High-current high temperature superconducting (HTS) cables have been developed for use in HTS power devices. This paper presented the structures of HTS cables, including Conductor on Round Core (CORC) cable, Twisted Stacked-tape Conductor (TSTC) cable and Double coaxial cable. Subsequently, three dimensional (3D) finite element method numerical models were built to analyze the electromagnetic characteristics of the cables, and the critical current of the cables is about 380 Ampere @77 K, self-field. Using the T-A formulation, the numerical model assumed a sheet approximation for conductors, which shortened computational time. The T-A formulation were verified by experiments on a superconducting tape. Then HTS cables with different configurations were made, as functions of different transport current and background magnetic field, and different pitches of Double Coaxial Cable inner conducting layer. According to the results, the AC losses of Double coaxial cable and CORC cable decreased 40% than the TSTC cable with different transport current, and the Double coaxial cable AC loss decreased 20% than the CORC cable when background magnetic field was in the range of 20-60 mT. Conclusions obtained from this study will be helpful for understanding the AC loss properties of HTS cables and useful in design of HTS power devices (such as HTS transformer), using HTS cables.