Frequency Dependent (FD) Lines

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

FD Model of a Line with Frequency Dependent Parameters

Icons and diagrams of FD models of lines

The following icons and diagrams are used to represent respectively the FD model of a 2-phase, 3-phase and 4-phase lines and the FD model of a 4-phase line.

Parameter description

General parameters

Length	The length of the line (km)
Data base key name	Key to access the line data base (optional package)

Mode parameters

Source of parameters (control panel, EMTP file): Specifies the source of the parameters;

EMTP file	The name of the EMTP file containing the line parameters
R0	Modal resistances for infinite frequency
T0	Delay for modal propagation
nZ	Number of poles for impedance functions and maximum number of poles
nA	Number of poles for propagation functions and maximum number of poles
Ti	Transformation matrix
KZ	Residues of impedance function
PZ	Pole of modal impedance function
KA:	Residues of modal propagation function
PA	Pole of modal propagation function

List of available signals

At acquisition, the signals made available by the sensors are the following:

V_bus label	Bus voltage (volt)
I (1, 2, 3)_bus label_(a, b, c)	Current for each phase (ampere)
Bhist_line label_bus label	Voltage of the equivalent source (volt)

The parameter control panel of the 2-phase FD model
This section presents the data for FD Lines and shows how to fill in the parameter control panels.

Data of a 2-phase FD line
Figures 7 - 48 and 7 - 49 show the geometrical data of a cable to be modelled by a 2-phase FD
model.

Geometrical Parameters of a Single Cable

Cable Arrangement

Calculation of electrical parameters and related parameter form
The calculation of the electrical parameters of a cable line from its geometrical parameters is done by the CABLE CONSTANTS auxiliary module of EMTP. Figure 7 - 50 shows the EMTP input file for the calculation of parameters of a cable line with geometrical parameters in Figures 7 - 48 and 7 - 49.

BEGIN NEW DATA CASE
C JFD SETUP
C HVDC DC CABLE CONSTANT
C CABLE CONSTANTS JFD SETUP
C REVISION DATE 1996.06.13 (CA-3) TYPE: PROTO-3
C (E=2.80)
CABLE CONSTANTS 1
C --+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
2 -1 1 0 1 1 1 2
3
C NO.1
12.50E-3 37.50E-3 60.00E-3 66.00E-3 73.60E-3 89.25E-3 94.00E-3
2.16E-8 1.0 1.0 2.80 22.00E-8 1.0 1.0 2.3
14.00E-8 10.0 1.0 4.0
0.21 0.1 50700.0
.NODES BUS1A BUS2A BUS1B BUS2B
C
.FIT-S 30
C ---RHO------><-----FREQ---->IDEC>IPNT><length>
0.21 0.0001 8 20 50700.0
BLANK ENDING FREQUENCY CARDS
BLANK
BLANK

The EMTP input file for the transmission line in Figure 7 - 48
The resulting EMTP output file (*.pun) contains the electrical cable parameters required by HYPERSIM®. The user can fill in manually the parameter form using the data from this file. However, it is much more convenient to provide the parameters of a FD line by specifying where this file is located. The data form used for a 2-phase FD model is shown in Figures 7 - 51 and 7 - 52.

The Data Form for a 2-Phase FD Model

The Data Form for a 2-Phase FD Line

The data form of the 4-phase FD model
The figures 7 - 54, 7 - 55 and 7 - 56 show the geometrical data of a D.C. line to simulated by a 4-phase FD model.

Details of a Conductor Bundle

Line Height

Calculation of electrical parameters and related parameter form
The calculation of the electrical parameters of a line from its geometrical parameters can be done with the LINE CONSTANTS auxiliary module of EMTP. The EMTP input file for calculation of
parameter of the FD model of the line with geometric data in Figures 7 - 54 to 7 - 56 is shown in Figure 7 - 57.

The EMTP Input File for Calculation of the FD Model of the Line

The resulting EMTP output file (*.pun) contains the electrical line parameters required by HYPERSIM®. The “.pun” file corresponding to the data in Figure 7 - 57 is shown in Figures 7 - 58 and 7 - 59.

The EMTP pun file corresponding to the input file

From the results in Figures 7 - 58 and 7 - 59, the user can manually fill in the data form shown in Figures 7 - 60 and 7 - 61. However, it is much more convenient to provide the parameters of a FD
line by specifying where this file is located.

The control panel for a 4-phase FD line

The control panel for a 4-phase FD line 2

Data of a 3-phase line
Figures 7 - 63 and 7 - 64 show the geometrical data of a line to be simulated by a 3 phase FD line
model.

Details of a conductor bundle 7-64

Calculation of electrical parameters and related parameter form
The calculation of electrical parameters of the line from the geometrical parameters in Figures 7- 63 and 7 - 64 is done by the LINE CONSTANTS auxiliary EMTP module. The EMTP input file for parameter calculation is shown in Figure 7 - 65.

The EMTP input file for calculation of the FD model of the line in Fig 7

The resulting EMTP output file (*.pun) contains the electrical line parameters required by HYPERSIM®. The “.pun” file corresponding to the data in Figure 7 - 65 is shown in Figure 7 - 66.

From the results in Figure 7 - 66, the user can fill in manually the data form shown in Figures 7 -67 and 7 - 68. However, it is much more convenient to provide the parameters of a FD line by specifying where this file is located.

The data form for a 3-phase FD line