Single phase Bergeron transmission line
This section describes Bergeron single phase transmission line based on a distributed parameter traveling wave model with lumped resistance.
Properties for this model are length of the line in kilometers, per length resistance in ohms/km, per length core and shield capacitance in farads/km, per length inductance in henries/km and execution rate in seconds.
Description
This model represents the L and C elements in a distributed manner while resistance R is lumped. In the case when line is lossless( r = 0), model is characterized by two values: the wave propagation speed and the characteristic impedance .
Transport delay is , where d is the length of the line and v is the propagation speed.
It is important to note that transport delay value must be greater than execution rate.
The model equations are:
math
And two current sources are:
This set of equations can be implemented for time discrete modelling of the line if the transport delay, τ, is integer multiple of the simulation step, T , or can be approximated as such: τ = NT.
For lossy lines, total resistance is lumped, at each end and in the middle of the line. When losses are taken into account, equations are obtained as:
where:
References
[1] Dommel, H., “Digital Computer Solution of Electromagnetic Transients in Single and Multiple Networks,” IEEE® Transactions on Power Apparatus and Systems, Vol. PAS-88, No. 4, April, 1969.