Some power engineering systems, such as efficient energy storage for power quality improvement, can be potentially made more efficient if implemented with large coils made of high temperature superconductors (HTS). However, the losses of HTS coils carrying AC current limit their usage in practical applications. It has been shown previously that a thin pancake coil with relatively large diameter can be modelled as straight tapes arranged in a face-to-face stack. This paper reviews those results. In addition, measurements on a more realistic larger HTS coil were carried out. It is shown that the model assumptions provide less accurate results for a larger coil.