Contents I. Introduction
The Ecodesign Regulations, which have been implemented in the European Union since 2014, have set maximum values for the losses of new transformers placed on the market. In order to meet these requirements, it has become very important for manufacturers to perform accurate calculations of losses within the transformer. Since transformers are supplied with AC voltage and current, the skin and proximity effects occur in the winding conductors leading to uneven distribution of current density across the conductor surface and increased losses. Classical analytical solutions [1], [2] for transformer winding losses due to the skin and proximity effect are based on a one-dimensional (lD) field solution in which the radial component of the field is neglected. The radial component occurs mainly at the top and bottom of the winding within the core window, and its inclusion requires a two-dimensional (2D) approach. In [3] 2D analytical formulas are developed for both skin and proximity losses within a circular conductor subjected to an arbitrary external magnetic field distribution. A hybrid 2D modeling approach for current diffusion in rectangular conductors is presented in [4] which divides rectangular conductors into current filaments in the vicinity of a nonlinear ferromagnetic material and is applied to windings of electrical machines. The 2D finite element method (FEM) based numerical approach in [5] models the transformer foil winding by introducing foil shape functions to avoid a large interconnected set of solid conductor models and thus reduce the model complexity and computation time.
