Electromagnetic characteristics of high temperature superconductor coated conductors applied to electric machines
Superconductor technology has attracted increasing attention during the last few years because of their advancements made in the material manufacturing technology and the reduction of cost. As a result, superconducting materials have been widely applied to power industries, of which one of the most promising and popular applications is the electric machine, which is the core component of power generation and consumption on the earth. The second-generation (2G) high temperature superconducting (HTS) coated conductor (CC) has become increasingly appealing among all the superconductors on account of its commercial availability and advantageous current carrying capacity. Therefore, HTS electric machines are believed to usher in a period of development opportunities. However, there still exist many challenges related to the efficiency, cost-effectiveness, reliability, and safety of HTS machines, and the alternating current (AC) loss of HTS CCs remains one of the most significant issues. Over the years, the effort of studying the AC loss of HTS CCs has yielded many outstanding research outcomes; however, most of them have been focused on the loss estimation at power frequencies under purely sinusoidal currents and magnetic fields. In fact, the electromagnetic environment in electric machines is abundant in high-frequency ripple fields and harmonics, especially for high-speed rotating machines. Therefore, the AC loss characteristics of HTS CCs at high frequencies remain unclear, to some extent. Aiming to analyse systematically the AC loss properties of HTS CCs applied to electrical machines within a wide frequency band, from the power frequency to kHz level, this thesis adopts analytical equations, numerical modelling methods, as well as experimental measurements. In doing so, this project hopes to contribute to the loss quantification and controlling of HTS CCs in electrical machines, providing a useful reference for the design of large-scale superconducting devices. This thesis starts by providing a comprehensive literature review of the state of the art of AC loss related studies. The analytical formulae, modelling methods, measurement approaches, as well as reduction techniques for the AC loss of HTS materials in both low- and high-frequency fields are systematically summed up. The review work clarifies the research status of the AC loss of superconducting materials applied to electric machines, elucidating that the electromagnetic loss characteristics of HTS CCs deserve further investigation, especially at high frequencies in high-speed rotating machines. Numerical models are an indispensable tool for studying the anisotropic electromagnetic properties of high temperature superconductors (HTSCs), thus numerical modelling is chosen as a primary method in this thesis to study the AC loss of HTS CCs employed in electric machines. The methodologies adopted to build the simulation models are introduced, which are based on Maxwell’s equations and the finite element method (FEM). The numerical models here are developed mainly through two formulations, namely T-formulation (T represents current vector potential) and H-formulation (H denotes magnetic field), which can be achieved by FORTRAN 90 or incorporated into COMSOL Multiphysics. Dynamic loss is a crucial component of the AC loss of HTS field windings in superconducting machines, which occurs when the HTS CC carrying a direct current (DC) is exposed to an AC magnetic field. Therefore, the dynamic loss of HTS CCs is explored in detail. The dependence of dynamic loss on the material properties (critical current density and n-value) is investigated. Then, a novel formulation is derived to describe the full-range variation of dynamic loss. At last, three new parameters are defined to characterise the non-linearity of dynamic resistance. The proposed analytical formulae and parameters are validated by the T-formulation based numerical model and experimental measurements. In superconducting machines, the HTS CCs are usually utilized in the form of stacks and coils. Therefore, besides a single HTS CC, the transport current loss, magnetization loss, dynamic loss, and the total AC loss of HTS stacks, coils (circular and racetrack coils), and trapped field stacks (TFSs) over a wide frequency band, from the power frequency to kHz level, are studied respectively. The H-formulation based 2D and 3D numerical models are mainly adopted here, which are validated by published experimental data. It is found that the widely used thin film approximation in modelling which only considers the superconducting layer of HTS CCs is inapplicable at high frequencies (higher than 100 Hz for magnetization loss) due to the skin effect, and the non-superconducting parts (the copper stabilizer, silver overlayer, and substrate) have to be taken into account. AC loss varies non-linearly with the frequency of the AC transport current or magnetic field because of the electromagnetic interactions between different layers. The shielding effect between different turns of an HTS coil is also explored, which can enhance the dynamic loss in the middle turns of the coil while the magnetization loss occupies the majority in the outer turns at high frequencies. The electromagnetic properties of a curved HTS TFS under high-frequency cross fields are investigated, too, which possesses geometrical applicability for cylindrical rotating shafts. It is demonstrated that the widely adopted 2D-axisymmetric models are inapplicable to study the anisotropic electromagnetic distributions of TFSs because of the emergence of the electromagnetic criss-cross. 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 TFS. In order to combine AC loss analysis and machine applications, a special magnet made of HTS coils in the form of a Halbach array is exploited in the designs of an air-cored wind turbine generator and an electrodynamic wheel (EDW) used for maglev, through numerical modelling in COMSOL Multiphysics. The HTS Halbach Array magnet (HAM) can focus the magnetic flux inside the coil loop, greatly increasing the magnetic flux density in the airgap and the power density of the machine. The HTS HAM represents a generic topology/approach for the design of fully air-cored superconducting machines. The proposed HTS HAM EDW can generate higher thrust and lift forces, and greatly reduce the weight of the magnets compared with the conventional design with permanent magnets (PMs), opening the way to future on-road maglev vehicles. It is also illustrated that, for modelling the electro-mechanical performance of large-scale HTS devices, e.g., synchronous electric machines, the HTS field coils can be reasonably equivalized as conventional ones carrying the same DC so that the computation complexity can be largely decreased. This thesis starts with the application of superconductors to electric machines, analyses thoroughly the loss characteristics of HTS CCs, stacks, coils, and TFSs over a wide frequency band from the power frequency to kHz level. It is believed that this research work can help researchers in the communities of applied superconductivity and electrical machines better understand the electromagnetic properties of different HTS topologies, provide a useful reference for the quantification and controlling of AC loss, and thus give a significant guideline for the design of high power density superconducting machines.