Foil coil windings

Overview

A foil coil is a winding obtained from a thin, rectangular, metallic sheet folded in a spiral-like shape, as shown in Figure 1. The sheet is covered by an insulating coating (varnish). This kind of coil design is common in electromagnetic devices such as power transformers and reactors.

Figure 1. A thin metallic sheet (a) folded in the shape of a foil coil (b).

The current density distribution in a foil-wound coil fed by a time-varying source depends on skin and proximity effects. Since the foil is usually very thin and made from a material with a high electrical conductivity, the skin effect along its thickness is negligible (i.e., the current density in each turn results practically uniform along a radial direction). On the other hand, the current density in each foil turn may greatly vary along the axial direction of the coil as a function of both position and frequency.

This anisotropic behavior is specific to foil coils and influences the Joule losses developed in the bulk of the coil material. Thus, Flux now provides a new subtype of the coil conductor region with losses and detailed geometric description that implements a homogenization technique to represent this type of coil efficiently in its 2D Steady State AC application. This technique is exclusive to foil coils and differs from the approach used in the other subtypes of coil conductor regions with losses and detailed geometric description representing stranded coils.

Using this new coil conductor region subtype spares the user from representing each turn of the foil coil with an individual solid conductor region (linked to its corresponding FE coupling component in a complicated electric circuit). While this latter approach is also legitimate and rigorous, it is usually very time consuming to set up in Flux due to the elaborate geometry and the refined mesh required. Moreover, the solving time with the new foil-wound coil conductor region subtype is significantly reduced when compared to the alternate solid conductor approach.

Example of application

The foil coil configuration shown in Figure 2 has been analyzed in the article Calculation of Current Distribution and Optimum Dimensions of Foil-Wound Air-Cored Reactors by M.M. El-Missiry (Proceedings of the Institution of Electrical Engineers, vol. 124, no. 11,November 1977, DOI: 10.1049/piee.1977.0218 ). In that work, the author presents a circuit-based, semi-analytical method to compute the current density distribution and several other electromagnetic quantities of a foil coil.

Figure 2. Cross section of one of the cylindrical Aluminum foil coils analyzed by M.M. El-Missiry in his article.

The coil in Figure 2 may be easily modeled in Flux 2D with the foil coil template available for coil conductor regions with losses and detailed geometrical description. Figure 3 shows the results obtained with an axisymmetric Steady State AC Magnetic application at 50 Hz and with an additional horizontal symmetry (i.e., only one quarter of the foil coil is represented). The development of a non-uniform current distribution pattern characteristic to foil coils may be verified in the color plot available in that figure.

Figure 3. Color plot of the current density (phasor module, peak value) and magnetic flux density field lines of the foil coil displayed in Figure 2. The FE coupling component assigned to the coil conductor region is fed by a 1 + j0 Vrms voltage source at 50 Hz.

A comparison between the current density results obtained with the approach described in that article and the solution evaluated with Flux 2D is provided in Figure 4. The graph in this figure displays the real and imaginary parts of the current density phasor (in RMS values) on a path from its upper extremity (0.0 p.u.) to its center (0.5 p.u.) along one of the centermost turns of the coil (as depicted in Figure 3).

Figure 4. Comparison between current density results yielded by Flux and El-Missiry's approach. The plot displays RMS current density values evaluated along the vertical path shown in Figure 3.

An additional comparison between measured lumped circuit parameters (provided in El-Missiry's article) and their corresponding values computed with Flux 2D (obtainable, for instance, with the help of I/O Parameters defined by formulas) is available in Table 1.

Table 1. Comparison between resistance and reactance measurements and the results yielded by Flux 2D for the Aluminum foil coil represented in Figure 2.

Lumped circuit parameter at 50 Hz	Measurement	Flux 2D	Deviation
Reactance	1.802 Ω	1.827 Ω	1.39%
Resistance	0.382 Ω	0.376 Ω	1.57%

The results from Figure 4 and from Table 1 show that the FEM solution evaluated with Flux 2D is in excellent agreement with both measurements and other numerical techniques.