The basic cable has a plurality of flat, tape-shaped ribbon superconductor wires assembled to form a stack having a rectangular cross section. The stack has a twist about the longitudinal axis of the stack. The wires are ReBCO (YBCO, GdBCO), BSCCO, or MgB2 tape conductors. The basic cables can be twisted together to form a larger cable that transmits higher electric current. The twisting is important in order to reduce undesired magnetic flux coupling between superconducting wires as well as to increase mechanical bendability . The superconducting cable is disposed within and spaced apart from an electrical insulator, and the space between the cable and the insulator provides a channel for coolant. A cryostat surrounds the insulator to create a return coolant channel for thermal insulation.