Considerations of voltage drop and losses in the design of helically-wound superconducting AC power transmission cables

Flexibility in a cable made using brittle superconductors is obtained by winding the superconductor and electrical insulation in the form of concentric helices. The axial stress due to contraction during cooldown of a helix which is rigidly attached at each end is reduced compared to a seamless tube. The radial contraction of the conductor is adjusted by selection of the pitch to match the greater contraction of the dielectric material. A choice of pitch for a simple helix which satisfies the contraction condition will, in general, generate an axial field in its interior which causes heating in any normal metal there, induces currents in metal surrounding the cable (e.g., armor) and causes an inductive voltage drop in the shield helix. A general expression for the self and mutual inductances of concentric helices is given and it is shown that the only configuration which minimizes heating and voltage drop consists of a core and shield each wound from a double helix, one inside the other and having almost equal pitches but opposite sense of winding.