Total AC Loss Research Articles

Numerical simulations on the AC loss of REBCO stacks under rotating magnetic fields

AC loss presents a significant challenge for high-temperature superconducting (HTS) rotating machines. To date, the behaviour of total AC loss (Qtol) (with current) and magnetization loss (Qm) (without current) in a single HTS tape under rotating magnetic fields (RF) have been explored. However, a research gap remains in understanding how these findings translate to the more complex HTS windings of rotating machines. Further exploration is needed to understand the loss behaviour of more complex HTS structures, such as HTS stacks. In this work, Qtol and Qm, in the HTS stacks under RF and a perpendicular AC standing wave magnetic field are numerically investigated. Two different RF models are considered: one is the Uni-RF model, characterized by a uniform field with equal field amplitudes and phases at each position, and the other is a non-uniform field created by a rotating Halbach array, referred to as the Hal-RF model. The dependence of AC loss on parameters such as the number of tapes in the stacks, tape width (2a), and the inclination angle (α) of tapes, which refers to the angle between the normal direction of the stack and the vertical direction, have been explored. The number of tapes in the stacks ranges from 1 to 16, α ranges from 0° to 90°, and the tape width includes 4 mm and 40 mm. Additionally, different rotating field directions are also considered. Interestingly, the analytical values from Brandt and Indenbom equation for Qm of a superconducting strip (BI-strip) are close to Qm results of the stacks under the standing wave at high fields, while they are over twice as high as those in the Hal-RF model at 1 T. This suggests the BI-strip equation is not reliable for predicting Qm under RF at high fields. We also show in the Hal-RF model that different rotation directions of the field lead to varying Qm and Qtol when asymmetric Jc (B, θ) data are applied. Moreover, it has been observed that the inclination angle has no impact on Qm under uniform RF while significantly impacts both Qm and Qtol in the Hal-RF model.

Experimental study on AC loss of 1G and 2G HTS coils with an identical structure, geometry and number of turns

Devices made of High Temperature Superconductor (HTS) will suffer AC loss during AC operations, which has unnegligible influence on energy consumption, overall efficiency, cooling cost, and operational stability of the devices. In this study, comparative measurements on 1G and 2G HTS coil samples with an identical structure, geometry, and number of turns were systematically conducted with a calorimetric method at different current values (I rmss) and frequencies (fs). The AC loss characteristics of the HTS samples were analyzed and compared based on the experimental results. The results show that eddy current and coupling play a more dominant role than magnetic hysteresis in the total AC loss of coils made of HTS tapes. The AC loss of both samples increases with I rms and f, but the AC loss is more sensitive to I rms than to f. Under the same conditions, the 1G coil sample has a slightly larger AC loss than the 2G one.

High temperature superconducting CORC cable with variable winding angles for low AC loss and high current carrying SMES system

Owing to the rising demand for enhanced high-current capacity within superconducting magnetic energy storage (SMES) system used in power grids, there is a growing focus on enhancing the current-carrying capability of SMES setups wound with conductor on round core (CORC) cables. However, it is crucial to note that the dissipation of AC losses in CORC cables during rapid charge and discharge cycles can substantially impact the safe operation of SMES. The CORC cable is crafted by spirally winding numerous ReBCO tapes around copper tubes. Even slight alterations in the winding angles of these tapes can result in shifts at current distribution across the ReBCO tapes, thus leading to differences in AC losses. Hence, the primary objective of this paper is to study the effect of varying winding angles of each ReBCO layer on AC loss. The adoption of variable angles results in the reduction of current flowing through the outermost tapes. And the AC losses in the outermost tapes happen to account for the majority of the total AC losses. Through simulations and experiments, it was observed that the AC loss in the CORC cable with variable angles (4 × 12, 25°–40°) was 25% lower than that in the case of fixed angles (3 × 11, 45°). These findings demonstrate a noteworthy downward trajectory in AC losses when variable angles are applied to the CORC cable. These insights hold significant value for the practical application of CORC cables within SMES systems.

Understanding ac losses in CORC cables of YBCO superconducting tapes by numerical simulations

Alternating current (ac) losses in conductor-on-rounded-core (CORC) cables of YBCO high-temperature superconducting (HTS) tapes are a significant challenge in HTS power applications. This study employs two finite element analysis (FEA) models to investigate the contributions from different ac loss components and provide approaches for reducing ac losses in cables. An FEA model based on the T-A formulation treats the cross section of thin superconducting layers as 1D lines and, therefore, only can predict the ac loss generated by the perpendicular magnetic field. In contrast, the model based on H-formulation can be performed on the actual 2D rectangular cross section HTS tapes to provide the total ac losses generated by magnetic fluxes penetrating from both the edges and surfaces of HTS tapes, although this model requires more computing time and memory. The 1D and 2D simulation models were validated by cross comparing the results from both models and by comparing sub-section and full cross section models. Subsequently, two models relate cable design and operational parameters to the surface and edge losses of a two-layer CORC cable by considering the (1) relative contributions of edge and surface losses to the overall ac losses; (2) effect of the current distribution between inner and outer HTS layers on ac losses; (3) impact of the tape alignment on ac losses in each HTS layer; (4) influence of the thickness of HTS layers on ac losses; (5) effect of size and number of inter-tape gaps on ac losses; and (6) contribution frequency on the ac losses. The research results given in this paper are therefore not only valuable to suggest strategies for reducing ac loss in multi-layer cables but also for developing more accurate and effective methods to calculate ac loss in CORC HTS cables.

Multifilament HTS Cables to Reduce AC Loss: Proof-of-Concept Experiments and Simulation

Reducing AC losses of HTS is essential for AC application since it can lower the constraint on the cryogenic cooling demand. Several studies have reported that the manufacturing of multi-filament HTS cables can reduce AC loss. However, large coupling losses were identified in the existing cables, due to the existence of coupled copper or soldering layers. We report in this paper a novel way to develop multi-filament HTS cables, mainly focusing on suppressing the coupling losses by reducing the contact resistivity within the HTS cables. Heat shrink tubes are used to directly insulate narrow HTS filaments into a cable structure. Sample cables were made with 4 mm and 2 mm wide HTS strips. Both transport losses and total AC losses in a rotational magnetic field were measured to quantify the AC loss reduction for the multi-filament HTS cables. The measurements were used to validate the modelling results, and to predict AC loss reduction for 1 mm wide HTS cable. The results showed loss reduction up to around 90% in the 1mm wide HTS cable compared with 4 mm cable. As a result, the proposed multi-filament HTS cables will have promising applications in reducing AC loss.

Magnetization AC losses of MgB2 wires with thin filaments and resistive sheath

Magnetization AC losses of fine-filamentary MgB2 wires with resistive CuNi sheaths were measured. The effects of varying the number of filaments (114–342, corresponding to effective filament diameters of 14–20 μm), twist pitch (10–30 mm) and outer sheath material on the total AC loss were studied. For a better understanding of individual loss contributions, the effects of varying applied temperature, magnetic field, and frequencies were examined. It is found that hysteresis loss per volume decreases with the reduced filament size and that coupling current losses play a dominant role. The effect of decoupling by twisting was clearly observed for the smallest twist pitches. Considering the possible degradation of transport currents by twisting, AC losses were also normalized by the critical currents of the same wires. While twisting to short pitch decreases losses significantly, it apparently does not reduce the transport current. Consequently, the fine-filamentary MgB2 wires with resistive CuNi sheath examined in this paper are excellent candidates for future low loss applications. Unlike ReBCO tapes, round MgB2 wires enable easy single strand twisting, and the braiding or cabling, of wires into a variety of specific shapes and diameters.

The effect of flux diverters on the AC loss of REBCO coil coupled with iron core

High temperature superconducting (HTS) coil coupled with iron core can be widely used in superconducting power equipment such as superconducting motor, superconducting current limiter, superconducting transformer and so on. The AC loss of HTS coil decreases the efficiency and reliability of superconducting machines, and also brought severe challenges to the cryogenic system. The introduction of iron core will have a negative impact on the AC loss of superconducting coil, and the iron core itself will also produce iron loss, which will affect the overall efficiency of the system. It is considered that the additional flux diverter at the end of the coil can effectively reduce the AC loss of the coil. However, whether this method is effective for the HTS coil coupled with iron core has not been studied. Therefore, this paper focuses on the influence of flux diverter on the AC loss of HTS coil coupled with iron core by H-formulation. The results show that the iron loss of flux diverter plays a leading role in the coil assembly at low transport current, and the introduction of flux diverter plays a positive role in reducing the total AC loss of coil assembly at high transport current.

Numerical Study on AC Loss Characteristics of Conductor on Round Core Cables Under Transport Current and Magnetic Field

Conductor on round core (CORC) cables wound by high-temperature superconducting (HTS) tapes have received much attention due to the advantages in power capacity and mechanical flexibility. This paper first developed a 3D model for a CORC cable through the finite-element method (FEM). Next, the total AC loss caused by transported current only was investigated, revealing the eddy current loss in the tube former contributes to the cable loss. The numerical CORC model was validated by published measurements. Moreover, the AC loss that resulted from a simultaneous presence of transport current and magnetic field was explored. With the induced current, the magnetisation loss generated in superconductors can increase the total loss. It is concluded that the addition of a magnetic field can result in a surge in the total loss of a current-carrying cable.

AC Losses of Quasi-Isotropic Conductor Carrying a DC Current in an AC Magnetic Field

The quasi-isotropic conductor stacked by the second generation (2G) high temperature superconducting (HTS) tapes is a promising choice for current transmission with low AC losses. In this paper, AC losses of quasi-isotropic conductor carrying a DC current in an AC magnetic field is studied by numerical and experimental methods at 77 K. AC losses are calculated by a two-dimensional finite element method (FEM) based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T-A</i> formulation. Meanwhile, the total AC losses dissipated in the quasi-isotropic conductor can be obtained from experimental data of dynamic loss and the magnetization loss measured by electrical means. The amplitude of the external AC magnetic field and the DC transport current are varied. Simulation results are in good agreement with the experimental ones and the magnetic field distribution of the entire system is discussed in detail. The dependence of AC losses on external AC magnetic field and DC transport current is obtained, which is very helpful for fully understanding AC losses characteristic of quasi-isotropic conductors.

Influence of Magnetic Iron Teeth in Motors Employing Superconductors for Field Excitation and AC Stator Windings

Synchronous machines are under consideration for applications on electrically propelled planes. Attractive features of such machines include high efficiency, low mass, and volume. To achieve these features, both rotor excitation field and ac stator winding coils employ superconductors. The dc field winding on the rotor experiences little harmonic fields. However, the stator winding, subjected to a full excitation field at rated frequency, experiences significant ac losses. The incorporation of laminated magnetic iron teeth is being considered for diverting the flux away from the superconducting coils to reduce the ac losses in air-core machines. Machines rated 3 MW at 4500 RPM were studied in this article. Two machines, with and without iron teeth within the stator winding, are compared for assessing the impact on the machine's efficiency, mass, and volume. This comparison shows that the inclusion of iron teeth increases total ac losses within the stator winding. This is so because the iron teeth direct the radial field away from the slot but increase the tangential field. Compared to the machine with no iron teeth (air-core), the machine with iron teeth has 10% higher losses, 4% higher volume, and 15% higher mass. The baseline iron teeth machine also creates high-frequency fields (61st harmonic field of 8.9% in the present case), which might present challenges for some electric power drives. The iron teeth in the stator winding also introduce a ground plane requiring thicker coil insulation that reduces available space for the stator winding. The absence of ground plane within the stator winding usually enables higher voltage designs. A machine having iron teeth and iron yoke (back iron) was observed to be high in losses, size, and mass. Based on these findings, it is recommended to forgo the iron teeth.

Analysis of AC Loss Contributions From Different Layers of HTS Tapes Using the A−V Formulation Model

This article presents a numerical model based on the definition of the scalar and vector potentials to calculate the ac losses generated in a high-temperature superconductor coated conductor tape by an ac transport current and by an ac external magnetic field applied with a generic orientation. The material characteristics of the different layers of a reference tape are included in the model equations, which allow analyzing the differences between a model including only the superconducting layer or all layers of the coated conductor. The model is applied to study the dependence of ac losses on the amplitude of the transport current and magnetic field (applied individually or combined) and their frequency. The numerical results are compared with analytical formulations, with a second numerical model based on the H -formulation, and with experimental results. The conditions at which the contribution of the nonsuperconducting layers to the total ac losses of the tape become relevant are analyzed. In particular, the dependence of losses on the frequency of the ac external magnetic field applied at different orientations, is investigated. The current density distribution computed on the conductor cross-section is used to explain the trend of the calculated losses.

Fully superconducting machine for electric aircraft propulsion: study of AC loss for HTS stator

Fully superconducting machines provide the high power density required for future electric aircraft propulsion. However, superconducting windings generate AC losses in AC electrical machine environments. These AC losses are difficult to eliminate at low temperatures, and they add an extra burden to the aircraft cooling system. Due to the heavy cooling penalty, AC loss in the HTS stator is one of the key topics in HTS machine design. In order to evaluate the AC loss of superconducting stator windings in a rotational machine environment, we designed and built a novel axial-flux high temperature superconducting (HTS) machine platform. The AC loss measurement is based on the calorimetric boiling-off of liquid nitrogen. Both total AC loss and magnetisation loss in the HTS stator are measured under the condition of a rotational magnetic field. This platform represents a key element in studying ways to minimise AC losses in an HTS stator, in order to maximise the efficiency of fully HTS machines.

Conceptual Design of a 5 T 200 mm 1 T/s Ramping NbTi Synchrotron Magnet for Cancer Treatment

Recently, a collaborative research to develop an allsuperconducting synchrotron system for cancer treatment was embarked by a team led by Electronics and Telecommunications Research Institute in Korea. The system requires a 5 T dipole magnet with a uniform field region in cylindrical shape of 130 mm in diameter and 3000 mm in length, and operates at a ramping rate of 1 T/s. As the first step of the project, this paper presents a conceptual design of the magnet that consists of six single-layer cosine windings made of the NbTi Rutherford cable. Key design results include: (1) spatial field uniformity, ΔB/B <; 2 x 10 -4 within a target space of |r| <; 65 mm; (2) total ac loss of the entire coils, 297 J per cycle for a normal operation of 1 T → 5 T → 1 T at the 1 T/s ramping rate; (3) ac-loss-oriented cryogenic load of 23 W; (4) peak temperature of 4.9 K within the magnet during the consecutive normal operation; (5) enthalpy margin of 2.1 mJ/cm 3 with the current sharing temperature of 5.65 K; and (6) adiabatic temperature rise of 87 K upon a quench.

Study on Reducing the Maximum Perpendicular Magnetic Field of HTS Coils Used on Synchronous Generator Armatures

In this paper, a 30-kW permanent magnet superconducting synchronous generator is proposed for the marine application. The perpendicular magnetic field on the high temperature superconducting (HTS) coils will cause a large drop in critical current and create much more ac loss. The magnetic field consists of two parts, i.e., self-field created by the transport current and external field created by the rotor rotation. It can be reduced by decreasing the distance between the HTS coil and back iron, increasing the distance between the HTS coil and iron teeth or adding the slot wedges in the open slots. These are effective methods to improve HTS armatures’ critical current by reducing the perpendicular magnetic field on the HTS coil surface. Changing the turns ratio of HTS coils has little influence on reducing the maximum perpendicular magnetic field. However, it could decrease the number of flux lines passing through the HTS coil and reduce the total ac loss of the HTS coil.

Electric Field and Energy Losses of Rounded Superconducting/Ferromagnetic Heterostructures at Self-Field Conditions

The ac losses induced by an alternating transport current in type-II superconductors is a well-known phenomenon, which still attracts much attention because of its intrinsic relevance for the proper development of practical applications. In the case of single core superconducting cables of cylindrical cross-section, it is possible to find exact analytical solutions at self field conditions, and it has been believed for nearly two decades that the use of an ideal soft ferromagnetic sheath with negligible magnetization losses will not affect the electromagnetic properties of the superconducting wire, and on the contrary due to the shielding magnetic properties of the ferromagnet, the total ac losses of the SC wire have to be reduced or as maximum they must be equal to the one for the bare superconductor at self-field conditions, what contraries the experimental evidences that show a non-negligible increase on the ac losses. In this paper, we explain the physical nature of this mysterious increase in the ac losses for rounded superconducting/ferromagnetic heterostrutures, which for the sake of generality, has been solved within the critical state theory, and a magnetic multipolar expansion that enables the direct coupling of the magnetostatic properties of the superconductor and an ideal soft ferromagnet. A significant increase in the transient electric field during excitation period has been observed, which might have utter implications on the adequate selection of insulation materials for superconducting/ferromagnetic heterostructures.

Numerical modelling of dynamic resistance in high-temperature superconducting coated-conductor wires

The use of superconducting wire within AC power systems is complicated by the dissipative interactions that occur when a superconductor is exposed to an alternating current and/or magnetic field, giving rise to a superconducting AC loss caused by the motion of vortices within the superconducting material. When a superconductor is exposed to an alternating field whilst carrying a constant DC transport current, a DC electrical resistance can be observed, commonly referred to as ‘dynamic resistance.’ Dynamic resistance is relevant to many potential high-temperature superconducting (HTS) applications and has been identified as critical to understanding the operating mechanism of HTS flux pump devices. In this paper, a 2D numerical model based on the finite-element method and implementing the H-formulation is used to calculate the dynamic resistance and total AC loss in a coated-conductor HTS wire carrying an arbitrary DC transport current and exposed to background AC magnetic fields up to 100 mT. The measured angular dependence of the superconducting properties of the wire are used as input data, and the model is validated using experimental data for magnetic fields perpendicular to the plane of the wire, as well as at angles of 30° and 60° to this axis. The model is used to obtain insights into the characteristics of such dynamic resistance, including its relationship with the applied current and field, the wire’s superconducting properties, the threshold field above which dynamic resistance is generated and the flux-flow resistance that arises when the total driven transport current exceeds the field-dependent critical current, Ic(B), of the wire. It is shown that the dynamic resistance can be mostly determined by the perpendicular field component with subtle differences determined by the angular dependence of the superconducting properties of the wire. The dynamic resistance in parallel fields is essentially negligible until Jc is exceeded and flux-flow resistance occurs.

AC Loss in HTS Fusion Cables: Measurements, Modeling, and Scaling Laws

Currently, the use of high-temperature superconducting (HTS) cables in the high-field sections of central solenoid (CS) of DEMO is one of the most appealing applications of the HTS cables in fusion magnets. Due to the pulsed operation of such coils minimization of the ac loss is necessary for the CS conductors. For the stacked-tape HTS cable layout proposed at the Swiss Plasma Center (SPC), the main contributions in the total ac loss-hysteresis loss in stacks, intra- and inter-strand coupling losses-have been studied. The electrical network model is used for the coupling losses, based on which the scaling laws for the ac energy loss are proposed. On the basis of the developed numerical tools, the assessment of the ac loss for the next HTS cable prototypes at SPC is also reported. More than 50% reduction of the total ac loss is expected compared with the first TF cable prototypes tested in the European DIPOle (EDIPO).

Design versions of HTS three-phase cables with the minimized value of AC losses

Design versions of HTS three-phase cables consisting of 2G HTS tapes have been investigated by the numerical simulation method with the aim of AC losses minimization. Two design versions of cables with the coaxial and extended rectangular cross-section shape are considered – the non-sectioned and sectioned one. In the latter each cable phase consists of sections connected in parallel. The optimal dimensions of sections and order of their alteration are chosen by appropriate calculations. The model used takes into account the current distribution between the sections and its non-uniformity within each single HTS tape as well. The following characteristics are varied: design version, dimension, positioning of extra copper layer in a cable, design of HTS tapes themselves and their mutual position. The dependence of AC losses on the latter two characteristics is considered in details, and the examples of cable designs optimized by the total set of characteristics for the medium class of voltages (10 – 60 kV) are given. At the critical current JC=5.1 кA per phase and current amplitudes lower than 0.85JC, the level of total AC losses does not exceed the natural cryostat heat losses.

AC losses in horizontally parallel HTS tapes for possible wireless power transfer applications

This paper presents the concept of using horizontally parallel HTS tapes with AC loss study, and the investigation on possible wireless power transfer (WPT) applications. An example of three parallel HTS tapes was proposed, whose AC loss study was carried out both from experiment using electrical method; and simulation using 2D H-formulation on the FEM platform of COMSOL Multiphysics. The electromagnetic induction around the three parallel tapes was monitored using COMSOL simulation. The electromagnetic induction and AC losses generated by a conventional three turn coil was simulated as well, and then compared to the case of three parallel tapes with the same AC transport current. The analysis demonstrates that HTS parallel tapes could be potentially used into wireless power transfer systems, which could have lower total AC losses than conventional HTS coils.

Investigation of AC losses in horizontally parallel HTS tapes

This paper presents an AC loss study of horizontally parallel HTS tapes. We proposed to use three parallel HTS tapes as an example. The AC losses of the middle and end tape of three parallel tapes have been measured using the electrical method and compared to those of an individual tape. The effect of the interaction between tapes on AC losses has been analysed, and compared with finite-element method (FEM) simulations using the 2D H-formulation implemented in COMSOL Multiphysics. By using FEM simulations, the cases of increasing number of parallel tapes have been considered, and the normalised ratio between the total average AC losses per tape and the AC losses of an individual single tape has been calculated for different gap distances. We proposed a new parameter, Ns, a turning point for number of tapes, to divide Stage 1 and Stage 2 for the AC loss study of horizontally parallel tapes. For Stage 1, N < Ns, the total average losses per tape increased with the increasing number of tapes. For Stage 2, N > Ns, the total average losses per tape decrease with the increasing number of tapes. The analysis demonstrates that horizontally parallel HTS tapes could be potentially used in superconducting devices like HTS transformers, which could retain or even reduce the total average AC losses per tape with large number of parallel tapes.