Variable Inductors in Star Connection
Purpose
Star-connected variable inductors with variable series resistors
Description
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
- This component is based on voltage controlled current sources. It may therefore not be connected in series with other current sources or inductors.
- The control signal for the momentary inductance values must be continuous. Discontinuous changes will produce non-physical results.
- Connecting anything with a finite impedance to the star-point will result in an error message.
The fundamental component equations are:
Mode 1 Operation
If all three phases are conducting, there are two independent loop equations (and state variables).
Using the fact that yields
where
Mode 2 Operation
If one phase - e.g. a - is open-circuited, only one independent loop equation (and state variable) remains:
Using yields
Mode 3 Operation
If two or all three phases are open-circuited, we have
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.