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Frequency Dependent, 4-ph


The FD line model is used to represent transmission lines with frequency-dependent distributed parameters.

The equivalent circuit is shown below.

The details regarding the model implementation can be found in [1].

Table of Contents

Mask and Parameters

The calculation of the electrical parameters of a line from its geometrical parameters can be done with the Line Data auxiliary module. The resulting EMTP output file (*.pun) contains the electrical line parameters required by HYPERSIM. The user can manually fill in the data form. However, preferably the user provides the parameters of an FD line by loading the pun file in the data form.

General Parameters

NameDescriptionUnitVariable = {Possible Values}
DescriptionUse this field to add information about the component
Description = {'string'}
EMTP (.pun) file for line parametersThe location (path) of the EMTP file (pun file) containing the line parameters
File = {''}
Transformation matrixTransformation matrix (6 x 6)

Ti = { [-1e64, 1e64] }

Line LengthThe length of the linekm

length = {0, 1e64}

Number of poles for the weighting functionNumber of poles for each phase (mode) of the propagation function

nA = { [0, 1, ..., 39, 40] }

Number of poles for the impedance functionNumber of poles for each phase (mode) of the characteristic impedance function

nZ = { [0, 1, ..., 39, 40] }

First coefficient for characteristic impedanceFirst coefficient for each phase (mode) of the characteristic impedance, i.e., the resistance value for infinite frequencyΩ

Ro = { [-1e64, 1e64] }

Propagation delayPropagation delay for each phases

To = { [-1e64, 1e64] }

Impedance Parameters

NameDescriptionUnitVariable = {Possible Values}
Impedance function coefficientsResidues of the impedance function for each phase

KZ = { [-1e64, 1e64] }

Impedance function polesPoles of the impedance function for each phase

PZ = { [-1e64, 1e64] }

Weighting Parameters

NameDescriptionUnitVariable = {Possible Values}
Weighting function coefficientsResidues of the weighting (propagation) function for each phase

KA = { [-1e64, 1e64] }

Weighting function polesPoles of the weighting (propagation) function for each phase

PA = { [-1e64, 1e64] }

Ports, Inputs, Outputs and Signals Available for Monitoring


This component supports a 4-phase transmission line



net_1_1Network connection of phase 1 left (+) side
net_1_2Network connection of phase 1 right side
net_2_1Network connection of phase 2 left (+) side
net_2_2Network connection of phase 2 right side
net_3_1Network connection of phase 3 left (+) side
net_3_2Network connection of phase 3 right side
net_4_1Network connection of phase 4 left (+) side
net_4_2Network connection of phase 4 right side






At acquisition, the signals available by the sensors are:

V_Node(1,2,3,4)_(1,2)Bus voltage for each phase (1,2,3,4)V
I(1,2,3,4)_Node(1,2,3,4)_(1,2)Current for each phase (1,2,3,4)A

The (1,2) in the previous table indicates the name of the bus at each end of the line (1 for left (+) side and 2 for the right side)

The Data of a 4-phase FD Model

The following figure shows the geometrical data of a DC transmission line as an example to simulate a 4-phase FD model. 

Details of a conductor bundle

The calculation of the electrical parameters can be done with the Line Data auxiliary moduleThe EMTP-type output file for the calculation of the parameters for the FD line model:

A portion of the pun file generated with the Line Data auxiliary module:


  1. J. R. Marti, "Accurate modelling of frequency-dependent transmission lines in electromagnetic transient simulations," IEEE Trans. Power App. Syst., vol. PAS-101, pp. 147-55, 01/1982.

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