A lumped winding model for use in transformer models for circuit simulation

Abstract

A lumped circuit model is derived for a winding in a multiwinding transformer. The model is intended to be used in transformer models for circuit simulation using electrical-network simulators. A hybrid (partly electrical, partly magnetic) modeling approach is adopted in which magnetic components are described using the capacitance-permeance analogy instead of the widespread resistance-reluctance analogy. The network correctly models energy storage and power dissipation due to DC series wire resistance and to eddy current losses, independent of the way of excitation of the winding (electrical and/or magnetic). All component values are frequency independent and are parameterized by geometrical parameters, winding data and material parameters. The mathematical continued-fraction approximation technique is applied to derive approximating circuits to model eddy current losses. A fourth-order circuit shows acceptably small errors up to a frequency of about a factor of 1500 above the frequency at which eddy-current losses become apparent. The model is applied in a six-layer two-winding transformer model. Calculations both in the frequency domain and in the time domain show good agreement with measurements.