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Variable 2-Winding Mutual Inductance

Purpose

Variable magnetic coupling between two windings

Description

pict

This component models two coupled windings with variable self and mutual inductivities and variable winding resistances. In the component icon the positive terminal of phase 1 is marked with a dot.

The component is controlled with three vector signals: the momentary resistance values [R1, R2]  , the momentary self and mutual inductance values [L1,L2,M ]  , and their derivative with respect to time [L1,L2,M ]  . It is the responsibility of the user to provide the correct derivatives. Depending on the connectivity, certain values of L1  , L2  , and M   create a singularity. This will lead to a runtime error.


Note 


The fundamental component equations are

v1 =-d(L1 ⋅i1)+ -d(M  ⋅i2)+ R1 ⋅i1
    dt         dt

v = -d(M  ⋅i)+ -d(L  ⋅i)+ R  ⋅i
 2  dt     1   dt  2  2     2 2

Mode 1 Operation

If the two winding currents are electrically independent, the two equations have to be solved simultaneously for the current derivatives:

[ L   M  ] [ i  ]  [ v  ]  [ L  + R     M     ] [ i ]
  M1  L   ⋅   1  =   v1  -     1   1           ⋅  i1
       2     i2       2         M     L2 +R2       2

Mode 2 Operation

If the two winding currents are electrically dependent, we have

i2 = i1

    -----1------  (                                 )
i1 = L1 +2M  + L2 ⋅ v1 + v2 - (L1 + 2M +L2 + R1 + R2)⋅i1

or

i2 = - i1

                  (                                 )
i1 = -----1------ ⋅ v1 - v2 - (L1 - 2M +L2 + R1 + R2)⋅i1
    L1 - 2M + L2

Mode 3 Operation

If one winding - e.g. winding 1 - is open-circuited, we have

i1 = 0

     1  (               )
i2 =---⋅ v2 - (L2 + R2) ⋅i2
    L2

Mode 4 Operation

If both windings are open-circuited, we have

i = i = 0
 1   2

Parameters

Initial currents
The initial currents at simulation start, in amperes (A). The direction of a positive initial current is indicated with a small arrow in the component symbol.

Probe Signals

Inductor voltages
The voltages across the windings.
Inductor currents
The currents in the windings.