I~q a previous paper 1 the author derived certain relationships connecting the size of a transformer and the acceptable core and leakage flux densities. Various simplifying assumptions were made, but all of these made the calculated size smaller than that of any transformer that could actually be constructed. It was shown that the smallest superconducting transformer, in which leakage fields were less than the lower critical field H~ 1 of the best superconductor, was but slightly smaller than that of an equivalent conventional transformer. Since the prospect of reducing the bulk of a transformer was a major reason for the interest in superconducting transformers, the above conclusion suggests that superconducting power transformers would be of little practical interest.
Recently there has been discussion of the technological uses of superconductivity, 2 in which the future of the superconducting transformer is also viewed pessimistically when losses in superconductors in alternating fields are considered. These losses appear to exist down to the lowest fields. All such losses were deliberately ignored in the previous paper.
In the first section we derive a formula for the winding volume of a transformer, which can be used to calculate the 'copper loss' in both conventional and superconducting transformers. In the second section we calculate the losses in superconducting transformers, and in the third section we show that only for very large transformers does superconductivity become competitive. The results are discussed in the last section.