Liquid nitrogen (LN2) is commonly used as the coolant of a high temperature superconductor (HTS) power cable. The LN2 is continuously cooled by a subcooler to maintain an appropriate operating temperature of the cable. This paper proposes two Joule-Thomson (JT) refrigeration cycles for subcooling the LN2 coolant by using nitrogen itself as the working fluid. Additionally, an innovative HTS cooling cycle, of which the cable coolant and the refrigerant are unified and supplied from the same source, is suggested and analyzed in detail. Among these cycles, the highest COP is obtained in the JT cycle with a vacuum pump (Cycle A) which is 0.115 at 78 K, and the Carnot efficiency is 32.8%. The integrated HTS cooling cycle (Cycle C) can reach the maximum COP of 0.087, and the Carnot efficiency of 24.8%. Although Cycle C has a relatively low cycle efficiency when compared to that of the separated refrigeration cycle, it can be a good alternative in engineering applications, because the assembled hardware has few machinery components in a more compact configuration than the other cycles.