Balanced Three-Phase Distributions of Tri-Axial Cable for Transmission Line

High Temperature Superconducting (HTS) cables have been intensively developed because of low loss and compactness, compared with conventional copper cables. A tri-axial cable composed of three concentric phases has been studied, because it has advantages such as reduced amount of HTS tapes and low heat-in-leak, compared with the three single-phase cables. However, there is an inherent imbalance in the three-phase distribution in the tri-axial cable due to differences in radii of the three-phase layers. We proposed a theory to obtain the balanced three-phase distribution for the tri-axial cable by treating two longitudinal cable sections together and adjusting all twist pitches. We derived a generalized formula as functions of winding pitches satisfying the balanced distribution. We designed and fabricated a short HTS tri-axial cable composed of 1 layer/phase to verify the proposed theory. The test results demonstrated that the theory is right for an equivalent impedance circuit model. The theory should be applied to the unbalanced three phase distributions caused by fabrication errors and inherent imbalance of capacitances in the tri-axial cable. We calculate the unbalanced three phase currents and voltages in steady state, and resolve them into symmetrical components to evaluate an imbalance ratio, which is defined as zero-sequence or negative-sequence to positive-sequence component. It is found that the fabrication errors of twist pitch and radius cause the imbalance ratios less than 1%, and the unbalanced capacitances of the cable of 10 km in length cause imbalance ratios of about 1%.