Transmission lines
This section describes the general properties of all transmission line type components in Schematic Editor.
- Lumped parameter, based on one or more π sections or RL sections;
- Distributed parameter, based on traveling wave theory and telegraphers equations.
Lumped parameter transmission line
Lumped parameters representation calculates the total series resistance, shunt resistance, series inductance, mutual inductance, ground capacitance and mutual capacitance of the transmission line based on the selected parameters and parameter definition specified in the individual component. Depending on the user selection of the model definition, the calculated parameters are applied into either a more complex π section (Transmission Line and Underground Cable) or a simpler RL section (capacitances are neglected from a π section). For short lines the effect of the capacitances is small and they can be neglected, for medium lines, their effect is important and they need to be considered.
Distributed parameters transmission line
The implementation of a distributed parameter line is based on the traveling wave theory and Telegraphers equations, which describe the time delay of traveling waves. Using Telegrapher's equations without series and shunt resistance elements, a solution can be obtained in a discrete-time representation with constant line parameters (necessary for computer implementation). Obtained is a four-port network with both sides (two ports each) being represented as Norton's equivalent current source and impedance. To then also account for the series resistance of the transmission line, it is added as a lumped series resistance to the existing circuit without significant loss of fidelity. Restructuring the equations of Norton's equivalent current source and impedance allows for the lumped elements to be transferred from the circuit and into equivalent equations. The obtained model is the well known Single Phase Bergeron Model.
The three-phase implementation may also contain cross-coupling elements (mutual inductances and mutual capacitances). This prevents a simple implementation of three parallel Single phase Bergeron models and requires decoupling, which is done inside the Three Phase Bergeron Model component and in real-time.