Saturable Inductor

Purpose

Inductor with piece-wise linear saturation

Library

Electrical / Passive Components

Description

This component provides a saturable inductor between its two electrical terminals. The inductor has a symmetrical piece-wise linear saturation characteristic defined by positive current/flux pairs. It is shown in Fig. 194.

../../_images/lsat1.svg — Fig. 194 Saturable inductor saturation characteristic

The operating mode of the saturable inductor is illustrated in Fig. 195.

../../_images/lsat_schema.svg — Fig. 195 Saturable inductor equivalent circuit

In the unsaturated state the current flows only through the main inductor \(L_0\). When the absolute value of the current exceeds the threshold \(I_1\), the breaker in series with the auxiliary inductor \(L_1\) is closed. The differential inductivity of the component thus becomes \(L_{\mathrm{diff}} = \frac{L_0 L_1}{L_0+L_1}\). On the other hand, the total inductivity is calculated as \(L_{\mathrm{total}} = \frac{L_0 i_0 + L_1 i_1}{i_0 + i_1}\), where \(i_0\) and \(i_1\) are the momentary inductor currents.

Note

In order to model a saturation characteristic with \(n\) segments, this component requires \(n\) ideal inductors and \(2(n-1)\) ideal switches. It is therefore advisable to use as few segments as possible.

Parameters

Current values: A vector of positive current values \(I\) in amperes \((\mathrm{A})\) defining the piece-wise linear saturation characteristic. The current values must be positive and strictly monotonic increasing. At least one value is required.
Flux values: A vector of positive flux values \(\Psi\) in \((\mathrm{Vs})\) defining the piece-wise linear saturation characteristic. The flux values must be positive and strictly monotonic increasing. The number of flux values must match the number of current values.
Initial current: The initial current through the inductor at simulation start, in amperes \((\mathrm{A})\). This parameter may either be a scalar or a vector corresponding to the implicit width of the component. The direction of a positive initial current is indicated by a small arrow at one of the terminals. The initial current default is 0.

Probe Signals

Inductor current: The current flowing through the inductor, in amperes \((\mathrm{A})\). The direction of a positive current is indicated with a small arrow at one of the terminals.
Inductor voltage: The voltage measured across the inductor, in volts \((\mathrm{V})\).
Saturation level: The saturation level indicates which sector of the piece-wise linear characteristic is currently applied. During linear operation, i.e. operation in the first sector, the saturation level is \(0\). The saturation level is negative for negative flux and current values.