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# Line Data

# Mask and Parameters

## Location of data Parameters

Name | Description | |
---|---|---|

Open an existing line case data file or use previously saved (click OK now) data for this device | Provide an existing line data file if you want to modify an existing case or use previously saved data for this device. To open the previously saved version simply click on the OK button, in this case the data is saved within the device and not in a file. | |

Convert an existing EMTP-V3 data file | Provide an existing EMTP-V3 (AUX) data file if you want to modify an existing old case. This device will try to translate the existing file to create a line case data compatible with HYPERSIM. The user should verify if the translation has been performed correctly by opening the line case data file with the first option on this page. The provided | |

Run an existing line case data file without opening its data | This option allows submitting directly an existing case file to the Line Data Calculation function. It can be also used to run old EMTP-V3 cases without translating them. | |

Create a new line case | This option allows to create a new case from scratch |

## Conductor Data Parameters

Once a (new) line case is selected (created), a new window with following parameters is open.

The Data tab allows entering the geometrical and electrical data of the transmission line. This include the electrical data of the conductors, their geometrical placement as well as a general description of the construction of the towers. The normally required information to characterize the transmission line is the geometric location of the conductors and their electrical characteristics. However, when the line geometry is not known, it is still possible to generate reasonably accurate line models from the 60-Hz (or any other specific frequency) positive and zero sequence impedance values.

Name | Description | Unit | ||||||
---|---|---|---|---|---|---|---|---|

Module | Allows to specify the type of data to be generated | |||||||

Line Model | To generate transmission line models for steady-state and for time-domain studies | |||||||

Line Parameters | To determine the resistance, inductance, and capacitance matrices for a multiphase overhead transmission line consisting of an arbitrary configuration of conductors | |||||||

Units | Identify the units used for conductor and line data. To facilitate the data entry, the units are mentioned next to each parameter. Two types of unit systems are allowed | |||||||

Metric | The SI system of units is used for conductor and line data | |||||||

English | The English system of units is used for conductor and line data | |||||||

Input option | The geometry of the conductors and the line data is either | |||||||

Standard Conductor Data | Specified directly with the Conductor data option | |||||||

Conductor Data for Line Rebuilt | Rebuilt (Line Rebuild) from the electrical parameters. | |||||||

Number of conductors | Selects the (N) number of conductors in the current system | |||||||

Conductor data table | Wire | The wire number | ||||||

Phase number | The phase number to which the conductor belongs. If more than one conductor is given the same phase number, this means that the conductors are electrically connected (connected in parallel). This is the case, for instance, of individually specified conductors in a bundle. It could also be used, for instance, to internally unite two parallel lines when it is not desired to preserve their individual identity. Phase numbers for conductors must follow the sequence 1, 2, 3,..., N with no missing phases. Set the phase number to 0 for a ground wire (ground is phase number zero, by definition) when the ground wire is not to be considered separately. | |||||||

DC resistance | DC resistance of the conductor in the specified unit | Ω/km or Ω/mi | ||||||

Outside diameter | Outside diameter of the conductor | cm or in | ||||||

Horizontal distance | Horizontal distance of the conductor from the reference point x=0 | m or ft | ||||||

Vertical Height at tower (tower VH) | Vertical height of the conductor above the ground at the tower | m or ft | ||||||

Vertical Height at Midspan (VH _{mid}) | Vertical Height of the conductor above the ground at the middle of the span. When both VH | m or ft | ||||||

Additional data for Wire | Allows specifying the data in the next items for each specified wire selected from the number list | |||||||

Skin effect correction | This option is to consider the skin effect correction of an equivalent tubular conductor. See also the Reactance model data description below for more information. | |||||||

Thick/Diam | Specify the Thickness/Diameter (T/D) factor which has to be less or equal of 0.5 | |||||||

None | To neglect the skin effect correction | |||||||

Solid conductor | Assume a solid conductor | |||||||

Galloway-Wedephol | Use Galloway-Wedephol’s correction formula for stranded conductors. This option is only available for Line Parameters. See the Permeability of outer strand description below. | |||||||

Bundled conductor | Specify a symmetrical bundle using
| |||||||

Number of conductors in the bundle | Number of conductors | |||||||

Spacing (cm) | Spacing (SEPAR) between adjacent conductors in the bundle | cm or in | ||||||

Angular position | Angular position (ALPHA) of the first conductor (or any conductor) of the bundle. Positive angles are measured counter-clock wise | |||||||

Reactance model data | Specify the model used for the calculation of the internal inductance of the conductor. With the default options the conductor internal inductance is corrected for skin effect assuming tubular conductor geometry. Alternative inductance options are possible that do not correct the conductor’s internal inductance. | |||||||

Relative permeability | This is the standard case used in both Line Model and Line Parameters calculation. The internal reactance is calculated and corrected for skin effect assuming tubular conductor geometry | |||||||

Permeability of outer strand | For use with Galloway-Wedepohl's equation for stranded conductors. The user must specify the relative permeability of the outer strand as well as the number of the outer strands in the conductor. This option is only available with Line Parameters | |||||||

Reactance for unit spacing | The reactance (not the inductance) is assumed to remain constant regardless of the frequency that may be specified in the frequency data. The reactance is in units of Ω/ km for Metric units and Ω/mile for English units. The unit spacing is 1 meter for Metric units and 1 foot for English units. This option is only available with Line Parameters. The name 1-foot spacing is for the case where the spacing among the three phases (expressed as geometric mean distance GMD) is 1 foot, with GMR given in feet as well | |||||||

| Reactance for unit spacing (as above) at 60 Hz. As opposed to the case above where the reactance is assumed to remain constant, it is now the inductance that is assumed to remain at its 60- Hz value. If frequencies other than 60 Hz are specified in the frequency data, the reactance will be changed proportionately. This option is only available with Line Parameters. Note that the relationship between reactances for 1-foot spacing and GMR (geometric mean radius) is given by: | |||||||

GMR | Geometric mean radius of the conductor, in units of cm if Metric or inches if English. This option is only available with Line Parameters | |||||||

GMR/r | Dimensionless ratio, where r is the conductor outer radius. For solid conductors, this ratio is equal to 0.7788. This option is only available with Line Parameters |

**Line Rebuild option Parameters**

Name | Description | Unit | |||
---|---|---|---|---|---|

Line Rebuild option | The conductor data for this option does not contain the line geometry as in the standard case, but the 60 Hz (or any other specific frequency) values of the zero and positive sequence impedances: 0 R , 0 L , 0 C , and 1 R , 1 L , 1 C . Optionally, for extra accuracy, the conductor's dc resistance can be supplied. From the 60 Hz parameter information, the Line Data module builds an equivalent balanced arrangement of phase conductors that matches the specified 60 Hz sequence parameters. It also estimates the skin effect characteristics of the conductors. This estimate is better if the conductor's dc resistance is specified. After rebuilding the line geometry and conductor characteristics, the requested line model is processed as in the ordinary case. Since the reconstructed line is assumed to be balanced, the transformation matrix is the same one used for balanced lines (generalized Clarke). The data fields required for this option are self-explanatory. It is noticed that if the dc resistance is set to 0, it will be automatically estimated by the program. |

## Model Parameters

Name | Description | Unit | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Select model | The Line-Model module can produce transmission line models for steady-state and for time-domain studies | ||||||||||

FD | Frequency-dependent model, FD model | ||||||||||

CP | Constant-parameter model | ||||||||||

Exact-PI | Exact frequency domain representation of a line at a given frequency, for steady-state and frequency scan simulations | ||||||||||

Wideband | Wideband line model | ||||||||||

FD | The FD option can be used to generate data fully compatible with the FD line model for time-domain and steady-state solutions. This model represents the true nature of a transmission line by modeling the line parameters as distributed and frequency-dependent. The line resistance and inductance are evaluated as functions of frequency, as determined by skin effect and ground return conditions. The capacitance is assumed constant. A non-zero constant shunt conductance The model is based on the approximation by rational functions of the line characteristic impedance A, given by the following equations:_{p} , R , L and C are the line parameters per unit length. A transformation matrix G T (also referred to as _{i} Q ) is used in this model to relate phase and modal quantities.The main simplification used in this model is the validity of the assumption that a constant real transformation matrix can be used to relate phase and modal quantities over an extended frequency range. | ||||||||||

Real T_{i} | In the general case of an untransposed line, the elements of the transformation matrix relating phase and modal quantities are complex numbers. Also, the matrix has different values at different frequencies. The FD model, however, makes the approximation of using a constant transformation matrix of real numbers for all frequencies in the modeling interval (default). The optimum frequency at which to evaluate this real constant transformation matrix can be determined automatically by the program (default option), or the user can specify it using the “Model frequency” option field. The optimum frequency determination procedure (Find Model frequency automatically) selects an optimum value of frequency for the range of switching transients. This value is based on asymptotic conditions for the particular line under consideration. Typical values are in the range from 500 Hz to 5 kHz with a mean around 1000 Hz. The selection of an optimum value is based on the constancy of After calling the eigenanalysis functions to evaluate the exact (complex) transformation matrix of the line at one frequency, the matrix is rotated and normalized. The imaginary part is then discarded and the remaining real part is taken as the "correct" transformation matrix to evaluate the line parameters and propagation functions at all frequencies. The errors due to this approximation are estimated in the Q-Error Table listed in the output file. | ||||||||||

Balanced line | The line is modeled as perfectly transposed. The diagonal and the off-diagonal elements in the reduced phase matrices (Z and _{phase} Y) are averaged out. The balanced-line transformation matrix used is the generalized Clarke transformation (αβ0) for an m-phase line. Unless the line is actually transposed, the results using this option are usually poorer than with the option “Real _{phase} T ”. Check the Q-Error table in the output listing for error indicators._{i} | ||||||||||

Double circuit line | This option is only selected for double-circuit lines. The line is modeled as consisting of two separate circuits, each circuit perfectly balanced with respect to itself and to the other circuit. Under these conditions, the only coupling between the two circuits is zero sequence coupling. A special transformation matrix corresponding to this condition is used. Unless the transposition scheme of the line approaches the ideal zero coupling condition on which this option is based, better results are usually obtained with the default “Real T ” option. Check the Q-Error Table in the output listing for an indication of the errors._{i} | ||||||||||

Frequency range | The “Frequency range” represents the frequency band for the fitting of the line characteristic impedance Z and propagation function _{c} A. The data fields required for this option are self-explanatory._{p} | ||||||||||

CP | The CP model (constant parameter line model) assumes that the line parameters R , L and C are constant, as calculated at the requested frequency in the “Model frequency” field. The model considers L and C to be distributed (ideal line) and R to be lumped at three places (line ends R/4 and line middle R/2 ). The shunt conductance G is taken as zero. The frequency dependence of the line parameters (represented in the FD model) is an important factor for the accurate simulation of waveform and peak values. However, the CP model is very robust, simple and fast. It also provides a good alternative for a first approximation analysis.
| ||||||||||

Real T_{i} | A constant real transformation matrix is calculated at a frequency determined automatically by the program (“Find Model frequency automatically”) or specified in the “Model frequency” field. The automatic procedure is similar to the FD model. | ||||||||||

Balanced line | The line is modeled as perfectly transposed. The balanced-line transformation matrix used is the generalized Clarke transformation (αβ0) for an m-phase line. In this case the frequency data is applicable only to modal parameters. | ||||||||||

Double circuit line | This option is only selected for double-circuit lines. The line is modeled as consisting of two separate circuits, each circuit perfectly balanced with respect to itself and to the other circuit. Under these conditions, the only coupling between the two circuits is zero sequence coupling. A special transformation matrix corresponding to this condition is used. In this case the frequency data is applicable only to modal parameters. | ||||||||||

Exact PI | The Exact PI is not supported by HYPERSIM. | ||||||||||

Wideband | This model represents the true nature of a transmission line by modelling the phase line parameters as complex distributed and frequency dependent. It is required to specify the 'Frequency range' for which the line propagation function and characteristic impedance are synthesized. | ||||||||||

Unbalanced line | The line is not continuously transposed | ||||||||||

Balanced line | The phase series and shunt matrices are balanced by averaging the diagonal and off-diagonal terms. | ||||||||||

Double circuit line | This option is only selected for double-circuit lines. The line is modeled as consisting of two separate circuits, each circuit perfectly balanced with respect to itself and to the other circuit. The phase series and shunt matrices are balanced by averaging the diagonal and off-diagonal terms. | ||||||||||

Frequency range | The “Frequency range” represents the frequency band for the fitting of the line characteristic admittance and propagation function. The data fields required for this option are self-explanatory. |

## Line Length Parameters

Name | Description | Unit | |||
---|---|---|---|---|---|

Line length | Length of the line/cable | km or miles | |||

Ground return resistivity | Ground resistivity value | Ω-m | |||

Ground wires are segmented | The continuous ground wire model assumes that the ground wire is grounded at each tower and is continuous between adjacent towers. The segmented ground wires are grounded at one tower and insulated at adjacent towers at both ends of the segmentation interval. |

## Output Options Parameters

Name | Description | Unit | ||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Special output options | Extra printout information level | Print out extra informative messages in the output file | ||||||||||||||||||||||||

Rotate matrix T_{i} | Rotate the modal transformation matrix to satisfy the specified condition. There are two options: - Rotate the transformation matrix to satisfy the condition: modal shunt conductance matrix G
_{m}= 0 when phase conductance matrix G_{phase}= 0 - Rotate the transformation matrix to minimize the imaginary part of its elements
| |||||||||||||||||||||||||

Extra output options | Modal parameters are calculated from the exact phase domain Z and Y matrices at the specified frequency. The modal transformation matrix i T is also presented in the output file. In all these calculations the shunt conductance matrix G is assumed to be zero. The check box required for this option are self-explanatory. | |||||||||||||||||||||||||

Test sources for Q-error indicators | Value of the voltage sources for the open-circuit/short-circuit Q-Error tests. - In the open circuit test, all the phases at the receiving end of the line are open.
- In the short circuit test, all the phases at the receiving end of the line are short circuited.
A Q-Error table is printed out by the “Line Model” module. This table gives an indication of the possible errors when using a constant real transformation matrix T is used in the FD and in the CP models. _{i} The errors shown in the Q-Error table correspond to single-frequency steady-state comparisons for unbalanced combinations of open and short circuit conditions. In these tests, all phases at the receiving end of the line are open or all phases are shorted. Unbalanced sources are connected at the sending end of the line. The values for those sources can be specified in the “Test sources for Q-error indicators” section in the output options tab. If not specified the program will use the following internal default values:
The percent errors shown in the Q-Error table for a given frequency correspond to the phase voltage or current that has the largest error. The Q-Error table is a qualitative guide and does not include all possible factors. As the frequency goes higher than about 1000 Hz, the resonant peaks in the open and short circuit | |||||||||||||||||||||||||

Override default test | For each phase specify a new value for sending end voltage, amplitude and phase, different from default values. |

## Options Parameters

Name | Description | Unit | |||
---|---|---|---|---|---|

Transposition | This option produces a line model for transposed lines based on the averaging of the series impedance and shunt admittance matrices. This procedure is only an approximation to the correct solution of modelling each transposition segment explicitly and then specifying the appropriate node connections in HYPERSIM. Averaging is valid only when the length of the transposition sections is several times smaller than the wavelength of the propagating signals. The sum of the lengths of all the transposition sections must equal the total length of the line as specified in the “Line length” tab. This provides a check on the correct specification of the transposition sections. There is no check, however, on the specification of the phase sequence. | ||||

Create a transposed line | This option produces a line model for transposed lines. | ||||

Number of transposition sections | Enter the number of transposition sections of the line. Then, indicate the span length for each section. | ||||

Phase sequence | Phase sequence in each transposition section. The phase numbers are specified in the conductor data section. | ||||

Phase Shunt conductance | This option allows the specification of values for the line shunt conductance G are assumed to be zero._{phase} When the conductance of a phase is set to 0, it means that the default 0.2x10-9 S/km value will be used. | ||||

Override default G | For each phase specify a new value for conductance G different from the default value. The new value can be specified either in S/km or S/miles |

## Fitting Parameters

Name | Description | Unit | |||
---|---|---|---|---|---|

Fitting options for FD model | This option tap is only available for FD line models. | ||||

Extra printout information level | Print out extra informative messages in the output file | ||||

Quick fit | Fewer iterations to be used during the fitting of Zc and Ap. This could affect the accuracy of the results with respect to the normal procedure. | ||||

Maximum number of poles | Maximum number of poles during the fitting process. The default value is 25. | ||||

Extra dynamics | Control the low frequency approximation of Ap by adding extra poles and zeros to the approximation of the low frequency region of the propagation function Ap. This allows a more accurate simulation of very short line sections (e.g. for breaker reignition studies) and of very low frequency (e.g. for trapped charge conditions). | ||||

Print comparison table for Zc and Ap | An output table is produced in the output file comparing the functions Zc and Ap to the approximating rational functions produced by the fitting process. | ||||

Printer plot | A printer plot is produced in the output file comparing the functions Zc and Ap to the corresponding approximations. | ||||

Print poles and zeros | Tables are produced in the output file showing the location of the poles and zeros of the rational function approximations of Zc and Ap. Also shown are the RC equivalent networks for Zc and the time domain exponential representation of of the approximating functions. |

## Save and run this case Parameters

Name | Description | Unit | |||
---|---|---|---|---|---|

Options for saving this case and generating model data | Before choosing to run this case, the user must provide a valid Case Data File identification which is the model identification and the device name. - For the "CP m-phase" device it is possible to load the generated model data into the device forms using the "Load data from file" option.
- For the "FD m-phase" device the model data file is selected directly in its data forms.
- For the "WB line" device the model data is selected in the WB fitter to generate line data.
| ||||

Current Case Data File name | Enter a unique name to save the model. | ||||

Run this case to create a model data file for the selected line model | Select this option if you want to generate line model data. When you click OK, HS will start a separate LINE DATA calculation function for generating line data. |

# Ports, Inputs, Outputs and Signals Available for Monitoring

## Ports

*None*

## Inputs

*None*

## Outputs

*None*

## Sensors

*None*

# Output data and Example

## Transformation matrices

For a perfectly balanced line, the modal transformation matrices to relate modal and phase quantities do not change with frequency (constant transformation matrices) and can be chosen to be real (e.g. generalized Clarke, as used by HYPERSIM). In the general case of the untransposed line, however, the transformation matrices change with frequency. The line currents transformation matrix **T _{i} ** is the matrix that diagonalizes the product

**Y**

_{phase}**Z**where

_{phase}**Y**is the shunt admittance matrix in phase quantities and

_{phase}**Z**is the series impedance matrix in phase quantities. The resulting Q (also called

_{phase}**T**) matrix, determined by the eigenanalysis routines, is complex. To standardize the results,

_{i}**T**is normalized, using the Euclidean Norm. The voltages transformation matrix

_{i}**T**(which diagonalizes the reverse product

_{v}**Z**

_{phase }**Y**) is not determined by the eigenanalysis routines but calculated directly from the relationship

_{phase}**T**=

_{v}**T**

_{i}^{-t}(where the superscript means inverse transposed).

In the case of the pi-exact (Exact-PI) model, the final form of the model is expressed in terms of self and mutual phase quantities, and there is no impediment in using exact complex transformation matrices at each frequency at which the model is produced. This model, however, is a one-frequency model, valid for steady-state solutions but not for transients simulations.

The CP model does not take into account the frequency dependence of the line parameters. The model is formulated in terms of modal quantities, with the modal parameters R, L, and C calculated exactly at only one frequency using the exact complex transformation matrix at that frequency. Since the model assumes zero modal conductances ( m G = 0), the columns of the transformation matrix **T _{i} ** are rotated to satisfy this condition. As a result of this rotation, the imaginary parts of the elements of

**T**usually become very small. Since the HYPERSIM requires

_{i}**T**to be purely real, only the real part of

_{i}**T**(after the indicated rotation) is retained in the model data file.

_{i}The FD model takes into account the frequency dependence of the line parameters and the distributed nature of the losses (including a finite inductance G). As in the case of the CP model, however, the FD model is formulated in terms of modal quantities, and also has the constraint of requiring a real constant transformation matrix **T _{i} ** . Even though the FD model does not assume zero modal conductances, the recommended criterion to rotate

**T**is the same as for the CP model, that is,

_{i}**T**is rotated to satisfy the condition

_{i}**G**= 0 for

_{mode}**G**= 0. This default rotation can be overridden with the “Rotate matrix Ti” drop down field in the output options tab. Since G is normally very small, the results obtained with both rotation criteria are very similar. It is nonetheless believed that the default rotation gives more physically consistent results.

_{phase }## Description of Line Parameters output file

The output file generated from Line Parameters has two main sections:

- Conductor characteristics
- Line parameters

**Conductor characteristics**

The information contained on the conductors in the data tab is printed for the record more or less in its original form, with the following exceptions:

- In place of height at tower and midspan, the average height is listed as y-coordinate.
- The order of the conductors in the “Conductor Data” table is arbitrary, while the order in the listing will always be as follows: conductors first encountered with phase numbers 1,2,3, ... , followed by conductors with already-existing phase numbers (= 2nd, 3rd, 4th, ... conductors in bundles or parallel circuits), followed by ground wires (wire number = 0).
- While a single conductor card may specify M conductors with the bundle option, all M conductors will be listed separately in the output.

**Line parameters**

Since all matrices are symmetric, only values in and below the diagonal (lower triangular) are printed. All matrices are complex, except the susceptance (or capacitance) matrices for the system of physical conductors and for the system of equivalent phase conductors. Real and imaginary parts are printed above each other, as indicated below.

The following matrices can be printed:

**Impedance matrices: **The matrix elements of the impedance matrices per kilometer or per mile are defined as follows:

- Z
_{i,k}the mutual impedance between i and k, - Z
_{i,i}the self impedance of i, with current returning through ground (and through ground wires if there are any and if they have been eliminated).

**Capacitance matrices:** The matrix elements of the susceptance (or capacitance) matrices per kilometre or mile are defined as follows:

- wC
_{i,k}the negative value of susceptance between i and k, - wC
_{i,i}the sum of all susceptances from i to all other conductors and to ground.

**Symmetrical components matrices:** Note that the matrices for symmetrical components have their rows ordered in the sequence "zero (0), positive (1), negative (2) of first three phase circuit, (0), (1), (2) of second three-phase circuit, etc.", whereas the columns have (1) and (2) exchanged and are thus ordered "(0), (2), (1) of first circuit, (0), (2), (1) of second circuit, etc.". This trick makes these matrices symmetrical again, as indicated below.

From this modified row and column numbering, it follows that:

Z_{1,1} = Z_{2,2} within any three phase circuit

Z_{1,0} = Z_{0,2} within any three phase circuit

Z_{1,0} = Z_{0,1} etc

If there are only two equivalent phase conductors, a two-pole DC line is assumed. In this case, zero sequence refers to the operation where equal currents go into both poles and return through ground (and through ground wires if they exist and were eliminated), and positive sequence refers to the operation where the current goes into one pole and returns through the other.

For three or more equivalent phase conductors, only three-phase circuits are assumed, with numbers 1,2,3 forming the first circuit, numbers 4,5,6 forming the next circuit, etc. If the number of phases were 7 or 8, the last one or two phases would simply be ignored. If the number were 9, then three three-phase circuits would be assumed.

## Data File format

**FD line**

After entering the remaining data in the “Line length” tab, The Model Data Calculation Function can be invoked from “Save and run this case” data tab to generate the model data file. The model can be used with the FD line model (FD m-phase device) by selecting the model data file after clicking on the “Select data file” button for “Time-domain model data”.

It can be used for steady-state and/or time-domain simulations in HYPERSIM. The FD model data file format for a sample line with 3 propagation modes is shown in the following figure. This is an automatically generated data file; the information below is provided only for documentation purposes.

**The following data lines are needed:**

- The first line is mandatory. It provides the model data calculation function identification, followed by the model option (FD) and the number of phases.
- The mode sections are identified by the mode number: -1,-2,-3…-N. If N is greater than 9, the following count must be used: -A,-B,-C….. Only the mode identification character is decoded by the actual line model “FD m-phase”. Each mode is associated to a wire on the “FD m-phase” device drawing, from top to bottom.
- The mode identification line is followed by the number of poles in the synthesized characteristic impedance Zc and the value of Zc at infinite frequency.
- The next lines contain the residues for the above number of poles.
- The next lines contain the poles.
- The line following the Zc poles presents the number of poles in the propagation function Ap and the travel time of the mode.
- The above line is followed by the residues of the poles of Ap.
- The residues of Ap are followed by the poles of Ap.
- The line following the last pole data line must be a comment line.
- The above comment line is followed by the always available transformation matrix Q ( Ti ).

Data is entered as a real matrix rows followed by imaginary matrix rows. Imaginary data is always 0, but present.

It is noticed that the number of modes must be equal to the number of wires (phases) in the device “FD m-phase”.

C LINE DATA, FD, 3 C Comments start with C 49 48 C LINE LENGTH = 2.2200E+02 KM C TRANSFORMATION MATRIX AT F = 1.0000E+03 HZ C The following line identifies the mode 1 (-1). The rest of this line is not C decoded. -1 1. -2 3 21 4.74462509318108402567E+02 2.283015427021728101D+02 9.575640649554595711D+02 2.013381477094321212D+02 6.061618998688145439D+02 -6.972729233161383036D+02 6.760451094099685143D+00 8.363043587952587643D+01 1.591355321753289900D+02 6.493018039972242832D+02 1.833223774853337545D+03 5.577558121371023844D+03 1.679503983644356776D+04 3.939444222663762048D+04 1.120239009613241506D+05 2.293957712303487351D+05 5.992245960304505425D+05 1.359085399919180200D+06 3.495434180024222005D+06 1.102754796920852736D+07 1.898582910228958726D+07 1.044347249584238678D+08 3.184377308326697461D-03 1.142659741453015743D+00 1.410247054729613758D+00 1.747385523651275863D+00 1.780662486687028201D+00 2.218827200258786547D+00 4.023109927718707013D+00 6.502239502807383609D+00 2.083985460432543846D+01 5.876541140540180663D+01 1.823876732116725918D+02 5.640593991713492414D+02 1.402308099704432834D+03 4.075276323700988542D+03 8.963552488252842522D+03 2.410076505448365424D+04 5.787837305888934497D+04 1.562438177227384003D+05 5.140558334568240098D+05 1.832975845465427265D+06 1.019662353574014083D+07 15 8.68087756699963456440E-04 2.446998953943564067D-05 1.101009379493385482D-01 2.729248310394779331D+00 1.163007709687541746D+00 1.330734909971337743D+01 7.270670599628982700D+01 9.703362572893102822D+01 2.288976028807581997D+02 5.706582308417526974D+02 5.873835810335974202D+03 -4.097508590341319177D+03 5.637155913727347070D+03 1.318633359546961449D+07 -1.321907020431305282D+07 2.433651981372164664D+04 1.985692975945386671D-02 2.159004563804076327D+01 2.350104352106030774D+02 2.515290357548743714D+02 5.765320412212246310D+02 1.309900558085271314D+03 1.870063871129507561D+03 3.001329244557226502D+03 3.984777264224765531D+03 5.937139251138488362D+03 6.065781934721424477D+03 1.163051851448095294D+04 1.990879557630283671D+04 1.992851726727190180D+04 2.981838019691102454D+04 -2 1. -2 3 14 2.72613957709204953517E+02 2.040928261573570808D+02 7.320340772647377889D+02 5.023996315103571533D+02 -2.447593159557985132D+02 4.070538193429653973D+01 5.386497094030494814D+00 2.716602807009862772D+02 5.259885608101141088D+02 1.204394272070120593D+02 1.015066436643730441D+02 1.272919440633899768D+02 1.181570571087700898D+02 3.410575508383083616D+03 1.402412764259435644D+05 2.827959091350378332D-03 1.100817723982985941D+00 1.468275521513094706D+00 1.657482856979041186D+00 2.067723976098531313D+00 2.509486139975520391D+00 4.585938122269856088D+00 8.520899497580858295D+00 9.624728164528338681D+00 1.457422452929704804D+01 2.403005241314601648D+01 3.912960424422755779D+01 1.791302848959001267D+03 7.388337549133962602D+04 18 7.48652637550797027920E-04 3.379262809620548266D-05 2.790741898524098583D-02 2.437873410569479660D+01 2.524031108790083167D+01 4.032006639563203976D+02 2.244921419547969435D+03 1.646662359713069964D+04 3.528314876257380820D+04 5.797372924111800239D+04 6.756604360794900276D+04 1.230227615342034958D+06 -7.470853275939022424D+05 1.043657001014848500D+08 -1.039677783588729799D+08 1.802076085009829104D+08 -1.814829657466953099D+08 1.576599275564814918D+07 -1.555168685457617417D+07 1.985225811826055523D-02 5.364714604810082221D+00 2.326199818676640916D+03 4.862941501813475952D+03 1.866557005247363486D+04 5.062422393492590345D+04 1.568762917443446931D+05 2.928418220667541609D+05 4.255624537142930785D+05 5.303951584052367834D+05 1.180557654378241627D+06 1.357218238814550918D+06 3.255399028247645125D+06 3.258623832750257105D+06 4.515348206166080199D+06 4.519821118733711541D+06 1.173308270877454057D+07 1.174470552294277214D+07 -3 1. -2 3 14 2.85812087797527453858E+02 2.068440416608754333D+02 7.434328788502074303D+02 6.141129744727347770D+02 -3.345703266681347259D+02 2.989634922878786227D+01 1.122342424280733475D+01 2.390496148121008844D+02 1.323054560993927225D+03 -6.484703783012250824D+02 1.128252634702326986D+02 1.301301011621264081D+02 1.247322428001669010D+02 1.957136191849841271D+04 2.984413252458497416D+06 2.867346487667737139D-03 1.099862837404594895D+00 1.480922641108804783D+00 1.650797701824323616D+00 2.039787231411344326D+00 2.491273901704059490D+00 4.341853487766006658D+00 8.903535913660869383D+00 9.283443531905913204D+00 1.461053974519216681D+01 2.397836184835597706D+01 3.982334892028816853D+01 1.001535962164031116D+04 1.534036532459646463D+06 15 7.42260779552304772975E-04 3.281517460210861976D-05 4.231843588743761791D-02 3.429455764932136219D+01 5.064001014999667660D+01 5.677989071445322224D+02 3.702826389013024254D+03 2.777021501646843171D+04 3.266723665610918033D+04 5.183239686396404286D+05 -1.329557821802375656D+04 -1.399472376895410998D+05 3.849242295078294724D+07 -3.893168894298432767D+07 8.090281889140170533D+05 -7.996364033324117772D+05 1.985274803339131394D-02 7.319178322505369039D+00 2.927930125718939053D+03 8.458745237649192859D+03 2.242598200799151527D+04 6.291347434485757549D+04 1.556321095858299814D+05 2.199676019453247718D+05 4.256247426522265305D+05 4.662550907182482770D+05 6.317486660880415002D+05 9.898985434087131871D+05 9.908791387987753842D+05 1.324181025567296334D+07 1.325492761823427491D+07 C Q MATRIX BY ROWS (IMAGINARY PART = 0) 0.57764932 -0.41240739 0.70710678 0.00000000 0.00000000 0.00000000 0.57663209 0.81227413 0.00000000 0.00000000 0.00000000 0.00000000 0.57764932 -0.41240739 -0.70710678 0.00000000 0.00000000 0.00000000

### **CP line**

After entering the remaining data in the “Line length” tab, The Model Data Calculation Function can be invoked from “Save and run this case” data tab to generate the model data file. The model can be used with the CP line model (CP m-phase device) by selecting the model data file (also called “model file”) through the “Load data file” option in the device data. It can be used for all simulation options of this device. The format of this file can be found in the documentation of the CP m-phase device.

### Example: 3-phase transmission line

The following figure shows the conductor data taken from the drawings in shown next.

This example evaluates an FD-line model for a 3-phase transmission line system having the following properties:

- The units are metric.
- The conductor data is specified directly.
- The system has 8 conductors: 2 tubular conductors for each phase and 2 solid conductors for the ground wire.

The complete view of conductor data is listed as:

Since the ground wires are numbered as 0, they will not appear in the model data. Wires with the same phase number are also counted as 1. In this case the generated model will only have 3 wires (3 modes).

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