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

TLDR

The study derives a squared‑field‑derivative method to calculate eddy‑current losses in round‑wire or litz‑wire transformer and inductor windings. The method analyzes two‑ and three‑dimensional field effects in multiple windings with arbitrary waveforms by using a frequency‑independent matrix from simple numerical magnetostatic field calculations, combined with a second matrix based on winding‑current derivatives to compute total AC loss. Experimental results confirm the accuracy of the method.

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.