WOLFRAM SYSTEMMODELER

SaturatingInductor

Simple model of an inductor with saturation

Wolfram Language

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SystemModel["Modelica.Electrical.Analog.Basic.SaturatingInductor"]
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Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

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
Lact vs. i
Fig. 2: Actual flux linkage Psi versus current i
Psi vs. 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 (4)

Inom

Value:

Type: Current (A)

Description: Nominal current

Lnom

Value:

Type: Inductance (H)

Description: Nominal inductance at Nominal current

Lzer

Value:

Type: Inductance (H)

Description: Inductance near current=0

Linf

Value:

Type: Inductance (H)

Description: Inductance at large currents

Connectors (2)

p

Type: PositivePin

Description: Positive electrical pin

n

Type: NegativePin

Description: Negative electrical pin

Used in Examples (1)

ShowSaturatingInductor

Modelica.Electrical.Analog.Examples

Simple demo to show behaviour of SaturatingInductor component

Used in Components (1)

SaturatingInductor

Modelica.Electrical.MultiPhase.Basic

Simple model of inductors with saturation