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 Results show that the existing definition of the dynamic region is no longer valid at kHz level, which shrinks rapidly with increasing frequency and magnetization loss plays a progressively important role due to skin effect.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.

Superconductor technology has recently attracted increasing attention in power-generation- and electrical-propulsion-related domains, as it provides a solution to the limited power density seen by the core component, electrical machines. Superconducting machines, characterized by both high power density and high efficiency, can effectively reduce the size and mass compared to conventional machine designs. This opens the way to large-scale purely electrical applications, e.g., all-electrical aircrafts. The alternating current (AC) loss of superconductors caused by time-varying transport currents or magnetic fields (or both) has impaired the efficiency and reliability of superconducting machines, bringing severe challenges to the cryogenic systems, too. Although much research has been conducted in terms of the qualitative and quantitative analysis of AC loss and its reduction methods, AC loss remains a crucial problem for the design of highly efficient superconducting machines, especially for those operating at high speeds for future aviation. Given that a critical review on the research advancement regarding the AC loss of superconductors has not been reported during the last dozen years, especially combined with electrical machines, this paper aims to clarify its research status and provide a useful reference for researchers working on superconducting machines. The adopted superconducting materials, analytical formulae, modelling methods, measurement approaches, as well as reduction techniques for AC loss of low-temperature superconductors (LTSs) and high-temperature superconductors (HTSs) in both low- and high-frequency fields have been systematically analyzed and summarized. Based on the authors’ previous research on the AC loss characteristics of HTS coated conductors (CCs), stacks, and coils at high frequencies, the challenges for the existing AC loss quantification methods have been elucidated, and multiple suggestions with respect to the AC loss reduction in superconducting machines have been put forward. This article systematically reviews the qualitative and quantitative analysis methods of AC loss as well as its reduction techniques in superconductors applied to electrical machines for the first time. It is believed to help deepen the understanding of AC loss and deliver a helpful guideline for the future development of superconducting machines and applied superconductivity.

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.

Dynamic resistance is a time-averaged direct current (DC) resistance in superconducting materials, which typically occurs when a superconductor is carrying a transport DC while simultaneously subject to a time-varying magnetic field. Dynamic resistance has recently attracted increasing attention as it not only causes detrimental dynamic loss in superconducting devices such as the nuclear magnetic resonance magnets and superconducting machines, but on the other hand, the generated dynamic voltage can be exploited in many applications, e.g. high temperature superconducting (HTS) flux pumps. This article reviews the physical mechanism as well as analytical, numerical modelling, and experimental approaches for quantifying dynamic resistance during the last few decades. Analytical formulae can be conveniently used to estimate the dynamic resistance/loss of a simple superconducting topology, e.g. a single rare-earth-barium-copper-oxide tape. However, in a complex superconducting device, such as a superconducting machine, the prediction of dynamic resistance/loss has to rely on versatile numerical modelling methods before carrying out experiments, especially at high frequencies up to the kHz level. The advantages, accuracies, drawbacks, and challenges of different quantification approaches for dynamic resistance/loss in various scenarios are all inclusively discussed. The application of dynamic resistance in HTS flux pumps is also presented. It is believed that this review can help enhance the understanding of dynamic resistance/loss in superconducting applications and provide a useful reference for future superconducting energy conversion systems.

Dynamic loss is significant for evaluating the performance of type-II high-temperature superconductor (HTS) coated conductors (CC), especially when used in electric machines. Although analytical expressions of dynamic loss have been proposed and verified for HTS CCs exposed to low external magnetic fields with a low current load rate, the non-linearity of dynamic loss at high current load ratios and simultaneous high magnetic fields is still unclear and cannot be predicted by the existing analytical equations. This paper proposes a completely new formulation to characterize the non-linearity of dynamic loss taking into account the J _c(B) dependence of CCs, which can be used for full ranges of both magnetic fields and current load ratios. The proposed analytical formulas have been verified by a T -formulation based numerical model and experiments. This paper comprehensively demonstrates the variation of dynamic loss and provides a meaningful reference of loss controlling for HTS CCs, which is vital for HTS machine windings to avoid quench.