SaturatingInductor

Simple model of an inductor with saturation

    SaturatingInductor

Library

Modelica/Electrical/Analog/Basic

Description

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

SaturatingInductor_0

NameLabelDescriptionData TypeValid Values

mo_Inom

Inom

Nominal current

Scalar

mo_Lnom

Lnom

Nominal inductance at Nominal current

Scalar

mo_Lzer

Lzer

Inductance near current=0

Scalar

mo_Linf

Linf

Inductance at large currents

Scalar

mo_Ipar

Ipar

Scalar

SaturatingInductor_1

NameLabelDescriptionData TypeValid Values

mo_v

v

v

Structure

mo_v/fixed

fixed

Cell of scalars

true
false

mo_v/start

start

Cell of scalars

mo_i

i

i

Structure

mo_i/fixed

fixed

Cell of scalars

true
false

mo_i/start

start

Cell of scalars

mo_Lact

Lact

Lact

Structure

mo_Lact/fixed

fixed

Cell of scalars

true
false

mo_Lact/start

start

Cell of scalars

mo_Psi

Psi

Psi

Structure

mo_Psi/fixed

fixed

Cell of scalars

true
false

mo_Psi/start

start

Cell of scalars

Ports

NameTypeDescriptionIO TypeNumber

p

implicit

Positive electrical pin

input

1

n

implicit

Negative electrical pin

output

1