Tm-Te Decomposition of Power Losses in Multi-Stranded Litz-Wires Used in Electronic Devices

Abstract

Abstract-Efficiency often constitutes the main goal in the design of a power system because the minimization of power losses in the magnetic components implies better and safer working conditions. The primary source of losses in a magnetic power component is usually associated with the current driven by the wire, which ranges from low to medium frequencies. New power system tendencies involve increasing working frequencies in order to reduce the size of devices, thus reducing costs. However, optimal design procedures involve increasingly complex solutions for improving system performance. For instance, using litz-type multi-stranded wires which have an internal structure to uniformly share the current between electrically equivalent strands, reducing the total power losses in the windings. The power losses in multi-stranded wires are generally classified into conduction losses and proximity losses due to currents induced by a magnetic field external to the strand. Both sources of loss have usually been analyzed independently, assuming certain conditions in order to simplify the derivation of expressions for calculating the correct values. In this paper, a unified analysis is performed given that both power losses are originated by the electromagnetic fields arising from external sources where the wire is immersed applying the decomposition into transversal magnetic (TM) and transversal electric (TE) components. The classical power losses, the so called conduction and proximity losses, can be calculated considering the TM modes under certain conditions. In addition, a new proximity loss contribution emerges from the TE modes under similar conditions.

Simplified design method for litz wire

“…One approach to that calculation is to derive the exact analytical solution for a single isolated cylinder immersed in a uniform field extending infinitely far away from the cylinder. This results in a Bessel function solution [1]- [5]. This is an exact solution for a single wire with nothing near it, but is only an approximation when wires are closer together [7], [9], [10], [18], and is usually no better than the seemingly less sophisticated Dowell method [19] when wires are tightly packed together as in a winding [18], [20].…”

“…5. r 2 can be replaced with an approximate average distance from the gap to the outer edge of the winding and used in (5). This average distance can be roughly estimated or can be more systematically calculated based on making the winding area of the annular region between r 1 and r 2 in Fig.…”

“…Because (20) is overly complicated for the theme of this paper, we found a curve fit for it (5) with parameters optimized to minimize the maximum percentage error at any point in the region of r 2 /r 1 up to 100. The fit has less than 1% error over this range.…”

“…Simple approaches, such as tables of recommended strand diameter by frequency, can backfire, in some cases leading to higher resistance than a simple solid-wire or foil winding, and almost always leading to higher cost and loss than could be achieved with more careful design. However, the literature on more sophisticated analysis and design approaches can be intimidating, with recommended approaches including Bessel functions [1]- [5], combinations of Bessel functions [6] or iterative application of them [7]; as well as complex permeability models [8], [9], among others [10]. Even the relatively simple approach in [11] requires a formula with ten terms raised to various powers.…”

Design and Implementation of a Test-Bench for Efficiency Measurement of Domestic Induction Heating Appliances

“…The main challenge to perform this calculation lies on the strong relation between the variables R 0 and ∆R, as they both depend on the magnitude and direction of the magnetic field [18]. As a consequence, R 0 varies depending on the absence or presence of a pot and its material.…”