A recursive methodology for modelling multi-stranded wires with multilevel helix structure

Abstract

Multi-stranded litz wires are commonly used in magnetic devices for power electronics applications at medium-high frequency range, from several kHz up to hundreds of kHz. For these applications, litz-wire structure favours the uniformity of driven current in the cross-sectional area of conductors, alleviating ac losses (skin and proximity effects) and improving the global efficiency of the application. These features are achieved by means of a special cable arrangement consisting of many isolated fine copper strands twisted together according to the manufacturing process. Often, the manufacturing process involves several twisting steps where bundles of moderate number of strands are successively twisted resulting in intricate cable structures. We present a mathematical description of the trajectories of copper strands with the purpose of obtaining the cable losses by means of Finite Element Analysis (FEA) simulation tools. Moreover, a nomenclature for this multilevel structures is also proposed. Parameters as the number of twisting steps, number of strands, strand diameter or pitch length, are included in this representation, allowing to compare the performance of different manufacturing solutions.

Efficient finite element modelling of litz wires in toroidal inductors

“…The inter‐slice positions of the strands in such geometries can be defined by the Frenet–Serret frame [11]. However, a simpler geometrical approach is adopted here which partly makes the strands follow the Frenet–Serret frame.…”

“…Analytical expressions, which are very handy for engineers because of their quick solutions, still have their limitations in accounting for different loss mechanisms when it comes to litz wires [11]. Many aspects like the number of strands and their diameter along with the twisting scheme and pitch come into play while designing inductor windings with litz wire.…”

“…To envisage the impact of frequency dependent phenomena in the design of the complex litz wire winding structure, the use of 3D finite element (FE) method (FEM) becomes necessary [11]. However, discretizing filamentary structures like litz wire strands in 3D will result into an extremely heavy computational problem.…”

A Versatile Simulation-Assisted Layered Mesh Analysis for Generalized Litz Wire Performance

“…Several analytical methods were established in the literature over the decades [6]- [11] all aimed at quick performance approximations. For more detailed predictions, three-dimensional numerical methods have been employed such as FEA [12] and the more novel partial element equivalent circuit (PEEC) method [13]- [15] which does not require the discretization of air. These 3D approaches are accurate given knowledge of the exact strand level construction, but suffer from computational limitations (memory, complexity, and long simulation times) due to the large number of mesh elements required.…”

“…Actual fabrication techniques lead to randomized strand positions and inaccuracies in all of the aforementioned models due to non-idealities in the current distribution. Plumed attempted to address this by introducing some randomization in the strand placement of his simulations [12], but exact packing information is required to model reality. As such, most approaches in the literature use the ideal assumption that each strand in the bundle carries equal current.…”