Circulating-current loss in transformer windings

Circulating-current loss in stranded windings of transformers has always attracted the attention of transformer designers. Analytical formulae based on the axial leakage field have long been used by designers for the calculation of circulating-current loss. The authors discuss these analytical formulae and compares them with 2-D finite element method (FEM) analysis, highlighting the errors involved in calculations for different types of windings. The analytical formulae contain little information on multiple transposition schemes. The paper clearly demonstrates that as the number of parallel conductors in the radial direction increases, analytical formulations should not be used, and in such cases, 2-D FEM is a better option for calculating circulating-current loss in different transposition schemes. The paper also analyses the circulating-current loss in the case of bunched conductors which are increasingly being used in power transformers. The work has helped to evolve comprehensive guidelines for transformer designers to estimate and control circulating current loss in windings