modelSaturatingInductor

Simple model of an inductor with saturation

Extends from Modelica.Electrical.Analog.Interfaces.OnePort (Component with two electrical pins p and n and current i from p to n).

Information

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).

**Tab. 1:** Characteristic parameters of the saturating inductor model
Variable	Description
`Inom`.	Nominal current
`Lnom`	Nominal inductance at nominal current
`Lzer`	Inductance near current = 0; `Lzer` has to be greater than `Lnom`
`Linf`	Inductance at large currents; `Linf` has to be less than `Lnom`

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.

Parameters

Type	Name	Description
SI.Current	Inom	Nominal current
SI.Inductance	Lnom	Nominal inductance at Nominal current
SI.Inductance	Lzer	Inductance near current=0
SI.Inductance	Linf	Inductance at large currents

Connectors

Type	Name	Default	Description
PositivePin	p (from TwoPin)		Positive electrical pin
NegativePin	n (from TwoPin)		Negative electrical pin

Components

Type	Name	Description
SI.Voltage	v (from TwoPin)	Voltage drop of the two pins (= p.v - n.v)
SI.Current	i (from OnePort)	Current flowing from pin p to pin n
SI.Inductance	Lact	Present inductance
SI.MagneticFlux	Psi	Present flux

Revisions

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