# Transport AC loss in high temperature superconducting coils

Thesis

In this dissertation, the problem of calculating and measuring AC losses in superconducting coils is addressed, with a particular focus on the transport AC loss of coils for electric machines. In order to model the superconducting coil's electromagnetic properties and calculate the AC loss, an existing two dimensional (2D) finite element model that implements a set of equations known as the H formulation, which directly solves the magnetic field components in 2D, is extended to model a superconducting coil, where the cross-section of the coil is modelled as a 2D stack of superconducting coated conductors. The model is also modified to allow the nclusion of a magnetic substrate, which is present in some commercially available HTS wire. The analysis raises a number of interesting points regarding the use of superconductors with magnetic substrates. In particular, the presence of a magnetic substrate affects the penetration of the magnetic flux front within the coil and increases the magnetic flux density within the penetrated region, both of which can increase the AC loss significantly. In order to investigate these findings further, a comprehensive analysis on stacks of tapes with weak and strong magnetic substrates is carried out, using a symmetric model that requires only one quarter of the cross-section to be modelled. In order to validate the modelling results, an extensive experimental setup is designed and built to measure the transport AC loss of a superconducting coil using an electrical method based on inductive compensation by means of a variable mutual inductance. Measurements are carried out on the superconducting racetrack coil and it is found that the experimental results agree with the modelling results for low current, but some phase drift occurs for higher current, which affects the accuracy of the measurement. In order to overcome this problem, a number of improvements are made to the initial setup to improve the lock-in amplifier's phase setting and other aspects of the measurement technique. New measurements are carried out on a single, circular pancake coil and the discrepancies between the experimental and modelling results are described in terms of the assumptions made in the model and aspects of the coil that cannot be modelled. Using the original measured properties of the superconducting tape, there is an order of magnitude difference between the experiment and model. The properties of the superconductor can degrade during the winding and cooling processes, and a critical current measurement of the coil showed that the tape critical current reduced from nearly 300 A, down to around 100 A. Applying this finding to the model, the experimental and modelling results show good agreement, and the difference in the slope of the AC loss curve can be described in terms of the B-dependent critical current dependency Jc(B) used in the model. Finally, methods used to mitigate AC loss in superconducting wires and coils are summarised, and the use of weak and strong magnetic materials as a flux diverter is investigated as a technique to reduce AC loss in superconducting coils. This technique can achieve a significant reduction in AC loss and does not require modification to the conductor itself, which can be detrimental to the superconductor's properties.