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Variable Inductor

Purpose

Inductance controlled by signal

Library

Electrical / Passive Components

Description

pict

This component models a variable inductor. The inductance is determined by the signal fed into the input of the component. The voltage across a variable inductance is determined by the equation

      di   dL
v = L ⋅dt + dt-⋅i

Since i   is the state variable the equation above must be solved for didt-  . The control signal must provide the values of both L   and ddtL   in the following form: [L1 L2 ...Ln -dL1 dL2 ...dLn ]
           dt   dt     dt . It is the responsibility of the user to provide the appropriate signals for a particular purpose (see further below).

If the component has multiple phases you can choose to include the inductive coupling of the phases. In this case the control signal vector must contain the elements of the inductivity matrix (row by row) and their derivatives with respect to time. The control signal thus has a width of 2 ⋅n2  , n   being the number of phases.


Note  The momentary inductance may not be set to zero. In case of coupled inductors, the inductivity matrix may not be singular.

There are two common use cases for variable inductors, which are described in detail below: saturable inductors, in which the inductance is a function of the current and actuators, in which the inductance is a function of an external quantity, such as a solenoid with a movable core.

For a more complex example of a variable inductor that depends on both the inductor current and an external quantity see the Switched Reluctance Machine.

Saturable Inductor Modeling

When specifying the characteristic of a saturable inductor, you need to distinguish carefully between the total inductivity L  (i) = Y∕i
 tot   and the differential inductivity L   (i) = dY∕di
  diff  . See also the piece-wise linear Saturable Inductor.

With the total inductivity L  (i) = Y∕i
 tot   you have

      dY-
v  =   dt
      -d
   =  dt (Ltot ⋅i)
           di   dLtot-
   =  Ltot ⋅dt + dt  ⋅i
   =  L   ⋅ di+ dLtot-⋅ di⋅i
      (tot dt    di ) dt
   =   L   + dLtot⋅i  ⋅ di ,
         tot    di      dt

which can be implemented as follows:

pict

With the differential inductivity Ldiff(i) = dY ∕di   you have

v  =  dY-
       dt
   =  dY-⋅ di
       di  dt
   =  Ldiff ⋅ di ,
           dt

which can be implemented as follows:

pict

Note that in both cases the dL
dt  -input of the Variable Inductor is zero!

Actuator Modeling

In an actuator the inductivity is determined by an external quantity such as the position x   of the movable core in a solenoid: L = L(x)  . Therefore you have

         di   dL-
v  =   L⋅dt + dt ⋅i
         di   dL- dx-
   =   L⋅dt + dx ⋅dt ⋅i ,

which can be implemented as follows:

pict

Note that x   is preferably calculated as the integral of dx ∕dt   rather than calculating dx∕dt   as the derivative of x  .

Parameters

Inductive coupling
Specifies whether the phases should be coupled inductively. This parameter determines how the elements of the control signal are interpreted. The default is off.
Initial current
The initial current through the inductor at simulation start, in amperes (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 in the component symbol. The default of the initial current is 0.

Probe Signals

Inductor current
The current flowing through the inductor, in amperes (A). The direction of a positive current is indicated with a small arrow in the component symbol.
Inductor voltage
The voltage measured across the inductor, in volts (V).