Victor Manuel Rodriguez Zermeno

Calculation of alternating current losses in stacks and coils made of second generation high temperature superconducting tapes for large scale applications

A homogenization method to model a stack of second generation High Temperature Superconducting tapes under AC applied transport current or magnetic field has been obtained. The idea is to find an anisotropic bulk equivalent for the stack such that the geometrical layout of the internal alternating structures of insulating, metallic, superconducting, and substrate layers is “washed” out while keeping the overall electromagnetic behavior of the original stack. We disregard assumptions upon the shape of the critical region and use a power law E–J relationship allowing for overcritical current densities to be considered. The method presented here allows for a computational speedup factor of up to 2 orders of magnitude when compared to full 2-D simulations taking into account the actual dimensions of the stacks without compromising accuracy.

A full 3D time-dependent electromagnetic model for Roebel cables

High temperature superconductor Roebel cables are well known for their large current capacity and low AC losses. For this reason they have become attractive candidates for many power applications. The continuous transposition of their strands reduces the coupling losses while ensuring better current sharing among them. However, since Roebel cables have a true 3D structure and are made of several high aspect ratio coated conductors, modelling and simulation of their electromagnetic properties is very challenging. Therefore, a realistic model taking into account the actual layout of the cable is unavoidably a large scale computational problem. In this work, we present a full 3D model of a Roebel cable with 14 strands. The model is based on the H-formulation, widely used for 2D problems. In order to keep the 3D features of the cable (in particular the magnetization currents near the transpositions), no simplifications are made other than the reduction of the modelled length according to the periodicity of the cable structure. The 3D model is used to study the dependence of AC losses on the amplitude of the AC applied magnetic field or transport current. Beyond the importance of simulating the Roebel cable layout, this work represents a further step into achieving 3D simulation of superconducting devices for real applications.

Self-Consistent Modeling of the

Numerical models for computing the effective critical current of devices made of high-temperature superconducting tapes require the knowledge of the Jc(B,θ) dependence, i.e., of the way the critical current density Jc depends on the magnetic flux density B and its orientation θ with respect to the tape. In this paper, we present a numerical model based on the critical state with angular field dependence of Jc to extract the Jc(B,θ) relation from experimental data. The model takes into account the self-field created by the tape, which gives an important contribution when the field applied in the experiments is low. The same model can be also used to compute the effective critical current of devices composed of electromagnetically interacting tapes. In this paper, we consider three examples: two differently current-rated Roebel cables composed of ten strands from REBCO coated conductors and a power cable prototype composed of 22 Bi-2223 tapes. The critical currents computed with the numerical model show good agreement with the measured ones. The simulations reveal also that several parameter sets in Jc(B,θ) give an equally good representation of the experimental characterization of the tapes and that the measured Ic values of cables are subjected to the influence of experimental conditions, such as Ic degradation due to the manufacturing and assembling process and nonuniformity of the tape properties. These two aspects make the determination of a very precise Jc(B,θ) expression probably unnecessary, as long as that expression is able to reproduce the main features of the observed angular dependence. The easiness of use of this model, which can be straightforwardly implemented in finite-element programs able to solve static electromagnetic problems, is very attractive both for researchers and device manufactures who want to characterize superconducting tapes and calculate the effective critical current of superconducting devices.

I_{c}

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.

of HTS Devices: How Accurate do Models Really Need to Be?

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 coils 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.

3D modeling and simulation of 2G HTS stacks and coils

In this contribution, we develop a refined numerical model of pancake coils assembled from a coated conductor Roebel cable, which includes the angular dependence of the critical current density Jc on the magnetic field and the actual (three-dimensional) shape of the current lead used to inject the current. Previous works of ours indicate that this latter has an important influence on the measured value of the AC losses. For the simulation of the superconductor, we used two alternative models based on different descriptions of the superconductors properties and implemented in different mathematical schemes. For the simulation of the current lead we use a full three-dimensional finite-element model. The results of the simulation are compared with measurements and the main issues related to the modeling and the measurement of Roebel coils are discussed in detail.

Numerical models for ac loss calculation in large-scale applications of HTS coated conductors

Nowadays, there is growing interest in using superconducting wires or tapes for the design and manufacture of devices such as cables, coils, rotating machinery, transformers and fault current limiters among others. Their high current capacity has made them the candidates of choice for manufacturing compact and light cables and coils that can be used in the large scale power applications described above. However, the performance of these cables and coils is limited by their critical current, which is determined by several factors, including the conductors material properties and the geometric layout of the device itself. In this work we present a self-consistent model for estimating the critical current of superconducting devices. This is of large importance when the operating conditions are such that the self-field produced by the current is comparable to the overall background field. The model is based on the asymptotic limit when time approaches infinity of Faradays equation written in terms of the magnetic vector potential. It uses a continuous E-J relationship and takes the angular dependence of the critical current density on the magnetic flux density into account. The proposed model is used to estimate the critical current of superconducting devices such as cables, coils, and coils made of transposed cables with very high accuracy. The high computing speed of this model makes it an ideal candidate for design optimization.

Self-Field Effects and AC Losses in Pancake Coils Assembled From Coated Conductor Roebel Cables

Roebel cables are a promising solution for high-current, low ac loss conductors for various applications, including magnets, rotating machines, and transformers, which generally require the cable to be wound in a coil. We recently assembled and characterized a 5 m long sample and wound it into pancake coils. In this contribution, we investigate the ac loss behavior of such pancake coils by means of numerical simulations based on two complementary models: the finite-element model based on the H-formulation and the minimum magnetic energy variation method based on the critical state. These two numerical models take into account the axis-symmetric geometry of the coil and its detailed structure, simulating each strand composing the cable. The local current density and magnetic field distributions are shown and the ac losses for various current amplitudes are computed. The influence of the number of turns and of their separation on the ac losses is investigated. The results of the computations are compared with the measurements and the main reasons for the observed discrepancy are discussed.

A self-consistent model for estimating the critical current of superconducting devices

In order to transport sufficiently high current, high-temperature superconductor 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 that the cable can effectively carry. In order to be able to predict the critical current of aforementioned 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 and 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 materials property. The numerical codes, which are open source, are made freely available to interested users.

AC Losses of Pancake Coils Made of Roebel Cable

Low-temperature superconducting wires, NbTi and Nb3Sn, designed for ac applications, such as CERN and ITER magnets, are composed of twisted multifilament structures. Under time-varying applied magnetic field, twisting decreases the induced electromotive forces between the filaments and is therefore an effective method to reduce interfilamentary coupling. In order to study coupling losses computationally with high precision, 3-D numerical models are needed. In this work, we use 3-D finite-element method simulations to study hysteresis and coupling losses in NbTi superconductors. We investigate the effect of twist pitch on ac losses. In practice, NbTi wires cannot be studied at the filament level due to the extremely complex geometries. However, the manufacturing of these wires is done by using filament bundles. Therefore, we consider wires that consist of homogenized filament bundles embedded in normal conducting matrix. In particular, we consider the effect of barriers around filament bundles and how filaments should be arranged in bundles to minimize the losses. The simulations show that the qualitative behavior of the model is consistent with the analytical results and it can be used, e.g., in optimization processes, where a comparison of wire geometries is needed. Additionally, when considering the coupling of filaments, the barrier plays a very important role in minimizing the losses.