Incomplete-penetration hysteresis losses in transmission line cables

At 77 K, the resistivity of ceramic, high-temperature superconductors grows gradually rather than sharply with increasing current. The critical-state theory of hysteresis losses therefore needs to be modified. This has been d one for slab conductors whose resistivity can be taken proportional to a po wer of the current density. Simple formulas have been derived in the limiti ng cases of incomplete penetration and full penetration when the losses are driven either by a sinusoidal transport current or a sinusoidal external m agnetic field. These formulas can be applied to multilayer transmission lin e cables once the current distribution within and among the layers has been determined. This distribution has been calculated tin the incomplete penet ration limit) by solving Maxwell's field equations. A formula is presented for the dependence of the hysteresis loss on winding angle. The formula is used to determine the optimum winding angle. (C) 1998 Elsevier Science B.V. All rights reserved.