Proximity losses in short coils of circular cylindrical windings

Proximity losses in short coils composed by cylindrical wires of circular cross sections are investigated. The main factor involved in proximity losses, the effect of window fill, is studied. Analytical solutions to the two-conductor problem show that the proximity effect can increase losses by up to three times the isolated skin effect loss. A 2D finite element analysis is employed to study systems consisting of a large number of conductors. It is shown that the introduction of conductor-to-conductor spacing can reduce proximity losses. The ranges of validity of the approximate one-dimensional equivalent sheet approach are determined