can also be used for AC transport loss measurement. However in this case particular care has to be taken because the eddy current loss in the current leads contributes to the total measured loss. We used numerical simulations to evaluate the contribution of the eddy current loss to the measured AC loss. With help of simulations one can determine whether the contribution of the eddy current loss is significant and possibly optimize the current leads to reduce that loss contribution.

Numerical modeling of superconductors is widely recognized as a powerful tool for interpreting experimental results, understanding physical mechanisms and predicting the performance of high-temperature superconductor (HTS) tapes, wires and devices. This is especially true for ac loss calculation, since a sufficiently low ac loss value is imperative to make these materials attractive for commercialization. In recent years, a large variety of numerical models, based on different techniques and implementations, have been proposed by researchers around the world, with the purpose of being able to estimate ac losses in HTSs quickly and accurately. This article presents a literature review of the methods for computing ac losses in HTS tapes, wires and devices. Technical superconductors have a relatively complex geometry (filaments, which might be twisted or transposed, or layers) and consist of different materials. As a result, different loss contributions exist. In this paper, we describe the ways of computing such loss contributions, which include hysteresis losses, eddy current losses, coupling losses, and losses in ferromagnetic materials. We also provide an estimation of the losses occurring in a variety of power applications., IEEE Transactions on Applied Superconductivity, 2013

In this paper we derive the integral equations for radially and polygonally arranged high-temperature superconductor thin tapes and we solve them by finite-element method. The superconductor is modeled with a non-linear power law, which allows the possibility of considering the dependence of the parameters on the magnetic field or the position. The ac losses are computed for a variety of geometrical configurations and for various values of the transport current. Differences with respect to existing analytical models, which are developed in the framework of the critical state model and only for certain values of the transport current, are pointed out.

With this paper we provide an effective method to solve a large class of problems related to the electromagnetic behavior of thin superconductors. Here all the problems are reduced to finding the weight functions for the Green integrals that represent the magnetic field components; these latter must satisfy the mixed boundary value conditions that naturally arise from the critical state assumptions. The use of the Erd\'elyi-Kober operators and of the Hankel transforms (and mostly the employment of their composition properties) is the keystone to unify the method toward the solution. In fact, the procedure consists always of the same steps and does not require any peculiar invention. For this reason the method, here presented in detail for the simplest cases that can be handled in analytical way (two parts boundary), can be directly extended to many other more complex geometries (three or more parts), which usually will require a numerical treatment. In this paper we use the operator technique to derive the current density and field distributions in perfectly conducting and superconducting thin discs and tapes subjected to a uniform magnetic field or carrying a transport current. Although analytical expressions for the field and current distributions have already been found by other authors in the past by using several other methods, their derivation is often cumbersome or missing key details, which makes it difficult for the reader to fully understand the derivation of the analytical formulas and, more importantly, to extend the same methods to solve similar new problems. On the contrary, the characterization of these cases as mixed boundary conditions has the advantage of referring to an immediate and na\"ive translation of physics into a consistent mathematical formulation whose possible extension to other cases is self-evident., Comment: The final publication is available at http://link.springer.com/article/10.1007/s00033-011-0185-5

Use of 2G HTS coated conductors in several power applications has become popular in recent years. Their large current density under high magnetic fields makes them suitable candidates for high power capacity applications such as stacks of tapes, coils, magnets, cables and current leads. For this reason, modeling and simulation of their electromagnetic properties is very desirable in the design and optimization processes. For many applications, when symmetries allow it, simple models consisting of 1D or 2D representations are well suited for providing a satisfying description of the problem at hand. However, certain designs such as racetrack coils and finite-length or non-straight stacks, do pose a 3D problem that cannot be easily reduced to a 2D configuration. Full 3D models have been developed, but their use for simulating superconducting devices is a very challenging task involving a large-scale computational problem. In this work, we present a new method to simulate the electromagnetic transient behavior of 2G HTS stacks and coils. The method, originally used to model stacks of straight superconducting tapes or circular coils in 2D, is now extended to 3D. The main idea is to construct an anisotropic bulk-like equivalent for the stack or coil, such that the geometrical layout of the internal alternating structures of insulating, metallic, superconducting and substrate layers is reduced while keeping the overall electromagnetic behavior of the original device. Besides the aforementioned interest in modeling and simulating 2G HTS coated conductors, this work provides a further step towards efficient 3D modeling and simulation of superconducting devices for large-scale applications.