Analysis of Balanced Three-Phase Current Distributions in a Tri-AxialCable

High Temperature Superconducting (HTS) cables have been studied because of low loss and compactness, compared with conventional copper cables. Three-phase cables are usually composed of three single-phase coaxial cables. Recently, a tri-axial cable, composed of three concentric phases, has been intensively developed, because it has advantages such as reduced amount of HTS tapes, small leakage fields and small heat loss in leak, compared with the three single-phase cables. However, there is an inherent imbalance in the three-phase currents in the tri-axial cable due to the differences in radii of the three-phase current layers. The imbalance of the currents causes additional loss and large leakage field in the cable, and deteriorates the electric power quality. Therefore, we introduce more variables to obtain the solutions of the balanced three-phase currents and homogeneous current distribution in each phase of the tri-axial cable. We propose a tri-axial cable composed of two longitudinal sections with different twist pitches, and hence the number of variables increases. We derive general equations satisfying both the balanced three-phase currents and homogeneous current distribution, as functions of winding pitches. Finally we apply the general equations to the simplest cable and find out reasonable twist pitches