Semi-numerical method for loss-calculation in foil-windings exposed to an air-gap field

Abstract

The calculation of Eddy current losses in foil windings exposed to a 2-D fringing field is a complex task, due to the current displacement along the height of the foil. For model based optimization of magnetic components, the loss calculation with a 2-D FEM simulation is not an option, due to the high computational ef1"ort. The existing alternative calculation methods, which allow for loss calculation with low computational effort, rely on approximations applicable only for a certain geometrical arrangement of the windings and the air gap. Therefore, a new semi-numerical method is developed to overcome these limitations.The method is based on the mirroring method and is applicable to arbitrary air gaps and winding arrangements. The accuracy of the new method is verified by measurements and the deviation of the model to the measured losses is below 15%.

Frequency-Dependent Inductance and Winding Loss Model for Gapped Foil Inductors

“…Hence, the magnetic field can extend inside the foil in y-direction relatively unhindered, resulting in a significant increase of eddy currents and thus, the effective resistance. This fact supports the hypothesis, that foil conductors perform poorly in the vicinity of air gaps [7].…”

“…Hence, in many cases the field is assumed to be 1D, even when an air gap is present [4]- [6], and the field significantly deviates from the 1D simplification. However, when foil conductors are considered, calculating the 2D magnetic field in the core window of gapped inductors is mandatory, because foil conductors are particularly sensitive to the air gap fringing field [7].…”

“…For considering a 2D magnetic field distribution, different per-unit-length winding loss models including an air gap fringing field have been presented. For example, [7], [8] propose semi-numerical models, where numerical or iterative field calculations are performed before the actual loss calculation. In those models, a numerical field calculation is necessary to consider the impact of the conductor current on the 2D magnetic field.…”

“…The reason is, that many 2D magnetic field models use the mirroring method to calculate the magnetic field in the core window (e.g. [7]), which would require numerical integration to obtain the magnetic energy.…”

Analytical Winding Power Loss Calculation in Gapped Magnetic Components

“…Although the approach is very simple and the reported results are in accordance with the experimental data, they can be applied only in components whose windings are arranged in a specific "layered" structure since they keep some of the limitations of 1D models and are not valid for components with incomplete layers. On the other hand, many methods [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] use the "intermediate step" of calculating the external magnetic field in order to evaluate the proximity loss, but the focus and application of each one, as well as the way that fields and the total winding loss are calculated are rather different. In this context, in order to facilitate the transition to the proposed method and having in mind that this paper is focused on the calculation of proximity loss (using a two-step calculation process: calculating fields and evaluating proximity loss using the previously calculated fields), this review is structured around two topics: the methods of calculating the overall magnetic field and the methods for the calculation of the loss in a conductor given an external magnetic field.…”