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# Wideband and Marti-FD-line Fitter

# Library

ARTEMiS/SSN/Lines

# Block

# Description

The Wideband and Marti-FD line fitter block manages the rational function fitting routines used by the SSN[1] Wideband Line/cable and Marti-FD line models.

Two fitters are available for the SSN Wideband line/cable model: one with automatic precision and another with manual adjustment of fitting parameters such as the number of poles and fittings weight. Both fitters use a standard vector fitting approach.

The Marti-FD-line fitter also uses the vector fitting methodology [2]. It is set to produce only real poles as required by the run-time Marti-FD-line model.

The fitters generate poles-residues files: .pun for Marti-FD-line and .dat for Wideband line/cable usable on the 2^{nd} generation of SSN line models (which takes these files directly as parameters). These .pun and .dat files are also compatible with EMTP-RV and Hypersim.

Depending on the type of transmission system, line or cable, this block allows the user to enter the line or cable data in the appropriate geometry GUI:

- SPS line parameter GUI for lines
- IREQ’s Crinoline GUI (developed under contract by Opal-RT)

# Masks

**Main panel of the Wideband and Marti-FD line fitter block**

**Scan Options pane**

**Wideband and Marti-FD option panes**

# Parameters

**Model Type: **the line or cable model to fit. Choices are Line (Wideband), Cable (Wideband), and Line (Modal domain FD-line)

**Line parameters filename (.mat): **SimPowerSystems Line parameter GUI filename (when Model Type is a line)

or

**Cable parameter filename (.geo): **Crinoline cable GUI filename (when Model Type is a cable)

**Open line parameter GUI: **Opens SimPowerSystems Line parameter GUI filename (when Model Type is a line)

or

**Open cable parameter GUI: **Opens Crinoline cable GUI filename (when Model Type is a cable)

**Line length (km) (Line Only):** The line length in km in the case of lines.

**NOTE:** The crinoline based GUI has a field to specify the cable length and the GUI length is used in this case.

**BUTTON: Start frequency scan and fitting of line model: **Pressing this button will start the line frequency scan and compute the selected line model rational function fittings.

*Scan option pane:*

**Minimum frequency (Hz):** the minimum frequency of the scan. If a DC line or cable is fitted, it is recommended to use 0.001 Hz here.

**Number of decades for scan:** Number of decades for the scan from the minimum frequency specified (*nd*).

**Number of points per decade:** The number of points per decade (*pd*). The fitting will use *nd*pd *points for the fitting.

*Wideband line option pane*

*Wideband line option pane*

**Fitter EMTP-type output file:** the name of the fitter file containing poles and residues for the Wideband line or cable fitting. This file is used by the run-time SSN Wideband line model of eMEGAsim and is compatible with Hypersim and EMTP-RV.

**Line to ground default admittance (mhos):** Default shunt admittance in mhos (or Siemens) used to compute line/cable characteristic functions. The default value of 2e-10 mhos is suggested like in EMTP-RV.

**Use new Wideband fitter (recommended)**: The GUI can use 2 different fitters for the SSN wideband line/cable. The traditional one is simple to use with a single-precision parameter to set. In the new Wideband fitter, all parameters such as the number of poles and fitting weight are selected by the user. We recommend using the traditional fitter if no special problem occurs. The new Wideband fitter can help in difficult cases where, for example, when low-frequency fitting accuracy is important.

*Traditional fitter options:*

**Fitting maximum relative error: (only with the traditional fitter):** the maximum relative error of the fitting. Poles number are adjusted automatically to meet this criterion.

*New Wideband fitter options.*

**H(****w) number of poles per mode: **Sets the number of poles per mode for the line propagation function H(w) (*Hnppm*). The model total number of *H(**w)* poles will be *Hnppm*nph* (*nph*=Number of phases, w is the angular frequency in rad/s). There is one mode per phase.

**DC correction**: use the Low-frequency and DC compensation approach described in [3]. Using the first propagation mode only, Hnppm new poles are used to decrease the obtained fitting error of H(w).

**Improved DC fit maximum frequency (Hz)**: when DC correction is checked, this set the maximum frequency for which the DC response is compensated.

**Yc(****w) total number of poles:** Set the total number of poles for the characteristic admittance *Y(**w).*

**Fitting weight**: apply some weight to the fitter as a function of frequency. Default is ‘Uniform’ which applies an equal weight to all frequencies. ‘1/f for f<1 Hz’ is also available and will apply weight greater than 1 to frequencies below 1 Hz; this will fit more precisely lower frequencies of the line/cable.

**Show fitting curves**: when checked, the fitting results will be displayed for Hmodal(w), H(w), and Yc(w).

**Generate EMTP-RV compatible YZ scan file**: when checked, the fitter will produce a .lyz or .cyz file compatible with EMTP-RV. The option can be used to compare line and cable Y Z parameters with EMTP-RV.

**Use EMTP-RV .lyz or .cyz file for fitting**: when checked, the scan is overridden and this file is read to obtain *Y Z* line cable data. This option can be used to use EMTP-RV line parameter calculations with eMEGAsim fitter.

*Marti FD-line options*

*Marti FD-line options*

Frequency of eigenvalue calculation (Hz): this is the frequency at which the modal transformation matrices are evaluated. This is actually the main approximation of the Marti FD-line model as compared to the Wideband one: the Marti model uses a constant modal transformation matrix for all frequencies. This approximation is exact for balanced lines, good for lightly unbalanced overhead lines but usually very bad for cables. This is why the Marti FD-line model fitter is only available for lines.

**Fitter EMTP-type output file (.pun):** the poles and residues file used by the run-time SSN Marti-type FD-line model of eMEGAsim. This file is compatible with EMTP-RV and Hypersim.

**Maximum number of Zc(****w) poles:** Maximum number of poles for the characteristic impedance of the line in the modal domain (*nzcp*).

**Maximum number of Ap(****w) poles:** Maximum number of poles for the propagation function of the line in the modal domain (*naap*).

For *Zc(**w)* and *Ap(**w)* poles, the specified number of poles is the maximum value. The fitter can produce less poles. The Marti FD-line fitter uses vector fitting but modified to produce only real poles. The maximum total number of poles is then equal to *nzcp*nph* and *naap*nph* for *Zc(**w)* and *Ap(**w)* respectively, with *nph* standing for the number of phases.

**Plot fitting: **print the fitting results when checked, for all modes.

# Line and cable parameter GUIs

The fitter GUI makes use of two different GUIs to input line or cable geometry, from which the admittance and impedance are computed for all frequencies.

**Overhead lines**

For overhead lines, the fitter uses the SimPowerSystems Line parameters GUI.

**SimPowerSystems Line parameter tool**

Note that after a geometry has been entered in this GUI, it must be saved for the fitter GUI to be used. The fitter GUI reads directly the geometry file (here a .mat file) to compute the line parameters. To examine a previously entered geometry, press the ‘Load user data’ button.

Note that the SimPowerSystems GUI does not have an entry for line length, therefore the line length is specified on the fitter GUI for lines.

**Cables**

For cables, the fitter GUI makes use of the Crinoline-based GUI, developed for Hydro-Quebec.

Note that after a geometry has been entered in this GUI, it must be saved for the fitter GUI in order to be used. The fitter GUI reads directly the geometry file (here a .geo file) to compute the cable parameters, including in this case the total cable length. To examine a previously entered geometry, one must select the proper geometry name from the cable GUI.

As the Crinoline cable GUI uses a database to access the various geometries and cable data, it can be practical to set the SSN_CABLEPARAM_USE_THIS_DATA_PATH in the MATLAB workspace parameter for pointing to your own cable database. For example,

SSN_CABLEPARAM_USE_THIS_DATA_PATH='C:\MATLAB_WORK\mycablegeometry';

sets the cable GUI database to the specified directory at the opening.

**Crinoline-based cable parameter calculation GUI**

# Examples

There are several simulation models with wideband line/cable and Marti type FD-lines available in the SSN line section of the demos.

## FD-Marti and Wideband comparison for overhead lines.

In the model ssn_WidebandvsMarti_3ph_735kV.slx, we compare the wideband and the Marti-type FD-line on a 100 km-735kV line during a single-phase-to-ground fault. The load is 10MW and 2 MVars.

**Model of 100km 735 kV line with Wideband and FD-line (number 1 and 2 are the measurement location)**

**Wideband fitting results. Left: amplitude of H, right: amplitude of Yc**

Sending end current (left) and receiving end voltage(right) with a single-phase-to-ground fault. Zoom at fault time. (Curves of both models are superposed almost perfectly).

This test would lead to the conclusion that the Marti-type FD-line model is sufficiently accurate to model overhead lines. As the Marti model is computationally less demanding than the Wideband one, this could be a good option to be used in real-time applications to decrease the total calculation time.

**Fitter options in the 735 kV case**

Settings for the fitters are: Fmin = 0.001 Hz, 8 decades and 10 poles each for Marti FD-line *Zc* and *Ap* functions. For the Wideband line, we used 7 poles per mode for* H* and 7 poles in total for *Yc* with DC correction is turned off.

**Marti FD-line fitting results, all modes. Left: amplitude of Zc, right: amplitude of Ap**

## Cable DC response using DC correction option

This test case compares the eMEGAsim Wideband line fitter to the one of EMTP-RV for very-low to DC frequency response in the time domain.

ssn_WB2_4phase_cable_EMTPcomparison model: comparison of Wideband line fitters

The model is available on the MATLAB path as **ssn_WB2_4phase_cable_EMTPcomparison.slx**. The test case is a simple energization of one of the cores with the receiving end connected to the ground. The other phases are sheath are not energized and are connected to 1 Ohms grounding resistance.

The SSN (eMEGAsim) fitter was set with the following parameters:

Min frequency: 0.0001 Hz (w/ DC correction) 0.001 Hz (/wo DC correction), 8 decade scan, 10 points per decade

Number of H(w) poles: 10 (w/ DC correction) 15 (/wo DC correction),

Number of Yc(w) poles: 20

Improved DC fit maximum frequency: 1 Hz (only with DC correction)

EMTP automatically assigns poles when required (precision set to 1%) and was set to 0.001 Hz, 8-decade scan, 10 points per decade. The EMTP-RV fitting file comes from an earlier version of EMTP-RV (3.5) which did not have the DC correction option yet.

**DC response with the three fitters**

The eMEGAsim (or SSN) fitter gave the best DC response, very close to the 107A found in theory. One reason to specify less H(w) poles in SSN when using DC correction option is that the latter option double the specified number of poles in the first propagation mode.

# References

[1] C. Dufour, J. Mahseredjian , J. Bélanger, “A Combined State-Space Nodal Method for the Simulation of Power System Transients”, IEEE Transactions on Power Delivery, Vol. 26, no. 2, pp. 928-935, April 2011.

[2] B. Gustavsen and A. Semlyen, "Rational approximation of frequency domain responses by vector fitting", IEEE Trans. Power Delivery, vol. 14, no. 3, pp. 1052-1061, July 1999.

[3] M. Cervantes, I. Kocar, J. Mahseredjian, and A. Ramirez, “Partitioned Fitting and DC Correction for the Simulation of Electromagnetic Transients in HVDC Systems,” IEEE PES Letters, June 2018.

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