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Variable Inductors in Star Connection

Purpose

Star-connected variable inductors with variable series resistors

Description

pict

This component models three variable inductors with variable resistors connected in series. The three phases are connected in a star-configuration. The star-point is accessible so that a voltmeter can be connected. However, it may not be loaded, i.e. the sum of all three phase currents must be zero at all times. In the component icon terminal a is marked with a dot.

The component is controlled with three vector signals - each vector having three elements - containing 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.


Note 


The fundamental component equations are:

vx = d-(Lx ⋅ix)+ Rx ⋅ix = Lx ⋅ix +(Lx + Rx)⋅ix
     dt

ia + ib + ic = 0

Mode 1 Operation

If all three phases are conducting, there are two independent loop equations (and state variables).

va - vb = La ⋅ia + (La + Ra) ⋅ia - Lb ⋅ib - (Lb + Rb)⋅ib

vb - vc = Lb ⋅ib + (Lb + Rb)⋅ib - Lc ⋅ic - (Lc + Rc) ⋅ic

Using the fact that ic = - ia - ib   yields

      LcvLab - LbvLca
ia = L-L--+-L-L-+-L-L--
     a  b   b c   c a

i = --LavLbc --LcvLab-
b   LaLb + LbLc + LcLa

where

vLxy = vxy - (Lx + Rx)⋅ix + (Ly + Ry)⋅iy.

Mode 2 Operation

If one phase - e.g. a - is open-circuited, only one independent loop equation (and state variable) remains:

vb - vc = Lb ⋅ib + (Lb + Rb)⋅ib - Lc ⋅ic - (Lc + Rc) ⋅ic

Using ic = - ib   yields

      v
ib =---Lbc--.
    Lb + Lc

Mode 3 Operation

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

i = i = i = 0.
 a   b   c

Parameters

Initial currents [ia0 ib0
] The initial currents in phases a and b at simulation start, in amperes (A). Currents flowing towards the star point are considered positive.

Probe Signals

Phase voltages
The three phase voltages measured between the component terminals and the star-point.