Computationally efficient winding loss calculation with multiple windings, arbitrary waveforms, and two-dimensional or three-dimensional field geometry

Abstract

The squared-field-derivative method for calculating eddy-current (proximity-effect) losses in round-wire or litz-wire transformer and inductor windings is derived. The method is capable of analyzing losses due to two-dimensional and three-dimensional field effects in multiple windings with arbitrary waveforms in each winding. It uses a simple set of numerical magnetostatic field calculations, which require orders of magnitude less computation time than numerical eddy-current solutions, to derive a frequency-independent matrix describing the transformer or inductor. This is combined with a second, independently calculated matrix, based on derivatives of winding currents, to compute total ac loss. Experiments confirm the accuracy of the method.Index Terms-Eddy currents, finite-element methods, inductors, magnetic devices, numerical field computation, power conversion, power transformers, proximity effect, skin effect.

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

“…can be easily obtained starting with the configuration of the strand immersed in a uniform longitudinal magnetic field H 0 z (r i ) because the field is not distorted by the induced currents in the conductor. Additionally, considering the azimuthal electric field inside the strand with a dependence shown in (22) associated with a surface current similar to (31), together with the fact that the magnetic field vanishes inside the conductor, it is possible to define the so called impedance boundary condition [48][49][50] establishing the relationship between the tangential magnetic and electric field in the surface of the strand. In this case, it should be noted that both the longitudinal electric field and the azimuthal electric field are tangential to the surface, thus:…”

“…Alternatively, simpler expressions can be obtained neglecting the influence of the strand induced currents over the external fields, in other words, the electromagnetic field is not distorted by the presence of the strand. Equivalently, in the latter case, a low-frequency approach is assumed with respect to the previous methodology, as followed in [21][22][23].…”

Practical Wide Frequency Approach for Calculating Eddy Current Losses in Transformer Windings

“…Eddy current losses in round wires, including skin and proximity effects in transformers are discussed by Dowell [1] and many new papers [2], [3], related to some extent to Dowell's interpretation and results.…”

Optimization of stranded-wire windings and comparison with litz wire on the basis of cost and loss

“…This section modifies the loss model for arbitrary waveforms and 2-D or 3-D field geometry, based on the squared field derivative (SFD) method for calculating loss [15], which is reviewed in Appendix II.…”

“…In [3], a procedure for calculating k ℓ for arbitrary waveforms and 2-D or 3-D field geometry is derived, such that (11) can still be used to accurately calculate losses, including the effects of fringing fields, mutual resistance effects [16], and non-sinusoidal waveforms. The calculation of k ℓ [3] is based on the squared field derivative (SFD) method for calculating loss [15]; the necessary formulas are summarized in Appendix II-A. If we can rewrite the stranded-wire loss model in terms of k ℓ , we will be able to use the method in [3] (Appendix II-A) to calculate k ℓ and it will possible to calculate loss in stranded wire for arbitrary waveforms and 2-D or 3-D field geometries.…”