High Temperature Superconducting Coated Conductors Research Articles

2D axisymmetric electromagnetic modeling of HTS coils based on T-A formulation with modified Newman boundary conditions

Abstract The T-A formulation based on thin film approximation has been widely used in electromagnetic modeling of high temperature superconducting (HTS) coated conductors (CCs). However, with the emergence of no-insulation (NI) HTS coils and its variant HTS coils, the electrical connection of HTS coils has become increasingly complex, and the traditional T-A formulation is challenging to handle the problems of conductors with non-negligible thickness and current sharing. This paper firstly describes the Neumann boundary condition of the T-A formulation under 2D axisymmetric symmetry in detail, as well as the conversion of different boundary conditions. And additional voltage variable is added to correct the Newman boundary condition from the perspective of circuit. Then, considering HTS CCs series or parallel stacking to carry current, the effectiveness of this method is verified by comparing with benchmark model. Finally, we extend the application range of the T-A formulation with modified Newman boundary conditions to simulate thick superconductors, and naturally process current sharing of azimuthal and radial current in circular NI HTS coils.

A quench detection method for parallel co-wound HTS coils based on current redistribution

High-temperature superconducting (HTS) coated conductors (CCs) have become the preferred material for superconducting magnet applications due to their high engineering current density and high mechanical strength. However, due to the low quench zone propagation velocity of CCs, magnets wound with CCs suffer from severe quench risks. Therefore, a rapid, sensitive, and reliable quench detection method is crucial for the safe operation of such HTS magnets. In this paper, we propose a quench detection method based on current redistribution, in which two pieces of HTS CCs are soldered together at each end and insulated in the middle part, which are then parallel co-wound into a double-pancake coil. The two tightly coupled windings and low resistance joints form a very low inductance current loop, resulting in fast current redistribution between the two co-windings even at the inception of quench (with still low quench voltage). We deduced analytical solutions of the current redistribution process under different magnet operational scenarios, including constant current operation, charging and discharging, and proposed quench detection criteria. Corresponding quench tests were performed on a small scale co-wound HTS coil, and the results well verified the analytical solutions and the effectiveness of the quench detection method. Our work may be useful for lowering the risks in HTS magnet quench in various applications.

Conceptual Design and Optimisation of HTS Roebel Tapes

The main obstacle for the application of the high-temperature superconducting (HTS) coated conductors (CCs) in AC energy applications is the relatively large AC loss. To tackle this, several forms of HTS cables for AC applications have been invented and investigated, such as the HTS Roebel cable, Cable on Round Conductor (CORC), and Twisted Stacked Tape Cable (TSTC). In this paper, the possibility of encapsulating Roebel cables into a single HTS CC is investigated, from which a novel conception of a Roebel tape is proposed. Compared with the existing HTS cables, HTS Roebel tapes are more compact, more capable at carrying large current with minimised AC losses, and easier to manufacture. A 3D finite element method (FEM) model of the Roebel tape is built to optimise the structure and verify the performance. The results show that, compared with normal ReBCO CCs, Roebel tapes with optimum patterns can reduce AC transport losses by 60% through field-cancelling and can reduce magnetisation losses by the factor of the filament number through patterning. With excellent loss reduction performance and high current capability, the Roebel tape shows great potential to become a revolutionary HTS cable for high-current power transmission and AC machine applications.

3D finite element modelling on racetrack coils using the homogeneous T-A formulation

High temperature superconducting (HTS) coated conductors (CCs) hold a promising feature in use of manufacturing kinds of magnets, coils, cables and so on. Its advantage on large-current-transporting capacity makes it suitable in MW-class machines and other large power electrical applications. In most situations, corresponding simulations were modeled in a 2D architecture. While, more complicated influences on ends of machines have been ignored artificially due to the simplification on model dimensions and huge expanses on the computational time. Therefore, comprehensive and full-scale models, which cannot easily be simplified as 1D or 2D representations, are urgent to analyze their electromagnetic behaviors in the early-stage design with an acceptable speed. In this paper, we propose a homogeneous T-A formulation for the 3D racetrack coil for the first time, which is treated as an anisotropic bulk-like equivalent to be modeled. Only the superconducting layer of HTS CCs has been preserved and other layers are ignored while still retaining its electromagnetic characteristics. This method in this paper has been fully verified with the widely accepted H formulation. However, the computational expense in T-A model is more than that of H model. At last, AC loss of a manufactured HTS double racetrack coil of one synchronous generator was measured and its experimental results are in good agreements with numerical profiles. This work has a guiding significance to accelerate the pace of 3D model and simulation in HTS applications.

Electromagnetic properties of curved HTS trapped field stacks under high-frequency cross fields for high-speed rotating machines

Superconducting electric propulsion systems, characterized by high power densities and efficiencies, provide a possibility to zero carbon emission for future aviation. Stacks of high temperature superconducting (HTS) coated conductors (CCs) have become an alternative for high field magnets applied to superconducting machines, given their excellent field trapping ability and thermal stability. High-frequency ripple fields always exist in high-speed electric machines. Most research work regarding HTS trapped field stacks (TFSs) was focused on their magnetization methods and amplitude of trapped flux density; however, their performance in the high-frequency environment remains unclear. Despite several numerical models established for flat HTS TFSs, a comprehensive analysis of curved ones is still lacking, which possess geometrical applicability for cylindrical rotating shafts. Aimed at exploring the electromagnetic properties of curved HTS TFSs applied to high-speed rotating machines, a 3D numerical model considering both the multilayer structure and the Jc (B) dependence of HTS CCs has been built. Current and magnetic flux density distributions, as well as loss properties of a curved HTS TFS have been studied in detail, under perpendicular and cross fields with varying frequencies ranging from 50 Hz to 20 kHz. Results have shown that, the widely adopted two-dimensional-axisymmetric models are inapplicable to study the electromagnetic distributions of TFSs because of the emergence of the electromagnetic criss-cross defined in this paper. High-frequency ripple fields can drive induced current towards the periphery of the HTS TFS due to the skin effect, leading to a fast rise of AC loss and even an irreversible demagnetization of the stack. This paper has qualified and quantified the high-frequency electromagnetic behaviours of curved HTS TFSs, providing a useful reference for their loss controlling and anti-demagnetization design in high-speed propulsion machines.

Magnetization Loss in HTS Coated Conductor Exposed to Harmonic External Magnetic Fields for Superconducting Rotating Machine Applications

Previous studies on magnetization AC loss of high temperature superconducting (HTS) coated conductors (CCs) taken into account the ideally sinusoidal external magnetic field, or non-sinusoidal by considering only the harmonics in phase with the fundamental component. However, realistically magnetic field often contains harmonics with different phase angles and amplitudes. In this paper, magnetization AC loss in HTS CC was studied, considering the phase angle φ of each harmonic; assuming superconductor is subjected to external magnetic field which is distorted by the 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> and the 5 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> harmonics. Phase angle of each harmonic was considered in the range of 0 to π and amplitude of fundamental magnetic field, was assumed as 10, 20, 50, and 100 mT. Different distortion level of magnetic field was considered too. It is concluded that phase angle of field harmonic has a significant effect on magnetization loss of HTS CCs.

Dynamic loss and magnetization loss of HTS coated conductors, stacks, and coils for high-speed synchronous machines

Dynamic loss is an essential parameter to consider for the design of high temperature superconducting (HTS) synchronous machine windings. For aerospace electric propulsion systems, the fundamental frequency component and harmonics in electric machines can attain kHz level because of the high rotating speed. However, for HTS coated conductors (CC), the existing definition of dynamic loss only considers the HTS layer, the validity of which at high frequencies is questionable. Besides, the variation of dynamic loss and magnetization loss under skin effect due to high frequency is still unknown. Additionally, the influence of shielding effects among distinct turns on the dynamic loss of HTS stacks and coils remains unclear. In response to the above concerns, by use of the H-formulation based numerical multilayer modelling method which considers all layers of a CC, the frequency dependence of dynamic loss and magnetization loss of HTS CCs, stacks and coils over a wide range up to 20 kHz has been investigated. Results show that the existing definition of the dynamic region is no longer valid at kHz level, which shrinks rapidly with increasing frequency and magnetization loss plays a progressively important role due to skin effect. Meanwhile, the shielding effect in HTS stacks and coils can enhance the significance of dynamic loss. This paper clarifies the characteristics of dynamic loss and magnetization loss of HTS CCs, stacks, and coils over a wide frequency band, which can serve as a useful reference for accurate loss controlling of machine windings in future aerospace HTS propulsion systems.

Loss characteristics of HTS coated conductors in field windings of electric aircraft propulsion motors

High-temperature superconducting (HTS) coated conductors (CCs) are widely regarded as a promising candidate to enable very high power density motors. These machines operate at high rotational speeds, with some designs going up to 12 000 rpm. HTS CCs are applied to the field windings of these motors to increase the magnetic loading and hence the power density. Even though the superconducting field windings operate with a DC current, due to the magnetic field environment, losses are present. This paper examines the dynamic and total loss characteristics of YBCO-coated conductors in the frequency range relevant to high-speed motors for electric aircraft propulsion. A multi-layer model was created using the H-formulation and the losses for each layer were highlighted. For the first time, it was shown that the DC transport current region in the HTS layer shrinks as the frequency of the applied field increases due to the increased magnetisation current around the edges of the CC, which reduces the dynamic loss per cycle as the frequency increases. To fully understand the loss distribution in the HTS CC, the total loss in the conductor was investigated. For an applied magnetic field of 100 mT and 800 Hz, more than 30% of the total loss occurs in the copper layer due to the decreased penetration depth of the magnetic field and the skin effect. Results show that to accurately model and understand the losses in superconducting field windings, a multi-layer model should be used, since a significant proportion of loss shifts towards the copper stabilizers. Over all, it was shown that both the dynamic loss as well as magnetisation loss play a crucial role in the estimation of the loss in superconducting field windings.

Dynamic loss of HTS field windings in rotating electric machines

High-temperature superconducting (HTS) coated conductors (CCs) are frequently applied under complex electromagnetic fields to develop powerful, compact and efficient rotating electric machines. In such electric machines, field windings constructed by HTS CCs are adopted to increase the magnetic loading of the machines. The HTS field windings work with DC currents and due to the time-varying magnetic field environment, dynamic losses occur. In addition to the AC magnetic field, there is a large DC background field, which is caused by the self-field of the HTS field windings. This paper investigates the dynamic loss in HTS CCs using an H-formulation based numerical model for a wide range of combined DC and AC magnetic fields under various load conditions, and two different methods have been used for calculating dynamic loss. The results show that a DC background field plays a vital role to accurately predict the dynamic losses in HTS CCs. A DC background field of 75 mT can triple the dynamic loss as compared to only applying an AC magnetic field. In addition, the theoretical definition for the dynamic region for the case of solely an AC field has been found inapplicable in the case of a DC background field. Finally, a case study is done based on our double claw pole power generator to estimate the dynamic loss in an actual rotating machine, which was found to be 13.3 W. A low dynamic loss was achieved through the generator field winding design, which prevents high magnetic field fluctuations in the winding, since it is located at a distance from the air gap and armature coils. Furthermore, the rotational speed is very low and hence the resultant magnetic field frequency is low as well.

A temperature-dependent multilayer model for direct current carrying HTS coated-conductors under perpendicular AC magnetic fields

When a type II superconductor carrying a direct current is subjected to a perpendicular oscillating magnetic field, a direct current (DC) voltage will appear. This voltage can either result from dynamic resistance effect or from flux flow effect, or both. The temperature variation in the superconductor plays an important role in the nature of the voltage, and there has been little study of this so far. This paper presents and experimentally verifies a 2D temperature-dependent multilayer model of the second generation (2G) high temperature superconducting (HTS) coated conductors (CC), which is based on H-formulation and a general heat transfer equation. The model has coupled the electromagnetic and thermal physics, and it can simulate the behavior of 2G HTS coated conductors in various working conditions where the temperature rise has a significant impact. Representative electromagnetic phenomena such as the dynamic resistance effect and the flux flow effect, and thermal behavior like quench and recovery have been simulated. This thermal-coupled model is a powerful tool to study the thermal-electromagnetic behaviors of 2G HTS coated conductors in different working conditions, especially when the impact of temperature rise is important. This multilayer model is also very useful in analyzing the impact of different layers in the 2G HTS CCs, especially the metal stabilizer layers. It has been proven to be a very powerful tool to help understand more complicated characteristics in the CCs which could not be accurately measured or simulated by previous numerical models. The work is indicative and very useful in designing ac magnetic field controlled persistent current switches and flux pumps, in terms of increasing the off-state resistance, analyzing different sources of losses, minimizing detrimental losses, and enhancing the safety and stability.

Modelling of electromagnetic loss in HTS coated conductors over a wide frequency band

Electromagnetic loss is a crucial factor to evaluate the performance of high temperature superconducting (HTS) coated conductors (CCs). Although the loss characteristics around power frequency have been well studied, it is still unclear how loss varies towards high frequencies above kHz level, which is important to a wide range of applications, such as wireless power transfer. This paper is to investigate the frequency dependence of both magnetization and transport current loss in HTS CCs and therefore, to provide comprehensive analyses through a detailed multilayer model reflecting their actual structures. In this paper, a T-formulation based multilayer numerical model for HTS CCs, consisting of HTS layer, substrate, silver overlayer, and copper stabilizers, has been developed. Both magnetization loss and transport current loss over a wide frequency range, from 50 Hz to 1 MHz, have been simulated and discussed. The results obtained by the existing thin film model based on T-formulation, multilayer model and homogenization model by H-formulation are also presented and compared. The proposed multilayer model has been validated by experimental measurements, which has proven the widely adopted HTS thin film model to be inapplicable for frequencies above 100 Hz. In addition, most magnetization losses occur in the copper stabilizers above 1.2 kHz due to skin effect. Results can be used to study the performance of HTS devices towards high frequencies at kHz or even MHz level.

Impact of Stabilizer Layers on the Thermal-Electromagnetic Characteristics of Direct Current Carrying HTS Coated Conductors under Perpendicular AC Magnetic Fields

When a type-II high Tc superconductor carrying a direct current is subjected to a perpendicular AC magnetic field, a direct current voltage will appear. This phenomenon is called dynamic resistance effect. In general, the high temperature superconducting (HTS) coated conductor (CC) has two stabilizer layers. However, the impacts of two stabilizer layers on the dynamic resistance, DC electrical field, losses, and temperature rise haven't been studied yet. This paper presents the impacts of the stabilizer layers and their resistivity on the dynamic resistance effect and HTS CC tape's thermal-electromagnetic behaviors by using a temperature dependent FEM model. This work reveals that the stabilizer impacts significantly on the dynamic resistance, dc voltage, power loss, and temperature rise. It is will help design high-performance AC magnetic field-controlled PCS and switches based HTS devices.

Transition frequency of transport ac losses in high temperature superconducting coated conductors

Experimental data reveal that the classical description of transport ac losses in high-temperature superconducting (HTS)-coated conductors (CCs), based on investigations at low frequencies, is incomplete in some aspects when transport currents in the kilohertz range are considered. More specifically, above a certain “transition frequency,” the ac losses per cycle no longer increase with the frequency as the theory predicts. Using a finite element model to allow for loss separation, we find that this phenomenon is caused by a combination of several factors that appear only above the transition frequency: the hysteresis and ferromagnetic losses per cycle are no longer independent of the frequency, while the eddy current losses per cycle no longer increase proportionally to the frequency. Based on a circuit model, we propose that the physical reason for this is that when the frequency increases, part of the supercurrent starts migrating into the metallic path. We argue that the current in the metallic path is not an eddy current but a transport current inductively coupled to the superconducting current. Finally, we discuss the relationship between the magnetic material magnetization, the critical current, and the transport current frequency. This study provides explicit insights into the frequency-dependent transport ac losses of HTS CCs in a broad frequency band, which is valuable for the design and optimization of HTS CC-based power devices.

Influence of Substrate Magnetism on Frequency-Dependent Transport Loss in HTS-Coated Conductors

The magnetism of substrate has significant influence on the transport loss in high temperature superconducting (HTS) coated conductors (CCs). Taking three types of substrates (i.e., nonmagnetic, weakly magnetic, and strongly magnetic) into account, a study on the frequency dependence (in the range of 10–1000 Hz) of transport loss in HTS CCs with these substrates is performed numerically and experimentally. Different loss components and magnetic field profile are calculated individually to clarify the effect of substrate magnetism. Results show that HTS CCs with magnetic substrate exhibit higher transport loss than CCs with nonmagnetic substrate. Both hysteresis loss in HTS layer and eddy current loss in conventional metal increase with the enhancement of substrate magnetism.

Numerical Study on Overcurrent Process of High-Temperature Superconducting Coated Conductors

Overcurrent performance of high-temperature superconducting (HTS) coated conductor (CC) is one of the most crucial parameters for industrial applications, especially in superconducting fault current limiters (SFCLs). Thus, numerical study of overcurrent process becomes desirable in design of these superconducting devices. In this paper, a field-circuit combined model is introduced to study the overcurrent process of HTS CCs. This model is built by both MATLAB and COMSOL. Circuit parameters, electromagnetic, and temperature distributions are individually calculated by different software. Temperature (T), magnetic intensity (B), and generated heat (Q) are used as real-time intermediate exchanging variables. Accuracy of this model is verified by short-fault experiments on straight HTS CC. Further applications, such as reclosing process and superconducting coils are both performed. Results obtained in this paper prove the validity of this model; this model can be helpful in future design of superconducting devices.

Simulation of Stacks of High-Temperature Superconducting Coated Conductors Magnetized by Pulsed Field Magnetization Using Controlled Magnetic Density Distribution Coils

High-temperature superconducting (HTS) stacks of coated conductors (CCs) can work as strong trapped field magnets (TFMs) and show potential in electrical applications. Pulsed field magnetization (PFM) is a practical method to magnetize such TFMs, but due to heat generation during the dynamic process, it cannot achieve a trapped field as high as field cooling can. In this work, we construct a 2-D electromagnetic-thermal coupled model to simulate stacks of HTS CCs with realistic laminated structures magnetized by PFM. The model considers temperature- and anisotropic magnetic-field-dependent J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> of HTS and other temperature-dependent thermal and electrical material properties. Based on the model, a configuration of controlled magnetic density distribution coils is suggested to improve the trapped field compared to that obtained by ordinary solenoids.

Modelling ac ripple currents in HTS coated conductors

Dc transmission using high temperature superconducting (HTS) coated conductors (CCs) offers a promising solution to the globally growing demand for effective, reliable and economic transmission of green energy up to the gigawatt level over very long distances. The credible estimation of the losses and thereby the heat dissipation involved, where ac ripples (introduced in rectification/ac–dc conversion) are viewed as a potential source of notable contribution, is highly essential for the rational design of practical HTS dc transmission cables and corresponding cryogenic systems to fulfil this demand. Here we report a targeted modelling study into the ac losses in a HTS CC subject to dc and ac ripple currents simultaneously, by solving Maxwell’s equations using the finite element method (FEM) in the commercial software package COMSOL. It is observed that the instantaneous loss exhibits only one peak per cycle in the HTS CC subject to sinusoidal ripples, given that the amplitude of the ac ripples is smaller than approximately 20% of that of the dc current. This is a distinct contrast to the usual observation of two peaks per cycle in a HTS CC subject to ac currents only. The unique mechanism is also revealed, which is directly associated with the finding that, around any local minima of the applied ac ripples, the critical state of −Jc is never reached at the edges of the HTS CC, as it should be according to the Bean model. When running further into the longer term, it is discovered that the ac ripple loss of the HTS CC in full-wave rectification decays monotonically, at a speed which is found to be insensitive to the frequency of the applied ripples within our targeted situations, to a relatively low level of approximately 1.38 × 10−4 W m−1 in around 1.7 s. Comparison between this level and other typical loss contributions in a HTS dc cable implies that ac ripple currents in HTS CCs should only be considered as a minor source of dissipation in superconducting dc transmission.

Impact of the Normal Zone Propagation Velocity of High-Temperature Superconducting Coated Conductors on Resistive Fault Current Limiters

The engineering critical current, i.e., Ic, of high-temperature superconducting coated conductors (HTS-CCs), today available on the market, is not a uniform parameter and varies significantly along the length of the conductors. In addition, commercial HTS-CCs have a low normal zone propagation velocity (NZPV). This property, together with the Ic inhomogeneity, exposes the HTS-CCs to local thermal instabilities. A crucial challenge for the design of resistive fault current limiters (RFCLs) based on HTS-CCs is to avoid the thermal runaway of the conductors; and in this respect, the enhancement of the NZPV is a promising solution. In recent years, several methods have been proposed, and many various techniques are now available. In this paper, we are interested to quantify the impact the enhancement of NZPV will have on the design of RFCLs based on HTS-CCs whichever is the adopted technical solution. For this reason, we use numerical models to analyze the effects of the NZPV enhancement on the limitation performance of an RFCL integrated in a medium-voltage power grid.

Heat transfer monitoring between quenched high-temperature superconducting coated conductors and liquid nitrogen

High-temperature superconducting coated conductors (HTS-CCs) are good candidates for resistive superconducting fault current limiter (RSFCL) applications. However, the high current density they can carry and their low thermal diffusivity expose them to the risk of thermal instability. In order to find the best compromise between stability and cost, it is important to study the heat transfer between HTS-CCs and the liquid nitrogen (LN2) bath. This paper presents an experimental method to monitor in real-time the temperature of a quenched HTS-CC during a current pulse. The current and the associated voltage are measured, giving a precise knowledge of the amount of energy dissipated in the tape. These values are compared with an adiabatic numerical thermal model which takes into account heat capacity temperature dependence of the stabilizer and substrate. The result is a precise estimation of the heat transfer to the liquid nitrogen bath at each time step. Measurements were taken on a bare tape and have been repeated using increasing Kapton® insulation layers. The different heat exchange regimes can be clearly identified. This experimental method enables us to characterize the recooling process after a quench. Finally, suggestions are done to reduce the temperature increase of the tape, at a rated current and given limitation time, using different thermal insulation thicknesses.

Analysis of the influence of the normal zone propagation velocity on the design of resistive fault current limiters

Commercial high-temperature superconducting coated conductors (HTS-CCs) have low thermal diffusivity and nonuniform critical current density. These two factors lead commercial HTS-CCs to a partial quench when they are subjected to a transport current around their average critical current (). The consequence is the appearance of localized resistive zones, and a high risk of thermal runaway can arise when HTS-CCs are used for resistive fault current limiter (RFCL) purposes. The enhancement of the normal zone propagation velocity (NZPV) of HTS-CCs is a desirable solution for achieving sufficient thermal stability while keeping the cost of RFCLs under an acceptable threshold. Even though in recent years, several valid methods to increase the NZPV have been proposed, their impact on the design of RFCLs is not clear. For this reason, we developed a one-dimensional numerical model that enables us to simulate HTS-CCs with enhanced NZPV and to study the limitation performance of a HTS-CC-based RFCL in real operating conditions. Our preliminary re sults demonstrate that the NZPV enhancement can effectively limit the needed amount of HTS-CCs with important economic benefits for the design of RFCLs.