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The purpose of this paper is to present a methodology for calculating eddy current losses in the core of a single-phase power voltage transformer, which, unlike a standard power transformer, has an open-type core (I-type core). In those apparatus, reduction of core losses is achieved by using a multipart open-type core that is created by merging a larger number of leaner cores.

3D FEM approach for calculation of eddy current losses in open-type cores based on a weak AλA formulation is presented. Method in which redundant degrees of freedom are eliminated is shown. This enables faster convergence of the simulation. The results are benchmarked using simulations with standard AVA formulation.

Results using weak AλA formulation with elimination of redundant degrees of freedom are in agreement with both simulation using only weak AλA formulation and with simulation based on AVA formulation.

The presented methodology is valid in linear cases, whereas the nonlinear case will be part of future work.

Presented procedure can be used for the optimization when designing the open-type core of apparatus like power voltage transformers.

The presented method is specifically adapted for calculating eddy currents in the open-type core. The method is based on a weak formulation for the magnetic vector potential A and the current vector potential λ, incorporating numerical homogenization and a straightforward elimination of redundant degrees of freedom, resulting in faster convergence of the simulation.

The purpose of this paper is to present a method for calculating frequency-dependent resistance when multiple current-carrying conductors are present.

Analytical and numerical formulations are presented. Both skin- and proximity-effects are considered in the numerical approach, whereas only skin-effect can be taken into account in analytical equations. The calculation is done using a self-developed integral equation-based field solver. The results are benchmarked using professional software based on the finite element method (FEM).

Results from the numerical approach are in agreement with FEM-based software throughout the whole frequency range. Analytical formulations yield unsatisfactory results in higher frequency range. When multiple conductors are mutually relatively close, the proximity-effect has an impact on effective resistance and has to be taken into account.

The methodology is presented using axially symmetrical conductors. However, the same procedure can be developed for straight conductors as well.

Presented fast and stable procedure can be used in most electromagnetic devices when frequency-dependent resistance needs to be precisely determined.

The value of the presented numerical methodology lies in its ability to take both skin- and proximity-effects into account. As conductors are densely packed in most electromagnetic devices, both effects influence the effective resistance. The method can be easily implemented using a self-developed solver and yields satisfactory results.