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This model approximates the behaviour of an inductor with the influence of saturation, i.e., the value of the inductance depends on the current flowing through the inductor (Fig. 1). The inductance decreases as current increases. Note, that hysteresis is not taken into account.

The approximation of the flux linkage is based on the atan function with an additional linear term, as shown in Fig. 2:

Psi = Linf*i + (Lzer - Linf)*Ipar*atan(i/Ipar)
L = Psi/i = Linf + (Lzer - Linf)*atan(i/Ipar)/(i/Ipar)

This approximation is with good performance and easy to adjust to a given characteristic with only four parameters (Tab. 1).

The parameter Ipar is calculated internally from the relationship:

Lnom = Linf + (Lzer - Linf)*atan(Inom/Ipar)/(Inom/Ipar)

Fig. 1: Actual inductance Lact versus current i

Fig. 2: Actual flux linkage Psi versus current i

The flux slope in Fig. 2 is equal to Lzer for small currents. The limit of the flux slope is Linf as the current i approaches infinity. The nominal flux is indicated by the product of the nominal inductance Lnom and the nominal current Inom.

Main Author:

Anton Haumer
Technical Consulting & Electrical Engineering
D-93049 Regensburg
Germany
email: a.haumer@haumer.at

Release Notes:

Jul 23, 2019: Improved by Anton Haumer

May 27, 2004: Implemented by Anton Haumer