When an abnormal condition occurs due to a fault current at a consumer location where electricity is supplied through a high-capacity and high-$T_c$ superconducting(HTS) cable, the HTS cable would be damaged if there is no appropriate measure to protect it. Therefore, appropriate measures are needed to protect HTS cables. The fault-current-limiting HTS cable that was suggested in this study performs an ideal transport current function in normal operations and plays a role in limiting a fault current in abnormal operation (i.e., when a fault current is applied). It has a structure that facilitated its self-current-limiting ability through device change and reconfiguration in the existing HTS cable without extra switching equipment. To complete this structure, it is essential to investigate about the selection of the superconducting wire. Therefore, in this paper, HTS wire using two types of different stabilization layer is compared and examined the stability and current limiting properties under the existence of a fault current.