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Variable Inductors in Delta Connection

Purpose

Delta-connected variable inductors with variable series resistors and variable series emf

Description

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This component models three variable inductors with variable resistors and variable voltage sources connected in series. The three phases are connected in a delta-configuration. In the component icon terminal a is marked with a dot.

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The component is controlled with four vector signals - each vector having three elements in the order ab, bc, ca - containing the emf, the momentary resistance values, the momentary inductance values, and their derivatives with respect to time. It is the responsibility of the user to provide the correct derivatives.

The currents measured in the three phases (iab  , ibc  , and ica  ) are provided as an output vector signal.


Note 


The fundamental component equations are:

      d
vab = --(Lab ⋅iab)+ Rab ⋅iab + eab = Lab ⋅iab + (Lab + Rab)⋅iab +eab
      dt

vbc = Lbc ⋅ibc + (Lbc + Rbc)⋅ibc + ebc

vca = Lca ⋅ica +(Lca +Rca) ⋅ica + eca

Mode 1 Operation

As long as current can flow freely in and out of all terminals the three phases are operating independently.

Mode 2 Operation

If one terminal - e.g. a - is open-circuited, we have

iab = ica

               1     (                                      )
iab = ica = ----------⋅ vbc + (Lab + Rab + Lca + Rca)⋅iab + eab + eca
           Lab + Lca

      1  (                  )
ibc = Lbc ⋅ vbc - (Lbc + Rbc)⋅ibc

Mode 3 Operation

If two or all three terminals are open-circuited, we have

iab = ibc = ica

iab = ibc = ica = - eab +-ebc +-eca-+-(Lab-+Lbc-+-Lca +-Rab +-Rbc +-Rca)-⋅iab
                                  Lab + Lbc + Lca

Parameters

Initial currents [iab0 ibc0 ica0
] The initial currents in phases ab, bc, and ca at simulation start, in amperes (A).

Probe Signals

Phase voltages
The three phase voltages vab  , vbc  , and vca  .
Phase currents
The three phase currents iab  , ibc  , and ica  .