A three-phase high-voltage superconducting cable having three hollow superconductors in a trefoil configuration and three heat shields disposed radially outward from the superconductors, all enclosed in an evacuated pipe. The heat shields are also in a trefoil configuration; they are electrically isolated from one another, from the superconductors, and from ground in order to suppress the flow of induced currents. The pipe provides mechanical protection of the foregoing elements, serves as vacuum vessel and carries the a-c shielding current induced by the cable load current.