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There are two main obstacles in front of the development of high temperature superconducting (HTS) technology for electric power network applications; tape price and cooling cost. In order to reduce cooling cost, it is vital to evaluate AC transport current loss of the tapes precisely and then reduce it by some design innovative approaches. In addition, AC transport current loss in HTS material is a critical design variable for large-scale power network applications such as HTS transformers, superconducting fault current limiters, and power cables, since they are continuously carrying the network/load current during their operating life. In existing power networks, harmonic production sources are commonly used and thus, currents are distorted. Therefore, the effect of nonsinusoidal current on the critical apparatus in the network such as transformer must be studied. In this paper, AC transport current loss of a single-turn 2G YBCO HTS coil was modeled and numerically calculated under nonsinusoidal transport current using finite element method. Furthermore, influence of dependency of critical current density to magnetic field on the AC transport current loss of HTS coil when carries distorted currents was considered. It was observed that nonsinusoidal current causes excessive losses in HTS coil. On the other hand, a case study on an HTS transformer supplying non-linear load was considered to study the loss increment as well as heat load change. It was observed that current harmonics increases the AC loss, and heat load of transformer and decreases the efficiency, consequently.