Frédéric Sirois

Potential and limits of numerical modelling for supporting the development of HTS devices

In this paper, we present a general review of the status of numerical modelling applied to the design of high temperature superconductor devices. The importance of this tool is emphasized at the beginning of the paper, followed by formal definitions of the notions of models, numerical methods and numerical models. The state-of-the-art models are listed, and the main limitations of existing numerical models are reported. Those limitations are shown to concern two aspects: on the one hand, the numerical performance (i.e. speed) of the methods themselves is not good enough yet; on the other hand, the availability of model file templates, material data and benchmark problems is clearly insufficient. Paths for improving those elements are indicated in the paper. Besides the technical aspects of the research to be further pursued, for instance in adaptive numerical methods, most recommendations command for an increased collective effort for sharing files, data, codes and their documentation.

Mutual Inductance Calculation Between Circular Filaments Arbitrarily Positioned in Space: Alternative to Grover's Formula

In this paper, we present the full derivation of a new formula for calculating the mutual inductance between inclined circular filaments arbitrarily positioned with respect to each other. Although such a formula was already proposed by Grover more than 50 years ago, the formula presented here is slightly more general and simpler to use, i.e., it involves only a sequential evaluation of expressions and the numerical resolution of a simple numerical integration. We derived the new formula using the method of vector potential, as opposed to Grovers approach, which was based on the Neumann formula. We validated the new formula through a series of examples, which are presented here. Finally, we present the relationship between the two general formulas (i.e., Grovers and our new one) explicitly (Example 12).

A new finite-element method simulation model for computing AC loss in roll assisted biaxially textured substrate YBCO tapes

This paper presents a new finite-element simulation model for computing the electromagnetic properties and AC losses in systems of YBCO (yttrium barium copper oxide) conductors on roll assisted biaxially textured substrates (RABiTS). In this model, the magnetic field dependent permeability and ferromagnetic loss of the substrates in RABiTS YBCO tapes are taken into account. The simulations were employed to simulate the AC loss in stacks of two parallel connected YBCO tapes. The simulation results are compared with the experimental data to check the validity of the simulation model. The result reveals an effective way of significantly reducing AC loss in YBCO tapes by stacking two RABiTS YBCO coated conductors with the appropriate relative tape orientation.

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.

Magneto-Thermal Modeling of Second-Generation HTS for Resistive Fault Current Limiter Design Purposes

Coated conductors (CCs) 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 CCs 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 high-temperature superconductor (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 FCLs made with CCs.

New Formulas for Mutual Inductance and Axial Magnetic Force Between a Thin Wall Solenoid and a Thick Circular Coil of Rectangular Cross-Section

This paper presents new analytic formulas for determining the mutual inductance and the axial magnetic force between two coaxial coils in air, namely a thick circular coil with rectangular cross-section and a thin wall solenoid. The mutual inductance and the magnetic force are expressed as complete elliptical integrals of the first and second kind, Heumans Lambda function and one well-behaved integral that must be solved numerically. All possible singular cases are automatically handled by the proposed formulas. The results of the work presented here have been verified by the filament method and previously published data. The new formulas provide a substantially simple alternative over previously published approaches, which involve either numerical techniques (finite element method, boundary element method, method of moments) or other semianalytic or analytic approaches.

Integral equations for the current density in thin conductors and their solution by the finite-element method

The current density and magnetic field distributions in thin conductors are important for several applications, and they can be computed by solving integral equations. This paper describes the implementation of a one-dimensional (1D) integral equation in a finite-element model. This numerical method does not require the use of ad hoc assumptions to avoid logarithmic divergences of the current density at the conductors edges and, by using a coupling with 2D electromagnetic models, it can be used to solve cases of increasing complexity. With respect to commonly used 2D models, it overcomes the typical problems linked to the mesh of conductors with high aspect ratio, such as the use of large memory and long computing times.

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}

In this paper we present a method for computing transport current ac losses in interacting thin superconductors. The method solves the integral equations for the sheet current density distribution and is specifically developed for those configurations where the symmetry of the current density distributions allows writing the equation in a self-consistent form, without the need for using an auxiliary 2D model to describe the interaction between superconducting tapes. This results in very short computation times and therefore the model can be very useful for optimizing the design of superconducting devices. The method has been tested for different cases of practical applications and the ac loss results have been compared with those obtained with analytical models and with experiments.

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

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.